%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP319-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:39:17 PM UTC 2026
% Result : Unsatisfiable 0.74s 0.65s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 28
% Syntax : Number of clauses : 175 ( 28 unt; 135 nHn; 152 RR)
% Number of literals : 370 ( 369 equ; 62 neg)
% Maximal clause size : 12 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_37,negated_conjecture,
( multiply(X6,sk_c9) != sk_c7
| inverse(X6) != sk_c7
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c7
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(c_0_28,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_29,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_30,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_31,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_32,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_33,plain,
multiply(inverse(inverse(inverse(X1))),X1) = identity,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_33]),c_0_32]) ).
cnf(c_0_35,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
prove_this_32 ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_26 ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c9,sk_c4) = identity
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c9,sk_c4) = identity
| multiply(sk_c2,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c8 ),
prove_this_14 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c9 ),
prove_this_31 ).
cnf(c_0_43,negated_conjecture,
( identity = sk_c3
| multiply(sk_c9,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_32,c_0_34]) ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_8 ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_25 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c2,sk_c9) = identity
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( identity = sk_c3
| inverse(sk_c9) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_43]),c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c9,sk_c4) = identity
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c9,sk_c4) = identity
| multiply(sk_c1,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_46]) ).
cnf(c_0_52,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_53,negated_conjecture,
( identity = sk_c3
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( identity = sk_c3
| multiply(sk_c4,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_13 ).
cnf(c_0_56,negated_conjecture,
( identity = sk_c9
| multiply(sk_c9,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
prove_this_4 ).
cnf(c_0_58,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_52]),c_0_44]) ).
cnf(c_0_59,negated_conjecture,
( identity = sk_c3
| multiply(inverse(sk_c4),sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_31,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( identity = sk_c8
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_7 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( identity = sk_c9
| inverse(sk_c9) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_56]),c_0_44]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
prove_this_3 ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_35,c_0_57]) ).
cnf(c_0_66,negated_conjecture,
( identity = sk_c3
| multiply(sk_c8,inverse(sk_c9)) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_34]) ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_20 ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
prove_this_2 ).
cnf(c_0_69,negated_conjecture,
( sk_c3 != sk_c8
| identity = sk_c8 ),
inference(ef,[status(thm)],[c_0_60]) ).
cnf(c_0_70,negated_conjecture,
( identity = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,negated_conjecture,
( identity = sk_c9
| multiply(sk_c4,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_63]) ).
cnf(c_0_72,negated_conjecture,
( identity = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_73,negated_conjecture,
( identity = sk_c3
| multiply(sk_c8,sk_c4) = sk_c4 ),
inference(spm,[status(thm)],[c_0_66,c_0_49]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_19 ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c4,sk_c9) = identity
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_67]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
prove_this_1 ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c4,sk_c9) = identity
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_35,c_0_68]) ).
cnf(c_0_78,negated_conjecture,
( sk_c3 != sk_c8
| multiply(sk_c8,X1) = X1 ),
inference(spm,[status(thm)],[c_0_30,c_0_69]) ).
cnf(c_0_79,negated_conjecture,
( identity = sk_c8
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_80,negated_conjecture,
( identity = sk_c7
| multiply(inverse(sk_c8),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_31,c_0_72]) ).
cnf(c_0_81,negated_conjecture,
( identity = sk_c3
| inverse(sk_c8) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_73]),c_0_35]) ).
cnf(c_0_82,negated_conjecture,
( identity = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_83,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
prove_this_34 ).
cnf(c_0_84,negated_conjecture,
( identity = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_85,negated_conjecture,
( sk_c3 != sk_c8
| sk_c7 = sk_c9
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_72,c_0_78]) ).
cnf(c_0_86,negated_conjecture,
( sk_c8 != sk_c9
| identity = sk_c9 ),
inference(ef,[status(thm)],[c_0_79]) ).
cnf(c_0_87,negated_conjecture,
( sk_c7 = sk_c9
| identity = sk_c7
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_30]) ).
cnf(c_0_88,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c9),sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_31,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
( identity = sk_c8
| multiply(sk_c3,X1) = X1 ),
inference(spm,[status(thm)],[c_0_30,c_0_60]) ).
cnf(c_0_90,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_28 ).
cnf(c_0_91,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_83]) ).
cnf(c_0_92,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c8),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_31,c_0_84]) ).
cnf(c_0_93,negated_conjecture,
( sk_c8 != sk_c9
| sk_c3 != sk_c8
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_94,negated_conjecture,
( sk_c8 != sk_c9
| sk_c3 = sk_c9
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_87,c_0_86]) ).
