%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP352-1 : 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 : n006.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 04:25:41 PM UTC 2026
% Result : Unsatisfiable 2.09s 1.97s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 24
% Syntax : Number of clauses : 181 ( 29 unt; 139 nHn; 151 RR)
% Number of literals : 424 ( 423 equ; 101 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 81 ( 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_16,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_21,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c6,sk_c5) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(X2,sk_c6) != sk_c5
| inverse(X2) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X3) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_25,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(c_0_24,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_25,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_26,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_27,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_28,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_29,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_16 ).
cnf(c_0_31,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( multiply(inverse(sk_c2),sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_21 ).
cnf(c_0_34,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_31]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c6) = sk_c2 ),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c6,multiply(sk_c5,X1)) = multiply(sk_c6,X1)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_38,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_25,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c2,multiply(sk_c6,X1)) = X1
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c6,inverse(sk_c5)) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_11 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_1 ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c5) = multiply(sk_c2,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_34,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c6,multiply(sk_c5,X1)) = multiply(sk_c7,X1)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_24,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( inverse(multiply(sk_c2,sk_c6)) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_34,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c1,multiply(sk_c7,X1)) = X1
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c7,inverse(sk_c5)) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_38]),c_0_31]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_6 ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c5) = sk_c5 ),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c5) = multiply(sk_c1,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c1,multiply(sk_c7,X1)) = multiply(sk_c6,X1)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_24,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_48,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( inverse(multiply(sk_c1,sk_c6)) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_34,c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c1,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( inverse(multiply(sk_c6,sk_c5)) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_56,c_0_42]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_34,c_0_57]) ).
cnf(c_0_59,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_40,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_53]) ).
cnf(c_0_62,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_59]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c6
| sk_c5 != sk_c6 ),
inference(ef,[status(thm)],[c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_61,c_0_44]) ).
cnf(c_0_65,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
prove_this_15 ).
cnf(c_0_66,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_25,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( identity = sk_c7
| sk_c5 != sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_63]),c_0_25]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_64,c_0_55]) ).
cnf(c_0_69,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
prove_this_14 ).
cnf(c_0_70,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_34,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c6,inverse(sk_c7)) = sk_c1
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_38]),c_0_31]) ).
cnf(c_0_72,negated_conjecture,
( inverse(sk_c7) = sk_c7
| sk_c5 != sk_c6 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_68]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
prove_this_4 ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c7 ),
prove_this_9 ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_69]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_25,c_0_70]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c1 = sk_c5 ),
inference(spm,[status(thm)],[c_0_44,c_0_57]) ).
cnf(c_0_80,negated_conjecture,
( multiply(inverse(sk_c4),sk_c7) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_27,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c4) = sk_c6 ),
prove_this_5 ).
cnf(c_0_82,negated_conjecture,
( multiply(inverse(sk_c4),sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_75]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
prove_this_10 ).
cnf(c_0_84,negated_conjecture,
( multiply(inverse(sk_c4),sk_c7) = sk_c6
| multiply(sk_c7,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_76]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_34,c_0_77]) ).
cnf(c_0_86,negated_conjecture,
multiply(sk_c6,sk_c7) = sk_c5,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_78]),c_0_79]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c6,sk_c5) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(X2,sk_c6) != sk_c5
| inverse(X2) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X3) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c6 ),
prove_this_26 ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c6) = sk_c7 ),
prove_this_19 ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c7,sk_c1) = identity
| sk_c5 = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c6) != sk_c5
| multiply(X4,sk_c7) != sk_c6
| inverse(X1) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c6
| inverse(X4) != sk_c7 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_93,negated_conjecture,
( multiply(inverse(sk_c4),sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
prove_this_20 ).
cnf(c_0_95,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_90]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c7) = sk_c1
| sk_c5 = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_91]),c_0_31]) ).
cnf(c_0_97,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
prove_this_22 ).
