%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX045+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 03:13:55 PM UTC 2026
% Result : Theorem 217.39s 28.30s
% Output : CNFRefutation 217.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 25
% Syntax : Number of formulae : 127 ( 28 unt; 0 def)
% Number of atoms : 332 ( 88 equ)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 336 ( 131 ~; 147 |; 33 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 239 ( 17 sgn 122 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(id21,axiom,
! [X16,X17] :
( '@=<_succeeds'(X16,X17)
<=> ( X16 = '0'
| ? [X1,X2] :
( '@=<_succeeds'(X1,X2)
& X17 = s(X2)
& X16 = s(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id21) ).
fof(id27,axiom,
! [X16] :
( nat_succeeds(X16)
<=> ( X16 = '0'
| ? [X17] :
( nat_succeeds(X17)
& X16 = s(X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id27) ).
fof('lemma-(leq:types)',axiom,
! [X18,X19] :
( '@=<_succeeds'(X18,X19)
=> nat_succeeds(X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(leq:types)') ).
fof('corollary-(plus:successor)',axiom,
! [X18,X19] :
( nat_succeeds(X18)
=> '@+'(s(X18),X19) = s('@+'(X18,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(plus:successor)') ).
fof('corollary-(plus:zero)',axiom,
! [X19] : '@+'('0',X19) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(plus:zero)') ).
fof('theorem-(leq:transitive)',axiom,
! [X18,X19,X20] :
( ( '@=<_succeeds'(X19,X20)
& '@=<_succeeds'(X18,X19) )
=> '@=<_succeeds'(X18,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem-(leq:transitive)') ).
fof('(@+)/2',axiom,
! [X18,X19,X20] :
( nat_succeeds(X18)
=> ( '@+'(X18,X19) = X20
<=> plus_succeeds(X18,X19,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','(@+)/2') ).
fof('lemma-(leq:plus:inverse)',conjecture,
! [X18,X19,X20] :
( ( '@=<_succeeds'('@+'(X18,X19),'@+'(X18,X20))
& nat_succeeds(X18) )
=> '@=<_succeeds'(X19,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(leq:plus:inverse)') ).
fof(id1,axiom,
! [X1] : '0' != s(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id1) ).
fof('lemma-(less:plus:inverse)',axiom,
! [X18,X19,X20] :
( ( '@<_succeeds'('@+'(X18,X19),'@+'(X18,X20))
& nat_succeeds(X18) )
=> '@<_succeeds'(X19,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(less:plus:inverse)') ).
fof('corollary-(less:leq:total)',axiom,
! [X18,X19] :
( ( nat_succeeds(X19)
& nat_succeeds(X18) )
=> ( '@=<_succeeds'(X19,X18)
| '@<_succeeds'(X18,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(less:leq:total)') ).
fof('lemma-(plus:types:3)',axiom,
! [X18,X19,X20] :
( ( nat_succeeds(X20)
& plus_succeeds(X18,X19,X20) )
=> nat_succeeds(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(plus:types:3)') ).
fof(id2,axiom,
! [X2,X3] :
( s(X2) = s(X3)
=> X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id2) ).
fof('lemma-(less:one)',axiom,
! [X18] :
( nat_succeeds(X18)
=> '@<_succeeds'(X18,s(X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(less:one)') ).
fof('lemma-(less:successor)',axiom,
! [X18,X19] :
( '@<_succeeds'(X18,X19)
=> ? [X20] : X19 = s(X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(less:successor)') ).
fof(id24,axiom,
! [X16,X17] :
( '@<_succeeds'(X16,X17)
<=> ( ? [X3] :
( X17 = s(X3)
& X16 = '0' )
| ? [X1,X2] :
( '@<_succeeds'(X1,X2)
& X17 = s(X2)
& X16 = s(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id24) ).
fof('theorem-(plus:commutative)',axiom,
! [X18,X19] :
( ( nat_succeeds(X19)
& nat_succeeds(X18) )
=> '@+'(X18,X19) = '@+'(X19,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem-(plus:commutative)') ).
fof('corollary-(less:plus:second)',axiom,
! [X18,X19] :
( nat_succeeds(X18)
=> '@<_succeeds'(X18,'@+'(X18,s(X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(less:plus:second)') ).
