%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL898+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 01:17:42 PM UTC 2026
% Result : Theorem 137.48s 25.61s
% Output : CNFRefutation 137.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 108 ( 85 unt; 0 def)
% Number of atoms : 136 ( 60 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 24 ~; 21 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 217 ( 19 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_07,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(sos_14,axiom,
! [X1] : '+'(X1,'1') = '1',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_14) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(sos_04,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).
fof(sos_12,axiom,
! [X1,X2] : '+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(sos_13,axiom,
! [X1] : '==>'('==>'(X1,'1'),'1') = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
fof(sos_01,axiom,
! [X1,X2,X3] : '+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
fof(sos_06,axiom,
! [X7,X8] :
( ( '>='(X8,X7)
& '>='(X7,X8) )
=> X7 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
fof(sos_08,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(sos_09,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
fof(sos_10,axiom,
! [X15,X16,X17] :
( '>='(X15,X16)
=> '>='('==>'(X16,X17),'==>'(X15,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
fof(sos_11,axiom,
! [X18,X19,X20] :
( '>='(X18,X19)
=> '>='('==>'(X20,X18),'==>'(X20,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_11) ).
fof(goals_15,conjecture,
! [X21,X22] : '==>'('==>'(X21,X22),X22) = '==>'('==>'(X22,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
fof(c_0_14,plain,
! [X35,X36,X37] :
( ( '>='('+'(X35,X36),X37)
| ~ '>='(X36,'==>'(X35,X37)) )
& ( '>='(X36,'==>'(X35,X37))
| ~ '>='('+'(X35,X36),X37) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])])]) ).
fof(c_0_15,plain,
! [X51] : '+'(X51,'1') = '1',
inference(variable_rename,[status(thm)],[sos_14]) ).
fof(c_0_16,plain,
! [X26,X27] : '+'(X26,X27) = '+'(X27,X26),
inference(variable_rename,[status(thm)],[sos_02]) ).
cnf(c_0_17,plain,
( ~ '>='('+'(X1,X2),X3)
| '>='(X2,'==>'(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
'+'(X1,'1') = '1',
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X29] : '>='(X29,X29),
inference(variable_rename,[status(thm)],[sos_04]) ).
cnf(c_0_20,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X48,X49] : '+'(X48,'==>'(X48,X49)) = '+'(X49,'==>'(X49,X48)),
inference(variable_rename,[status(thm)],[sos_12]) ).
cnf(c_0_22,plain,
( ~ '>='('1',X2)
| '>='('1','==>'(X1,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X50] : '==>'('==>'(X50,'1'),'1') = X50,
inference(variable_rename,[status(thm)],[sos_13]) ).
fof(c_0_25,plain,
! [X23,X24,X25] : '+'('+'(X23,X24),X25) = '+'(X23,'+'(X24,X25)),
inference(variable_rename,[status(thm)],[sos_01]) ).
fof(c_0_26,plain,
! [X28] : '+'(X28,'0') = X28,
inference(variable_rename,[status(thm)],[sos_03]) ).
cnf(c_0_27,plain,
'+'('1',X1) = '1',
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_28,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
'>='('1','==>'(X1,'1')),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
'==>'('==>'(X1,'1'),'1') = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
'+'(X1,'==>'(X1,'1')) = '1',
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
'>='('1',X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
'+'(X1,'+'(X2,X3)) = '+'(X2,'+'(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_20]),c_0_31]) ).
fof(c_0_36,plain,
! [X33,X34] :
( X33 = X34
| ~ '>='(X34,X33)
| ~ '>='(X33,X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])])]) ).
cnf(c_0_37,plain,
( ~ '>='(X1,X2)
| '>='('0','==>'(X1,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_38,plain,
'>='('==>'(X1,'1'),'==>'(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_33]),c_0_34])]) ).
fof(c_0_39,plain,
! [X38] : '>='(X38,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
cnf(c_0_40,plain,
'+'(X1,'+'('==>'(X1,'1'),X2)) = '1',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_33]),c_0_27]) ).
