TSTP Solution File: LCL890+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL890+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 07:00:05 EDT 2023
% Result : Theorem 40.97s 41.06s
% Output : CNFRefutation 40.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 191 ( 149 unt; 8 typ; 0 def)
% Number of atoms : 228 ( 77 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 33 ~; 30 |; 7 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 305 ( 38 sgn; 60 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
'+': ( $i * $i ) > $i ).
tff(decl_23,type,
'0': $i ).
tff(decl_24,type,
'1': $i ).
tff(decl_25,type,
'>=': ( $i * $i ) > $o ).
tff(decl_26,type,
'==>': ( $i * $i ) > $i ).
tff(decl_27,type,
esk1_0: $i ).
tff(decl_28,type,
esk2_0: $i ).
tff(decl_29,type,
esk3_0: $i ).
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(sos_10,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
fof(sos_09,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
fof(sos_08,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(goals_14,conjecture,
! [X21,X22,X23] :
( ( '>='('==>'(X21,X22),X21)
& X23 = '==>'(X23,X22) )
=> '>='(X23,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(sos_13,axiom,
! [X1,X2] : '+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
fof(sos_07,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(sos_01,axiom,
! [X1,X2,X3] : '+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
fof(sos_06,axiom,
! [X4,X5,X6] :
( ( '>='(X4,X5)
& '>='(X5,X6) )
=> '>='(X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
fof(sos_11,axiom,
! [X15,X16,X17] :
( '>='(X15,X16)
=> '>='('==>'(X16,X17),'==>'(X15,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_11) ).
fof(sos_12,axiom,
! [X18,X19,X20] :
( '>='(X18,X19)
=> '>='('==>'(X20,X18),'==>'(X20,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(sos_05,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
fof(c_0_13,plain,
! [X29] : '+'(X29,'0') = X29,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_14,plain,
! [X27,X28] : '+'(X27,X28) = '+'(X28,X27),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_15,plain,
! [X41,X42,X43] :
( ~ '>='(X41,X42)
| '>='('+'(X41,X43),'+'(X42,X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])]) ).
fof(c_0_16,plain,
! [X40] : '>='(X40,'0'),
inference(variable_rename,[status(thm)],[sos_09]) ).
cnf(c_0_17,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X37,X38,X39] :
( ( ~ '>='('+'(X37,X38),X39)
| '>='(X38,'==>'(X37,X39)) )
& ( ~ '>='(X38,'==>'(X37,X39))
| '>='('+'(X37,X38),X39) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_08])]) ).
cnf(c_0_20,plain,
( '>='('+'(X1,X3),'+'(X2,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_23,negated_conjecture,
~ ! [X21,X22,X23] :
( ( '>='('==>'(X21,X22),X21)
& X23 = '==>'(X23,X22) )
=> '>='(X23,X21) ),
inference(assume_negation,[status(cth)],[goals_14]) ).
fof(c_0_24,plain,
! [X50,X51] : '+'(X50,'==>'(X50,X51)) = '+'(X51,'==>'(X51,X50)),
inference(variable_rename,[status(thm)],[sos_13]) ).
fof(c_0_25,plain,
! [X35,X36] :
( ~ '>='(X35,X36)
| ~ '>='(X36,X35)
| X35 = X36 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
cnf(c_0_26,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
'>='('+'(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
fof(c_0_28,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_23])])]) ).
fof(c_0_29,plain,
! [X24,X25,X26] : '+'('+'(X24,X25),X26) = '+'(X24,'+'(X25,X26)),
inference(variable_rename,[status(thm)],[sos_01]) ).
cnf(c_0_30,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X32,X33,X34] :
( ~ '>='(X32,X33)
| ~ '>='(X33,X34)
| '>='(X32,X34) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).
