%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV490+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 : n014.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 05:23:32 PM UTC 2026
% Result : Theorem 273.12s 132.80s
% Output : CNFRefutation 276.32s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_1175)
% 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(di,conjecture,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> ( ( X1 != X2
=> a(X1,X2) = real_zero )
& ( X1 = X2
=> a(X1,X2) != real_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',di) ).
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_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> ( ( X1 != X2
=> a(X1,X2) = real_zero )
& ( X1 = X2
=> a(X1,X2) != real_zero ) ) ),
inference(assume_negation,[status(cth)],[di]) ).
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_leq(esk2_0,n)
& int_leq(int_one,esk3_0)
& int_leq(esk3_0,n)
& ( esk2_0 = esk3_0
| esk2_0 != esk3_0 )
& ( a(esk2_0,esk3_0) = real_zero
| esk2_0 != esk3_0 )
& ( esk2_0 = esk3_0
| a(esk2_0,esk3_0) != real_zero )
& ( a(esk2_0,esk3_0) = real_zero
| a(esk2_0,esk3_0) != real_zero ) ),
inference(distribute,[status(thm)],[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,negated_conjecture,
( esk2_0 = esk3_0
| a(esk2_0,esk3_0) != real_zero ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_46,plain,
( int_leq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[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,
( a(esk2_0,esk3_0) = real_zero
| 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(esk2_0,n),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_52,negated_conjecture,
int_leq(int_one,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_53,negated_conjecture,
int_leq(int_one,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_54,plain,
real_zero != real_one,
inference(split_conjunct,[status(thm)],[real_constants]),
[final] ).
cnf(i_0_55,axiom,
X1 = X1 ).
cnf(i_0_56,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_57,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_58,axiom,
( X1 != X2
| a(X1,X3) = a(X2,X3) ) ).
cnf(i_0_59,axiom,
( X1 != X2
| a(X3,X1) = a(X3,X2) ) ).
cnf(i_0_60,axiom,
( X1 != X2
| plus(X1,X3) = plus(X2,X3) ) ).
cnf(i_0_61,axiom,
( X1 != X2
| plus(X3,X1) = plus(X3,X2) ) ).
cnf(i_0_62,axiom,
( X1 != X2
| ~ int_less(X1,X3)
| int_less(X2,X3) ) ).
cnf(i_0_63,axiom,
( X1 != X2
| ~ int_less(X3,X1)
| int_less(X3,X2) ) ).
cnf(i_0_64,axiom,
( X1 != X2
| ~ int_leq(X1,X3)
| int_leq(X2,X3) ) ).
cnf(i_0_65,axiom,
( X1 != X2
| ~ int_leq(X3,X1)
| int_leq(X3,X2) ) ).
cnf(i_0_66,axiom,
( X1 != X2
| ~ epred1_2(X1,X3)
| epred1_2(X2,X3) ) ).
cnf(i_0_67,axiom,
( X1 != X2
| ~ epred1_2(X3,X1)
| epred1_2(X3,X2) ) ).
cnf(i_0_2142,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_1175]) ).
cnf(i_0_2144,plain,
plus(X1,X2) = plus(plus(X1,int_zero),X2),
inference(rename_variables,[],[i_0_1175]) ).
cnf(i_0_2169,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_1176]) ).
cnf(i_0_2171,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_1176]) ).
cnf(i_0_2176,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_1176]) ).
cnf(i_0_2182,plain,
plus(X1,X2) = plus(X1,plus(X2,int_zero)),
inference(rename_variables,[],[i_0_1176]) ).
cnf(i_0_275,plain,
~ int_less(plus(plus(int_zero,int_one),plus(X1,int_zero)),X1),
inference(scs_inference,[],[i_0_151,i_0_77,i_0_274,i_0_241,i_0_273,i_0_115,i_0_225,i_0_227,i_0_39,i_0_70,i_0_40,i_0_41,i_0_36,i_0_62,i_0_63]) ).
cnf(i_0_307,plain,
~ int_less(plus(int_zero,int_one),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_71,i_0_77,i_0_84,i_0_272,i_0_47,i_0_43,i_0_80,i_0_235,i_0_261,i_0_294,i_0_39,i_0_70,i_0_41,i_0_36,i_0_57,i_0_62,i_0_63]) ).
cnf(i_0_377,plain,
int_less(int_zero,plus(int_one,plus(int_zero,esk3_0))),
inference(scs_inference,[],[i_0_351,i_0_40]) ).
cnf(i_0_378,plain,
int_leq(X1,plus(X1,plus(int_zero,esk3_0))),
inference(rename_variables,[],[i_0_351]) ).
cnf(i_0_380,plain,
int_leq(X1,plus(int_one,X1)),
inference(scs_inference,[],[i_0_89,i_0_351,i_0_40,i_0_39]) ).
cnf(i_0_382,plain,
int_leq(int_one,plus(plus(int_zero,esk2_0),int_zero)),
inference(scs_inference,[],[i_0_89,i_0_351,i_0_169,i_0_40,i_0_39,i_0_41]) ).
cnf(i_0_385,plain,
~ int_less(plus(esk2_0,X1),X1),
inference(scs_inference,[],[i_0_73,i_0_89,i_0_261,i_0_351,i_0_169,i_0_40,i_0_39,i_0_41,i_0_36]) ).
cnf(i_0_389,plain,
~ int_less(plus(int_zero,plus(X1,int_zero)),X1),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_89,i_0_261,i_0_351,i_0_133,i_0_169,i_0_40,i_0_39,i_0_41,i_0_36,i_0_63]) ).
cnf(i_0_391,plain,
~ int_less(plus(int_one,int_zero),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_47,i_0_89,i_0_261,i_0_351,i_0_133,i_0_169,i_0_98,i_0_40,i_0_39,i_0_41,i_0_36,i_0_63,i_0_62]) ).
cnf(i_0_465,plain,
int_leq(int_one,plus(int_zero,plus(int_one,esk2_0))),
inference(scs_inference,[],[i_0_227,i_0_447,i_0_39,i_0_41]) ).
cnf(i_0_466,plain,
int_less(X1,plus(X1,plus(int_one,esk2_0))),
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_468,plain,
~ int_less(plus(X1,esk3_0),X1),
inference(scs_inference,[],[i_0_71,i_0_227,i_0_447,i_0_39,i_0_41,i_0_36]) ).
cnf(i_0_471,plain,
~ int_less(esk3_0,plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_71,i_0_47,i_0_227,i_0_447,i_0_299,i_0_39,i_0_41,i_0_36,i_0_63]) ).
