%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP238-1 : TPTP v9.2.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 04:24:54 PM UTC 2026
% Result : Unsatisfiable 1.97s 1.96s
% Output : CNFRefutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 25
% Syntax : Number of clauses : 137 ( 24 unt; 97 nHn; 120 RR)
% Number of literals : 415 ( 414 equ; 186 neg)
% Maximal clause size : 16 ( 3 avg)
% Maximal term depth : 4 ( 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 : 119 ( 5 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_25,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_36,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_32,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_61,negated_conjecture,
( inverse(sk_c11) != sk_c10
| inverse(X1) != sk_c11
| multiply(X1,sk_c10) != sk_c11
| multiply(sk_c11,X2) != sk_c10
| multiply(X3,sk_c11) != X2
| inverse(X3) != sk_c11
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| multiply(X6,sk_c10) != sk_c11
| multiply(X7,X8) != sk_c10
| inverse(X7) != X8
| multiply(X8,sk_c11) != sk_c10
| inverse(X9) != sk_c10
| multiply(X9,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_49,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_59,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_59) ).
cnf(prove_this_39,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_51,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_56,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
cnf(prove_this_52,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
cnf(prove_this_57,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_57) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
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,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
prove_this_25 ).
cnf(c_0_30,negated_conjecture,
( multiply(inverse(sk_c6),sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c11 ),
prove_this_24 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( multiply(inverse(sk_c1),sk_c11) = sk_c10
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
prove_this_15 ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
prove_this_36 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| multiply(sk_c4,sk_c5) = sk_c11 ),
prove_this_41 ).
cnf(c_0_38,negated_conjecture,
( multiply(inverse(sk_c6),sk_c11) = sk_c10
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c11 ),
prove_this_14 ).
cnf(c_0_40,negated_conjecture,
( multiply(inverse(sk_c7),sk_c10) = sk_c8
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| inverse(sk_c7) = sk_c8 ),
prove_this_37 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(sk_c4,sk_c5) = sk_c11 ),
prove_this_31 ).
cnf(c_0_43,negated_conjecture,
( multiply(inverse(sk_c4),sk_c11) = sk_c5
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| inverse(sk_c4) = sk_c5 ),
prove_this_42 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( multiply(inverse(sk_c4),sk_c11) = sk_c5
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| inverse(sk_c4) = sk_c5 ),
prove_this_32 ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c11) != sk_c10
| inverse(X1) != sk_c11
| multiply(X1,sk_c10) != sk_c11
| multiply(sk_c11,X2) != sk_c10
| multiply(X3,sk_c11) != X2
| inverse(X3) != sk_c11
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| multiply(X6,sk_c10) != sk_c11
| multiply(X7,X8) != sk_c10
| inverse(X7) != X8
| multiply(X8,sk_c11) != sk_c10
| inverse(X9) != sk_c10
| multiply(X9,sk_c11) != sk_c10 ),
prove_this_61 ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c9) = sk_c10 ),
prove_this_9 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c4,multiply(sk_c5,X1)) = multiply(sk_c11,X1)
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| multiply(sk_c5,sk_c11) = sk_c5 ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_53,negated_conjecture,
multiply(sk_c11,sk_c11) = sk_c10,
inference(spm,[status(thm)],[c_0_33,c_0_45]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_46]),c_0_26]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(sk_c5,sk_c11) = sk_c5 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c11,multiply(X1,sk_c11)) != sk_c10
| multiply(inverse(X2),sk_c11) != sk_c10
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| multiply(X6,sk_c10) != sk_c11
| inverse(sk_c11) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11
| inverse(X1) != sk_c11
| inverse(X6) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_49])])]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_26,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| inverse(sk_c9) = sk_c10 ),
prove_this_49 ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c9) = sk_c10 ),
prove_this_59 ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| inverse(sk_c9) = sk_c10 ),
prove_this_39 ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| multiply(sk_c4,sk_c5) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( multiply(inverse(sk_c11),sk_c10) = sk_c3
| identity = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_54]) ).
cnf(c_0_63,negated_conjecture,
multiply(inverse(sk_c11),sk_c10) = sk_c11,
inference(spm,[status(thm)],[c_0_28,c_0_53]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_55]),c_0_26]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| multiply(sk_c11,multiply(X1,sk_c11)) != sk_c10
| multiply(inverse(X2),sk_c11) != sk_c10
| multiply(inverse(X3),sk_c10) != sk_c11
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X3,inverse(X3)) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| multiply(X6,sk_c10) != sk_c11
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11
| inverse(X1) != sk_c11
| inverse(X6) != sk_c11 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| multiply(sk_c10,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_58]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| inverse(sk_c2) = sk_c11 ),
inference(spm,[status(thm)],[c_0_26,c_0_59]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(sk_c10,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_60]) ).
