%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP012-2 : 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 : n008.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 04:23:33 PM UTC 2026
% Result : Unsatisfiable 0.31s 1.61s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 42)
% 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(inverse_b_multiply_inverse_a_is_d,hypothesis,
product(inverse(b),inverse(a),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
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(a_multiply_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_multiply_b_is_c) ).
cnf(prove_c_inverse_equals_d,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_equals_d) ).
cnf(i_0_11,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1,
[final] ).
cnf(i_0_12,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2,
[final] ).
cnf(i_0_13,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2,
[final] ).
cnf(i_0_14,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1,
[final] ).
cnf(i_0_15,hypothesis,
product(inverse(b),inverse(a),d),
inverse_b_multiply_inverse_a_is_d,
[final] ).
cnf(i_0_16,axiom,
product(inverse(X1),X1,identity),
left_inverse,
[final] ).
cnf(i_0_17,axiom,
product(X1,inverse(X1),identity),
right_inverse,
[final] ).
cnf(i_0_18,axiom,
product(identity,X1,X1),
left_identity,
[final] ).
cnf(i_0_19,axiom,
product(X1,identity,X1),
right_identity,
[final] ).
cnf(i_0_20,hypothesis,
product(a,b,c),
a_multiply_b_is_c,
[final] ).
cnf(i_0_21,negated_conjecture,
inverse(c) != d,
prove_c_inverse_equals_d,
[final] ).
cnf(i_0_22,axiom,
X1 = X1 ).
cnf(i_0_23,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_24,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_25,axiom,
( X1 != X2
| inverse(X1) = inverse(X2) ) ).
cnf(i_0_26,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_27,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_28,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_22_001,axiom,
X1 = X1 ).
cnf(i_0_23_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_24_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_25_004,axiom,
( X1 != X2
| inverse(X1) = inverse(X2) ) ).
cnf(i_0_26_005,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_27_006,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_28_007,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_29,plain,
~ product(identity,d,inverse(c)),
inference(scs_inference,[],[i_0_21,i_0_18,i_0_13]) ).
cnf(i_0_30,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_31,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_32,plain,
d != inverse(c),
inference(scs_inference,[],[i_0_21,i_0_18,i_0_30,i_0_13,i_0_28]) ).
cnf(i_0_33,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_34,plain,
~ product(identity,inverse(c),d),
inference(scs_inference,[],[i_0_21,i_0_18,i_0_30,i_0_33,i_0_19,i_0_13,i_0_28,i_0_11]) ).
cnf(i_0_35,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_36,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_37,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_38,plain,
~ product(c,d,identity),
inference(scs_inference,[],[i_0_21,i_0_18,i_0_30,i_0_33,i_0_19,i_0_36,i_0_16,i_0_13,i_0_28,i_0_11,i_0_12]) ).
cnf(i_0_39,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_40,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_41,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_42,plain,
( X1 != identity
| ~ product(X1,d,inverse(c)) ),
inference(scs_inference,[],[i_0_21,i_0_18,i_0_30,i_0_33,i_0_19,i_0_36,i_0_16,i_0_13,i_0_28,i_0_11,i_0_12,i_0_26]) ).
cnf(i_0_43,plain,
~ product(identity,d,inverse(c)),
inference(equality_inference,[],[42]) ).
cnf(i_0_44,plain,
multiply(X1,inverse(X1)) = identity,
inference(scs_inference,[],[i_0_14,i_0_17,i_0_13]) ).
cnf(i_0_45,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_46,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_47,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_48,plain,
multiply(identity,d) != inverse(c),
inference(scs_inference,[],[i_0_29,i_0_14,i_0_46,i_0_17,i_0_13,i_0_28]) ).
cnf(i_0_49,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_50,plain,
~ product(multiply(X1,inverse(X1)),d,inverse(c)),
inference(scs_inference,[],[i_0_29,i_0_14,i_0_46,i_0_17,i_0_13,i_0_28,i_0_26]) ).