fof('lemma-(leq:plus:second)',axiom,
! [X18,X19,X20] :
( ( '@=<_succeeds'(X19,X20)
& nat_succeeds(X18) )
=> '@=<_succeeds'('@+'(X18,X19),'@+'(X18,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(leq:plus:second)') ).
fof('corollary-(less:plus)',axiom,
! [X18,X19] :
( '@<_succeeds'(X18,X19)
=> ? [X20] : '@+'(X18,s(X20)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(less:plus)') ).
fof('lemma-(less:types)',axiom,
! [X18,X19] :
( '@<_succeeds'(X18,X19)
=> nat_succeeds(X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(less:types)') ).
fof('corollary-(leq:plus:first)',axiom,
! [X18,X19] :
( nat_succeeds(X18)
=> '@=<_succeeds'(X18,'@+'(X18,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(leq:plus:first)') ).
fof('lemma-(plus:types:1)',axiom,
! [X18,X19,X20] :
( plus_succeeds(X18,X19,X20)
=> nat_succeeds(X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(plus:types:1)') ).
fof('theorem-(less:leq:transitive)',axiom,
! [X18,X19,X20] :
( ( '@=<_succeeds'(X19,X20)
& '@<_succeeds'(X18,X19) )
=> '@<_succeeds'(X18,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem-(less:leq:transitive)') ).
fof('lemma-(less:plus:second)',axiom,
! [X18,X19,X20] :
( ( '@<_succeeds'(X19,X20)
& nat_succeeds(X18) )
=> '@<_succeeds'('@+'(X18,X19),'@+'(X18,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(less:plus:second)') ).
fof(c_0_25,plain,
! [X26,X27,X30,X31,X32,X33] :
( ( '@=<_succeeds'(X30,X31)
| X30 != '0' )
& ( '@=<_succeeds'(X30,X31)
| ~ '@=<_succeeds'(X32,X33)
| X31 != s(X33)
| X30 != s(X32) )
& ( ~ '@=<_succeeds'(X26,X27)
| X26 = '0'
| '@=<_succeeds'(esk4_2(X26,X27),esk5_2(X26,X27)) )
& ( ~ '@=<_succeeds'(X26,X27)
| X26 = '0'
| X27 = s(esk5_2(X26,X27)) )
& ( ~ '@=<_succeeds'(X26,X27)
| X26 = '0'
| X26 = s(esk4_2(X26,X27)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[id21])])])])])])]) ).
fof(c_0_26,plain,
! [X138,X140,X141] :
( ( nat_succeeds(X140)
| X140 != '0' )
& ( nat_succeeds(X140)
| ~ nat_succeeds(X141)
| X140 != s(X141) )
& ( ~ nat_succeeds(X138)
| X138 = '0'
| nat_succeeds(esk18_1(X138)) )
& ( ~ nat_succeeds(X138)
| X138 = '0'
| X138 = s(esk18_1(X138)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[id27])])])])])])]) ).
fof(c_0_27,plain,
! [X34,X35] :
( nat_succeeds(X34)
| ~ '@=<_succeeds'(X34,X35) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['lemma-(leq:types)'])])]) ).
cnf(c_0_28,plain,
( ~ '@=<_succeeds'(X2,X4)
| X3 != s(X4)
| X1 != s(X2)
| '@=<_succeeds'(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_29,plain,
! [X83,X84] :
( '@+'(s(X83),X84) = s('@+'(X83,X84))
| ~ nat_succeeds(X83) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['corollary-(plus:successor)'])])]) ).
fof(c_0_30,plain,
! [X82] : '@+'('0',X82) = X82,
inference(variable_rename,[status(thm)],['corollary-(plus:zero)']) ).
cnf(c_0_31,plain,
( X1 != '0'
| nat_succeeds(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( ~ '@=<_succeeds'(X1,X2)
| nat_succeeds(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( ~ '@=<_succeeds'(X1,X2)
| '@=<_succeeds'(s(X1),s(X2)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_28])]) ).
cnf(c_0_34,plain,
( X1 != '0'
| '@=<_succeeds'(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_35,plain,
! [X57,X58,X59] :
( '@=<_succeeds'(X57,X59)
| ~ '@=<_succeeds'(X58,X59)
| ~ '@=<_succeeds'(X57,X58) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['theorem-(leq:transitive)'])])]) ).