cnf(c_0_41,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_42,plain,
'+'(X1,'+'(X2,'==>'(X1,'1'))) = '1',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_18]) ).
cnf(c_0_43,plain,
'+'(X1,'+'('==>'(X1,X2),X3)) = '+'(X2,'+'('==>'(X2,X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_31]) ).
cnf(c_0_44,plain,
( ~ '>='(X2,X1)
| ~ '>='(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
'>='('0','==>'('==>'(X1,'1'),'==>'(X1,X2))),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
'+'(X1,'+'(X2,X3)) = '+'(X2,'+'(X3,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_48,plain,
'+'(X1,'+'(X2,'==>'(X2,'==>'(X1,'1')))) = '1',
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_49,plain,
'>='('0','==>'(X1,'==>'(X2,'+'(X2,X1)))),
inference(spm,[status(thm)],[c_0_37,c_0_41]) ).
cnf(c_0_50,plain,
'+'(X1,'+'('==>'(X1,X2),'==>'(X2,'1'))) = '1',
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,plain,
'==>'('==>'(X1,'1'),'==>'(X1,X2)) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_52,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_53,plain,
'>='(X1,'==>'(X2,'==>'(X3,'+'(X3,'+'(X2,X1))))),
inference(spm,[status(thm)],[c_0_17,c_0_41]) ).
cnf(c_0_54,plain,
'+'(X1,'+'(X2,'==>'(X1,'==>'(X2,'1')))) = '1',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_20]) ).
cnf(c_0_55,plain,
( ~ '>='(X1,'==>'(X2,X3))
| '>='('+'(X2,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_56,plain,
! [X39,X40,X41] :
( '>='('+'(X39,X41),'+'(X40,X41))
| ~ '>='(X39,X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])])]) ).
cnf(c_0_57,plain,
'==>'(X1,'==>'(X2,'+'(X2,X1))) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_49]),c_0_46])]) ).
cnf(c_0_58,plain,
'+'('==>'(X1,'1'),'==>'('==>'(X1,X2),'1')) = '1',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_59,plain,
'>='('==>'(X1,'==>'(X2,'1')),'==>'(X2,'==>'(X1,'1'))),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
( ~ '>='('+'(X1,X2),X3)
| '>='(X1,'==>'(X2,X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_61,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_55,c_0_23]) ).
fof(c_0_62,plain,
! [X42,X43,X44] :
( '>='('==>'(X43,X44),'==>'(X42,X44))
| ~ '>='(X42,X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])])]) ).
cnf(c_0_63,plain,
( ~ '>='(X1,X2)
| '>='('+'(X1,X3),'+'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
'==>'('==>'('==>'(X1,X2),'1'),X1) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_30]) ).
cnf(c_0_65,plain,
'==>'(X1,'==>'(X2,'1')) = '==>'(X2,'==>'(X1,'1')),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_59]),c_0_59])]) ).
cnf(c_0_66,plain,
'>='(X1,'==>'('==>'(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,plain,
( ~ '>='(X1,X2)
| '>='('==>'(X2,X3),'==>'(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_68,plain,
! [X45,X46,X47] :
( '>='('==>'(X47,X45),'==>'(X47,X46))
| ~ '>='(X45,X46) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])])]) ).
cnf(c_0_69,plain,
'>='('+'(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_46]),c_0_52]) ).
cnf(c_0_70,plain,
'+'(X1,'==>'(X1,'==>'('==>'(X1,X2),'1'))) = '==>'('==>'(X1,X2),'1'),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_64]),c_0_32]) ).
cnf(c_0_71,plain,
'==>'('==>'(X1,'1'),'==>'(X2,'1')) = '==>'(X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_30]) ).
cnf(c_0_72,plain,
( ~ '>='('==>'('==>'(X1,X2),X2),X1)
| '==>'('==>'(X1,X2),X2) = X1 ),
inference(spm,[status(thm)],[c_0_44,c_0_66]) ).
cnf(c_0_73,plain,
'>='('==>'('==>'('==>'(X1,X2),X2),X3),'==>'(X1,X3)),
inference(spm,[status(thm)],[c_0_67,c_0_66]) ).
