%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP313-1 : 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 : n023.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 04:25:31 PM UTC 2026
% Result : Unsatisfiable 1.77s 1.89s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 25
% Syntax : Number of clauses : 170 ( 24 unt; 131 nHn; 146 RR)
% Number of literals : 403 ( 402 equ; 99 neg)
% Maximal clause size : 14 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 73 ( 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(prove_this_46,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_45,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_49,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_48,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_47,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
cnf(prove_this_33,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_50,negated_conjecture,
( multiply(sk_c8,sk_c9) != sk_c7
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c8
| multiply(X4,sk_c9) != sk_c8
| inverse(X4) != sk_c9
| multiply(X5,sk_c8) != sk_c7
| inverse(X5) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8
| multiply(X6,sk_c7) != sk_c9
| inverse(X6) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_50) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_39,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_38,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
cnf(c_0_25,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_26,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_27,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_28,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_29,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_30,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_28]) ).
cnf(c_0_31,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c5) = sk_c8 ),
prove_this_46 ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
prove_this_32 ).
cnf(c_0_34,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c2) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
prove_this_45 ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
prove_this_31 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_34,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c8) = sk_c5
| sk_c3 = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_41]),c_0_31]) ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c6) = sk_c7 ),
prove_this_35 ).
cnf(c_0_47,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_26,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c6) = sk_c7 ),
prove_this_49 ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_34,c_0_46]) ).
cnf(c_0_52,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_26,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( sk_c3 = sk_c2
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c9 ),
prove_this_48 ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c9 ),
prove_this_34 ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_34,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c7) = sk_c7
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_34,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_34,c_0_55]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_34,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( inverse(sk_c8) = sk_c2
| sk_c3 = sk_c2
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c8) = sk_c3
| sk_c3 = sk_c2
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_59,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( sk_c6 = sk_c7
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c9
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c7,sk_c7) = identity
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_26,c_0_58]) ).
cnf(c_0_68,negated_conjecture,
( sk_c3 = sk_c2
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
prove_this_5 ).
cnf(c_0_70,negated_conjecture,
( inverse(sk_c9) = sk_c9
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_52,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
prove_this_47 ).
cnf(c_0_72,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
prove_this_33 ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c7,multiply(sk_c9,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_25,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c9,sk_c9) = identity
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_26,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_34,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_34,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c8,sk_c9) != sk_c7
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c8
| multiply(X4,sk_c9) != sk_c8
| inverse(X4) != sk_c9
| multiply(X5,sk_c8) != sk_c7
| inverse(X5) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8
| multiply(X6,sk_c7) != sk_c9
| inverse(X6) != sk_c7 ),
prove_this_50 ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c3 = sk_c2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_31])]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,negated_conjecture,
( sk_c3 = sk_c2
| multiply(X1,sk_c7) != sk_c9
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(X5,sk_c8) != sk_c7
| multiply(X6,sk_c9) != sk_c8
| inverse(X1) != sk_c7
| inverse(X2) != sk_c8
| inverse(X3) != sk_c9
| inverse(X4) != sk_c8
| inverse(X5) != sk_c8
| inverse(X6) != sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_81,negated_conjecture,
( sk_c3 = sk_c2
| multiply(X1,sk_c8) != sk_c7
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,sk_c8) != sk_c7
| multiply(X5,sk_c9) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c9
| inverse(X3) != sk_c8
| inverse(X4) != sk_c8
| inverse(X5) != sk_c9 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_26]),c_0_34])]),c_0_68]) ).
cnf(c_0_82,negated_conjecture,
( sk_c3 = sk_c2
| multiply(X1,sk_c9) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c7
| multiply(X4,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8
| inverse(X4) != sk_c9 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_26]),c_0_34])]),c_0_53]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c7,X1) = X1
| sk_c3 = sk_c2 ),
inference(spm,[status(thm)],[c_0_27,c_0_53]) ).
cnf(c_0_84,negated_conjecture,
( sk_c3 = sk_c2
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c9
| identity != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_26]),c_0_34])]) ).
cnf(c_0_85,negated_conjecture,
( sk_c3 = sk_c2
| sk_c9 = sk_c8 ),
inference(spm,[status(thm)],[c_0_79,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
( sk_c3 = sk_c2
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_68]),c_0_85]) ).
