%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP036-3 : 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 : n009.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 04:23:38 PM UTC 2026
% Result : Unsatisfiable 0.22s 1.62s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 30
% Syntax : Number of clauses : 62 ( 28 unt; 0 nHn; 45 RR)
% Number of literals : 127 ( 27 equ; 72 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 126 ( 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/sandbox2/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/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(total_function2,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(closure_of_product_and_inverse,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,inverse(X2),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(another_left_inverse,hypothesis,
( product(another_inverse(X1),X1,another_identity)
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_left_inverse) ).
cnf(another_right_inverse,hypothesis,
( product(X1,another_inverse(X1),another_identity)
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_inverse) ).
cnf(another_left_identity,hypothesis,
( product(another_identity,X1,X1)
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_left_identity) ).
cnf(another_right_identity,hypothesis,
( product(X1,another_identity,X1)
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(another_inverse_in_subgroup,hypothesis,
( subgroup_member(another_inverse(X1))
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_inverse_in_subgroup) ).
cnf(another_identity_in_subgroup,hypothesis,
subgroup_member(another_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_identity_in_subgroup) ).
cnf(prove_identity_equals_another_identity,negated_conjecture,
identity != another_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_identity_equals_another_identity) ).
cnf(i_0_16,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1,
[final] ).
cnf(i_0_17,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2,
[final] ).
cnf(i_0_18,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2,
[final] ).
cnf(i_0_19,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,inverse(X2),X3) ),
closure_of_product_and_inverse,
[final] ).
cnf(i_0_20,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1,
[final] ).
cnf(i_0_21,hypothesis,
( product(another_inverse(X1),X1,another_identity)
| ~ subgroup_member(X1) ),
another_left_inverse,
[final] ).
cnf(i_0_22,hypothesis,
( product(X1,another_inverse(X1),another_identity)
| ~ subgroup_member(X1) ),
another_right_inverse,
[final] ).
cnf(i_0_23,hypothesis,
( product(another_identity,X1,X1)
| ~ subgroup_member(X1) ),
another_left_identity,
[final] ).
cnf(i_0_24,hypothesis,
( product(X1,another_identity,X1)
| ~ subgroup_member(X1) ),
another_right_identity,
[final] ).
cnf(i_0_25,axiom,
product(inverse(X1),X1,identity),
left_inverse,
[final] ).
cnf(i_0_26,axiom,
product(X1,inverse(X1),identity),
right_inverse,
[final] ).
cnf(i_0_27,axiom,
product(identity,X1,X1),
left_identity,
[final] ).
cnf(i_0_28,axiom,
product(X1,identity,X1),
right_identity,
[final] ).
cnf(i_0_29,hypothesis,
( subgroup_member(another_inverse(X1))
| ~ subgroup_member(X1) ),
another_inverse_in_subgroup,
[final] ).
cnf(i_0_30,hypothesis,
subgroup_member(another_identity),
another_identity_in_subgroup,
[final] ).
cnf(i_0_31,negated_conjecture,
identity != another_identity,
prove_identity_equals_another_identity,
[final] ).
cnf(i_0_32,axiom,
X1 = X1 ).
cnf(i_0_33,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_34,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_35,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_37,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_38,axiom,
( X1 != X2
| ~ subgroup_member(X1)
| subgroup_member(X2) ) ).
cnf(i_0_32_001,axiom,
X1 = X1 ).
cnf(i_0_33_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_34_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_35_004,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_36_005,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_37_006,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_38_007,axiom,
( X1 != X2
| ~ subgroup_member(X1)
| subgroup_member(X2) ) ).
cnf(i_0_39,plain,
~ product(identity,another_identity,identity),
inference(scs_inference,[],[i_0_31,i_0_27,i_0_18]) ).
cnf(i_0_40,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_41,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_42,plain,
inverse(another_identity) != identity,
inference(scs_inference,[],[i_0_31,i_0_27,i_0_25,i_0_18,i_0_35]) ).
cnf(i_0_43,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_44,plain,
another_identity != identity,
inference(scs_inference,[],[i_0_31,i_0_27,i_0_40,i_0_25,i_0_18,i_0_35,i_0_37]) ).
cnf(i_0_45,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_46,plain,
~ product(identity,identity,another_identity),
inference(scs_inference,[],[i_0_31,i_0_27,i_0_40,i_0_45,i_0_25,i_0_18,i_0_35,i_0_37,i_0_16]) ).
cnf(i_0_47,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_48,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_49,plain,
~ product(X1,another_identity,X1),
inference(scs_inference,[],[i_0_31,i_0_27,i_0_40,i_0_45,i_0_25,i_0_43,i_0_18,i_0_35,i_0_37,i_0_16,i_0_17]) ).
cnf(i_0_50,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_51,plain,
subgroup_member(multiply(another_identity,inverse(another_identity))),
inference(scs_inference,[],[i_0_31,i_0_27,i_0_40,i_0_45,i_0_20,i_0_25,i_0_43,i_0_30,i_0_18,i_0_35,i_0_37,i_0_16,i_0_17,i_0_19]) ).
cnf(i_0_52,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_53,plain,
( ~ product(X1,inverse(X2),X3)
| subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2) ),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_54,plain,
$false,
inference(scs_inference,[],[i_0_31,i_0_27,i_0_40,i_0_45,i_0_20,i_0_25,i_0_43,i_0_30,i_0_18,i_0_35,i_0_37,i_0_16,i_0_17,i_0_19,i_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP036-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.13/0.32 % Computer : n009.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 18:17:56 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 0.22/1.62 % Version : CSE_E---1.7
% 0.22/1.62 % Problem : theBenchmark.p
% 0.22/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.22/1.62 % SZS output start CNFRefutation
% See solution above
% 0.22/1.66 % Total time : 1.273s
%------------------------------------------------------------------------------