fof(c_0_36,plain,
! [X156,X157,X158] :
( ( ~ nat_succeeds(X156)
| '@+'(X156,X157) = X158
| ~ plus_succeeds(X156,X157,X158) )
& ( ~ nat_succeeds(X156)
| plus_succeeds(X156,X157,X158)
| '@+'(X156,X157) != X158 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['(@+)/2'])])])]) ).
fof(c_0_37,negated_conjecture,
~ ! [X18,X19,X20] :
( ( '@=<_succeeds'('@+'(X18,X19),'@+'(X18,X20))
& nat_succeeds(X18) )
=> '@=<_succeeds'(X19,X20) ),
inference(assume_negation,[status(cth)],['lemma-(leq:plus:inverse)']) ).
fof(c_0_38,plain,
! [X1] : '0' != s(X1),
inference(fof_simplification,[status(thm)],[id1]) ).
fof(c_0_39,plain,
! [X111,X112,X113] :
( '@<_succeeds'(X112,X113)
| ~ '@<_succeeds'('@+'(X111,X112),'@+'(X111,X113))
| ~ nat_succeeds(X111) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['lemma-(less:plus:inverse)'])])]) ).
cnf(c_0_40,plain,
( ~ nat_succeeds(X1)
| '@+'(s(X1),X2) = s('@+'(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,plain,
'@+'('0',X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,plain,
nat_succeeds('0'),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_43,plain,
( ~ '@=<_succeeds'(X1,X2)
| nat_succeeds(s(X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_44,plain,
'@=<_succeeds'('0',X1),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_45,plain,
( ~ '@=<_succeeds'(X2,X3)
| ~ '@=<_succeeds'(X1,X2)
| '@=<_succeeds'(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_46,plain,
! [X47,X48] :
( '@=<_succeeds'(X48,X47)
| '@<_succeeds'(X47,X48)
| ~ nat_succeeds(X48)
| ~ nat_succeeds(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['corollary-(less:leq:total)'])])]) ).
fof(c_0_47,plain,
! [X165,X166,X167] :
( nat_succeeds(X166)
| ~ nat_succeeds(X167)
| ~ plus_succeeds(X165,X166,X167) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['lemma-(plus:types:3)'])])]) ).
cnf(c_0_48,plain,
( ~ nat_succeeds(X1)
| '@+'(X1,X2) != X3
| plus_succeeds(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_49,negated_conjecture,
( ~ '@=<_succeeds'(esk2_0,esk3_0)
& '@=<_succeeds'('@+'(esk1_0,esk2_0),'@+'(esk1_0,esk3_0))
& nat_succeeds(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
fof(c_0_50,plain,
! [X143,X144] :
( X143 = X144
| s(X143) != s(X144) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[id2])])]) ).
fof(c_0_51,plain,
! [X117] : '0' != s(X117),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_38])]) ).
cnf(c_0_52,plain,
( ~ '@<_succeeds'('@+'(X1,X2),'@+'(X1,X3))
| ~ nat_succeeds(X1)
| '@<_succeeds'(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_53,plain,
'@+'(s('0'),X1) = s(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_54,plain,
nat_succeeds(s('0')),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_55,plain,
! [X153] :
( '@<_succeeds'(X153,s(X153))
| ~ nat_succeeds(X153) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['lemma-(less:one)'])])]) ).
cnf(c_0_56,plain,
( ~ '@=<_succeeds'(X1,'0')
| '@=<_succeeds'(X1,X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_57,plain,
( ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| '@=<_succeeds'(X2,X1)
| '@<_succeeds'(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,plain,
( ~ nat_succeeds(X3)
| ~ plus_succeeds(X1,X2,X3)
| nat_succeeds(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
( ~ nat_succeeds(X1)
| plus_succeeds(X1,X2,'@+'(X1,X2)) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_60,negated_conjecture,
'@=<_succeeds'('@+'(esk1_0,esk2_0),'@+'(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,plain,
( s(X1) != s(X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_62,plain,
( ~ nat_succeeds(X1)
| X1 = '0'
| X1 = s(esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_63,plain,
'0' != s(X1),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_64,plain,
! [X145,X146] :
( X146 = s(esk19_2(X145,X146))
| ~ '@<_succeeds'(X145,X146) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['lemma-(less:successor)'])])])]) ).