cnf(c_0_33,plain,
'>='(X1,'==>'(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
esk3_0 = '==>'(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
'+'(X1,'==>'(X1,'0')) = '==>'('0',X1),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_37,plain,
( '0' = X1
| ~ '>='('0',X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_38,plain,
'>='(X1,'==>'(X2,'0')),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_39,plain,
( '>='(X1,X3)
| ~ '>='(X1,X2)
| ~ '>='(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,negated_conjecture,
'>='(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
'>='('+'(X1,X2),X1),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_42,plain,
'+'(X1,'+'('==>'(X1,'0'),X2)) = '+'('==>'('0',X1),X2),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
'==>'(X1,'0') = '0',
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
'>='('==>'(esk1_0,esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_45,negated_conjecture,
( '>='(X1,esk3_0)
| ~ '>='(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,plain,
'>='('+'('==>'('0',X1),X2),X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
'==>'('0',X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_43]),c_0_17]) ).
cnf(c_0_48,negated_conjecture,
( '>='(X1,esk1_0)
| ~ '>='(X1,'==>'(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_44]) ).
cnf(c_0_49,plain,
( '>='('0','==>'(X1,X2))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_50,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_41,c_0_30]) ).
cnf(c_0_51,negated_conjecture,
'>='('+'(esk2_0,X1),esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_52,negated_conjecture,
'>='(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_48,c_0_33]) ).
fof(c_0_53,plain,
! [X44,X45,X46] :
( ~ '>='(X44,X45)
| '>='('==>'(X45,X46),'==>'(X44,X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])]) ).
cnf(c_0_54,plain,
'>='('0','==>'('+'(X1,X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_46]),c_0_47]) ).
cnf(c_0_55,plain,
( '>='('+'(X2,X1),X3)
| ~ '>='(X1,'==>'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_56,plain,
'>='('+'(X1,'+'(X2,'==>'('+'(X1,X2),X3))),X3),
inference(spm,[status(thm)],[c_0_50,c_0_35]) ).
fof(c_0_57,plain,
! [X47,X48,X49] :
( ~ '>='(X47,X48)
| '>='('==>'(X49,X47),'==>'(X49,X48)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_12])]) ).
cnf(c_0_58,negated_conjecture,
'>='(X1,'==>'(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_26,c_0_51]) ).
fof(c_0_59,plain,
! [X31] : '>='(X31,X31),
inference(variable_rename,[status(thm)],[sos_05]) ).
cnf(c_0_60,negated_conjecture,
( '>='(X1,esk1_0)
| ~ '>='(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_52]) ).
cnf(c_0_61,plain,
( '>='('==>'(X2,X3),'==>'(X1,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_63,plain,
'==>'('+'(X1,X2),X1) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_54]),c_0_21])]) ).
cnf(c_0_64,plain,
( '>='(X1,'==>'('+'(X2,X3),X4))
| ~ '>='('+'(X2,'+'(X3,X1)),X4) ),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_65,plain,
'>='('+'(X1,'+'(X2,'==>'(X2,'==>'(X1,X3)))),X3),
inference(spm,[status(thm)],[c_0_55,c_0_50]) ).
cnf(c_0_66,plain,
'>='('+'(X1,'==>'('+'(X2,X1),X3)),'==>'(X2,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_56]) ).
cnf(c_0_67,plain,
( '>='('==>'(X3,X1),'==>'(X3,X2))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_68,negated_conjecture,
'==>'(esk2_0,esk3_0) = '0',
inference(spm,[status(thm)],[c_0_37,c_0_58]) ).
cnf(c_0_69,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_70,negated_conjecture,
'>='('+'(esk2_0,X1),esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_46]),c_0_47]) ).
cnf(c_0_71,negated_conjecture,
'>='('==>'(esk1_0,X1),'==>'(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_52]) ).
cnf(c_0_72,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='(X1,X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_73,plain,
'>='(X1,'==>'('==>'(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_62,c_0_50]) ).
cnf(c_0_74,plain,
'+'(X1,'+'('==>'(X1,X2),X3)) = '+'(X2,'+'('==>'(X2,X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_35]) ).
cnf(c_0_75,plain,
'==>'('+'(X1,X2),X2) = '0',
inference(spm,[status(thm)],[c_0_63,c_0_18]) ).
