%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP221-1 : 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 : n017.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 12:39:01 PM UTC 2026
% Result : Unsatisfiable 13.65s 2.41s
% Output : CNFRefutation 13.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 29
% Syntax : Number of clauses : 146 ( 26 unt; 116 nHn; 123 RR)
% Number of literals : 311 ( 310 equ; 54 neg)
% Maximal clause size : 14 ( 2 avg)
% Maximal term depth : 5 ( 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 : 63 ( 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_20,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_44,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_43,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
cnf(prove_this_48,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
cnf(prove_this_42,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_38,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_37,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_47,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_46,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_40,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_34,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_49,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c10
| inverse(sk_c10) != sk_c9
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != X4
| multiply(sk_c10,X4) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != X3
| multiply(X2,X3) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
cnf(c_0_29,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_30,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_31,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_32,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_33,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_34,plain,
multiply(inverse(inverse(inverse(X1))),X1) = identity,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c2) = sk_c3 ),
prove_this_20 ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_44 ).
cnf(c_0_37,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_34]),c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
prove_this_19 ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c3,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
prove_this_43 ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_42,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_48 ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c3,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c10) = sk_c6
| multiply(sk_c3,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c10) = sk_c6
| multiply(sk_c10,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
prove_this_42 ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
prove_this_14 ).
cnf(c_0_51,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c3,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_37]) ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
prove_this_38 ).
cnf(c_0_54,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c10,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c10,sk_c7) = identity
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c10,sk_c7) = identity
| multiply(sk_c4,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_49]) ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
prove_this_13 ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c10) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_37,c_0_50]) ).
cnf(c_0_59,negated_conjecture,
( sk_c6 = sk_c9
| inverse(sk_c3) = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_51]),c_0_52]) ).
cnf(c_0_60,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
prove_this_37 ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c10) = sk_c6
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(spm,[status(thm)],[c_0_37,c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( sk_c6 = sk_c9
| inverse(sk_c10) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_54]),c_0_52]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c4) = sk_c10 ),
prove_this_47 ).
cnf(c_0_64,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_65,negated_conjecture,
( identity = sk_c5
| multiply(sk_c10,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_66,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
prove_this_32 ).
cnf(c_0_67,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c2,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_59]) ).
cnf(c_0_69,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c4,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_62]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c5 ),
prove_this_41 ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c4,sk_c10) = identity
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_63]) ).
cnf(c_0_73,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_74,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_64]) ).
cnf(c_0_75,negated_conjecture,
( identity = sk_c5
| inverse(sk_c10) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_65]),c_0_52]) ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
prove_this_31 ).
cnf(c_0_77,negated_conjecture,
( inverse(sk_c10) = sk_c6
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(spm,[status(thm)],[c_0_37,c_0_66]) ).
cnf(c_0_78,negated_conjecture,
( identity = sk_c9
| sk_c6 = sk_c9 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_79,negated_conjecture,
( identity = sk_c5
| sk_c6 = sk_c9 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c10 ),
prove_this_46 ).
cnf(c_0_81,negated_conjecture,
( identity = sk_c5
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_82,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_42]),c_0_52]) ).
cnf(c_0_83,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_30,c_0_74]) ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
prove_this_36 ).
cnf(c_0_85,negated_conjecture,
( identity = sk_c5
| multiply(sk_c7,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_75]) ).
cnf(c_0_86,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c1) = sk_c10 ),
prove_this_2 ).
cnf(c_0_87,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_88,negated_conjecture,
( sk_c6 = sk_c9
| sk_c5 = sk_c9 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
prove_this_40 ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c4,sk_c10) = identity
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_80]) ).
cnf(c_0_91,negated_conjecture,
( identity = sk_c5
| multiply(inverse(sk_c7),sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_32,c_0_81]) ).
cnf(c_0_92,negated_conjecture,
( identity = sk_c5
| inverse(sk_c7) = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_65]),c_0_83]),c_0_31]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
prove_this_35 ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c7,sk_c10) = identity
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_84]) ).
cnf(c_0_95,negated_conjecture,
( identity = sk_c8
| identity = sk_c5 ),
inference(spm,[status(thm)],[c_0_81,c_0_85]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
prove_this_1 ).
cnf(c_0_97,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_86]) ).
cnf(c_0_98,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_29,c_0_42]) ).
cnf(c_0_99,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c10,sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_100,negated_conjecture,
( identity = sk_c5
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_101,negated_conjecture,
( identity = sk_c5
| multiply(sk_c10,sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_102,negated_conjecture,
( identity = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_103,negated_conjecture,
( identity = sk_c8
| multiply(X1,sk_c5) = X1 ),
inference(spm,[status(thm)],[c_0_52,c_0_95]) ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( inverse(sk_c10) = sk_c6
| multiply(sk_c10,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_37,c_0_97]) ).
cnf(c_0_106,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c5,X1) = X1 ),
inference(spm,[status(thm)],[c_0_31,c_0_79]) ).
cnf(c_0_107,negated_conjecture,
( identity = sk_c10
| sk_c6 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_42]),c_0_52]) ).