cnf(c_0_95,negated_conjecture,
( identity = sk_c8
| multiply(sk_c8,inverse(sk_c3)) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_88]),c_0_34]) ).
cnf(c_0_96,negated_conjecture,
( identity = sk_c8
| inverse(sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_89]) ).
cnf(c_0_97,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_16 ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_29,c_0_90]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c2,sk_c9) = identity
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_91]) ).
cnf(c_0_100,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_101,negated_conjecture,
( identity = sk_c8
| multiply(sk_c7,inverse(sk_c9)) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_92]),c_0_34]) ).
cnf(c_0_102,negated_conjecture,
( sk_c8 != sk_c9
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_103,negated_conjecture,
( sk_c8 = sk_c9
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_44]) ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c8) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(spm,[status(thm)],[c_0_34,c_0_97]) ).
cnf(c_0_105,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_10 ).
cnf(c_0_106,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_97]) ).
cnf(c_0_107,negated_conjecture,
( identity = sk_c3
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_108,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_100]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_15 ).
cnf(c_0_110,negated_conjecture,
identity = sk_c8,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_35])]),c_0_103]) ).
cnf(c_0_111,negated_conjecture,
( inverse(sk_c8) = sk_c1
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_34,c_0_104]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_105]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_35,c_0_106]) ).
cnf(c_0_114,negated_conjecture,
( identity = sk_c3
| inverse(sk_c8) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_107]),c_0_44]) ).
cnf(c_0_115,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_17 ).
cnf(c_0_116,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_29,c_0_108]) ).
cnf(c_0_117,negated_conjecture,
( inverse(sk_c8) = sk_c1
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_34,c_0_109]) ).
cnf(c_0_118,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_110]) ).
cnf(c_0_119,negated_conjecture,
( sk_c5 != sk_c1
| inverse(sk_c8) = sk_c1 ),
inference(ef,[status(thm)],[c_0_111]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_9 ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_35,c_0_105]) ).
cnf(c_0_122,negated_conjecture,
( identity = sk_c9
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_123,negated_conjecture,
( identity = sk_c5
| identity = sk_c3 ),
inference(spm,[status(thm)],[c_0_114,c_0_81]) ).
cnf(c_0_124,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(spm,[status(thm)],[c_0_34,c_0_115]) ).
cnf(c_0_125,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c1 ),
inference(spm,[status(thm)],[c_0_34,c_0_111]) ).
cnf(c_0_126,plain,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_110]),c_0_110]) ).
cnf(c_0_127,plain,
multiply(X1,inverse(X1)) = sk_c8,
inference(rw,[status(thm)],[c_0_35,c_0_110]) ).
cnf(c_0_128,negated_conjecture,
( sk_c5 = sk_c7
| inverse(sk_c8) = sk_c1 ),
inference(rw,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_129,plain,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[c_0_30,c_0_110]) ).
cnf(c_0_130,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_11 ).
cnf(c_0_131,negated_conjecture,
( sk_c5 != sk_c1
| multiply(sk_c1,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_119]) ).
cnf(c_0_132,negated_conjecture,
( identity = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_133,negated_conjecture,
( identity = sk_c9
| inverse(sk_c8) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_122]),c_0_44]) ).
cnf(c_0_134,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_116,c_0_103]) ).
cnf(c_0_135,negated_conjecture,
( sk_c3 != sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_116,c_0_69]) ).
cnf(c_0_136,negated_conjecture,
( identity = sk_c3
| sk_c5 = sk_c8 ),
inference(rw,[status(thm)],[c_0_123,c_0_110]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_18 ).
cnf(c_0_138,negated_conjecture,
( inverse(sk_c8) = sk_c1
| inverse(sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_34,c_0_124]) ).
cnf(c_0_139,negated_conjecture,
( sk_c1 = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(rw,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_140,negated_conjecture,
( sk_c1 = sk_c8
| sk_c5 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_141,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_34,c_0_130]) ).
cnf(c_0_142,negated_conjecture,
( sk_c1 = sk_c9
| inverse(sk_c5) = sk_c8 ),
inference(rw,[status(thm)],[c_0_105,c_0_118]) ).
cnf(c_0_143,negated_conjecture,
( sk_c1 = sk_c9
| sk_c5 = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_118]),c_0_118]) ).
cnf(c_0_144,negated_conjecture,
( sk_c5 != sk_c1
| identity = sk_c9
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_145,negated_conjecture,
( sk_c5 = sk_c8
| identity = sk_c9
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_146,negated_conjecture,
( sk_c3 != sk_c8
| sk_c5 = sk_c8
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_111,c_0_135]) ).
