%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV486+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 : Tue May 5 05:23:31 PM UTC 2026
% Result : Theorem 178.01s 138.53s
% Output : CNFRefutation 180.91s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_69)
% Comments :
%------------------------------------------------------------------------------
fof(qii,hypothesis,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( int_less(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = real_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qii) ).
fof(lt,conjecture,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_less(X1,X2)
& int_leq(X2,n) )
=> a(X1,X2) = real_zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lt) ).
fof(plus_and_order1,axiom,
! [X4,X5,X6,X7] :
( ( int_less(X4,X5)
& int_leq(X6,X7) )
=> int_leq(plus(X4,X6),plus(X5,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_order1) ).
fof(plus_and_inverse,axiom,
! [X1,X2] :
( int_less(X1,X2)
<=> ? [X3] :
( plus(X1,X3) = X2
& int_less(int_zero,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_inverse) ).
fof(int_less_transitive,axiom,
! [X1,X2,X3] :
( ( int_less(X1,X2)
& int_less(X2,X3) )
=> int_less(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_transitive) ).
fof(int_leq,axiom,
! [X1,X2] :
( int_leq(X1,X2)
<=> ( int_less(X1,X2)
| X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_leq) ).
fof(one_successor_of_zero,axiom,
! [X1] :
( int_less(int_zero,X1)
<=> int_leq(int_one,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_successor_of_zero) ).
fof(int_less_total,axiom,
! [X1,X2] :
( int_less(X1,X2)
| int_leq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_total) ).
fof(plus_commutative,axiom,
! [X1,X2] : plus(X1,X2) = plus(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_commutative) ).
fof(int_less_irreflexive,axiom,
! [X1,X2] :
( int_less(X1,X2)
=> X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_irreflexive) ).
fof(plus_zero,axiom,
! [X1] : plus(X1,int_zero) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).
fof(int_zero_one,axiom,
int_less(int_zero,int_one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_zero_one) ).
fof(real_constants,axiom,
real_zero != real_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_constants) ).
fof(i_0_13,plain,
! [X2,X1] :
( epred1_2(X1,X2)
<=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( int_less(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = real_zero ) ) ) ),
introduced(definition) ).
fof(i_0_14,plain,
! [X2,X1] :
( epred1_2(X1,X2)
=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( int_less(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = real_zero ) ) ) ),
inference(split_equiv,[status(thm)],[i_0_13]) ).
fof(i_0_15,hypothesis,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> epred1_2(X1,X2) ),
inference(apply_def,[status(thm)],[qii,c_0_13]) ).
fof(i_0_16,negated_conjecture,
~ ! [X1,X2] :
( ( int_leq(int_one,X1)
& int_less(X1,X2)
& int_leq(X2,n) )
=> a(X1,X2) = real_zero ),
inference(assume_negation,[status(cth)],[lt]) ).
fof(i_0_17,plain,
! [X65,X66,X67,X68,X69,X70,X71] :
( ( ~ int_less(int_zero,X67)
| X66 != plus(X65,X67)
| ~ int_leq(int_one,X68)
| ~ int_leq(X68,X65)
| a(plus(X68,X67),X68) = real_zero
| ~ epred1_2(X66,X65) )
& ( ~ int_leq(int_one,X69)
| ~ int_leq(X69,X65)
| a(X69,X69) = real_one
| ~ epred1_2(X66,X65) )
& ( ~ int_less(int_zero,X70)
| X65 != plus(X66,X70)
| ~ int_leq(int_one,X71)
| ~ int_leq(X71,X66)
| a(X71,plus(X71,X70)) = real_zero
| ~ epred1_2(X66,X65) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_14])])])]) ).
fof(i_0_18,plain,
! [X50,X51,X52,X53] :
( ~ int_less(X50,X51)
| ~ int_leq(X52,X53)
| int_leq(plus(X50,X52),plus(X51,X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[plus_and_order1])]) ).
fof(i_0_19,hypothesis,
! [X61,X62] :
( ~ int_leq(int_one,X61)
| ~ int_leq(X61,n)
| ~ int_leq(int_one,X62)
| ~ int_leq(X62,n)
| epred1_2(X61,X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_15])]) ).
fof(i_0_20,plain,
! [X54,X55,X57,X58,X59] :
( ( plus(X54,esk1_2(X54,X55)) = X55
| ~ int_less(X54,X55) )
& ( int_less(int_zero,esk1_2(X54,X55))
| ~ int_less(X54,X55) )
& ( plus(X57,X59) != X58
| ~ int_less(int_zero,X59)
| int_less(X57,X58) ) ),
inference(distribute,[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)],[plus_and_inverse])])])])])]) ).