cnf(c_0_108,negated_conjecture,
( sk_c9 = sk_c10
| identity = sk_c5 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_109,negated_conjecture,
( sk_c9 = sk_c10
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c10,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
( sk_c6 = sk_c9
| inverse(sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_106]) ).
cnf(c_0_112,negated_conjecture,
( sk_c6 = sk_c9
| sk_c5 = sk_c10 ),
inference(spm,[status(thm)],[c_0_79,c_0_107]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
prove_this_21 ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
prove_this_34 ).
cnf(c_0_115,negated_conjecture,
( sk_c5 = sk_c8
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_116,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_8 ).
cnf(c_0_117,negated_conjecture,
( sk_c6 = sk_c9
| inverse(sk_c10) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_110]),c_0_52]) ).
cnf(c_0_118,negated_conjecture,
( sk_c6 = sk_c9
| inverse(sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_119,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
prove_this_15 ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c2,sk_c3) = identity
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_42,c_0_113]) ).
cnf(c_0_121,negated_conjecture,
( sk_c9 = sk_c10
| multiply(X1,sk_c8) = X1 ),
inference(spm,[status(thm)],[c_0_52,c_0_109]) ).
cnf(c_0_122,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_123,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_7 ).
cnf(c_0_124,negated_conjecture,
( inverse(sk_c10) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_37,c_0_116]) ).
cnf(c_0_125,negated_conjecture,
( identity = sk_c1
| sk_c6 = sk_c9 ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_126,negated_conjecture,
( identity = sk_c9
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_127,negated_conjecture,
sk_c9 = sk_c10,
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_128,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_129,negated_conjecture,
( sk_c6 = sk_c9
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_78,c_0_125]) ).
cnf(c_0_130,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_98]),c_0_52]) ).
cnf(c_0_131,negated_conjecture,
( identity = sk_c10
| multiply(sk_c6,sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127]),c_0_127]) ).
cnf(c_0_132,negated_conjecture,
( sk_c6 = sk_c9
| multiply(sk_c9,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_133,negated_conjecture,
( identity = sk_c10
| inverse(sk_c6) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_42]) ).
cnf(c_0_134,negated_conjecture,
( sk_c6 = sk_c9
| multiply(inverse(sk_c9),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_32,c_0_132]) ).
cnf(c_0_135,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c10
| inverse(sk_c10) != sk_c9
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != X4
| multiply(sk_c10,X4) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != X3
| multiply(X2,X3) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ),
inference(fof_simplification,[status(thm)],[prove_this_49]) ).
cnf(c_0_136,negated_conjecture,
( identity = sk_c6
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_133]),c_0_31]) ).
cnf(c_0_137,negated_conjecture,
( identity = sk_c10
| sk_c6 = sk_c10 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_127]),c_0_30]),c_0_127]),c_0_127]) ).
cnf(c_0_138,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c10
| inverse(sk_c10) != sk_c9
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != X4
| multiply(sk_c10,X4) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != X3
| multiply(X2,X3) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ),
c_0_135 ).
cnf(c_0_139,negated_conjecture,
identity = sk_c10,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_136]),c_0_137]) ).
cnf(c_0_140,negated_conjecture,
( identity != sk_c9
| inverse(X5) != sk_c10
| inverse(X2) != sk_c10
| inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(inverse(X3),sk_c10) != sk_c9
| multiply(sk_c10,multiply(X2,sk_c10)) != sk_c9
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_138])])]),c_0_42]) ).
cnf(c_0_141,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_52,c_0_139]) ).
cnf(c_0_142,plain,
multiply(sk_c10,X1) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_139]) ).
cnf(c_0_143,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_139]),c_0_139]) ).
cnf(c_0_144,negated_conjecture,
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(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_127]),c_0_127]),c_0_127]),c_0_127]),c_0_127]),c_0_127]),c_0_127]),c_0_141]),c_0_142]),c_0_141]),c_0_142]),c_0_141]),c_0_141]),c_0_141]),c_0_143]),c_0_139])])])])])]),c_0_143])]) ).
cnf(c_0_145,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_86,c_0_144]),c_0_144]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP221-1 : 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 : n017.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 20:02:11 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 13.65/2.41 % Version: 3.5.1
% 13.65/2.41 % Preprocessing class: FSMSSMSMSSSNFFN.
% 13.65/2.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.65/2.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 13.65/2.41 % Starting new_bool_3 with 300s (1) cores
% 13.65/2.41 % Starting new_bool_1 with 300s (1) cores
% 13.65/2.41 % Starting sh5l with 300s (1) cores
% 13.65/2.41 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 510603 completed with status 0
% 13.65/2.41 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 13.65/2.41 % Preprocessing class: FSMSSMSMSSSNFFN.
% 13.65/2.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.65/2.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 13.65/2.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.65/2.41 % No SInE strategy applied
% 13.65/2.41 % Search class: FGHPS-FFMM21-SFFFFFNN
% 13.65/2.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.65/2.41 % Starting SubtermCWHack with 136s (1) cores
% 13.65/2.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 13.65/2.41 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 13.65/2.41 % Starting new_bool_3 with 136s (1) cores
% 13.65/2.41 % Starting new_bool_1 with 136s (1) cores
% 13.65/2.41 % SubtermCWHack with pid 510607 completed with status 0
% 13.65/2.41 % Result found by SubtermCWHack
% 13.65/2.41 % Preprocessing class: FSMSSMSMSSSNFFN.
