%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP113-1 : TPTP v9.2.1. Released v1.1.0.
% 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 : n015.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 04:23:52 PM UTC 2026
% Result : Unsatisfiable 25.64s 15.28s
% Output : CNFRefutation 25.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 16
% Syntax : Number of clauses : 163 ( 39 unt; 114 nHn; 117 RR)
% Number of literals : 429 ( 428 equ; 44 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(right_inverse,axiom,
multiply(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(all_of_group1,hypothesis,
( X1 = a
| X1 = b
| X1 = c
| X1 = identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_of_group1) ).
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(c_not_identity,hypothesis,
c != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_not_identity) ).
cnf(b_not_identity,hypothesis,
b != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_identity) ).
cnf(a_not_identity,hypothesis,
a != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_identity) ).
cnf(a_not_b,hypothesis,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_b) ).
cnf(b_not_c,hypothesis,
b != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_c) ).
cnf(a_not_c,hypothesis,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_c) ).
cnf(condition_b,negated_conjecture,
( multiply(b,b) != c
| multiply(b,multiply(b,b)) != a
| multiply(b,multiply(b,multiply(b,b))) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition_b) ).
cnf(square_identity,negated_conjecture,
( multiply(a,a) != identity
| multiply(b,b) != identity
| multiply(c,c) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_identity) ).
cnf(condition_a,negated_conjecture,
( multiply(a,a) != b
| multiply(a,multiply(a,a)) != c
| multiply(a,multiply(a,multiply(a,a))) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition_a) ).
cnf(condition_c,negated_conjecture,
( multiply(c,c) != a
| multiply(c,multiply(c,c)) != b
| multiply(c,multiply(c,multiply(c,c))) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition_c) ).
cnf(c_0_16,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_17,axiom,
multiply(X1,inverse(X1)) = identity,
right_inverse ).
cnf(c_0_18,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_19,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_20,hypothesis,
( X1 = a
| X1 = b
| X1 = c
| X1 = identity ),
all_of_group1 ).
cnf(c_0_21,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_16]) ).
cnf(c_0_23,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_24,hypothesis,
( X1 = c
| X1 = b
| X1 = a
| X2 = c
| X2 = b
| X2 = a
| X2 = X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_20]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_16]) ).
cnf(c_0_26,hypothesis,
( inverse(X1) = X1
| X1 = c
| X1 = b
| X1 = a ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_27,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_28,hypothesis,
( multiply(X1,X2) = c
| multiply(X1,X2) = b
| multiply(X1,X2) = a
| inverse(X1) = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_23]) ).
cnf(c_0_29,hypothesis,
c != identity,
c_not_identity ).
cnf(c_0_30,hypothesis,
b != identity,
b_not_identity ).
cnf(c_0_31,hypothesis,
a != identity,
a_not_identity ).
cnf(c_0_32,hypothesis,
( multiply(X1,c) = identity
| inverse(X1) = a
| inverse(X1) = b
| inverse(X1) = X2
| X2 = a
| X2 = b
| X2 = c ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_33,hypothesis,
( multiply(inverse(X1),X2) = c
| multiply(inverse(X1),X2) = b
| multiply(inverse(X1),X2) = a
| X1 = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_23]) ).
cnf(c_0_34,hypothesis,
( multiply(X1,X1) = identity
| X1 = a
| X1 = b
| X1 = c ),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_35,hypothesis,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_27]),c_0_27]),c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_36,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_23]) ).
cnf(c_0_37,hypothesis,
( multiply(X1,c) = identity
| inverse(X1) = b
| inverse(X1) = a
| inverse(X1) = identity ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_32]),c_0_21]),c_0_21]),c_0_21]),c_0_31]),c_0_30]),c_0_29]) ).
cnf(c_0_38,hypothesis,
( inverse(X1) = c
| inverse(X1) = b
| inverse(X1) = a
| inverse(X1) = X1 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_39,hypothesis,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_35]),c_0_36]) ).
