%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP113-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:37:54 PM UTC 2026
% Result : Unsatisfiable 48.47s 6.60s
% Output : CNFRefutation 48.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 16
% Syntax : Number of clauses : 148 ( 41 unt; 93 nHn; 119 RR)
% Number of literals : 368 ( 367 equ; 59 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 : 42 ( 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(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(right_inverse,axiom,
multiply(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(all_of_group1,hypothesis,
( X1 = identity
| X1 = c
| X1 = b
| X1 = a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',all_of_group1) ).
cnf(a_not_identity,hypothesis,
a != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_identity) ).
cnf(b_not_identity,hypothesis,
b != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_not_identity) ).
cnf(c_not_identity,hypothesis,
c != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_not_identity) ).
cnf(a_not_c,hypothesis,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).
cnf(b_not_c,hypothesis,
b != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_not_c) ).
cnf(a_not_b,hypothesis,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_b) ).
cnf(condition_b,negated_conjecture,
( multiply(b,multiply(b,multiply(b,b))) != identity
| multiply(b,multiply(b,b)) != a
| multiply(b,b) != c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition_b) ).
cnf(square_identity,negated_conjecture,
( multiply(c,c) != identity
| multiply(b,b) != identity
| multiply(a,a) != identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',square_identity) ).
cnf(condition_c,negated_conjecture,
( multiply(c,multiply(c,multiply(c,c))) != identity
| multiply(c,multiply(c,c)) != b
| multiply(c,c) != a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition_c) ).
cnf(condition_a,negated_conjecture,
( multiply(a,multiply(a,multiply(a,a))) != identity
| multiply(a,multiply(a,a)) != c
| multiply(a,a) != b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition_a) ).
cnf(c_0_16,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_17,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_18,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_19,axiom,
multiply(X1,inverse(X1)) = identity,
right_inverse ).
cnf(c_0_20,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_22,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,hypothesis,
( X1 = identity
| X1 = c
| X1 = b
| X1 = a ),
all_of_group1 ).
cnf(c_0_24,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_17]),c_0_21]) ).
cnf(c_0_25,hypothesis,
( X1 = a
| X1 = b
| X1 = c
| inverse(X1) = X1 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,hypothesis,
( inverse(X1) = X1
| inverse(X1) = c
| inverse(X1) = b
| inverse(X1) = a ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,hypothesis,
( X2 = X1
| X2 = a
| X2 = b
| X2 = c
| X1 = a
| X1 = b
| X1 = c ),
inference(spm,[status(thm)],[c_0_23,c_0_23]) ).
cnf(c_0_28,hypothesis,
a != identity,
inference(fof_simplification,[status(thm)],[a_not_identity]) ).
cnf(c_0_29,hypothesis,
b != identity,
inference(fof_simplification,[status(thm)],[b_not_identity]) ).
cnf(c_0_30,hypothesis,
c != identity,
inference(fof_simplification,[status(thm)],[c_not_identity]) ).
cnf(c_0_31,hypothesis,
( inverse(a) = a
| inverse(a) = b
| inverse(a) = c ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_26])]) ).
cnf(c_0_32,hypothesis,
( X2 = c
| X2 = b
| X2 = a
| inverse(X1) = X2
| inverse(X1) = b
| inverse(X1) = a
| multiply(c,X1) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_33,hypothesis,
a != identity,
c_0_28 ).
cnf(c_0_34,hypothesis,
b != identity,
c_0_29 ).
cnf(c_0_35,hypothesis,
c != identity,
c_0_30 ).
cnf(c_0_36,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_37,hypothesis,
( inverse(a) = b
| inverse(a) = a
| multiply(a,c) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_38,hypothesis,
( inverse(X1) = identity
| inverse(X1) = a
| inverse(X1) = b
| multiply(c,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_22,c_0_32]),c_0_22]),c_0_22]),c_0_22]),c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_39,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_36]),c_0_21]) ).