cnf(i_0_473,plain,
~ int_less(plus(plus(X1,int_zero),esk3_0),X1),
inference(scs_inference,[],[i_0_71,i_0_43,i_0_47,i_0_227,i_0_447,i_0_299,i_0_439,i_0_39,i_0_41,i_0_36,i_0_63,i_0_62]) ).
cnf(i_0_475,plain,
int_less(int_zero,plus(int_one,esk3_0)),
inference(scs_inference,[],[i_0_71,i_0_43,i_0_47,i_0_227,i_0_447,i_0_299,i_0_439,i_0_39,i_0_41,i_0_36,i_0_63,i_0_62,i_0_40]) ).
cnf(i_0_479,plain,
int_less(X1,plus(X1,plus(int_one,esk3_0))),
inference(scs_inference,[],[i_0_50,i_0_52,i_0_71,i_0_43,i_0_115,i_0_47,i_0_227,i_0_447,i_0_299,i_0_439,i_0_39,i_0_41,i_0_36,i_0_63,i_0_62,i_0_40,i_0_69,i_0_70]) ).
cnf(i_0_493,plain,
int_leq(int_zero,plus(int_one,esk2_0)),
inference(scs_inference,[],[i_0_443,i_0_39]) ).
cnf(i_0_606,plain,
int_leq(X1,plus(X1,plus(int_one,esk2_0))),
inference(scs_inference,[],[i_0_447,i_0_39]) ).
cnf(i_0_608,plain,
~ int_less(plus(X1,plus(int_zero,esk3_0)),X1),
inference(scs_inference,[],[i_0_71,i_0_321,i_0_447,i_0_39,i_0_36]) ).
cnf(i_0_637,plain,
~ int_less(plus(plus(int_one,esk2_0),int_zero),int_zero),
inference(scs_inference,[],[i_0_151,i_0_443,i_0_229,i_0_39,i_0_36]) ).
cnf(i_0_659,plain,
~ int_less(plus(plus(int_one,esk2_0),X1),X1),
inference(scs_inference,[],[i_0_73,i_0_447,i_0_263,i_0_39,i_0_36]) ).
cnf(i_0_660,plain,
int_less(X1,plus(X1,plus(int_one,esk2_0))),
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_680,plain,
int_leq(X1,plus(X1,plus(int_zero,esk3_0))),
inference(rename_variables,[],[i_0_351]) ).
cnf(i_0_796,plain,
~ int_less(plus(X1,int_one),X1),
inference(rename_variables,[],[i_0_441]) ).
cnf(i_0_1092,plain,
~ int_less(plus(plus(esk2_0,int_one),int_one),int_zero),
inference(scs_inference,[],[i_0_43,i_0_1079,i_0_1055,i_0_39,i_0_62]) ).
cnf(i_0_1094,plain,
~ int_less(plus(plus(esk2_0,int_one),plus(X1,X2)),plus(X2,X1)),
inference(scs_inference,[],[i_0_43,i_0_1093,i_0_1082,i_0_1079,i_0_1055,i_0_39,i_0_62,i_0_63]) ).
cnf(i_0_1095,plain,
~ int_less(plus(plus(esk2_0,int_one),X1),X1),
inference(rename_variables,[],[i_0_1082]) ).
cnf(i_0_1096,plain,
int_less(int_zero,plus(int_one,plus(esk2_0,int_one))),
inference(scs_inference,[],[i_0_43,i_0_1093,i_0_1082,i_0_1079,i_0_1055,i_0_39,i_0_62,i_0_63,i_0_40]) ).
cnf(i_0_1438,plain,
int_less(int_zero,esk1_2(int_zero,plus(int_one,esk2_0))),
inference(scs_inference,[],[i_0_443,i_0_35]) ).
cnf(i_0_1703,plain,
int_leq(plus(int_zero,int_one),plus(int_zero,plus(esk2_0,int_one))),
inference(scs_inference,[],[i_0_1669,i_0_1085,i_0_35,i_0_42]) ).
cnf(i_0_1705,plain,
int_zero != esk1_2(int_zero,esk3_0),
inference(scs_inference,[],[i_0_1669,i_0_1085,i_0_35,i_0_42,i_0_44]) ).
cnf(i_0_1911,plain,
~ int_less(plus(plus(X1,int_zero),int_one),X1),
inference(rename_variables,[],[i_0_361]) ).
cnf(i_0_2041,plain,
~ int_less(plus(X1,int_one),X1),
inference(rename_variables,[],[i_0_441]) ).
cnf(i_0_330,plain,
~ int_less(plus(plus(int_zero,int_one),int_zero),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_151,i_0_47,i_0_80,i_0_293,i_0_307,i_0_227,i_0_39,i_0_70,i_0_41,i_0_36,i_0_62]) ).
cnf(i_0_332,plain,
~ int_less(plus(int_one,int_one),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_151,i_0_304,i_0_47,i_0_331,i_0_80,i_0_293,i_0_307,i_0_227,i_0_39,i_0_70,i_0_41,i_0_36,i_0_62,i_0_63]) ).
cnf(i_0_416,plain,
~ int_less(plus(esk2_0,plus(X1,int_zero)),X1),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_157,i_0_227,i_0_385,i_0_206,i_0_39,i_0_41,i_0_36,i_0_63]) ).
cnf(i_0_417,plain,
~ int_less(plus(esk2_0,X1),X1),
inference(rename_variables,[],[i_0_385]) ).
cnf(i_0_418,plain,
~ int_less(plus(plus(X1,int_zero),esk2_0),X1),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_43,i_0_157,i_0_227,i_0_385,i_0_206,i_0_39,i_0_41,i_0_36,i_0_63,i_0_62]) ).
cnf(i_0_495,plain,
int_leq(int_one,plus(int_zero,plus(int_one,esk3_0))),
inference(scs_inference,[],[i_0_443,i_0_479,i_0_39,i_0_41]) ).
cnf(i_0_496,plain,
int_less(X1,plus(X1,plus(int_one,esk3_0))),
inference(rename_variables,[],[i_0_479]) ).
cnf(i_0_498,plain,
~ int_less(plus(esk2_0,int_one),int_zero),
inference(scs_inference,[],[i_0_73,i_0_443,i_0_479,i_0_39,i_0_41,i_0_36]) ).
cnf(i_0_501,plain,
~ int_less(esk2_0,plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_73,i_0_47,i_0_443,i_0_479,i_0_356,i_0_39,i_0_41,i_0_36,i_0_63]) ).
