%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP263-1 : 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 : n021.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 04:25:05 PM UTC 2026
% Result : Unsatisfiable 2.05s 1.95s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 26
% Syntax : Number of clauses : 163 ( 32 unt; 113 nHn; 128 RR)
% Number of literals : 398 ( 397 equ; 128 neg)
% Maximal clause size : 15 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 107 ( 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_18,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_38,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_39,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_48,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_51,negated_conjecture,
( multiply(X1,sk_c11) != sk_c10
| inverse(X1) != sk_c11
| multiply(X2,sk_c10) != sk_c9
| inverse(X2) != sk_c10
| multiply(sk_c9,sk_c10) != 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_51) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_49,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_33,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_45,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_45) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(c_0_26,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_27,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_28,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_29,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_30,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_31,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_29]) ).
cnf(c_0_32,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c7) = sk_c6 ),
prove_this_18 ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c8 ),
prove_this_19 ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c6 ),
prove_this_8 ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c7) = sk_c6 ),
prove_this_38 ).
cnf(c_0_39,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c1) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c8 ),
prove_this_9 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c7) = sk_c6 ),
prove_this_28 ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c8 ),
prove_this_39 ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c7) = sk_c6 ),
prove_this_48 ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c1,sk_c11) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( multiply(X1,sk_c11) != sk_c10
| inverse(X1) != sk_c11
| multiply(X2,sk_c10) != sk_c9
| inverse(X2) != sk_c10
| multiply(sk_c9,sk_c10) != 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_51 ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c8 ),
prove_this_29 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c2) = sk_c10
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c8 ),
prove_this_49 ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_33,c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X6,sk_c11) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c10
| inverse(X6) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_49])]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c2,sk_c10) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
( multiply(X1,sk_c10) = X1
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_32,c_0_55]) ).
cnf(c_0_61,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_62,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X6,sk_c11) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c10
| inverse(X6) != sk_c11
| identity != sk_c11 ),
inference(rw,[status(thm)],[c_0_56,c_0_39]) ).
cnf(c_0_63,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
( sk_c7 = sk_c8
| sk_c9 = sk_c11 ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( sk_c7 = sk_c8
| inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X6,sk_c11) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c10
| inverse(X6) != sk_c11 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_59]) ).
cnf(c_0_67,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_27,c_0_65]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c10,X1) = X1
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_55]) ).
cnf(c_0_69,negated_conjecture,
( sk_c7 = sk_c8
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| inverse(X1) != identity
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_27]),c_0_67]),c_0_33])]) ).
cnf(c_0_70,negated_conjecture,
( inverse(sk_c10) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
( sk_c7 = sk_c8
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| identity != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_27]),c_0_70]) ).
cnf(c_0_72,negated_conjecture,
( sk_c7 = sk_c8
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c11) != sk_c10
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_63]),c_0_64]) ).
cnf(c_0_73,negated_conjecture,
( sk_c7 = sk_c8
| multiply(X1,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X3,sk_c11) != sk_c10
| inverse(X1) != sk_c11
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_27]),c_0_33])]),c_0_63]) ).
cnf(c_0_74,negated_conjecture,
( sk_c7 = sk_c8
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c11) != sk_c10
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_48]),c_0_40]) ).
cnf(c_0_75,negated_conjecture,
( sk_c7 = sk_c8
| multiply(X1,sk_c11) != sk_c10
| inverse(X1) != sk_c11 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_27]),c_0_33])]),c_0_63]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c6,sk_c7) = identity
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_77,negated_conjecture,
sk_c7 = sk_c8,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_33])]),c_0_27]),c_0_55]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c6,sk_c8) = identity
| inverse(sk_c1) = sk_c11 ),
inference(rw,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c6,sk_c8) = identity
| multiply(sk_c1,sk_c11) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_78]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c1,sk_c11) = identity
| inverse(sk_c6) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_79]),c_0_32]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c8,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_41]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c1,sk_c11) = identity
| multiply(sk_c8,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_23 ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c8,sk_c6) = identity
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_85,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
prove_this_24 ).
cnf(c_0_87,negated_conjecture,
( inverse(sk_c8) = sk_c6
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_84]),c_0_32]) ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
prove_this_33 ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_34 ).
cnf(c_0_91,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c6,sk_c8) = identity
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_87]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c10,multiply(sk_c2,X1)) = X1
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_88]) ).
cnf(c_0_94,negated_conjecture,
( multiply(inverse(sk_c2),sk_c9) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_89]) ).
cnf(c_0_95,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_33,c_0_90]) ).
cnf(c_0_96,negated_conjecture,
( multiply(inverse(multiply(X1,sk_c6)),X1) = sk_c8
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_32]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_93,c_0_89]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c8,multiply(sk_c6,X1)) = X1
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_84]),c_0_28]) ).
cnf(c_0_100,negated_conjecture,
( multiply(X1,multiply(sk_c6,sk_c8)) = X1
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_96]),c_0_33]),c_0_26]) ).
cnf(c_0_101,negated_conjecture,
( multiply(inverse(sk_c4),sk_c9) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_97]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
inference(spm,[status(thm)],[c_0_33,c_0_98]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c6,sk_c8) = multiply(sk_c8,sk_c6)
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_104,negated_conjecture,
multiply(sk_c10,sk_c9) = sk_c10,
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_105,negated_conjecture,
( multiply(X1,multiply(sk_c8,sk_c6)) = X1
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_100,c_0_103]) ).
cnf(c_0_106,negated_conjecture,
identity = sk_c9,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_104]),c_0_27]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_41 ).
cnf(c_0_108,negated_conjecture,
( multiply(X1,multiply(sk_c8,sk_c6)) = X1
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c9
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_106]),c_0_106]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
prove_this_45 ).