cnf(c_0_65,plain,
( ~ '@<_succeeds'(s(X1),s(X2))
| '@<_succeeds'(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_53])]) ).
cnf(c_0_66,plain,
( ~ nat_succeeds(X1)
| '@<_succeeds'(X1,s(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_67,plain,
! [X128,X129,X133,X134,X135,X136,X137] :
( ( '@<_succeeds'(X133,X134)
| X134 != s(X137)
| X133 != '0' )
& ( '@<_succeeds'(X133,X134)
| ~ '@<_succeeds'(X135,X136)
| X134 != s(X136)
| X133 != s(X135) )
& ( ~ '@<_succeeds'(X128,X129)
| '@<_succeeds'(esk15_2(X128,X129),esk16_2(X128,X129))
| X129 = s(esk17_2(X128,X129)) )
& ( ~ '@<_succeeds'(X128,X129)
| '@<_succeeds'(esk15_2(X128,X129),esk16_2(X128,X129))
| X128 = '0' )
& ( ~ '@<_succeeds'(X128,X129)
| X129 = s(esk16_2(X128,X129))
| X129 = s(esk17_2(X128,X129)) )
& ( ~ '@<_succeeds'(X128,X129)
| X129 = s(esk16_2(X128,X129))
| X128 = '0' )
& ( ~ '@<_succeeds'(X128,X129)
| X128 = s(esk15_2(X128,X129))
| X129 = s(esk17_2(X128,X129)) )
& ( ~ '@<_succeeds'(X128,X129)
| X128 = s(esk15_2(X128,X129))
| X128 = '0' ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[id24])])])])])])]) ).
cnf(c_0_68,negated_conjecture,
~ '@=<_succeeds'(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_69,plain,
( ~ nat_succeeds(X1)
| '@=<_succeeds'(X1,X2)
| '@<_succeeds'('0',X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_42])]) ).
cnf(c_0_70,plain,
( ~ nat_succeeds(X2)
| ~ nat_succeeds('@+'(X2,X1))
| nat_succeeds(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_71,negated_conjecture,
nat_succeeds('@+'(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_32,c_0_60]) ).
cnf(c_0_72,negated_conjecture,
nat_succeeds(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_73,plain,
( ~ nat_succeeds(X1)
| X1 = '0'
| nat_succeeds(esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_74,plain,
( ~ nat_succeeds(s(X1))
| esk18_1(s(X1)) = X1 ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62])]),c_0_63]) ).
fof(c_0_75,plain,
! [X93,X94] :
( '@+'(X93,X94) = '@+'(X94,X93)
| ~ nat_succeeds(X94)
| ~ nat_succeeds(X93) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['theorem-(plus:commutative)'])])]) ).
cnf(c_0_76,plain,
( ~ '@<_succeeds'(X1,X2)
| X2 = s(esk19_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_77,plain,
( ~ nat_succeeds(s(X1))
| '@<_succeeds'(X1,s(X1)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_78,plain,
( ~ '@<_succeeds'(X2,X1)
| X2 = s(esk15_2(X2,X1))
| X1 = s(esk17_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_79,negated_conjecture,
( ~ nat_succeeds(esk2_0)
| '@<_succeeds'('0',esk2_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_80,negated_conjecture,
nat_succeeds(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_81,plain,
( ~ nat_succeeds(s(X1))
| nat_succeeds(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_63]) ).
fof(c_0_82,plain,
! [X104,X105] :
( '@<_succeeds'(X104,'@+'(X104,s(X105)))
| ~ nat_succeeds(X104) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['corollary-(less:plus:second)'])])]) ).
cnf(c_0_83,plain,
( ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| '@+'(X1,X2) = '@+'(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_84,plain,
( ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X2)
| esk19_2(X1,X2) = esk18_1(X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_76]) ).
cnf(c_0_85,plain,
( ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X2)
| '@<_succeeds'(esk17_2(X1,X2),X2)
| s(esk15_2(X1,X2)) = X1 ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_86,negated_conjecture,
'@<_succeeds'('0',esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_87,plain,
( ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X2)
| nat_succeeds(esk19_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_76]) ).
