TSTP Solution File: SWV492+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV492+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n025.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 : Thu Aug 31 21:41:32 EDT 2023
% Result : Theorem 17.02s 17.16s
% Output : CNFRefutation 17.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 30
% Syntax : Number of formulae : 220 ( 23 unt; 16 typ; 0 def)
% Number of atoms : 654 ( 180 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 718 ( 268 ~; 359 |; 62 &)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 7 >; 7 *; 0 +; 0 <<)
% 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 : 256 ( 1 sgn; 81 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
int_leq: ( $i * $i ) > $o ).
tff(decl_23,type,
int_less: ( $i * $i ) > $o ).
tff(decl_24,type,
int_zero: $i ).
tff(decl_25,type,
int_one: $i ).
tff(decl_26,type,
plus: ( $i * $i ) > $i ).
tff(decl_27,type,
real_zero: $i ).
tff(decl_28,type,
real_one: $i ).
tff(decl_29,type,
n: $i ).
tff(decl_30,type,
a: ( $i * $i ) > $i ).
tff(decl_31,type,
qr: ( $i * $i ) > $i ).
tff(decl_32,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_33,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk2_0: $i ).
tff(decl_35,type,
esk3_0: $i ).
tff(decl_36,type,
esk4_0: $i ).
tff(decl_37,type,
esk5_0: $i ).
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_irreflexive,axiom,
! [X1,X2] :
( int_less(X1,X2)
=> X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_irreflexive) ).
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(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_less(X1,X2)
| int_leq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_total) ).
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_zero,axiom,
! [X1] : plus(X1,int_zero) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).
fof(qih,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) = qr(plus(X3,X8),X3) ) )
& ! [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',qih) ).
fof(lti,conjecture,
( ! [X1,X2] :
( ( int_leq(int_one,X1)
& int_less(X1,X2)
& int_leq(X2,n) )
=> a(X1,X2) = real_zero )
& ! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X2,n)
& X1 = X2 )
=> a(X1,X2) != real_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lti) ).
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,
! [X25,X26,X28,X29,X30] :
( ( plus(X25,esk1_2(X25,X26)) = X26
| ~ int_less(X25,X26) )
& ( int_less(int_zero,esk1_2(X25,X26))
| ~ int_less(X25,X26) )
& ( plus(X28,X30) != X29
| ~ int_less(int_zero,X30)
| int_less(X28,X29) ) ),
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(c_0_14,plain,
! [X14,X15] :
( ~ int_less(X14,X15)
| X14 != X15 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_irreflexive])]) ).
fof(c_0_15,plain,
! [X11,X12,X13] :
( ~ int_less(X11,X12)
| ~ int_less(X12,X13)
| int_less(X11,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_transitive])]) ).
cnf(c_0_16,plain,
( int_less(X1,X3)
| plus(X1,X2) != X3
| ~ int_less(int_zero,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( ~ int_less(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( int_less(X1,X3)
| ~ int_less(X1,X2)
| ~ int_less(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( int_less(X1,plus(X1,X2))
| ~ int_less(int_zero,X2) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
~ int_less(X1,X1),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( int_less(X1,plus(X2,X3))
| ~ int_less(int_zero,X3)
| ~ int_less(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( ~ int_less(plus(X1,X2),X1)
| ~ int_less(int_zero,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
( plus(X1,esk1_2(X1,X2)) = X2
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
( int_less(int_zero,esk1_2(X1,X2))
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_25,plain,
! [X9,X10] :
( ( ~ int_leq(X9,X10)
| int_less(X9,X10)
| X9 = X10 )
& ( ~ int_less(X9,X10)
| int_leq(X9,X10) )
& ( X9 != X10
| int_leq(X9,X10) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_leq])])]) ).
fof(c_0_26,plain,
! [X18,X19] : plus(X18,X19) = plus(X19,X18),
inference(variable_rename,[status(thm)],[plus_commutative]) ).