cnf(c_0_40,hypothesis,
( inverse(X1) = X2
| multiply(X1,X2) = a
| multiply(X1,X2) = b
| multiply(X1,X2) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_23]),c_0_21]) ).
cnf(c_0_41,hypothesis,
a != c,
inference(fof_simplification,[status(thm)],[a_not_c]) ).
cnf(c_0_42,hypothesis,
b != c,
inference(fof_simplification,[status(thm)],[b_not_c]) ).
cnf(c_0_43,hypothesis,
( inverse(b) = a
| inverse(b) = b
| inverse(b) = c ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_26])]) ).
cnf(c_0_44,hypothesis,
( inverse(a) = a
| multiply(b,a) = identity
| multiply(a,c) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_37]) ).
cnf(c_0_45,hypothesis,
( identity = X1
| X1 = b
| X1 = a
| multiply(c,inverse(X1)) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_38]),c_0_24]),c_0_24]) ).
cnf(c_0_46,hypothesis,
( inverse(X2) = X1
| multiply(X2,X1) = b
| multiply(X2,X1) = a
| multiply(X1,inverse(c)) = inverse(X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,hypothesis,
a != c,
c_0_41 ).
cnf(c_0_48,hypothesis,
b != c,
c_0_42 ).
cnf(c_0_49,hypothesis,
( inverse(a) = b
| inverse(a) = a
| multiply(c,a) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_31]) ).
cnf(c_0_50,hypothesis,
( inverse(b) = b
| inverse(b) = a
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_43]) ).
cnf(c_0_51,hypothesis,
( multiply(a,a) = identity
| multiply(a,c) = identity
| multiply(b,a) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_44]) ).
cnf(c_0_52,hypothesis,
( inverse(X1) = identity
| inverse(X1) = c
| multiply(X1,c) = a
| multiply(X1,c) = b ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]),c_0_35]) ).
cnf(c_0_53,hypothesis,
( inverse(c) = a
| inverse(c) = b
| inverse(c) = c ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_26])]) ).
cnf(c_0_54,hypothesis,
( inverse(a) = a
| multiply(b,a) = identity
| multiply(c,a) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_49]) ).
cnf(c_0_55,hypothesis,
( inverse(b) = a
| multiply(b,b) = identity
| multiply(b,c) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_50]) ).
cnf(c_0_56,hypothesis,
( inverse(b) = a
| multiply(a,c) = identity
| multiply(a,a) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_51]),c_0_21]) ).
cnf(c_0_57,hypothesis,
( inverse(b) = c
| multiply(b,c) = b
| multiply(b,c) = a ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_52]),c_0_35]),c_0_34]),c_0_33]) ).
cnf(c_0_58,hypothesis,
( inverse(c) = b
| inverse(c) = a
| multiply(c,c) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_53]) ).
cnf(c_0_59,hypothesis,
( multiply(a,a) = identity
| multiply(c,a) = identity
| multiply(b,a) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_54]) ).
cnf(c_0_60,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_39]),c_0_24]) ).
cnf(c_0_61,hypothesis,
( multiply(b,a) = identity
| multiply(b,c) = identity
| multiply(b,b) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_55]) ).
cnf(c_0_62,hypothesis,
a != b,
inference(fof_simplification,[status(thm)],[a_not_b]) ).
cnf(c_0_63,hypothesis,
( multiply(a,a) = identity
| multiply(a,c) = identity
| multiply(b,c) = a
| multiply(b,c) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_47]) ).
cnf(c_0_64,hypothesis,
( inverse(b) = c
| inverse(c) = a
| multiply(c,c) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_58]) ).
cnf(c_0_65,hypothesis,
( inverse(c) = a
| multiply(b,a) = identity
| multiply(a,a) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_59]),c_0_21]) ).