fof(i_0_21,plain,
! [X40,X41,X42] :
( ~ int_less(X40,X41)
| ~ int_less(X41,X42)
| int_less(X40,X42) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_transitive])]) ).
fof(i_0_22,plain,
! [X38,X39] :
( ( ~ int_leq(X38,X39)
| int_less(X38,X39)
| X38 = X39 )
& ( ~ int_less(X38,X39)
| int_leq(X38,X39) )
& ( X38 != X39
| int_leq(X38,X39) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_leq])])]) ).
fof(i_0_23,plain,
! [X60] :
( ( ~ int_less(int_zero,X60)
| int_leq(int_one,X60) )
& ( ~ int_leq(int_one,X60)
| int_less(int_zero,X60) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[one_successor_of_zero])]) ).
fof(i_0_24,plain,
! [X45,X46] :
( int_less(X45,X46)
| int_leq(X46,X45) ),
inference(variable_rename,[status(thm)],[int_less_total]) ).
fof(i_0_25,plain,
! [X47,X48] : plus(X47,X48) = plus(X48,X47),
inference(variable_rename,[status(thm)],[plus_commutative]) ).
fof(i_0_26,plain,
! [X43,X44] :
( ~ int_less(X43,X44)
| X43 != X44 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_irreflexive])]) ).
fof(i_0_27,negated_conjecture,
( int_leq(int_one,esk2_0)
& int_less(esk2_0,esk3_0)
& int_leq(esk3_0,n)
& a(esk2_0,esk3_0) != real_zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_16])])]) ).
fof(i_0_28,plain,
! [X49] : plus(X49,int_zero) = X49,
inference(variable_rename,[status(thm)],[plus_zero]) ).
cnf(i_0_29,plain,
( a(plus(X4,X1),X4) = real_zero
| ~ int_less(int_zero,X1)
| X2 != plus(X3,X1)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X3)
| ~ epred1_2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_30,plain,
( a(X4,plus(X4,X1)) = real_zero
| ~ int_less(int_zero,X1)
| X2 != plus(X3,X1)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X3)
| ~ epred1_2(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_31,plain,
( int_leq(plus(X1,X3),plus(X2,X4))
| ~ int_less(X1,X2)
| ~ int_leq(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_32,hypothesis,
( epred1_2(X1,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_33,plain,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ epred1_2(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_34,plain,
( plus(X1,esk1_2(X1,X2)) = X2
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_35,plain,
( int_less(int_zero,esk1_2(X1,X2))
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_36,plain,
( int_less(X1,X3)
| ~ int_less(X1,X2)
| ~ int_less(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_37,plain,
( int_less(X1,X3)
| plus(X1,X2) != X3
| ~ int_less(int_zero,X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_38,plain,
( int_less(X1,X2)
| X1 = X2
| ~ int_leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_39,plain,
( int_leq(X1,X2)
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_40,plain,
( int_less(int_zero,X1)
| ~ int_leq(int_one,X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_41,plain,
( int_leq(int_one,X1)
| ~ int_less(int_zero,X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_42,plain,
( int_less(X1,X2)
| int_leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_43,plain,
plus(X1,X2) = plus(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_44,plain,
( ~ int_less(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_45,plain,
( int_leq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_46,negated_conjecture,
a(esk2_0,esk3_0) != real_zero,
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_47,plain,
plus(X1,int_zero) = X1,
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_48,negated_conjecture,
int_less(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_49,plain,
int_less(int_zero,int_one),
inference(split_conjunct,[status(thm)],[int_zero_one]),
[final] ).
cnf(i_0_50,negated_conjecture,
int_leq(esk3_0,n),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_51,negated_conjecture,
int_leq(int_one,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_52,plain,
real_zero != real_one,
inference(split_conjunct,[status(thm)],[real_constants]),
[final] ).
cnf(i_0_53,axiom,
X1 = X1 ).
cnf(i_0_54,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_55,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_56,axiom,
( X1 != X2
| a(X1,X3) = a(X2,X3) ) ).
cnf(i_0_57,axiom,
( X1 != X2
| a(X3,X1) = a(X3,X2) ) ).
cnf(i_0_58,axiom,
( X1 != X2
| plus(X1,X3) = plus(X2,X3) ) ).
cnf(i_0_59,axiom,
( X1 != X2
| plus(X3,X1) = plus(X3,X2) ) ).
cnf(i_0_60,axiom,
( X1 != X2
| ~ int_less(X1,X3)
| int_less(X2,X3) ) ).
cnf(i_0_61,axiom,
( X1 != X2
| ~ int_less(X3,X1)
| int_less(X3,X2) ) ).
