%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP210-1 : 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 : n002.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 12:42:54 PM UTC 2026
% Result : Unsatisfiable 1.90s 0.69s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 22
% Syntax : Number of clauses : 122 ( 29 unt; 84 nHn; 97 RR)
% Number of literals : 256 ( 255 equ; 56 neg)
% Maximal clause size : 13 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 69 ( 5 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,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_40,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_39,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_41,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c10) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != X2
| multiply(X1,X2) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_25,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(c_0_22,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_23,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_24,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_25,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_27,plain,
multiply(inverse(inverse(inverse(X1))),X1) = identity,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_27]),c_0_26]) ).
cnf(c_0_29,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c2 ),
prove_this_16 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c2 ),
prove_this_15 ).
cnf(c_0_32,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c7,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c7,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_8 ).
cnf(c_0_36,negated_conjecture,
( identity = sk_c8
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_38,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_7 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c7,sk_c10) = identity
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c2 ),
prove_this_14 ).
cnf(c_0_42,negated_conjecture,
( identity = sk_c8
| inverse(sk_c2) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_36]),c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
prove_this_40 ).
cnf(c_0_44,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_29]),c_0_37]) ).
cnf(c_0_45,negated_conjecture,
( identity = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c2 ),
prove_this_12 ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_6 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c1,sk_c2) = identity
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_41]) ).
cnf(c_0_49,negated_conjecture,
( identity = sk_c8
| multiply(sk_c1,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c10 ),
prove_this_39 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c7,sk_c10) = identity
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_43]) ).
cnf(c_0_52,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_44]),c_0_28]) ).
cnf(c_0_53,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c1),sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_4 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c1) = sk_c2 ),
prove_this_11 ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_46]) ).
cnf(c_0_57,negated_conjecture,
( identity = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,negated_conjecture,
( identity = sk_c10
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_45,c_0_49]) ).
cnf(c_0_59,negated_conjecture,
( identity = sk_c8
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_28]) ).
cnf(c_0_61,negated_conjecture,
( identity = sk_c8
| multiply(sk_c10,inverse(sk_c2)) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_28]) ).
cnf(c_0_62,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c3) = sk_c10 ),
prove_this_32 ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
prove_this_3 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_54]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c1,sk_c2) = identity
| multiply(sk_c5,sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_29,c_0_55]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c1,sk_c2) = identity
| multiply(sk_c5,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_56]) ).
cnf(c_0_67,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c10),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_25,c_0_57]) ).
cnf(c_0_68,negated_conjecture,
( identity = sk_c10
| multiply(sk_c8,X1) = X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_58]) ).
cnf(c_0_69,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c3),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_25,c_0_59]) ).
cnf(c_0_70,plain,
multiply(X1,multiply(X2,multiply(inverse(multiply(X1,X2)),X3))) = X3,
inference(spm,[status(thm)],[c_0_22,c_0_60]) ).
cnf(c_0_71,negated_conjecture,
( identity = sk_c8
| multiply(sk_c10,sk_c1) = sk_c1 ),
inference(spm,[status(thm)],[c_0_61,c_0_42]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c3) = sk_c10 ),
prove_this_31 ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c7,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_62]) ).
cnf(c_0_74,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_75,negated_conjecture,
( identity = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_76,negated_conjecture,
( identity = sk_c9
| multiply(sk_c1,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_77,negated_conjecture,
( identity = sk_c10
| multiply(sk_c9,inverse(sk_c8)) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_67]),c_0_28]) ).
cnf(c_0_78,negated_conjecture,
( identity = sk_c10
| inverse(sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_68]) ).
cnf(c_0_79,negated_conjecture,
( identity = sk_c8
| multiply(sk_c10,inverse(sk_c9)) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_69]),c_0_28]) ).
cnf(c_0_80,negated_conjecture,
( identity = sk_c8
| multiply(sk_c10,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_60]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c10,sk_c3) = identity
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_72]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c10,sk_c3) = identity
| multiply(sk_c7,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_73]) ).
cnf(c_0_83,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_74]) ).
cnf(c_0_84,negated_conjecture,
( identity = sk_c10
| identity = sk_c9 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_85,negated_conjecture,
( sk_c9 = sk_c10
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_37]) ).
cnf(c_0_86,negated_conjecture,
( identity = sk_c8
| inverse(sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_87,negated_conjecture,
( identity = sk_c8
| multiply(sk_c10,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_88,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_23,c_0_83]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
prove_this_30 ).
cnf(c_0_90,negated_conjecture,
identity = sk_c10,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_84]),c_0_85]) ).
cnf(c_0_91,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c3,sk_c9) = sk_c10 ),
prove_this_36 ).