cnf(c_0_147,negated_conjecture,
( sk_c3 = sk_c8
| sk_c5 = sk_c8 ),
inference(spm,[status(thm)],[c_0_110,c_0_136]) ).
cnf(c_0_148,negated_conjecture,
( inverse(sk_c8) = sk_c1
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_34,c_0_137]) ).
cnf(c_0_149,negated_conjecture,
( sk_c1 = sk_c8
| inverse(sk_c7) = sk_c6 ),
inference(rw,[status(thm)],[c_0_138,c_0_126]) ).
cnf(c_0_150,negated_conjecture,
( sk_c1 = sk_c8
| inverse(sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_151,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_12 ).
cnf(c_0_152,negated_conjecture,
( sk_c1 = sk_c9
| inverse(sk_c7) = sk_c6 ),
inference(rw,[status(thm)],[c_0_141,c_0_118]) ).
cnf(c_0_153,negated_conjecture,
( sk_c1 = sk_c9
| inverse(sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_154,negated_conjecture,
( sk_c5 != sk_c1
| sk_c7 = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_144,c_0_103]) ).
cnf(c_0_155,negated_conjecture,
( sk_c8 = sk_c9
| sk_c5 = sk_c8 ),
inference(spm,[status(thm)],[c_0_103,c_0_145]) ).
cnf(c_0_156,negated_conjecture,
( sk_c1 = sk_c8
| sk_c5 = sk_c8 ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_157,negated_conjecture,
( sk_c1 = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_148,c_0_126]) ).
cnf(c_0_158,negated_conjecture,
( sk_c6 = sk_c8
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_159,negated_conjecture,
( sk_c1 = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(rw,[status(thm)],[c_0_151,c_0_118]) ).
cnf(c_0_160,negated_conjecture,
( sk_c6 = sk_c8
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_161,negated_conjecture,
( sk_c1 != sk_c8
| sk_c8 = sk_c9
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_162,negated_conjecture,
( sk_c7 = sk_c8
| sk_c1 = sk_c8 ),
inference(spm,[status(thm)],[c_0_156,c_0_140]) ).
cnf(c_0_163,negated_conjecture,
( sk_c7 = sk_c9
| sk_c1 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_129]) ).
cnf(c_0_164,negated_conjecture,
( sk_c7 = sk_c9
| sk_c1 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_129]) ).
cnf(c_0_165,negated_conjecture,
( multiply(X6,sk_c9) != sk_c7
| inverse(X6) != sk_c7
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c7
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(fof_simplification,[status(thm)],[prove_this_37]) ).
cnf(c_0_166,negated_conjecture,
( sk_c7 = sk_c8
| sk_c8 = sk_c9 ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_167,negated_conjecture,
sk_c7 = sk_c9,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_102]) ).
cnf(c_0_168,negated_conjecture,
( multiply(X6,sk_c9) != sk_c7
| inverse(X6) != sk_c7
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c7
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
c_0_165 ).
cnf(c_0_169,negated_conjecture,
sk_c8 = sk_c9,
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_170,negated_conjecture,
( inverse(X5) != sk_c8
| inverse(X1) != sk_c9
| inverse(X4) != sk_c9
| inverse(X3) != sk_c8
| inverse(X2) != sk_c7
| multiply(X5,sk_c8) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c9) != sk_c7
| multiply(sk_c8,sk_c9) != sk_c7
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8 ),
inference(er,[status(thm)],[c_0_168]) ).
cnf(c_0_171,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_118,c_0_169]) ).
cnf(c_0_172,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_129,c_0_169]) ).
cnf(c_0_173,plain,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_169]),c_0_169]) ).
cnf(c_0_174,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_118]),c_0_118])])]),c_0_171]),c_0_172]),c_0_169]),c_0_129]),c_0_167]),c_0_171]),c_0_167]),c_0_171]),c_0_169]),c_0_167]),c_0_167]),c_0_173]),c_0_169]),c_0_173]),c_0_169])])])])]),c_0_173])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP319-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:09:04 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.74/0.65 % Version: 3.5.1
% 0.74/0.65 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.74/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.74/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.74/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.74/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.74/0.65 % Starting sh5l with 300s (1) cores
% 0.74/0.65 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 2244356 completed with status 0
% 0.74/0.65 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.74/0.65 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.74/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.74/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.74/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.74/0.65 % No SInE strategy applied
% 0.74/0.65 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.74/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.74/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.74/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.74/0.65 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.74/0.65 % Starting new_bool_3 with 136s (1) cores
% 0.74/0.65 % Starting new_bool_1 with 136s (1) cores
% 0.74/0.65 % SubtermCWHack with pid 2244360 completed with status 0
% 0.74/0.65 % Result found by SubtermCWHack
% 0.74/0.65 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.74/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.74/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.74/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.74/0.65 % No SInE strategy applied
% 0.74/0.65 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.74/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.74/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.74/0.65 % Preprocessing time : 0.001 s
% 0.74/0.65
% 0.74/0.65 % Proof found!
