%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP306-1 : 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 : n002.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 1.47s 1.80s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 21
% Syntax : Number of clauses : 140 ( 39 unt; 89 nHn; 115 RR)
% Number of literals : 295 ( 294 equ; 67 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 4 ( 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 : 63 ( 1 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_7,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_1,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(c_0_21,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_22,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_23,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_24,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
prove_this_7 ).
cnf(c_0_26,negated_conjecture,
( multiply(inverse(sk_c3),sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c3) = sk_c8 ),
prove_this_8 ).
cnf(c_0_28,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c6,
prove_this_1 ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| sk_c6 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c2
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c3,sk_c8) = sk_c7 ),
prove_this_12 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c2
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( multiply(inverse(sk_c3),sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c2
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c8 ),
prove_this_13 ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c2
| inverse(sk_c1) = sk_c2
| sk_c6 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_28])]) ).
cnf(c_0_36,negated_conjecture,
multiply(inverse(sk_c8),sk_c6) = sk_c7,
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
prove_this_2 ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c2
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( sk_c6 = sk_c8
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_38]),c_0_22]) ).
cnf(c_0_41,negated_conjecture,
( multiply(inverse(sk_c3),sk_c7) = sk_c8
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_24,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
prove_this_3 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c8,X1) = X1
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_9 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c6,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c6
| sk_c6 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_28]) ).
cnf(c_0_46,negated_conjecture,
( sk_c6 = sk_c8
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c1,multiply(sk_c2,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_21,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_19 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
prove_this_22 ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c6,sk_c6) = sk_c7
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_36,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( sk_c6 = sk_c8
| sk_c7 != sk_c8 ),
inference(ef,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_28]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c6
| inverse(X1) != sk_c8
| inverse(X3) != sk_c8 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_28])])])]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_4 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c7
| sk_c6 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_46]),c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_24,c_0_52]) ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
prove_this_14 ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X3) != sk_c8 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
( sk_c6 = sk_c8
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_55]),c_0_22]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,multiply(X1,multiply(X2,sk_c8))) != sk_c7
| multiply(inverse(X3),sk_c7) != sk_c8
| multiply(X3,inverse(X3)) != sk_c8
| inverse(multiply(X1,X2)) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8 ),
inference(spm,[status(thm)],[c_0_58,c_0_21]) ).
cnf(c_0_63,negated_conjecture,
multiply(sk_c8,multiply(sk_c7,X1)) = multiply(sk_c6,X1),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_54]) ).
cnf(c_0_65,negated_conjecture,
sk_c6 = sk_c8,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_59]),c_0_51]) ).
cnf(c_0_66,negated_conjecture,
( multiply(inverse(sk_c2),sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_24,c_0_48]) ).
cnf(c_0_67,negated_conjecture,
( multiply(inverse(sk_c2),sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_24,c_0_60]) ).
cnf(c_0_68,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_24,c_0_44]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c2,multiply(sk_c1,X1)) = X1
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_61]),c_0_23]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c1,sk_c8) = multiply(sk_c8,sk_c6)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_47,c_0_60]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c6,multiply(X1,sk_c8)) != sk_c7
| multiply(inverse(X2),sk_c7) != sk_c8
| inverse(multiply(sk_c7,X1)) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c6,multiply(sk_c8,X1)) = X1
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_64]),c_0_23]) ).
cnf(c_0_73,negated_conjecture,
identity = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_65]),c_0_22]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_68,c_0_57]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c2,multiply(sk_c8,sk_c6)) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(multiply(sk_c7,sk_c8)) != sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| sk_c7 != sk_c8 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
multiply(sk_c7,X1) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_73]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[c_0_74,c_0_65]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c8 ),
inference(rw,[status(thm)],[c_0_54,c_0_65]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c1,sk_c2) = multiply(sk_c8,sk_c8)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_47,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
( multiply(inverse(sk_c2),sk_c8) = multiply(sk_c8,sk_c6)
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_24,c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_80]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_44,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_66,c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(X1,sk_c8) != sk_c7
| inverse(X1) != sk_c8 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_80]),c_0_28]),c_0_65])]),c_0_84]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[c_0_85,c_0_65]) ).
cnf(c_0_88,negated_conjecture,
multiply(sk_c8,sk_c5) = sk_c7,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_80]),c_0_87]) ).
cnf(c_0_89,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
prove_this_6 ).
cnf(c_0_90,negated_conjecture,
multiply(inverse(sk_c8),sk_c7) = sk_c5,
inference(spm,[status(thm)],[c_0_24,c_0_88]) ).
cnf(c_0_91,negated_conjecture,
multiply(inverse(inverse(sk_c8)),sk_c7) = sk_c6,
inference(spm,[status(thm)],[c_0_24,c_0_36]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_22,c_0_89]) ).
cnf(c_0_93,negated_conjecture,
multiply(inverse(sk_c8),X1) = multiply(sk_c5,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_90]),c_0_78]) ).
cnf(c_0_94,negated_conjecture,
multiply(inverse(inverse(sk_c8)),sk_c7) = sk_c8,
inference(rw,[status(thm)],[c_0_91,c_0_65]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c8) = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_65]),c_0_73]) ).