cnf(c_0_40,hypothesis,
( multiply(inverse(X1),c) = identity
| X1 = a
| X1 = b
| identity = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_36]),c_0_36]) ).
cnf(c_0_41,hypothesis,
( multiply(X1,inverse(multiply(X2,X1))) = c
| multiply(X1,inverse(multiply(X2,X1))) = b
| multiply(X1,inverse(multiply(X2,X1))) = a
| X2 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_20]),c_0_23]) ).
cnf(c_0_42,hypothesis,
( inverse(b) = a
| inverse(b) = b
| inverse(b) = c ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_38])]) ).
cnf(c_0_43,hypothesis,
( multiply(c,X1) = identity
| multiply(c,X1) = b
| multiply(c,X1) = a
| inverse(X1) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,hypothesis,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_45,hypothesis,
( multiply(X1,inverse(multiply(X2,X1))) = c
| inverse(X2) = a
| inverse(X2) = b
| X2 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_35]),c_0_35]) ).
cnf(c_0_46,hypothesis,
( multiply(c,b) = a
| multiply(c,b) = b
| multiply(c,b) = identity ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_31]),c_0_30]),c_0_29]) ).
cnf(c_0_47,hypothesis,
( inverse(X1) = b
| inverse(X1) = a
| inverse(c) = X1
| X1 = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_18]),c_0_17]),c_0_23]) ).
cnf(c_0_48,hypothesis,
( multiply(c,b) = b
| multiply(c,b) = a
| inverse(c) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_46]),c_0_23]) ).
cnf(c_0_49,hypothesis,
( inverse(c) = X1
| inverse(X1) = a
| inverse(b) = X1
| X1 = identity ),
inference(spm,[status(thm)],[c_0_36,c_0_47]) ).
cnf(c_0_50,hypothesis,
( multiply(c,b) = a
| multiply(c,b) = b
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_48]) ).
cnf(c_0_51,hypothesis,
( inverse(a) = a
| inverse(a) = b
| inverse(a) = c ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_38])]) ).
cnf(c_0_52,hypothesis,
( inverse(b) = X1
| inverse(c) = X1
| inverse(a) = X1
| X1 = identity ),
inference(spm,[status(thm)],[c_0_36,c_0_49]) ).
cnf(c_0_53,hypothesis,
( multiply(b,c) = identity
| multiply(c,b) = a
| inverse(c) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_50]),c_0_17]) ).
cnf(c_0_54,hypothesis,
( multiply(b,c) = identity
| inverse(b) = b
| inverse(b) = a ),
inference(spm,[status(thm)],[c_0_17,c_0_42]) ).
cnf(c_0_55,hypothesis,
( multiply(a,c) = identity
| inverse(a) = b
| inverse(a) = a ),
inference(spm,[status(thm)],[c_0_17,c_0_51]) ).
cnf(c_0_56,hypothesis,
( inverse(a) = X1
| inverse(b) = X1
| inverse(X1) = c
| X1 = identity ),
inference(spm,[status(thm)],[c_0_36,c_0_52]) ).
cnf(c_0_57,hypothesis,
( inverse(c) = c
| inverse(c) = a
| inverse(c) = b ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_38])]) ).
cnf(c_0_58,hypothesis,
( multiply(c,b) = a
| multiply(b,c) = identity ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_53]),c_0_23]),c_0_29]) ).
cnf(c_0_59,hypothesis,
( multiply(b,c) = identity
| multiply(b,b) = identity
| inverse(b) = a ),
inference(spm,[status(thm)],[c_0_17,c_0_54]) ).
cnf(c_0_60,hypothesis,
( multiply(a,c) = identity
| multiply(a,b) = identity
| inverse(a) = a ),
inference(spm,[status(thm)],[c_0_17,c_0_55]) ).
cnf(c_0_61,hypothesis,
( inverse(X1) = c
| inverse(a) = X1
| inverse(X1) = b
| X1 = identity ),
inference(spm,[status(thm)],[c_0_36,c_0_56]) ).
