## TSTP Solution File: PUZ001+1 by E---3.1

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : PUZ001+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 13:14:54 EDT 2023

% Result   : Theorem 0.21s 0.50s
% Output   : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   49 (  18 unt;   0 def)
%            Number of atoms       :   89 (  25 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   73 (  33   ~;  28   |;   2   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :   39 (   0 sgn;  25   !;   3   ?)

%------------------------------------------------------------------------------
fof(pel55_4,axiom,
! [X1,X2] :
( killed(X1,X2)
=> hates(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942',pel55_4) ).

fof(pel55_1,axiom,
? [X1] :
( lives(X1)
& killed(X1,agatha) ),
file('/export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942',pel55_1) ).

fof(pel55_3,axiom,
! [X1] :
( lives(X1)
=> ( X1 = agatha
| X1 = butler
| X1 = charles ) ),
file('/export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942',pel55_3) ).

fof(pel55_10,axiom,
! [X1] :
? [X2] : ~ hates(X1,X2),
file('/export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942',pel55_10) ).

fof(pel55_5,axiom,
! [X1,X2] :
( killed(X1,X2)
=> ~ richer(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942',pel55_5) ).

fof(pel55_8,axiom,
! [X1] :
( ~ richer(X1,agatha)
=> hates(butler,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942',pel55_8) ).

fof(pel55_6,axiom,
! [X1] :
( hates(agatha,X1)
=> ~ hates(charles,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942',pel55_6) ).

fof(pel55_9,axiom,
! [X1] :
( hates(agatha,X1)
=> hates(butler,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942',pel55_9) ).

fof(pel55_7,axiom,
! [X1] :
( X1 != butler
=> hates(agatha,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942',pel55_7) ).

fof(pel55_11,axiom,
agatha != butler,
file('/export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942',pel55_11) ).

fof(pel55,conjecture,
killed(agatha,agatha),
file('/export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942',pel55) ).

fof(c_0_11,plain,
! [X4,X5] :
( ~ killed(X4,X5)
| hates(X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel55_4])]) ).

fof(c_0_12,plain,
( lives(esk1_0)
& killed(esk1_0,agatha) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[pel55_1])]) ).

fof(c_0_13,plain,
! [X8] :
( ~ lives(X8)
| X8 = agatha
| X8 = butler
| X8 = charles ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel55_3])]) ).

fof(c_0_14,plain,
! [X1] :
? [X2] : ~ hates(X1,X2),
inference(fof_simplification,[status(thm)],[pel55_10]) ).

fof(c_0_15,plain,
! [X1,X2] :
( killed(X1,X2)
=> ~ richer(X1,X2) ),
inference(fof_simplification,[status(thm)],[pel55_5]) ).

fof(c_0_16,plain,
! [X1] :
( ~ richer(X1,agatha)
=> hates(butler,X1) ),
inference(fof_simplification,[status(thm)],[pel55_8]) ).

fof(c_0_17,plain,
! [X1] :
( hates(agatha,X1)
=> ~ hates(charles,X1) ),
inference(fof_simplification,[status(thm)],[pel55_6]) ).

cnf(c_0_18,plain,
( hates(X1,X2)
| ~ killed(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,plain,
killed(esk1_0,agatha),
inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
( X1 = agatha
| X1 = butler
| X1 = charles
| ~ lives(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
lives(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_22,plain,
! [X13] : ~ hates(X13,esk2_1(X13)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_14])]) ).

fof(c_0_23,plain,
! [X12] :
( ~ hates(agatha,X12)
| hates(butler,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel55_9])]) ).

fof(c_0_24,plain,
! [X6,X7] :
( ~ killed(X6,X7)
| ~ richer(X6,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).

fof(c_0_25,plain,
! [X11] :
( richer(X11,agatha)
| hates(butler,X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])]) ).

fof(c_0_26,plain,
! [X9] :
( ~ hates(agatha,X9)
| ~ hates(charles,X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).

cnf(c_0_27,plain,
hates(esk1_0,agatha),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_28,plain,
( esk1_0 = charles
| esk1_0 = butler
| esk1_0 = agatha ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_29,plain,
~ hates(X1,esk2_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_30,plain,
( hates(butler,X1)
| ~ hates(agatha,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).

fof(c_0_31,plain,
! [X10] :
( X10 = butler
| hates(agatha,X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel55_7])]) ).

cnf(c_0_32,plain,
( ~ killed(X1,X2)
| ~ richer(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_33,plain,
( richer(X1,agatha)
| hates(butler,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_34,plain,
( ~ hates(agatha,X1)
| ~ hates(charles,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_35,plain,
( esk1_0 = agatha
| esk1_0 = butler
| hates(charles,agatha) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_36,plain,
~ hates(agatha,esk2_1(butler)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_37,plain,
( X1 = butler
| hates(agatha,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_38,plain,
( hates(butler,X1)
| ~ killed(X1,agatha) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,plain,
( esk1_0 = butler
| esk1_0 = agatha
| ~ hates(agatha,agatha) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,plain,
agatha != butler,
inference(split_conjunct,[status(thm)],[pel55_11]) ).

cnf(c_0_41,plain,
esk2_1(butler) = butler,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_42,plain,
hates(butler,esk1_0),
inference(spm,[status(thm)],[c_0_38,c_0_19]) ).

cnf(c_0_43,plain,
( esk1_0 = agatha
| esk1_0 = butler ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_40]) ).

cnf(c_0_44,plain,
~ hates(butler,butler),
inference(spm,[status(thm)],[c_0_29,c_0_41]) ).

fof(c_0_45,negated_conjecture,
~ killed(agatha,agatha),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[pel55])]) ).

cnf(c_0_46,plain,
esk1_0 = agatha,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).