cnf(c_0_96,negated_conjecture,
multiply(sk_c5,sk_c7) = sk_c5,
inference(rw,[status(thm)],[c_0_90,c_0_93]) ).
cnf(c_0_97,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_5 ).
cnf(c_0_98,negated_conjecture,
multiply(sk_c5,multiply(sk_c8,X1)) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_93]) ).
cnf(c_0_99,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c8,
inference(rw,[status(thm)],[c_0_28,c_0_65]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| sk_c5 = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_93]),c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_10 ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c8 ),
inference(rw,[status(thm)],[c_0_97,c_0_65]) ).
cnf(c_0_103,negated_conjecture,
multiply(sk_c5,sk_c8) = sk_c7,
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_104,negated_conjecture,
( sk_c5 = sk_c8
| sk_c5 = sk_c4 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_100]),c_0_93]),c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( multiply(inverse(sk_c4),sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_101]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_11 ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| sk_c5 = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_102]),c_0_28]),c_0_65]) ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| sk_c5 = sk_c8 ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_110,negated_conjecture,
( sk_c5 = sk_c8
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_111,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_109]) ).
cnf(c_0_112,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c4) = sk_c8 ),
prove_this_16 ).
cnf(c_0_113,negated_conjecture,
( sk_c5 = sk_c8
| sk_c7 != sk_c8 ),
inference(ef,[status(thm)],[c_0_110]) ).
cnf(c_0_114,negated_conjecture,
( multiply(inverse(inverse(sk_c1)),sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| inverse(sk_c1) = sk_c2 ),
inference(spm,[status(thm)],[c_0_22,c_0_112]) ).
cnf(c_0_116,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c4,sk_c8) = sk_c5 ),
prove_this_15 ).
cnf(c_0_117,negated_conjecture,
sk_c5 = sk_c8,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_110]),c_0_28]),c_0_65]),c_0_113]) ).
cnf(c_0_118,negated_conjecture,
( multiply(inverse(inverse(sk_c1)),sk_c2) = sk_c8
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[c_0_114,c_0_88]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(rw,[status(thm)],[c_0_115,c_0_73]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(rw,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| sk_c7 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_22]),c_0_73])]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c8
| sk_c7 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_120]),c_0_22]),c_0_73])]) ).
cnf(c_0_123,negated_conjecture,
( sk_c7 = sk_c8
| sk_c4 = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_121]),c_0_93]),c_0_117]),c_0_28]),c_0_65]) ).
cnf(c_0_124,negated_conjecture,
multiply(sk_c8,sk_c8) = sk_c7,
inference(rw,[status(thm)],[c_0_103,c_0_117]) ).
cnf(c_0_125,negated_conjecture,
sk_c7 = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124])]) ).
cnf(c_0_126,plain,
multiply(inverse(X1),X1) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_73]),c_0_125]) ).
cnf(c_0_127,plain,
multiply(inverse(inverse(X1)),sk_c8) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_126]) ).
cnf(c_0_128,plain,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[c_0_78,c_0_125]) ).
cnf(c_0_129,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_127]),c_0_128]) ).
cnf(c_0_130,negated_conjecture,
multiply(inverse(sk_c8),X1) = multiply(sk_c8,X1),
inference(rw,[status(thm)],[c_0_93,c_0_117]) ).
cnf(c_0_131,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_127,c_0_129]) ).
cnf(c_0_132,negated_conjecture,
multiply(inverse(sk_c8),X1) = X1,
inference(rw,[status(thm)],[c_0_130,c_0_128]) ).
cnf(c_0_133,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_131]),c_0_131]) ).
cnf(c_0_134,negated_conjecture,
multiply(inverse(inverse(sk_c8)),X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_132]) ).
cnf(c_0_135,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| inverse(X1) != sk_c8
| inverse(X3) != sk_c8 ),
inference(rw,[status(thm)],[c_0_53,c_0_65]) ).
cnf(c_0_136,plain,
multiply(X1,inverse(X1)) = sk_c8,
inference(spm,[status(thm)],[c_0_126,c_0_133]) ).
cnf(c_0_137,negated_conjecture,
inverse(sk_c8) = sk_c8,
inference(spm,[status(thm)],[c_0_134,c_0_126]) ).
cnf(c_0_138,negated_conjecture,
inverse(X1) != sk_c8,
inference(cn,[status(thm)],[inference(rw,[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)],[c_0_135,c_0_125]),c_0_125]),c_0_125]),c_0_131]),c_0_128]),c_0_131]),c_0_136]),c_0_131]),c_0_137])])])]),c_0_137])]) ).
cnf(c_0_139,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_137,c_0_138]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP306-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n002.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:31:46 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.47/1.80 % Version : CSE_E---1.7
% 1.47/1.80 % Problem : theBenchmark.p
% 1.47/1.80 % SZS status Unsatisfiable for theBenchmark.p
% 1.47/1.80 % SZS output start CNFRefutation
% See solution above
% 1.57/1.80 % Total time : 1.369s
%------------------------------------------------------------------------------