cnf(i_0_503,plain,
~ int_less(plus(esk3_0,int_zero),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_73,i_0_47,i_0_502,i_0_443,i_0_479,i_0_356,i_0_471,i_0_39,i_0_41,i_0_36,i_0_63,i_0_62]) ).
cnf(i_0_519,plain,
int_leq(int_zero,plus(int_one,esk3_0)),
inference(scs_inference,[],[i_0_475,i_0_39]) ).
cnf(i_0_521,plain,
~ int_less(plus(plus(X1,esk3_0),int_zero),X1),
inference(scs_inference,[],[i_0_151,i_0_227,i_0_475,i_0_39,i_0_36]) ).
cnf(i_0_569,plain,
~ int_less(plus(esk3_0,int_one),int_zero),
inference(scs_inference,[],[i_0_73,i_0_475,i_0_169,i_0_39,i_0_36]) ).
cnf(i_0_620,plain,
int_leq(X1,plus(X1,plus(int_one,esk3_0))),
inference(scs_inference,[],[i_0_479,i_0_39]) ).
cnf(i_0_622,plain,
~ int_less(plus(plus(int_zero,esk2_0),X1),X1),
inference(scs_inference,[],[i_0_73,i_0_293,i_0_479,i_0_39,i_0_36]) ).
cnf(i_0_640,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_zero,esk3_0)),X1),
inference(scs_inference,[],[i_0_151,i_0_77,i_0_443,i_0_608,i_0_229,i_0_39,i_0_36,i_0_63]) ).
cnf(i_0_641,plain,
~ int_less(plus(X1,plus(int_zero,esk3_0)),X1),
inference(rename_variables,[],[i_0_608]) ).
cnf(i_0_672,plain,
~ int_less(plus(plus(int_one,esk3_0),int_zero),int_zero),
inference(scs_inference,[],[i_0_151,i_0_475,i_0_348,i_0_39,i_0_36]) ).
cnf(i_0_682,plain,
int_leq(int_zero,plus(int_one,plus(int_zero,esk3_0))),
inference(scs_inference,[],[i_0_377,i_0_39]) ).
cnf(i_0_684,plain,
~ int_less(plus(X1,plus(int_one,int_one)),X1),
inference(scs_inference,[],[i_0_71,i_0_195,i_0_377,i_0_39,i_0_36]) ).
cnf(i_0_695,plain,
int_less(X1,plus(X1,plus(int_one,esk3_0))),
inference(rename_variables,[],[i_0_479]) ).
cnf(i_0_699,plain,
~ int_less(plus(plus(int_one,esk2_0),X1),X1),
inference(rename_variables,[],[i_0_659]) ).
cnf(i_0_756,plain,
int_leq(X1,plus(X1,plus(int_one,esk2_0))),
inference(rename_variables,[],[i_0_606]) ).
cnf(i_0_985,plain,
~ int_less(plus(X1,esk3_0),X1),
inference(rename_variables,[],[i_0_468]) ).
cnf(i_0_1009,plain,
~ int_less(plus(plus(int_one,esk2_0),X1),X1),
inference(rename_variables,[],[i_0_659]) ).
cnf(i_0_1034,plain,
~ int_less(plus(plus(int_one,esk2_0),X1),X1),
inference(rename_variables,[],[i_0_659]) ).
cnf(i_0_1100,plain,
int_leq(int_zero,plus(int_one,plus(esk2_0,int_one))),
inference(scs_inference,[],[i_0_1096,i_0_39]) ).
cnf(i_0_1102,plain,
~ int_less(plus(plus(X1,X2),plus(esk2_0,int_one)),plus(X2,X1)),
inference(scs_inference,[],[i_0_43,i_0_1094,i_0_1096,i_0_39,i_0_62]) ).
cnf(i_0_1104,plain,
~ int_less(plus(plus(esk2_0,int_one),int_one),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_43,i_0_1092,i_0_47,i_0_1094,i_0_1096,i_0_39,i_0_62,i_0_63]) ).
cnf(i_0_1177,plain,
int_leq(plus(int_zero,int_zero),plus(int_one,int_zero)),
inference(scs_inference,[],[i_0_391,i_0_787,i_0_80,i_0_77,i_0_35,i_0_34,i_0_58,i_0_59,i_0_60,i_0_61,i_0_42]) ).
cnf(i_0_1250,plain,
int_leq(X1,plus(int_one,X1)),
inference(rename_variables,[],[i_0_380]) ).
cnf(i_0_1402,plain,
int_less(int_zero,esk1_2(int_zero,plus(int_one,esk3_0))),
inference(scs_inference,[],[i_0_475,i_0_35]) ).
cnf(i_0_1585,plain,
~ int_less(plus(int_zero,plus(X1,int_zero)),X1),
inference(rename_variables,[],[i_0_389]) ).
cnf(i_0_1791,plain,
~ int_less(plus(plus(int_zero,int_one),plus(X1,int_zero)),X1),
inference(rename_variables,[],[i_0_275]) ).
cnf(i_0_2009,plain,
~ int_less(plus(esk2_0,X1),X1),
inference(rename_variables,[],[i_0_385]) ).
cnf(i_0_2062,plain,
int_leq(X1,plus(plus(X1,int_zero),esk3_0)),
inference(scs_inference,[],[i_0_473,i_0_42]) ).
cnf(i_0_2086,plain,
~ int_less(plus(plus(X1,int_zero),esk3_0),X1),
inference(rename_variables,[],[i_0_473]) ).
cnf(i_0_524,plain,
~ int_less(plus(esk2_0,int_one),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_151,i_0_47,i_0_227,i_0_475,i_0_498,i_0_39,i_0_36,i_0_63]) ).
cnf(i_0_526,plain,
~ int_less(plus(esk2_0,int_zero),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_151,i_0_47,i_0_525,i_0_227,i_0_475,i_0_501,i_0_498,i_0_39,i_0_36,i_0_63,i_0_62]) ).
cnf(i_0_652,plain,
~ int_less(plus(plus(int_zero,esk2_0),plus(X1,int_zero)),X1),
inference(scs_inference,[],[i_0_71,i_0_77,i_0_43,i_0_160,i_0_622,i_0_197,i_0_39,i_0_36,i_0_62,i_0_63]) ).
cnf(i_0_653,plain,
~ int_less(plus(plus(int_zero,esk2_0),X1),X1),
inference(rename_variables,[],[i_0_622]) ).
