%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP249-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:39:05 PM UTC 2026
% Result : Unsatisfiable 2.09s 0.76s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 21
% Syntax : Number of clauses : 113 ( 32 unt; 69 nHn; 89 RR)
% Number of literals : 265 ( 264 equ; 82 neg)
% Maximal clause size : 12 ( 2 avg)
% Maximal term depth : 4 ( 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 : 69 ( 2 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_4,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_23,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_37,negated_conjecture,
( multiply(X6,sk_c7) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
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_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_4 ).
cnf(c_0_26,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(inverse(sk_c5),sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_5 ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
prove_this_16 ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(inverse(sk_c2),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
prove_this_22 ).
cnf(c_0_32,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c9 ),
prove_this_11 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c6
| multiply(inverse(sk_c1),sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c9 ),
prove_this_10 ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,multiply(sk_c5,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c8 ),
prove_this_23 ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(inverse(sk_c5),sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c7 ),
prove_this_17 ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c6
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( multiply(X6,sk_c7) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8 ),
inference(fof_simplification,[status(thm)],[prove_this_37]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,multiply(sk_c2,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( multiply(X6,sk_c7) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8 ),
c_0_42 ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( identity = sk_c8
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_46]),c_0_22]) ).
cnf(c_0_51,negated_conjecture,
( inverse(X5) != sk_c9
| inverse(X4) != sk_c8
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(X5,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,inverse(X1)) != sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8 ),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_2 ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_1 ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_3 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c5,multiply(sk_c6,X1)) = multiply(sk_c8,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_39,c_0_48]) ).
cnf(c_0_57,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_49]),c_0_49]) ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
prove_this_19 ).
cnf(c_0_59,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_22,c_0_49]) ).
cnf(c_0_60,negated_conjecture,
identity = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_50]),c_0_22])]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
prove_this_33 ).
cnf(c_0_62,negated_conjecture,
( inverse(X4) != sk_c9
| inverse(X3) != sk_c8
| inverse(X2) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c9
| multiply(X1,inverse(X1)) != sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c5,sk_c6) = multiply(sk_c8,sk_c8) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c8) = sk_c2
| inverse(sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,plain,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(inverse(sk_c3),sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_24,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
prove_this_27 ).
cnf(c_0_68,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X2) != sk_c8
| multiply(X3,sk_c9) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c9
| multiply(X1,inverse(X1)) != sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_62,c_0_52]) ).
cnf(c_0_69,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_57,c_0_53]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(inverse(inverse(sk_c5)),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_35,c_0_63]) ).
cnf(c_0_72,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
prove_this_13 ).
cnf(c_0_73,negated_conjecture,
( sk_c7 = sk_c8
| inverse(sk_c8) = sk_c2 ),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,negated_conjecture,
( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c9
| multiply(X1,inverse(X1)) != sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,negated_conjecture,
( identity = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_27]),c_0_22]) ).
cnf(c_0_77,negated_conjecture,
( identity = sk_c7
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_71]),c_0_22]) ).
cnf(c_0_78,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_72,c_0_65]) ).
cnf(c_0_79,negated_conjecture,
( sk_c2 = sk_c8
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_65,c_0_73]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c7
| multiply(inverse(sk_c4),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
prove_this_32 ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c7,sk_c8) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c9
| multiply(X1,inverse(X1)) != sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_57])]),c_0_22]),c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(rw,[status(thm)],[c_0_77,c_0_60]) ).
cnf(c_0_84,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_86,negated_conjecture,
( multiply(X1,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_57]),c_0_22]),c_0_76]) ).
cnf(c_0_87,negated_conjecture,
sk_c7 = sk_c8,
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c7
| multiply(sk_c9,sk_c9) = sk_c8
| multiply(inverse(sk_c3),sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_24,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c9 ),
prove_this_26 ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c7,sk_c8) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_22]),c_0_76]) ).
cnf(c_0_91,negated_conjecture,
multiply(sk_c8,sk_c8) = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_87])]) ).
cnf(c_0_92,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c9) = sk_c7
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,negated_conjecture,
multiply(sk_c1,sk_c9) = sk_c8,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_87]),c_0_87]),c_0_87]),c_0_91])]),c_0_54]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_80,c_0_92]) ).
