%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV492+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 02:55:45 PM UTC 2026
% Result : Theorem 213.56s 31.97s
% Output : CNFRefutation 213.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 208 ( 25 unt; 0 def)
% Number of atoms : 666 ( 186 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 731 ( 273 ~; 359 |; 67 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 262 ( 1 sgn 87 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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_and_inverse,axiom,
! [X1,X2] :
( int_less(X1,X2)
<=> ? [X3] :
( int_less(int_zero,X3)
& plus(X1,X3) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_inverse) ).
fof(int_less_transitive,axiom,
! [X1,X2,X3] :
( ( int_less(X2,X3)
& int_less(X1,X2) )
=> int_less(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_transitive) ).
fof(int_leq,axiom,
! [X1,X2] :
( int_leq(X1,X2)
<=> ( X1 = X2
| int_less(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_leq) ).
fof(plus_commutative,axiom,
! [X1,X2] : plus(X1,X2) = plus(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_commutative) ).
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_leq(X2,X1)
| int_less(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_total) ).
fof(plus_and_order1,axiom,
! [X4,X5,X6,X7] :
( ( int_leq(X6,X7)
& int_less(X4,X5) )
=> int_leq(plus(X4,X6),plus(X5,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_order1) ).
fof(plus_zero,axiom,
! [X1] : plus(X1,int_zero) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).
fof(lti,conjecture,
( ! [X1,X2] :
( ( X1 = X2
& int_leq(X2,n)
& int_leq(int_one,X1) )
=> a(X1,X2) != real_zero )
& ! [X1,X2] :
( ( int_leq(X2,n)
& int_less(X1,X2)
& int_leq(int_one,X1) )
=> a(X1,X2) = real_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lti) ).
fof(qih,hypothesis,
! [X1,X2] :
( ( int_leq(X2,n)
& int_leq(int_one,X2)
& int_leq(X1,n)
& int_leq(int_one,X1) )
=> ( ! [X8] :
( ( X2 = plus(X1,X8)
& int_less(int_zero,X8) )
=> ! [X3] :
( ( int_leq(X3,X1)
& int_leq(int_one,X3) )
=> a(X3,plus(X3,X8)) = real_zero ) )
& ! [X3] :
( ( int_leq(X3,X2)
& int_leq(int_one,X3) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( X1 = plus(X2,X8)
& int_less(int_zero,X8) )
=> ! [X3] :
( ( int_leq(X3,X2)
& int_leq(int_one,X3) )
=> a(plus(X3,X8),X3) = qr(plus(X3,X8),X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qih) ).
fof(real_constants,axiom,
real_zero != real_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_constants) ).
fof(int_zero_one,axiom,
int_less(int_zero,int_one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_zero_one) ).
fof(c_0_13,plain,
! [X1,X2] :
( int_less(X1,X2)
=> X1 != X2 ),
inference(fof_simplification,[status(thm)],[int_less_irreflexive]) ).
fof(c_0_14,plain,
! [X25,X26,X28,X29,X30] :
( ( int_less(X28,X29)
| ~ int_less(int_zero,X30)
| plus(X28,X30) != X29 )
& ( ~ int_less(X25,X26)
| int_less(int_zero,esk1_2(X25,X26)) )
& ( ~ int_less(X25,X26)
| plus(X25,esk1_2(X25,X26)) = X26 ) ),
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)],[plus_and_inverse])])])])])])]) ).
fof(c_0_15,plain,
! [X14,X15] :
( X14 != X15
| ~ int_less(X14,X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_16,plain,
! [X11,X12,X13] :
( int_less(X11,X13)
| ~ int_less(X12,X13)
| ~ int_less(X11,X12) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_transitive])])]) ).
cnf(c_0_17,plain,
( ~ int_less(int_zero,X2)
| plus(X1,X2) != X3
| int_less(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( X1 != X2
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ int_less(X2,X3)
| ~ int_less(X1,X2)
| int_less(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( ~ int_less(int_zero,X2)
| int_less(X1,plus(X1,X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
~ int_less(X1,X1),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( ~ int_less(X1,X2)
| ~ int_less(int_zero,X3)
| int_less(X1,plus(X2,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( ~ int_less(int_zero,X2)
| ~ int_less(plus(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
( ~ int_less(X1,X2)
| plus(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,plain,
( ~ int_less(X1,X2)
| int_less(int_zero,esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_26,plain,
! [X9,X10] :
( ( int_leq(X9,X10)
| X9 != X10 )
& ( int_leq(X9,X10)
| ~ int_less(X9,X10) )
& ( X9 = X10
| int_less(X9,X10)
| ~ int_leq(X9,X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_leq])])])]) ).
fof(c_0_27,plain,
! [X18,X19] : plus(X18,X19) = plus(X19,X18),
inference(variable_rename,[status(thm)],[plus_commutative]) ).
cnf(c_0_28,plain,
( ~ int_less(X2,X1)
| ~ int_less(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,plain,
( ~ int_leq(X1,X2)
| X1 = X2
| int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_30,plain,
! [X31] :
( ( int_less(int_zero,X31)
| ~ int_leq(int_one,X31) )
& ( int_leq(int_one,X31)
| ~ int_less(int_zero,X31) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[one_successor_of_zero])])]) ).