cnf(c_0_98,negated_conjecture,
( sk_c5 = sk_c6
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c6) != sk_c5
| multiply(X4,sk_c7) != sk_c6
| inverse(X1) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c6
| inverse(X4) != sk_c7 ),
inference(spm,[status(thm)],[c_0_92,c_0_73]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_100,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| sk_c5 = sk_c6 ),
inference(rw,[status(thm)],[c_0_95,c_0_86]) ).
cnf(c_0_101,negated_conjecture,
( inverse(sk_c1) = sk_c7
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_34,c_0_96]) ).
cnf(c_0_102,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c6) = sk_c2 ),
inference(spm,[status(thm)],[c_0_34,c_0_97]) ).
cnf(c_0_103,negated_conjecture,
( sk_c5 = sk_c6
| multiply(X1,multiply(X2,sk_c6)) != sk_c7
| inverse(multiply(X1,X2)) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| multiply(X4,sk_c6) != sk_c5
| multiply(X5,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(X4) != sk_c6
| inverse(X5) != sk_c7 ),
inference(spm,[status(thm)],[c_0_98,c_0_24]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| sk_c5 = sk_c6 ),
inference(rw,[status(thm)],[c_0_99,c_0_86]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_106,negated_conjecture,
( inverse(sk_c6) = sk_c2
| inverse(sk_c7) = sk_c3 ),
inference(spm,[status(thm)],[c_0_34,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( sk_c5 = sk_c6
| inverse(multiply(X1,sk_c2)) != sk_c6
| multiply(X1,sk_c5) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c6) != sk_c5
| multiply(X4,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c6
| inverse(X4) != sk_c7 ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_108,negated_conjecture,
( sk_c5 = sk_c6
| identity = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_105]),c_0_25]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c3,multiply(sk_c7,X1)) = X1
| inverse(sk_c6) = sk_c2 ),
inference(spm,[status(thm)],[c_0_27,c_0_106]) ).
cnf(c_0_110,negated_conjecture,
( sk_c5 = sk_c6
| multiply(inverse(sk_c2),sk_c5) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c6) != sk_c5
| multiply(X3,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c6
| inverse(X3) != sk_c7
| identity != sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_25]),c_0_66]) ).
cnf(c_0_111,negated_conjecture,
( inverse(sk_c6) = sk_c6
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_66,c_0_108]) ).
cnf(c_0_112,negated_conjecture,
( inverse(sk_c6) = sk_c2
| sk_c5 = sk_c6
| sk_c1 = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_91]),c_0_31]) ).
cnf(c_0_113,negated_conjecture,
( multiply(inverse(sk_c2),sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_99]) ).
cnf(c_0_114,negated_conjecture,
( sk_c5 = sk_c6
| multiply(inverse(sk_c2),sk_c5) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c6) != sk_c5
| multiply(X3,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c6
| inverse(X3) != sk_c7 ),
inference(spm,[status(thm)],[c_0_110,c_0_108]) ).
cnf(c_0_115,negated_conjecture,
( sk_c1 = sk_c3
| sk_c5 = sk_c6
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_116,negated_conjecture,
multiply(inverse(sk_c6),sk_c5) = sk_c7,
inference(spm,[status(thm)],[c_0_27,c_0_86]) ).
cnf(c_0_117,negated_conjecture,
( multiply(inverse(sk_c2),sk_c5) = sk_c6
| sk_c5 = sk_c6 ),
inference(rw,[status(thm)],[c_0_113,c_0_86]) ).
cnf(c_0_118,negated_conjecture,
( sk_c1 = sk_c3
| sk_c5 = sk_c6
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c6) != sk_c5
| multiply(X3,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c6
| inverse(X3) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116])]) ).
cnf(c_0_119,negated_conjecture,
( sk_c1 = sk_c3
| sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_115]),c_0_116]) ).
cnf(c_0_120,negated_conjecture,
( sk_c5 = sk_c6
| sk_c1 = sk_c3
| multiply(X1,sk_c6) != sk_c5
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != sk_c6
| inverse(X2) != sk_c7
| identity != sk_c7 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_25]),c_0_34]),c_0_119]) ).
