TSTP Solution File: LCL890+1 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : LCL890+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:23:02 EDT 2023
% Result : Theorem 236.28s 31.10s
% Output : CNFRefutation 236.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 13
% Syntax : Number of formulae : 166 ( 133 unt; 0 def)
% Number of atoms : 210 ( 63 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 76 ( 32 ~; 29 |; 7 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 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 : 260 ( 27 sgn; 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_03) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_02) ).
fof(sos_07,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_07) ).
fof(sos_09,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_09) ).
fof(sos_08,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_08) ).
fof(sos_10,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_10) ).
fof(sos_11,axiom,
! [X15,X16,X17] :
( '>='(X15,X16)
=> '>='('==>'(X16,X17),'==>'(X15,X17)) ),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_11) ).
fof(goals_14,conjecture,
! [X21,X22,X23] :
( ( '>='('==>'(X21,X22),X21)
& X23 = '==>'(X23,X22) )
=> '>='(X23,X21) ),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',goals_14) ).
fof(sos_13,axiom,
! [X1,X2] : '+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_13) ).
fof(sos_06,axiom,
! [X4,X5,X6] :
( ( '>='(X4,X5)
& '>='(X5,X6) )
=> '>='(X4,X6) ),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_06) ).
fof(sos_01,axiom,
! [X1,X2,X3] : '+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_01) ).
fof(sos_05,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_05) ).
fof(sos_12,axiom,
! [X18,X19,X20] :
( '>='(X18,X19)
=> '>='('==>'(X20,X18),'==>'(X20,X19)) ),
file('/export/starexec/sandbox2/tmp/tmp.T61zaNkT1J/E---3.1_2398.p',sos_12) ).
fof(c_0_13,plain,
! [X53] : '+'(X53,'0') = X53,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_14,plain,
! [X51,X52] : '+'(X51,X52) = '+'(X52,X51),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_15,plain,
! [X31,X32] :
( ~ '>='(X31,X32)
| ~ '>='(X32,X31)
| X31 = X32 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
fof(c_0_16,plain,
! [X36] : '>='(X36,'0'),
inference(variable_rename,[status(thm)],[sos_09]) ).
fof(c_0_17,plain,
! [X33,X34,X35] :
( ( ~ '>='('+'(X33,X34),X35)
| '>='(X34,'==>'(X33,X35)) )
& ( ~ '>='(X34,'==>'(X33,X35))
| '>='('+'(X33,X34),X35) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_08])]) ).
fof(c_0_18,plain,
! [X37,X38,X39] :
( ~ '>='(X37,X38)
| '>='('+'(X37,X39),'+'(X38,X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])]) ).
cnf(c_0_19,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X40,X41,X42] :
( ~ '>='(X40,X41)
| '>='('==>'(X41,X42),'==>'(X40,X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])]) ).
fof(c_0_22,negated_conjecture,
~ ! [X21,X22,X23] :
( ( '>='('==>'(X21,X22),X21)
& X23 = '==>'(X23,X22) )
=> '>='(X23,X21) ),
inference(assume_negation,[status(cth)],[goals_14]) ).
fof(c_0_23,plain,
! [X46,X47] : '+'(X46,'==>'(X46,X47)) = '+'(X47,'==>'(X47,X46)),
inference(variable_rename,[status(thm)],[sos_13]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( '>='('+'(X1,X3),'+'(X2,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,plain,
( '>='('==>'(X2,X3),'==>'(X1,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_30,negated_conjecture,
( '>='('==>'(esk1_0,esk2_0),esk1_0)
& esk3_0 = '==>'(esk3_0,esk2_0)
& ~ '>='(esk3_0,esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
cnf(c_0_31,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( '0' = X1
| ~ '>='('0',X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
'>='(X1,'==>'(X2,'0')),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
fof(c_0_34,plain,
! [X28,X29,X30] :
( ~ '>='(X28,X29)
| ~ '>='(X29,X30)
| '>='(X28,X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).
cnf(c_0_35,plain,
'>='('+'(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_28]) ).