cnf(i_0_51,plain,
product(b,d,multiply(identity,inverse(a))),
inference(scs_inference,[],[i_0_29,i_0_14,i_0_46,i_0_49,i_0_17,i_0_45,i_0_15,i_0_13,i_0_28,i_0_26,i_0_11]) ).
cnf(i_0_52,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_53,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_54,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_55,plain,
product(multiply(X1,identity),inverse(identity),multiply(X1,identity)),
inference(scs_inference,[],[i_0_29,i_0_14,i_0_46,i_0_49,i_0_52,i_0_17,i_0_45,i_0_53,i_0_15,i_0_13,i_0_28,i_0_26,i_0_11,i_0_12]) ).
cnf(i_0_56,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_57,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_58,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_59,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_60,plain,
identity = multiply(X1,inverse(X1)),
inference(scs_inference,[],[i_0_29,i_0_14,i_0_46,i_0_49,i_0_52,i_0_17,i_0_45,i_0_53,i_0_15,i_0_13,i_0_28,i_0_26,i_0_11,i_0_12,i_0_23]) ).
cnf(i_0_61,plain,
( X1 != d
| ~ product(multiply(X2,inverse(X2)),X1,inverse(c)) ),
inference(scs_inference,[],[i_0_29,i_0_14,i_0_46,i_0_49,i_0_52,i_0_17,i_0_45,i_0_53,i_0_15,i_0_13,i_0_28,i_0_26,i_0_11,i_0_12,i_0_23,i_0_27]) ).
cnf(i_0_62,plain,
~ product(multiply(X1,inverse(X1)),d,inverse(c)),
inference(equality_inference,[],[61]) ).
cnf(i_0_63,plain,
~ product(d,identity,inverse(c)),
inference(scs_inference,[],[i_0_21,i_0_19,i_0_13]) ).
cnf(i_0_64,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_65,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_66,plain,
~ product(d,multiply(X1,inverse(X1)),inverse(c)),
inference(scs_inference,[],[i_0_21,i_0_44,i_0_19,i_0_13,i_0_27]) ).
cnf(i_0_67,plain,
~ product(c,d,multiply(X1,inverse(X1))),
inference(scs_inference,[],[i_0_21,i_0_44,i_0_38,i_0_19,i_0_13,i_0_27,i_0_28]) ).
cnf(i_0_68,plain,
~ product(multiply(X1,inverse(X1)),inverse(c),d),
inference(scs_inference,[],[i_0_21,i_0_44,i_0_34,i_0_38,i_0_19,i_0_13,i_0_27,i_0_28,i_0_26]) ).
cnf(i_0_69,plain,
product(multiply(X1,identity),multiply(inverse(identity),inverse(identity)),multiply(X1,identity)),
inference(scs_inference,[],[i_0_21,i_0_44,i_0_55,i_0_34,i_0_38,i_0_19,i_0_14,i_0_13,i_0_27,i_0_28,i_0_26,i_0_11]) ).
cnf(i_0_70,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_71,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_72,plain,
~ product(b,d,inverse(a)),
inference(scs_inference,[],[i_0_21,i_0_44,i_0_55,i_0_34,i_0_20,i_0_38,i_0_19,i_0_14,i_0_70,i_0_13,i_0_27,i_0_28,i_0_26,i_0_11,i_0_12]) ).
cnf(i_0_73,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_74,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_75,plain,
inverse(identity) = identity,
inference(scs_inference,[],[i_0_18,i_0_17,i_0_13]) ).
cnf(i_0_76,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_77,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_78,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_79,plain,
multiply(identity,inverse(a)) != inverse(a),
inference(scs_inference,[],[i_0_72,i_0_51,i_0_18,i_0_17,i_0_13,i_0_28]) ).
cnf(i_0_80,plain,
inverse(d) != c,
inference(scs_inference,[],[i_0_72,i_0_51,i_0_18,i_0_38,i_0_16,i_0_17,i_0_13,i_0_28,i_0_26]) ).