cnf(c_0_62,hypothesis,
( multiply(c,c) = identity
| inverse(c) = b
| inverse(c) = a ),
inference(spm,[status(thm)],[c_0_17,c_0_57]) ).
cnf(c_0_63,hypothesis,
( multiply(inverse(c),a) = b
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_58]) ).
cnf(c_0_64,hypothesis,
( multiply(b,b) = identity
| multiply(b,c) = identity
| multiply(a,b) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_59]) ).
cnf(c_0_65,hypothesis,
( multiply(a,b) = identity
| multiply(a,c) = identity
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_60]) ).
cnf(c_0_66,hypothesis,
( multiply(a,X1) = identity
| inverse(X1) = b
| inverse(X1) = c
| X1 = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_61]) ).
cnf(c_0_67,hypothesis,
( multiply(c,c) = identity
| multiply(b,c) = identity
| inverse(c) = a ),
inference(spm,[status(thm)],[c_0_19,c_0_62]) ).
cnf(c_0_68,hypothesis,
( multiply(a,inverse(b)) = c
| multiply(b,c) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_63]),c_0_36]) ).
cnf(c_0_69,hypothesis,
( multiply(X1,c) = identity
| inverse(X1) = b
| inverse(a) = X1
| X1 = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_61]) ).
cnf(c_0_70,hypothesis,
( multiply(a,b) = identity
| multiply(b,b) = identity
| inverse(c) = b ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_64]),c_0_21]),c_0_16]) ).
cnf(c_0_71,hypothesis,
( multiply(a,a) = identity
| multiply(a,b) = identity
| inverse(c) = a ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_65]),c_0_21]),c_0_16]) ).
cnf(c_0_72,hypothesis,
a != b,
a_not_b ).
cnf(c_0_73,hypothesis,
( multiply(a,X1) = identity
| multiply(X1,c) = identity
| inverse(X1) = b
| X1 = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_66]) ).
cnf(c_0_74,hypothesis,
( multiply(b,c) = identity
| multiply(c,c) = identity
| inverse(a) = c ),
inference(spm,[status(thm)],[c_0_36,c_0_67]) ).
cnf(c_0_75,hypothesis,
( multiply(b,c) = identity
| multiply(a,b) = c
| inverse(a) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_30]) ).
cnf(c_0_76,hypothesis,
b != c,
b_not_c ).
cnf(c_0_77,hypothesis,
( multiply(c,a) = identity
| inverse(a) = b
| inverse(a) = a ),
inference(spm,[status(thm)],[c_0_19,c_0_51]) ).
cnf(c_0_78,hypothesis,
( multiply(a,a) = identity
| multiply(b,b) = identity
| multiply(a,b) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_79,hypothesis,
( multiply(a,b) = identity
| multiply(b,c) = identity
| multiply(a,b) = c ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_73]),c_0_30]) ).
cnf(c_0_80,hypothesis,
( multiply(a,b) = c
| multiply(c,c) = identity
| multiply(b,c) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_81,hypothesis,
( multiply(b,inverse(a)) = inverse(c)
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_58]) ).
cnf(c_0_82,hypothesis,
( multiply(X1,c) = identity
| inverse(X1) = a
| inverse(X1) = b
| X1 = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_47]) ).
cnf(c_0_83,hypothesis,
( multiply(inverse(a),c) = inverse(b)
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_58]) ).
cnf(c_0_84,hypothesis,
( multiply(c,a) = identity
| multiply(b,a) = identity
| inverse(a) = a ),
inference(spm,[status(thm)],[c_0_19,c_0_77]) ).
cnf(c_0_85,hypothesis,
( multiply(a,b) = identity
| multiply(a,a) = identity
| inverse(b) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_78]),c_0_23]) ).
cnf(c_0_86,hypothesis,
( multiply(a,b) = c
| multiply(a,b) = identity
| inverse(b) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_79]),c_0_23]) ).
cnf(c_0_87,hypothesis,
( multiply(b,c) = identity
| multiply(a,b) = c
| inverse(c) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_80]),c_0_23]) ).