cnf(c_0_36,plain,
'>='('==>'('0',X1),'==>'(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_37,negated_conjecture,
esk3_0 = '==>'(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
'+'(X1,'==>'(X1,'0')) = '==>'('0',X1),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_39,plain,
'==>'(X1,'0') = '0',
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_40,plain,
! [X48,X49,X50] : '+'('+'(X48,X49),X50) = '+'(X48,'+'(X49,X50)),
inference(variable_rename,[status(thm)],[sos_01]) ).
cnf(c_0_41,plain,
( '>='(X1,X3)
| ~ '>='(X1,X2)
| ~ '>='(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
'>='('==>'(esk1_0,esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,plain,
'>='('+'(X1,X2),X1),
inference(spm,[status(thm)],[c_0_35,c_0_20]) ).
cnf(c_0_44,negated_conjecture,
'>='('==>'('0',esk2_0),esk3_0),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
'==>'('0',X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_19]) ).
cnf(c_0_46,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( '>='(X1,esk1_0)
| ~ '>='(X1,'==>'(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_43,c_0_31]) ).
cnf(c_0_49,negated_conjecture,
'>='(esk2_0,esk3_0),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
'+'(X1,'+'('==>'(X1,'0'),X2)) = '+'('==>'('0',X1),X2),
inference(spm,[status(thm)],[c_0_46,c_0_38]) ).
cnf(c_0_51,negated_conjecture,
'>='('==>'('0',esk2_0),esk1_0),
inference(spm,[status(thm)],[c_0_47,c_0_36]) ).
cnf(c_0_52,plain,
( '>='('+'(X2,X1),X3)
| ~ '>='(X1,'==>'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_53,plain,
'>='('+'(X1,'+'(X2,'==>'('+'(X1,X2),X3))),X3),
inference(spm,[status(thm)],[c_0_48,c_0_46]) ).
cnf(c_0_54,negated_conjecture,
( '>='(X1,esk3_0)
| ~ '>='(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_49]) ).
cnf(c_0_55,plain,
'>='('+'('==>'('0',X1),X2),X1),
inference(spm,[status(thm)],[c_0_43,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
'>='(esk2_0,esk1_0),
inference(rw,[status(thm)],[c_0_51,c_0_45]) ).
cnf(c_0_57,plain,
( '>='(X1,'==>'('+'(X2,X3),X4))
| ~ '>='('+'(X2,'+'(X3,X1)),X4) ),
inference(spm,[status(thm)],[c_0_26,c_0_46]) ).
cnf(c_0_58,plain,
'>='('+'(X1,'+'(X2,'==>'(X2,'==>'(X1,X3)))),X3),
inference(spm,[status(thm)],[c_0_52,c_0_48]) ).
cnf(c_0_59,plain,
'>='('+'(X1,'==>'('+'(X2,X1),X3)),'==>'(X2,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
'>='('+'(esk2_0,X1),esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_45]) ).
fof(c_0_61,plain,
! [X27] : '>='(X27,X27),
inference(variable_rename,[status(thm)],[sos_05]) ).
cnf(c_0_62,negated_conjecture,
( '>='(X1,esk1_0)
| ~ '>='(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_56]) ).
cnf(c_0_63,plain,
'>='('==>'(X1,'==>'(X2,X3)),'==>'('+'(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
'>='('+'(X1,'==>'('+'(esk3_0,X1),esk2_0)),esk3_0),
inference(spm,[status(thm)],[c_0_59,c_0_37]) ).
cnf(c_0_65,negated_conjecture,
'>='(X1,'==>'(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_26,c_0_60]) ).
cnf(c_0_66,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_67,negated_conjecture,
'>='('+'(esk2_0,X1),esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_55]),c_0_45]) ).
cnf(c_0_68,negated_conjecture,
'>='('==>'(esk1_0,X1),'==>'(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_56]) ).
cnf(c_0_69,plain,
'+'(X1,'+'(X2,X3)) = '+'(X2,'+'(X3,X1)),
inference(spm,[status(thm)],[c_0_46,c_0_20]) ).
