%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL900+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 49.17s 7.67s
% Output : CNFRefutation 49.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 128 ( 103 unt; 0 def)
% Number of atoms : 161 ( 79 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 61 ( 28 ~; 25 |; 3 &)
% ( 1 <=>; 4 =>; 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 : 262 ( 35 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(sos_09,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(sos_08,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_06,axiom,
! [X7,X8] :
( ( '>='(X8,X7)
& '>='(X7,X8) )
=> X7 = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(sos_07,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(sos_12,axiom,
! [X1] : '+'(X1,'1') = '1',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(sos_04,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(sos_05,axiom,
! [X4,X5,X6] :
( ( '>='(X5,X6)
& '>='(X4,X5) )
=> '>='(X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(sos_13,axiom,
! [X1,X2] : '==>'('==>'(X1,X2),X2) = '==>'('==>'(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
fof(sos_11,axiom,
! [X18,X19,X20] :
( '>='(X18,X19)
=> '>='('==>'(X20,X18),'==>'(X20,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
fof(sos_01,axiom,
! [X1,X2,X3] : '+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
fof(goals_14,conjecture,
! [X21,X22] : '+'(X21,'==>'(X21,X22)) = '+'(X22,'==>'(X22,X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(c_0_13,plain,
! [X28] : '+'(X28,'0') = X28,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_14,plain,
! [X26,X27] : '+'(X26,X27) = '+'(X27,X26),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_15,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])])]) ).
fof(c_0_16,plain,
! [X38] : '>='(X38,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
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,
! [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])])]) ).
fof(c_0_20,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_21,plain,
! [X48] : '+'(X48,'1') = '1',
inference(variable_rename,[status(thm)],[sos_12]) ).
fof(c_0_22,plain,
! [X29] : '>='(X29,X29),
inference(variable_rename,[status(thm)],[sos_04]) ).
cnf(c_0_23,plain,
( ~ '>='(X1,X2)
| '>='('+'(X1,X3),'+'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( ~ '>='(X2,X1)
| ~ '>='(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( ~ '>='('+'(X1,X2),X3)
| '>='(X2,'==>'(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
'+'(X1,'1') = '1',
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,plain,
! [X30,X31,X32] :
( '>='(X30,X32)
| ~ '>='(X31,X32)
| ~ '>='(X30,X31) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])])]) ).
cnf(c_0_30,plain,
( ~ '>='(X1,'==>'(X2,X3))
| '>='('+'(X2,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
'>='('+'(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
fof(c_0_33,plain,
! [X49,X50] : '==>'('==>'(X49,X50),X50) = '==>'('==>'(X50,X49),X49),
inference(variable_rename,[status(thm)],[sos_13]) ).
cnf(c_0_34,plain,
( ~ '>='('0',X1)
| '0' = X1 ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_35,plain,
'>='(X1,'==>'(X2,'0')),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_36,plain,
'+'('1',X1) = '1',
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_37,plain,
( ~ '>='(X2,X3)
| ~ '>='(X1,X2)
| '>='(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,plain,
'>='(X1,'==>'(X2,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_40,plain,
'==>'('==>'(X1,X2),X2) = '==>'('==>'(X2,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
'==>'(X1,'0') = '0',
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_42,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_43,plain,
'>='('1',X1),
inference(spm,[status(thm)],[c_0_32,c_0_36]) ).
cnf(c_0_44,plain,
( ~ '>='(X1,'+'(X3,'==>'(X3,X2)))
| '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
'>='('+'(X1,X2),'+'('==>'(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_46,plain,
'==>'('==>'('0',X1),X1) = '0',
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
( ~ '>='(X1,X2)
| '>='('==>'(X3,X1),'==>'(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_48,plain,
! [X23,X24,X25] : '+'('+'(X23,X24),X25) = '+'(X23,'+'(X24,X25)),
inference(variable_rename,[status(thm)],[sos_01]) ).