cnf(c_0_92,negated_conjecture,
( identity = sk_c8
| inverse(sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_28,c_0_86]) ).
cnf(c_0_93,negated_conjecture,
( identity = sk_c8
| inverse(sk_c3) = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_87]),c_0_88]),c_0_24]) ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c10) = sk_c3
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_28,c_0_89]) ).
cnf(c_0_95,plain,
multiply(sk_c10,X1) = X1,
inference(rw,[status(thm)],[c_0_24,c_0_90]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
prove_this_35 ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_91]) ).
cnf(c_0_98,negated_conjecture,
( sk_c9 = sk_c10
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_99,plain,
multiply(X1,inverse(X1)) = sk_c10,
inference(rw,[status(thm)],[c_0_29,c_0_90]) ).
cnf(c_0_100,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c10) = sk_c3 ),
inference(rw,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_101,negated_conjecture,
( sk_c8 != sk_c10
| identity = sk_c10 ),
inference(ef,[status(thm)],[c_0_58]) ).
cnf(c_0_102,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c10) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != X2
| multiply(X1,X2) != sk_c10 ),
inference(fof_simplification,[status(thm)],[prove_this_41]) ).
cnf(c_0_103,negated_conjecture,
( identity = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_104,negated_conjecture,
( sk_c8 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_85,c_0_98]) ).
cnf(c_0_105,negated_conjecture,
( sk_c3 = sk_c10
| sk_c8 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_95]) ).
cnf(c_0_106,negated_conjecture,
( sk_c8 != sk_c10
| multiply(sk_c10,X1) = X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_101]) ).
cnf(c_0_107,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c10) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != X2
| multiply(X1,X2) != sk_c10 ),
c_0_102 ).
cnf(c_0_108,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(rw,[status(thm)],[c_0_103,c_0_90]) ).
cnf(c_0_109,negated_conjecture,
( sk_c9 = sk_c10
| sk_c3 = sk_c10 ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_110,negated_conjecture,
( sk_c8 != sk_c10
| inverse(sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_106]) ).
cnf(c_0_111,negated_conjecture,
( identity != sk_c10
| identity != sk_c9
| inverse(X5) != sk_c10
| inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_107])])]),c_0_29]),c_0_29]) ).
cnf(c_0_112,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_37,c_0_90]) ).
cnf(c_0_113,negated_conjecture,
sk_c9 = sk_c10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_95])]) ).
cnf(c_0_114,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_90]),c_0_90]) ).
cnf(c_0_115,negated_conjecture,
( identity = sk_c8
| inverse(sk_c10) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_71]),c_0_29]) ).
cnf(c_0_116,negated_conjecture,
( sk_c8 != sk_c10
| inverse(sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[c_0_110,c_0_90]) ).
cnf(c_0_117,negated_conjecture,
( inverse(X2) != sk_c10
| inverse(X1) != sk_c10 ),
inference(cn,[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_90]),c_0_90])]),c_0_112]),c_0_95]),c_0_113]),c_0_112]),c_0_113]),c_0_113]),c_0_112]),c_0_113]),c_0_112]),c_0_113]),c_0_112]),c_0_113])])])])]),c_0_114])]) ).
cnf(c_0_118,negated_conjecture,
inverse(sk_c10) = sk_c10,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_90]),c_0_90]),c_0_116]) ).
cnf(c_0_119,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c10 ),
prove_this_25 ).
cnf(c_0_120,negated_conjecture,
inverse(X1) != sk_c10,
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_121,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_119,c_0_120]),c_0_120]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP210-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:08:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 1.90/0.69 % Version: 3.5.1
% 1.90/0.69 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.90/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.90/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.90/0.69 % Starting new_bool_3 with 300s (1) cores
% 1.90/0.69 % Starting new_bool_1 with 300s (1) cores
% 1.90/0.69 % Starting sh5l with 300s (1) cores
% 1.90/0.69 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1593673 completed with status 0
% 1.90/0.69 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 1.90/0.69 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.90/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.90/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.90/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.90/0.69 % No SInE strategy applied
% 1.90/0.69 % Search class: FGHPS-FFMM21-SFFFFFNN
% 1.90/0.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.90/0.69 % Starting SubtermCWHack with 136s (1) cores
% 1.90/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 1.90/0.69 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.90/0.69 % Starting new_bool_3 with 136s (1) cores
% 1.90/0.69 % Starting new_bool_1 with 136s (1) cores
% 1.90/0.69 % SubtermCWHack with pid 1593678 completed with status 0
% 1.90/0.69 % Result found by SubtermCWHack
% 1.90/0.69 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.90/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.90/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.90/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.90/0.69 % No SInE strategy applied
% 1.90/0.69 % Search class: FGHPS-FFMM21-SFFFFFNN
% 1.90/0.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.90/0.69 % Starting SubtermCWHack with 136s (1) cores
% 1.90/0.69 % Preprocessing time : 0.001 s
% 1.90/0.69
% 1.90/0.69 % Proof found!