cnf(c_0_70,negated_conjecture,
'>='('==>'(X1,esk3_0),'==>'('+'(esk3_0,X1),esk2_0)),
inference(spm,[status(thm)],[c_0_63,c_0_37]) ).
cnf(c_0_71,negated_conjecture,
'>='('==>'('+'(esk3_0,X1),esk2_0),'==>'(X1,esk3_0)),
inference(spm,[status(thm)],[c_0_26,c_0_64]) ).
cnf(c_0_72,plain,
'>='('+'(X1,'+'('==>'(X1,X2),X3)),'+'(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_48]),c_0_46]) ).
cnf(c_0_73,negated_conjecture,
'==>'(esk2_0,esk3_0) = '0',
inference(spm,[status(thm)],[c_0_32,c_0_65]) ).
cnf(c_0_74,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_26,c_0_66]) ).
cnf(c_0_75,negated_conjecture,
'>='(X1,'==>'(esk2_0,esk1_0)),
inference(spm,[status(thm)],[c_0_26,c_0_67]) ).
cnf(c_0_76,plain,
( '>='('0','==>'(X1,X2))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_77,negated_conjecture,
'>='('+'(esk2_0,'==>'(esk1_0,X1)),X1),
inference(spm,[status(thm)],[c_0_52,c_0_68]) ).
cnf(c_0_78,plain,
( '>='('+'(X1,X2),'==>'(X3,X4))
| ~ '>='('+'(X2,'+'(X3,X1)),X4) ),
inference(spm,[status(thm)],[c_0_26,c_0_69]) ).
cnf(c_0_79,plain,
'>='('+'(X1,'+'('==>'(X1,X2),X3)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_55]),c_0_45]) ).
cnf(c_0_80,negated_conjecture,
'==>'('+'(esk3_0,X1),esk2_0) = '==>'(X1,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_70]),c_0_71])]) ).
cnf(c_0_81,plain,
'>='('+'('==>'(X1,X2),X3),'==>'(X1,'+'(X2,X3))),
inference(spm,[status(thm)],[c_0_26,c_0_72]) ).
cnf(c_0_82,negated_conjecture,
'+'(esk3_0,esk3_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_73]),c_0_19]),c_0_37]) ).
cnf(c_0_83,plain,
'>='('+'(X1,'+'(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_84,plain,
'>='(X1,'==>'(X2,'+'(X1,X2))),
inference(spm,[status(thm)],[c_0_74,c_0_20]) ).
cnf(c_0_85,negated_conjecture,
'==>'(esk2_0,esk1_0) = '0',
inference(spm,[status(thm)],[c_0_32,c_0_75]) ).
cnf(c_0_86,negated_conjecture,
'>='('0','==>'('+'(esk2_0,'==>'(esk1_0,X1)),X1)),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_87,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_88,plain,
'>='('+'(X1,X2),'==>'('==>'(X2,X3),X3)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
fof(c_0_89,plain,
! [X43,X44,X45] :
( ~ '>='(X43,X44)
| '>='('==>'(X45,X43),'==>'(X45,X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_12])]) ).
cnf(c_0_90,negated_conjecture,
'==>'('+'(X1,esk3_0),esk2_0) = '==>'(X1,esk3_0),
inference(spm,[status(thm)],[c_0_80,c_0_20]) ).
cnf(c_0_91,negated_conjecture,
'>='('+'(esk3_0,'==>'(X1,esk3_0)),'==>'(X1,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_20]) ).
cnf(c_0_92,negated_conjecture,
'+'(esk3_0,'+'(esk3_0,X1)) = '+'(esk2_0,X1),
inference(spm,[status(thm)],[c_0_46,c_0_82]) ).
cnf(c_0_93,plain,
'>='('+'(X1,'+'(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_83,c_0_20]) ).
cnf(c_0_94,plain,
'>='('+'(X1,X2),'+'('==>'(X3,'+'(X1,X3)),X2)),
inference(spm,[status(thm)],[c_0_27,c_0_84]) ).
cnf(c_0_95,negated_conjecture,
'+'(esk1_0,'==>'(esk1_0,esk2_0)) = esk2_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_85]),c_0_19]) ).