% 13.65/2.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.65/2.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 13.65/2.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.65/2.41 % No SInE strategy applied
% 13.65/2.41 % Search class: FGHPS-FFMM21-SFFFFFNN
% 13.65/2.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.65/2.41 % Starting SubtermCWHack with 136s (1) cores
% 13.65/2.41 % Preprocessing time : 0.001 s
% 13.65/2.41
% 13.65/2.41 % Proof found!
% 13.65/2.41 % SZS status Unsatisfiable
% 13.65/2.41 % SZS output start CNFRefutation
% See solution above
% 13.65/2.41 % Parsed axioms : 52
% 13.65/2.41 % Removed by relevancy pruning/SinE : 0
% 13.65/2.41 % Initial clauses : 52
% 13.65/2.41 % Removed in clause preprocessing : 0
% 13.65/2.41 % Initial clauses in saturation : 52
% 13.65/2.41 % Processed clauses : 57806
% 13.65/2.41 % ...of these trivial : 301
% 13.65/2.41 % ...subsumed : 52448
% 13.65/2.41 % ...remaining for further processing : 5057
% 13.65/2.41 % Other redundant clauses eliminated : 7
% 13.65/2.41 % Clauses deleted for lack of memory : 0
% 13.65/2.41 % Backward-subsumed : 102
% 13.65/2.41 % Backward-rewritten : 2584
% 13.65/2.41 % Generated clauses : 452181
% 13.65/2.41 % ...of the previous two non-redundant : 443677
% 13.65/2.41 % ...aggressively subsumed : 0
% 13.65/2.41 % Contextual simplify-reflections : 7
% 13.65/2.41 % Paramodulations : 452078
% 13.65/2.41 % Factorizations : 18
% 13.65/2.41 % NegExts : 0
% 13.65/2.41 % Equation resolutions : 7
% 13.65/2.41 % Disequality decompositions : 0
% 13.65/2.41 % Total rewrite steps : 97738
% 13.65/2.41 % ...of those cached : 95513
% 13.65/2.41 % Propositional unsat checks : 0
% 13.65/2.41 % Propositional check models : 0
% 13.65/2.41 % Propositional check unsatisfiable : 0
% 13.65/2.41 % Propositional clauses : 0
% 13.65/2.41 % Propositional clauses after purity: 0
% 13.65/2.41 % Propositional unsat core size : 0
% 13.65/2.41 % Propositional preprocessing time : 0.000
% 13.65/2.41 % Propositional encoding time : 0.000
% 13.65/2.41 % Propositional solver time : 0.000
% 13.65/2.41 % Success case prop preproc time : 0.000
% 13.65/2.41 % Success case prop encoding time : 0.000
% 13.65/2.41 % Success case prop solver time : 0.000
% 13.65/2.41 % Current number of processed clauses : 2286
% 13.65/2.41 % Positive orientable unit clauses : 19
% 13.65/2.41 % Positive unorientable unit clauses: 0
% 13.65/2.41 % Negative unit clauses : 1
% 13.65/2.41 % Non-unit-clauses : 2266
% 13.65/2.41 % Current number of unprocessed clauses: 214129
% 13.65/2.41 % ...number of literals in the above : 640959
% 13.65/2.41 % Current number of archived formulas : 0
% 13.65/2.41 % Current number of archived clauses : 2769
% 13.65/2.41 % Clause-clause subsumption calls (NU) : 1234602
% 13.65/2.41 % Rec. Clause-clause subsumption calls : 945282
% 13.65/2.41 % Non-unit clause-clause subsumptions : 52539
% 13.65/2.41 % Unit Clause-clause subsumption calls : 1641
% 13.65/2.41 % Rewrite failures with RHS unbound : 0
% 13.65/2.41 % BW rewrite match attempts : 101
% 13.65/2.41 % BW rewrite match successes : 52
% 13.65/2.41 % Condensation attempts : 0
% 13.65/2.41 % Condensation successes : 0
% 13.65/2.41 % Termbank termtop insertions : 3311219
% 13.65/2.41 % Search garbage collected termcells : 40
% 13.65/2.41
% 13.65/2.41 % -------------------------------------------------
% 13.65/2.41 % User time : 1.852 s
% 13.65/2.41 % System time : 0.074 s
% 13.65/2.41 % Total time : 1.926 s
% 13.65/2.41 % Maximum resident set size: 3608 pages
% 13.65/2.41
% 13.65/2.41 % -------------------------------------------------
% 13.65/2.41 % User time : 9.161 s
% 13.65/2.41 % System time : 0.396 s
% 13.65/2.41 % Total time : 9.556 s
% 13.65/2.41 % Maximum resident set size: 4864 pages
% 13.65/2.41 % E exiting
%------------------------------------------------------------------------------