%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP022-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.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 0.19s 1.78s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 23
% Syntax : Number of clauses : 48 ( 26 unt; 0 nHn; 29 RR)
% Number of literals : 93 ( 29 equ; 52 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(total_function2,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(prove_inverse_of_inverse_is_original,negated_conjecture,
inverse(inverse(a)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_inverse_is_original) ).
cnf(i_0_9,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1,
[final] ).
cnf(i_0_10,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2,
[final] ).
cnf(i_0_11,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2,
[final] ).
cnf(i_0_12,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1,
[final] ).
cnf(i_0_13,axiom,
product(inverse(X1),X1,identity),
left_inverse,
[final] ).
cnf(i_0_14,axiom,
product(X1,inverse(X1),identity),
right_inverse,
[final] ).
cnf(i_0_15,axiom,
product(identity,X1,X1),
left_identity,
[final] ).
cnf(i_0_16,axiom,
product(X1,identity,X1),
right_identity,
[final] ).
cnf(i_0_17,negated_conjecture,
inverse(inverse(a)) != a,
prove_inverse_of_inverse_is_original,
[final] ).
cnf(i_0_18,axiom,
X1 = X1 ).
cnf(i_0_19,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_20,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_21,axiom,
( X1 != X2
| inverse(X1) = inverse(X2) ) ).
cnf(i_0_22,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_23,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_24,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_18_001,axiom,
X1 = X1 ).
cnf(i_0_19_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_20_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_21_004,axiom,
( X1 != X2
| inverse(X1) = inverse(X2) ) ).
cnf(i_0_22_005,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_23_006,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_24_007,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_25,plain,
~ product(identity,a,inverse(inverse(a))),
inference(scs_inference,[],[i_0_17,i_0_15,i_0_11]) ).
cnf(i_0_26,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_27,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_28,plain,
a != inverse(inverse(a)),
inference(scs_inference,[],[i_0_17,i_0_15,i_0_26,i_0_11,i_0_24]) ).
cnf(i_0_29,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_30,plain,
~ product(identity,inverse(inverse(a)),a),
inference(scs_inference,[],[i_0_17,i_0_15,i_0_26,i_0_29,i_0_16,i_0_11,i_0_24,i_0_9]) ).
cnf(i_0_31,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_32,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_33,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_34,plain,
~ product(inverse(a),a,identity),
inference(scs_inference,[],[i_0_17,i_0_15,i_0_26,i_0_29,i_0_16,i_0_32,i_0_13,i_0_11,i_0_24,i_0_9,i_0_10]) ).
cnf(i_0_35,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_36,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_37,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_38,plain,
( X1 != identity
| ~ product(X1,a,inverse(inverse(a))) ),
inference(scs_inference,[],[i_0_17,i_0_15,i_0_26,i_0_29,i_0_16,i_0_32,i_0_13,i_0_11,i_0_24,i_0_9,i_0_10,i_0_22]) ).
cnf(i_0_40,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_42,plain,
$false,
inference(scs_inference,[],[i_0_17,i_0_15,i_0_26,i_0_29,i_0_16,i_0_32,i_0_13,i_0_36,i_0_11,i_0_24,i_0_9,i_0_10,i_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.21 % Problem : GRP022-1 : TPTP v9.2.1. Released v1.0.0.
% 0.03/0.21 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.47 % Computer : n028.cluster.edu
% 0.12/0.47 % Model : x86_64 x86_64
% 0.12/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.47 % Memory : 8042.1875MB
% 0.12/0.47 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.47 % CPULimit : 300
% 0.12/0.47 % WCLimit : 300
% 0.12/0.47 % DateTime : Mon May 4 18:17:01 EDT 2026
% 0.12/0.47 % CPUTime :
% 0.12/0.48 % start to proof: theBenchmark
% 0.19/1.78 % Version : CSE_E---1.7
% 0.19/1.78 % Problem : theBenchmark.p
% 0.19/1.78 % SZS status Unsatisfiable for theBenchmark.p
% 0.19/1.78 % SZS output start CNFRefutation
% See solution above
% 0.24/1.83 % Total time : 1.288s
%------------------------------------------------------------------------------