cnf(c_0_96,negated_conjecture,
'==>'('+'(esk2_0,'==>'(esk1_0,X1)),X1) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_86]),c_0_25])]) ).
cnf(c_0_97,plain,
'>='(X1,'==>'(X2,'==>'('==>'(X2,X3),X3))),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_98,plain,
( '>='('==>'(X3,X1),'==>'(X3,X2))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_99,plain,
'>='(X1,'==>'('==>'(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_87,c_0_48]) ).
cnf(c_0_100,negated_conjecture,
'>='('==>'(esk3_0,'==>'(X1,esk2_0)),'==>'(X1,esk3_0)),
inference(spm,[status(thm)],[c_0_63,c_0_90]) ).
cnf(c_0_101,negated_conjecture,
'>='('==>'(X1,esk3_0),'==>'(esk3_0,'==>'(X1,esk2_0))),
inference(spm,[status(thm)],[c_0_26,c_0_91]) ).
cnf(c_0_102,plain,
'>='('+'(X1,'+'(X2,X3)),'+'(X1,X2)),
inference(spm,[status(thm)],[c_0_43,c_0_46]) ).
cnf(c_0_103,negated_conjecture,
'+'(esk3_0,'+'(X1,'==>'(X1,esk3_0))) = '+'(esk2_0,'==>'(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_92,c_0_31]) ).
cnf(c_0_104,negated_conjecture,
'>='('+'(esk3_0,'==>'(esk1_0,esk3_0)),esk1_0),
inference(spm,[status(thm)],[c_0_47,c_0_91]) ).
cnf(c_0_105,plain,
'>='('+'(X1,X2),'==>'(X3,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_93]) ).
cnf(c_0_106,negated_conjecture,
'>='('+'(esk1_0,X1),'+'('==>'('==>'(esk1_0,esk2_0),esk2_0),X1)),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_107,negated_conjecture,
'+'(X1,'==>'(X1,'+'(esk2_0,'==>'(esk1_0,X1)))) = '+'(esk2_0,'==>'(esk1_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_96]),c_0_19]) ).
cnf(c_0_108,plain,
'==>'(X1,'==>'('==>'(X1,X2),X2)) = '0',
inference(spm,[status(thm)],[c_0_32,c_0_97]) ).
cnf(c_0_109,plain,
'>='('==>'(X1,X2),'==>'(X1,'==>'('==>'(X2,X3),X3))),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_110,negated_conjecture,
'==>'(esk3_0,'==>'(X1,esk2_0)) = '==>'(X1,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_100]),c_0_101])]) ).
cnf(c_0_111,negated_conjecture,
( '>='('+'(esk3_0,X1),'==>'(esk3_0,X2))
| ~ '>='('+'(esk2_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_92]) ).
cnf(c_0_112,plain,
( '>='(X1,X2)
| ~ '>='(X1,'+'(X3,'==>'(X3,X2))) ),
inference(spm,[status(thm)],[c_0_41,c_0_48]) ).
cnf(c_0_113,negated_conjecture,
'>='('+'(esk2_0,'==>'(esk3_0,X1)),'+'(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_114,negated_conjecture,
'>='('==>'(esk1_0,esk3_0),'==>'(esk3_0,esk1_0)),
inference(spm,[status(thm)],[c_0_26,c_0_104]) ).
cnf(c_0_115,negated_conjecture,
'+'(esk3_0,'+'(X1,esk3_0)) = '+'(esk2_0,X1),
inference(spm,[status(thm)],[c_0_92,c_0_20]) ).
cnf(c_0_116,plain,
'+'(X1,'+'('==>'(X1,X2),X3)) = '+'(X2,'+'('==>'(X2,X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_31]),c_0_46]) ).
cnf(c_0_117,plain,
'>='(X1,'==>'(X2,'==>'(X3,X2))),
inference(spm,[status(thm)],[c_0_26,c_0_105]) ).