cnf(c_0_76,plain,
'>='('==>'(X1,'==>'(X2,X3)),'==>'('+'(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_77,negated_conjecture,
'>='('+'(X1,'==>'('+'(esk3_0,X1),esk2_0)),esk3_0),
inference(spm,[status(thm)],[c_0_66,c_0_34]) ).
cnf(c_0_78,plain,
'>='('+'(X1,'+'(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_79,plain,
'>='('==>'(X1,'+'(X2,X3)),'==>'(X1,X3)),
inference(spm,[status(thm)],[c_0_67,c_0_27]) ).
cnf(c_0_80,negated_conjecture,
'+'(esk3_0,esk3_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_68]),c_0_17]),c_0_34]) ).
cnf(c_0_81,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_26,c_0_69]) ).
cnf(c_0_82,negated_conjecture,
'>='(X1,'==>'(esk2_0,esk1_0)),
inference(spm,[status(thm)],[c_0_26,c_0_70]) ).
cnf(c_0_83,negated_conjecture,
'>='('+'(esk2_0,'==>'(esk1_0,X1)),X1),
inference(spm,[status(thm)],[c_0_55,c_0_71]) ).
cnf(c_0_84,plain,
'>='(X1,'==>'(X2,'==>'('==>'(X1,X3),X3))),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_85,plain,
'==>'('+'(X1,'+'('==>'(X1,X2),X3)),X2) = '0',
inference(spm,[status(thm)],[c_0_63,c_0_74]) ).
cnf(c_0_86,plain,
'+'(X1,'==>'(X1,'+'(X2,X1))) = '+'(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_75]),c_0_17]) ).
cnf(c_0_87,negated_conjecture,
'>='('==>'(X1,esk3_0),'==>'('+'(esk3_0,X1),esk2_0)),
inference(spm,[status(thm)],[c_0_76,c_0_34]) ).
cnf(c_0_88,negated_conjecture,
'>='('==>'('+'(esk3_0,X1),esk2_0),'==>'(X1,esk3_0)),
inference(spm,[status(thm)],[c_0_26,c_0_77]) ).
cnf(c_0_89,plain,
'>='('+'(X1,'+'('==>'(X1,X2),X3)),'+'(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_50]),c_0_35]) ).
cnf(c_0_90,plain,
'>='('+'(X1,'+'(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_78,c_0_18]) ).
cnf(c_0_91,negated_conjecture,
'>='('==>'(esk3_0,'+'(X1,esk2_0)),esk3_0),
inference(spm,[status(thm)],[c_0_79,c_0_34]) ).
cnf(c_0_92,negated_conjecture,
'+'(esk3_0,'+'(esk3_0,X1)) = '+'(esk2_0,X1),
inference(spm,[status(thm)],[c_0_35,c_0_80]) ).
cnf(c_0_93,plain,
'>='(X1,'==>'(X2,'+'(X1,X2))),
inference(spm,[status(thm)],[c_0_81,c_0_18]) ).
cnf(c_0_94,negated_conjecture,
'==>'(esk2_0,esk1_0) = '0',
inference(spm,[status(thm)],[c_0_37,c_0_82]) ).
cnf(c_0_95,negated_conjecture,
'>='('0','==>'('+'(esk2_0,'==>'(esk1_0,X1)),X1)),
inference(spm,[status(thm)],[c_0_49,c_0_83]) ).
cnf(c_0_96,plain,
'>='('+'(X1,X2),'==>'('==>'(X2,X3),X3)),
inference(spm,[status(thm)],[c_0_55,c_0_84]) ).
cnf(c_0_97,plain,
'==>'('+'(X1,'+'(X2,'==>'(X1,X3))),X3) = '0',
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_98,negated_conjecture,
'==>'('+'(esk3_0,X1),esk2_0) = '==>'(X1,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_87]),c_0_88])]) ).
cnf(c_0_99,plain,
'>='('+'('==>'(X1,X2),X3),'==>'(X1,'+'(X2,X3))),
inference(spm,[status(thm)],[c_0_26,c_0_89]) ).