cnf(c_0_87,negated_conjecture,
( sk_c3 = sk_c2
| multiply(X1,sk_c8) != sk_c7
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c9 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_26]),c_0_34])]),c_0_68]) ).
cnf(c_0_88,negated_conjecture,
( sk_c3 = sk_c2
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_26]),c_0_34])]),c_0_53]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c7 ),
prove_this_42 ).
cnf(c_0_90,negated_conjecture,
( sk_c3 = sk_c2
| identity != sk_c8 ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_34])]),c_0_26]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c8 ),
prove_this_39 ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c6) = sk_c7 ),
prove_this_28 ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c7,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
sk_c3 = sk_c2,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_68]),c_0_85]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
prove_this_25 ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c7,sk_c6) = identity
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[c_0_96,c_0_94]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c7,sk_c6) = identity
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c8,sk_c5) = identity
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_103,negated_conjecture,
( inverse(sk_c7) = sk_c6
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_101]),c_0_31]) ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c8) = sk_c5
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_102]),c_0_31]) ).
cnf(c_0_105,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c6,sk_c7) = identity
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_103]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| sk_c7 = sk_c9
| sk_c5 = sk_c2 ),
inference(spm,[status(thm)],[c_0_61,c_0_104]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| sk_c7 = sk_c9
| sk_c5 = sk_c2 ),
inference(spm,[status(thm)],[c_0_44,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c5,sk_c8) = identity
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_104]) ).
cnf(c_0_110,negated_conjecture,
( inverse(sk_c8) = sk_c5
| inverse(sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_34,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
( sk_c5 = sk_c2
| sk_c7 = sk_c9
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_112,negated_conjecture,
( sk_c5 = sk_c2
| sk_c7 = sk_c9
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_113,negated_conjecture,
( inverse(sk_c8) = sk_c2
| sk_c5 != sk_c2 ),
inference(ef,[status(thm)],[c_0_110]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
prove_this_24 ).
cnf(c_0_115,negated_conjecture,
( sk_c7 = sk_c9
| sk_c5 = sk_c2 ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c2,sk_c8) = identity
| sk_c5 != sk_c2 ),
inference(spm,[status(thm)],[c_0_26,c_0_113]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_118,negated_conjecture,
( sk_c7 = sk_c9
| identity = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_115]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c7,X1) = X1
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_118]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c9 ),
prove_this_41 ).
cnf(c_0_121,negated_conjecture,
( sk_c7 = sk_c9
| identity = sk_c6 ),
inference(spm,[status(thm)],[c_0_101,c_0_119]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c9 ),
inference(rw,[status(thm)],[c_0_120,c_0_94]) ).
cnf(c_0_123,negated_conjecture,
( multiply(sk_c6,X1) = X1
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_121]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c9 ),
prove_this_6 ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_126,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_1 ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c4) = sk_c9 ),
prove_this_2 ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c6,multiply(sk_c7,X1)) = multiply(sk_c9,X1)
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_25,c_0_124]) ).
cnf(c_0_129,negated_conjecture,
sk_c7 = sk_c9,
inference(spm,[status(thm)],[c_0_117,c_0_125]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c4,multiply(sk_c9,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_25,c_0_126]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c9,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_127]) ).
cnf(c_0_132,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_133,negated_conjecture,
( multiply(sk_c6,multiply(sk_c9,X1)) = multiply(sk_c9,X1)
| multiply(sk_c8,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_129]),c_0_129]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c8,sk_c4) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_31]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c8,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_56]) ).
cnf(c_0_136,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_25,c_0_132]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c9
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_132]),c_0_31]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c4
| multiply(sk_c8,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[c_0_134,c_0_129]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c6,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[c_0_135,c_0_129]) ).
cnf(c_0_140,negated_conjecture,
( identity = sk_c6
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_132]),c_0_31]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c9
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_138]),c_0_132]),c_0_31]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c8,sk_c2) = identity
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_139]),c_0_132]),c_0_31]) ).
cnf(c_0_143,negated_conjecture,
( identity = sk_c8
| sk_c6 != sk_c8 ),
inference(ef,[status(thm)],[c_0_140]) ).