cnf(c_0_118,plain,
'>='('==>'('+'(X1,X2),X3),'==>'(X2,'==>'(X1,X3))),
inference(spm,[status(thm)],[c_0_26,c_0_59]) ).
cnf(c_0_119,negated_conjecture,
'>='('+'(esk1_0,'==>'('==>'('==>'(esk1_0,esk2_0),esk2_0),esk2_0)),esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_19]),c_0_108]),c_0_19]) ).
cnf(c_0_120,negated_conjecture,
'>='('==>'(esk3_0,X1),'==>'('==>'(X1,esk2_0),esk3_0)),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_121,negated_conjecture,
'>='('+'(esk3_0,'==>'(esk2_0,X1)),'==>'(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_111,c_0_48]) ).
cnf(c_0_122,negated_conjecture,
'>='('+'(esk2_0,'==>'(esk3_0,'==>'(esk3_0,X1))),X1),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_123,negated_conjecture,
'>='('+'('==>'(esk1_0,esk3_0),X1),'+'('==>'(esk3_0,esk1_0),X1)),
inference(spm,[status(thm)],[c_0_27,c_0_114]) ).
cnf(c_0_124,negated_conjecture,
'+'(X1,'+'(esk3_0,'==>'(X1,esk3_0))) = '+'(esk2_0,'==>'(esk3_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_20]) ).
cnf(c_0_125,plain,
'==>'(X1,'==>'(X2,X1)) = '0',
inference(spm,[status(thm)],[c_0_32,c_0_117]) ).
cnf(c_0_126,plain,
'+'(X1,'+'('==>'(X1,X2),'==>'('==>'(X2,X1),X3))) = '+'(X2,'+'(X3,'==>'(X3,'==>'(X2,X1)))),
inference(spm,[status(thm)],[c_0_116,c_0_31]) ).
cnf(c_0_127,negated_conjecture,
'==>'('+'(X1,'==>'(X1,esk3_0)),esk2_0) = '==>'('==>'(esk3_0,X1),esk3_0),
inference(spm,[status(thm)],[c_0_80,c_0_31]) ).
cnf(c_0_128,plain,
'==>'('+'(X1,X2),X3) = '==>'(X2,'==>'(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_118]),c_0_63])]) ).
cnf(c_0_129,negated_conjecture,
'>='('==>'('==>'('==>'(esk1_0,esk2_0),esk2_0),esk2_0),'==>'(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_26,c_0_119]) ).
cnf(c_0_130,negated_conjecture,
'>='('==>'(X1,esk3_0),'==>'('==>'('==>'(X1,esk2_0),esk2_0),esk3_0)),
inference(spm,[status(thm)],[c_0_120,c_0_110]) ).
cnf(c_0_131,plain,
'>='('==>'('==>'('==>'(X1,X2),X2),X3),'==>'(X1,X3)),
inference(spm,[status(thm)],[c_0_29,c_0_99]) ).
cnf(c_0_132,negated_conjecture,
'>='('==>'(esk2_0,X1),'==>'(esk3_0,'==>'(esk3_0,X1))),
inference(spm,[status(thm)],[c_0_26,c_0_121]) ).
cnf(c_0_133,negated_conjecture,
'>='('==>'(esk3_0,'==>'(esk3_0,X1)),'==>'(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_122]) ).
cnf(c_0_134,negated_conjecture,
'>='(esk2_0,'+'(esk3_0,esk1_0)),
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(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]),c_0_19]),c_0_69]),c_0_20]),c_0_126]),c_0_125]),c_0_19]),c_0_20]) ).
cnf(c_0_135,negated_conjecture,
'==>'('==>'(X1,esk3_0),'==>'(X1,esk2_0)) = '==>'('==>'(esk3_0,X1),esk3_0),
inference(rw,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_136,negated_conjecture,
'==>'('==>'('==>'(esk1_0,esk2_0),esk2_0),esk2_0) = '==>'(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_129]),c_0_99])]) ).
cnf(c_0_137,negated_conjecture,
'==>'('==>'('==>'(X1,esk2_0),esk2_0),esk3_0) = '==>'(X1,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_130]),c_0_131])]) ).