cnf(c_0_88,hypothesis,
( inverse(c) = multiply(b,b)
| multiply(a,b) = c
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_81,c_0_75]) ).
cnf(c_0_89,hypothesis,
( multiply(b,c) = identity
| multiply(a,b) = c
| inverse(b) = a ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_82]),c_0_30]) ).
cnf(c_0_90,hypothesis,
( inverse(b) = multiply(b,c)
| multiply(a,b) = c
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_83,c_0_75]) ).
cnf(c_0_91,hypothesis,
( multiply(b,b) = identity
| multiply(b,c) = identity
| multiply(b,a) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_59]) ).
cnf(c_0_92,hypothesis,
( multiply(b,a) = identity
| multiply(c,a) = identity
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_84]) ).
cnf(c_0_93,hypothesis,
( multiply(X1,a) = identity
| inverse(X1) = b
| inverse(X1) = c
| X1 = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_61]) ).
cnf(c_0_94,hypothesis,
( multiply(a,b) = c
| multiply(a,a) = identity
| multiply(a,b) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_76]) ).
cnf(c_0_95,hypothesis,
( multiply(b,b) = c
| multiply(a,b) = c
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,hypothesis,
( multiply(b,c) = a
| multiply(a,b) = c
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_97,hypothesis,
( multiply(b,a) = identity
| multiply(b,b) = identity
| inverse(c) = b ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_91]),c_0_21]),c_0_16]) ).
cnf(c_0_98,hypothesis,
( multiply(a,a) = identity
| multiply(b,a) = identity
| inverse(c) = a ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_92]),c_0_23]) ).
cnf(c_0_99,hypothesis,
( multiply(X1,a) = identity
| multiply(X1,c) = identity
| inverse(X1) = b
| X1 = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_93]) ).
cnf(c_0_100,hypothesis,
( multiply(a,a) = identity
| multiply(a,b) = c
| inverse(b) = a ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_94]),c_0_21]),c_0_16]) ).
cnf(c_0_101,hypothesis,
( multiply(a,b) = c
| multiply(b,b) = c
| inverse(b) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_95]),c_0_23]) ).
cnf(c_0_102,hypothesis,
a != c,
a_not_c ).
cnf(c_0_103,hypothesis,
( multiply(a,b) = c
| multiply(b,c) = a
| inverse(b) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_96]),c_0_23]) ).
cnf(c_0_104,hypothesis,
( multiply(a,a) = identity
| multiply(b,b) = identity
| multiply(b,a) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_72]) ).
cnf(c_0_105,hypothesis,
( multiply(b,a) = identity
| multiply(b,c) = identity
| multiply(a,b) = c ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_99]),c_0_30]) ).
cnf(c_0_106,negated_conjecture,
( multiply(b,b) != c
| multiply(b,multiply(b,b)) != a
| multiply(b,multiply(b,multiply(b,b))) != identity ),
condition_b ).
cnf(c_0_107,hypothesis,
( multiply(b,b) = c
| multiply(a,b) = c
| multiply(a,a) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]) ).
cnf(c_0_108,hypothesis,
( multiply(b,c) = a
| multiply(a,b) = c
| multiply(a,a) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_103]),c_0_102]) ).
cnf(c_0_109,hypothesis,
( multiply(b,a) = identity
| multiply(a,a) = identity
| inverse(b) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_104]),c_0_23]) ).
cnf(c_0_110,hypothesis,
( multiply(a,b) = c
| multiply(b,a) = identity
| inverse(b) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_105]),c_0_23]) ).
cnf(c_0_111,negated_conjecture,
( multiply(a,a) = identity
| multiply(a,b) = c
| multiply(b,multiply(b,c)) != identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]) ).
cnf(c_0_112,hypothesis,
( multiply(a,b) = c
| multiply(a,a) = identity
| multiply(b,a) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_76]) ).
cnf(c_0_113,hypothesis,
( multiply(a,b) = c
| multiply(a,a) = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_108]),c_0_112]) ).
cnf(c_0_114,hypothesis,
( inverse(b) = b
| inverse(b) = a
| inverse(c) = b ),
inference(spm,[status(thm)],[c_0_36,c_0_42]) ).