cnf(i_0_62,axiom,
( X1 != X2
| ~ int_leq(X1,X3)
| int_leq(X2,X3) ) ).
cnf(i_0_63,axiom,
( X1 != X2
| ~ int_leq(X3,X1)
| int_leq(X3,X2) ) ).
cnf(i_0_64,axiom,
( X1 != X2
| ~ epred1_2(X1,X3)
| epred1_2(X2,X3) ) ).
cnf(i_0_65,axiom,
( X1 != X2
| ~ epred1_2(X3,X1)
| epred1_2(X3,X2) ) ).
cnf(i_0_84,plain,
~ int_less(esk3_0,esk2_0),
inference(scs_inference,[],[i_0_46,i_0_48,i_0_51,i_0_69,i_0_43,i_0_47,i_0_49,i_0_54,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68,i_0_55,i_0_36]) ).
cnf(i_0_85,plain,
~ int_less(X1,X1),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_87,plain,
int_less(X1,plus(int_one,X1)),
inference(scs_inference,[],[i_0_46,i_0_48,i_0_51,i_0_69,i_0_43,i_0_47,i_0_49,i_0_54,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68,i_0_55,i_0_36,i_0_37]) ).
cnf(i_0_90,plain,
~ int_less(plus(esk3_0,int_zero),esk2_0),
inference(scs_inference,[],[i_0_46,i_0_48,i_0_51,i_0_69,i_0_43,i_0_47,i_0_83,i_0_49,i_0_54,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68,i_0_55,i_0_36,i_0_37,i_0_60]) ).
cnf(i_0_92,plain,
~ int_less(esk3_0,plus(esk2_0,int_zero)),
inference(scs_inference,[],[i_0_46,i_0_48,i_0_51,i_0_69,i_0_43,i_0_47,i_0_83,i_0_91,i_0_49,i_0_54,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68,i_0_55,i_0_36,i_0_37,i_0_60,i_0_61]) ).
cnf(i_0_94,plain,
int_leq(int_one,plus(int_zero,int_one)),
inference(scs_inference,[],[i_0_46,i_0_48,i_0_51,i_0_69,i_0_43,i_0_47,i_0_83,i_0_91,i_0_49,i_0_54,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68,i_0_55,i_0_36,i_0_37,i_0_60,i_0_61,i_0_41]) ).
cnf(i_0_104,plain,
int_leq(X1,X1),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_105,plain,
int_leq(X1,X1),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_122,plain,
~ int_less(plus(X1,X2),plus(X2,X1)),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_125,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_130,plain,
~ int_less(plus(X1,X2),plus(X2,X1)),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_132,plain,
~ int_less(plus(X1,X2),plus(X2,X1)),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_138,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_142,plain,
int_leq(X1,X1),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_161,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_183,plain,
int_less(X1,plus(X1,esk2_0)),
inference(scs_inference,[],[i_0_74,i_0_68]) ).
cnf(i_0_199,plain,
~ int_less(plus(X1,int_zero),X1),
inference(rename_variables,[],[i_0_147]) ).
cnf(i_0_225,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_309,plain,
~ int_less(X1,X1),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_312,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_316,plain,
int_leq(X1,X1),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_341,plain,
~ int_less(plus(X1,X2),plus(X2,X1)),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_346,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_411,plain,
~ int_less(plus(X1,int_zero),X1),
inference(rename_variables,[],[i_0_147]) ).
cnf(i_0_440,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_509,plain,
int_less(X1,plus(esk2_0,X1)),
inference(scs_inference,[],[i_0_43,i_0_74,i_0_37]) ).
cnf(i_0_970,plain,
a(X1,X2) = a(plus(X1,int_zero),X2),
inference(scs_inference,[],[i_0_71,i_0_56]) ).
cnf(i_0_971,plain,
a(X1,X2) = a(X1,plus(X2,int_zero)),
inference(scs_inference,[],[i_0_71,i_0_56,i_0_57]) ).
cnf(i_0_972,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(scs_inference,[],[i_0_71,i_0_56,i_0_57,i_0_58]) ).
cnf(i_0_973,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(scs_inference,[],[i_0_71,i_0_56,i_0_57,i_0_58,i_0_59]) ).
cnf(i_0_994,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_996,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_999,plain,
int_leq(plus(X1,X2),plus(X2,X1)),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_1006,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1010,plain,
int_leq(plus(X1,X2),plus(X2,X1)),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_1038,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1040,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1069,plain,
~ int_less(X1,X1),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_1079,plain,
int_leq(plus(X1,int_zero),X1),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_1089,plain,
int_leq(plus(X1,int_zero),X1),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_1114,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1116,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1123,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1141,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1144,plain,
int_leq(plus(X1,X2),plus(X2,X1)),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_1146,plain,
int_leq(plus(X1,int_zero),X1),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_1176,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1228,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1235,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1269,plain,
int_leq(X1,X1),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_1272,plain,
int_less(int_zero,esk1_2(int_zero,esk1_2(int_zero,int_one))),
inference(scs_inference,[],[i_0_1240,i_0_35]) ).