cnf(c_0_100,plain,
'>='('+'(X1,X2),'==>'(X3,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_90]) ).
cnf(c_0_101,negated_conjecture,
'>='('0','==>'('==>'(esk3_0,'+'(X1,esk2_0)),esk3_0)),
inference(spm,[status(thm)],[c_0_49,c_0_91]) ).
cnf(c_0_102,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_103,plain,
'>='('+'(X1,'+'('==>'(X1,X2),X3)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_46]),c_0_47]) ).
cnf(c_0_104,negated_conjecture,
'+'(esk3_0,'+'(X1,'==>'(X1,esk3_0))) = '+'(esk2_0,'==>'(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_92,c_0_30]) ).
cnf(c_0_105,plain,
'>='('+'(X1,X2),'+'('==>'(X3,'+'(X1,X3)),X2)),
inference(spm,[status(thm)],[c_0_20,c_0_93]) ).
cnf(c_0_106,negated_conjecture,
'+'(esk1_0,'==>'(esk1_0,esk2_0)) = esk2_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_94]),c_0_17]) ).
cnf(c_0_107,negated_conjecture,
'==>'('+'(esk2_0,'==>'(esk1_0,X1)),X1) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_95]),c_0_21])]) ).
cnf(c_0_108,plain,
'>='(X1,'==>'(X2,'==>'('==>'(X2,X3),X3))),
inference(spm,[status(thm)],[c_0_62,c_0_96]) ).
cnf(c_0_109,plain,
'==>'('+'(X1,'+'('==>'(X1,X2),'==>'(X2,X3))),X3) = '0',
inference(spm,[status(thm)],[c_0_97,c_0_74]) ).
cnf(c_0_110,negated_conjecture,
'==>'('+'(X1,esk3_0),esk2_0) = '==>'(X1,esk3_0),
inference(spm,[status(thm)],[c_0_98,c_0_18]) ).
cnf(c_0_111,negated_conjecture,
'>='('+'(esk3_0,'==>'(X1,esk3_0)),'==>'(X1,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_80]),c_0_18]) ).
cnf(c_0_112,plain,
'>='(X1,'==>'(X2,'==>'(X3,X2))),
inference(spm,[status(thm)],[c_0_26,c_0_100]) ).
cnf(c_0_113,negated_conjecture,
'==>'('==>'(esk3_0,'+'(X1,esk2_0)),esk3_0) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_101]),c_0_21])]) ).
cnf(c_0_114,negated_conjecture,
'>='('+'(esk3_0,'==>'(esk2_0,X1)),'==>'(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_102,c_0_50]) ).
cnf(c_0_115,negated_conjecture,
'>='('+'(esk2_0,'==>'(esk3_0,'==>'(esk3_0,X1))),X1),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_116,negated_conjecture,
'>='('+'(esk1_0,X1),'+'('==>'('==>'(esk1_0,esk2_0),esk2_0),X1)),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_117,negated_conjecture,
'+'(X1,'==>'(X1,'+'(esk2_0,'==>'(esk1_0,X1)))) = '+'(esk2_0,'==>'(esk1_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_107]),c_0_17]) ).
cnf(c_0_118,plain,
'==>'(X1,'==>'('==>'(X1,X2),X2)) = '0',
inference(spm,[status(thm)],[c_0_37,c_0_108]) ).
cnf(c_0_119,negated_conjecture,
'>='('+'('==>'(esk3_0,X1),'==>'(X1,esk2_0)),esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_109]),c_0_17]) ).
cnf(c_0_120,negated_conjecture,
'>='('==>'(esk3_0,'==>'(X1,esk2_0)),'==>'(X1,esk3_0)),
inference(spm,[status(thm)],[c_0_76,c_0_110]) ).
cnf(c_0_121,negated_conjecture,
'>='('==>'(X1,esk3_0),'==>'(esk3_0,'==>'(X1,esk2_0))),
inference(spm,[status(thm)],[c_0_26,c_0_111]) ).