cnf(i_0_729,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_zero,esk3_0)),X1),
inference(rename_variables,[],[i_0_640]) ).
cnf(i_0_753,plain,
int_leq(X1,plus(X1,plus(int_one,esk3_0))),
inference(rename_variables,[],[i_0_620]) ).
cnf(i_0_793,plain,
~ int_less(plus(int_zero,esk3_0),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_43,i_0_788,i_0_71,i_0_503,i_0_80,i_0_293,i_0_774,i_0_783,i_0_41,i_0_39,i_0_37,i_0_36,i_0_62]) ).
cnf(i_0_795,plain,
~ int_less(plus(plus(X1,X2),int_one),plus(X2,X1)),
inference(scs_inference,[],[i_0_43,i_0_788,i_0_794,i_0_71,i_0_503,i_0_441,i_0_80,i_0_293,i_0_774,i_0_783,i_0_41,i_0_39,i_0_37,i_0_36,i_0_62,i_0_63]) ).
cnf(i_0_797,plain,
int_less(X1,plus(X1,plus(esk3_0,int_zero))),
inference(scs_inference,[],[i_0_43,i_0_788,i_0_794,i_0_71,i_0_503,i_0_441,i_0_80,i_0_293,i_0_774,i_0_783,i_0_41,i_0_39,i_0_37,i_0_36,i_0_62,i_0_63,i_0_70]) ).
cnf(i_0_799,plain,
int_less(int_zero,plus(int_one,plus(esk2_0,int_zero))),
inference(scs_inference,[],[i_0_43,i_0_788,i_0_794,i_0_71,i_0_503,i_0_441,i_0_80,i_0_293,i_0_774,i_0_783,i_0_41,i_0_39,i_0_37,i_0_36,i_0_62,i_0_63,i_0_70,i_0_40]) ).
cnf(i_0_968,plain,
~ int_less(plus(X1,plus(int_one,int_one)),X1),
inference(rename_variables,[],[i_0_684]) ).
cnf(i_0_1030,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_zero,esk3_0)),X1),
inference(rename_variables,[],[i_0_640]) ).
cnf(i_0_1111,plain,
~ int_less(plus(int_one,plus(esk2_0,int_one)),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_43,i_0_1104,i_0_1073,i_0_39,i_0_62]) ).
cnf(i_0_1121,plain,
int_leq(plus(int_zero,int_zero),plus(int_one,int_one)),
inference(scs_inference,[],[i_0_332,i_0_1042,i_0_49,i_0_47,i_0_58,i_0_59,i_0_60,i_0_61,i_0_35,i_0_34,i_0_42]) ).
cnf(i_0_1123,plain,
int_zero != plus(esk2_0,int_one),
inference(scs_inference,[],[i_0_332,i_0_1042,i_0_49,i_0_47,i_0_58,i_0_59,i_0_60,i_0_61,i_0_35,i_0_34,i_0_42,i_0_44]) ).
cnf(i_0_1125,plain,
~ int_leq(int_one,plus(plus(int_zero,int_zero),int_zero)),
inference(scs_inference,[],[i_0_332,i_0_174,i_0_1042,i_0_49,i_0_47,i_0_58,i_0_59,i_0_60,i_0_61,i_0_35,i_0_34,i_0_42,i_0_44,i_0_40]) ).
cnf(i_0_1128,plain,
plus(int_zero,real_one) != real_zero,
inference(scs_inference,[],[i_0_332,i_0_174,i_0_302,i_0_1042,i_0_49,i_0_47,i_0_58,i_0_59,i_0_60,i_0_61,i_0_35,i_0_34,i_0_42,i_0_44,i_0_40,i_0_56]) ).
cnf(i_0_1129,plain,
~ int_less(int_one,plus(plus(int_zero,int_zero),int_zero)),
inference(scs_inference,[],[i_0_332,i_0_174,i_0_302,i_0_1042,i_0_49,i_0_47,i_0_58,i_0_59,i_0_60,i_0_61,i_0_35,i_0_34,i_0_42,i_0_44,i_0_40,i_0_56,i_0_39]) ).
cnf(i_0_1131,plain,
epred1_2(plus(esk3_0,int_zero),esk3_0),
inference(scs_inference,[],[i_0_92,i_0_332,i_0_174,i_0_302,i_0_1042,i_0_49,i_0_47,i_0_77,i_0_58,i_0_59,i_0_60,i_0_61,i_0_35,i_0_34,i_0_42,i_0_44,i_0_40,i_0_56,i_0_39,i_0_66]) ).
cnf(i_0_1133,plain,
epred1_2(esk3_0,plus(esk3_0,int_zero)),
inference(scs_inference,[],[i_0_92,i_0_332,i_0_174,i_0_302,i_0_1042,i_0_49,i_0_47,i_0_77,i_0_1132,i_0_58,i_0_59,i_0_60,i_0_61,i_0_35,i_0_34,i_0_42,i_0_44,i_0_40,i_0_56,i_0_39,i_0_66,i_0_67]) ).
cnf(i_0_1135,plain,
int_leq(plus(int_zero,esk3_0),plus(plus(esk2_0,int_one),n)),
inference(scs_inference,[],[i_0_50,i_0_92,i_0_332,i_0_174,i_0_302,i_0_1042,i_0_49,i_0_47,i_0_77,i_0_1132,i_0_58,i_0_59,i_0_60,i_0_61,i_0_35,i_0_34,i_0_42,i_0_44,i_0_40,i_0_56,i_0_39,i_0_66,i_0_67,i_0_31]) ).
cnf(i_0_1966,plain,
~ int_less(plus(esk2_0,plus(X1,int_zero)),X1),
inference(rename_variables,[],[i_0_416]) ).
cnf(i_0_2027,plain,
~ int_less(plus(plus(X1,int_zero),esk2_0),X1),
inference(rename_variables,[],[i_0_418]) ).
cnf(i_0_549,plain,
~ int_less(plus(int_one,esk2_0),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_71,i_0_77,i_0_43,i_0_261,i_0_126,i_0_524,i_0_235,i_0_39,i_0_36,i_0_63,i_0_62]) ).
cnf(i_0_551,plain,
int_less(int_zero,plus(plus(int_one,esk3_0),int_zero)),
inference(scs_inference,[],[i_0_71,i_0_77,i_0_43,i_0_261,i_0_126,i_0_524,i_0_235,i_0_39,i_0_36,i_0_63,i_0_62,i_0_40]) ).
