%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP349-1 : 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 : n005.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 0.19s 0.54s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 19
% Syntax : Number of clauses : 118 ( 33 unt; 68 nHn; 96 RR)
% Number of literals : 279 ( 278 equ; 100 neg)
% Maximal clause size : 16 ( 2 avg)
% Maximal term depth : 4 ( 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 : 67 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_23,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_51,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_52,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
cnf(prove_this_53,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_53) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_65,negated_conjecture,
( multiply(X7,sk_c8) != sk_c9
| inverse(X6) != X7
| multiply(X6,X7) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| inverse(X5) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X1) != X2
| multiply(X1,X2) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_65) ).
cnf(prove_this_61,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
cnf(c_0_19,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_20,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_21,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_22,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_23,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_24,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_25,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).
cnf(c_0_27,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
prove_this_34 ).
cnf(c_0_29,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c9 ),
prove_this_26 ).
cnf(c_0_30,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
prove_this_33 ).
cnf(c_0_32,negated_conjecture,
( identity = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c10) = sk_c8 ),
prove_this_18 ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c2) = sk_c1
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( identity = sk_c9
| multiply(sk_c4,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c10) = sk_c8 ),
prove_this_22 ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( identity = sk_c9
| inverse(sk_c2) = sk_c1 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c10) = sk_c8
| multiply(inverse(sk_c6),sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c10) = sk_c8 ),
prove_this_23 ).
cnf(c_0_42,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_43,negated_conjecture,
( sk_c4 != sk_c8
| inverse(sk_c10) = sk_c8 ),
inference(ef,[status(thm)],[c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c10) = sk_c8 ),
prove_this_19 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c9 ),
prove_this_27 ).
cnf(c_0_46,negated_conjecture,
( identity = sk_c9
| multiply(sk_c1,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_38]) ).
cnf(c_0_47,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c10) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
inverse(multiply(inverse(X1),X1)) = identity,
inference(spm,[status(thm)],[c_0_20,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( sk_c4 != sk_c8
| inverse(sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_26,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( identity = multiply(sk_c10,sk_c8)
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( identity = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_20,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( identity = sk_c9
| inverse(sk_c10) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_48]),c_0_20]) ).
cnf(c_0_55,negated_conjecture,
( identity = sk_c9
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_56,negated_conjecture,
( sk_c4 != sk_c8
| inverse(multiply(sk_c10,sk_c8)) = identity ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
multiply(sk_c10,sk_c8) = sk_c9,
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c9) = sk_c9
| inverse(sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c9) = sk_c9
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_53,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c10) = sk_c8 ),
prove_this_20 ).
cnf(c_0_61,negated_conjecture,
( sk_c4 != sk_c8
| identity = inverse(sk_c9) ),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
( sk_c4 = sk_c8
| inverse(sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c8 ),
prove_this_51 ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c10) = sk_c5
| inverse(sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c3) = sk_c8 ),
prove_this_52 ).
cnf(c_0_66,negated_conjecture,
inverse(sk_c9) = sk_c9,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_61]),c_0_26]),c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( sk_c4 != sk_c8
| identity = multiply(sk_c10,sk_c8) ),
inference(spm,[status(thm)],[c_0_27,c_0_43]) ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c8) = sk_c3
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( inverse(sk_c8) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_44]) ).
cnf(c_0_70,negated_conjecture,
( sk_c5 != sk_c8
| inverse(sk_c10) = sk_c8 ),
inference(ef,[status(thm)],[c_0_64]) ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c8) = sk_c3
| inverse(sk_c5) = sk_c10 ),
inference(spm,[status(thm)],[c_0_26,c_0_65]) ).
cnf(c_0_72,negated_conjecture,
identity = multiply(sk_c9,sk_c9),
inference(spm,[status(thm)],[c_0_20,c_0_66]) ).
cnf(c_0_73,negated_conjecture,
( sk_c4 != sk_c8
| identity = sk_c9 ),
inference(rw,[status(thm)],[c_0_67,c_0_57]) ).
cnf(c_0_74,negated_conjecture,
( sk_c3 = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,negated_conjecture,
( sk_c5 != sk_c8
| inverse(sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_26,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c10) = sk_c5
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_26,c_0_71]) ).
cnf(c_0_77,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_20,c_0_20]) ).
cnf(c_0_78,negated_conjecture,
( inverse(sk_c10) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_54,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c10) = sk_c4
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_55,c_0_72]) ).
cnf(c_0_80,negated_conjecture,
( sk_c4 != sk_c8
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(spm,[status(thm)],[c_0_73,c_0_72]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c8 ),
prove_this_53 ).
cnf(c_0_82,negated_conjecture,
( sk_c3 = sk_c10
| multiply(inverse(sk_c10),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_22,c_0_74]) ).
cnf(c_0_83,negated_conjecture,
( sk_c5 != sk_c8
| sk_c3 = sk_c10
| inverse(sk_c10) = sk_c5 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,negated_conjecture,
multiply(inverse(X1),X1) = multiply(sk_c9,sk_c9),
inference(spm,[status(thm)],[c_0_77,c_0_66]) ).