cnf(c_0_122,plain,
'+'(X1,'+'('==>'(X1,X2),'==>'('==>'(X2,X1),X3))) = '+'(X2,'+'(X3,'==>'(X3,'==>'(X2,X1)))),
inference(spm,[status(thm)],[c_0_74,c_0_30]) ).
cnf(c_0_123,plain,
'==>'(X1,'==>'(X2,X1)) = '0',
inference(spm,[status(thm)],[c_0_37,c_0_112]) ).
cnf(c_0_124,negated_conjecture,
'==>'('==>'(esk3_0,'+'(esk2_0,X1)),esk3_0) = '0',
inference(spm,[status(thm)],[c_0_113,c_0_18]) ).
cnf(c_0_125,negated_conjecture,
'>='('==>'(esk2_0,X1),'==>'(esk3_0,'==>'(esk3_0,X1))),
inference(spm,[status(thm)],[c_0_26,c_0_114]) ).
cnf(c_0_126,negated_conjecture,
'>='('==>'(esk3_0,'==>'(esk3_0,X1)),'==>'(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_115]) ).
cnf(c_0_127,plain,
( '==>'(X1,'+'(X1,X2)) = X2
| ~ '>='('==>'(X1,'+'(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_81]) ).
cnf(c_0_128,plain,
'>='('==>'(X1,'+'(X2,X3)),'==>'(X1,X2)),
inference(spm,[status(thm)],[c_0_67,c_0_41]) ).
cnf(c_0_129,plain,
'>='('==>'('+'(X1,X2),X3),'==>'(X2,'==>'(X1,X3))),
inference(spm,[status(thm)],[c_0_26,c_0_66]) ).
cnf(c_0_130,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_116,c_0_117]),c_0_118]),c_0_17]),c_0_118]),c_0_17]) ).
cnf(c_0_131,negated_conjecture,
'>='('==>'(esk3_0,X1),'==>'('==>'(X1,esk2_0),esk3_0)),
inference(spm,[status(thm)],[c_0_62,c_0_119]) ).
cnf(c_0_132,negated_conjecture,
'==>'(esk3_0,'==>'(X1,esk2_0)) = '==>'(X1,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_120]),c_0_121])]) ).
cnf(c_0_133,negated_conjecture,
'+'(esk3_0,'+'(X1,esk3_0)) = '+'(esk2_0,X1),
inference(spm,[status(thm)],[c_0_92,c_0_18]) ).
cnf(c_0_134,plain,
'>='('==>'(X1,'+'(X2,'==>'(X2,X3))),'==>'(X1,X3)),
inference(spm,[status(thm)],[c_0_67,c_0_50]) ).
cnf(c_0_135,plain,
'+'(X1,'==>'('==>'('==>'(X2,X1),X1),X2)) = '+'(X2,'==>'(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_118]),c_0_123]),c_0_22]),c_0_17]),c_0_18]) ).
cnf(c_0_136,negated_conjecture,
'==>'('==>'(esk3_0,'+'(X1,'==>'(X1,esk2_0))),esk3_0) = '0',
inference(spm,[status(thm)],[c_0_124,c_0_30]) ).
cnf(c_0_137,negated_conjecture,
'==>'(esk3_0,'==>'(esk3_0,X1)) = '==>'(esk2_0,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_125]),c_0_126])]) ).
cnf(c_0_138,plain,
'==>'(X1,'+'(X2,'==>'(X2,X1))) = '==>'(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_30]),c_0_128])]) ).
cnf(c_0_139,negated_conjecture,
'==>'('+'(X1,'==>'(X1,esk3_0)),esk2_0) = '==>'('==>'(esk3_0,X1),esk3_0),
inference(spm,[status(thm)],[c_0_98,c_0_30]) ).
cnf(c_0_140,plain,
'==>'('+'(X1,X2),X3) = '==>'(X2,'==>'(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_129]),c_0_76])]) ).