% 1.90/0.69 % SZS status Unsatisfiable
% 1.90/0.69 % SZS output start CNFRefutation
% See solution above
% 1.90/0.69 % Parsed axioms : 44
% 1.90/0.69 % Removed by relevancy pruning/SinE : 0
% 1.90/0.69 % Initial clauses : 44
% 1.90/0.69 % Removed in clause preprocessing : 0
% 1.90/0.69 % Initial clauses in saturation : 44
% 1.90/0.69 % Processed clauses : 10639
% 1.90/0.69 % ...of these trivial : 51
% 1.90/0.69 % ...subsumed : 9143
% 1.90/0.69 % ...remaining for further processing : 1445
% 1.90/0.69 % Other redundant clauses eliminated : 7
% 1.90/0.69 % Clauses deleted for lack of memory : 0
% 1.90/0.69 % Backward-subsumed : 31
% 1.90/0.69 % Backward-rewritten : 674
% 1.90/0.69 % Generated clauses : 60679
% 1.90/0.69 % ...of the previous two non-redundant : 58539
% 1.90/0.69 % ...aggressively subsumed : 0
% 1.90/0.69 % Contextual simplify-reflections : 2
% 1.90/0.69 % Paramodulations : 60611
% 1.90/0.69 % Factorizations : 8
% 1.90/0.69 % NegExts : 0
% 1.90/0.69 % Equation resolutions : 7
% 1.90/0.69 % Disequality decompositions : 0
% 1.90/0.69 % Total rewrite steps : 24309
% 1.90/0.69 % ...of those cached : 23032
% 1.90/0.69 % Propositional unsat checks : 0
% 1.90/0.69 % Propositional check models : 0
% 1.90/0.69 % Propositional check unsatisfiable : 0
% 1.90/0.69 % Propositional clauses : 0
% 1.90/0.69 % Propositional clauses after purity: 0
% 1.90/0.69 % Propositional unsat core size : 0
% 1.90/0.69 % Propositional preprocessing time : 0.000
% 1.90/0.69 % Propositional encoding time : 0.000
% 1.90/0.69 % Propositional solver time : 0.000
% 1.90/0.69 % Success case prop preproc time : 0.000
% 1.90/0.69 % Success case prop encoding time : 0.000
% 1.90/0.69 % Success case prop solver time : 0.000
% 1.90/0.69 % Current number of processed clauses : 681
% 1.90/0.69 % Positive orientable unit clauses : 18
% 1.90/0.69 % Positive unorientable unit clauses: 0
% 1.90/0.69 % Negative unit clauses : 1
% 1.90/0.69 % Non-unit-clauses : 662
% 1.90/0.69 % Current number of unprocessed clauses: 28714
% 1.90/0.69 % ...number of literals in the above : 76869
% 1.90/0.69 % Current number of archived formulas : 0
% 1.90/0.69 % Current number of archived clauses : 762
% 1.90/0.69 % Clause-clause subsumption calls (NU) : 112393
% 1.90/0.69 % Rec. Clause-clause subsumption calls : 104823
% 1.90/0.69 % Non-unit clause-clause subsumptions : 9155
% 1.90/0.69 % Unit Clause-clause subsumption calls : 969
% 1.90/0.69 % Rewrite failures with RHS unbound : 0
% 1.90/0.69 % BW rewrite match attempts : 99
% 1.90/0.69 % BW rewrite match successes : 48
% 1.90/0.69 % Condensation attempts : 0
% 1.90/0.69 % Condensation successes : 0
% 1.90/0.69 % Termbank termtop insertions : 450853
% 1.90/0.69 % Search garbage collected termcells : 38
% 1.90/0.69
% 1.90/0.69 % -------------------------------------------------
% 1.90/0.69 % User time : 0.252 s
% 1.90/0.69 % System time : 0.012 s
% 1.90/0.69 % Total time : 0.264 s
% 1.90/0.69 % Maximum resident set size: 3656 pages
% 1.90/0.69
% 1.90/0.69 % -------------------------------------------------
% 1.90/0.69 % User time : 1.214 s
% 1.90/0.69 % System time : 0.060 s
% 1.90/0.69 % Total time : 1.274 s
% 1.90/0.69 % Maximum resident set size: 4608 pages
% 1.90/0.69 % E exiting
%------------------------------------------------------------------------------