cnf(c_0_49,plain,
( ~ '>='(X1,'1')
| X1 = '1' ),
inference(spm,[status(thm)],[c_0_26,c_0_43]) ).
cnf(c_0_50,plain,
'>='('+'(X1,'==>'('==>'(X2,X1),X3)),X3),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
( ~ '>='(X1,X2)
| '>='('0','==>'(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_52,plain,
'>='('+'('==>'('0',X1),X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_46]),c_0_24])]) ).
cnf(c_0_53,plain,
'>='('==>'(X1,'1'),'==>'(X1,X2)),
inference(spm,[status(thm)],[c_0_47,c_0_43]) ).
cnf(c_0_54,plain,
( ~ '>='('1',X2)
| '>='(X1,'==>'('1',X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_36]) ).
cnf(c_0_55,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_56,plain,
'+'(X1,'==>'('==>'(X2,X1),'1')) = '1',
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,plain,
'>='('0','==>'('+'(X1,'==>'(X1,X2)),X2)),
inference(spm,[status(thm)],[c_0_51,c_0_38]) ).
cnf(c_0_58,plain,
'>='('==>'('0',X1),X1),
inference(spm,[status(thm)],[c_0_52,c_0_17]) ).
cnf(c_0_59,plain,
'>='('0','==>'('==>'(X1,'1'),'==>'(X1,X2))),
inference(spm,[status(thm)],[c_0_51,c_0_53]) ).
cnf(c_0_60,plain,
'>='(X1,'==>'('1',X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_43])]) ).
cnf(c_0_61,plain,
'+'(X1,'+'(X2,X3)) = '+'(X2,'+'(X3,X1)),
inference(spm,[status(thm)],[c_0_55,c_0_18]) ).
cnf(c_0_62,plain,
'+'(X1,'==>'('==>'('==>'(X1,X2),X2),'1')) = '1',
inference(spm,[status(thm)],[c_0_56,c_0_40]) ).
cnf(c_0_63,plain,
'==>'('+'(X1,'==>'(X1,X2)),X2) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_57]),c_0_24])]) ).
cnf(c_0_64,plain,
'==>'('0',X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_58]),c_0_39])]) ).
cnf(c_0_65,plain,
'==>'('==>'(X1,'1'),'==>'(X1,X2)) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_59]),c_0_24])]) ).
cnf(c_0_66,plain,
'==>'('1',X1) = '0',
inference(spm,[status(thm)],[c_0_34,c_0_60]) ).
cnf(c_0_67,plain,
'+'(X1,'+'(X2,X3)) = '+'(X3,'+'(X2,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_18]) ).
cnf(c_0_68,plain,
'+'(X1,'+'('==>'(X1,X2),'==>'(X2,'1'))) = '1',
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_55]) ).
cnf(c_0_69,plain,
'==>'(X1,'==>'('==>'(X1,'1'),X2)) = '0',
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_40]),c_0_66]),c_0_64]) ).
cnf(c_0_70,plain,
'>='('0','==>'(X1,X1)),
inference(spm,[status(thm)],[c_0_51,c_0_31]) ).
cnf(c_0_71,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_72,plain,
'>='('+'(X1,'==>'(X1,'1')),X2),
inference(spm,[status(thm)],[c_0_30,c_0_53]) ).
cnf(c_0_73,plain,
'+'('==>'(X1,'1'),'+'(X2,'==>'(X2,X1))) = '1',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_18]) ).
cnf(c_0_74,plain,
'==>'('==>'('==>'('==>'(X1,'1'),X2),X1),X1) = '==>'('==>'(X1,'1'),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_69]),c_0_64]) ).
cnf(c_0_75,plain,
'==>'(X1,X1) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_70]),c_0_24])]) ).
cnf(c_0_76,plain,
'>='(X1,'==>'(X2,'==>'(X3,'+'(X3,'+'(X2,X1))))),
inference(spm,[status(thm)],[c_0_27,c_0_71]) ).