cnf(c_0_66,hypothesis,
( inverse(c) = b
| multiply(b,b) = identity
| multiply(b,a) = identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_22]),c_0_18]) ).
cnf(c_0_67,hypothesis,
a != b,
c_0_62 ).
cnf(c_0_68,hypothesis,
( multiply(b,c) = a
| multiply(a,c) = identity
| multiply(a,a) = identity ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_63]),c_0_17]),c_0_35]) ).
cnf(c_0_69,hypothesis,
( inverse(b) = c
| multiply(a,c) = identity
| multiply(c,c) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_64]) ).
cnf(c_0_70,hypothesis,
( multiply(a,a) = identity
| multiply(b,a) = identity
| multiply(b,b) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_71,hypothesis,
( inverse(c) = a
| inverse(a) = b
| inverse(a) = a ),
inference(spm,[status(thm)],[c_0_24,c_0_31]) ).
cnf(c_0_72,hypothesis,
( inverse(c) = b
| inverse(b) = b
| inverse(b) = a ),
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_73,hypothesis,
( multiply(a,a) = identity
| multiply(a,c) = identity
| multiply(inverse(b),a) = c ),
inference(spm,[status(thm)],[c_0_20,c_0_68]) ).
cnf(c_0_74,hypothesis,
( multiply(c,c) = identity
| multiply(a,c) = identity
| multiply(a,a) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_56]),c_0_47]) ).
cnf(c_0_75,hypothesis,
( inverse(b) = b
| multiply(b,a) = identity
| multiply(a,a) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_70]),c_0_21]) ).
cnf(c_0_76,hypothesis,
( inverse(a) = a
| inverse(a) = b
| inverse(b) = a
| inverse(b) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_67]) ).
cnf(c_0_77,hypothesis,
( multiply(a,c) = identity
| multiply(a,a) = identity
| multiply(a,inverse(c)) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_73]),c_0_24]) ).
cnf(c_0_78,hypothesis,
( inverse(c) = c
| multiply(a,a) = identity
| multiply(a,c) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_74]),c_0_21]) ).
cnf(c_0_79,hypothesis,
( multiply(a,a) = identity
| multiply(b,a) = identity
| multiply(b,c) = a
| multiply(b,c) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_57]),c_0_48]) ).
cnf(c_0_80,hypothesis,
( inverse(b) = a
| inverse(a) = b
| inverse(a) = a
| multiply(b,b) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_76]) ).
cnf(c_0_81,hypothesis,
( multiply(a,c) = b
| multiply(a,a) = identity
| multiply(a,c) = identity ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_82,hypothesis,
( multiply(b,c) = a
| multiply(b,a) = identity
| multiply(a,a) = identity ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_79]),c_0_17]),c_0_35]) ).
cnf(c_0_83,hypothesis,
( inverse(a) = b
| inverse(a) = a
| multiply(b,b) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_80]) ).
cnf(c_0_84,hypothesis,
( inverse(a) = c
| multiply(a,a) = identity
| multiply(a,c) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_81]),c_0_21]) ).
cnf(c_0_85,hypothesis,
( multiply(a,a) = identity
| multiply(b,a) = identity
| multiply(inverse(b),a) = c ),
inference(spm,[status(thm)],[c_0_20,c_0_82]) ).
cnf(c_0_86,hypothesis,
( multiply(b,b) = identity
| multiply(a,c) = b
| multiply(a,a) = identity ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_47]),c_0_48]) ).
cnf(c_0_87,hypothesis,
( multiply(b,a) = c
| multiply(b,a) = identity
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_85,c_0_75]) ).
cnf(c_0_88,hypothesis,
( inverse(b) = b
| multiply(a,a) = identity
| multiply(a,c) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_86]),c_0_21]) ).
cnf(c_0_89,hypothesis,
( inverse(b) = a
| multiply(a,a) = identity
| multiply(b,a) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_87]),c_0_21]) ).