cnf(c_0_138,negated_conjecture,
'==>'(esk3_0,'==>'(esk3_0,X1)) = '==>'(esk2_0,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_132]),c_0_133])]) ).
cnf(c_0_139,negated_conjecture,
'>='('0','==>'(esk2_0,'+'(esk3_0,esk1_0))),
inference(spm,[status(thm)],[c_0_76,c_0_134]) ).
cnf(c_0_140,plain,
'>='('0','==>'('+'(X1,X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_55]),c_0_45]) ).
cnf(c_0_141,negated_conjecture,
'==>'('==>'('==>'(esk1_0,esk2_0),esk3_0),esk3_0) = '==>'('==>'(esk3_0,esk1_0),esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]),c_0_135]),c_0_110]) ).
cnf(c_0_142,plain,
( '==>'(X1,'+'(X1,X2)) = X2
| ~ '>='('==>'(X1,'+'(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_74]) ).
cnf(c_0_143,plain,
'>='('==>'(X1,'+'(X2,'==>'(X2,X3))),'==>'(X1,X3)),
inference(spm,[status(thm)],[c_0_98,c_0_48]) ).
cnf(c_0_144,negated_conjecture,
'>='('==>'(esk2_0,X1),'==>'('==>'('==>'(esk3_0,X1),esk2_0),esk3_0)),
inference(spm,[status(thm)],[c_0_120,c_0_138]) ).
cnf(c_0_145,negated_conjecture,
'==>'(esk2_0,'+'(esk3_0,esk1_0)) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_139]),c_0_25])]) ).
cnf(c_0_146,plain,
'==>'('+'(X1,X2),X1) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_140]),c_0_25])]) ).
cnf(c_0_147,plain,
'>='('+'('==>'(X1,X2),X3),'==>'(X1,'+'(X2,'+'('==>'(X2,X1),X3)))),
inference(spm,[status(thm)],[c_0_74,c_0_116]) ).
cnf(c_0_148,negated_conjecture,
'+'('==>'('==>'(esk3_0,esk1_0),esk3_0),'==>'('==>'(esk1_0,esk2_0),esk3_0)) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_141]),c_0_125]),c_0_19]),c_0_20]) ).
cnf(c_0_149,plain,
'==>'(X1,'+'(X1,'==>'(X1,X2))) = '==>'(X1,X2),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_150,negated_conjecture,
'>='('0','==>'('==>'('==>'(esk3_0,'+'(esk3_0,esk1_0)),esk2_0),esk3_0)),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_151,plain,
'+'(X1,'==>'(X1,'+'(X1,X2))) = '+'(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_146]),c_0_19]) ).
cnf(c_0_152,negated_conjecture,
'>='('0','==>'('==>'(esk1_0,esk3_0),'==>'(esk3_0,esk1_0))),
inference(spm,[status(thm)],[c_0_76,c_0_114]) ).
cnf(c_0_153,negated_conjecture,
'>='('==>'('==>'(esk1_0,esk2_0),esk3_0),'==>'(esk3_0,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_138]),c_0_85]),c_0_28]),c_0_20]),c_0_149]) ).
cnf(c_0_154,negated_conjecture,
'==>'('==>'('==>'(esk3_0,'+'(esk3_0,esk1_0)),esk2_0),esk3_0) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_150]),c_0_25])]) ).
cnf(c_0_155,negated_conjecture,
'==>'('==>'(esk3_0,'+'(esk3_0,X1)),esk3_0) = '==>'(X1,esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_151]),c_0_80]) ).
cnf(c_0_156,negated_conjecture,
'==>'('==>'(esk1_0,esk3_0),'==>'(esk3_0,esk1_0)) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_152]),c_0_25])]) ).
cnf(c_0_157,negated_conjecture,
'==>'('==>'(esk1_0,esk2_0),esk3_0) = '==>'(esk3_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_153]),c_0_120])]) ).
cnf(c_0_158,negated_conjecture,
'==>'('==>'(esk3_0,'+'(esk3_0,esk1_0)),esk2_0) = '+'(esk3_0,'==>'(esk1_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_154]),c_0_19]),c_0_110]),c_0_155]) ).