cnf(i_0_81,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_82,plain,
~ product(inverse(d),inverse(c),identity),
inference(scs_inference,[],[i_0_63,i_0_72,i_0_51,i_0_18,i_0_77,i_0_38,i_0_16,i_0_17,i_0_76,i_0_13,i_0_28,i_0_26,i_0_11]) ).
cnf(i_0_83,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_84,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_85,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_86,plain,
~ product(c,d,inverse(identity)),
inference(scs_inference,[],[i_0_63,i_0_72,i_0_51,i_0_18,i_0_77,i_0_83,i_0_38,i_0_16,i_0_17,i_0_76,i_0_84,i_0_13,i_0_28,i_0_26,i_0_11,i_0_12]) ).
cnf(i_0_87,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_88,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_89,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_90,plain,
identity = inverse(identity),
inference(scs_inference,[],[i_0_63,i_0_72,i_0_51,i_0_18,i_0_77,i_0_83,i_0_38,i_0_16,i_0_17,i_0_76,i_0_84,i_0_13,i_0_28,i_0_26,i_0_11,i_0_12,i_0_23]) ).
cnf(i_0_91,plain,
multiply(X1,inverse(X1)) = inverse(identity),
inference(scs_inference,[],[i_0_44,i_0_63,i_0_72,i_0_51,i_0_18,i_0_77,i_0_83,i_0_38,i_0_16,i_0_17,i_0_76,i_0_84,i_0_13,i_0_28,i_0_26,i_0_11,i_0_12,i_0_23,i_0_24]) ).
cnf(i_0_92,plain,
( X1 != d
| ~ product(b,X1,inverse(a)) ),
inference(scs_inference,[],[i_0_44,i_0_63,i_0_72,i_0_51,i_0_18,i_0_77,i_0_83,i_0_38,i_0_16,i_0_17,i_0_76,i_0_84,i_0_13,i_0_28,i_0_26,i_0_11,i_0_12,i_0_23,i_0_24,i_0_27]) ).
cnf(i_0_93,plain,
~ product(b,d,inverse(a)),
inference(equality_inference,[],[92]) ).
cnf(i_0_94,plain,
inverse(identity) = multiply(X1,inverse(X1)),
inference(scs_inference,[],[i_0_91,i_0_23]) ).
cnf(i_0_95,plain,
~ product(a,b,inverse(d)),
inference(scs_inference,[],[i_0_91,i_0_80,i_0_20,i_0_23,i_0_13]) ).
cnf(i_0_96,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_97,plain,
~ product(d,inverse(identity),inverse(c)),
inference(scs_inference,[],[i_0_75,i_0_91,i_0_63,i_0_80,i_0_20,i_0_23,i_0_13,i_0_27]) ).
cnf(i_0_98,plain,
~ product(inverse(d),inverse(c),inverse(identity)),
inference(scs_inference,[],[i_0_75,i_0_91,i_0_63,i_0_82,i_0_80,i_0_20,i_0_23,i_0_13,i_0_27,i_0_28]) ).
cnf(i_0_99,plain,
~ product(inverse(identity),d,inverse(c)),
inference(scs_inference,[],[i_0_75,i_0_91,i_0_63,i_0_29,i_0_82,i_0_80,i_0_20,i_0_23,i_0_13,i_0_27,i_0_28,i_0_26]) ).
cnf(i_0_100,plain,
~ product(identity,inverse(inverse(d)),inverse(c)),
inference(scs_inference,[],[i_0_75,i_0_91,i_0_63,i_0_29,i_0_82,i_0_80,i_0_20,i_0_19,i_0_17,i_0_23,i_0_13,i_0_27,i_0_28,i_0_26,i_0_11]) ).
cnf(i_0_101,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_102,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_103,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_104,plain,
~ product(inverse(inverse(b)),inverse(c),inverse(a)),
inference(scs_inference,[],[i_0_75,i_0_91,i_0_63,i_0_29,i_0_68,i_0_82,i_0_80,i_0_20,i_0_15,i_0_19,i_0_14,i_0_17,i_0_23,i_0_13,i_0_27,i_0_28,i_0_26,i_0_11,i_0_12]) ).