cnf(c_0_121,negated_conjecture,
( sk_c1 = sk_c3
| sk_c5 = sk_c6
| multiply(X1,sk_c6) != sk_c5
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != sk_c6
| inverse(X2) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_108]),c_0_119]) ).
cnf(c_0_122,negated_conjecture,
( inverse(sk_c2) = sk_c6
| sk_c1 = sk_c3
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_34,c_0_112]) ).
cnf(c_0_123,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
prove_this_25 ).
cnf(c_0_124,negated_conjecture,
( sk_c5 = sk_c6
| sk_c1 = sk_c3
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_104]),c_0_122]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c5 = sk_c6 ),
inference(rw,[status(thm)],[c_0_90,c_0_86]) ).
cnf(c_0_126,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_34,c_0_123]) ).
cnf(c_0_127,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
prove_this_12 ).
cnf(c_0_128,negated_conjecture,
( sk_c1 = sk_c3
| sk_c5 = sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_101]) ).
cnf(c_0_129,negated_conjecture,
( inverse(sk_c6) = sk_c4
| inverse(sk_c6) = sk_c2 ),
inference(spm,[status(thm)],[c_0_34,c_0_126]) ).
cnf(c_0_130,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c7 ),
prove_this_24 ).
cnf(c_0_131,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_132,negated_conjecture,
( inverse(sk_c3) = sk_c7
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_133,negated_conjecture,
( inverse(sk_c6) = sk_c2
| inverse(sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_34,c_0_129]) ).
cnf(c_0_134,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c6) = sk_c2 ),
inference(spm,[status(thm)],[c_0_34,c_0_130]) ).
cnf(c_0_135,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_38]) ).
cnf(c_0_136,negated_conjecture,
( multiply(sk_c3,multiply(sk_c7,X1)) = X1
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c6,multiply(sk_c4,X1)) = X1
| inverse(sk_c6) = sk_c2 ),
inference(spm,[status(thm)],[c_0_27,c_0_133]) ).
cnf(c_0_138,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| sk_c5 = sk_c6
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_134,c_0_111]) ).
cnf(c_0_139,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_88]) ).
cnf(c_0_140,negated_conjecture,
( inverse(multiply(sk_c3,sk_c7)) = identity
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_141,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_125,c_0_128]) ).
cnf(c_0_142,negated_conjecture,
( inverse(sk_c6) = sk_c2
| sk_c2 = sk_c6
| sk_c5 = sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_86])]) ).
cnf(c_0_143,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c5
| sk_c5 = sk_c6 ),
inference(rw,[status(thm)],[c_0_139,c_0_86]) ).
cnf(c_0_144,negated_conjecture,
( inverse(sk_c6) = identity
| sk_c5 = sk_c6 ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_145,negated_conjecture,
( sk_c5 = sk_c6
| sk_c2 = sk_c6 ),
inference(spm,[status(thm)],[c_0_111,c_0_142]) ).
cnf(c_0_146,negated_conjecture,
( sk_c5 = sk_c6
| sk_c5 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_26]) ).
cnf(c_0_147,negated_conjecture,
( sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_145]),c_0_116]) ).
cnf(c_0_148,negated_conjecture,
sk_c5 = sk_c6,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_146]),c_0_147]) ).
cnf(c_0_149,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_34,c_0_127]) ).
cnf(c_0_150,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
prove_this_7 ).
cnf(c_0_151,negated_conjecture,
identity = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_148]),c_0_25]) ).
cnf(c_0_152,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
prove_this_8 ).
cnf(c_0_153,negated_conjecture,
( inverse(sk_c7) = sk_c1
| inverse(sk_c7) = sk_c3 ),
inference(spm,[status(thm)],[c_0_34,c_0_149]) ).
cnf(c_0_154,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c3 ),
inference(spm,[status(thm)],[c_0_34,c_0_150]) ).
cnf(c_0_155,plain,
multiply(X1,sk_c7) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_151]) ).