cnf(i_0_1284,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1288,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1293,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1295,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1337,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1341,plain,
~ int_less(X1,X1),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_1346,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1359,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1396,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1402,plain,
int_less(int_zero,esk1_2(int_zero,esk1_2(esk2_0,esk3_0))),
inference(scs_inference,[],[i_0_1376,i_0_35]) ).
cnf(i_0_1438,plain,
int_leq(plus(X1,X2),plus(X2,X1)),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_1451,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1460,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1479,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1508,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1512,plain,
~ int_less(X1,X1),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_1517,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1522,plain,
int_less(int_zero,esk1_2(int_zero,esk2_0)),
inference(scs_inference,[],[i_0_74,i_0_35]) ).
cnf(i_0_1562,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1569,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1571,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1641,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1669,plain,
~ int_less(plus(X1,int_zero),X1),
inference(rename_variables,[],[i_0_147]) ).
cnf(i_0_1682,plain,
int_leq(plus(X1,int_zero),X1),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_1697,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1734,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1792,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1811,plain,
int_leq(plus(X1,X2),plus(X2,X1)),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_1859,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1893,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1894,plain,
int_leq(plus(X1,int_zero),X1),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_1937,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1980,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_1986,plain,
X1 = plus(X1,int_zero),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_107,plain,
int_leq(X1,plus(X1,int_one)),
inference(scs_inference,[],[i_0_80,i_0_39]) ).
cnf(i_0_109,plain,
int_less(int_zero,plus(int_one,int_one)),
inference(scs_inference,[],[i_0_80,i_0_39,i_0_40]) ).
cnf(i_0_111,plain,
~ int_less(X1,plus(X1,int_zero)),
inference(scs_inference,[],[i_0_71,i_0_80,i_0_39,i_0_40,i_0_44]) ).
cnf(i_0_113,plain,
int_leq(X1,plus(X1,int_zero)),
inference(scs_inference,[],[i_0_71,i_0_80,i_0_39,i_0_40,i_0_44,i_0_45]) ).
cnf(i_0_115,plain,
int_less(X1,plus(X1,plus(int_one,int_zero))),
inference(scs_inference,[],[i_0_71,i_0_80,i_0_87,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68]) ).
cnf(i_0_116,plain,
int_less(X1,plus(int_one,X1)),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_118,plain,
int_leq(int_one,plus(int_zero,plus(int_one,int_zero))),
inference(scs_inference,[],[i_0_71,i_0_80,i_0_87,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68,i_0_41]) ).
cnf(i_0_120,plain,
~ int_less(plus(int_one,int_one),int_one),
inference(scs_inference,[],[i_0_71,i_0_76,i_0_80,i_0_87,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68,i_0_41,i_0_36]) ).
cnf(i_0_121,plain,
int_less(X1,plus(X1,int_one)),
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_124,plain,
int_less(X1,plus(plus(X1,esk2_0),int_zero)),
inference(scs_inference,[],[i_0_71,i_0_76,i_0_80,i_0_87,i_0_74,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68,i_0_41,i_0_36,i_0_37]) ).
cnf(i_0_127,plain,
a(esk2_0,esk3_0) != plus(int_zero,real_zero),
inference(scs_inference,[],[i_0_71,i_0_82,i_0_76,i_0_80,i_0_87,i_0_74,i_0_43,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68,i_0_41,i_0_36,i_0_37,i_0_55]) ).
cnf(i_0_129,plain,
~ int_less(X1,plus(int_zero,X1)),
inference(scs_inference,[],[i_0_71,i_0_125,i_0_82,i_0_76,i_0_122,i_0_80,i_0_87,i_0_74,i_0_43,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68,i_0_41,i_0_36,i_0_37,i_0_55,i_0_60]) ).
cnf(i_0_131,plain,
~ int_less(plus(int_zero,X1),X1),
inference(scs_inference,[],[i_0_71,i_0_125,i_0_82,i_0_76,i_0_122,i_0_130,i_0_80,i_0_87,i_0_74,i_0_43,i_0_39,i_0_40,i_0_44,i_0_45,i_0_68,i_0_41,i_0_36,i_0_37,i_0_55,i_0_60,i_0_61]) ).