cnf(c_0_111,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_29,c_0_107]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_42 ).
cnf(c_0_113,negated_conjecture,
( multiply(X1,sk_c9) = X1
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,negated_conjecture,
( multiply(inverse(sk_c5),sk_c11) = sk_c8
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_29,c_0_110]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
prove_this_46 ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c9,X1) = X1
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_113]),c_0_29]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_12 ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| sk_c9 = sk_c10
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_118]),c_0_27]) ).
cnf(c_0_122,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_33,c_0_119]) ).
cnf(c_0_123,negated_conjecture,
( sk_c11 = sk_c10
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_120]),c_0_27]),c_0_106])]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| sk_c9 = sk_c11 ),
inference(rw,[status(thm)],[c_0_121,c_0_106]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_126,negated_conjecture,
( inverse(sk_c11) = sk_c3
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_33,c_0_122]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
prove_this_2 ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c10
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_104,c_0_123]) ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c11
| sk_c11 = sk_c10 ),
inference(spm,[status(thm)],[c_0_124,c_0_123]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c3,multiply(sk_c11,X1)) = multiply(sk_c10,X1)
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_26,c_0_125]) ).
cnf(c_0_131,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
prove_this_11 ).
cnf(c_0_132,negated_conjecture,
( inverse(sk_c11) = sk_c1
| sk_c3 != sk_c1 ),
inference(ef,[status(thm)],[c_0_126]) ).
cnf(c_0_133,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_127]) ).
cnf(c_0_135,negated_conjecture,
sk_c11 = sk_c10,
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c10,inverse(sk_c11)) = sk_c3
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_39]),c_0_32]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_131]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c1,sk_c11) = identity
| sk_c3 != sk_c1 ),
inference(spm,[status(thm)],[c_0_27,c_0_132]) ).
cnf(c_0_139,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = sk_c9,
inference(rw,[status(thm)],[c_0_133,c_0_106]) ).
cnf(c_0_140,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_106]),c_0_135]),c_0_135]) ).
cnf(c_0_141,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_32,c_0_106]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c10
| sk_c3 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_135]),c_0_39]),c_0_106]),c_0_135]) ).
cnf(c_0_143,negated_conjecture,
( multiply(sk_c3,multiply(sk_c11,X1)) = multiply(sk_c10,X1)
| multiply(sk_c11,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_137]) ).
cnf(c_0_144,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c9
| sk_c3 != sk_c1 ),
inference(rw,[status(thm)],[c_0_138,c_0_106]) ).
cnf(c_0_145,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| sk_c1 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_39]),c_0_106]),c_0_141]) ).
cnf(c_0_146,negated_conjecture,
( sk_c3 = sk_c9
| sk_c1 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_142]),c_0_39]),c_0_106]),c_0_141]) ).
cnf(c_0_147,negated_conjecture,
( multiply(sk_c3,multiply(sk_c10,X1)) = multiply(sk_c10,X1)
| multiply(sk_c10,sk_c1) = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_106]),c_0_135]),c_0_135]) ).
cnf(c_0_148,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c3 != sk_c1 ),
inference(rw,[status(thm)],[c_0_144,c_0_135]) ).
cnf(c_0_149,negated_conjecture,
( sk_c1 = sk_c9
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_141]) ).
cnf(c_0_150,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_28,c_0_106]) ).
cnf(c_0_151,negated_conjecture,
( multiply(sk_c10,sk_c1) = sk_c9
| sk_c3 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_147]),c_0_26]),c_0_139]),c_0_141]) ).
cnf(c_0_152,negated_conjecture,
( sk_c9 = sk_c10
| sk_c3 != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_150])]) ).
cnf(c_0_153,negated_conjecture,
sk_c9 = sk_c10,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_149]),c_0_141])]),c_0_152]) ).
cnf(c_0_154,plain,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_106]),c_0_106]) ).
cnf(c_0_155,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(inverse(X2),sk_c10) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(sk_c9,sk_c10) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X4,sk_c10) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X6,sk_c10) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c10
| inverse(X6) != sk_c10
| sk_c9 != sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_106]),c_0_135]),c_0_135]),c_0_135]),c_0_135]),c_0_135]),c_0_135]),c_0_135]) ).
cnf(c_0_156,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_141,c_0_153]) ).
cnf(c_0_157,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_153]),c_0_153]) ).
cnf(c_0_158,plain,
multiply(inverse(X1),X1) = sk_c9,
inference(rw,[status(thm)],[c_0_27,c_0_106]) ).
cnf(c_0_159,negated_conjecture,
( inverse(multiply(X1,inverse(X2))) != inverse(X2)
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(X2) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_150])]),c_0_156]),c_0_156]),c_0_153]),c_0_156]),c_0_156]),c_0_153]),c_0_156]),c_0_153])])])])])]),c_0_157])]) ).
cnf(c_0_160,plain,
multiply(inverse(X1),X1) = sk_c10,
inference(rw,[status(thm)],[c_0_158,c_0_153]) ).
cnf(c_0_161,negated_conjecture,
inverse(X1) != sk_c10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_157]),c_0_33])]) ).
cnf(c_0_162,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_90,c_0_161]),c_0_161]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP263-1 : 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
% 0.17/0.33 % Computer : n021.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon May 4 18:31:55 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 2.05/1.95 % Version : CSE_E---1.7
% 2.05/1.95 % Problem : theBenchmark.p
% 2.05/1.95 % SZS status Unsatisfiable for theBenchmark.p
% 2.05/1.95 % SZS output start CNFRefutation
% See solution above
% 2.05/1.95 % Total time : 1.372s
%------------------------------------------------------------------------------