%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP023-2 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.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 : Tue May 5 04:23:35 PM UTC 2026
% Result : Unsatisfiable 0.12s 1.51s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of clauses : 29 ( 19 unt; 0 nHn; 10 RR)
% Number of literals : 41 ( 40 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(right_inverse,axiom,
multiply(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(prove_inverse_of_id_is_id,negated_conjecture,
inverse(identity) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_id_is_id) ).
cnf(i_0_6,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity,
[final] ).
cnf(i_0_7,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse,
[final] ).
cnf(i_0_8,axiom,
multiply(X1,inverse(X1)) = identity,
right_inverse,
[final] ).
cnf(i_0_9,axiom,
multiply(identity,X1) = X1,
left_identity,
[final] ).
cnf(i_0_10,axiom,
multiply(X1,identity) = X1,
right_identity,
[final] ).
cnf(i_0_11,negated_conjecture,
inverse(identity) != identity,
prove_inverse_of_id_is_id,
[final] ).
cnf(i_0_12,axiom,
X1 = X1 ).
cnf(i_0_13,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_14,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_15,axiom,
( X1 != X2
| multiply(X1,X3) = multiply(X2,X3) ) ).
cnf(i_0_16,axiom,
( X1 != X2
| multiply(X3,X1) = multiply(X3,X2) ) ).
cnf(i_0_17,axiom,
( X1 != X2
| inverse(X1) = inverse(X2) ) ).
cnf(i_0_12_001,axiom,
X1 = X1 ).
cnf(i_0_13_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_14_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_15_004,axiom,
( X1 != X2
| multiply(X1,X3) = multiply(X2,X3) ) ).
cnf(i_0_16_005,axiom,
( X1 != X2
| multiply(X3,X1) = multiply(X3,X2) ) ).
cnf(i_0_17_006,axiom,
( X1 != X2
| inverse(X1) = inverse(X2) ) ).
cnf(i_0_18,plain,
X1 = multiply(identity,X1),
inference(scs_inference,[],[i_0_9,i_0_13]) ).
cnf(i_0_19,plain,
inverse(identity) != multiply(identity,identity),
inference(scs_inference,[],[i_0_11,i_0_9,i_0_13,i_0_14]) ).
cnf(i_0_20,plain,
multiply(identity,X1) = X1,
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_21,plain,
X1 = multiply(X1,identity),
inference(scs_inference,[],[i_0_10,i_0_13]) ).
cnf(i_0_22,plain,
$false,
inference(scs_inference,[],[i_0_11,i_0_10,i_0_7,i_0_13,i_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP023-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 13:17:11 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.24 % start to proof: theBenchmark
% 0.12/1.51 % Version : CSE_E---1.7
% 0.12/1.51 % Problem : theBenchmark.p
% 0.12/1.51 % SZS status Unsatisfiable for theBenchmark.p
% 0.12/1.51 % SZS output start CNFRefutation
% See solution above
% 0.12/1.52 % Total time : 1.261s
%------------------------------------------------------------------------------