cnf(c_0_31,plain,
plus(X1,X2) = plus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
( ~ int_leq(X1,X2)
| ~ int_less(X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( ~ int_less(int_zero,X1)
| int_leq(int_one,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( ~ int_less(int_zero,X1)
| ~ int_less(plus(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
fof(c_0_35,plain,
! [X16,X17] :
( int_leq(X17,X16)
| int_less(X16,X17) ),
inference(variable_rename,[status(thm)],[int_less_total]) ).
cnf(c_0_36,plain,
( ~ int_leq(X2,X1)
| ~ int_leq(X1,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_37,plain,
( ~ int_less(X1,X2)
| int_leq(int_one,esk1_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_38,plain,
( ~ int_less(X2,X1)
| ~ int_less(int_zero,X2)
| ~ int_less(X1,esk1_2(X2,X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_24]) ).
cnf(c_0_39,plain,
( int_leq(X2,X1)
| int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
( ~ int_less(int_zero,X2)
| int_less(X1,plus(X2,X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_31]) ).
cnf(c_0_41,plain,
( ~ int_leq(esk1_2(X1,X2),int_one)
| ~ int_less(X1,X2)
| esk1_2(X1,X2) = int_one ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( ~ int_less(X1,X2)
| ~ int_less(int_zero,X1)
| int_leq(esk1_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_43,plain,
! [X21,X22,X23,X24] :
( int_leq(plus(X21,X23),plus(X22,X24))
| ~ int_leq(X23,X24)
| ~ int_less(X21,X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[plus_and_order1])])]) ).
fof(c_0_44,plain,
! [X20] : plus(X20,int_zero) = X20,
inference(variable_rename,[status(thm)],[plus_zero]) ).
fof(c_0_45,plain,
! [X2,X1] :
( epred1_2(X1,X2)
<=> ( ! [X8] :
( ( X2 = plus(X1,X8)
& int_less(int_zero,X8) )
=> ! [X3] :
( ( int_leq(X3,X1)
& int_leq(int_one,X3) )
=> a(X3,plus(X3,X8)) = real_zero ) )
& ! [X3] :
( ( int_leq(X3,X2)
& int_leq(int_one,X3) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( X1 = plus(X2,X8)
& int_less(int_zero,X8) )
=> ! [X3] :
( ( int_leq(X3,X2)
& int_leq(int_one,X3) )
=> a(plus(X3,X8),X3) = qr(plus(X3,X8),X3) ) ) ) ),
introduced(definition) ).
cnf(c_0_46,plain,
( ~ int_less(X1,X2)
| ~ int_less(int_zero,X1)
| int_less(esk1_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_24]) ).
cnf(c_0_47,plain,
( ~ int_less(int_zero,X1)
| ~ int_less(X1,int_one)
| esk1_2(X1,int_one) = int_one ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
( ~ int_leq(X3,X4)
| ~ int_less(X1,X2)
| int_leq(plus(X1,X3),plus(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,plain,
plus(X1,int_zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_50,plain,
! [X2,X1] :
( epred1_2(X1,X2)
=> ( ! [X8] :
( ( X2 = plus(X1,X8)
& int_less(int_zero,X8) )
=> ! [X3] :
( ( int_leq(X3,X1)
& int_leq(int_one,X3) )
=> a(X3,plus(X3,X8)) = real_zero ) )
& ! [X3] :
( ( int_leq(X3,X2)
& int_leq(int_one,X3) )
=> a(X3,X3) = real_one )
& ! [X8] :
( ( X1 = plus(X2,X8)
& int_less(int_zero,X8) )
=> ! [X3] :
( ( int_leq(X3,X2)
& int_leq(int_one,X3) )
=> a(plus(X3,X8),X3) = qr(plus(X3,X8),X3) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
( ~ int_less(X1,int_one)
| ~ int_less(int_zero,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_21]) ).
cnf(c_0_52,plain,
( ~ int_leq(X2,X3)
| ~ int_less(X1,X4)
| int_leq(plus(X1,X2),plus(X3,X4)) ),
inference(spm,[status(thm)],[c_0_48,c_0_31]) ).
cnf(c_0_53,plain,
plus(int_zero,X1) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_31]) ).
fof(c_0_54,negated_conjecture,
~ ( ! [X1,X2] :
( ( X1 = X2
& int_leq(X2,n)
& int_leq(int_one,X1) )
=> a(X1,X2) != real_zero )
& ! [X1,X2] :
( ( int_leq(X2,n)
& int_less(X1,X2)
& int_leq(int_one,X1) )
=> a(X1,X2) = real_zero ) ),
inference(assume_negation,[status(cth)],[lti]) ).
fof(c_0_55,plain,
! [X38,X39,X40,X41,X42,X43,X44] :
( ( ~ epred1_2(X39,X38)
| a(X44,plus(X44,X43)) = real_zero
| ~ int_leq(X44,X39)
| ~ int_leq(int_one,X44)
| X38 != plus(X39,X43)
| ~ int_less(int_zero,X43) )
& ( ~ epred1_2(X39,X38)
| a(X42,X42) = real_one
| ~ int_leq(X42,X38)
| ~ int_leq(int_one,X42) )
& ( ~ epred1_2(X39,X38)
| a(plus(X41,X40),X41) = qr(plus(X41,X40),X41)
| ~ int_leq(X41,X38)
| ~ int_leq(int_one,X41)
| X39 != plus(X38,X40)
| ~ int_less(int_zero,X40) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])])]) ).
fof(c_0_56,hypothesis,
! [X1,X2] :
( ( int_leq(X2,n)
& int_leq(int_one,X2)
& int_leq(X1,n)
& int_leq(int_one,X1) )
=> epred1_2(X1,X2) ),
inference(apply_def,[status(thm)],[qih,c_0_45]) ).