cnf(i_0_663,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_zero,esk2_0)),X1),
inference(scs_inference,[],[i_0_73,i_0_43,i_0_447,i_0_263,i_0_652,i_0_39,i_0_36,i_0_62]) ).
cnf(i_0_665,plain,
~ int_less(plus(plus(int_one,int_zero),plus(X1,int_zero)),X1),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_650,i_0_43,i_0_447,i_0_263,i_0_652,i_0_39,i_0_36,i_0_62,i_0_63]) ).
cnf(i_0_803,plain,
int_leq(int_one,plus(int_zero,plus(esk3_0,int_zero))),
inference(scs_inference,[],[i_0_797,i_0_41]) ).
cnf(i_0_804,plain,
int_less(X1,plus(X1,plus(esk3_0,int_zero))),
inference(rename_variables,[],[i_0_797]) ).
cnf(i_0_813,plain,
int_less(X1,plus(X1,plus(esk3_0,int_zero))),
inference(rename_variables,[],[i_0_797]) ).
cnf(i_0_963,plain,
int_leq(int_zero,plus(int_one,plus(esk2_0,int_zero))),
inference(scs_inference,[],[i_0_799,i_0_39]) ).
cnf(i_0_965,plain,
~ int_less(plus(int_zero,plus(X1,esk3_0)),X1),
inference(scs_inference,[],[i_0_43,i_0_799,i_0_521,i_0_39,i_0_62]) ).
cnf(i_0_967,plain,
~ int_less(plus(plus(X1,X2),plus(int_one,int_one)),plus(X2,X1)),
inference(scs_inference,[],[i_0_43,i_0_966,i_0_684,i_0_799,i_0_521,i_0_39,i_0_62,i_0_63]) ).
cnf(i_0_1209,plain,
int_less(X1,plus(X1,plus(esk3_0,int_zero))),
inference(rename_variables,[],[i_0_797]) ).
cnf(i_0_1671,plain,
int_leq(plus(int_zero,int_zero),plus(int_one,plus(esk2_0,int_one))),
inference(scs_inference,[],[i_0_1111,i_0_80,i_0_35,i_0_42]) ).
cnf(i_0_2012,plain,
int_less(X1,plus(X1,plus(esk3_0,int_zero))),
inference(rename_variables,[],[i_0_797]) ).
cnf(i_0_572,plain,
~ int_less(plus(int_one,esk2_0),int_zero),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_549,i_0_475,i_0_169,i_0_39,i_0_36,i_0_63]) ).
cnf(i_0_574,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,int_one)),X1),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_549,i_0_43,i_0_475,i_0_169,i_0_547,i_0_39,i_0_36,i_0_63,i_0_62]) ).
cnf(i_0_576,plain,
int_less(int_zero,plus(plus(int_one,esk2_0),int_zero)),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_549,i_0_43,i_0_475,i_0_169,i_0_547,i_0_39,i_0_36,i_0_63,i_0_62,i_0_40]) ).
cnf(i_0_675,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,int_zero)),X1),
inference(scs_inference,[],[i_0_151,i_0_43,i_0_475,i_0_348,i_0_665,i_0_39,i_0_36,i_0_62]) ).
cnf(i_0_677,plain,
~ int_less(plus(plus(plus(X1,int_zero),int_zero),plus(int_zero,esk2_0)),X1),
inference(scs_inference,[],[i_0_151,i_0_77,i_0_663,i_0_43,i_0_475,i_0_348,i_0_665,i_0_39,i_0_36,i_0_62,i_0_63]) ).
cnf(i_0_678,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_zero,esk2_0)),X1),
inference(rename_variables,[],[i_0_663]) ).
cnf(i_0_692,plain,
int_leq(int_zero,plus(plus(int_one,esk3_0),int_zero)),
inference(scs_inference,[],[i_0_551,i_0_39]) ).
cnf(i_0_694,plain,
~ int_less(plus(plus(int_one,esk3_0),X1),X1),
inference(scs_inference,[],[i_0_73,i_0_479,i_0_551,i_0_39,i_0_36]) ).
cnf(i_0_698,plain,
~ int_less(plus(plus(int_one,esk2_0),plus(X1,int_zero)),X1),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_479,i_0_659,i_0_551,i_0_39,i_0_36,i_0_63]) ).
cnf(i_0_700,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,esk2_0)),X1),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_43,i_0_479,i_0_659,i_0_551,i_0_39,i_0_36,i_0_63,i_0_62]) ).
cnf(i_0_806,plain,
int_leq(X1,plus(X1,plus(esk3_0,int_zero))),
inference(scs_inference,[],[i_0_797,i_0_804,i_0_41,i_0_39]) ).
cnf(i_0_808,plain,
int_less(X1,plus(plus(int_zero,int_one),X1)),
inference(scs_inference,[],[i_0_43,i_0_82,i_0_797,i_0_804,i_0_41,i_0_39,i_0_37]) ).
cnf(i_0_812,plain,
~ int_less(plus(plus(esk3_0,int_zero),X1),X1),
inference(scs_inference,[],[i_0_43,i_0_73,i_0_82,i_0_797,i_0_804,i_0_41,i_0_39,i_0_37,i_0_36]) ).
cnf(i_0_816,plain,
~ int_less(plus(int_zero,esk2_0),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_43,i_0_810,i_0_73,i_0_526,i_0_82,i_0_797,i_0_804,i_0_41,i_0_39,i_0_37,i_0_36,i_0_62]) ).
cnf(i_0_818,plain,
~ int_less(plus(X1,X2),plus(int_zero,plus(X2,X1))),
inference(scs_inference,[],[i_0_43,i_0_810,i_0_817,i_0_73,i_0_526,i_0_770,i_0_82,i_0_797,i_0_804,i_0_41,i_0_39,i_0_37,i_0_36,i_0_62,i_0_63]) ).
cnf(i_0_820,plain,
int_less(int_zero,plus(int_one,plus(esk3_0,int_zero))),
inference(scs_inference,[],[i_0_43,i_0_810,i_0_817,i_0_73,i_0_526,i_0_770,i_0_82,i_0_797,i_0_804,i_0_41,i_0_39,i_0_37,i_0_36,i_0_62,i_0_63,i_0_40]) ).
cnf(i_0_898,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_zero,esk2_0)),X1),
inference(rename_variables,[],[i_0_663]) ).
cnf(i_0_2131,plain,
int_leq(X1,plus(int_zero,plus(X1,esk3_0))),
inference(scs_inference,[],[i_0_965,i_0_42]) ).