cnf(c_0_74,plain,
( ~ '>='(X1,X2)
| '>='('==>'(X3,X1),'==>'(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_75,plain,
'>='('+'(X1,X2),X1),
inference(spm,[status(thm)],[c_0_69,c_0_20]) ).
cnf(c_0_76,plain,
'+'('==>'(X1,'1'),'==>'('==>'(X2,X1),X1)) = '==>'('==>'(X2,X1),'1'),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_71]) ).
cnf(c_0_77,plain,
'==>'('==>'('==>'(X1,X2),X2),X2) = '==>'(X1,X2),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,plain,
'>='('+'(X1,'+'(X2,'==>'('+'(X1,X2),X3))),X3),
inference(spm,[status(thm)],[c_0_61,c_0_31]) ).
cnf(c_0_79,plain,
( ~ '>='('==>'(X1,'+'(X1,X2)),X2)
| '==>'(X1,'+'(X1,X2)) = X2 ),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_80,plain,
'>='('==>'(X1,'+'(X2,X3)),'==>'(X1,X2)),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_81,plain,
'+'('==>'(X1,'1'),'==>'(X2,X1)) = '==>'('==>'('==>'(X2,X1),X1),'1'),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,plain,
'>='('+'(X1,'==>'('+'(X2,X1),X3)),'==>'(X2,X3)),
inference(spm,[status(thm)],[c_0_17,c_0_78]) ).
cnf(c_0_83,plain,
( ~ '>='('+'(X2,'+'(X3,X1)),X4)
| '>='(X1,'==>'('+'(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_17,c_0_31]) ).
cnf(c_0_84,plain,
'>='('+'(X1,'+'(X2,'==>'(X2,'==>'(X1,X3)))),X3),
inference(spm,[status(thm)],[c_0_55,c_0_61]) ).
cnf(c_0_85,plain,
'==>'(X1,'+'(X2,'==>'(X2,X1))) = '==>'(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_28]),c_0_80])]) ).
cnf(c_0_86,plain,
'+'(X1,'==>'(X1,X2)) = '==>'('==>'(X1,'==>'('==>'(X1,X2),'1')),'1'),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_71]),c_0_30]),c_0_65]) ).
cnf(c_0_87,plain,
'>='('==>'('+'(X1,X2),X3),'==>'(X2,'==>'(X1,X3))),
inference(spm,[status(thm)],[c_0_17,c_0_82]) ).
cnf(c_0_88,plain,
'>='('==>'(X1,'==>'(X2,X3)),'==>'('+'(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,plain,
( ~ '>='('0',X1)
| '0' = X1 ),
inference(spm,[status(thm)],[c_0_44,c_0_46]) ).
cnf(c_0_90,plain,
'>='(X1,'==>'(X2,'0')),
inference(spm,[status(thm)],[c_0_17,c_0_46]) ).
cnf(c_0_91,plain,
'>='(X1,'==>'(X2,'+'(X1,X2))),
inference(spm,[status(thm)],[c_0_60,c_0_23]) ).
cnf(c_0_92,plain,
'==>'(X1,'==>'('==>'(X2,'==>'('==>'(X2,X1),'1')),'1')) = '==>'(X1,X2),
inference(rw,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_93,plain,
'>='('0','==>'(X1,'==>'('==>'(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_37,c_0_66]) ).
cnf(c_0_94,plain,
'==>'('+'(X1,X2),X3) = '==>'(X2,'==>'(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_87]),c_0_88])]) ).
cnf(c_0_95,plain,
'+'(X1,'==>'(X1,'0')) = '==>'('0',X1),
inference(spm,[status(thm)],[c_0_52,c_0_28]) ).
cnf(c_0_96,plain,
'==>'(X1,'0') = '0',
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
fof(c_0_97,negated_conjecture,
~ ! [X21,X22] : '==>'('==>'(X21,X22),X22) = '==>'('==>'(X22,X21),X21),
inference(assume_negation,[status(cth)],[goals_15]) ).