cnf(c_0_57,plain,
( ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X2)
| ~ int_less(plus(X1,X2),int_one) ),
inference(spm,[status(thm)],[c_0_51,c_0_22]) ).
cnf(c_0_58,plain,
( ~ int_leq(X1,X2)
| ~ int_less(int_zero,X3)
| int_leq(X1,plus(X2,X3)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_59,negated_conjecture,
~ ( ! [X1,X2] :
( ( X1 = X2
& int_leq(X2,n)
& int_leq(int_one,X1) )
=> a(X1,X2) != real_zero )
& ! [X1,X2] :
( ( int_leq(X2,n)
& int_less(X1,X2)
& int_leq(int_one,X1) )
=> a(X1,X2) = real_zero ) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
cnf(c_0_60,plain,
( ~ epred1_2(X3,X2)
| ~ int_leq(X4,X3)
| ~ int_leq(int_one,X4)
| X2 != plus(X3,X1)
| ~ int_less(int_zero,X1)
| a(X4,plus(X4,X1)) = real_zero ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_61,hypothesis,
! [X32,X33] :
( epred1_2(X32,X33)
| ~ int_leq(X33,n)
| ~ int_leq(int_one,X33)
| ~ int_leq(X32,n)
| ~ int_leq(int_one,X32) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])]) ).
cnf(c_0_62,plain,
( ~ int_less(X2,X1)
| ~ int_less(int_zero,X2)
| ~ int_less(X1,int_one) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_24]),c_0_25]) ).
cnf(c_0_63,plain,
( ~ int_leq(X1,X2)
| ~ int_leq(plus(X2,X3),X1)
| ~ int_less(int_zero,X3)
| X1 = plus(X2,X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_58]) ).
fof(c_0_64,negated_conjecture,
( ( a(esk2_0,esk3_0) != real_zero
| a(esk4_0,esk5_0) = real_zero )
& ( a(esk2_0,esk3_0) != real_zero
| esk4_0 = esk5_0 )
& ( a(esk2_0,esk3_0) != real_zero
| int_leq(esk5_0,n) )
& ( a(esk2_0,esk3_0) != real_zero
| int_leq(int_one,esk4_0) )
& ( int_leq(esk3_0,n)
| a(esk4_0,esk5_0) = real_zero )
& ( int_leq(esk3_0,n)
| esk4_0 = esk5_0 )
& ( int_leq(esk3_0,n)
| int_leq(esk5_0,n) )
& ( int_leq(esk3_0,n)
| int_leq(int_one,esk4_0) )
& ( int_less(esk2_0,esk3_0)
| a(esk4_0,esk5_0) = real_zero )
& ( int_less(esk2_0,esk3_0)
| esk4_0 = esk5_0 )
& ( int_less(esk2_0,esk3_0)
| int_leq(esk5_0,n) )
& ( int_less(esk2_0,esk3_0)
| int_leq(int_one,esk4_0) )
& ( int_leq(int_one,esk2_0)
| a(esk4_0,esk5_0) = real_zero )
& ( int_leq(int_one,esk2_0)
| esk4_0 = esk5_0 )
& ( int_leq(int_one,esk2_0)
| int_leq(esk5_0,n) )
& ( int_leq(int_one,esk2_0)
| int_leq(int_one,esk4_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])])]) ).
cnf(c_0_65,plain,
( ~ int_leq(X1,X3)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ epred1_2(X3,plus(X3,X2))
| a(X1,plus(X1,X2)) = real_zero ),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_66,hypothesis,
( ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_67,plain,
( ~ int_less(X2,X1)
| ~ int_less(int_zero,X2)
| int_leq(int_one,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_39]) ).
cnf(c_0_68,plain,
( ~ int_leq(int_one,X1)
| int_less(int_zero,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_69,plain,
( ~ int_leq(X1,X3)
| ~ int_leq(X2,X1)
| ~ int_less(X3,X2)
| X1 = X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_24]),c_0_25]) ).
cnf(c_0_70,negated_conjecture,
( int_less(esk2_0,esk3_0)
| esk4_0 = esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_71,plain,
( ~ int_less(X1,X2)
| int_leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_72,hypothesis,
( ~ int_leq(X1,X3)
| ~ int_leq(int_one,X3)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,plus(X3,X2))
| ~ int_leq(plus(X3,X2),n)
| ~ int_less(int_zero,X2)
| a(X1,plus(X1,X2)) = real_zero ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,plain,
( ~ int_leq(int_one,X2)
| ~ int_less(X2,X1)
| int_leq(int_one,X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
( X1 != X2
| int_leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_75,negated_conjecture,
( ~ int_leq(X1,esk2_0)
| ~ int_leq(esk3_0,X1)
| X1 = esk3_0
| esk4_0 = esk5_0 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,plain,
( int_leq(X2,X1)
| int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_39]) ).
cnf(c_0_77,hypothesis,
( ~ int_leq(X1,X2)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X3,n)
| ~ int_less(X2,X3)
| a(X1,plus(X1,esk1_2(X2,X3))) = real_zero ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_24]),c_0_73]),c_0_25]) ).
cnf(c_0_78,plain,
int_leq(X1,X1),
inference(er,[status(thm)],[c_0_74]) ).
cnf(c_0_79,plain,
( ~ int_leq(X1,X3)
| ~ int_leq(X2,X1)
| int_leq(X2,X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_69,c_0_39]) ).