cnf(c_0_90,hypothesis,
( multiply(b,a) = identity
| multiply(a,a) = identity
| multiply(a,inverse(c)) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_85]),c_0_24]) ).
cnf(c_0_91,hypothesis,
( multiply(a,c) = b
| multiply(a,a) = identity
| multiply(b,a) = c ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_67]) ).
cnf(c_0_92,hypothesis,
( multiply(a,a) = b
| multiply(a,a) = identity
| multiply(b,a) = identity ),
inference(spm,[status(thm)],[c_0_90,c_0_65]) ).
cnf(c_0_93,hypothesis,
( multiply(a,a) = identity
| multiply(a,c) = b
| multiply(a,a) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_35]) ).
cnf(c_0_94,negated_conjecture,
( multiply(b,multiply(b,multiply(b,b))) != identity
| multiply(b,multiply(b,b)) != a
| multiply(b,b) != c ),
inference(fof_simplification,[status(thm)],[condition_b]) ).
cnf(c_0_95,hypothesis,
( multiply(a,a) = b
| multiply(a,a) = identity
| multiply(inverse(a),b) = c ),
inference(spm,[status(thm)],[c_0_20,c_0_93]) ).
cnf(c_0_96,hypothesis,
( inverse(a) = b
| multiply(a,a) = identity
| multiply(a,a) = b ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_92]),c_0_22]),c_0_18]) ).
cnf(c_0_97,negated_conjecture,
( multiply(b,multiply(b,multiply(b,b))) != identity
| multiply(b,multiply(b,b)) != a
| multiply(b,b) != c ),
c_0_94 ).
cnf(c_0_98,hypothesis,
( multiply(b,b) = c
| multiply(a,a) = identity
| multiply(a,a) = b ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_99,negated_conjecture,
( multiply(b,c) != a
| multiply(b,multiply(b,c)) != identity
| multiply(a,a) = b
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_100,hypothesis,
( multiply(a,a) = identity
| multiply(a,a) = b
| multiply(a,c) = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_68]),c_0_92]) ).
cnf(c_0_101,hypothesis,
( multiply(a,a) = b
| multiply(a,a) = identity ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_100]),c_0_34]) ).
cnf(c_0_102,hypothesis,
( inverse(a) = a
| multiply(a,a) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_101]),c_0_21]) ).
cnf(c_0_103,hypothesis,
( inverse(b) = b
| inverse(b) = a
| multiply(c,b) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_43]) ).
cnf(c_0_104,hypothesis,
( multiply(a,a) = b
| multiply(a,multiply(a,X1)) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_101]),c_0_18]) ).
cnf(c_0_105,hypothesis,
( multiply(a,c) = b
| multiply(a,c) = a
| multiply(a,a) = b ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_102]),c_0_47]),c_0_33]) ).
cnf(c_0_106,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_19]),c_0_18]) ).
cnf(c_0_107,hypothesis,
( inverse(c) = a
| multiply(c,b) = identity
| multiply(c,c) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_58]) ).
cnf(c_0_108,hypothesis,
( inverse(b) = a
| multiply(b,b) = identity
| multiply(c,b) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_103]) ).
cnf(c_0_109,hypothesis,
( multiply(a,a) = c
| multiply(a,c) = identity
| multiply(a,a) = identity ),
inference(spm,[status(thm)],[c_0_73,c_0_56]) ).
cnf(c_0_110,hypothesis,
( multiply(a,b) = c
| multiply(a,a) = b
| multiply(a,c) = a ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
( multiply(c,c) != identity
| multiply(b,b) != identity
| multiply(a,a) != identity ),
inference(fof_simplification,[status(thm)],[square_identity]) ).
cnf(c_0_112,hypothesis,
( multiply(c,c) = identity
| multiply(c,b) = identity
| multiply(c,multiply(a,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,hypothesis,
( inverse(a) = b
| multiply(c,b) = identity
| multiply(b,b) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_108]) ).