cnf(c_0_69,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
prove_this_10 ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_37,c_0_61]) ).
cnf(c_0_71,negated_conjecture,
( identity = sk_c10
| sk_c3 = sk_c11 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,negated_conjecture,
( identity = sk_c11
| sk_c3 = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_64]),c_0_63]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| multiply(inverse(X1),sk_c11) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| inverse(X3) != sk_c10
| inverse(X4) != sk_c11
| inverse(X5) != sk_c11 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c10,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_63,c_0_69]) ).
cnf(c_0_75,negated_conjecture,
( multiply(inverse(sk_c2),sk_c3) = sk_c11
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( sk_c3 = sk_c11
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(sk_c10,sk_c11) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c10
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| inverse(X4) != sk_c11 ),
inference(spm,[status(thm)],[c_0_73,c_0_57]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c10,X1) = X1
| sk_c3 = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_71]) ).
cnf(c_0_79,negated_conjecture,
( multiply(inverse(sk_c9),sk_c10) = sk_c11
| multiply(sk_c10,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( multiply(inverse(sk_c2),sk_c11) = sk_c11
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
prove_this_51 ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c10 ),
prove_this_56 ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| sk_c3 = sk_c11
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(sk_c11,sk_c10) != sk_c10
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| inverse(X4) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_76]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c11,X1) = X1
| sk_c3 = sk_c11 ),
inference(spm,[status(thm)],[c_0_27,c_0_72]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_79,c_0_50]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| sk_c10 = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_53])]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| sk_c10 = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_82]),c_0_53])]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| sk_c3 = sk_c11
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| inverse(X4) != sk_c11 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,negated_conjecture,
multiply(sk_c10,sk_c10) = sk_c11,
inference(spm,[status(thm)],[c_0_63,c_0_85]) ).
cnf(c_0_90,negated_conjecture,
( multiply(inverse(sk_c4),sk_c11) = sk_c5
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c4) = sk_c5 ),
prove_this_52 ).
cnf(c_0_92,negated_conjecture,
( multiply(inverse(sk_c7),sk_c10) = sk_c8
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_87]) ).
cnf(c_0_93,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c7) = sk_c8 ),
prove_this_57 ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| sk_c3 = sk_c11
| multiply(sk_c11,sk_c10) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c11
| multiply(X3,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_57]),c_0_89])]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c5
| inverse(sk_c2) = sk_c11
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c8
| inverse(sk_c2) = sk_c11
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| sk_c3 = sk_c11
| multiply(X1,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c11
| multiply(X3,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11
| inverse(X3) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_84]),c_0_76]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c9) = sk_c10 ),
prove_this_29 ).
cnf(c_0_99,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c9) = sk_c10 ),
prove_this_19 ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c5
| sk_c10 = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_95]),c_0_53])]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c8
| sk_c10 = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_96]),c_0_53])]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| sk_c3 = sk_c11
| multiply(X1,sk_c10) != sk_c11
| multiply(X2,sk_c10) != sk_c11
| inverse(X1) != sk_c11
| inverse(X2) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_53]),c_0_57]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c10,sk_c9) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_98]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_26,c_0_99]) ).
cnf(c_0_105,negated_conjecture,
( sk_c10 = sk_c11
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_100]),c_0_26]) ).
cnf(c_0_106,negated_conjecture,
( sk_c10 = sk_c11
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_101]),c_0_26]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| sk_c3 = sk_c11
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(sk_c11,sk_c11) != sk_c10
| multiply(sk_c2,sk_c11) != sk_c10
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| inverse(X4) != sk_c11 ),
inference(spm,[status(thm)],[c_0_73,c_0_67]) ).
cnf(c_0_109,negated_conjecture,
multiply(inverse(sk_c10),sk_c11) = sk_c10,
inference(spm,[status(thm)],[c_0_28,c_0_89]) ).
cnf(c_0_110,negated_conjecture,
sk_c10 = sk_c11,
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| sk_c3 = sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_103]),c_0_104]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(sk_c2,sk_c11) != sk_c10
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| inverse(X4) != sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_53])]) ).
cnf(c_0_113,negated_conjecture,
identity = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_26]),c_0_110]) ).
cnf(c_0_114,negated_conjecture,
( sk_c3 = sk_c11
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_78,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c10,sk_c9) = identity
| multiply(inverse(X1),sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X2) != sk_c10
| inverse(X3) != sk_c11
| inverse(X4) != sk_c11
| sk_c3 != sk_c10 ),
inference(spm,[status(thm)],[c_0_112,c_0_66]) ).
cnf(c_0_116,plain,
multiply(sk_c11,X1) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_113]) ).