cnf(c_0_80,negated_conjecture,
( ~ int_leq(X1,esk2_0)
| int_leq(X1,esk3_0)
| X1 = esk3_0
| esk4_0 = esk5_0 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( a(esk2_0,esk3_0) != real_zero
| esk4_0 = esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_82,hypothesis,
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| ~ int_less(X1,X2)
| a(X1,X2) = real_zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_24]),c_0_78])]) ).
cnf(c_0_83,negated_conjecture,
( int_leq(int_one,esk2_0)
| esk4_0 = esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_84,negated_conjecture,
( int_leq(esk3_0,n)
| esk4_0 = esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_85,negated_conjecture,
( ~ int_leq(X1,esk2_0)
| ~ int_leq(esk3_0,X2)
| int_leq(X1,X2)
| esk3_0 = X1
| esk4_0 = esk5_0 ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_86,plain,
( ~ int_leq(X1,X2)
| ~ int_less(X3,X1)
| int_less(X3,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_87,negated_conjecture,
( int_leq(esk3_0,n)
| int_leq(int_one,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_88,negated_conjecture,
( ~ int_leq(esk2_0,n)
| esk4_0 = esk5_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_84]),c_0_70]) ).
cnf(c_0_89,negated_conjecture,
( ~ int_leq(X1,esk2_0)
| int_leq(X1,n)
| esk3_0 = X1
| esk4_0 = esk5_0 ),
inference(spm,[status(thm)],[c_0_85,c_0_84]) ).
cnf(c_0_90,plain,
( ~ epred1_2(X3,X2)
| ~ int_leq(X1,X2)
| ~ int_leq(int_one,X1)
| a(X1,X1) = real_one ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_91,negated_conjecture,
( ~ int_less(X1,esk3_0)
| int_leq(int_one,esk4_0)
| int_less(X1,n)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,negated_conjecture,
( int_less(esk2_0,esk3_0)
| int_leq(int_one,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_93,negated_conjecture,
( int_less(esk2_0,esk3_0)
| int_leq(esk5_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_94,negated_conjecture,
( esk4_0 = esk5_0
| esk3_0 = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_78])]) ).
cnf(c_0_95,hypothesis,
( ~ int_leq(X1,X2)
| ~ int_leq(int_one,X3)
| ~ int_leq(int_one,X2)
| ~ int_leq(X3,n)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X1)
| a(X1,X1) = real_one ),
inference(spm,[status(thm)],[c_0_90,c_0_66]) ).
fof(c_0_96,plain,
real_zero != real_one,
inference(fof_simplification,[status(thm)],[real_constants]) ).
cnf(c_0_97,negated_conjecture,
( ~ int_less(n,esk3_0)
| int_leq(int_one,esk4_0)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_91]) ).
cnf(c_0_98,negated_conjecture,
( ~ int_less(X1,esk2_0)
| int_leq(int_one,esk4_0)
| int_less(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_92]) ).
cnf(c_0_99,negated_conjecture,
( int_leq(esk3_0,n)
| int_leq(esk5_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_100,negated_conjecture,
( ~ int_less(X1,esk2_0)
| int_leq(esk5_0,n)
| int_less(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_93]) ).
cnf(c_0_101,negated_conjecture,
( int_less(esk2_0,esk3_0)
| a(esk4_0,esk5_0) = real_zero ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_102,negated_conjecture,
esk4_0 = esk5_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_94]),c_0_21]) ).
cnf(c_0_103,hypothesis,
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,n)
| a(X1,X1) = real_one ),
inference(spm,[status(thm)],[c_0_95,c_0_78]) ).
fof(c_0_104,plain,
real_zero != real_one,
inference(fof_nnf,[status(thm)],[c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( a(esk2_0,esk3_0) != real_zero
| int_leq(int_one,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_106,negated_conjecture,
( int_leq(int_one,esk2_0)
| int_leq(int_one,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_107,negated_conjecture,
( ~ int_less(n,esk2_0)
| int_leq(int_one,esk4_0)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_108,negated_conjecture,
( ~ int_less(X1,esk3_0)
| int_leq(esk5_0,n)
| int_less(X1,n)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_86,c_0_99]) ).
cnf(c_0_109,negated_conjecture,
( ~ int_less(int_zero,esk2_0)
| int_leq(int_one,esk3_0)
| int_leq(esk5_0,n) ),
inference(spm,[status(thm)],[c_0_33,c_0_100]) ).
cnf(c_0_110,negated_conjecture,
( int_leq(int_one,esk2_0)
| int_leq(esk5_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_111,negated_conjecture,
( int_less(esk2_0,esk3_0)
| a(esk5_0,esk5_0) = real_zero ),
inference(rw,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_112,hypothesis,
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,n)
| a(X1,X1) = real_one ),
inference(spm,[status(thm)],[c_0_103,c_0_78]) ).
cnf(c_0_113,plain,
real_zero != real_one,
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_114,negated_conjecture,
( int_leq(int_one,esk5_0)
| int_less(esk2_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_92,c_0_102]) ).
cnf(c_0_115,negated_conjecture,
( int_leq(esk3_0,n)
| a(esk4_0,esk5_0) = real_zero ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_116,negated_conjecture,
( a(esk2_0,esk3_0) != real_zero
| a(esk4_0,esk5_0) = real_zero ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_117,negated_conjecture,
( int_leq(int_one,esk2_0)
| a(esk4_0,esk5_0) = real_zero ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_118,negated_conjecture,
( a(esk2_0,esk3_0) != real_zero
| int_leq(int_one,esk5_0) ),
inference(rw,[status(thm)],[c_0_105,c_0_102]) ).
