%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP350-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:39:22 PM UTC 2026
% Result : Unsatisfiable 41.17s 6.59s
% Output : CNFRefutation 41.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 22
% Syntax : Number of clauses : 121 ( 19 unt; 96 nHn; 105 RR)
% Number of literals : 284 ( 283 equ; 72 neg)
% Maximal clause size : 17 ( 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 : 55 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_52,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_51,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_42,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_41,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_54,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_53,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_53) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_71,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c11
| multiply(sk_c9,sk_c11) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c11) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_71) ).
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)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_25]) ).
cnf(c_0_27,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_26]) ).
cnf(c_0_28,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c10 ),
prove_this_52 ).
cnf(c_0_29,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c10) = sk_c9 ),
prove_this_12 ).
cnf(c_0_30,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_27]) ).
cnf(c_0_31,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
prove_this_1 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
prove_this_51 ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c10) = sk_c2
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
prove_this_2 ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
prove_this_42 ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
prove_this_41 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c10) = sk_c9 ),
prove_this_11 ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c10) = sk_c2
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
cnf(c_0_42,negated_conjecture,
( sk_c2 = sk_c9
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
prove_this_21 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_23,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_32 ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
( sk_c2 = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,negated_conjecture,
( sk_c2 = sk_c9
| inverse(sk_c11) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_42]),c_0_27]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
prove_this_54 ).
cnf(c_0_51,negated_conjecture,
( identity = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_43]),c_0_23]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c11,sk_c3) = identity
| multiply(inverse(sk_c1),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_47,c_0_38]) ).
cnf(c_0_56,negated_conjecture,
( sk_c2 = sk_c9
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( sk_c2 = sk_c9
| inverse(sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c10) = sk_c9 ),
prove_this_14 ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c10,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_50]) ).
cnf(c_0_60,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c10),sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_25,c_0_51]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(inverse(inverse(sk_c3)),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_25,c_0_52]) ).
cnf(c_0_62,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
prove_this_22 ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(inverse(sk_c1),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_25,c_0_55]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
prove_this_31 ).
cnf(c_0_66,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_67,negated_conjecture,
( sk_c2 = sk_c9
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_58]) ).
cnf(c_0_69,negated_conjecture,
( inverse(sk_c10) = sk_c2
| multiply(sk_c10,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_59]) ).
cnf(c_0_70,negated_conjecture,
( identity = sk_c10
| multiply(inverse(sk_c10),multiply(sk_c9,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_60]) ).
cnf(c_0_71,negated_conjecture,
( identity = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_23]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(sk_c11,multiply(sk_c3,X1)) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_63]),c_0_24]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c11,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_74,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_50]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
prove_this_5 ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
prove_this_53 ).
cnf(c_0_77,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_66,c_0_27]) ).
cnf(c_0_78,negated_conjecture,
( identity = sk_c10
| sk_c2 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_67]),c_0_23]) ).
cnf(c_0_79,negated_conjecture,
( sk_c2 = sk_c9
| multiply(sk_c10,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_80,negated_conjecture,
( identity = sk_c10
| multiply(sk_c11,sk_c11) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_23]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c10) = sk_c2
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_30,c_0_74]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(inverse(sk_c5),sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_25,c_0_75]) ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
prove_this_6 ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
prove_this_13 ).
cnf(c_0_86,negated_conjecture,
( inverse(sk_c10) = sk_c2
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_76]) ).
cnf(c_0_87,negated_conjecture,
( sk_c2 = sk_c9
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_88,negated_conjecture,
( sk_c2 = sk_c9
| inverse(sk_c10) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_79]),c_0_27]) ).
cnf(c_0_89,negated_conjecture,
( identity = sk_c10
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_90,negated_conjecture,
( inverse(sk_c10) = sk_c2
| multiply(sk_c4,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_82]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_75]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_93,negated_conjecture,
( sk_c2 = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_94,negated_conjecture,
( sk_c4 = sk_c10
| sk_c2 = sk_c9 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_95,negated_conjecture,
identity = sk_c10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_89]),c_0_23])]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_90]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = multiply(sk_c11,sk_c11) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
( sk_c2 = sk_c9
| multiply(sk_c10,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_23,c_0_87]) ).
cnf(c_0_99,negated_conjecture,
( sk_c2 = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_100,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_95]),c_0_95]) ).