cnf(c_0_27,plain,
( ~ int_less(X1,X2)
| ~ int_less(X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,plain,
( int_less(X1,X2)
| X1 = X2
| ~ int_leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_29,plain,
! [X31] :
( ( ~ int_less(int_zero,X31)
| int_leq(int_one,X31) )
& ( ~ int_leq(int_one,X31)
| int_less(int_zero,X31) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[one_successor_of_zero])]) ).
cnf(c_0_30,plain,
plus(X1,X2) = plus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ int_less(X2,X1)
| ~ int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( int_leq(int_one,X1)
| ~ int_less(int_zero,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
( ~ int_less(plus(X1,X2),X2)
| ~ int_less(int_zero,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
fof(c_0_34,plain,
! [X16,X17] :
( int_less(X16,X17)
| int_leq(X17,X16) ),
inference(variable_rename,[status(thm)],[int_less_total]) ).
cnf(c_0_35,plain,
( X1 = X2
| ~ int_leq(X1,X2)
| ~ int_leq(X2,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_36,plain,
( int_leq(int_one,esk1_2(X1,X2))
| ~ int_less(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_37,plain,
( ~ int_less(X1,esk1_2(X2,X1))
| ~ int_less(int_zero,X2)
| ~ int_less(X2,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_38,plain,
( int_less(X1,X2)
| int_leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
( int_less(X1,plus(X2,X1))
| ~ int_less(int_zero,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_40,plain,
( esk1_2(X1,X2) = int_one
| ~ int_less(X1,X2)
| ~ int_leq(esk1_2(X1,X2),int_one) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( int_leq(esk1_2(X1,X2),X2)
| ~ int_less(int_zero,X1)
| ~ int_less(X1,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_42,plain,
! [X21,X22,X23,X24] :
( ~ int_less(X21,X22)
| ~ int_leq(X23,X24)
| int_leq(plus(X21,X23),plus(X22,X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[plus_and_order1])]) ).
fof(c_0_43,plain,
! [X20] : plus(X20,int_zero) = X20,
inference(variable_rename,[status(thm)],[plus_zero]) ).
fof(c_0_44,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) = qr(plus(X3,X8),X3) ) )
& ! [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) ).
cnf(c_0_45,plain,
( int_less(esk1_2(X1,X2),X2)
| ~ int_less(int_zero,X1)
| ~ int_less(X1,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_23]) ).
cnf(c_0_46,plain,
( esk1_2(X1,int_one) = int_one
| ~ int_less(X1,int_one)
| ~ int_less(int_zero,X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
( int_leq(plus(X1,X3),plus(X2,X4))
| ~ int_less(X1,X2)
| ~ int_leq(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
plus(X1,int_zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_49,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) = qr(plus(X3,X8),X3) ) )
& ! [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)],[c_0_44]) ).
cnf(c_0_50,plain,
( ~ int_less(int_zero,X1)
| ~ int_less(X1,int_one) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_20]) ).
cnf(c_0_51,plain,
( int_leq(plus(X1,X2),plus(X3,X4))
| ~ int_less(X1,X4)
| ~ int_leq(X2,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_30]) ).
cnf(c_0_52,plain,
plus(int_zero,X1) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_30]) ).
fof(c_0_53,plain,
! [X38,X39,X40,X41,X42,X43,X44] :
( ( ~ int_less(int_zero,X40)
| X39 != plus(X38,X40)
| ~ int_leq(int_one,X41)
| ~ int_leq(X41,X38)
| a(plus(X41,X40),X41) = qr(plus(X41,X40),X41)
| ~ epred1_2(X39,X38) )
& ( ~ int_leq(int_one,X42)
| ~ int_leq(X42,X38)
| a(X42,X42) = real_one
| ~ epred1_2(X39,X38) )
& ( ~ int_less(int_zero,X43)
| X38 != plus(X39,X43)
| ~ int_leq(int_one,X44)
| ~ int_leq(X44,X39)
| a(X44,plus(X44,X43)) = real_zero
| ~ epred1_2(X39,X38) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
fof(c_0_54,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)],[qih,c_0_44]) ).
cnf(c_0_55,plain,
( ~ int_less(plus(X1,X2),int_one)
| ~ int_less(int_zero,X2)
| ~ int_less(int_zero,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_21]) ).