cnf(c_0_119,negated_conjecture,
( int_leq(int_one,esk2_0)
| int_leq(int_one,esk5_0) ),
inference(rw,[status(thm)],[c_0_106,c_0_102]) ).
cnf(c_0_120,negated_conjecture,
( int_leq(int_one,esk5_0)
| int_leq(esk3_0,n) ),
inference(rw,[status(thm)],[c_0_87,c_0_102]) ).
cnf(c_0_121,negated_conjecture,
( int_leq(int_one,esk4_0)
| int_leq(esk2_0,n)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_107,c_0_39]) ).
cnf(c_0_122,plain,
( ~ int_leq(X2,int_zero)
| ~ int_less(X1,X3)
| int_leq(plus(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_123,plain,
( int_leq(int_one,X1)
| int_leq(X1,int_zero) ),
inference(spm,[status(thm)],[c_0_33,c_0_39]) ).
cnf(c_0_124,negated_conjecture,
( ~ int_less(int_zero,esk3_0)
| int_leq(int_one,n)
| int_leq(esk5_0,n)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_33,c_0_108]) ).
cnf(c_0_125,negated_conjecture,
( int_leq(esk5_0,n)
| int_leq(int_one,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_68]),c_0_110]) ).
cnf(c_0_126,negated_conjecture,
( ~ int_less(int_zero,esk2_0)
| int_leq(int_one,esk3_0)
| int_leq(int_one,esk4_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_98]) ).
cnf(c_0_127,plain,
( ~ int_leq(plus(X1,X2),X1)
| ~ int_less(int_zero,X2)
| plus(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_128,plain,
( ~ int_leq(X2,X3)
| ~ int_less(X1,int_zero)
| int_leq(plus(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_48,c_0_53]) ).
cnf(c_0_129,negated_conjecture,
( ~ int_leq(int_one,n)
| int_less(esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]),c_0_93]),c_0_114]) ).
cnf(c_0_130,negated_conjecture,
( int_leq(esk3_0,n)
| a(esk5_0,esk5_0) = real_zero ),
inference(rw,[status(thm)],[c_0_115,c_0_102]) ).
cnf(c_0_131,negated_conjecture,
( a(esk2_0,esk3_0) != real_zero
| a(esk5_0,esk5_0) = real_zero ),
inference(rw,[status(thm)],[c_0_116,c_0_102]) ).
cnf(c_0_132,negated_conjecture,
( int_leq(int_one,esk2_0)
| a(esk5_0,esk5_0) = real_zero ),
inference(rw,[status(thm)],[c_0_117,c_0_102]) ).
cnf(c_0_133,negated_conjecture,
( a(esk2_0,esk3_0) != real_zero
| int_leq(esk5_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_134,hypothesis,
( ~ int_leq(esk2_0,n)
| int_leq(int_one,esk5_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_82]),c_0_119]),c_0_120]),c_0_114]) ).
cnf(c_0_135,negated_conjecture,
( int_leq(esk2_0,n)
| int_leq(int_one,esk5_0)
| n = esk3_0 ),
inference(rw,[status(thm)],[c_0_121,c_0_102]) ).
cnf(c_0_136,plain,
( ~ int_leq(X1,int_zero)
| ~ int_less(int_zero,X2)
| int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_122,c_0_53]) ).
cnf(c_0_137,plain,
int_less(int_zero,int_one),
inference(split_conjunct,[status(thm)],[int_zero_one]) ).
cnf(c_0_138,plain,
( ~ int_leq(X1,X2)
| int_leq(int_one,X2)
| int_leq(X1,int_zero)
| X1 = int_one ),
inference(spm,[status(thm)],[c_0_79,c_0_123]) ).
cnf(c_0_139,negated_conjecture,
( int_leq(esk5_0,n)
| int_leq(int_one,n)
| n = esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_68]),c_0_125]) ).
cnf(c_0_140,plain,
( ~ int_leq(plus(X1,X2),X2)
| ~ int_less(int_zero,X1)
| plus(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_34,c_0_29]) ).
cnf(c_0_141,negated_conjecture,
( int_leq(int_one,esk4_0)
| int_leq(int_one,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_68]),c_0_106]) ).
cnf(c_0_142,plain,
( ~ int_leq(X2,X1)
| ~ int_less(X1,int_zero)
| ~ int_less(int_zero,X2)
| plus(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_143,negated_conjecture,
( ~ int_less(n,esk3_0)
| int_leq(esk5_0,n)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_108]) ).
cnf(c_0_144,negated_conjecture,
( ~ int_leq(X1,esk2_0)
| ~ int_leq(esk3_0,X1)
| ~ int_leq(int_one,n)
| X1 = esk3_0 ),
inference(spm,[status(thm)],[c_0_69,c_0_129]) ).
cnf(c_0_145,negated_conjecture,
( ~ int_leq(int_one,n)
| int_leq(esk3_0,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_112]),c_0_113]),c_0_99]),c_0_120]) ).
cnf(c_0_146,hypothesis,
( ~ int_leq(esk2_0,n)
| a(esk5_0,esk5_0) = real_zero ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_82]),c_0_132]),c_0_130]),c_0_111]) ).
cnf(c_0_147,negated_conjecture,
( ~ int_leq(esk2_0,n)
| int_leq(esk5_0,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_82]),c_0_110]),c_0_99]),c_0_93]) ).