cnf(i_0_144,plain,
int_less(X1,plus(X1,int_one)),
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_145,plain,
int_less(X1,plus(X1,int_one)),
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_208,plain,
int_less(X1,plus(int_one,X1)),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_210,plain,
int_less(X1,plus(int_one,X1)),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_213,plain,
int_less(X1,plus(X1,plus(int_zero,esk2_0))),
inference(scs_inference,[],[i_0_183,i_0_68]) ).
cnf(i_0_214,plain,
int_less(X1,plus(X1,esk2_0)),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_216,plain,
int_leq(int_zero,esk2_0),
inference(scs_inference,[],[i_0_74,i_0_183,i_0_68,i_0_39]) ).
cnf(i_0_219,plain,
int_less(X1,plus(X1,esk2_0)),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_230,plain,
int_less(X1,plus(X1,plus(int_zero,int_one))),
inference(scs_inference,[],[i_0_80,i_0_68]) ).
cnf(i_0_231,plain,
int_less(X1,plus(X1,int_one)),
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_233,plain,
int_leq(int_zero,int_one),
inference(scs_inference,[],[i_0_49,i_0_80,i_0_68,i_0_39]) ).
cnf(i_0_289,plain,
int_leq(X1,plus(X1,esk2_0)),
inference(scs_inference,[],[i_0_183,i_0_39]) ).
cnf(i_0_306,plain,
int_leq(X1,plus(int_one,X1)),
inference(scs_inference,[],[i_0_87,i_0_39]) ).
cnf(i_0_308,plain,
~ int_less(esk2_0,int_zero),
inference(scs_inference,[],[i_0_74,i_0_87,i_0_69,i_0_39,i_0_36]) ).
cnf(i_0_340,plain,
int_less(X1,plus(X1,esk2_0)),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_530,plain,
int_less(X1,plus(X1,int_one)),
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_544,plain,
int_less(X1,plus(int_one,X1)),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_561,plain,
int_less(X1,plus(X1,esk2_0)),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_590,plain,
int_less(X1,plus(esk2_0,X1)),
inference(rename_variables,[],[i_0_509]) ).
cnf(i_0_621,plain,
int_less(X1,plus(int_one,X1)),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_658,plain,
int_less(X1,plus(int_one,X1)),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_683,plain,
int_less(X1,plus(int_one,X1)),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_697,plain,
int_leq(X1,plus(esk2_0,X1)),
inference(scs_inference,[],[i_0_509,i_0_39]) ).
cnf(i_0_974,plain,
int_less(int_zero,esk1_2(X1,plus(esk2_0,X1))),
inference(scs_inference,[],[i_0_509,i_0_71,i_0_56,i_0_57,i_0_58,i_0_59,i_0_35]) ).
cnf(i_0_976,plain,
plus(int_zero,esk1_2(int_zero,int_one)) = int_one,
inference(scs_inference,[],[i_0_509,i_0_71,i_0_49,i_0_56,i_0_57,i_0_58,i_0_59,i_0_35,i_0_34]) ).
cnf(i_0_1015,plain,
int_less(int_zero,esk1_2(X1,plus(X1,int_one))),
inference(scs_inference,[],[i_0_80,i_0_35]) ).
cnf(i_0_1017,plain,
plus(esk2_0,esk1_2(esk2_0,esk3_0)) = esk3_0,
inference(scs_inference,[],[i_0_80,i_0_48,i_0_35,i_0_34]) ).
cnf(i_0_1045,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_972]) ).
cnf(i_0_1047,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_972]) ).
cnf(i_0_1055,plain,
int_less(int_zero,esk1_2(X1,plus(X1,esk2_0))),
inference(scs_inference,[],[i_0_183,i_0_35]) ).
cnf(i_0_1057,plain,
plus(int_zero,esk1_2(int_zero,esk2_0)) = esk2_0,
inference(scs_inference,[],[i_0_183,i_0_74,i_0_35,i_0_34]) ).
cnf(i_0_1059,plain,
a(plus(X1,X2),X3) = a(plus(X2,X1),X3),
inference(scs_inference,[],[i_0_183,i_0_74,i_0_43,i_0_35,i_0_34,i_0_56]) ).
cnf(i_0_1060,plain,
a(X1,plus(X2,X3)) = a(X1,plus(X3,X2)),
inference(scs_inference,[],[i_0_183,i_0_74,i_0_43,i_0_35,i_0_34,i_0_56,i_0_57]) ).
cnf(i_0_1061,plain,
plus(plus(X1,X2),X3) = plus(plus(X2,X1),X3),
inference(scs_inference,[],[i_0_183,i_0_74,i_0_43,i_0_35,i_0_34,i_0_56,i_0_57,i_0_58]) ).