cnf(c_0_77,plain,
'+'(X1,'+'(X2,'==>'(X1,'==>'(X2,'1')))) = '1',
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_40]),c_0_66]),c_0_64]),c_0_18]) ).
cnf(c_0_78,plain,
'+'(X1,'==>'(X1,'1')) = '1',
inference(spm,[status(thm)],[c_0_49,c_0_72]) ).
cnf(c_0_79,plain,
( ~ '>='('+'(X2,'+'(X3,X1)),X4)
| '>='(X1,'==>'('+'(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_27,c_0_55]) ).
cnf(c_0_80,plain,
'+'(X1,'+'(X2,'==>'(X2,'==>'(X1,'1')))) = '1',
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_64]),c_0_75]),c_0_64]) ).
cnf(c_0_81,plain,
'>='('0','==>'('+'(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_51,c_0_32]) ).
cnf(c_0_82,plain,
'>='('==>'(X1,'==>'(X2,'1')),'==>'(X2,'==>'(X1,'1'))),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,plain,
( ~ '>='('==>'(X1,'==>'(X2,'+'(X2,'+'(X1,X3)))),X3)
| '==>'(X1,'==>'(X2,'+'(X2,'+'(X1,X3)))) = X3 ),
inference(spm,[status(thm)],[c_0_26,c_0_76]) ).
cnf(c_0_84,plain,
'+'(X1,'+'(X2,'==>'('+'(X1,X2),'1'))) = '1',
inference(spm,[status(thm)],[c_0_55,c_0_78]) ).
cnf(c_0_85,plain,
'>='('==>'(X1,'==>'(X2,'1')),'==>'('+'(X2,X1),X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_43])]) ).
cnf(c_0_86,plain,
( ~ '>='('==>'(X1,'+'(X1,X2)),X2)
| '==>'(X1,'+'(X1,X2)) = X2 ),
inference(spm,[status(thm)],[c_0_26,c_0_71]) ).
cnf(c_0_87,plain,
'>='('==>'(X1,'+'(X2,'==>'(X2,X3))),'==>'(X1,X3)),
inference(spm,[status(thm)],[c_0_47,c_0_38]) ).
cnf(c_0_88,plain,
'==>'('+'(X1,X2),X2) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_81]),c_0_24])]) ).
cnf(c_0_89,plain,
'>='('0','==>'(X1,'==>'(X2,X1))),
inference(spm,[status(thm)],[c_0_51,c_0_39]) ).
cnf(c_0_90,plain,
'==>'(X1,'==>'(X2,'1')) = '==>'(X2,'==>'(X1,'1')),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_82]),c_0_82])]) ).
cnf(c_0_91,plain,
'==>'('+'(X1,X2),'1') = '==>'(X2,'==>'(X1,'1')),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85])]) ).
cnf(c_0_92,plain,
'==>'(X1,'+'(X1,'==>'(X1,X2))) = '==>'(X1,X2),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_93,plain,
'==>'('+'(X1,X2),X1) = '0',
inference(spm,[status(thm)],[c_0_88,c_0_18]) ).
cnf(c_0_94,plain,
'==>'(X1,'==>'(X2,X1)) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_89]),c_0_24])]) ).
cnf(c_0_95,plain,
'==>'('==>'(X1,'1'),'==>'(X2,'1')) = '==>'(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_74]),c_0_75]),c_0_64]),c_0_75]),c_0_64]) ).
cnf(c_0_96,plain,
'==>'('+'(X1,X2),'==>'(X3,'1')) = '==>'(X3,'==>'(X2,'==>'(X1,'1'))),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_97,plain,
'==>'('==>'(X1,X2),'+'(X1,'==>'(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_92]),c_0_93]),c_0_64]) ).