cnf(c_0_148,negated_conjecture,
( int_leq(int_one,esk5_0)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_149,plain,
( ~ int_leq(X1,int_zero)
| int_leq(X1,int_one) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_150,negated_conjecture,
( int_leq(esk5_0,int_zero)
| int_leq(int_one,n)
| esk5_0 = int_one
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_151,plain,
( ~ int_leq(X2,int_zero)
| ~ int_less(X1,X2)
| ~ int_less(int_zero,X1)
| plus(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_140,c_0_122]) ).
cnf(c_0_152,negated_conjecture,
( ~ int_leq(X1,esk5_0)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,esk5_0)
| int_leq(int_one,esk3_0)
| a(X1,X1) = real_one ),
inference(spm,[status(thm)],[c_0_95,c_0_125]) ).
cnf(c_0_153,negated_conjecture,
( int_leq(int_one,esk3_0)
| int_leq(int_one,esk5_0) ),
inference(rw,[status(thm)],[c_0_141,c_0_102]) ).
cnf(c_0_154,negated_conjecture,
( ~ int_leq(X1,esk5_0)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,esk5_0)
| int_leq(int_one,esk2_0)
| a(X1,X1) = real_one ),
inference(spm,[status(thm)],[c_0_95,c_0_110]) ).
cnf(c_0_155,plain,
( ~ int_leq(X1,X2)
| ~ int_less(X2,int_zero)
| ~ int_less(int_zero,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_142]),c_0_21]) ).
cnf(c_0_156,negated_conjecture,
( ~ int_less(n,esk2_0)
| int_leq(esk5_0,n)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_143,c_0_100]) ).
cnf(c_0_157,negated_conjecture,
( ~ int_leq(n,esk2_0)
| ~ int_leq(int_one,n)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_158,hypothesis,
( ~ int_leq(int_one,n)
| ~ int_leq(esk2_0,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_112]),c_0_113]),c_0_147]),c_0_134]) ).
cnf(c_0_159,negated_conjecture,
( ~ int_leq(esk5_0,int_one)
| esk5_0 = int_one
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_36,c_0_148]) ).
cnf(c_0_160,negated_conjecture,
( int_leq(esk5_0,int_one)
| int_leq(int_one,n)
| n = esk3_0
| esk5_0 = int_one ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_161,plain,
( ~ int_leq(X2,int_zero)
| ~ int_less(X1,X2)
| ~ int_less(int_zero,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_151]),c_0_21]) ).
cnf(c_0_162,negated_conjecture,
( ~ int_leq(X1,esk5_0)
| ~ int_leq(int_one,X1)
| int_leq(int_one,esk3_0)
| a(X1,X1) = real_one ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_125]),c_0_153]) ).
cnf(c_0_163,negated_conjecture,
( ~ int_leq(X1,esk5_0)
| ~ int_leq(int_one,X1)
| int_leq(int_one,esk2_0)
| a(X1,X1) = real_one ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_110]),c_0_119]) ).
cnf(c_0_164,negated_conjecture,
( ~ int_leq(esk3_0,X1)
| ~ int_less(X1,int_zero)
| ~ int_less(int_zero,esk2_0)
| int_leq(esk5_0,n) ),
inference(spm,[status(thm)],[c_0_155,c_0_100]) ).
cnf(c_0_165,plain,
( ~ int_leq(X1,X2)
| ~ int_leq(int_one,X1)
| int_leq(int_one,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_73,c_0_29]) ).
cnf(c_0_166,negated_conjecture,
( int_leq(esk5_0,n)
| int_leq(esk2_0,n)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_156,c_0_39]) ).
cnf(c_0_167,negated_conjecture,
( ~ int_leq(int_one,n)
| n = esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_76]),c_0_158]) ).
cnf(c_0_168,negated_conjecture,
( int_leq(int_one,n)
| n = esk3_0
| esk5_0 = int_one ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_169,plain,
( ~ int_leq(int_one,X1)
| ~ int_leq(X2,int_zero)
| ~ int_less(X1,X2) ),
inference(spm,[status(thm)],[c_0_161,c_0_68]) ).
cnf(c_0_170,negated_conjecture,
( int_leq(int_one,esk3_0)
| int_less(esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_162]),c_0_78])]),c_0_113]),c_0_153]) ).
cnf(c_0_171,negated_conjecture,
int_leq(int_one,esk2_0),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_163]),c_0_78])]),c_0_113]),c_0_119]) ).
cnf(c_0_172,plain,
( ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(X1,int_zero) ),
inference(spm,[status(thm)],[c_0_155,c_0_68]) ).
cnf(c_0_173,negated_conjecture,
( ~ int_leq(esk3_0,X1)
| ~ int_less(X1,int_zero)
| int_leq(esk5_0,n) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_68]),c_0_110]) ).
cnf(c_0_174,negated_conjecture,
( ~ int_leq(esk5_0,X1)
| int_leq(int_one,X1)
| esk5_0 = X1
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_165,c_0_148]) ).
cnf(c_0_175,negated_conjecture,
( int_leq(esk5_0,n)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_147,c_0_166]) ).
cnf(c_0_176,negated_conjecture,
( n = esk3_0
| esk5_0 = int_one ),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_177,negated_conjecture,
int_leq(int_one,esk3_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_171])]),c_0_123]) ).