cnf(c_0_85,negated_conjecture,
multiply(sk_c9,sk_c9) = sk_c9,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_86,negated_conjecture,
( inverse(sk_c8) = sk_c3
| multiply(sk_c5,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_26,c_0_81]) ).
cnf(c_0_87,negated_conjecture,
( sk_c5 != sk_c8
| sk_c3 = sk_c10
| multiply(sk_c5,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_88,negated_conjecture,
multiply(inverse(X1),X1) = sk_c9,
inference(rw,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_4 ).
cnf(c_0_90,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
prove_this_2 ).
cnf(c_0_91,negated_conjecture,
( multiply(X7,sk_c8) != sk_c9
| inverse(X6) != X7
| multiply(X6,X7) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| inverse(X5) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X1) != X2
| multiply(X1,X2) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(fof_simplification,[status(thm)],[prove_this_65]) ).
cnf(c_0_92,negated_conjecture,
( sk_c5 != sk_c8
| sk_c8 = sk_c10
| sk_c3 = sk_c10
| inverse(sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
prove_this_61 ).
cnf(c_0_94,negated_conjecture,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_88]),c_0_26]) ).
cnf(c_0_95,negated_conjecture,
( inverse(sk_c10) = sk_c5
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_89]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c10) = sk_c4
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_90]) ).
cnf(c_0_97,negated_conjecture,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_88]),c_0_22]) ).
cnf(c_0_98,negated_conjecture,
multiply(inverse(sk_c10),sk_c9) = sk_c8,
inference(spm,[status(thm)],[c_0_22,c_0_57]) ).
cnf(c_0_99,negated_conjecture,
( multiply(X7,sk_c8) != sk_c9
| inverse(X6) != X7
| multiply(X6,X7) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| inverse(X5) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X1) != X2
| multiply(X1,X2) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
c_0_91 ).
cnf(c_0_100,negated_conjecture,
( sk_c5 != sk_c8
| sk_c3 = sk_c10
| sk_c8 = sk_c10 ),
inference(spm,[status(thm)],[c_0_75,c_0_92]) ).
cnf(c_0_101,negated_conjecture,
( sk_c5 = sk_c10
| sk_c3 = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_94]) ).
cnf(c_0_102,negated_conjecture,
( sk_c4 != sk_c8
| sk_c5 = sk_c8
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_43,c_0_95]) ).
cnf(c_0_103,negated_conjecture,
( sk_c8 = sk_c10
| inverse(sk_c10) = sk_c4 ),
inference(rw,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_104,negated_conjecture,
inverse(sk_c10) = sk_c8,
inference(rw,[status(thm)],[c_0_98,c_0_94]) ).
cnf(c_0_105,negated_conjecture,
( inverse(X5) != sk_c8
| inverse(X4) != sk_c10
| inverse(X3) != sk_c10
| inverse(sk_c10) != sk_c8
| multiply(X5,sk_c9) != sk_c8
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_99])]) ).
cnf(c_0_106,negated_conjecture,
( sk_c5 != sk_c8
| sk_c8 = sk_c10
| sk_c5 = sk_c10 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_107,negated_conjecture,
( sk_c4 != sk_c8
| sk_c8 = sk_c10
| sk_c5 = sk_c8 ),
inference(rw,[status(thm)],[c_0_102,c_0_97]) ).
cnf(c_0_108,negated_conjecture,
( sk_c4 = sk_c8
| sk_c8 = sk_c10 ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( inverse(X5) != sk_c8
| inverse(X4) != sk_c10
| inverse(X3) != sk_c10
| inverse(sk_c10) != sk_c8
| multiply(X5,sk_c9) != sk_c8
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8
| multiply(inverse(X2),sk_c8) != sk_c9
| multiply(inverse(X1),sk_c8) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_57])]) ).
cnf(c_0_110,negated_conjecture,
sk_c8 = sk_c10,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]) ).
cnf(c_0_111,negated_conjecture,
multiply(X1,inverse(X1)) = sk_c9,
inference(spm,[status(thm)],[c_0_88,c_0_26]) ).
cnf(c_0_112,negated_conjecture,
( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X1),sk_c10) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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_109,c_0_97]),c_0_97])]),c_0_110]),c_0_110]),c_0_110]),c_0_111]),c_0_111]),c_0_94]),c_0_94]),c_0_110]),c_0_104]),c_0_110]),c_0_110]),c_0_110])])])]),c_0_104]),c_0_110])]) ).
cnf(c_0_113,negated_conjecture,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[c_0_104,c_0_110]) ).
cnf(c_0_114,negated_conjecture,
multiply(sk_c10,sk_c10) = sk_c9,
inference(rw,[status(thm)],[c_0_57,c_0_110]) ).
cnf(c_0_115,negated_conjecture,
( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(inverse(X1),sk_c10) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114])]) ).
cnf(c_0_116,negated_conjecture,
( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_113]),c_0_114])]) ).