cnf(c_0_98,plain,
'==>'('==>'('==>'(X1,X2),X2),X2) = '==>'('0','==>'(X1,X2)),
inference(spm,[status(thm)],[c_0_40,c_0_94]) ).
cnf(c_0_99,plain,
'==>'('==>'(X1,'1'),X2) = '==>'('==>'(X2,'1'),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_74]),c_0_75]),c_0_64]),c_0_75]),c_0_64]) ).
cnf(c_0_100,plain,
'==>'(X1,'==>'(X2,'==>'(X3,'1'))) = '==>'(X2,'==>'(X3,'==>'(X1,'1'))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_55]),c_0_91]),c_0_91]),c_0_96]) ).
cnf(c_0_101,plain,
'==>'('==>'(X1,'==>'(X2,'1')),'1') = '+'(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_91]),c_0_55]),c_0_80]) ).
cnf(c_0_102,plain,
'==>'('==>'('==>'(X1,X2),X2),X2) = '==>'(X1,X2),
inference(rw,[status(thm)],[c_0_98,c_0_64]) ).
cnf(c_0_103,plain,
'==>'('==>'(X1,'1'),'1') = '==>'('0',X1),
inference(spm,[status(thm)],[c_0_40,c_0_66]) ).
cnf(c_0_104,plain,
'==>'('+'(X1,X2),X3) = '==>'(X1,'==>'(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_95]),c_0_101]) ).
cnf(c_0_105,plain,
'==>'('==>'('==>'(X1,X2),X2),X1) = '==>'(X2,X1),
inference(spm,[status(thm)],[c_0_102,c_0_40]) ).
cnf(c_0_106,plain,
'==>'(X1,'==>'(X2,X3)) = '==>'(X2,'==>'(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_103]),c_0_64]),c_0_101]),c_0_104]) ).
cnf(c_0_107,plain,
'==>'('==>'(X1,'1'),'1') = X1,
inference(rw,[status(thm)],[c_0_103,c_0_64]) ).
cnf(c_0_108,plain,
'+'(X1,'==>'('==>'('==>'(X1,'1'),X2),X2)) = '+'(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_105]),c_0_101]) ).
cnf(c_0_109,plain,
'==>'('==>'('==>'(X1,X2),X2),'==>'(X3,X2)) = '==>'(X3,'==>'(X1,X2)),
inference(spm,[status(thm)],[c_0_106,c_0_102]) ).
cnf(c_0_110,plain,
'+'('==>'(X1,'1'),X2) = '==>'('==>'(X2,X1),'1'),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_74]),c_0_75]),c_0_64]),c_0_75]),c_0_64]) ).
cnf(c_0_111,plain,
'+'(X1,'==>'(X2,'1')) = '==>'('==>'(X1,X2),'1'),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_99]),c_0_107]) ).
cnf(c_0_112,plain,
'==>'('==>'(X1,'+'(X2,X3)),'1') = '+'('==>'(X3,'==>'(X2,'1')),X1),
inference(spm,[status(thm)],[c_0_101,c_0_101]) ).
cnf(c_0_113,plain,
'==>'('==>'('==>'(X1,'+'(X2,X1)),X2),'1') = '==>'('==>'('==>'(X1,'1'),X2),'1'),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_90]),c_0_101]),c_0_110]),c_0_110]) ).
cnf(c_0_114,plain,
'+'('==>'(X1,'==>'(X2,'1')),X3) = '+'(X3,'==>'(X2,'==>'(X1,'1'))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_104]),c_0_112]) ).
cnf(c_0_115,plain,
'==>'('==>'(X1,'+'(X2,X1)),X2) = '==>'('==>'(X1,'1'),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_113]),c_0_107]) ).
cnf(c_0_116,plain,
( ~ '>='(X1,X3)
| '>='(X1,'==>'(X2,X3)) ),
inference(spm,[status(thm)],[c_0_37,c_0_39]) ).