% 0.74/0.65 % SZS status Unsatisfiable
% 0.74/0.65 % SZS output start CNFRefutation
% See solution above
% 1.84/0.65 % Parsed axioms : 40
% 1.84/0.65 % Removed by relevancy pruning/SinE : 0
% 1.84/0.65 % Initial clauses : 40
% 1.84/0.65 % Removed in clause preprocessing : 0
% 1.84/0.65 % Initial clauses in saturation : 40
% 1.84/0.65 % Processed clauses : 4510
% 1.84/0.65 % ...of these trivial : 83
% 1.84/0.65 % ...subsumed : 3359
% 1.84/0.65 % ...remaining for further processing : 1068
% 1.84/0.65 % Other redundant clauses eliminated : 6
% 1.84/0.65 % Clauses deleted for lack of memory : 0
% 1.84/0.65 % Backward-subsumed : 115
% 1.84/0.65 % Backward-rewritten : 674
% 1.84/0.65 % Generated clauses : 27439
% 1.84/0.65 % ...of the previous two non-redundant : 25440
% 1.84/0.65 % ...aggressively subsumed : 0
% 1.84/0.65 % Contextual simplify-reflections : 7
% 1.84/0.65 % Paramodulations : 27399
% 1.84/0.65 % Factorizations : 36
% 1.84/0.65 % NegExts : 0
% 1.84/0.65 % Equation resolutions : 6
% 1.84/0.65 % Disequality decompositions : 0
% 1.84/0.65 % Total rewrite steps : 11838
% 1.84/0.65 % ...of those cached : 11175
% 1.84/0.65 % Propositional unsat checks : 0
% 1.84/0.65 % Propositional check models : 0
% 1.84/0.65 % Propositional check unsatisfiable : 0
% 1.84/0.65 % Propositional clauses : 0
% 1.84/0.65 % Propositional clauses after purity: 0
% 1.84/0.65 % Propositional unsat core size : 0
% 1.84/0.65 % Propositional preprocessing time : 0.000
% 1.84/0.65 % Propositional encoding time : 0.000
% 1.84/0.65 % Propositional solver time : 0.000
% 1.84/0.65 % Success case prop preproc time : 0.000
% 1.84/0.65 % Success case prop encoding time : 0.000
% 1.84/0.65 % Success case prop solver time : 0.000
% 1.84/0.65 % Current number of processed clauses : 277
% 1.84/0.65 % Positive orientable unit clauses : 22
% 1.84/0.65 % Positive unorientable unit clauses: 0
% 1.84/0.65 % Negative unit clauses : 0
% 1.84/0.65 % Non-unit-clauses : 255
% 1.84/0.65 % Current number of unprocessed clauses: 6923
% 1.84/0.65 % ...number of literals in the above : 17720
% 1.84/0.65 % Current number of archived formulas : 0
% 1.84/0.65 % Current number of archived clauses : 789
% 1.84/0.65 % Clause-clause subsumption calls (NU) : 38862
% 1.84/0.65 % Rec. Clause-clause subsumption calls : 37738
% 1.84/0.65 % Non-unit clause-clause subsumptions : 3455
% 1.84/0.65 % Unit Clause-clause subsumption calls : 617
% 1.84/0.65 % Rewrite failures with RHS unbound : 0
% 1.84/0.65 % BW rewrite match attempts : 68
% 1.84/0.65 % BW rewrite match successes : 35
% 1.84/0.65 % Condensation attempts : 0
% 1.84/0.65 % Condensation successes : 0
% 1.84/0.65 % Termbank termtop insertions : 204925
% 1.84/0.65 % Search garbage collected termcells : 34
% 1.84/0.65
% 1.84/0.65 % -------------------------------------------------
% 1.84/0.65 % User time : 0.184 s
% 1.84/0.65 % System time : 0.013 s
% 1.84/0.65 % Total time : 0.197 s
% 1.84/0.65 % Maximum resident set size: 3652 pages
% 1.84/0.65
% 1.84/0.65 % -------------------------------------------------
% 1.84/0.65 % User time : 0.948 s
% 1.84/0.65 % System time : 0.044 s
% 1.84/0.65 % Total time : 0.992 s
% 1.84/0.65 % Maximum resident set size: 4864 pages
% 1.84/0.65 % E exiting
%------------------------------------------------------------------------------