cnf(i_0_105,plain,
~ product(multiply(X1,inverse(X1)),inverse(c),d),
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_106,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_107,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_108,plain,
~ product(inverse(b),inverse(a),inverse(c)),
inference(scs_inference,[],[i_0_21,i_0_15,i_0_13]) ).
cnf(i_0_109,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_110,plain,
inverse(c) != inverse(inverse(d)),
inference(scs_inference,[],[i_0_21,i_0_100,i_0_18,i_0_15,i_0_13,i_0_27]) ).
cnf(i_0_111,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_112,plain,
c != inverse(d),
inference(scs_inference,[],[i_0_21,i_0_95,i_0_100,i_0_18,i_0_20,i_0_15,i_0_13,i_0_27,i_0_28]) ).
cnf(i_0_113,plain,
~ product(inverse(identity),inverse(inverse(d)),inverse(c)),
inference(scs_inference,[],[i_0_21,i_0_75,i_0_95,i_0_100,i_0_18,i_0_20,i_0_15,i_0_13,i_0_27,i_0_28,i_0_26]) ).
cnf(i_0_114,plain,
~ product(inverse(a),inverse(d),b),
inference(scs_inference,[],[i_0_21,i_0_75,i_0_95,i_0_100,i_0_18,i_0_111,i_0_20,i_0_15,i_0_17,i_0_13,i_0_27,i_0_28,i_0_26,i_0_11]) ).
cnf(i_0_115,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_116,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_117,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_118,plain,
~ product(b,inverse(c),inverse(a)),
inference(scs_inference,[],[i_0_21,i_0_75,i_0_95,i_0_100,i_0_34,i_0_18,i_0_111,i_0_16,i_0_20,i_0_15,i_0_17,i_0_13,i_0_27,i_0_28,i_0_26,i_0_11,i_0_12]) ).
cnf(i_0_119,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_120,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_121,plain,
multiply(inverse(b),inverse(a)) != inverse(c),
inference(scs_inference,[],[i_0_108,i_0_14,i_0_28]) ).
cnf(i_0_122,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_123,plain,
~ product(inverse(identity),inverse(c),d),
inference(scs_inference,[],[i_0_94,i_0_108,i_0_68,i_0_14,i_0_28,i_0_26]) ).
cnf(i_0_124,plain,
~ product(multiply(X1,inverse(X1)),inverse(c),d),
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_125,plain,
~ product(inverse(c),inverse(inverse(a)),inverse(b)),
inference(scs_inference,[],[i_0_94,i_0_108,i_0_68,i_0_19,i_0_14,i_0_16,i_0_28,i_0_26,i_0_12]) ).
cnf(i_0_126,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_127,plain,
product(inverse(X1),X1,identity),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_128,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_129,plain,
( X1 != inverse(a)
| ~ product(inverse(b),X1,inverse(c)) ),
inference(scs_inference,[],[i_0_94,i_0_108,i_0_68,i_0_19,i_0_14,i_0_16,i_0_28,i_0_26,i_0_12,i_0_27]) ).
cnf(i_0_130,plain,
( X1 != a
| ~ product(inverse(b),inverse(X1),inverse(c)) ),
inference(scs_inference,[],[i_0_94,i_0_108,i_0_68,i_0_19,i_0_14,i_0_16,i_0_28,i_0_26,i_0_12,i_0_27,i_0_25]) ).
cnf(i_0_131,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_132,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_133,plain,
( ~ product(inverse(b),inverse(X1),inverse(c))
| ~ product(inverse(b),X2,inverse(c))
| ~ product(X2,identity,inverse(a)) ),
inference(scs_inference,[],[i_0_94,i_0_108,i_0_68,i_0_19,i_0_126,i_0_14,i_0_16,i_0_28,i_0_26,i_0_12,i_0_27,i_0_25,i_0_11]) ).