cnf(c_0_88,plain,
( ~ nat_succeeds(X1)
| '@<_succeeds'(X1,'@+'(X1,s(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_89,plain,
( ~ nat_succeeds(X1)
| '@+'(X1,s('0')) = s(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_53]),c_0_54])]) ).
cnf(c_0_90,plain,
( ~ '@<_succeeds'(X2,X1)
| ~ nat_succeeds(X1)
| s(esk18_1(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_76,c_0_84]) ).
cnf(c_0_91,negated_conjecture,
'@<_succeeds'(esk17_2('0',esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_80])]),c_0_63]) ).
cnf(c_0_92,plain,
( ~ '@<_succeeds'(X2,X1)
| ~ nat_succeeds(X1)
| nat_succeeds(esk18_1(X1)) ),
inference(spm,[status(thm)],[c_0_87,c_0_84]) ).
cnf(c_0_93,plain,
( ~ '@<_succeeds'(X1,s(X2))
| esk17_2(X1,s(X2)) = X2
| s(esk15_2(X1,s(X2))) = X1 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_78])]) ).
cnf(c_0_94,plain,
'@<_succeeds'('0',s(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_41]),c_0_42])]) ).
fof(c_0_95,plain,
! [X63,X64,X65] :
( '@=<_succeeds'('@+'(X63,X64),'@+'(X63,X65))
| ~ '@=<_succeeds'(X64,X65)
| ~ nat_succeeds(X63) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['lemma-(leq:plus:second)'])])]) ).
fof(c_0_96,plain,
! [X98,X99] :
( '@+'(X98,s(esk12_2(X98,X99))) = X99
| ~ '@<_succeeds'(X98,X99) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['corollary-(less:plus)'])])])]) ).
fof(c_0_97,plain,
! [X178,X179] :
( nat_succeeds(X178)
| ~ '@<_succeeds'(X178,X179) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['lemma-(less:types)'])])]) ).
fof(c_0_98,plain,
! [X69,X70] :
( '@=<_succeeds'(X69,'@+'(X69,X70))
| ~ nat_succeeds(X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['corollary-(leq:plus:first)'])])]) ).
fof(c_0_99,plain,
! [X159,X160,X161] :
( nat_succeeds(X159)
| ~ plus_succeeds(X159,X160,X161) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['lemma-(plus:types:1)'])])]) ).
cnf(c_0_100,plain,
( ~ nat_succeeds(X1)
| plus_succeeds(X1,s('0'),s(X1)) ),
inference(spm,[status(thm)],[c_0_59,c_0_89]) ).
cnf(c_0_101,negated_conjecture,
s(esk18_1(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_80])]) ).
cnf(c_0_102,negated_conjecture,
nat_succeeds(esk18_1(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_86]),c_0_80])]) ).
cnf(c_0_103,plain,
esk17_2('0',s(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_93])]),c_0_94])]) ).
fof(c_0_104,plain,
! [X54,X55,X56] :
( '@<_succeeds'(X54,X56)
| ~ '@=<_succeeds'(X55,X56)
| ~ '@<_succeeds'(X54,X55) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['theorem-(less:leq:transitive)'])])]) ).
cnf(c_0_105,plain,
( ~ '@=<_succeeds'(X2,X3)
| ~ nat_succeeds(X1)
| '@=<_succeeds'('@+'(X1,X2),'@+'(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_106,plain,
( ~ '@<_succeeds'(X1,X2)
| '@+'(X1,s(esk12_2(X1,X2))) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_107,plain,
( ~ '@<_succeeds'(X1,X2)
| nat_succeeds(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_108,plain,
( ~ nat_succeeds(X1)
| '@=<_succeeds'(X1,'@+'(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_109,plain,
( ~ nat_succeeds(X1)
| ~ plus_succeeds(X1,X2,X3)
| '@+'(X1,X2) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_110,plain,
( ~ plus_succeeds(X1,X2,X3)
| nat_succeeds(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_111,negated_conjecture,
plus_succeeds(esk18_1(esk2_0),s('0'),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102])]) ).
cnf(c_0_112,negated_conjecture,
esk18_1(esk2_0) = esk17_2('0',esk2_0),
inference(spm,[status(thm)],[c_0_103,c_0_101]) ).
