## TSTP Solution File: LAT270-2 by Leo-III---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Leo-III---1.7.0
% Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 : Sat Sep 17 18:12:12 EDT 2022

% Result   : Unsatisfiable 2.49s 1.52s
% Output   : Refutation 2.75s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   21 (   9 unt;  10 typ;   0 def)
%            Number of atoms       :   17 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   86 (   8   ~;   6   |;   0   &;  72   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (  10 usr;   7 con; 0-4 aty)
%            Number of variables   :    6 (   0   ^   6   !;   0   ?;   6   :)

%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: \$i > \$i > \$i > \$o ).

thf(v_a_type,type,
v_a: \$i ).

thf(v_A_type,type,
v_A: \$i ).

thf(t_a_type,type,
t_a: \$i ).

thf(v_b_type,type,
v_b: \$i ).

thf(c_lessequals_type,type,
c_lessequals: \$i > \$i > \$i > \$o ).

thf(v_S_type,type,
v_S: \$i ).

thf(c_Tarski_Ointerval_type,type,
c_Tarski_Ointerval: \$i > \$i > \$i > \$i > \$i ).

thf(v_r_type,type,
v_r: \$i ).

thf(tc_set_type,type,
tc_set: \$i > \$i ).

thf(1,negated_conjecture,
c_in @ v_a @ v_A @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(6,plain,
c_in @ v_a @ v_A @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(4,negated_conjecture,
~ ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(9,plain,
~ ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(2,negated_conjecture,
c_in @ v_b @ v_A @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(7,plain,
c_in @ v_b @ v_A @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,axiom,
! [C: \$i,B: \$i,A: \$i] :
( ~ ( c_in @ A @ v_A @ t_a )
| ~ ( c_in @ B @ v_A @ t_a )
| ~ ( c_lessequals @ C @ ( c_Tarski_Ointerval @ v_r @ B @ A @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ C @ v_A @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0) ).

thf(11,plain,
! [C: \$i,B: \$i,A: \$i] :
( ~ ( c_in @ A @ v_A @ t_a )
| ~ ( c_in @ B @ v_A @ t_a )
| ~ ( c_lessequals @ C @ ( c_Tarski_Ointerval @ v_r @ B @ A @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ C @ v_A @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,negated_conjecture,
c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(8,plain,
c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(16,plain,
\$false,
inference(e,[status(thm)],[6,9,7,11,8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% 0.14/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n027.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Sep  1 13:11:18 EDT 2022
% 0.15/0.35  % CPUTime  :
% 0.84/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.93  % [INFO] 	 Parsing done (105ms).
% 1.22/0.94  % [INFO] 	 Running in sequential loop mode.
% 1.48/1.14  % [INFO] 	 eprover registered as external prover.
% 1.48/1.14  % [INFO] 	 cvc4 registered as external prover.
% 1.48/1.15  % [INFO] 	 Scanning for conjecture ...
% 1.76/1.20  % [INFO] 	 Found a conjecture and 1 axioms. Running axiom selection ...
% 1.76/1.22  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.76/1.23  % [INFO] 	 Problem is propositional (TPTP CNF).
% 1.76/1.23  % [INFO] 	 Type checking passed.
% 1.76/1.23  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ...
% 2.49/1.52  % External prover 'e' found a proof!
% 2.49/1.52  % [INFO] 	 Killing All external provers ...
% 2.49/1.52  % Time passed: 1031ms (effective reasoning time: 577ms)
% 2.49/1.52  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 2.49/1.52  % Axioms used in derivation (1): cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0
% 2.49/1.52  % No. of inferences in proof: 11
% 2.49/1.52  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1031 ms resp. 577 ms w/o parsing
% 2.75/1.54  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.75/1.54  % [INFO] 	 Killing All external provers ...
%------------------------------------------------------------------------------
```