cnf(c_0_114,hypothesis,
( inverse(a) = c
| multiply(a,a) = identity
| multiply(a,a) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_109]),c_0_21]) ).
cnf(c_0_115,hypothesis,
( multiply(a,a) = b
| multiply(a,b) = c ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_110]),c_0_17]),c_0_35]) ).
cnf(c_0_116,negated_conjecture,
( multiply(c,c) != identity
| multiply(b,b) != identity
| multiply(a,a) != identity ),
c_0_111 ).
cnf(c_0_117,hypothesis,
( multiply(c,b) = identity
| multiply(c,c) = identity
| multiply(a,a) = b ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_101]),c_0_21]),c_0_47]) ).
cnf(c_0_118,hypothesis,
( multiply(b,b) = identity
| multiply(c,b) = identity
| multiply(a,a) = b ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_102]),c_0_67]) ).
cnf(c_0_119,hypothesis,
( multiply(b,b) = identity
| multiply(a,a) = c
| multiply(a,a) = identity ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_114]),c_0_47]),c_0_48]) ).
cnf(c_0_120,hypothesis,
( multiply(a,c) = b
| multiply(a,a) = b ),
inference(spm,[status(thm)],[c_0_104,c_0_115]) ).
cnf(c_0_121,negated_conjecture,
( multiply(a,a) = b
| multiply(c,b) = identity ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),c_0_101]) ).
cnf(c_0_122,hypothesis,
( inverse(b) = b
| multiply(a,a) = identity
| multiply(a,a) = c ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_119]),c_0_21]) ).
cnf(c_0_123,hypothesis,
( multiply(a,a) = b
| multiply(inverse(a),c) = b ),
inference(spm,[status(thm)],[c_0_20,c_0_115]) ).
cnf(c_0_124,hypothesis,
( multiply(a,a) = b
| multiply(inverse(b),a) = inverse(c) ),
inference(spm,[status(thm)],[c_0_60,c_0_120]) ).
cnf(c_0_125,negated_conjecture,
( inverse(b) = c
| multiply(a,a) = b ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_121]),c_0_22]),c_0_18]) ).
cnf(c_0_126,hypothesis,
( multiply(a,a) = c
| multiply(a,a) = identity
| multiply(b,a) = c ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_89]),c_0_67]) ).
cnf(c_0_127,negated_conjecture,
( multiply(c,multiply(c,multiply(c,c))) != identity
| multiply(c,multiply(c,c)) != b
| multiply(c,c) != a ),
inference(fof_simplification,[status(thm)],[condition_c]) ).
cnf(c_0_128,hypothesis,
( multiply(a,a) = b
| multiply(c,inverse(b)) = a ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_123]),c_0_24]) ).
cnf(c_0_129,negated_conjecture,
( inverse(c) = b
| multiply(a,a) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_121]),c_0_21]) ).
cnf(c_0_130,hypothesis,
( multiply(a,a) = b
| inverse(c) = multiply(c,a) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_131,hypothesis,
( multiply(a,a) = identity
| multiply(a,a) = c
| multiply(inverse(b),c) = a ),
inference(spm,[status(thm)],[c_0_20,c_0_126]) ).
cnf(c_0_132,negated_conjecture,
( multiply(c,multiply(c,multiply(c,c))) != identity
| multiply(c,multiply(c,c)) != b
| multiply(c,c) != a ),
c_0_127 ).
cnf(c_0_133,hypothesis,
( multiply(c,c) = a
| multiply(a,a) = b ),
inference(spm,[status(thm)],[c_0_128,c_0_125]) ).
cnf(c_0_134,negated_conjecture,
( multiply(a,a) = b
| multiply(c,a) = b ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_135,hypothesis,
( multiply(a,a) = c
| multiply(a,a) = identity
| multiply(c,inverse(a)) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_131]),c_0_24]) ).