cnf(c_0_159,negated_conjecture,
'>='(X1,'==>'('==>'(esk1_0,esk3_0),'+'('==>'(esk3_0,esk1_0),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_156]),c_0_28]) ).
cnf(c_0_160,negated_conjecture,
'+'('==>'(esk3_0,esk1_0),'==>'(esk1_0,esk2_0)) = '+'(esk3_0,'==>'(esk1_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_157]),c_0_20]),c_0_110]) ).
cnf(c_0_161,negated_conjecture,
'==>'('==>'(esk1_0,esk3_0),'+'(esk3_0,'==>'(esk1_0,esk3_0))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_158]),c_0_155]),c_0_138]),c_0_145]),c_0_45]) ).
cnf(c_0_162,negated_conjecture,
'>='('==>'(esk1_0,esk2_0),esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_161]) ).
cnf(c_0_163,negated_conjecture,
'>='('0','==>'(esk3_0,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_162]),c_0_157]) ).
cnf(c_0_164,negated_conjecture,
~ '>='(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_165,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_163]),c_0_19]),c_0_164]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : LCL890+1 : TPTP v8.1.2. Released v5.5.0.
% 0.09/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n002.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 2400
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Oct 2 12:50:14 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.52 Running first-order theorem proving
% 0.22/0.52 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/tmp/tmp.T61zaNkT1J/E---3.1_2398.p
% 236.28/31.10 # Version: 3.1pre001
% 236.28/31.10 # Preprocessing class: FSMSSMSSSSSNFFN.
% 236.28/31.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 236.28/31.10 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 236.28/31.10 # Starting new_bool_3 with 300s (1) cores
% 236.28/31.10 # Starting new_bool_1 with 300s (1) cores
% 236.28/31.10 # Starting sh5l with 300s (1) cores
% 236.28/31.10 # sh5l with pid 2518 completed with status 0
% 236.28/31.10 # Result found by sh5l
% 236.28/31.10 # Preprocessing class: FSMSSMSSSSSNFFN.
% 236.28/31.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 236.28/31.10 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 236.28/31.10 # Starting new_bool_3 with 300s (1) cores
% 236.28/31.10 # Starting new_bool_1 with 300s (1) cores
% 236.28/31.10 # Starting sh5l with 300s (1) cores
% 236.28/31.10 # SinE strategy is gf500_gu_R04_F100_L20000
% 236.28/31.10 # Search class: FHUSM-FFSF22-SFFFFFNN
% 236.28/31.10 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 236.28/31.10 # Starting G----_Y1346__C12_02_nc_F1_AE_CS_SP_S2S with 181s (1) cores
% 236.28/31.10 # G----_Y1346__C12_02_nc_F1_AE_CS_SP_S2S with pid 2524 completed with status 0
% 236.28/31.10 # Result found by G----_Y1346__C12_02_nc_F1_AE_CS_SP_S2S
% 236.28/31.10 # Preprocessing class: FSMSSMSSSSSNFFN.
% 236.28/31.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 236.28/31.10 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 236.28/31.10 # Starting new_bool_3 with 300s (1) cores
% 236.28/31.10 # Starting new_bool_1 with 300s (1) cores
% 236.28/31.10 # Starting sh5l with 300s (1) cores
% 236.28/31.10 # SinE strategy is gf500_gu_R04_F100_L20000
% 236.28/31.10 # Search class: FHUSM-FFSF22-SFFFFFNN
% 236.28/31.10 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 236.28/31.10 # Starting G----_Y1346__C12_02_nc_F1_AE_CS_SP_S2S with 181s (1) cores
% 236.28/31.10 # Preprocessing time : 0.001 s
% 236.28/31.10 # Presaturation interreduction done
% 236.28/31.10
% 236.28/31.10 # Proof found!