cnf(c_0_117,plain,
'+'(X1,'==>'(X2,'+'(X3,'==>'(X3,X2)))) = '+'('==>'(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_95]),c_0_110]),c_0_101]),c_0_18]) ).
cnf(c_0_118,plain,
'>='(X1,'==>'(X2,'==>'(X3,X1))),
inference(spm,[status(thm)],[c_0_116,c_0_39]) ).
fof(c_0_119,negated_conjecture,
~ ! [X21,X22] : '+'(X21,'==>'(X21,X22)) = '+'(X22,'==>'(X22,X21)),
inference(assume_negation,[status(cth)],[goals_14]) ).
cnf(c_0_120,plain,
'==>'(X1,'+'(X2,'==>'(X2,X1))) = '==>'(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_117]),c_0_17]) ).
cnf(c_0_121,plain,
'>='('0','==>'(X1,'==>'(X2,'==>'(X3,X1)))),
inference(spm,[status(thm)],[c_0_51,c_0_118]) ).
fof(c_0_122,negated_conjecture,
'+'(esk1_0,'==>'(esk1_0,esk2_0)) != '+'(esk2_0,'==>'(esk2_0,esk1_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_119])])])]) ).
cnf(c_0_123,plain,
'==>'('==>'(X1,X2),'+'(X2,'==>'(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_120]),c_0_63]),c_0_64]) ).
cnf(c_0_124,plain,
'==>'(X1,'==>'(X2,'==>'(X3,X1))) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_121]),c_0_24])]) ).
cnf(c_0_125,negated_conjecture,
'+'(esk1_0,'==>'(esk1_0,esk2_0)) != '+'(esk2_0,'==>'(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_126,plain,
'+'(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_123,c_0_123]),c_0_104]),c_0_124]),c_0_18]),c_0_64]) ).
cnf(c_0_127,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_126])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL900+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 01:10:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.17/7.67 % Version: 3.5.1
% 49.17/7.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 49.17/7.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 49.17/7.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 49.17/7.67 % Starting new_bool_3 with 300s (1) cores
% 49.17/7.67 % Starting new_bool_1 with 300s (1) cores
% 49.17/7.67 % Starting sh5l with 300s (1) cores
% 49.17/7.67 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3836083 completed with status 0
% 49.17/7.67 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 49.17/7.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 49.17/7.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 49.17/7.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 49.17/7.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 49.17/7.67 % No SInE strategy applied
% 49.17/7.67 % Search class: FHUSM-FFSF22-SFFFFFNN
% 49.17/7.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 49.17/7.67 % Starting SubtermCWHack with 136s (1) cores
% 49.17/7.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 49.17/7.67 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 49.17/7.67 % Starting new_bool_3 with 136s (1) cores
% 49.17/7.67 % Starting new_bool_1 with 136s (1) cores
% 49.17/7.67 % H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with pid 3836092 completed with status 0
% 49.17/7.67 % Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S
% 49.17/7.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 49.17/7.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 49.17/7.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 49.17/7.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 49.17/7.67 % No SInE strategy applied
% 49.17/7.67 % Search class: FHUSM-FFSF22-SFFFFFNN
% 49.17/7.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 49.17/7.67 % Starting SubtermCWHack with 136s (1) cores
% 49.17/7.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 49.17/7.67 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 49.17/7.67 % Preprocessing time : 0.001 s
% 49.17/7.67 % Presaturation interreduction done
% 49.17/7.67
% 49.17/7.67 % Proof found!