cnf(c_0_178,plain,
( ~ int_less(X2,X1)
| int_leq(int_one,X1)
| int_less(X2,int_zero)
| X1 = int_zero ),
inference(spm,[status(thm)],[c_0_86,c_0_123]) ).
cnf(c_0_179,plain,
( ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| int_leq(int_zero,X1) ),
inference(spm,[status(thm)],[c_0_172,c_0_39]) ).
cnf(c_0_180,negated_conjecture,
( ~ int_leq(X1,int_zero)
| ~ int_leq(esk3_0,X1)
| int_leq(esk5_0,n)
| X1 = int_zero ),
inference(spm,[status(thm)],[c_0_173,c_0_29]) ).
cnf(c_0_181,negated_conjecture,
( int_leq(int_one,n)
| n = esk3_0
| n = esk5_0 ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_182,hypothesis,
( ~ int_leq(esk2_0,esk3_0)
| esk5_0 = int_one ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_176]),c_0_177])]) ).
cnf(c_0_183,negated_conjecture,
( ~ int_leq(int_one,n)
| int_leq(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_71,c_0_129]) ).
cnf(c_0_184,plain,
( ~ int_leq(X2,X1)
| int_leq(int_one,X1)
| int_less(X2,int_zero)
| X2 = X1
| X1 = int_zero ),
inference(spm,[status(thm)],[c_0_178,c_0_29]) ).
cnf(c_0_185,negated_conjecture,
( ~ int_leq(esk5_0,X1)
| int_leq(int_zero,X1)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_179,c_0_148]) ).
cnf(c_0_186,negated_conjecture,
( ~ int_leq(n,int_zero)
| int_leq(esk5_0,n)
| int_zero = n ),
inference(spm,[status(thm)],[c_0_180,c_0_99]) ).
cnf(c_0_187,negated_conjecture,
( n = esk3_0
| n = esk5_0 ),
inference(spm,[status(thm)],[c_0_167,c_0_181]) ).
cnf(c_0_188,negated_conjecture,
( ~ int_leq(int_one,n)
| esk5_0 = int_one ),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_189,negated_conjecture,
( ~ int_leq(esk5_0,X1)
| int_leq(int_one,X1)
| X1 = int_zero
| n = esk3_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_21]) ).
cnf(c_0_190,negated_conjecture,
( int_leq(esk5_0,n)
| int_leq(int_one,n)
| int_zero = n ),
inference(spm,[status(thm)],[c_0_186,c_0_123]) ).
cnf(c_0_191,hypothesis,
( ~ int_leq(esk2_0,esk3_0)
| n = esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_187]),c_0_177])]) ).
cnf(c_0_192,negated_conjecture,
esk5_0 = int_one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_176]),c_0_177])]) ).
cnf(c_0_193,negated_conjecture,
( int_leq(int_one,n)
| n = esk3_0
| int_zero = n ),
inference(spm,[status(thm)],[c_0_189,c_0_190]) ).
cnf(c_0_194,hypothesis,
( ~ int_leq(esk2_0,esk3_0)
| n = int_one ),
inference(rw,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_195,negated_conjecture,
( esk3_0 != esk5_0
| n = esk5_0 ),
inference(ef,[status(thm)],[c_0_187]) ).
cnf(c_0_196,negated_conjecture,
( n = esk3_0
| int_zero = n ),
inference(spm,[status(thm)],[c_0_167,c_0_193]) ).
cnf(c_0_197,negated_conjecture,
( ~ int_leq(int_one,n)
| n = int_one ),
inference(spm,[status(thm)],[c_0_194,c_0_183]) ).
cnf(c_0_198,negated_conjecture,
( n = int_one
| n = esk3_0 ),
inference(rw,[status(thm)],[c_0_187,c_0_192]) ).
cnf(c_0_199,negated_conjecture,
( esk3_0 != int_one
| n = int_one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_195,c_0_192]),c_0_192]) ).
cnf(c_0_200,negated_conjecture,
( int_less(n,int_one)
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_137,c_0_196]) ).
cnf(c_0_201,negated_conjecture,
n = int_one,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_177])]),c_0_199]) ).
cnf(c_0_202,negated_conjecture,
( ~ int_leq(int_one,n)
| ~ int_less(esk3_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_129]) ).
cnf(c_0_203,negated_conjecture,
esk3_0 = int_one,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_200,c_0_201]),c_0_201]),c_0_21]) ).
cnf(c_0_204,negated_conjecture,
~ int_less(int_one,esk2_0),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_202,c_0_201]),c_0_78])]),c_0_203]) ).
cnf(c_0_205,hypothesis,
~ int_leq(esk2_0,int_one),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_201]),c_0_201]),c_0_78])]) ).
cnf(c_0_206,negated_conjecture,
esk2_0 = int_one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_29]),c_0_171])]) ).
cnf(c_0_207,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_206]),c_0_78])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV492+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 08:54:12 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 213.56/31.97 % Version: 3.5.1
% 213.56/31.97 % Preprocessing class: FSMSSMSSSSSNFFN.
% 213.56/31.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 213.56/31.97 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 213.56/31.97 % Starting new_bool_3 with 300s (1) cores
% 213.56/31.97 % Starting new_bool_1 with 300s (1) cores
% 213.56/31.97 % Starting sh5l with 300s (1) cores
% 213.56/31.97 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2479659 completed with status 0
% 213.56/31.97 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 213.56/31.97 % Preprocessing class: FSMSSMSSSSSNFFN.