cnf(c_0_56,plain,
( int_leq(X1,plus(X2,X3))
| ~ int_less(int_zero,X3)
| ~ int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_57,negated_conjecture,
~ ( ! [X1,X2] :
( ( int_leq(int_one,X1)
& int_less(X1,X2)
& int_leq(X2,n) )
=> a(X1,X2) = real_zero )
& ! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X2,n)
& X1 = X2 )
=> a(X1,X2) != real_zero ) ),
inference(assume_negation,[status(cth)],[lti]) ).
cnf(c_0_58,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)],[c_0_53]) ).
fof(c_0_59,hypothesis,
! [X32,X33] :
( ~ int_leq(int_one,X32)
| ~ int_leq(X32,n)
| ~ int_leq(int_one,X33)
| ~ int_leq(X33,n)
| epred1_2(X32,X33) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])]) ).
cnf(c_0_60,plain,
( ~ int_less(X1,int_one)
| ~ int_less(int_zero,X2)
| ~ int_less(X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_23]),c_0_24]) ).
cnf(c_0_61,plain,
( X1 = plus(X2,X3)
| ~ int_less(int_zero,X3)
| ~ int_leq(plus(X2,X3),X1)
| ~ int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_56]) ).
fof(c_0_62,negated_conjecture,
( ( int_leq(int_one,esk4_0)
| int_leq(int_one,esk2_0) )
& ( int_leq(esk5_0,n)
| int_leq(int_one,esk2_0) )
& ( esk4_0 = esk5_0
| int_leq(int_one,esk2_0) )
& ( a(esk4_0,esk5_0) = real_zero
| int_leq(int_one,esk2_0) )
& ( int_leq(int_one,esk4_0)
| int_less(esk2_0,esk3_0) )
& ( int_leq(esk5_0,n)
| int_less(esk2_0,esk3_0) )
& ( esk4_0 = esk5_0
| int_less(esk2_0,esk3_0) )
& ( a(esk4_0,esk5_0) = real_zero
| int_less(esk2_0,esk3_0) )
& ( int_leq(int_one,esk4_0)
| int_leq(esk3_0,n) )
& ( int_leq(esk5_0,n)
| int_leq(esk3_0,n) )
& ( esk4_0 = esk5_0
| int_leq(esk3_0,n) )
& ( a(esk4_0,esk5_0) = real_zero
| int_leq(esk3_0,n) )
& ( int_leq(int_one,esk4_0)
| a(esk2_0,esk3_0) != real_zero )
& ( int_leq(esk5_0,n)
| a(esk2_0,esk3_0) != real_zero )
& ( esk4_0 = esk5_0
| a(esk2_0,esk3_0) != real_zero )
& ( a(esk4_0,esk5_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)],[c_0_57])])])]) ).
cnf(c_0_63,plain,
( a(X1,plus(X1,X2)) = real_zero
| ~ epred1_2(X3,plus(X3,X2))
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X3) ),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_64,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)],[c_0_59]) ).
cnf(c_0_65,plain,
( int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_less(X2,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_38]) ).
cnf(c_0_66,plain,
( int_less(int_zero,X1)
| ~ int_leq(int_one,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_67,plain,
( X1 = X2
| ~ int_less(X3,X2)
| ~ int_leq(X2,X1)
| ~ int_leq(X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_23]),c_0_24]) ).
cnf(c_0_68,negated_conjecture,
( esk4_0 = esk5_0
| int_less(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,plain,
( int_leq(X1,X2)
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_70,hypothesis,
( a(X1,plus(X1,X2)) = real_zero
| ~ int_less(int_zero,X2)
| ~ int_leq(plus(X3,X2),n)
| ~ int_leq(int_one,plus(X3,X2))
| ~ int_leq(int_one,X1)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X3)
| ~ int_leq(X1,X3) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
( int_leq(int_one,X1)
| ~ int_less(X2,X1)
| ~ int_leq(int_one,X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,plain,
( int_leq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_73,negated_conjecture,
( esk4_0 = esk5_0
| X1 = esk3_0
| ~ int_leq(esk3_0,X1)
| ~ int_leq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
( int_leq(X1,X2)
| int_leq(X2,X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_38]) ).