cnf(i_0_597,plain,
~ int_less(plus(plus(plus(X1,int_zero),int_zero),plus(int_one,int_one)),X1),
inference(scs_inference,[],[i_0_151,i_0_77,i_0_574,i_0_261,i_0_206,i_0_39,i_0_36,i_0_63]) ).
cnf(i_0_598,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,int_one)),X1),
inference(rename_variables,[],[i_0_574]) ).
cnf(i_0_599,plain,
~ int_less(plus(int_one,esk3_0),int_zero),
inference(scs_inference,[],[i_0_151,i_0_77,i_0_574,i_0_43,i_0_261,i_0_206,i_0_569,i_0_39,i_0_36,i_0_63,i_0_62]) ).
cnf(i_0_601,plain,
int_less(int_zero,plus(plus(int_one,int_one),int_zero)),
inference(scs_inference,[],[i_0_151,i_0_77,i_0_574,i_0_43,i_0_261,i_0_206,i_0_569,i_0_39,i_0_36,i_0_63,i_0_62,i_0_40]) ).
cnf(i_0_687,plain,
~ int_less(plus(plus(plus(X1,int_zero),int_zero),plus(int_one,int_zero)),X1),
inference(scs_inference,[],[i_0_71,i_0_77,i_0_675,i_0_195,i_0_377,i_0_39,i_0_36,i_0_63]) ).
cnf(i_0_688,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,int_zero)),X1),
inference(rename_variables,[],[i_0_675]) ).
cnf(i_0_705,plain,
int_leq(int_zero,plus(plus(int_one,esk2_0),int_zero)),
inference(scs_inference,[],[i_0_576,i_0_39]) ).
cnf(i_0_707,plain,
~ int_less(plus(plus(plus(X1,int_zero),int_zero),plus(int_one,esk2_0)),X1),
inference(scs_inference,[],[i_0_77,i_0_700,i_0_576,i_0_39,i_0_63]) ).
cnf(i_0_708,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,esk2_0)),X1),
inference(rename_variables,[],[i_0_700]) ).
cnf(i_0_715,plain,
~ int_less(plus(plus(int_one,esk3_0),X1),X1),
inference(rename_variables,[],[i_0_694]) ).
cnf(i_0_828,plain,
int_leq(X1,plus(plus(int_zero,int_one),X1)),
inference(scs_inference,[],[i_0_808,i_0_787,i_0_41,i_0_39]) ).
cnf(i_0_830,plain,
int_less(X1,plus(plus(int_zero,esk3_0),X1)),
inference(scs_inference,[],[i_0_43,i_0_227,i_0_808,i_0_787,i_0_41,i_0_39,i_0_37]) ).
cnf(i_0_834,plain,
~ int_less(plus(int_zero,plus(int_zero,int_one)),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_43,i_0_832,i_0_330,i_0_227,i_0_808,i_0_787,i_0_41,i_0_39,i_0_37,i_0_62]) ).
cnf(i_0_841,plain,
int_leq(X1,plus(X1,plus(esk3_0,int_zero))),
inference(rename_variables,[],[i_0_806]) ).
cnf(i_0_883,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,int_one)),X1),
inference(rename_variables,[],[i_0_574]) ).
cnf(i_0_895,plain,
~ int_less(plus(plus(esk3_0,int_zero),X1),X1),
inference(rename_variables,[],[i_0_812]) ).
cnf(i_0_927,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,int_zero)),X1),
inference(rename_variables,[],[i_0_675]) ).
cnf(i_0_944,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,esk2_0)),X1),
inference(rename_variables,[],[i_0_700]) ).
cnf(i_0_972,plain,
int_leq(int_zero,plus(int_one,plus(esk3_0,int_zero))),
inference(scs_inference,[],[i_0_820,i_0_39]) ).
cnf(i_0_974,plain,
~ int_less(plus(plus(int_one,int_one),plus(X1,X2)),plus(X2,X1)),
inference(scs_inference,[],[i_0_43,i_0_967,i_0_820,i_0_39,i_0_62]) ).
cnf(i_0_976,plain,
~ int_less(plus(plus(X1,X2),plus(int_zero,esk2_0)),plus(X2,X1)),
inference(scs_inference,[],[i_0_43,i_0_975,i_0_967,i_0_790,i_0_820,i_0_39,i_0_62,i_0_63]) ).
cnf(i_0_1001,plain,
~ int_less(plus(plus(int_one,esk3_0),X1),X1),
inference(rename_variables,[],[i_0_694]) ).
cnf(i_0_1027,plain,
~ int_less(plus(plus(int_one,esk3_0),X1),X1),
inference(rename_variables,[],[i_0_694]) ).
cnf(i_0_1242,plain,
~ int_less(plus(X1,X2),plus(int_zero,plus(X2,X1))),
inference(rename_variables,[],[i_0_818]) ).
cnf(i_0_1245,plain,
int_less(X1,plus(plus(int_zero,int_one),X1)),
inference(rename_variables,[],[i_0_808]) ).
cnf(i_0_1254,plain,
int_less(X1,plus(plus(int_zero,int_one),X1)),
inference(rename_variables,[],[i_0_808]) ).
cnf(i_0_1547,plain,
~ int_less(plus(X1,X2),plus(int_zero,plus(X2,X1))),
inference(rename_variables,[],[i_0_818]) ).
cnf(i_0_1660,plain,
~ int_less(plus(plus(int_one,esk2_0),plus(X1,int_zero)),X1),
inference(rename_variables,[],[i_0_698]) ).
cnf(i_0_2029,plain,
int_leq(X1,plus(X1,plus(esk3_0,int_zero))),
inference(rename_variables,[],[i_0_806]) ).
cnf(i_0_2071,plain,
int_less(X1,plus(plus(int_zero,int_one),X1)),
inference(rename_variables,[],[i_0_808]) ).
cnf(i_0_2084,plain,
int_less(X1,plus(plus(int_zero,int_one),X1)),
inference(rename_variables,[],[i_0_808]) ).
cnf(i_0_611,plain,
~ int_less(plus(int_one,esk3_0),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_71,i_0_599,i_0_47,i_0_321,i_0_447,i_0_39,i_0_36,i_0_63]) ).
cnf(i_0_613,plain,
~ int_less(plus(plus(int_zero,esk3_0),X1),X1),
inference(scs_inference,[],[i_0_71,i_0_599,i_0_43,i_0_47,i_0_321,i_0_447,i_0_39,i_0_36,i_0_63,i_0_62]) ).