% 236.28/31.10 # SZS status Theorem
% 236.28/31.10 # SZS output start CNFRefutation
% See solution above
% 236.28/31.10 # Parsed axioms : 14
% 236.28/31.10 # Removed by relevancy pruning/SinE : 1
% 236.28/31.10 # Initial clauses : 16
% 236.28/31.10 # Removed in clause preprocessing : 0
% 236.28/31.10 # Initial clauses in saturation : 16
% 236.28/31.10 # Processed clauses : 43494
% 236.28/31.10 # ...of these trivial : 25693
% 236.28/31.10 # ...subsumed : 8523
% 236.28/31.10 # ...remaining for further processing : 9278
% 236.28/31.10 # Other redundant clauses eliminated : 0
% 236.28/31.10 # Clauses deleted for lack of memory : 0
% 236.28/31.10 # Backward-subsumed : 12
% 236.28/31.10 # Backward-rewritten : 4020
% 236.28/31.10 # Generated clauses : 2706908
% 236.28/31.10 # ...of the previous two non-redundant : 1505325
% 236.28/31.10 # ...aggressively subsumed : 0
% 236.28/31.10 # Contextual simplify-reflections : 0
% 236.28/31.10 # Paramodulations : 2706908
% 236.28/31.10 # Factorizations : 0
% 236.28/31.10 # NegExts : 0
% 236.28/31.10 # Equation resolutions : 0
% 236.28/31.10 # Total rewrite steps : 4119194
% 236.28/31.10 # Propositional unsat checks : 0
% 236.28/31.10 # Propositional check models : 0
% 236.28/31.10 # Propositional check unsatisfiable : 0
% 236.28/31.10 # Propositional clauses : 0
% 236.28/31.10 # Propositional clauses after purity: 0
% 236.28/31.10 # Propositional unsat core size : 0
% 236.28/31.10 # Propositional preprocessing time : 0.000
% 236.28/31.10 # Propositional encoding time : 0.000
% 236.28/31.10 # Propositional solver time : 0.000
% 236.28/31.10 # Success case prop preproc time : 0.000
% 236.28/31.10 # Success case prop encoding time : 0.000
% 236.28/31.10 # Success case prop solver time : 0.000
% 236.28/31.10 # Current number of processed clauses : 5230
% 236.28/31.10 # Positive orientable unit clauses : 4898
% 236.28/31.10 # Positive unorientable unit clauses: 42
% 236.28/31.10 # Negative unit clauses : 1
% 236.28/31.10 # Non-unit-clauses : 289
% 236.28/31.10 # Current number of unprocessed clauses: 1456759
% 236.28/31.10 # ...number of literals in the above : 1556703
% 236.28/31.10 # Current number of archived formulas : 0
% 236.28/31.10 # Current number of archived clauses : 4048
% 236.28/31.10 # Clause-clause subsumption calls (NU) : 23785
% 236.28/31.10 # Rec. Clause-clause subsumption calls : 23785
% 236.28/31.10 # Non-unit clause-clause subsumptions : 7627
% 236.28/31.10 # Unit Clause-clause subsumption calls : 909
% 236.28/31.10 # Rewrite failures with RHS unbound : 0
% 236.28/31.10 # BW rewrite match attempts : 308757
% 236.28/31.10 # BW rewrite match successes : 5463
% 236.28/31.10 # Condensation attempts : 0
% 236.28/31.10 # Condensation successes : 0
% 236.28/31.10 # Termbank termtop insertions : 41088867
% 236.28/31.10
% 236.28/31.10 # -------------------------------------------------
% 236.28/31.10 # User time : 28.505 s
% 236.28/31.10 # System time : 0.934 s
% 236.28/31.10 # Total time : 29.439 s
% 236.28/31.10 # Maximum resident set size: 1748 pages
% 236.28/31.10
% 236.28/31.10 # -------------------------------------------------
% 236.28/31.10 # User time : 28.508 s
% 236.28/31.10 # System time : 0.936 s
% 236.28/31.10 # Total time : 29.443 s
% 236.28/31.10 # Maximum resident set size: 1704 pages
% 236.28/31.10 % E---3.1 exiting
% 236.28/31.10 % E---3.1 exiting
%------------------------------------------------------------------------------