cnf(c_0_136,negated_conjecture,
( multiply(c,multiply(c,a)) != identity
| multiply(a,a) = b ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_134]) ).
cnf(c_0_137,negated_conjecture,
( multiply(a,multiply(a,multiply(a,a))) != identity
| multiply(a,multiply(a,a)) != c
| multiply(a,a) != b ),
inference(fof_simplification,[status(thm)],[condition_a]) ).
cnf(c_0_138,hypothesis,
( multiply(c,c) = b
| multiply(a,a) = identity
| multiply(a,a) = c ),
inference(spm,[status(thm)],[c_0_135,c_0_114]) ).
cnf(c_0_139,negated_conjecture,
multiply(a,a) = b,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_134]),c_0_121]) ).
cnf(c_0_140,hypothesis,
( inverse(c) = a
| multiply(a,a) = identity
| multiply(a,a) = c ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_109]),c_0_22]),c_0_18]) ).
cnf(c_0_141,negated_conjecture,
( multiply(a,multiply(a,multiply(a,a))) != identity
| multiply(a,multiply(a,a)) != c
| multiply(a,a) != b ),
c_0_137 ).
cnf(c_0_142,hypothesis,
multiply(c,c) = b,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_139]),c_0_139]),c_0_48]),c_0_34]) ).
cnf(c_0_143,hypothesis,
inverse(c) = a,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_139]),c_0_139]),c_0_48]),c_0_34]) ).
cnf(c_0_144,negated_conjecture,
( multiply(a,b) != c
| multiply(a,multiply(a,b)) != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_139]),c_0_139]),c_0_139])]) ).
cnf(c_0_145,hypothesis,
multiply(a,b) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_142]),c_0_143]) ).
cnf(c_0_146,hypothesis,
multiply(a,c) = identity,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_139]),c_0_139]),c_0_34]),c_0_48]) ).
cnf(c_0_147,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_145]),c_0_146]),c_0_145])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP113-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:00:46 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.47/6.60 % Version: 3.5.1
% 48.47/6.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 48.47/6.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.47/6.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 48.47/6.60 % Starting new_bool_3 with 300s (1) cores
% 48.47/6.60 % Starting new_bool_1 with 300s (1) cores
% 48.47/6.60 % Starting sh5l with 300s (1) cores
% 48.47/6.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1574432 completed with status 0
% 48.47/6.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 48.47/6.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 48.47/6.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.47/6.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 48.47/6.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 48.47/6.60 % No SInE strategy applied
% 48.47/6.60 % Search class: FGHPM-FFSF21-MFFFFFNN
% 48.47/6.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 48.47/6.60 % Starting SubtermCWHack with 136s (1) cores
% 48.47/6.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 48.47/6.60 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 48.47/6.60 % Starting new_bool_3 with 136s (1) cores
% 48.47/6.60 % Starting new_bool_1 with 136s (1) cores
% 48.47/6.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1574437 completed with status 0
% 48.47/6.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 48.47/6.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 48.47/6.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.47/6.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 48.47/6.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 48.47/6.60 % No SInE strategy applied
% 48.47/6.60 % Search class: FGHPM-FFSF21-MFFFFFNN
% 48.47/6.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 48.47/6.60 % Starting SubtermCWHack with 136s (1) cores
% 48.47/6.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 48.47/6.60 % Preprocessing time : 0.001 s
% 48.47/6.60 % Presaturation interreduction done
% 48.47/6.60
% 48.47/6.60 % Proof found!