% 49.17/7.67 % SZS status Theorem
% 49.17/7.67 % SZS output start CNFRefutation
% See solution above
% 49.17/7.67 % Parsed axioms : 14
% 49.17/7.67 % Removed by relevancy pruning/SinE : 0
% 49.17/7.67 % Initial clauses : 15
% 49.17/7.67 % Removed in clause preprocessing : 0
% 49.17/7.67 % Initial clauses in saturation : 15
% 49.17/7.67 % Processed clauses : 21484
% 49.17/7.67 % ...of these trivial : 5136
% 49.17/7.67 % ...subsumed : 14722
% 49.17/7.67 % ...remaining for further processing : 1626
% 49.17/7.67 % Other redundant clauses eliminated : 0
% 49.17/7.67 % Clauses deleted for lack of memory : 0
% 49.17/7.67 % Backward-subsumed : 5
% 49.17/7.67 % Backward-rewritten : 569
% 49.17/7.67 % Generated clauses : 676970
% 49.17/7.67 % ...of the previous two non-redundant : 300464
% 49.17/7.67 % ...aggressively subsumed : 0
% 49.17/7.67 % Contextual simplify-reflections : 0
% 49.17/7.67 % Paramodulations : 676970
% 49.17/7.67 % Factorizations : 0
% 49.17/7.67 % NegExts : 0
% 49.17/7.67 % Equation resolutions : 0
% 49.17/7.67 % Disequality decompositions : 0
% 49.17/7.67 % Total rewrite steps : 1044179
% 49.17/7.67 % ...of those cached : 925456
% 49.17/7.67 % Propositional unsat checks : 0
% 49.17/7.67 % Propositional check models : 0
% 49.17/7.67 % Propositional check unsatisfiable : 0
% 49.17/7.67 % Propositional clauses : 0
% 49.17/7.67 % Propositional clauses after purity: 0
% 49.17/7.67 % Propositional unsat core size : 0
% 49.17/7.67 % Propositional preprocessing time : 0.000
% 49.17/7.67 % Propositional encoding time : 0.000
% 49.17/7.67 % Propositional solver time : 0.000
% 49.17/7.67 % Success case prop preproc time : 0.000
% 49.17/7.67 % Success case prop encoding time : 0.000
% 49.17/7.67 % Success case prop solver time : 0.000
% 49.17/7.67 % Current number of processed clauses : 1037
% 49.17/7.67 % Positive orientable unit clauses : 835
% 49.17/7.67 % Positive unorientable unit clauses: 12
% 49.17/7.67 % Negative unit clauses : 0
% 49.17/7.67 % Non-unit-clauses : 190
% 49.17/7.67 % Current number of unprocessed clauses: 278197
% 49.17/7.67 % ...number of literals in the above : 312758
% 49.17/7.67 % Current number of archived formulas : 0
% 49.17/7.67 % Current number of archived clauses : 589
% 49.17/7.67 % Clause-clause subsumption calls (NU) : 44142
% 49.17/7.67 % Rec. Clause-clause subsumption calls : 43762
% 49.17/7.67 % Non-unit clause-clause subsumptions : 14402
% 49.17/7.67 % Unit Clause-clause subsumption calls : 550
% 49.17/7.67 % Rewrite failures with RHS unbound : 0
% 49.17/7.67 % BW rewrite match attempts : 38060
% 49.17/7.67 % BW rewrite match successes : 1272
% 49.17/7.67 % Condensation attempts : 0
% 49.17/7.67 % Condensation successes : 0
% 49.17/7.67 % Termbank termtop insertions : 7028552
% 49.17/7.67 % Search garbage collected termcells : 118
% 49.17/7.67
% 49.17/7.67 % -------------------------------------------------
% 49.17/7.67 % User time : 6.606 s
% 49.17/7.67 % System time : 0.279 s
% 49.17/7.67 % Total time : 6.885 s
% 49.17/7.67 % Maximum resident set size: 3392 pages
% 49.17/7.67
% 49.17/7.67 % -------------------------------------------------
% 49.17/7.67 % User time : 33.172 s
% 49.17/7.67 % System time : 1.530 s
% 49.17/7.67 % Total time : 34.702 s
% 49.17/7.67 % Maximum resident set size: 4864 pages
% 49.17/7.67 % E exiting
%------------------------------------------------------------------------------