%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP390-1 : 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 : n013.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 04:26:00 PM UTC 2026
% Result : Unsatisfiable 9.67s 6.98s
% Output : CNFRefutation 9.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 27
% Syntax : Number of clauses : 159 ( 26 unt; 112 nHn; 136 RR)
% Number of literals : 417 ( 416 equ; 147 neg)
% Maximal clause size : 12 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 103 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_37,negated_conjecture,
( inverse(sk_c8) != sk_c7
| inverse(X1) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,X3) != sk_c8
| inverse(X2) != X3
| multiply(X3,sk_c7) != sk_c8
| multiply(X4,sk_c9) != sk_c8
| inverse(X4) != sk_c9
| multiply(X5,sk_c8) != sk_c7
| inverse(X5) != sk_c8
| inverse(X6) != sk_c9
| multiply(X6,sk_c8) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_25,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
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,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_34,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_32,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(c_0_27,negated_conjecture,
( inverse(sk_c8) != sk_c7
| inverse(X1) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,X3) != sk_c8
| inverse(X2) != X3
| multiply(X3,sk_c7) != sk_c8
| multiply(X4,sk_c9) != sk_c8
| inverse(X4) != sk_c9
| multiply(X5,sk_c8) != sk_c7
| inverse(X5) != sk_c8
| inverse(X6) != sk_c9
| multiply(X6,sk_c8) != sk_c9 ),
prove_this_37 ).
cnf(c_0_28,negated_conjecture,
( multiply(inverse(X1),sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c7
| multiply(X4,sk_c9) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| inverse(X2) != sk_c9
| inverse(X3) != sk_c8
| inverse(X4) != sk_c9
| inverse(X5) != sk_c9 ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_1 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c7
| multiply(X4,sk_c9) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c8
| inverse(X4) != sk_c9
| inverse(X5) != sk_c9 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_25 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_19 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_31 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(X2,sk_c8) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X2) != sk_c8
| inverse(X3) != sk_c9
| inverse(X4) != sk_c9 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_13 ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
prove_this_7 ).
cnf(c_0_37,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_38,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_39,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X1) != sk_c8
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_41,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_18 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(X1,multiply(X2,sk_c8)) != sk_c7
| inverse(multiply(X1,X2)) != sk_c8
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| inverse(X4) != sk_c9 ),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( multiply(inverse(sk_c2),sk_c8) = sk_c3
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
prove_this_33 ).
cnf(c_0_46,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( multiply(inverse(sk_c1),sk_c9) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_12 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(multiply(X1,inverse(sk_c2))) != sk_c8
| multiply(X1,sk_c3) != sk_c7
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9 ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( multiply(inverse(sk_c5),sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_45]) ).
cnf(c_0_51,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(multiply(X1,sk_c3)) != sk_c8
| multiply(X1,sk_c3) != sk_c7
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9 ),
inference(spm,[status(thm)],[c_0_49,c_0_31]) ).
cnf(c_0_54,negated_conjecture,
( multiply(inverse(inverse(sk_c5)),sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
prove_this_34 ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(multiply(X1,inverse(sk_c8))) != sk_c8
| multiply(X1,identity) != sk_c7
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9 ),
inference(spm,[status(thm)],[c_0_43,c_0_38]) ).
cnf(c_0_57,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_51]),c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c6) = sk_c9 ),
prove_this_5 ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c4) = sk_c9 ),
prove_this_2 ).
cnf(c_0_60,negated_conjecture,
( multiply(inverse(sk_c6),sk_c9) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
prove_this_17 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(multiply(X1,multiply(X2,sk_c3))) != sk_c8
| multiply(X1,multiply(X2,sk_c3)) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| inverse(X4) != sk_c9 ),
inference(spm,[status(thm)],[c_0_53,c_0_37]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_38]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(multiply(X1,sk_c7)) != sk_c8
| multiply(X1,identity) != sk_c7
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9 ),
inference(spm,[status(thm)],[c_0_56,c_0_29]) ).
cnf(c_0_65,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c9) = sk_c6 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c9) = sk_c4 ),
inference(spm,[status(thm)],[c_0_57,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(multiply(X1,sk_c8)) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(X2,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9 ),
inference(spm,[status(thm)],[c_0_62,c_0_32]) ).
cnf(c_0_69,negated_conjecture,
( multiply(inverse(sk_c3),sk_c8) = sk_c7
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_41,c_0_63]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(X1,sk_c9) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(sk_c7) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| identity != sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_39]),c_0_39]) ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c8) = sk_c7
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,negated_conjecture,
( multiply(inverse(sk_c1),sk_c9) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
prove_this_11 ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(X1,sk_c9) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(sk_c7) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_75,negated_conjecture,
( inverse(sk_c7) = sk_c8
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_57,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( multiply(inverse(inverse(sk_c2)),sk_c3) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_44]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| sk_c6 = sk_c4
| multiply(X1,sk_c9) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_31]),c_0_38]) ).