cnf(c_0_117,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_113]),c_0_114])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP349-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 20 20:09:49 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 0.19/0.54 % Version: 3.5.1
% 0.19/0.54 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.54 % Starting sh5l with 300s (1) cores
% 0.19/0.54 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1659333 completed with status 0
% 0.19/0.54 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.19/0.54 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.54 % No SInE strategy applied
% 0.19/0.54 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.19/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.19/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.19/0.54 % Starting new_bool_3 with 136s (1) cores
% 0.19/0.54 % Starting new_bool_1 with 136s (1) cores
% 0.19/0.54 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1659338 completed with status 0
% 0.19/0.54 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.19/0.54 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.54 % No SInE strategy applied
% 0.19/0.54 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.19/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.19/0.54 % Preprocessing time : 0.002 s
% 0.19/0.54 % Presaturation interreduction done
% 0.19/0.54
% 0.19/0.54 % Proof found!
% 0.19/0.54 % SZS status Unsatisfiable
% 0.19/0.54 % SZS output start CNFRefutation
% See solution above
% 0.19/0.54 % Parsed axioms : 68
% 0.19/0.54 % Removed by relevancy pruning/SinE : 0
% 0.19/0.54 % Initial clauses : 68
% 0.19/0.54 % Removed in clause preprocessing : 0
% 0.19/0.54 % Initial clauses in saturation : 68
% 0.19/0.54 % Processed clauses : 1353
% 0.19/0.54 % ...of these trivial : 86
% 0.19/0.54 % ...subsumed : 664
% 0.19/0.54 % ...remaining for further processing : 603
% 0.19/0.54 % Other redundant clauses eliminated : 4
% 0.19/0.54 % Clauses deleted for lack of memory : 0
% 0.19/0.54 % Backward-subsumed : 57
% 0.19/0.54 % Backward-rewritten : 301
% 0.19/0.54 % Generated clauses : 5741
% 0.19/0.54 % ...of the previous two non-redundant : 5432
% 0.19/0.54 % ...aggressively subsumed : 0
% 0.19/0.54 % Contextual simplify-reflections : 11
% 0.19/0.54 % Paramodulations : 5737
% 0.19/0.54 % Factorizations : 2
% 0.19/0.54 % NegExts : 0
% 0.19/0.54 % Equation resolutions : 4
% 0.19/0.54 % Disequality decompositions : 0
% 0.19/0.54 % Total rewrite steps : 2250
% 0.19/0.54 % ...of those cached : 2104
% 0.19/0.54 % Propositional unsat checks : 0
% 0.19/0.54 % Propositional check models : 0
% 0.19/0.54 % Propositional check unsatisfiable : 0
% 0.19/0.54 % Propositional clauses : 0
% 0.19/0.54 % Propositional clauses after purity: 0
% 0.19/0.54 % Propositional unsat core size : 0
% 0.19/0.54 % Propositional preprocessing time : 0.000
% 0.19/0.54 % Propositional encoding time : 0.000
% 0.19/0.54 % Propositional solver time : 0.000
% 0.19/0.54 % Success case prop preproc time : 0.000
% 0.19/0.54 % Success case prop encoding time : 0.000
% 0.19/0.54 % Success case prop solver time : 0.000
% 0.19/0.54 % Current number of processed clauses : 175
% 0.19/0.54 % Positive orientable unit clauses : 14
% 0.19/0.54 % Positive unorientable unit clauses: 0
% 0.19/0.54 % Negative unit clauses : 0
% 0.19/0.54 % Non-unit-clauses : 161
% 0.19/0.54 % Current number of unprocessed clauses: 3356
% 0.19/0.54 % ...number of literals in the above : 11149
% 0.19/0.54 % Current number of archived formulas : 0
% 0.19/0.54 % Current number of archived clauses : 426
% 0.19/0.54 % Clause-clause subsumption calls (NU) : 7493
% 0.19/0.54 % Rec. Clause-clause subsumption calls : 6212
% 0.19/0.54 % Non-unit clause-clause subsumptions : 680
% 0.19/0.54 % Unit Clause-clause subsumption calls : 861
% 0.19/0.54 % Rewrite failures with RHS unbound : 17
% 0.19/0.54 % BW rewrite match attempts : 76
% 0.19/0.54 % BW rewrite match successes : 44
% 0.19/0.54 % Condensation attempts : 0
% 0.19/0.54 % Condensation successes : 0
% 0.19/0.54 % Termbank termtop insertions : 56384
% 0.19/0.54 % Search garbage collected termcells : 43
% 0.19/0.54
% 0.19/0.54 % -------------------------------------------------
% 0.19/0.54 % User time : 0.076 s
% 0.19/0.54 % System time : 0.011 s
% 0.19/0.54 % Total time : 0.087 s
% 0.19/0.54 % Maximum resident set size: 3664 pages
% 0.19/0.54
% 0.19/0.54 % -------------------------------------------------
% 0.19/0.54 % User time : 0.393 s
% 0.19/0.54 % System time : 0.029 s
% 0.19/0.54 % Total time : 0.422 s
% 0.19/0.54 % Maximum resident set size: 4864 pages
% 0.19/0.54 % E exiting
%------------------------------------------------------------------------------