cnf(c_0_101,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[c_0_96,c_0_95]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c3,multiply(sk_c11,X1)) = multiply(sk_c10,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_32]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c11,sk_c11) = sk_c11 ),
inference(spm,[status(thm)],[c_0_75,c_0_97]) ).
cnf(c_0_104,negated_conjecture,
( identity = sk_c9
| sk_c2 = sk_c9 ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_105,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_85,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
( sk_c2 = sk_c10
| multiply(sk_c4,sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_101]),c_0_100]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c3,sk_c11) = multiply(sk_c10,sk_c11) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_108,negated_conjecture,
( sk_c2 = sk_c9
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_78,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( sk_c9 = sk_c10
| sk_c2 = sk_c10 ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_110,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c11
| multiply(sk_c9,sk_c11) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c11) != sk_c9 ),
inference(fof_simplification,[status(thm)],[prove_this_71]) ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c10,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_32,c_0_107]) ).
cnf(c_0_112,negated_conjecture,
sk_c9 = sk_c10,
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_113,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c11
| multiply(sk_c9,sk_c11) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c11) != sk_c9 ),
c_0_110 ).
cnf(c_0_114,negated_conjecture,
multiply(sk_c10,sk_c11) = sk_c10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112])]) ).
cnf(c_0_115,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| inverse(X4) != sk_c11
| inverse(X3) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(X6,sk_c10) != sk_c11
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,inverse(X2)) != sk_c11
| multiply(sk_c9,sk_c11) != sk_c10
| multiply(sk_c10,sk_c11) != sk_c9
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_113])]) ).
cnf(c_0_116,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_95]) ).
cnf(c_0_117,negated_conjecture,
sk_c11 = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_114]),c_0_23]),c_0_95]) ).
cnf(c_0_118,negated_conjecture,
( inverse(X2) != sk_c10
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_100]),c_0_116]),c_0_117]),c_0_117]),c_0_116]),c_0_112]),c_0_112]),c_0_117]),c_0_116]),c_0_117]),c_0_116]),c_0_112]),c_0_117]),c_0_116]),c_0_112]),c_0_116]),c_0_116]),c_0_117]),c_0_112]),c_0_117]),c_0_117])])])])])]),c_0_100])]) ).
cnf(c_0_119,negated_conjecture,
( inverse(X1) != X1
| inverse(X1) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_100]),c_0_116]),c_0_116]),c_0_116])]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_119,c_0_100]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP350-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.52 % Computer : n011.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Sun Sep 20 20:09:55 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.52 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.56 Running first-order theorem proving
% 0.15/0.56 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 41.17/6.59 % Version: 3.5.1
% 41.17/6.59 % Preprocessing class: FSLSSMSMSSSNFFN.
% 41.17/6.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 41.17/6.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 41.17/6.59 % Starting new_bool_3 with 300s (1) cores
% 41.17/6.59 % Starting new_bool_1 with 300s (1) cores
% 41.17/6.59 % Starting sh5l with 300s (1) cores
% 41.17/6.59 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 68111 completed with status 0
% 41.17/6.59 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 41.17/6.59 % Preprocessing class: FSLSSMSMSSSNFFN.
% 41.17/6.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 41.17/6.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 41.17/6.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 41.17/6.59 % No SInE strategy applied
% 41.17/6.59 % Search class: FGHPS-FFMM21-SFFFFFNN
% 41.17/6.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 41.17/6.59 % Starting SubtermCWHack with 136s (1) cores
% 41.17/6.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 41.17/6.59 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 41.17/6.59 % Starting new_bool_3 with 136s (1) cores
% 41.17/6.59 % Starting new_bool_1 with 136s (1) cores
% 41.17/6.59 % new_bool_1 with pid 68119 completed with status 0
% 41.17/6.59 % Result found by new_bool_1
% 41.17/6.59 % Preprocessing class: FSLSSMSMSSSNFFN.
% 41.17/6.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 41.17/6.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 41.17/6.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 41.17/6.59 % No SInE strategy applied
% 41.17/6.59 % Search class: FGHPS-FFMM21-SFFFFFNN
% 41.17/6.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 41.17/6.59 % Starting SubtermCWHack with 136s (1) cores
% 41.17/6.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 41.17/6.59 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 41.17/6.59 % Starting new_bool_3 with 136s (1) cores
% 41.17/6.59 % Starting new_bool_1 with 136s (1) cores
% 41.17/6.59 % Preprocessing time : 0.001 s
% 41.17/6.59 % Presaturation interreduction done
% 41.17/6.59
% 41.17/6.59 % Proof found!