cnf(c_0_117,negated_conjecture,
( sk_c3 = sk_c11
| sk_c9 = sk_c11 ),
inference(spm,[status(thm)],[c_0_72,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
( sk_c9 = sk_c11
| multiply(inverse(X1),sk_c11) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,sk_c11) != sk_c11
| multiply(X3,sk_c11) != sk_c11
| multiply(X4,sk_c11) != sk_c11
| inverse(X2) != sk_c11
| inverse(X3) != sk_c11
| inverse(X4) != sk_c11 ),
inference(csr,[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)],[c_0_115,c_0_110]),c_0_110]),c_0_110]),c_0_110]),c_0_110]),c_0_110]),c_0_110]),c_0_116]),c_0_113]),c_0_117]) ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c11) = sk_c11
| sk_c9 = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_110]),c_0_110]),c_0_116]),c_0_113]) ).
cnf(c_0_120,negated_conjecture,
( sk_c9 = sk_c11
| multiply(X1,sk_c11) != sk_c11
| multiply(X2,sk_c11) != sk_c11
| multiply(X3,sk_c11) != sk_c11
| inverse(X1) != sk_c11
| inverse(X2) != sk_c11
| inverse(X3) != sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_116])]) ).
cnf(c_0_121,negated_conjecture,
( sk_c9 = sk_c11
| multiply(X1,sk_c11) != sk_c11
| multiply(X2,sk_c11) != sk_c11
| inverse(X1) != sk_c11
| inverse(X2) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_116]),c_0_119]) ).
cnf(c_0_122,negated_conjecture,
( sk_c9 = sk_c11
| multiply(X1,sk_c11) != sk_c11
| inverse(X1) != sk_c11 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_116]),c_0_119]) ).
cnf(c_0_123,negated_conjecture,
( inverse(sk_c9) = sk_c11
| inverse(sk_c11) = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_110]),c_0_110]) ).
cnf(c_0_124,negated_conjecture,
sk_c9 = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_119]),c_0_116])]) ).
cnf(c_0_125,plain,
multiply(inverse(X1),X1) = sk_c11,
inference(rw,[status(thm)],[c_0_26,c_0_113]) ).
cnf(c_0_126,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_28]) ).
cnf(c_0_127,negated_conjecture,
inverse(sk_c11) = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]) ).
cnf(c_0_128,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_129,plain,
multiply(X1,inverse(X1)) = sk_c11,
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_130,negated_conjecture,
( multiply(inverse(X1),sk_c11) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c11
| multiply(X1,inverse(X1)) != sk_c11
| multiply(X2,inverse(X2)) != sk_c11
| multiply(X3,sk_c11) != sk_c11
| multiply(X4,sk_c11) != sk_c11
| multiply(X5,sk_c11) != sk_c11
| multiply(X6,sk_c11) != sk_c11
| inverse(X4) != sk_c11
| inverse(X5) != sk_c11
| inverse(X3) != sk_c11
| inverse(X6) != sk_c11 ),
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)],[c_0_56,c_0_110]),c_0_110]),c_0_110]),c_0_110]),c_0_110]),c_0_110]),c_0_110]),c_0_110]),c_0_110]),c_0_116]),c_0_127])]) ).
cnf(c_0_131,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_127]),c_0_116]) ).
cnf(c_0_132,negated_conjecture,
( multiply(inverse(X1),sk_c11) != sk_c11
| multiply(inverse(X2),sk_c11) != sk_c11
| multiply(X3,sk_c11) != sk_c11
| multiply(X4,sk_c11) != sk_c11
| multiply(X5,sk_c11) != sk_c11
| multiply(X6,sk_c11) != sk_c11
| inverse(X4) != sk_c11
| inverse(X5) != sk_c11
| inverse(X3) != sk_c11
| inverse(X6) != sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_129]),c_0_129])]) ).
cnf(c_0_133,plain,
multiply(X1,sk_c11) = X1,
inference(spm,[status(thm)],[c_0_131,c_0_125]) ).
cnf(c_0_134,negated_conjecture,
( inverse(X1) != sk_c11
| 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(er,[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_132,c_0_133]),c_0_133]),c_0_133]),c_0_133]),c_0_133]),c_0_133])])])])]),c_0_127])]) ).
cnf(c_0_135,negated_conjecture,
inverse(X1) != sk_c11,
inference(spm,[status(thm)],[c_0_134,c_0_127]) ).
cnf(c_0_136,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_127,c_0_135]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP238-1 : TPTP v9.2.1. Released v2.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.34 % Computer : n022.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 4 18:30:21 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.97/1.96 % Version : CSE_E---1.7
% 1.97/1.96 % Problem : theBenchmark.p
% 1.97/1.96 % SZS status Unsatisfiable for theBenchmark.p
% 1.97/1.96 % SZS output start CNFRefutation
% See solution above
% 1.97/1.96 % Total time : 1.371s
%------------------------------------------------------------------------------