cnf(i_0_615,plain,
int_less(int_zero,plus(int_one,plus(int_one,esk2_0))),
inference(scs_inference,[],[i_0_71,i_0_599,i_0_43,i_0_47,i_0_321,i_0_447,i_0_39,i_0_36,i_0_63,i_0_62,i_0_40]) ).
cnf(i_0_712,plain,
int_leq(int_zero,plus(plus(int_one,int_one),int_zero)),
inference(scs_inference,[],[i_0_601,i_0_39]) ).
cnf(i_0_714,plain,
~ int_less(plus(plus(int_one,esk3_0),plus(X1,int_zero)),X1),
inference(scs_inference,[],[i_0_77,i_0_694,i_0_601,i_0_39,i_0_63]) ).
cnf(i_0_716,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,esk3_0)),X1),
inference(scs_inference,[],[i_0_77,i_0_43,i_0_694,i_0_601,i_0_39,i_0_63,i_0_62]) ).
cnf(i_0_843,plain,
int_leq(X1,plus(plus(int_zero,esk3_0),X1)),
inference(scs_inference,[],[i_0_830,i_0_39]) ).
cnf(i_0_845,plain,
int_less(X1,plus(plus(int_zero,esk2_0),X1)),
inference(scs_inference,[],[i_0_43,i_0_261,i_0_830,i_0_39,i_0_37]) ).
cnf(i_0_856,plain,
int_leq(X1,plus(plus(int_zero,int_one),X1)),
inference(rename_variables,[],[i_0_828]) ).
cnf(i_0_1318,plain,
int_less(X1,plus(plus(int_zero,esk3_0),X1)),
inference(rename_variables,[],[i_0_830]) ).
cnf(i_0_2139,plain,
int_less(X1,plus(plus(int_zero,esk3_0),X1)),
inference(rename_variables,[],[i_0_830]) ).
cnf(i_0_2153,plain,
int_less(X1,plus(plus(int_zero,esk3_0),X1)),
inference(rename_variables,[],[i_0_830]) ).
cnf(i_0_626,plain,
~ int_less(plus(plus(int_zero,esk3_0),plus(X1,int_zero)),X1),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_613,i_0_293,i_0_479,i_0_39,i_0_36,i_0_63]) ).
cnf(i_0_627,plain,
~ int_less(plus(plus(int_zero,esk3_0),X1),X1),
inference(rename_variables,[],[i_0_613]) ).
cnf(i_0_628,plain,
~ int_less(plus(esk3_0,int_one),plus(int_zero,int_zero)),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_613,i_0_43,i_0_293,i_0_479,i_0_611,i_0_39,i_0_36,i_0_63,i_0_62]) ).
cnf(i_0_630,plain,
int_less(int_zero,plus(int_one,plus(int_one,esk3_0))),
inference(scs_inference,[],[i_0_73,i_0_77,i_0_613,i_0_43,i_0_293,i_0_479,i_0_611,i_0_39,i_0_36,i_0_63,i_0_62,i_0_40]) ).
cnf(i_0_720,plain,
int_leq(int_zero,plus(int_one,plus(int_one,esk2_0))),
inference(scs_inference,[],[i_0_615,i_0_39]) ).
cnf(i_0_722,plain,
~ int_less(plus(plus(plus(X1,int_zero),int_zero),plus(int_one,esk3_0)),X1),
inference(scs_inference,[],[i_0_77,i_0_716,i_0_615,i_0_39,i_0_63]) ).
cnf(i_0_723,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,esk3_0)),X1),
inference(rename_variables,[],[i_0_716]) ).
cnf(i_0_836,plain,
~ int_less(plus(plus(int_zero,esk3_0),plus(X1,X2)),plus(X2,X1)),
inference(scs_inference,[],[i_0_43,i_0_832,i_0_835,i_0_330,i_0_613,i_0_227,i_0_808,i_0_787,i_0_41,i_0_39,i_0_37,i_0_62,i_0_63]) ).
cnf(i_0_837,plain,
~ int_less(plus(plus(int_zero,esk3_0),X1),X1),
inference(rename_variables,[],[i_0_613]) ).
cnf(i_0_838,plain,
int_less(int_zero,plus(plus(int_zero,int_one),int_one)),
inference(scs_inference,[],[i_0_43,i_0_832,i_0_835,i_0_330,i_0_613,i_0_227,i_0_808,i_0_787,i_0_41,i_0_39,i_0_37,i_0_62,i_0_63,i_0_40]) ).
cnf(i_0_858,plain,
int_leq(X1,plus(plus(int_zero,esk2_0),X1)),
inference(scs_inference,[],[i_0_845,i_0_39]) ).
cnf(i_0_860,plain,
int_less(X1,plus(plus(int_one,int_zero),X1)),
inference(scs_inference,[],[i_0_43,i_0_89,i_0_845,i_0_39,i_0_37]) ).
cnf(i_0_873,plain,
int_leq(X1,plus(plus(int_zero,esk3_0),X1)),
inference(rename_variables,[],[i_0_843]) ).
cnf(i_0_957,plain,
~ int_less(plus(plus(X1,int_zero),plus(int_one,esk3_0)),X1),
inference(rename_variables,[],[i_0_716]) ).
cnf(i_0_1380,plain,
int_less(X1,plus(plus(int_zero,esk2_0),X1)),
inference(rename_variables,[],[i_0_845]) ).
cnf(i_0_1730,plain,
~ int_less(plus(plus(int_one,esk3_0),plus(X1,int_zero)),X1),
inference(rename_variables,[],[i_0_714]) ).
cnf(i_0_726,plain,
int_leq(int_zero,plus(int_one,plus(int_one,esk3_0))),
inference(scs_inference,[],[i_0_630,i_0_39]) ).
cnf(i_0_728,plain,
~ int_less(plus(plus(plus(X1,int_zero),int_zero),plus(int_zero,esk3_0)),X1),
inference(scs_inference,[],[i_0_77,i_0_630,i_0_640,i_0_39,i_0_63]) ).
cnf(i_0_849,plain,
~ int_less(plus(plus(X1,X2),plus(int_zero,esk3_0)),plus(X2,X1)),
inference(scs_inference,[],[i_0_43,i_0_847,i_0_261,i_0_836,i_0_830,i_0_39,i_0_37,i_0_62]) ).