cnf(c_0_115,hypothesis,
( inverse(a) = b
| inverse(a) = a
| inverse(c) = a ),
inference(spm,[status(thm)],[c_0_36,c_0_51]) ).
cnf(c_0_116,hypothesis,
( multiply(inverse(a),c) = b
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_113]) ).
cnf(c_0_117,hypothesis,
( inverse(a) = a
| inverse(a) = b
| inverse(b) = a
| inverse(b) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_72]) ).
cnf(c_0_118,hypothesis,
( multiply(a,c) = identity
| multiply(a,a) = identity
| multiply(b,c) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_73]),c_0_31]) ).
cnf(c_0_119,hypothesis,
( multiply(b,b) = identity
| inverse(b) = a
| inverse(a) = b
| inverse(a) = a ),
inference(spm,[status(thm)],[c_0_17,c_0_117]) ).
cnf(c_0_120,hypothesis,
( multiply(a,a) = identity
| multiply(a,c) = identity ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_118]),c_0_19]),c_0_29]) ).
cnf(c_0_121,hypothesis,
( multiply(b,b) = identity
| inverse(a) = a
| inverse(a) = b ),
inference(spm,[status(thm)],[c_0_36,c_0_119]) ).
cnf(c_0_122,hypothesis,
( multiply(a,a) = identity
| inverse(a) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_120]),c_0_23]) ).
cnf(c_0_123,hypothesis,
( multiply(a,a) = identity
| multiply(b,b) = identity ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_102]),c_0_76]) ).
cnf(c_0_124,hypothesis,
( multiply(c,inverse(b)) = a
| multiply(a,a) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_116]),c_0_36]) ).
cnf(c_0_125,hypothesis,
( multiply(a,a) = identity
| inverse(b) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_123]),c_0_23]) ).
cnf(c_0_126,hypothesis,
( multiply(c,X1) = identity
| inverse(X1) = a
| inverse(X1) = b
| X1 = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_47]) ).
cnf(c_0_127,hypothesis,
( multiply(a,a) = identity
| multiply(c,b) = a ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_128,hypothesis,
( multiply(c,X1) = identity
| multiply(b,X1) = identity
| inverse(X1) = a
| X1 = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_126]) ).
cnf(c_0_129,hypothesis,
( multiply(inverse(c),a) = inverse(b)
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_113]) ).
cnf(c_0_130,hypothesis,
( multiply(a,a) = identity
| inverse(c) = a ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_120]),c_0_21]),c_0_16]) ).
cnf(c_0_131,hypothesis,
( multiply(inverse(c),a) = b
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_127]) ).
cnf(c_0_132,negated_conjecture,
( multiply(a,a) != identity
| multiply(b,b) != identity
| multiply(c,c) != identity ),
square_identity ).
cnf(c_0_133,hypothesis,
( multiply(c,c) = identity
| multiply(b,c) = identity
| multiply(a,a) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_128]),c_0_29]) ).
cnf(c_0_134,hypothesis,
( inverse(b) = multiply(a,a)
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_135,hypothesis,
( multiply(a,inverse(b)) = c
| multiply(a,a) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_131]),c_0_36]) ).
cnf(c_0_136,negated_conjecture,
( multiply(a,a) = b
| multiply(b,c) = identity
| multiply(a,a) != identity
| multiply(b,b) != identity ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_137,hypothesis,
( multiply(a,a) = b
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_125,c_0_134]) ).
cnf(c_0_138,negated_conjecture,
( multiply(a,a) != b
| multiply(a,multiply(a,a)) != c
| multiply(a,multiply(a,multiply(a,a))) != identity ),
condition_a ).
cnf(c_0_139,hypothesis,
( multiply(a,multiply(a,a)) = c
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_135,c_0_134]) ).
cnf(c_0_140,hypothesis,
( multiply(X1,c) = identity
| multiply(X1,b) = identity
| inverse(X1) = a
| X1 = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_82]) ).