cnf(c_0_75,hypothesis,
( a(X1,plus(X1,esk1_2(X2,X3))) = real_zero
| ~ int_less(X2,X3)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_23]),c_0_71]),c_0_24]) ).
cnf(c_0_76,plain,
int_leq(X1,X1),
inference(er,[status(thm)],[c_0_72]) ).
cnf(c_0_77,plain,
( X1 = X2
| int_leq(X2,X3)
| ~ int_leq(X2,X1)
| ~ int_leq(X1,X3) ),
inference(spm,[status(thm)],[c_0_67,c_0_38]) ).
cnf(c_0_78,negated_conjecture,
( esk4_0 = esk5_0
| X1 = esk3_0
| int_leq(X1,esk3_0)
| ~ int_leq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,negated_conjecture,
( esk4_0 = esk5_0
| a(esk2_0,esk3_0) != real_zero ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_80,hypothesis,
( a(X1,X2) = real_zero
| ~ int_less(X1,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_23]),c_0_76])]) ).
cnf(c_0_81,negated_conjecture,
( esk4_0 = esk5_0
| int_leq(int_one,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_82,negated_conjecture,
( esk4_0 = esk5_0
| int_leq(esk3_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_83,negated_conjecture,
( esk4_0 = esk5_0
| esk3_0 = X1
| int_leq(X1,X2)
| ~ int_leq(esk3_0,X2)
| ~ int_leq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,plain,
( X1 = X2
| int_less(X3,X2)
| ~ int_less(X3,X1)
| ~ int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_28]) ).
cnf(c_0_85,negated_conjecture,
( int_leq(int_one,esk4_0)
| int_leq(esk3_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_86,negated_conjecture,
( esk4_0 = esk5_0
| ~ int_leq(esk2_0,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_82]),c_0_68]) ).
cnf(c_0_87,negated_conjecture,
( esk4_0 = esk5_0
| esk3_0 = X1
| int_leq(X1,n)
| ~ int_leq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_83,c_0_82]) ).
cnf(c_0_88,plain,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ epred1_2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_89,negated_conjecture,
( n = esk3_0
| int_less(X1,n)
| int_leq(int_one,esk4_0)
| ~ int_less(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,negated_conjecture,
( int_leq(int_one,esk4_0)
| int_less(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_91,negated_conjecture,
( int_leq(esk5_0,n)
| int_less(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_92,negated_conjecture,
( esk3_0 = esk2_0
| esk4_0 = esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_76])]) ).
cnf(c_0_93,hypothesis,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_one,X3)
| ~ int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_64]) ).
cnf(c_0_94,negated_conjecture,
( n = esk3_0
| int_leq(int_one,esk4_0)
| ~ int_less(n,esk3_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_89]) ).
cnf(c_0_95,negated_conjecture,
( int_less(X1,esk3_0)
| int_leq(int_one,esk4_0)
| ~ int_less(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_90]) ).
cnf(c_0_96,negated_conjecture,
( int_leq(esk5_0,n)
| int_leq(esk3_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_97,negated_conjecture,
( int_less(X1,esk3_0)
| int_leq(esk5_0,n)
| ~ int_less(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_91]) ).
cnf(c_0_98,negated_conjecture,
( a(esk4_0,esk5_0) = real_zero
| int_less(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_99,negated_conjecture,
esk4_0 = esk5_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_92]),c_0_20]) ).
cnf(c_0_100,hypothesis,
( a(X1,X1) = real_one
| ~ int_leq(int_one,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,n) ),
inference(spm,[status(thm)],[c_0_93,c_0_76]) ).
cnf(c_0_101,negated_conjecture,
( int_leq(int_one,esk4_0)
| a(esk2_0,esk3_0) != real_zero ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_102,negated_conjecture,
( int_leq(int_one,esk4_0)
| int_leq(int_one,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_103,negated_conjecture,
( n = esk3_0
| int_leq(int_one,esk4_0)
| ~ int_less(n,esk2_0) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_104,negated_conjecture,
( n = esk3_0
| int_less(X1,n)
| int_leq(esk5_0,n)
| ~ int_less(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_84,c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( int_leq(esk5_0,n)
| int_leq(int_one,esk3_0)
| ~ int_less(int_zero,esk2_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_97]) ).
