## TSTP Solution File: LCL666+1.001 by LEO-II---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n015.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  : 600s
% DateTime : Sun Jul 17 12:25:20 EDT 2022

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   33 (  23 unt;   4 typ;   0 def)
%            Number of atoms       :  148 (  34 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :  224 (  75   ~;  39   |;  12   &;  98   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   24 (   0   ^  20   !;   4   ?;  24   :)

%------------------------------------------------------------------------------
thf(tp_p101,type,
p101: \$i > \$o ).

thf(tp_p201,type,
p201: \$i > \$o ).

thf(tp_r1,type,
r1: \$i > \$i > \$o ).

thf(tp_sK1_X,type,
sK1_X: \$i ).

thf(1,axiom,
! [X: \$i] : ( r1 @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

thf(2,conjecture,
~ ? [X: \$i] :
~ ( ~ ! [Y: \$i] :
( ~ ( r1 @ X @ Y )
| ~ ( ( p201 @ Y )
& ( p101 @ Y ) ) )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).

thf(3,negated_conjecture,
( ( ~ ? [X: \$i] :
~ ( ~ ! [Y: \$i] :
( ~ ( r1 @ X @ Y )
| ~ ( ( p201 @ Y )
& ( p101 @ Y ) ) )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ) )
= \$false ),
inference(negate_conjecture,[status(cth)],[2]) ).

thf(4,plain,
( ( ~ ? [X: \$i] :
~ ( ~ ! [Y: \$i] :
( ~ ( r1 @ X @ Y )
| ~ ( ( p201 @ Y )
& ( p101 @ Y ) ) )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ) )
= \$false ),
inference(unfold_def,[status(thm)],[3]) ).

thf(5,plain,
( ( ! [X: \$i] : ( r1 @ X @ X ) )
= \$true ),
inference(unfold_def,[status(thm)],[1]) ).

thf(6,plain,
( ( ? [X: \$i] :
~ ( ~ ! [Y: \$i] :
( ~ ( r1 @ X @ Y )
| ~ ( ( p201 @ Y )
& ( p101 @ Y ) ) )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ) )
= \$true ),
inference(polarity_switch,[status(thm)],[4]) ).

thf(7,plain,
( ( ! [SY3: \$i] :
( ~ ( r1 @ sK1_X @ SY3 )
| ~ ( p101 @ SY3 )
| ~ ( p201 @ SY3 ) )
& ( p101 @ sK1_X )
& ( p201 @ sK1_X ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
( ( ! [X: \$i] : ( r1 @ X @ X ) )
= \$true ),
inference(copy,[status(thm)],[5]) ).

thf(9,plain,
( ( ! [SY3: \$i] :
( ~ ( r1 @ sK1_X @ SY3 )
| ~ ( p101 @ SY3 )
| ~ ( p201 @ SY3 ) )
& ( p101 @ sK1_X )
& ( p201 @ sK1_X ) )
= \$true ),
inference(copy,[status(thm)],[7]) ).

thf(10,plain,
( ( ~ ( ~ ! [SX0: \$i] :
( ~ ( r1 @ sK1_X @ SX0 )
| ~ ( p101 @ SX0 )
| ~ ( p201 @ SX0 ) )
| ~ ~ ( ~ ( p101 @ sK1_X )
| ~ ( p201 @ sK1_X ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[9]) ).

thf(11,plain,
! [SV1: \$i] :
( ( r1 @ SV1 @ SV1 )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).

thf(12,plain,
( ( ~ ! [SX0: \$i] :
( ~ ( r1 @ sK1_X @ SX0 )
| ~ ( p101 @ SX0 )
| ~ ( p201 @ SX0 ) )
| ~ ~ ( ~ ( p101 @ sK1_X )
| ~ ( p201 @ sK1_X ) ) )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).

thf(13,plain,
( ( ~ ! [SX0: \$i] :
( ~ ( r1 @ sK1_X @ SX0 )
| ~ ( p101 @ SX0 )
| ~ ( p201 @ SX0 ) ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).

thf(14,plain,
( ( ~ ~ ( ~ ( p101 @ sK1_X )
| ~ ( p201 @ sK1_X ) ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).

thf(15,plain,
( ( ! [SX0: \$i] :
( ~ ( r1 @ sK1_X @ SX0 )
| ~ ( p101 @ SX0 )
| ~ ( p201 @ SX0 ) ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).

thf(16,plain,
( ( ~ ( ~ ( p101 @ sK1_X )
| ~ ( p201 @ sK1_X ) ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).

thf(17,plain,
! [SV2: \$i] :
( ( ~ ( r1 @ sK1_X @ SV2 )
| ~ ( p101 @ SV2 )
| ~ ( p201 @ SV2 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(18,plain,
( ( ~ ( p101 @ sK1_X )
| ~ ( p201 @ sK1_X ) )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(19,plain,
! [SV2: \$i] :
( ( ( ~ ( r1 @ sK1_X @ SV2 ) )
= \$true )
| ( ( ~ ( p101 @ SV2 )
| ~ ( p201 @ SV2 ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).

thf(20,plain,
( ( ~ ( p101 @ sK1_X ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).

thf(21,plain,
( ( ~ ( p201 @ sK1_X ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).

thf(22,plain,
! [SV2: \$i] :
( ( ( r1 @ sK1_X @ SV2 )
= \$false )
| ( ( ~ ( p101 @ SV2 )
| ~ ( p201 @ SV2 ) )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(23,plain,
( ( p101 @ sK1_X )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).

thf(24,plain,
( ( p201 @ sK1_X )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).

thf(25,plain,
! [SV2: \$i] :
( ( ( ~ ( p101 @ SV2 ) )
= \$true )
| ( ( ~ ( p201 @ SV2 ) )
= \$true )
| ( ( r1 @ sK1_X @ SV2 )
= \$false ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(26,plain,
! [SV2: \$i] :
( ( ( p101 @ SV2 )
= \$false )
| ( ( ~ ( p201 @ SV2 ) )
= \$true )
| ( ( r1 @ sK1_X @ SV2 )
= \$false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(27,plain,
! [SV2: \$i] :
( ( ( p201 @ SV2 )
= \$false )
| ( ( p101 @ SV2 )
= \$false )
| ( ( r1 @ sK1_X @ SV2 )
= \$false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(28,plain,
\$false = \$true,
inference(fo_atp_e,[status(thm)],[11,27,24,23]) ).

thf(29,plain,
\$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n015.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jul  4 22:32:32 EDT 2022
% 0.13/0.33  % CPUTime  :
% 0.13/0.34
% 0.13/0.34   No.of.Axioms: 1
% 0.13/0.34
% 0.13/0.34   Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.34  (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.13/0.37
% 0.13/0.37  ********************************
% 0.13/0.37  *   All subproblems solved!    *
% 0.13/0.37  ********************************
% 0.13/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.37
% 0.13/0.37  %**** Beginning of derivation protocol ****
% 0.13/0.37  % SZS output start CNFRefutation
% See solution above
% 0.13/0.37
% 0.13/0.37  %**** End of derivation protocol ****
% 0.13/0.37  %**** no. of clauses in derivation: 29 ****
% 0.13/0.37  %**** clause counter: 28 ****
% 0.13/0.37
% 0.13/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------
```