cnf(i_0_1062,plain,
plus(X1,plus(X2,X3)) = plus(X1,plus(X3,X2)),
inference(scs_inference,[],[i_0_183,i_0_74,i_0_43,i_0_35,i_0_34,i_0_56,i_0_57,i_0_58,i_0_59]) ).
cnf(i_0_1075,plain,
a(X1,X2) = a(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_970]) ).
cnf(i_0_1086,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_973]) ).
cnf(i_0_1112,plain,
a(X1,X2) = a(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_971]) ).
cnf(i_0_1156,plain,
int_less(X1,plus(esk2_0,X1)),
inference(rename_variables,[],[i_0_509]) ).
cnf(i_0_1184,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_972]) ).
cnf(i_0_1214,plain,
int_less(int_zero,esk1_2(X1,plus(int_one,X1))),
inference(scs_inference,[],[i_0_87,i_0_35]) ).
cnf(i_0_1252,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_973]) ).
cnf(i_0_1319,plain,
int_less(X1,plus(esk2_0,X1)),
inference(rename_variables,[],[i_0_509]) ).
cnf(i_0_1339,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_972]) ).
cnf(i_0_1344,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_972]) ).
cnf(i_0_1363,plain,
a(X1,X2) = a(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_971]) ).
cnf(i_0_1385,plain,
a(X1,X2) = a(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_970]) ).
cnf(i_0_1387,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_973]) ).
cnf(i_0_1416,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_972]) ).
cnf(i_0_1453,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_973]) ).
cnf(i_0_1458,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_973]) ).
cnf(i_0_1534,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_972]) ).
cnf(i_0_1549,plain,
int_less(int_zero,esk1_2(int_zero,esk1_2(int_zero,esk2_0))),
inference(scs_inference,[],[i_0_1522,i_0_35]) ).
cnf(i_0_1592,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_973]) ).
cnf(i_0_1598,plain,
a(X1,X2) = a(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_970]) ).
cnf(i_0_1703,plain,
int_less(X1,plus(esk2_0,X1)),
inference(rename_variables,[],[i_0_509]) ).
cnf(i_0_1732,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_973]) ).
cnf(i_0_1757,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_972]) ).
cnf(i_0_1809,plain,
a(X1,X2) = a(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_970]) ).
cnf(i_0_1836,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_973]) ).
cnf(i_0_1838,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_973]) ).
cnf(i_0_1929,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_972]) ).
cnf(i_0_1933,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_972]) ).
cnf(i_0_1984,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_973]) ).
cnf(i_0_151,plain,
int_less(X1,plus(X1,plus(int_one,int_one))),
inference(scs_inference,[],[i_0_109,i_0_47,i_0_44,i_0_45,i_0_68]) ).
cnf(i_0_153,plain,
int_leq(X1,plus(X1,plus(int_one,int_zero))),
inference(scs_inference,[],[i_0_115,i_0_109,i_0_47,i_0_44,i_0_45,i_0_68,i_0_39]) ).
cnf(i_0_155,plain,
int_less(int_zero,plus(int_one,plus(int_one,int_zero))),
inference(scs_inference,[],[i_0_115,i_0_109,i_0_47,i_0_44,i_0_45,i_0_68,i_0_39,i_0_40]) ).
cnf(i_0_157,plain,
int_leq(int_one,plus(plus(int_zero,esk2_0),int_zero)),
inference(scs_inference,[],[i_0_115,i_0_124,i_0_109,i_0_47,i_0_44,i_0_45,i_0_68,i_0_39,i_0_40,i_0_41]) ).
cnf(i_0_158,plain,
int_less(X1,plus(plus(X1,esk2_0),int_zero)),
inference(rename_variables,[],[i_0_124]) ).
cnf(i_0_160,plain,
int_less(X1,plus(plus(X1,int_one),int_zero)),
inference(scs_inference,[],[i_0_71,i_0_115,i_0_124,i_0_109,i_0_47,i_0_49,i_0_44,i_0_45,i_0_68,i_0_39,i_0_40,i_0_41,i_0_37]) ).
cnf(i_0_163,plain,
~ int_less(plus(int_zero,esk3_0),esk2_0),
inference(scs_inference,[],[i_0_48,i_0_71,i_0_115,i_0_131,i_0_124,i_0_109,i_0_47,i_0_49,i_0_44,i_0_45,i_0_68,i_0_39,i_0_40,i_0_41,i_0_37,i_0_36]) ).
cnf(i_0_164,plain,
~ int_less(plus(int_zero,X1),X1),
inference(rename_variables,[],[i_0_131]) ).