cnf(c_0_95,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_96,negated_conjecture,
multiply(sk_c1,multiply(sk_c9,X1)) = multiply(sk_c8,X1),
inference(spm,[status(thm)],[c_0_21,c_0_93]) ).
cnf(c_0_97,negated_conjecture,
multiply(sk_c9,sk_c9) = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_87])]) ).
cnf(c_0_98,negated_conjecture,
multiply(sk_c8,multiply(sk_c8,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_93]),c_0_65]) ).
cnf(c_0_99,negated_conjecture,
multiply(sk_c1,sk_c8) = multiply(sk_c8,sk_c9),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_100,negated_conjecture,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_98]),c_0_91]),c_0_65]) ).
cnf(c_0_101,negated_conjecture,
multiply(sk_c1,sk_c8) = sk_c9,
inference(rw,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_102,negated_conjecture,
multiply(sk_c1,X1) = multiply(sk_c9,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_101]),c_0_100]) ).
cnf(c_0_103,negated_conjecture,
multiply(sk_c1,multiply(sk_c9,X1)) = X1,
inference(rw,[status(thm)],[c_0_96,c_0_100]) ).
cnf(c_0_104,negated_conjecture,
multiply(sk_c9,multiply(sk_c9,X1)) = X1,
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_105,plain,
multiply(inverse(X1),X1) = sk_c8,
inference(rw,[status(thm)],[c_0_22,c_0_60]) ).
cnf(c_0_106,negated_conjecture,
multiply(inverse(sk_c9),X1) = multiply(sk_c9,X1),
inference(spm,[status(thm)],[c_0_24,c_0_104]) ).
cnf(c_0_107,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_49,c_0_60]) ).
cnf(c_0_108,plain,
multiply(X1,inverse(X1)) = sk_c8,
inference(spm,[status(thm)],[c_0_105,c_0_57]) ).
cnf(c_0_109,negated_conjecture,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_107]) ).
cnf(c_0_110,negated_conjecture,
( inverse(X1) != sk_c9
| inverse(X2) != sk_c8
| multiply(X1,sk_c9) != sk_c8 ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_65]),c_0_87]),c_0_107]),c_0_108]),c_0_107]),c_0_87]),c_0_107]),c_0_107]),c_0_87]),c_0_87])])])])]),c_0_109]),c_0_65])]) ).
cnf(c_0_111,negated_conjecture,
( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8 ),
inference(spm,[status(thm)],[c_0_110,c_0_65]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_109]),c_0_97])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP249-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n015.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 20 20:10:50 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.09/0.76 % Version: 3.5.1
% 2.09/0.76 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.09/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.09/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.09/0.76 % Starting new_bool_3 with 300s (1) cores
% 2.09/0.76 % Starting new_bool_1 with 300s (1) cores
% 2.09/0.76 % Starting sh5l with 300s (1) cores
% 2.09/0.76 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3819284 completed with status 0
% 2.09/0.76 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 2.09/0.76 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.09/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.09/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.09/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.09/0.76 % No SInE strategy applied
% 2.09/0.76 % Search class: FGHPS-FFMM21-SFFFFFNN
% 2.09/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.09/0.76 % Starting SubtermCWHack with 136s (1) cores
% 2.09/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.09/0.76 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.09/0.76 % Starting new_bool_3 with 136s (1) cores
% 2.09/0.76 % Starting new_bool_1 with 136s (1) cores
% 2.09/0.76 % new_bool_1 with pid 3819294 completed with status 0
% 2.09/0.76 % Result found by new_bool_1
% 2.09/0.76 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.09/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.09/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.09/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.09/0.76 % No SInE strategy applied
% 2.09/0.76 % Search class: FGHPS-FFMM21-SFFFFFNN
% 2.09/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.09/0.76 % Starting SubtermCWHack with 136s (1) cores
% 2.09/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.09/0.76 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.09/0.76 % Starting new_bool_3 with 136s (1) cores
% 2.09/0.76 % Starting new_bool_1 with 136s (1) cores
% 2.09/0.76 % Preprocessing time : 0.001 s
% 2.09/0.76 % Presaturation interreduction done
% 2.09/0.76
% 2.09/0.76 % Proof found!