cnf(c_0_144,negated_conjecture,
identity = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_141]),c_0_132]),c_0_31])]) ).
cnf(c_0_145,negated_conjecture,
( inverse(sk_c8) = sk_c2
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_142]),c_0_31]) ).
cnf(c_0_146,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c8) = sk_c2 ),
inference(rw,[status(thm)],[c_0_44,c_0_129]) ).
cnf(c_0_147,negated_conjecture,
( inverse(sk_c8) = sk_c8
| sk_c6 != sk_c8 ),
inference(spm,[status(thm)],[c_0_52,c_0_143]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c7 ),
prove_this_38 ).
cnf(c_0_149,plain,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_144]),c_0_144]) ).
cnf(c_0_150,negated_conjecture,
( inverse(sk_c8) = sk_c2
| sk_c6 = sk_c8 ),
inference(rw,[status(thm)],[c_0_145,c_0_144]) ).
cnf(c_0_151,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| sk_c2 = sk_c8
| sk_c6 != sk_c8 ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_152,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_144]) ).
cnf(c_0_153,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[c_0_148,c_0_94]) ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c8 ),
inference(rw,[status(thm)],[c_0_91,c_0_94]) ).
cnf(c_0_155,negated_conjecture,
( sk_c2 = sk_c8
| sk_c5 = sk_c8
| sk_c6 != sk_c8 ),
inference(spm,[status(thm)],[c_0_110,c_0_147]) ).
cnf(c_0_156,negated_conjecture,
( sk_c6 = sk_c8
| sk_c2 = sk_c8 ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_157,negated_conjecture,
( sk_c2 = sk_c8
| sk_c5 = sk_c9
| sk_c6 != sk_c8 ),
inference(rw,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_158,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[c_0_153,c_0_129]) ).
cnf(c_0_159,negated_conjecture,
( inverse(sk_c5) = sk_c8
| sk_c2 = sk_c9 ),
inference(rw,[status(thm)],[c_0_154,c_0_152]) ).
cnf(c_0_160,negated_conjecture,
( sk_c5 = sk_c8
| sk_c2 = sk_c8 ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_161,negated_conjecture,
( sk_c5 = sk_c9
| sk_c2 = sk_c8 ),
inference(spm,[status(thm)],[c_0_157,c_0_156]) ).
cnf(c_0_162,negated_conjecture,
( sk_c2 = sk_c9
| sk_c5 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_152]),c_0_152]) ).
cnf(c_0_163,negated_conjecture,
( sk_c2 = sk_c9
| sk_c5 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_159]),c_0_149]) ).
cnf(c_0_164,negated_conjecture,
( sk_c2 = sk_c8
| sk_c9 = sk_c8 ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_165,negated_conjecture,
( sk_c9 = sk_c8
| sk_c2 = sk_c9 ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_166,negated_conjecture,
( multiply(sk_c8,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(X1,sk_c9) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(X5,sk_c8) != sk_c9
| multiply(X6,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c8
| inverse(X3) != sk_c9
| inverse(X4) != sk_c8
| inverse(X5) != sk_c8
| inverse(X6) != sk_c9 ),
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_77,c_0_129]),c_0_129]),c_0_129]),c_0_129]),c_0_129]),c_0_129]) ).
cnf(c_0_167,plain,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_144]) ).
cnf(c_0_168,negated_conjecture,
sk_c9 = sk_c8,
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_169,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_152]),c_0_152]),c_0_152])])])]),c_0_167]),c_0_168]),c_0_168]),c_0_168]),c_0_168]),c_0_152]),c_0_168]),c_0_152]),c_0_168]),c_0_168]),c_0_152]),c_0_168]),c_0_152]),c_0_168]),c_0_168]),c_0_149]),c_0_168]),c_0_168])])])])]),c_0_149])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP313-1 : 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 : n023.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 18:32:08 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.77/1.89 % Version : CSE_E---1.7
% 1.77/1.89 % Problem : theBenchmark.p
% 1.77/1.89 % SZS status Unsatisfiable for theBenchmark.p
% 1.77/1.89 % SZS output start CNFRefutation
% See solution above
% 1.77/1.89 % Total time : 1.371s
%------------------------------------------------------------------------------