cnf(c_0_106,negated_conjecture,
( int_leq(esk5_0,n)
| int_leq(int_one,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_107,negated_conjecture,
( a(esk5_0,esk5_0) = real_zero
| int_less(esk2_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_108,hypothesis,
( a(X1,X1) = real_one
| ~ int_leq(int_one,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(spm,[status(thm)],[c_0_100,c_0_76]) ).
cnf(c_0_109,plain,
real_zero != real_one,
inference(split_conjunct,[status(thm)],[real_constants]) ).
cnf(c_0_110,negated_conjecture,
( int_less(esk2_0,esk3_0)
| int_leq(int_one,esk5_0) ),
inference(rw,[status(thm)],[c_0_90,c_0_99]) ).
cnf(c_0_111,negated_conjecture,
( a(esk4_0,esk5_0) = real_zero
| int_leq(esk3_0,n) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_112,negated_conjecture,
( a(esk4_0,esk5_0) = real_zero
| a(esk2_0,esk3_0) != real_zero ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_113,negated_conjecture,
( a(esk4_0,esk5_0) = real_zero
| int_leq(int_one,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_114,negated_conjecture,
( int_leq(int_one,esk5_0)
| a(esk2_0,esk3_0) != real_zero ),
inference(rw,[status(thm)],[c_0_101,c_0_99]) ).
cnf(c_0_115,negated_conjecture,
( int_leq(int_one,esk5_0)
| int_leq(int_one,esk2_0) ),
inference(rw,[status(thm)],[c_0_102,c_0_99]) ).
cnf(c_0_116,negated_conjecture,
( int_leq(esk3_0,n)
| int_leq(int_one,esk5_0) ),
inference(rw,[status(thm)],[c_0_85,c_0_99]) ).
cnf(c_0_117,negated_conjecture,
( n = esk3_0
| int_leq(esk2_0,n)
| int_leq(int_one,esk4_0) ),
inference(spm,[status(thm)],[c_0_103,c_0_38]) ).
cnf(c_0_118,plain,
( int_leq(plus(X1,X2),X3)
| ~ int_less(X1,X3)
| ~ int_leq(X2,int_zero) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_119,plain,
( int_leq(X1,int_zero)
| int_leq(int_one,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_120,negated_conjecture,
( n = esk3_0
| int_leq(esk5_0,n)
| int_leq(int_one,n)
| ~ int_less(int_zero,esk3_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_104]) ).
cnf(c_0_121,negated_conjecture,
( int_leq(int_one,esk3_0)
| int_leq(esk5_0,n) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_66]),c_0_106]) ).
cnf(c_0_122,negated_conjecture,
( int_leq(int_one,esk4_0)
| int_leq(int_one,esk3_0)
| ~ int_less(int_zero,esk2_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_95]) ).
cnf(c_0_123,plain,
( plus(X1,X2) = X1
| ~ int_less(int_zero,X2)
| ~ int_leq(plus(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_28]) ).
cnf(c_0_124,plain,
( int_leq(plus(X1,X2),X3)
| ~ int_less(X1,int_zero)
| ~ int_leq(X2,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_52]) ).
cnf(c_0_125,negated_conjecture,
( int_less(esk2_0,esk3_0)
| ~ int_leq(int_one,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]),c_0_91]),c_0_110]) ).
cnf(c_0_126,negated_conjecture,
( a(esk5_0,esk5_0) = real_zero
| int_leq(esk3_0,n) ),
inference(rw,[status(thm)],[c_0_111,c_0_99]) ).
cnf(c_0_127,negated_conjecture,
( a(esk5_0,esk5_0) = real_zero
| a(esk2_0,esk3_0) != real_zero ),
inference(rw,[status(thm)],[c_0_112,c_0_99]) ).
