%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP307-1 : TPTP v9.2.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 04:25:21 PM UTC 2026
% Result : Unsatisfiable 10.57s 7.18s
% Output : CNFRefutation 10.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 27
% Syntax : Number of clauses : 153 ( 23 unt; 113 nHn; 134 RR)
% Number of literals : 356 ( 355 equ; 90 neg)
% Maximal clause size : 16 ( 2 avg)
% Maximal term depth : 4 ( 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 : 59 ( 1 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(prove_this_52,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_51,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_45,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_36,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c2
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_54,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
cnf(prove_this_56,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_56) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_55,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_53,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_53) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_61,negated_conjecture,
( multiply(sk_c11,sk_c10) != sk_c9
| inverse(sk_c11) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(sk_c11,X1) != sk_c10
| multiply(X2,sk_c11) != X1
| inverse(X2) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
cnf(c_0_27,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_28,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_29,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_30,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_30]) ).
cnf(c_0_32,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_33,plain,
multiply(inverse(X1),identity) = inverse(X1),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_34,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_35,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_52 ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
prove_this_12 ).
cnf(c_0_38,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_51 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| inverse(sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_45 ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_35 ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_11 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(spm,[status(thm)],[c_0_30,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
prove_this_36 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_5 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c11) = sk_c3
| sk_c1 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_47]),c_0_33]) ).
cnf(c_0_54,negated_conjecture,
( multiply(inverse(inverse(sk_c5)),sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c2
| inverse(sk_c5) = sk_c8 ),
prove_this_46 ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c10
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c11,X1)
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
prove_this_7 ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c10 ),
prove_this_54 ).
cnf(c_0_60,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c3) = sk_c11
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c2
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_28]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
prove_this_56 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_25 ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c10
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_56]),c_0_28]) ).
cnf(c_0_66,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
prove_this_16 ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c5,sk_c11) = multiply(sk_c11,sk_c10)
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c10) = multiply(sk_c4,identity)
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_34,c_0_59]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,negated_conjecture,
( multiply(inverse(sk_c1),sk_c2) = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_62]) ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_55 ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_32,c_0_63]) ).
cnf(c_0_73,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_64]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
prove_this_26 ).
cnf(c_0_75,negated_conjecture,
( multiply(inverse(sk_c11),sk_c10) = sk_c2
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_65]) ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_15 ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| inverse(sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_32,c_0_66]) ).
cnf(c_0_78,negated_conjecture,
( multiply(inverse(sk_c5),multiply(sk_c11,sk_c10)) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_67]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
prove_this_6 ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_53 ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c10) = sk_c4 ),
inference(rw,[status(thm)],[c_0_68,c_0_35]) ).
cnf(c_0_83,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_29,c_0_32]) ).
cnf(c_0_84,negated_conjecture,
( sk_c1 = sk_c9
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_69]),c_0_28]) ).
cnf(c_0_85,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
prove_this_14 ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c2) = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| multiply(sk_c11,sk_c2) = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_70,c_0_72]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c2
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| multiply(sk_c9,sk_c10) = sk_c2
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_75,c_0_77]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c8,multiply(sk_c11,sk_c10)) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_92,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_80]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
prove_this_2 ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_13 ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_38,c_0_81]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_38,c_0_82]) ).
cnf(c_0_97,negated_conjecture,
( inverse(sk_c10) = sk_c10
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_98,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_38,c_0_85]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_88]),c_0_28]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c2
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_102,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_58]) ).
cnf(c_0_103,negated_conjecture,
( multiply(inverse(sk_c8),sk_c11) = multiply(sk_c11,sk_c10)
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_91]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_106,negated_conjecture,
( inverse(sk_c11) = sk_c1
| sk_c1 = sk_c9
| sk_c4 = sk_c10 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_107,negated_conjecture,
( inverse(sk_c11) = sk_c9
| sk_c1 = sk_c9
| sk_c4 = sk_c10 ),
inference(spm,[status(thm)],[c_0_98,c_0_97]) ).
cnf(c_0_108,negated_conjecture,
( identity = sk_c11
| identity = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_99]),c_0_28]) ).
cnf(c_0_109,negated_conjecture,
( identity = sk_c11
| sk_c2 = sk_c11 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c11,sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| sk_c9 != sk_c11 ),
inference(ef,[status(thm)],[c_0_104]) ).
cnf(c_0_112,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_105]) ).
cnf(c_0_113,negated_conjecture,
( sk_c4 = sk_c10
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_114,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_51]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c4,sk_c10) = identity
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_32,c_0_59]) ).
cnf(c_0_116,negated_conjecture,
identity = sk_c11,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_108]),c_0_109]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c10
| sk_c9 != sk_c10 ),
inference(ef,[status(thm)],[c_0_110]) ).
cnf(c_0_118,negated_conjecture,
( identity = sk_c10
| sk_c9 != sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_111]),c_0_28]) ).
cnf(c_0_119,negated_conjecture,
( multiply(inverse(sk_c10),sk_c9) = sk_c10
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_114,c_0_79]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c4,sk_c10) = identity
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_115]) ).