cnf(i_0_166,plain,
~ int_less(X1,plus(plus(X1,int_zero),int_zero)),
inference(scs_inference,[],[i_0_48,i_0_71,i_0_161,i_0_115,i_0_111,i_0_131,i_0_124,i_0_109,i_0_47,i_0_49,i_0_44,i_0_45,i_0_68,i_0_39,i_0_40,i_0_41,i_0_37,i_0_36,i_0_60]) ).
cnf(i_0_167,plain,
~ int_less(X1,plus(X1,int_zero)),
inference(rename_variables,[],[i_0_111]) ).
cnf(i_0_169,plain,
~ int_less(plus(int_zero,X1),X1),
inference(rename_variables,[],[i_0_131]) ).
cnf(i_0_178,plain,
int_less(X1,plus(plus(X1,esk2_0),int_zero)),
inference(rename_variables,[],[i_0_124]) ).
cnf(i_0_179,plain,
int_leq(X1,plus(X1,int_one)),
inference(rename_variables,[],[i_0_107]) ).
cnf(i_0_180,plain,
int_less(X1,plus(plus(X1,esk2_0),int_zero)),
inference(rename_variables,[],[i_0_124]) ).
cnf(i_0_181,plain,
int_leq(X1,plus(X1,int_one)),
inference(rename_variables,[],[i_0_107]) ).
cnf(i_0_193,plain,
int_less(X1,plus(X1,plus(int_one,int_zero))),
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_194,plain,
~ int_less(X1,plus(int_zero,X1)),
inference(rename_variables,[],[i_0_129]) ).
cnf(i_0_197,plain,
~ int_less(X1,plus(int_zero,X1)),
inference(rename_variables,[],[i_0_129]) ).
cnf(i_0_218,plain,
int_leq(int_one,plus(int_zero,esk2_0)),
inference(scs_inference,[],[i_0_74,i_0_183,i_0_214,i_0_68,i_0_39,i_0_41]) ).
cnf(i_0_235,plain,
int_leq(int_one,plus(int_zero,plus(int_zero,esk2_0))),
inference(scs_inference,[],[i_0_49,i_0_213,i_0_80,i_0_68,i_0_39,i_0_41]) ).
cnf(i_0_236,plain,
int_less(X1,plus(X1,plus(int_zero,esk2_0))),
inference(rename_variables,[],[i_0_213]) ).
cnf(i_0_246,plain,
int_leq(X1,plus(X1,plus(int_zero,int_one))),
inference(scs_inference,[],[i_0_230,i_0_39]) ).
cnf(i_0_248,plain,
int_leq(int_one,plus(int_zero,plus(int_zero,int_one))),
inference(scs_inference,[],[i_0_230,i_0_39,i_0_41]) ).
cnf(i_0_249,plain,
int_less(X1,plus(X1,plus(int_zero,int_one))),
inference(rename_variables,[],[i_0_230]) ).
cnf(i_0_251,plain,
~ int_less(esk3_0,int_zero),
inference(scs_inference,[],[i_0_74,i_0_230,i_0_84,i_0_39,i_0_41,i_0_36]) ).
cnf(i_0_253,plain,
~ int_less(plus(esk3_0,int_zero),int_zero),
inference(scs_inference,[],[i_0_74,i_0_47,i_0_230,i_0_84,i_0_39,i_0_41,i_0_36,i_0_60]) ).
cnf(i_0_258,plain,
int_leq(X1,plus(X1,int_zero)),
inference(rename_variables,[],[i_0_113]) ).
cnf(c_0_1035,plain,
X1 = plus(X1,int_zero),
i_0_125 ).
cnf(c_0_1036,plain,
plus(X1,X2) = plus(X2,X1),
i_0_43 ).
cnf(c_0_1037,plain,
( a(X1,plus(X1,X2)) = real_zero
| ~ int_less(int_zero,X2)
| X3 != plus(X4,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X4)
| ~ epred1_2(X4,X3) ),
i_0_30 ).
cnf(c_0_1038,plain,
( int_leq(plus(X1,X2),plus(X3,X4))
| ~ int_less(X1,X3)
| ~ int_leq(X2,X4) ),
i_0_31 ).
cnf(c_0_1039,plain,
plus(int_zero,X1) = X1,
inference(spm,[status(thm)],[c_0_1035,c_0_1036]) ).
cnf(c_0_1040,plain,
( int_less(int_zero,X1)
| ~ int_leq(int_one,X1) ),
i_0_40 ).
cnf(c_0_1041,negated_conjecture,
int_leq(int_one,esk2_0),
i_0_51 ).
cnf(c_0_1042,plain,
( a(X1,plus(X1,X2)) = real_zero
| ~ epred1_2(X3,plus(X3,X2))
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X3)
| ~ int_less(int_zero,X2) ),
inference(er,[status(thm)],[c_0_1037]) ).