% 48.47/6.60 % SZS status Unsatisfiable
% 48.47/6.60 % SZS output start CNFRefutation
% See solution above
% 48.47/6.60 % Parsed axioms : 16
% 48.47/6.60 % Removed by relevancy pruning/SinE : 0
% 48.47/6.60 % Initial clauses : 16
% 48.47/6.60 % Removed in clause preprocessing : 0
% 48.47/6.60 % Initial clauses in saturation : 16
% 48.47/6.60 % Processed clauses : 5441
% 48.47/6.60 % ...of these trivial : 117
% 48.47/6.60 % ...subsumed : 4672
% 48.47/6.60 % ...remaining for further processing : 652
% 48.47/6.60 % Other redundant clauses eliminated : 3876
% 48.47/6.60 % Clauses deleted for lack of memory : 0
% 48.47/6.60 % Backward-subsumed : 133
% 48.47/6.60 % Backward-rewritten : 265
% 48.47/6.60 % Generated clauses : 193530
% 48.47/6.60 % ...of the previous two non-redundant : 184225
% 48.47/6.60 % ...aggressively subsumed : 0
% 48.47/6.60 % Contextual simplify-reflections : 8
% 48.47/6.60 % Paramodulations : 188158
% 48.47/6.60 % Factorizations : 1496
% 48.47/6.60 % NegExts : 0
% 48.47/6.60 % Equation resolutions : 3876
% 48.47/6.60 % Disequality decompositions : 0
% 48.47/6.60 % Total rewrite steps : 123748
% 48.47/6.60 % ...of those cached : 120858
% 48.47/6.60 % Propositional unsat checks : 0
% 48.47/6.60 % Propositional check models : 0
% 48.47/6.60 % Propositional check unsatisfiable : 0
% 48.47/6.60 % Propositional clauses : 0
% 48.47/6.60 % Propositional clauses after purity: 0
% 48.47/6.60 % Propositional unsat core size : 0
% 48.47/6.60 % Propositional preprocessing time : 0.000
% 48.47/6.60 % Propositional encoding time : 0.000
% 48.47/6.60 % Propositional solver time : 0.000
% 48.47/6.60 % Success case prop preproc time : 0.000
% 48.47/6.60 % Success case prop encoding time : 0.000
% 48.47/6.60 % Success case prop solver time : 0.000
% 48.47/6.60 % Current number of processed clauses : 238
% 48.47/6.60 % Positive orientable unit clauses : 32
% 48.47/6.60 % Positive unorientable unit clauses: 0
% 48.47/6.60 % Negative unit clauses : 6
% 48.47/6.60 % Non-unit-clauses : 200
% 48.47/6.60 % Current number of unprocessed clauses: 178500
% 48.47/6.60 % ...number of literals in the above : 1847579
% 48.47/6.60 % Current number of archived formulas : 0
% 48.47/6.60 % Current number of archived clauses : 414
% 48.47/6.60 % Clause-clause subsumption calls (NU) : 81092
% 48.47/6.60 % Rec. Clause-clause subsumption calls : 14783
% 48.47/6.60 % Non-unit clause-clause subsumptions : 4499
% 48.47/6.60 % Unit Clause-clause subsumption calls : 1563
% 48.47/6.60 % Rewrite failures with RHS unbound : 0
% 48.47/6.60 % BW rewrite match attempts : 25
% 48.47/6.60 % BW rewrite match successes : 15
% 48.47/6.60 % Condensation attempts : 0
% 48.47/6.60 % Condensation successes : 0
% 48.47/6.60 % Termbank termtop insertions : 3391360
% 48.47/6.60 % Search garbage collected termcells : 44
% 48.47/6.60
% 48.47/6.60 % -------------------------------------------------
% 48.47/6.60 % User time : 5.808 s
% 48.47/6.60 % System time : 0.210 s
% 48.47/6.60 % Total time : 6.018 s
% 48.47/6.60 % Maximum resident set size: 3640 pages
% 48.47/6.60
% 48.47/6.60 % -------------------------------------------------
% 48.47/6.60 % User time : 29.224 s
% 48.47/6.60 % System time : 1.069 s
% 48.47/6.60 % Total time : 30.293 s
% 48.47/6.60 % Maximum resident set size: 4864 pages
% 48.47/6.60 % E exiting
%------------------------------------------------------------------------------