cnf(c_0_141,negated_conjecture,
( multiply(a,a) = b
| multiply(b,c) = identity
| multiply(b,b) != identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_30]) ).
cnf(c_0_142,negated_conjecture,
multiply(a,a) = identity,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_137]),c_0_120]) ).
cnf(c_0_143,hypothesis,
( multiply(c,a) = a
| multiply(c,a) = b
| multiply(c,a) = identity ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_43]),c_0_31]),c_0_30]),c_0_29]) ).
cnf(c_0_144,hypothesis,
( multiply(a,a) = b
| inverse(a) = a ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_137]),c_0_23]) ).
cnf(c_0_145,hypothesis,
( multiply(b,b) = identity
| multiply(b,c) = identity
| multiply(a,a) = c ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_140]),c_0_30]) ).
cnf(c_0_146,negated_conjecture,
( multiply(b,c) = identity
| multiply(b,b) != identity ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_142]),c_0_30]) ).
cnf(c_0_147,hypothesis,
( multiply(c,a) = b
| multiply(c,a) = a
| inverse(a) = c ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_143]),c_0_21]),c_0_16]) ).
cnf(c_0_148,hypothesis,
inverse(a) = a,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_142]),c_0_30]) ).
cnf(c_0_149,hypothesis,
( multiply(a,a) = c
| multiply(b,b) = identity
| inverse(c) = b ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_145]),c_0_21]),c_0_16]) ).
cnf(c_0_150,hypothesis,
( inverse(c) = b
| multiply(b,b) != identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_146]),c_0_21]),c_0_16]) ).
cnf(c_0_151,hypothesis,
( multiply(c,a) = a
| multiply(c,a) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_102]) ).
cnf(c_0_152,hypothesis,
inverse(c) = b,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_142]),c_0_29]),c_0_150]) ).
cnf(c_0_153,hypothesis,
( multiply(c,a) = a
| multiply(b,b) = a ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_151]),c_0_152]) ).
cnf(c_0_154,hypothesis,
multiply(b,b) = a,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_153]),c_0_17]),c_0_152]),c_0_30]) ).
cnf(c_0_155,hypothesis,
inverse(b) = c,
inference(spm,[status(thm)],[c_0_36,c_0_152]) ).
cnf(c_0_156,negated_conjecture,
( multiply(c,c) != a
| multiply(c,multiply(c,c)) != b
| multiply(c,multiply(c,multiply(c,c))) != identity ),
condition_c ).
cnf(c_0_157,hypothesis,
( multiply(inverse(X1),c) = X2
| multiply(X1,X2) = a
| multiply(X1,X2) = b
| multiply(X1,X2) = X3
| X3 = a
| X3 = b
| X3 = c ),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_158,hypothesis,
multiply(c,a) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_154]),c_0_155]) ).
cnf(c_0_159,negated_conjecture,
( multiply(c,multiply(c,multiply(c,c))) = b
| multiply(c,multiply(c,multiply(c,c))) = a
| multiply(c,multiply(c,c)) = identity
| multiply(c,multiply(c,c)) != b
| multiply(c,c) != a ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_19])]),c_0_31]),c_0_30]),c_0_29]) ).
cnf(c_0_160,hypothesis,
multiply(c,c) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_158]),c_0_155]),c_0_148]) ).
cnf(c_0_161,hypothesis,
multiply(c,b) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_152]) ).
cnf(c_0_162,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160]),c_0_158]),c_0_161]),c_0_160]),c_0_158]),c_0_161]),c_0_160]),c_0_158]),c_0_160]),c_0_158]),c_0_160])]),c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP113-1 : TPTP v9.2.1. Released v1.1.0.
% 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
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:22:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 25.64/15.28 % Version : CSE_E---1.7
% 25.64/15.28 % Problem : theBenchmark.p
% 25.64/15.28 % SZS status Unsatisfiable for theBenchmark.p
% 25.64/15.28 % SZS output start CNFRefutation
% See solution above
% 25.74/15.38 % Total time : 11.389s
%------------------------------------------------------------------------------