cnf(c_0_98,plain,
'>='(X1,'==>'('==>'(X1,X2),'+'(X2,'==>'(X2,X1)))),
inference(spm,[status(thm)],[c_0_91,c_0_28]) ).
cnf(c_0_99,plain,
'==>'('==>'('==>'(X1,X2),X2),X1) = '==>'(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_71]),c_0_71]),c_0_71]),c_0_71]) ).
cnf(c_0_100,plain,
'==>'(X1,'==>'('==>'(X1,X2),X2)) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_93]),c_0_46])]) ).
cnf(c_0_101,plain,
'+'(X1,X2) = '==>'('==>'(X2,'==>'(X1,'1')),'1'),
inference(spm,[status(thm)],[c_0_30,c_0_94]) ).
cnf(c_0_102,plain,
'==>'('0',X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96]),c_0_32]) ).
fof(c_0_103,negated_conjecture,
'==>'('==>'(esk1_0,esk2_0),esk2_0) != '==>'('==>'(esk2_0,esk1_0),esk1_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])])])]) ).
cnf(c_0_104,plain,
'>='('==>'('==>'(X1,X2),X2),'==>'('==>'(X2,X1),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]),c_0_101]),c_0_102]),c_0_30]) ).
cnf(c_0_105,negated_conjecture,
'==>'('==>'(esk1_0,esk2_0),esk2_0) != '==>'('==>'(esk2_0,esk1_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_106,plain,
'==>'('==>'(X1,X2),X2) = '==>'('==>'(X2,X1),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_104]),c_0_104])]) ).
cnf(c_0_107,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL898+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/5.47 % Computer : n009.cluster.edu
% 0.19/5.47 % Model : x86_64 x86_64
% 0.19/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.47 % Memory : 8046.5625MB
% 0.19/5.47 % OS : Linux 6.8.0-71-generic
% 0.19/5.47 % CPULimit : 300
% 0.19/5.47 % WCLimit : 300
% 0.19/5.47 % DateTime : Mon Sep 21 01:10:33 UTC 2026
% 0.19/5.48 % CPUTime :
% 0.19/5.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/5.55 Running first-order theorem proving
% 0.24/5.55 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
% 137.48/25.61 % Version: 3.5.1
% 137.48/25.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 137.48/25.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.48/25.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 137.48/25.61 % Starting new_bool_3 with 300s (1) cores
% 137.48/25.61 % Starting new_bool_1 with 300s (1) cores
% 137.48/25.61 % Starting sh5l with 300s (1) cores
% 137.48/25.61 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 523522 completed with status 0
% 137.48/25.61 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 137.48/25.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 137.48/25.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.48/25.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 137.48/25.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 137.48/25.61 % No SInE strategy applied
% 137.48/25.61 % Search class: FHUSM-FFSF22-SFFFFFNN
% 137.48/25.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 137.48/25.61 % Starting SubtermCWHack with 136s (1) cores
% 137.48/25.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 137.48/25.61 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 137.48/25.61 % Starting new_bool_3 with 136s (1) cores
% 137.48/25.61 % Starting new_bool_1 with 136s (1) cores
% 137.48/25.61 % H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with pid 523530 completed with status 0
% 137.48/25.61 % Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S
% 137.48/25.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 137.48/25.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.48/25.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 137.48/25.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 137.48/25.61 % No SInE strategy applied
% 137.48/25.61 % Search class: FHUSM-FFSF22-SFFFFFNN
% 137.48/25.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 137.48/25.61 % Starting SubtermCWHack with 136s (1) cores
% 137.48/25.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 137.48/25.61 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 137.48/25.61 % Preprocessing time : 0.002 s
% 137.48/25.61 % Presaturation interreduction done
% 137.48/25.61
% 137.48/25.61 % Proof found!