cnf(i_0_851,plain,
~ int_less(plus(plus(int_one,int_zero),plus(X1,X2)),plus(X2,X1)),
inference(scs_inference,[],[i_0_43,i_0_847,i_0_850,i_0_650,i_0_261,i_0_836,i_0_830,i_0_39,i_0_37,i_0_62,i_0_63]) ).
cnf(i_0_853,plain,
int_less(int_zero,plus(plus(int_zero,esk3_0),int_one)),
inference(scs_inference,[],[i_0_43,i_0_847,i_0_850,i_0_650,i_0_261,i_0_836,i_0_830,i_0_39,i_0_37,i_0_62,i_0_63,i_0_40]) ).
cnf(c_0_1152,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_1153,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_1152]) ).
cnf(c_0_1154,plain,
( plus(X1,esk1_2(X1,X2)) = X2
| ~ int_less(X1,X2) ),
i_0_34 ).
cnf(c_0_1155,plain,
( int_less(int_zero,esk1_2(X1,X2))
| ~ int_less(X1,X2) ),
i_0_35 ).
cnf(c_0_1156,plain,
( int_leq(X1,X2)
| X1 != X2 ),
i_0_46 ).
cnf(c_0_1157,plain,
( a(X1,plus(X1,esk1_2(X2,X3))) = real_zero
| ~ epred1_2(X2,X3)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ int_less(X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_1153,c_0_1154]),c_0_1155]) ).
cnf(c_0_1158,plain,
int_leq(X1,X1),
inference(er,[status(thm)],[c_0_1156]) ).
cnf(c_0_1159,plain,
( a(plus(X1,X2),X1) = real_zero
| ~ int_less(int_zero,X2)
| X3 != plus(X4,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X4)
| ~ epred1_2(X3,X4) ),
i_0_29 ).
cnf(c_0_1160,negated_conjecture,
( esk2_0 = esk3_0
| a(esk2_0,esk3_0) != real_zero ),
i_0_45 ).
cnf(c_0_1161,plain,
( a(X1,X2) = real_zero
| ~ epred1_2(X1,X2)
| ~ int_leq(int_one,X1)
| ~ int_less(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1157,c_0_1154]),c_0_1158])]) ).
cnf(c_0_1162,negated_conjecture,
int_leq(int_one,esk2_0),
i_0_53 ).
cnf(c_0_1163,plain,
( a(plus(X1,X2),X1) = real_zero
| ~ epred1_2(plus(X3,X2),X3)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X3)
| ~ int_less(int_zero,X2) ),
inference(er,[status(thm)],[c_0_1159]) ).
cnf(c_0_1164,negated_conjecture,
( esk2_0 = esk3_0
| ~ epred1_2(esk2_0,esk3_0)
| ~ int_less(esk2_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1160,c_0_1161]),c_0_1162])]) ).
cnf(c_0_1165,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_1166,negated_conjecture,
int_leq(esk3_0,n),
i_0_50 ).
cnf(c_0_1167,negated_conjecture,
int_leq(esk2_0,n),
i_0_51 ).
cnf(c_0_1168,negated_conjecture,
int_leq(int_one,esk3_0),
i_0_52 ).
cnf(c_0_1169,plain,
( int_less(X1,X2)
| X1 = X2
| ~ int_leq(X1,X2) ),
i_0_38 ).
cnf(c_0_1170,plain,
( int_less(X1,X2)
| int_leq(X2,X1) ),
i_0_42 ).
cnf(c_0_1171,plain,
( a(plus(X1,esk1_2(X2,X3)),X1) = real_zero
| ~ epred1_2(X3,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ int_less(X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_1163,c_0_1154]),c_0_1155]) ).
cnf(c_0_1172,hypothesis,
( esk2_0 = esk3_0
| ~ int_less(esk2_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1164,c_0_1165]),c_0_1166]),c_0_1167]),c_0_1168]),c_0_1162])]) ).
cnf(c_0_1173,plain,
( X1 = X2
| int_less(X2,X1)
| int_less(X1,X2) ),
inference(spm,[status(thm)],[c_0_1169,c_0_1170]) ).
cnf(c_0_1174,plain,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ epred1_2(X3,X2) ),
i_0_33 ).
cnf(c_0_1175,plain,
( a(X1,X2) = real_zero
| ~ epred1_2(X1,X2)
| ~ int_leq(int_one,X2)
| ~ int_less(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1171,c_0_1154]),c_0_1158])]) ).
cnf(c_0_1176,plain,
( esk2_0 = esk3_0
| int_less(esk3_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_1172,c_0_1173]) ).
cnf(c_0_1177,negated_conjecture,
( a(esk3_0,esk3_0) = real_one
| ~ epred1_2(X1,X2)
| ~ int_leq(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_1174,c_0_1168]) ).
cnf(c_0_1178,plain,
epred1_2(esk3_0,plus(esk3_0,int_zero)),
i_0_1133 ).
cnf(c_0_1179,plain,
plus(X1,int_zero) = X1,
i_0_47 ).
cnf(c_0_1180,negated_conjecture,
( esk2_0 = esk3_0
| ~ epred1_2(esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1160,c_0_1175]),c_0_1168])]),c_0_1176]) ).
cnf(c_0_1181,plain,
( a(esk3_0,esk3_0) = real_one
| ~ epred1_2(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_1177,c_0_1158]) ).
cnf(c_0_1182,plain,
epred1_2(esk3_0,esk3_0),
inference(rw,[status(thm)],[c_0_1178,c_0_1179]) ).
cnf(c_0_1183,negated_conjecture,
( a(esk2_0,esk3_0) = real_zero
| esk2_0 != esk3_0 ),
i_0_48 ).
cnf(c_0_1184,hypothesis,
esk2_0 = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1180,c_0_1165]),c_0_1166]),c_0_1167]),c_0_1168]),c_0_1162])]) ).
cnf(c_0_1185,plain,
a(esk3_0,esk3_0) = real_one,
inference(spm,[status(thm)],[c_0_1181,c_0_1182]) ).
cnf(c_0_1186,plain,
real_zero != real_one,
i_0_54 ).
cnf(c_0_1187,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1183,c_0_1184]),c_0_1185]),c_0_1184])]),c_0_1186]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV490+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
% 0.14/0.33 % Computer : n014.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 05:19:06 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 273.12/132.80 % Version : CSE_E---1.7
% 273.12/132.80 % Problem : theBenchmark.p
% 273.12/132.80 % SZS status Theorem for theBenchmark.p
% 273.12/132.80 % SZS output start CNFRefutation
% See solution above
% 276.32/135.96 % Total time : 131.329s
%------------------------------------------------------------------------------