cnf(c_0_156,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
prove_this_13 ).
cnf(c_0_157,negated_conjecture,
( multiply(sk_c1,multiply(sk_c7,X1)) = multiply(sk_c6,X1)
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_24,c_0_152]) ).
cnf(c_0_158,negated_conjecture,
( multiply(sk_c7,sk_c7) = identity
| sk_c5 != sk_c6 ),
inference(spm,[status(thm)],[c_0_25,c_0_72]) ).
cnf(c_0_159,negated_conjecture,
( sk_c3 = sk_c7
| sk_c1 = sk_c7
| sk_c5 != sk_c6 ),
inference(spm,[status(thm)],[c_0_153,c_0_72]) ).
cnf(c_0_160,negated_conjecture,
inverse(sk_c7) = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_148])]) ).
cnf(c_0_161,negated_conjecture,
( inverse(sk_c7) = sk_c3
| sk_c1 = sk_c6 ),
inference(rw,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_162,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_34,c_0_156]) ).
cnf(c_0_163,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| sk_c1 = sk_c5
| sk_c5 != sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_31]),c_0_86]) ).
cnf(c_0_164,negated_conjecture,
( sk_c1 = sk_c7
| sk_c3 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_148])]) ).
cnf(c_0_165,negated_conjecture,
( sk_c1 = sk_c6
| sk_c3 = sk_c7 ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_166,negated_conjecture,
( inverse(sk_c3) = sk_c7
| sk_c1 = sk_c7 ),
inference(rw,[status(thm)],[c_0_149,c_0_160]) ).
cnf(c_0_167,plain,
multiply(sk_c7,X1) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_151]) ).
cnf(c_0_168,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| sk_c1 = sk_c7
| sk_c5 != sk_c6 ),
inference(spm,[status(thm)],[c_0_162,c_0_72]) ).
cnf(c_0_169,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| sk_c1 = sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_148]),c_0_148])]) ).
cnf(c_0_170,negated_conjecture,
( sk_c3 = sk_c7
| sk_c7 = sk_c6 ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_171,negated_conjecture,
( multiply(sk_c3,X1) = X1
| sk_c1 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_166]),c_0_167]) ).
cnf(c_0_172,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| sk_c1 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_148])]) ).
cnf(c_0_173,negated_conjecture,
( sk_c1 = sk_c6
| sk_c7 = sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_167])]) ).
cnf(c_0_174,negated_conjecture,
( sk_c1 = sk_c7
| sk_c7 = sk_c6 ),
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_175,negated_conjecture,
sk_c7 = sk_c6,
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_176,negated_conjecture,
( multiply(sk_c6,sk_c5) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c6) != sk_c5
| multiply(X4,sk_c7) != sk_c6
| inverse(X1) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c6
| inverse(X4) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_86])]) ).
cnf(c_0_177,plain,
multiply(sk_c6,X1) = X1,
inference(rw,[status(thm)],[c_0_167,c_0_175]) ).
cnf(c_0_178,plain,
multiply(X1,sk_c6) = X1,
inference(rw,[status(thm)],[c_0_155,c_0_175]) ).
cnf(c_0_179,negated_conjecture,
inverse(sk_c6) = sk_c6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_175]),c_0_175]) ).
cnf(c_0_180,negated_conjecture,
$false,
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_176,c_0_148]),c_0_148]),c_0_177]),c_0_175]),c_0_178]),c_0_175]),c_0_178]),c_0_175]),c_0_178]),c_0_175]),c_0_178]),c_0_175]),c_0_175])])])])])]),c_0_179])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP352-1 : 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 : n006.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 18:32:46 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.09/1.97 % Version : CSE_E---1.7
% 2.09/1.97 % Problem : theBenchmark.p
% 2.09/1.97 % SZS status Unsatisfiable for theBenchmark.p
% 2.09/1.97 % SZS output start CNFRefutation
% See solution above
% 2.09/1.98 % Total time : 1.367s
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