cnf(c_0_141,negated_conjecture,
'>='('==>'('==>'('==>'(esk1_0,esk2_0),esk2_0),esk2_0),'==>'(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_26,c_0_130]) ).
cnf(c_0_142,negated_conjecture,
'>='('==>'(X1,esk3_0),'==>'('==>'('==>'(X1,esk2_0),esk2_0),esk3_0)),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_143,plain,
'>='('==>'('==>'('==>'(X1,X2),X2),X3),'==>'(X1,X3)),
inference(spm,[status(thm)],[c_0_61,c_0_73]) ).
cnf(c_0_144,negated_conjecture,
'>='('+'(X1,esk3_0),'==>'(esk3_0,'+'(esk2_0,X1))),
inference(spm,[status(thm)],[c_0_81,c_0_133]) ).
cnf(c_0_145,negated_conjecture,
'>='('==>'(esk3_0,X1),'==>'(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_40]) ).
cnf(c_0_146,plain,
'==>'(X1,'+'(X1,'==>'(X1,X2))) = '==>'(X1,X2),
inference(spm,[status(thm)],[c_0_127,c_0_134]) ).
cnf(c_0_147,negated_conjecture,
'==>'(esk3_0,'+'(X1,'==>'(X1,esk2_0))) = '+'(esk3_0,'==>'(esk2_0,X1)),
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_136]),c_0_47]),c_0_137]),c_0_138]),c_0_17]) ).
cnf(c_0_148,negated_conjecture,
'==>'('==>'(X1,esk3_0),'==>'(X1,esk2_0)) = '==>'('==>'(esk3_0,X1),esk3_0),
inference(rw,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_149,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_31,c_0_141]),c_0_73])]) ).
cnf(c_0_150,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_31,c_0_142]),c_0_143])]) ).
cnf(c_0_151,plain,
'+'(X1,'==>'(X1,'+'(X1,X2))) = '+'(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_63]),c_0_17]) ).
cnf(c_0_152,negated_conjecture,
( '>='(X1,'==>'(esk3_0,'+'(esk2_0,X2)))
| ~ '>='(X1,'+'(X2,esk3_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_144]) ).
cnf(c_0_153,negated_conjecture,
'>='('+'('==>'(esk3_0,X1),X2),'+'('==>'(esk2_0,X1),X2)),
inference(spm,[status(thm)],[c_0_20,c_0_145]) ).
cnf(c_0_154,negated_conjecture,
'==>'(esk3_0,'+'(esk2_0,'==>'(esk2_0,X1))) = '+'(esk3_0,'==>'(esk2_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_92]) ).
cnf(c_0_155,negated_conjecture,
'>='('+'(esk3_0,'==>'(esk1_0,esk3_0)),esk1_0),
inference(spm,[status(thm)],[c_0_48,c_0_111]) ).
cnf(c_0_156,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_148,c_0_149]),c_0_150]),c_0_148]),c_0_132]) ).
cnf(c_0_157,plain,
'==>'('==>'(X1,'+'(X1,X2)),'==>'(X1,X3)) = '==>'(X2,'==>'(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_151]),c_0_140]) ).
cnf(c_0_158,plain,
'==>'('==>'(X1,'+'(X2,X1)),'==>'(X1,X3)) = '==>'(X1,'==>'(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_86]),c_0_140]) ).
cnf(c_0_159,plain,
( '>='('==>'(X1,X2),'==>'(X1,X3))
| ~ '>='('+'(X2,'==>'(X2,X1)),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_160,negated_conjecture,
'>='('+'(esk3_0,'==>'(esk3_0,X1)),'+'(esk3_0,'==>'(esk2_0,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_18]),c_0_154]) ).
cnf(c_0_161,negated_conjecture,
'>='('==>'(esk1_0,esk3_0),'==>'(esk3_0,esk1_0)),
inference(spm,[status(thm)],[c_0_26,c_0_155]) ).
cnf(c_0_162,plain,
'>='('+'('==>'(X1,X2),X3),'==>'(X1,'+'(X2,'+'('==>'(X2,X1),X3)))),
inference(spm,[status(thm)],[c_0_81,c_0_74]) ).