cnf(c_0_80,negated_conjecture,
multiply(sk_c9,sk_c9) = sk_c8,
inference(spm,[status(thm)],[c_0_60,c_0_77]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| sk_c6 = sk_c4
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_38]),c_0_57])]),c_0_79]) ).
cnf(c_0_82,negated_conjecture,
multiply(inverse(sk_c9),sk_c8) = sk_c9,
inference(spm,[status(thm)],[c_0_41,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| sk_c6 = sk_c4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_57])]) ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c9 ),
prove_this_26 ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_24 ).
cnf(c_0_86,negated_conjecture,
( multiply(inverse(sk_c4),sk_c8) = sk_c9
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_41,c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c2 ),
inference(spm,[status(thm)],[c_0_57,c_0_84]) ).
cnf(c_0_88,negated_conjecture,
( multiply(inverse(sk_c2),sk_c8) = sk_c3
| multiply(sk_c6,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_41,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c9 ),
prove_this_20 ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c2
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( multiply(inverse(inverse(sk_c2)),sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_41,c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c6,sk_c8) = sk_c9 ),
prove_this_30 ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c9
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_86,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = identity
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_38,c_0_90]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_38]) ).
cnf(c_0_96,negated_conjecture,
multiply(sk_c9,multiply(sk_c9,X1)) = multiply(sk_c8,X1),
inference(spm,[status(thm)],[c_0_37,c_0_80]) ).
cnf(c_0_97,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_38,c_0_57]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| sk_c6 = sk_c4
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c6,multiply(sk_c8,X1)) = multiply(sk_c9,X1)
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_37,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
multiply(sk_c8,inverse(sk_c9)) = sk_c9,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_51]) ).
cnf(c_0_101,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_38,c_0_51]) ).
cnf(c_0_102,negated_conjecture,
( sk_c6 = sk_c4
| identity = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_98]),c_0_38])]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c6,sk_c9) = identity
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_97]) ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c8) = sk_c8
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_105,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_41,c_0_37]) ).
cnf(c_0_106,negated_conjecture,
( multiply(inverse(sk_c4),sk_c8) = sk_c9
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_79]) ).
cnf(c_0_107,negated_conjecture,
( inverse(sk_c6) = sk_c9
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_103]),c_0_51]) ).
cnf(c_0_108,negated_conjecture,
( sk_c6 = sk_c4
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_71,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( multiply(inverse(multiply(X1,inverse(sk_c4))),multiply(X1,sk_c9)) = sk_c8
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_110,negated_conjecture,
( inverse(sk_c4) = sk_c9
| sk_c7 = sk_c8
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_111,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
prove_this_4 ).
cnf(c_0_112,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c9 ),
prove_this_8 ).
cnf(c_0_113,negated_conjecture,
( multiply(X1,sk_c8) = X1
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_51,c_0_102]) ).
cnf(c_0_114,negated_conjecture,
( multiply(inverse(sk_c4),sk_c8) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_33]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c9 ),
prove_this_32 ).
cnf(c_0_116,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_38])]) ).
cnf(c_0_117,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_57,c_0_111]) ).
cnf(c_0_118,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c9) = sk_c1 ),
inference(spm,[status(thm)],[c_0_57,c_0_112]) ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c9) = sk_c1 ),
inference(spm,[status(thm)],[c_0_57,c_0_73]) ).
cnf(c_0_120,negated_conjecture,
( inverse(sk_c4) = sk_c9
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_86,c_0_113]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_122,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
prove_this_3 ).
cnf(c_0_123,negated_conjecture,
( inverse(sk_c8) = sk_c8
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_101,c_0_116]) ).
cnf(c_0_124,negated_conjecture,
( inverse(sk_c8) = sk_c7
| sk_c5 != sk_c7 ),
inference(ef,[status(thm)],[c_0_117]) ).
cnf(c_0_125,negated_conjecture,
( inverse(sk_c8) = identity
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_38,c_0_113]) ).
cnf(c_0_126,negated_conjecture,
( inverse(sk_c9) = sk_c1
| inverse(sk_c9) = sk_c4 ),
inference(spm,[status(thm)],[c_0_57,c_0_118]) ).
cnf(c_0_127,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c6) = sk_c9 ),
prove_this_35 ).
cnf(c_0_128,negated_conjecture,
( inverse(sk_c9) = sk_c1
| inverse(sk_c9) = sk_c6 ),
inference(spm,[status(thm)],[c_0_57,c_0_119]) ).