cnf(c_0_122,plain,
inverse(sk_c11) = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_116]),c_0_116]) ).
cnf(c_0_123,negated_conjecture,
( multiply(inverse(sk_c11),sk_c10) = sk_c10
| sk_c9 != sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_117]) ).
cnf(c_0_124,negated_conjecture,
( multiply(X1,sk_c10) = X1
| sk_c9 != sk_c11 ),
inference(spm,[status(thm)],[c_0_35,c_0_118]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_119,c_0_97]) ).
cnf(c_0_126,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_120]),c_0_28]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c11,sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_116]),c_0_116]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| sk_c9 = sk_c11 ),
inference(spm,[status(thm)],[c_0_94,c_0_122]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c11,sk_c10) != sk_c9
| inverse(sk_c11) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(sk_c11,X1) != sk_c10
| multiply(X2,sk_c11) != X1
| inverse(X2) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
prove_this_61 ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c10,X1) = X1
| sk_c9 != sk_c11 ),
inference(spm,[status(thm)],[c_0_29,c_0_118]) ).
cnf(c_0_131,negated_conjecture,
( inverse(sk_c11) = sk_c10
| sk_c9 != sk_c10
| sk_c9 != sk_c11 ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_132,negated_conjecture,
( sk_c1 = sk_c9
| identity = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_125]),c_0_28]) ).
cnf(c_0_133,negated_conjecture,
( sk_c1 = sk_c9
| identity = sk_c11
| sk_c9 = sk_c11 ),
inference(spm,[status(thm)],[c_0_126,c_0_69]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c11,sk_c1) = sk_c11
| sk_c9 = sk_c11 ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c11,multiply(X1,sk_c11)) != sk_c10
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(sk_c11,sk_c10) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(sk_c11) != sk_c9
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11
| inverse(X1) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_129])])]) ).
cnf(c_0_136,negated_conjecture,
( inverse(sk_c10) = identity
| sk_c9 != sk_c11 ),
inference(spm,[status(thm)],[c_0_130,c_0_32]) ).
cnf(c_0_137,negated_conjecture,
( inverse(sk_c10) = sk_c11
| sk_c9 != sk_c10
| sk_c9 != sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_131]) ).
cnf(c_0_138,negated_conjecture,
( identity = sk_c11
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_65,c_0_99]) ).
cnf(c_0_139,negated_conjecture,
( sk_c9 = sk_c11
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_140,negated_conjecture,
( sk_c9 = sk_c11
| sk_c1 = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_134]),c_0_28]),c_0_116]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c11,multiply(X1,sk_c11)) != sk_c10
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(sk_c11,sk_c10) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(sk_c11) != sk_c9
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11
| inverse(X1) != sk_c11
| identity != sk_c11 ),
inference(rw,[status(thm)],[c_0_135,c_0_32]) ).
cnf(c_0_142,negated_conjecture,
( identity = sk_c11
| sk_c9 != sk_c11
| sk_c9 != sk_c10 ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_143,negated_conjecture,
( sk_c10 = sk_c11
| sk_c9 != sk_c11 ),
inference(spm,[status(thm)],[c_0_118,c_0_138]) ).
cnf(c_0_144,negated_conjecture,
sk_c9 = sk_c11,
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c11,multiply(X1,sk_c11)) != sk_c10
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(sk_c11,sk_c10) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(sk_c11) != sk_c9
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11
| inverse(X1) != sk_c11
| sk_c9 != sk_c11
| sk_c9 != sk_c10 ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_146,plain,
multiply(X1,sk_c11) = X1,
inference(rw,[status(thm)],[c_0_35,c_0_116]) ).
cnf(c_0_147,plain,
multiply(sk_c11,X1) = X1,
inference(rw,[status(thm)],[c_0_29,c_0_116]) ).
cnf(c_0_148,negated_conjecture,
sk_c10 = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144])]) ).
cnf(c_0_149,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(X2) != sk_c11 ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_122])]),c_0_146]),c_0_147]),c_0_148]),c_0_148]),c_0_146]),c_0_148]),c_0_146]),c_0_144]),c_0_144]),c_0_148]),c_0_146]),c_0_148]),c_0_146]),c_0_144]),c_0_146]),c_0_148]),c_0_144]),c_0_148]),c_0_144]),c_0_148])])])])]),c_0_122])]) ).
cnf(c_0_150,plain,
multiply(inverse(X1),X1) = sk_c11,
inference(rw,[status(thm)],[c_0_28,c_0_116]) ).
cnf(c_0_151,negated_conjecture,
inverse(X1) != sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_122]),c_0_34]),c_0_35])]) ).
cnf(c_0_152,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_36,c_0_151]),c_0_151]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP307-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n027.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 18:31:50 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 10.57/7.18 % Version : CSE_E---1.7
% 10.57/7.18 % Problem : theBenchmark.p
% 10.57/7.18 % SZS status Unsatisfiable for theBenchmark.p
% 10.57/7.18 % SZS output start CNFRefutation
% See solution above
% 10.64/7.22 % Total time : 5.369s
%------------------------------------------------------------------------------