cnf(c_0_47,negated_conjecture,
~ killed(agatha,agatha),
inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_48,plain,
\$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_46]),c_0_47]),
[proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : PUZ001+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14  % Command    : run_E %s %d THM
% 0.14/0.36  % Computer : n005.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat Aug 26 22:12:53 EDT 2023
% 0.14/0.36  % CPUTime    :
% 0.21/0.49  Running first-order theorem provingRunning: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.RuJRU1737L/Vampire---4.8_9942
% 0.21/0.49  # Version: 3.1pre001
% 0.21/0.50  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.50  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.50  # Starting sh5l with 300s (1) cores
% 0.21/0.50  # sh5l with pid 10126 completed with status 0
% 0.21/0.50  # Result found by sh5l
% 0.21/0.50  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.50  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.50  # Starting sh5l with 300s (1) cores
% 0.21/0.50  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.50  # Search class: FGHSF-FFSS11-SFFFFFNN
% 0.21/0.50  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.50  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.21/0.50  # SAT001_MinMin_p005000_rr_RG with pid 10133 completed with status 0
% 0.21/0.50  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.21/0.50  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.50  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.50  # Starting sh5l with 300s (1) cores
% 0.21/0.50  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.50  # Search class: FGHSF-FFSS11-SFFFFFNN
% 0.21/0.50  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.50  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.21/0.50  # Preprocessing time       : 0.001 s
% 0.21/0.50  # Presaturation interreduction done
% 0.21/0.50
% 0.21/0.50  # Proof found!
% 0.21/0.50  # SZS status Theorem
% 0.21/0.50  # SZS output start CNFRefutation
% See solution above
% 0.21/0.50  # Parsed axioms                        : 14
% 0.21/0.50  # Removed by relevancy pruning/SinE    : 0
% 0.21/0.50  # Initial clauses                      : 15
% 0.21/0.50  # Removed in clause preprocessing      : 0
% 0.21/0.50  # Initial clauses in saturation        : 15
% 0.21/0.50  # Processed clauses                    : 53
% 0.21/0.50  # ...of these trivial                  : 0
% 0.21/0.50  # ...subsumed                          : 2
% 0.21/0.50  # ...remaining for further processing  : 51
% 0.21/0.50  # Other redundant clauses eliminated   : 0
% 0.21/0.50  # Clauses deleted for lack of memory   : 0
% 0.21/0.50  # Backward-subsumed                    : 9
% 0.21/0.50  # Backward-rewritten                   : 6
% 0.21/0.50  # Generated clauses                    : 43
% 0.21/0.50  # ...of the previous two non-redundant : 40
% 0.21/0.50  # ...aggressively subsumed             : 0
% 0.21/0.50  # Contextual simplify-reflections      : 0
% 0.21/0.50  # Paramodulations                      : 38
% 0.21/0.50  # Factorizations                       : 5
% 0.21/0.50  # NegExts                              : 0
% 0.21/0.50  # Equation resolutions                 : 0
% 0.21/0.50  # Total rewrite steps                  : 13
% 0.21/0.50  # Propositional unsat checks           : 0
% 0.21/0.50  #    Propositional check models        : 0
% 0.21/0.50  #    Propositional check unsatisfiable : 0
% 0.21/0.50  #    Propositional clauses             : 0
% 0.21/0.50  #    Propositional clauses after purity: 0
% 0.21/0.50  #    Propositional unsat core size     : 0
% 0.21/0.50  #    Propositional preprocessing time  : 0.000
% 0.21/0.50  #    Propositional encoding time       : 0.000
% 0.21/0.50  #    Propositional solver time         : 0.000
% 0.21/0.50  #    Success case prop preproc time    : 0.000
% 0.21/0.50  #    Success case prop encoding time   : 0.000
% 0.21/0.50  #    Success case prop solver time     : 0.000
% 0.21/0.50  # Current number of processed clauses  : 21
% 0.21/0.50  #    Positive orientable unit clauses  : 6
% 0.21/0.50  #    Positive unorientable unit clauses: 0
% 0.21/0.50  #    Negative unit clauses             : 7
% 0.21/0.50  #    Non-unit-clauses                  : 8
% 0.21/0.50  # Current number of unprocessed clauses: 7
% 0.21/0.50  # ...number of literals in the above   : 18
% 0.21/0.50  # Current number of archived formulas  : 0
% 0.21/0.50  # Current number of archived clauses   : 30
% 0.21/0.50  # Clause-clause subsumption calls (NU) : 23
% 0.21/0.50  # Rec. Clause-clause subsumption calls : 21
% 0.21/0.50  # Non-unit clause-clause subsumptions  : 7
% 0.21/0.50  # Unit Clause-clause subsumption calls : 13
% 0.21/0.50  # Rewrite failures with RHS unbound    : 0
% 0.21/0.50  # BW rewrite match attempts            : 2
% 0.21/0.50  # BW rewrite match successes           : 2
% 0.21/0.50  # Condensation attempts                : 0
% 0.21/0.50  # Condensation successes               : 0
% 0.21/0.50  # Termbank termtop insertions          : 834
% 0.21/0.50
% 0.21/0.50  # -------------------------------------------------
% 0.21/0.50  # User time                : 0.006 s
% 0.21/0.50  # System time              : 0.001 s
% 0.21/0.50  # Total time               : 0.007 s
% 0.21/0.50  # Maximum resident set size: 1756 pages
% 0.21/0.50
% 0.21/0.50  # -------------------------------------------------
% 0.21/0.50  # User time                : 0.008 s
% 0.21/0.50  # System time              : 0.003 s
% 0.21/0.50  # Total time               : 0.010 s
% 0.21/0.50  # Maximum resident set size: 1680 pages
% 0.21/0.50  % E---3.1 exiting
%------------------------------------------------------------------------------
```