cnf(c_0_129,negated_conjecture,
( inverse(sk_c9) = sk_c4
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_57,c_0_120]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c3,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_37,c_0_121]) ).
cnf(c_0_131,negated_conjecture,
multiply(sk_c9,sk_c8) = multiply(sk_c8,sk_c9),
inference(spm,[status(thm)],[c_0_96,c_0_80]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_133,negated_conjecture,
( multiply(X1,sk_c8) = X1
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_51,c_0_116]) ).
cnf(c_0_134,negated_conjecture,
( sk_c7 = sk_c8
| sk_c5 != sk_c7 ),
inference(spm,[status(thm)],[c_0_124,c_0_123]) ).
cnf(c_0_135,negated_conjecture,
( sk_c6 = sk_c4
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_71,c_0_125]) ).
cnf(c_0_136,negated_conjecture,
( inverse(sk_c9) = sk_c4
| sk_c1 != sk_c4 ),
inference(ef,[status(thm)],[c_0_126]) ).
cnf(c_0_137,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c6 ),
inference(spm,[status(thm)],[c_0_57,c_0_127]) ).
cnf(c_0_138,negated_conjecture,
( sk_c6 = sk_c4
| sk_c1 = sk_c4 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_139,negated_conjecture,
( multiply(sk_c3,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_140,negated_conjecture,
sk_c7 = sk_c8,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_134]) ).
cnf(c_0_141,negated_conjecture,
( multiply(X1,sk_c7) = X1
| sk_c6 = sk_c4 ),
inference(spm,[status(thm)],[c_0_51,c_0_135]) ).
cnf(c_0_142,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| sk_c6 = sk_c4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138]) ).
cnf(c_0_143,negated_conjecture,
( multiply(sk_c3,multiply(sk_c8,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_144,negated_conjecture,
( sk_c6 = sk_c4
| sk_c3 = sk_c8 ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_145,negated_conjecture,
multiply(inverse(sk_c9),multiply(sk_c8,X1)) = multiply(sk_c9,X1),
inference(spm,[status(thm)],[c_0_37,c_0_82]) ).
cnf(c_0_146,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c9
| identity = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_97]),c_0_51]) ).
cnf(c_0_147,negated_conjecture,
( inverse(sk_c4) = sk_c9
| sk_c3 = sk_c8
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_107,c_0_144]) ).
cnf(c_0_148,negated_conjecture,
( identity = sk_c3
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_38]),c_0_80]) ).
cnf(c_0_149,negated_conjecture,
( sk_c3 = sk_c8
| identity = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_147]),c_0_38])]) ).
cnf(c_0_150,negated_conjecture,
identity = sk_c8,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_148]),c_0_149]) ).
cnf(c_0_151,negated_conjecture,
( multiply(inverse(X1),sk_c7) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c7
| multiply(X4,sk_c9) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| inverse(X2) != sk_c9
| inverse(X3) != sk_c8
| inverse(X4) != sk_c9
| inverse(X5) != sk_c9
| identity != sk_c8 ),
inference(rw,[status(thm)],[c_0_28,c_0_97]) ).
cnf(c_0_152,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_51,c_0_150]) ).
cnf(c_0_153,negated_conjecture,
( multiply(inverse(X1),sk_c8) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c8
| multiply(X4,sk_c9) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c8
| inverse(X2) != sk_c9
| inverse(X3) != sk_c8
| inverse(X4) != sk_c9
| inverse(X5) != sk_c9
| identity != sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_140]),c_0_140]),c_0_140]) ).
cnf(c_0_154,plain,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_150]),c_0_150]) ).
cnf(c_0_155,negated_conjecture,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[c_0_82,c_0_152]) ).
cnf(c_0_156,negated_conjecture,
( multiply(X1,sk_c9) != sk_c8
| inverse(X2) != sk_c8
| inverse(X1) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_150])]),c_0_152]),c_0_152]),c_0_152]),c_0_152]),c_0_154])])])])]),c_0_155]),c_0_154])]) ).
cnf(c_0_157,negated_conjecture,
inverse(X1) != sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_80]),c_0_155])]) ).
cnf(c_0_158,plain,
$false,
inference(sr,[status(thm)],[c_0_154,c_0_157]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP390-1 : 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 : n013.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 18:33:56 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 9.67/6.98 % Version : CSE_E---1.7
% 9.67/6.98 % Problem : theBenchmark.p
% 9.67/6.98 % SZS status Unsatisfiable for theBenchmark.p
% 9.67/6.98 % SZS output start CNFRefutation
% See solution above
% 9.67/7.01 % Total time : 5.372s
%------------------------------------------------------------------------------