cnf(c_0_1043,plain,
plus(esk2_0,esk1_2(esk2_0,esk3_0)) = esk3_0,
i_0_1017 ).
cnf(c_0_1044,plain,
( int_leq(X1,plus(X2,X3))
| ~ int_leq(X1,X3)
| ~ int_less(int_zero,X2) ),
inference(spm,[status(thm)],[c_0_1038,c_0_1039]) ).
cnf(c_0_1045,negated_conjecture,
int_less(int_zero,esk2_0),
inference(spm,[status(thm)],[c_0_1040,c_0_1041]) ).
cnf(c_0_1046,plain,
( a(X1,plus(X1,esk1_2(esk2_0,esk3_0))) = real_zero
| ~ epred1_2(esk2_0,esk3_0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,esk2_0)
| ~ int_less(int_zero,esk1_2(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_1042,c_0_1043]) ).
cnf(c_0_1047,plain,
int_leq(X1,X1),
i_0_104 ).
cnf(c_0_1048,negated_conjecture,
a(esk2_0,esk3_0) != real_zero,
i_0_46 ).
cnf(c_0_1049,plain,
( int_leq(X1,esk3_0)
| ~ int_leq(X1,esk1_2(esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1044,c_0_1043]),c_0_1045])]) ).
cnf(c_0_1050,plain,
( int_leq(int_one,X1)
| ~ int_less(int_zero,X1) ),
i_0_41 ).
cnf(c_0_1051,plain,
( int_less(X1,X2)
| X1 = X2
| ~ int_leq(X1,X2) ),
i_0_38 ).
cnf(c_0_1052,negated_conjecture,
int_leq(esk3_0,n),
i_0_50 ).
cnf(c_0_1053,plain,
( ~ epred1_2(esk2_0,esk3_0)
| ~ int_less(int_zero,esk1_2(esk2_0,esk3_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1046,c_0_1043]),c_0_1041]),c_0_1047])]),c_0_1048]) ).
cnf(c_0_1054,plain,
( int_less(int_zero,esk1_2(X1,X2))
| ~ int_less(X1,X2) ),
i_0_35 ).
cnf(c_0_1055,negated_conjecture,
int_less(esk2_0,esk3_0),
i_0_48 ).
cnf(c_0_1056,plain,
( int_leq(int_one,esk3_0)
| ~ int_less(int_zero,esk1_2(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_1049,c_0_1050]) ).
cnf(c_0_1057,plain,
( int_less(X1,X2)
| ~ int_less(X1,X3)
| ~ int_less(X3,X2) ),
i_0_36 ).
cnf(c_0_1058,negated_conjecture,
( n = esk3_0
| int_less(esk3_0,n) ),
inference(spm,[status(thm)],[c_0_1051,c_0_1052]) ).
cnf(c_0_1059,plain,
~ epred1_2(esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1053,c_0_1054]),c_0_1055])]) ).
cnf(c_0_1060,hypothesis,
( epred1_2(X1,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n) ),
i_0_32 ).
cnf(c_0_1061,plain,
int_leq(int_one,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1056,c_0_1054]),c_0_1055])]) ).
cnf(c_0_1062,negated_conjecture,
( n = esk3_0
| int_less(X1,n)
| ~ int_less(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_1057,c_0_1058]) ).
cnf(c_0_1063,hypothesis,
~ int_leq(esk2_0,n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1059,c_0_1060]),c_0_1052]),c_0_1061]),c_0_1041])]) ).
cnf(c_0_1064,plain,
( int_leq(X1,X2)
| ~ int_less(X1,X2) ),
i_0_39 ).
cnf(c_0_1065,negated_conjecture,
( n = esk3_0
| int_less(esk2_0,n) ),
inference(spm,[status(thm)],[c_0_1062,c_0_1055]) ).
cnf(c_0_1066,plain,
~ int_less(esk2_0,n),
inference(spm,[status(thm)],[c_0_1063,c_0_1064]) ).
cnf(c_0_1067,negated_conjecture,
n = esk3_0,
inference(sr,[status(thm)],[c_0_1065,c_0_1066]) ).
cnf(c_0_1068,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1066,c_0_1067]),c_0_1055])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV486+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 05:19:17 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 178.01/138.53 % Version : CSE_E---1.7
% 178.01/138.53 % Problem : theBenchmark.p
% 178.01/138.53 % SZS status Theorem for theBenchmark.p
% 178.01/138.53 % SZS output start CNFRefutation
% See solution above
% 180.91/141.42 % Total time : 138.162s
%------------------------------------------------------------------------------