cnf(i_0_134,plain,
~ product(inverse(b),inverse(a),inverse(c)),
inference(equality_inference,[],[129]) ).
cnf(i_0_135,plain,
~ product(inverse(b),inverse(a),inverse(c)),
inference(equality_inference,[],[130]) ).
cnf(i_0_136,plain,
X1 = multiply(identity,X1),
inference(scs_inference,[],[i_0_18,i_0_14,i_0_13]) ).
cnf(i_0_137,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_138,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_139,plain,
inverse(inverse(d)) != inverse(c),
inference(scs_inference,[],[i_0_18,i_0_17,i_0_82,i_0_14,i_0_13,i_0_27]) ).
cnf(i_0_140,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_141,plain,
multiply(d,inverse(identity)) != inverse(c),
inference(scs_inference,[],[i_0_18,i_0_17,i_0_97,i_0_82,i_0_14,i_0_137,i_0_13,i_0_27,i_0_28]) ).
cnf(i_0_142,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_143,plain,
~ product(inverse(c),identity,d),
inference(scs_inference,[],[i_0_63,i_0_18,i_0_17,i_0_97,i_0_82,i_0_19,i_0_14,i_0_137,i_0_13,i_0_27,i_0_28,i_0_12]) ).
cnf(i_0_144,plain,
product(X1,identity,X1),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_145,plain,
product(identity,X1,X1),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_146,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_147,plain,
~ product(inverse(c),inverse(identity),d),
inference(scs_inference,[],[i_0_63,i_0_18,i_0_17,i_0_140,i_0_97,i_0_67,i_0_82,i_0_19,i_0_14,i_0_137,i_0_142,i_0_13,i_0_27,i_0_28,i_0_12,i_0_11]) ).
cnf(i_0_148,plain,
product(X1,X2,multiply(X1,X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_149,plain,
~ product(c,d,multiply(X1,inverse(X1))),
inference(rename_variables,[],[i_0_67]) ).
cnf(i_0_150,plain,
product(X1,inverse(X1),identity),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_151,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_152,plain,
multiply(identity,identity) = identity,
inference(scs_inference,[],[i_0_63,i_0_18,i_0_17,i_0_140,i_0_97,i_0_67,i_0_82,i_0_19,i_0_14,i_0_137,i_0_142,i_0_13,i_0_27,i_0_28,i_0_12,i_0_11,i_0_23]) ).
cnf(i_0_153,plain,
multiply(X1,inverse(X1)) = multiply(identity,identity),
inference(scs_inference,[],[i_0_44,i_0_63,i_0_18,i_0_17,i_0_140,i_0_97,i_0_67,i_0_82,i_0_19,i_0_14,i_0_137,i_0_142,i_0_13,i_0_27,i_0_28,i_0_12,i_0_11,i_0_23,i_0_24]) ).
cnf(i_0_154,plain,
( X1 != a
| ~ product(X1,b,inverse(d)) ),
inference(scs_inference,[],[i_0_44,i_0_63,i_0_95,i_0_18,i_0_17,i_0_140,i_0_97,i_0_67,i_0_82,i_0_19,i_0_14,i_0_137,i_0_142,i_0_13,i_0_27,i_0_28,i_0_12,i_0_11,i_0_23,i_0_24,i_0_26]) ).
cnf(i_0_155,plain,
~ product(a,b,inverse(d)),
inference(equality_inference,[],[154]) ).
cnf(i_0_156,plain,
$false,
inference(scs_inference,[],[i_0_136,i_0_79,i_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP012-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.15/0.32 % Computer : n008.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 18:16:43 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.31/1.61 % Version : CSE_E---1.7
% 0.31/1.61 % Problem : theBenchmark.p
% 0.31/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.31/1.61 % SZS output start CNFRefutation
% See solution above
% 0.52/1.87 % Total time : 1.273s
%------------------------------------------------------------------------------