% 2.09/0.76 % SZS status Unsatisfiable
% 2.09/0.76 % SZS output start CNFRefutation
% See solution above
% 2.09/0.76 % Parsed axioms : 40
% 2.09/0.76 % Removed by relevancy pruning/SinE : 0
% 2.09/0.76 % Initial clauses : 40
% 2.09/0.76 % Removed in clause preprocessing : 0
% 2.09/0.76 % Initial clauses in saturation : 40
% 2.09/0.76 % Processed clauses : 3232
% 2.09/0.76 % ...of these trivial : 514
% 2.09/0.76 % ...subsumed : 1419
% 2.09/0.76 % ...remaining for further processing : 1299
% 2.09/0.76 % Other redundant clauses eliminated : 47
% 2.09/0.76 % Clauses deleted for lack of memory : 0
% 2.09/0.76 % Backward-subsumed : 284
% 2.09/0.76 % Backward-rewritten : 928
% 2.09/0.76 % Generated clauses : 23668
% 2.09/0.76 % ...of the previous two non-redundant : 21908
% 2.09/0.76 % ...aggressively subsumed : 0
% 2.09/0.76 % Contextual simplify-reflections : 123
% 2.09/0.76 % Paramodulations : 23616
% 2.09/0.76 % Factorizations : 8
% 2.09/0.76 % NegExts : 0
% 2.09/0.76 % Equation resolutions : 47
% 2.09/0.76 % Disequality decompositions : 0
% 2.09/0.76 % Total rewrite steps : 13072
% 2.09/0.76 % ...of those cached : 10594
% 2.09/0.76 % Propositional unsat checks : 0
% 2.09/0.76 % Propositional check models : 0
% 2.09/0.76 % Propositional check unsatisfiable : 0
% 2.09/0.76 % Propositional clauses : 0
% 2.09/0.76 % Propositional clauses after purity: 0
% 2.09/0.76 % Propositional unsat core size : 0
% 2.09/0.76 % Propositional preprocessing time : 0.000
% 2.09/0.76 % Propositional encoding time : 0.000
% 2.09/0.76 % Propositional solver time : 0.000
% 2.09/0.76 % Success case prop preproc time : 0.000
% 2.09/0.76 % Success case prop encoding time : 0.000
% 2.09/0.76 % Success case prop solver time : 0.000
% 2.09/0.76 % Current number of processed clauses : 44
% 2.09/0.76 % Positive orientable unit clauses : 43
% 2.09/0.76 % Positive unorientable unit clauses: 0
% 2.09/0.76 % Negative unit clauses : 0
% 2.09/0.76 % Non-unit-clauses : 1
% 2.09/0.76 % Current number of unprocessed clauses: 722
% 2.09/0.76 % ...number of literals in the above : 5910
% 2.09/0.76 % Current number of archived formulas : 0
% 2.09/0.76 % Current number of archived clauses : 1252
% 2.09/0.76 % Clause-clause subsumption calls (NU) : 41053
% 2.09/0.76 % Rec. Clause-clause subsumption calls : 10054
% 2.09/0.76 % Non-unit clause-clause subsumptions : 1802
% 2.09/0.76 % Unit Clause-clause subsumption calls : 1071
% 2.09/0.76 % Rewrite failures with RHS unbound : 0
% 2.09/0.76 % BW rewrite match attempts : 236
% 2.09/0.76 % BW rewrite match successes : 81
% 2.09/0.76 % Condensation attempts : 0
% 2.09/0.76 % Condensation successes : 0
% 2.09/0.76 % Termbank termtop insertions : 430693
% 2.09/0.76 % Search garbage collected termcells : 34
% 2.09/0.76
% 2.09/0.76 % -------------------------------------------------
% 2.09/0.76 % User time : 0.299 s
% 2.09/0.76 % System time : 0.014 s
% 2.09/0.76 % Total time : 0.313 s
% 2.09/0.76 % Maximum resident set size: 3652 pages
% 2.09/0.76
% 2.09/0.76 % -------------------------------------------------
% 2.09/0.76 % User time : 1.380 s
% 2.09/0.76 % System time : 0.062 s
% 2.09/0.76 % Total time : 1.442 s
% 2.09/0.76 % Maximum resident set size: 4864 pages
% 2.09/0.76 % E exiting
%------------------------------------------------------------------------------