% 41.17/6.59 % SZS status Unsatisfiable
% 41.17/6.59 % SZS output start CNFRefutation
% See solution above
% 41.17/6.59 % Parsed axioms : 74
% 41.17/6.59 % Removed by relevancy pruning/SinE : 0
% 41.17/6.59 % Initial clauses : 74
% 41.17/6.59 % Removed in clause preprocessing : 0
% 41.17/6.59 % Initial clauses in saturation : 74
% 41.17/6.59 % Processed clauses : 62865
% 41.17/6.59 % ...of these trivial : 950
% 41.17/6.59 % ...subsumed : 55635
% 41.17/6.59 % ...remaining for further processing : 6280
% 41.17/6.59 % Other redundant clauses eliminated : 347
% 41.17/6.59 % Clauses deleted for lack of memory : 0
% 41.17/6.59 % Backward-subsumed : 1359
% 41.17/6.59 % Backward-rewritten : 4385
% 41.17/6.59 % Generated clauses : 466534
% 41.17/6.59 % ...of the previous two non-redundant : 462301
% 41.17/6.59 % ...aggressively subsumed : 0
% 41.17/6.59 % Contextual simplify-reflections : 480
% 41.17/6.59 % Paramodulations : 466184
% 41.17/6.59 % Factorizations : 12
% 41.17/6.59 % NegExts : 0
% 41.17/6.59 % Equation resolutions : 358
% 41.17/6.59 % Disequality decompositions : 0
% 41.17/6.59 % Total rewrite steps : 101345
% 41.17/6.59 % ...of those cached : 99439
% 41.17/6.59 % Propositional unsat checks : 1
% 41.17/6.59 % Propositional check models : 0
% 41.17/6.59 % Propositional check unsatisfiable : 0
% 41.17/6.59 % Propositional clauses : 0
% 41.17/6.59 % Propositional clauses after purity: 0
% 41.17/6.59 % Propositional unsat core size : 0
% 41.17/6.59 % Propositional preprocessing time : 0.000
% 41.17/6.59 % Propositional encoding time : 0.227
% 41.17/6.59 % Propositional solver time : 0.076
% 41.17/6.59 % Success case prop preproc time : 0.000
% 41.17/6.59 % Success case prop encoding time : 0.000
% 41.17/6.59 % Success case prop solver time : 0.000
% 41.17/6.59 % Current number of processed clauses : 450
% 41.17/6.59 % Positive orientable unit clauses : 18
% 41.17/6.59 % Positive unorientable unit clauses: 0
% 41.17/6.59 % Negative unit clauses : 0
% 41.17/6.59 % Non-unit-clauses : 432
% 41.17/6.59 % Current number of unprocessed clauses: 389995
% 41.17/6.59 % ...number of literals in the above : 2554455
% 41.17/6.59 % Current number of archived formulas : 0
% 41.17/6.59 % Current number of archived clauses : 5818
% 41.17/6.59 % Clause-clause subsumption calls (NU) : 3841802
% 41.17/6.59 % Rec. Clause-clause subsumption calls : 769195
% 41.17/6.59 % Non-unit clause-clause subsumptions : 57423
% 41.17/6.59 % Unit Clause-clause subsumption calls : 5270
% 41.17/6.59 % Rewrite failures with RHS unbound : 0
% 41.17/6.59 % BW rewrite match attempts : 121
% 41.17/6.59 % BW rewrite match successes : 97
% 41.17/6.59 % Condensation attempts : 0
% 41.17/6.59 % Condensation successes : 0
% 41.17/6.59 % Termbank termtop insertions : 11947221
% 41.17/6.59 % Search garbage collected termcells : 47
% 41.17/6.59
% 41.17/6.59 % -------------------------------------------------
% 41.17/6.59 % User time : 5.605 s
% 41.17/6.59 % System time : 0.253 s
% 41.17/6.59 % Total time : 5.857 s
% 41.17/6.59 % Maximum resident set size: 3668 pages
% 41.17/6.59
% 41.17/6.59 % -------------------------------------------------
% 41.17/6.59 % User time : 28.235 s
% 41.17/6.59 % System time : 1.333 s
% 41.17/6.59 % Total time : 29.567 s
% 41.17/6.59 % Maximum resident set size: 4864 pages
% 41.17/6.59 % E exiting
%------------------------------------------------------------------------------