cnf(c_0_163,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_30,c_0_156]),c_0_123]),c_0_17]),c_0_18]) ).
cnf(c_0_164,plain,
'==>'(X1,'==>'(X2,X3)) = '==>'(X2,'==>'(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_18]),c_0_158]) ).
cnf(c_0_165,negated_conjecture,
'>='('==>'(X1,esk3_0),'==>'(X1,'+'(esk3_0,'==>'(esk2_0,X1)))),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_166,negated_conjecture,
'>='('0','==>'('==>'(esk1_0,esk3_0),'==>'(esk3_0,esk1_0))),
inference(spm,[status(thm)],[c_0_49,c_0_161]) ).
cnf(c_0_167,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_162,c_0_163]),c_0_137]),c_0_94]),c_0_22]),c_0_18]),c_0_146]) ).
cnf(c_0_168,negated_conjecture,
'==>'(X1,'==>'('==>'(X1,esk3_0),esk2_0)) = '==>'('==>'(esk3_0,X1),esk3_0),
inference(rw,[status(thm)],[c_0_148,c_0_164]) ).
cnf(c_0_169,negated_conjecture,
'==>'(X1,'+'(esk3_0,'==>'(esk2_0,X1))) = '==>'(X1,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_165]),c_0_128])]) ).
cnf(c_0_170,plain,
'>='(X1,'==>'(X2,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_41]) ).
cnf(c_0_171,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_31,c_0_166]),c_0_21])]) ).
cnf(c_0_172,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_31,c_0_167]),c_0_131])]) ).
cnf(c_0_173,negated_conjecture,
'==>'(X1,'+'(X1,'==>'('==>'(esk3_0,X1),esk3_0))) = '==>'('==>'(esk3_0,X1),esk3_0),
inference(spm,[status(thm)],[c_0_146,c_0_168]) ).
cnf(c_0_174,negated_conjecture,
'==>'(X1,'==>'(X2,'+'(esk3_0,'==>'(esk2_0,X1)))) = '==>'(X2,'==>'(X1,esk3_0)),
inference(spm,[status(thm)],[c_0_164,c_0_169]) ).
cnf(c_0_175,plain,
'==>'(X1,X1) = '0',
inference(spm,[status(thm)],[c_0_37,c_0_170]) ).
cnf(c_0_176,negated_conjecture,
'>='(X1,'==>'('==>'(esk1_0,esk3_0),'+'('==>'(esk3_0,esk1_0),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_171]),c_0_22]) ).
cnf(c_0_177,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_30,c_0_172]),c_0_18]),c_0_132]) ).
cnf(c_0_178,negated_conjecture,
'==>'('==>'(X1,esk3_0),'+'(esk3_0,'==>'(X1,esk3_0))) = esk3_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_68]),c_0_17]),c_0_68]),c_0_17]),c_0_175]),c_0_43]),c_0_47]),c_0_18]),c_0_175]),c_0_43]),c_0_47]) ).
cnf(c_0_179,negated_conjecture,
'>='('==>'(esk1_0,esk2_0),esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_178]) ).
cnf(c_0_180,negated_conjecture,
'>='('0','==>'(esk3_0,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_179]),c_0_172]) ).
cnf(c_0_181,negated_conjecture,
~ '>='(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_182,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_180]),c_0_17]),c_0_181]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL890+1 : TPTP v8.1.2. Released v5.5.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 01:53:24 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 40.97/41.06 % Version : CSE_E---1.5
% 40.97/41.06 % Problem : theBenchmark.p
% 40.97/41.06 % Proof found
% 40.97/41.06 % SZS status Theorem for theBenchmark.p
% 40.97/41.06 % SZS output start Proof
% See solution above
% 40.97/41.07 % Total time : 40.496000 s
% 40.97/41.07 % SZS output end Proof
% 40.97/41.07 % Total time : 40.501000 s
%------------------------------------------------------------------------------