% 213.56/31.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 213.56/31.97 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 213.56/31.97 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 213.56/31.97 % No SInE strategy applied
% 213.56/31.97 % Search class: FGHSS-FFMM22-SFFFFFNN
% 213.56/31.97 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 213.56/31.97 % Starting SubtermCWHack with 136s (1) cores
% 213.56/31.97 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 213.56/31.97 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 213.56/31.97 % Starting new_bool_3 with 136s (1) cores
% 213.56/31.97 % Starting new_bool_1 with 136s (1) cores
% 213.56/31.97 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 2479666 completed with status 0
% 213.56/31.97 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 213.56/31.97 % Preprocessing class: FSMSSMSSSSSNFFN.
% 213.56/31.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 213.56/31.97 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 213.56/31.97 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 213.56/31.97 % No SInE strategy applied
% 213.56/31.97 % Search class: FGHSS-FFMM22-SFFFFFNN
% 213.56/31.97 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 213.56/31.97 % Starting SubtermCWHack with 136s (1) cores
% 213.56/31.97 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 213.56/31.97 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 213.56/31.97 % Preprocessing time : 0.001 s
% 213.56/31.97 % Presaturation interreduction done
% 213.56/31.97
% 213.56/31.97 % Proof found!
% 213.56/31.97 % SZS status Theorem
% 213.56/31.97 % SZS output start CNFRefutation
% See solution above
% 213.56/31.97 % Parsed axioms : 13
% 213.56/31.97 % Removed by relevancy pruning/SinE : 0
% 213.56/31.97 % Initial clauses : 36
% 213.56/31.97 % Removed in clause preprocessing : 0
% 213.56/31.97 % Initial clauses in saturation : 36
% 213.56/31.97 % Processed clauses : 54528
% 213.56/31.97 % ...of these trivial : 16
% 213.56/31.97 % ...subsumed : 47385
% 213.56/31.97 % ...remaining for further processing : 7127
% 213.56/31.97 % Other redundant clauses eliminated : 85
% 213.56/31.97 % Clauses deleted for lack of memory : 0
% 213.56/31.97 % Backward-subsumed : 1288
% 213.56/31.97 % Backward-rewritten : 2866
% 213.56/31.97 % Generated clauses : 1189022
% 213.56/31.97 % ...of the previous two non-redundant : 1097681
% 213.56/31.97 % ...aggressively subsumed : 0
% 213.56/31.97 % Contextual simplify-reflections : 360
% 213.56/31.97 % Paramodulations : 1188793
% 213.56/31.97 % Factorizations : 144
% 213.56/31.97 % NegExts : 0
% 213.56/31.97 % Equation resolutions : 85
% 213.56/31.97 % Disequality decompositions : 0
% 213.56/31.97 % Total rewrite steps : 148755
% 213.56/31.97 % ...of those cached : 148666
% 213.56/31.97 % Propositional unsat checks : 1
% 213.56/31.97 % Propositional check models : 1
% 213.56/31.97 % Propositional check unsatisfiable : 0
% 213.56/31.97 % Propositional clauses : 0
% 213.56/31.97 % Propositional clauses after purity: 0
% 213.56/31.97 % Propositional unsat core size : 0
% 213.56/31.97 % Propositional preprocessing time : 0.000
% 213.56/31.97 % Propositional encoding time : 0.703
% 213.56/31.97 % Propositional solver time : 0.063
% 213.56/31.97 % Success case prop preproc time : 0.000
% 213.56/31.97 % Success case prop encoding time : 0.000
% 213.56/31.97 % Success case prop solver time : 0.000
% 213.56/31.97 % Current number of processed clauses : 2932
% 213.56/31.97 % Positive orientable unit clauses : 10
% 213.56/31.97 % Positive unorientable unit clauses: 1
% 213.56/31.97 % Negative unit clauses : 4
% 213.56/31.97 % Non-unit-clauses : 2917
% 213.56/31.97 % Current number of unprocessed clauses: 1033155
% 213.56/31.97 % ...number of literals in the above : 7337552
% 213.56/31.97 % Current number of archived formulas : 0
% 213.56/31.97 % Current number of archived clauses : 4190
% 213.56/31.97 % Clause-clause subsumption calls (NU) : 4733334
% 213.56/31.97 % Rec. Clause-clause subsumption calls : 765266
% 213.56/31.97 % Non-unit clause-clause subsumptions : 43913
% 213.56/31.97 % Unit Clause-clause subsumption calls : 6124
% 213.56/31.97 % Rewrite failures with RHS unbound : 0
% 213.56/31.97 % BW rewrite match attempts : 16
% 213.56/31.97 % BW rewrite match successes : 13
% 213.56/31.97 % Condensation attempts : 0
% 213.56/31.97 % Condensation successes : 0
% 213.56/31.97 % Termbank termtop insertions : 22849475
% 213.56/31.97 % Search garbage collected termcells : 453
% 213.56/31.97
% 213.56/31.97 % -------------------------------------------------
% 213.56/31.97 % User time : 29.634 s
% 213.56/31.97 % System time : 0.904 s
% 213.56/31.97 % Total time : 30.539 s
% 213.56/31.97 % Maximum resident set size: 3604 pages
% 213.56/31.97
% 213.56/31.97 % -------------------------------------------------
% 213.56/31.97 % User time : 146.245 s
% 213.56/31.97 % System time : 5.214 s
% 213.56/31.97 % Total time : 151.460 s
% 213.56/31.97 % Maximum resident set size: 4608 pages
% 213.56/31.97 % E exiting
%------------------------------------------------------------------------------