% 137.48/25.61 % SZS status Theorem
% 137.48/25.61 % SZS output start CNFRefutation
% See solution above
% 137.48/25.61 % Parsed axioms : 15
% 137.48/25.61 % Removed by relevancy pruning/SinE : 0
% 137.48/25.61 % Initial clauses : 16
% 137.48/25.61 % Removed in clause preprocessing : 0
% 137.48/25.61 % Initial clauses in saturation : 16
% 137.48/25.61 % Processed clauses : 28896
% 137.48/25.61 % ...of these trivial : 6466
% 137.48/25.61 % ...subsumed : 20409
% 137.48/25.61 % ...remaining for further processing : 2021
% 137.48/25.61 % Other redundant clauses eliminated : 0
% 137.48/25.61 % Clauses deleted for lack of memory : 0
% 137.48/25.61 % Backward-subsumed : 12
% 137.48/25.61 % Backward-rewritten : 1244
% 137.48/25.61 % Generated clauses : 1016423
% 137.48/25.61 % ...of the previous two non-redundant : 541210
% 137.48/25.61 % ...aggressively subsumed : 0
% 137.48/25.61 % Contextual simplify-reflections : 0
% 137.48/25.61 % Paramodulations : 1016423
% 137.48/25.61 % Factorizations : 0
% 137.48/25.61 % NegExts : 0
% 137.48/25.61 % Equation resolutions : 0
% 137.48/25.61 % Disequality decompositions : 0
% 137.48/25.61 % Total rewrite steps : 1594094
% 137.48/25.61 % ...of those cached : 1408778
% 137.48/25.61 % Propositional unsat checks : 0
% 137.48/25.61 % Propositional check models : 0
% 137.48/25.61 % Propositional check unsatisfiable : 0
% 137.48/25.61 % Propositional clauses : 0
% 137.48/25.61 % Propositional clauses after purity: 0
% 137.48/25.61 % Propositional unsat core size : 0
% 137.48/25.61 % Propositional preprocessing time : 0.000
% 137.48/25.61 % Propositional encoding time : 0.000
% 137.48/25.61 % Propositional solver time : 0.000
% 137.48/25.61 % Success case prop preproc time : 0.000
% 137.48/25.61 % Success case prop encoding time : 0.000
% 137.48/25.61 % Success case prop solver time : 0.000
% 137.48/25.61 % Current number of processed clauses : 749
% 137.48/25.61 % Positive orientable unit clauses : 634
% 137.48/25.61 % Positive unorientable unit clauses: 5
% 137.48/25.61 % Negative unit clauses : 0
% 137.48/25.61 % Non-unit-clauses : 110
% 137.48/25.61 % Current number of unprocessed clauses: 495989
% 137.48/25.61 % ...number of literals in the above : 551778
% 137.48/25.61 % Current number of archived formulas : 0
% 137.48/25.61 % Current number of archived clauses : 1272
% 137.48/25.61 % Clause-clause subsumption calls (NU) : 57599
% 137.48/25.61 % Rec. Clause-clause subsumption calls : 57301
% 137.48/25.61 % Non-unit clause-clause subsumptions : 19677
% 137.48/25.61 % Unit Clause-clause subsumption calls : 1530
% 137.48/25.61 % Rewrite failures with RHS unbound : 0
% 137.48/25.61 % BW rewrite match attempts : 65346
% 137.48/25.61 % BW rewrite match successes : 1944
% 137.48/25.61 % Condensation attempts : 0
% 137.48/25.61 % Condensation successes : 0
% 137.48/25.61 % Termbank termtop insertions : 12425953
% 137.48/25.61 % Search garbage collected termcells : 118
% 137.48/25.61
% 137.48/25.61 % -------------------------------------------------
% 137.48/25.61 % User time : 18.959 s
% 137.48/25.61 % System time : 0.646 s
% 137.48/25.61 % Total time : 19.604 s
% 137.48/25.61 % Maximum resident set size: 3648 pages
% 137.48/25.61
% 137.48/25.61 % -------------------------------------------------
% 137.48/25.61 % User time : 95.077 s
% 137.48/25.61 % System time : 3.540 s
% 137.48/25.61 % Total time : 98.618 s
% 137.48/25.61 % Maximum resident set size: 4864 pages
% 137.48/25.61 % E exiting
%------------------------------------------------------------------------------