cnf(c_0_113,plain,
( ~ '@=<_succeeds'(X2,X3)
| ~ '@<_succeeds'(X1,X2)
| '@<_succeeds'(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_114,plain,
( ~ '@=<_succeeds'(X2,s(esk12_2(X1,X3)))
| ~ '@<_succeeds'(X1,X3)
| '@=<_succeeds'('@+'(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_115,plain,
'@=<_succeeds'(s('0'),s(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_53]),c_0_54])]) ).
cnf(c_0_116,plain,
( ~ plus_succeeds(X1,X2,X3)
| '@+'(X1,X2) = X3 ),
inference(csr,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_117,negated_conjecture,
plus_succeeds(esk17_2('0',esk2_0),s('0'),esk2_0),
inference(rw,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_118,negated_conjecture,
( ~ '@<_succeeds'(X1,'@+'(esk1_0,esk2_0))
| '@<_succeeds'(X1,'@+'(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_113,c_0_60]) ).
fof(c_0_119,plain,
! [X101,X102,X103] :
( '@<_succeeds'('@+'(X101,X102),'@+'(X101,X103))
| ~ '@<_succeeds'(X102,X103)
| ~ nat_succeeds(X101) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['lemma-(less:plus:second)'])])]) ).
cnf(c_0_120,plain,
( ~ '@<_succeeds'(X1,X2)
| '@=<_succeeds'('@+'(X1,s('0')),X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_121,negated_conjecture,
'@+'(esk17_2('0',esk2_0),s('0')) = esk2_0,
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_122,negated_conjecture,
( ~ '@<_succeeds'('@+'(esk1_0,X1),'@+'(esk1_0,esk2_0))
| '@<_succeeds'(X1,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_118]),c_0_72])]) ).
cnf(c_0_123,plain,
( ~ '@<_succeeds'(X2,X3)
| ~ nat_succeeds(X1)
| '@<_succeeds'('@+'(X1,X2),'@+'(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_124,negated_conjecture,
( ~ '@<_succeeds'(esk17_2('0',esk2_0),X1)
| '@=<_succeeds'(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_125,negated_conjecture,
( ~ '@<_succeeds'(X1,esk2_0)
| '@<_succeeds'(X1,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_72])]) ).
cnf(c_0_126,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_91])]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX045+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 10:21:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 217.39/28.30 % Version: 3.5.1
% 217.39/28.30 % Preprocessing class: FSLSSMSSSSSNFFN.
% 217.39/28.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 217.39/28.30 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 217.39/28.30 % Starting new_bool_3 with 300s (1) cores
% 217.39/28.30 % Starting new_bool_1 with 300s (1) cores
% 217.39/28.30 % Starting sh5l with 300s (1) cores
% 217.39/28.30 % new_bool_1 with pid 837393 completed with status 0
% 217.39/28.30 % Result found by new_bool_1
% 217.39/28.30 % Preprocessing class: FSLSSMSSSSSNFFN.
% 217.39/28.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 217.39/28.30 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 217.39/28.30 % Starting new_bool_3 with 300s (1) cores
% 217.39/28.30 % Starting new_bool_1 with 300s (1) cores
% 217.39/28.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 217.39/28.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 217.39/28.30 % Search class: FGHSF-FFMF32-MFFFFFNN
% 217.39/28.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 217.39/28.30 % Starting SubtermCWHack with 31s (1) cores
% 217.39/28.30 % SubtermCWHack with pid 837396 completed with status 0
% 217.39/28.30 % Result found by SubtermCWHack
% 217.39/28.30 % Preprocessing class: FSLSSMSSSSSNFFN.
% 217.39/28.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 217.39/28.30 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 217.39/28.30 % Starting new_bool_3 with 300s (1) cores
% 217.39/28.30 % Starting new_bool_1 with 300s (1) cores
% 217.39/28.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 217.39/28.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 217.39/28.30 % Search class: FGHSF-FFMF32-MFFFFFNN
% 217.39/28.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 217.39/28.30 % Starting SubtermCWHack with 31s (1) cores
% 217.39/28.30 % Preprocessing time : 0.003 s
% 217.39/28.30
% 217.39/28.30 % Proof found!
% 217.39/28.30 % SZS status Theorem
% 217.39/28.30 % SZS output start CNFRefutation
% See solution above
% 217.39/28.30 % Parsed axioms : 114
% 217.39/28.30 % Removed by relevancy pruning/SinE : 57
% 217.39/28.30 % Initial clauses : 85
% 217.39/28.30 % Removed in clause preprocessing : 0
% 217.39/28.30 % Initial clauses in saturation : 85
% 217.39/28.30 % Processed clauses : 41819
% 217.39/28.30 % ...of these trivial : 1762
% 217.39/28.30 % ...subsumed : 33200
% 217.39/28.30 % ...remaining for further processing : 6857
% 217.39/28.30 % Other redundant clauses eliminated : 540
% 217.39/28.30 % Clauses deleted for lack of memory : 0
% 217.39/28.30 % Backward-subsumed : 526
% 217.39/28.30 % Backward-rewritten : 365
% 217.39/28.30 % Generated clauses : 1038454
% 217.39/28.30 % ...of the previous two non-redundant : 961748
% 217.39/28.30 % ...aggressively subsumed : 0
% 217.39/28.30 % Contextual simplify-reflections : 356
% 217.39/28.30 % Paramodulations : 1037911
% 217.39/28.30 % Factorizations : 0
% 217.39/28.30 % NegExts : 0
% 217.39/28.30 % Equation resolutions : 543
% 217.39/28.30 % Disequality decompositions : 0
% 217.39/28.30 % Total rewrite steps : 275242
% 217.39/28.30 % ...of those cached : 269493
% 217.39/28.30 % Propositional unsat checks : 0
% 217.39/28.30 % Propositional check models : 0
% 217.39/28.30 % Propositional check unsatisfiable : 0
% 217.39/28.30 % Propositional clauses : 0
% 217.39/28.30 % Propositional clauses after purity: 0
% 217.39/28.30 % Propositional unsat core size : 0
% 217.39/28.30 % Propositional preprocessing time : 0.000
% 217.39/28.30 % Propositional encoding time : 0.000
% 217.39/28.30 % Propositional solver time : 0.000
% 217.39/28.30 % Success case prop preproc time : 0.000
% 217.39/28.30 % Success case prop encoding time : 0.000
% 217.39/28.30 % Success case prop solver time : 0.000
% 217.39/28.30 % Current number of processed clauses : 5952
% 217.39/28.30 % Positive orientable unit clauses : 1232
% 217.39/28.30 % Positive unorientable unit clauses: 0
% 217.39/28.30 % Negative unit clauses : 562
% 217.39/28.30 % Non-unit-clauses : 4158
% 217.39/28.30 % Current number of unprocessed clauses: 917857
% 217.39/28.30 % ...number of literals in the above : 3582265
% 217.39/28.30 % Current number of archived formulas : 0
% 217.39/28.30 % Current number of archived clauses : 896
% 217.39/28.30 % Clause-clause subsumption calls (NU) : 1396362
% 217.39/28.30 % Rec. Clause-clause subsumption calls : 581337
% 217.39/28.30 % Non-unit clause-clause subsumptions : 18363
% 217.39/28.30 % Unit Clause-clause subsumption calls : 155649
% 217.39/28.30 % Rewrite failures with RHS unbound : 0
% 217.39/28.30 % BW rewrite match attempts : 19846
% 217.39/28.30 % BW rewrite match successes : 260
% 217.39/28.30 % Condensation attempts : 0
% 217.39/28.30 % Condensation successes : 0
% 217.39/28.30 % Termbank termtop insertions : 25226813
% 217.39/28.30 % Search garbage collected termcells : 1893
% 217.39/28.30
% 217.39/28.30 % -------------------------------------------------
% 217.39/28.30 % User time : 26.199 s
% 217.39/28.30 % System time : 1.014 s
% 217.39/28.30 % Total time : 27.214 s
% 217.39/28.30 % Maximum resident set size: 4020 pages
% 217.39/28.30
% 217.39/28.30 % -------------------------------------------------
% 217.39/28.30 % User time : 26.203 s
% 217.39/28.30 % System time : 1.023 s
% 217.39/28.30 % Total time : 27.226 s
% 217.39/28.30 % Maximum resident set size: 4864 pages
% 217.39/28.30 % E exiting
%------------------------------------------------------------------------------