cnf(c_0_128,negated_conjecture,
( a(esk5_0,esk5_0) = real_zero
| int_leq(int_one,esk2_0) ),
inference(rw,[status(thm)],[c_0_113,c_0_99]) ).
cnf(c_0_129,negated_conjecture,
( int_leq(esk5_0,n)
| a(esk2_0,esk3_0) != real_zero ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_130,hypothesis,
( int_leq(int_one,esk5_0)
| ~ int_leq(esk2_0,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_80]),c_0_115]),c_0_116]),c_0_110]) ).
cnf(c_0_131,negated_conjecture,
( n = esk3_0
| int_leq(int_one,esk5_0)
| int_leq(esk2_0,n) ),
inference(rw,[status(thm)],[c_0_117,c_0_99]) ).
cnf(c_0_132,plain,
( int_leq(X1,X2)
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,int_zero) ),
inference(spm,[status(thm)],[c_0_118,c_0_52]) ).
cnf(c_0_133,plain,
int_less(int_zero,int_one),
inference(split_conjunct,[status(thm)],[int_zero_one]) ).
cnf(c_0_134,plain,
( X1 = int_one
| int_leq(X1,int_zero)
| int_leq(int_one,X2)
| ~ int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_119]) ).
cnf(c_0_135,negated_conjecture,
( n = esk3_0
| int_leq(int_one,n)
| int_leq(esk5_0,n) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_66]),c_0_121]) ).
cnf(c_0_136,plain,
( plus(X1,X2) = X2
| ~ int_less(int_zero,X1)
| ~ int_leq(plus(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_137,negated_conjecture,
( int_leq(int_one,esk3_0)
| int_leq(int_one,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_66]),c_0_102]) ).
cnf(c_0_138,plain,
( plus(X1,X2) = X1
| ~ int_less(int_zero,X2)
| ~ int_less(X1,int_zero)
| ~ int_leq(X2,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_139,negated_conjecture,
( n = esk3_0
| int_leq(esk5_0,n)
| ~ int_less(n,esk3_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_104]) ).
cnf(c_0_140,negated_conjecture,
( X1 = esk3_0
| ~ int_leq(int_one,n)
| ~ int_leq(esk3_0,X1)
| ~ int_leq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_67,c_0_125]) ).
cnf(c_0_141,negated_conjecture,
( int_leq(esk3_0,n)
| ~ int_leq(int_one,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_108]),c_0_109]),c_0_96]),c_0_116]) ).
cnf(c_0_142,hypothesis,
( a(esk5_0,esk5_0) = real_zero
| ~ int_leq(esk2_0,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_80]),c_0_128]),c_0_126]),c_0_107]) ).
cnf(c_0_143,negated_conjecture,
( int_leq(esk5_0,n)
| ~ int_leq(esk2_0,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_80]),c_0_106]),c_0_96]),c_0_91]) ).
cnf(c_0_144,negated_conjecture,
( n = esk3_0
| int_leq(int_one,esk5_0) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_145,plain,
( int_leq(X1,int_one)
| ~ int_leq(X1,int_zero) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_146,negated_conjecture,
( n = esk3_0
| esk5_0 = int_one
| int_leq(int_one,n)
| int_leq(esk5_0,int_zero) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_147,plain,
( plus(X1,X2) = X2
| ~ int_less(int_zero,X1)
| ~ int_less(X1,X2)
| ~ int_leq(X2,int_zero) ),
inference(spm,[status(thm)],[c_0_136,c_0_118]) ).
cnf(c_0_148,negated_conjecture,
( a(X1,X1) = real_one
| int_leq(int_one,esk3_0)
| ~ int_leq(int_one,esk5_0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_93,c_0_121]) ).
cnf(c_0_149,negated_conjecture,
( int_leq(int_one,esk5_0)
| int_leq(int_one,esk3_0) ),
inference(rw,[status(thm)],[c_0_137,c_0_99]) ).
cnf(c_0_150,negated_conjecture,
( a(X1,X1) = real_one
| int_leq(int_one,esk2_0)
| ~ int_leq(int_one,esk5_0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_93,c_0_106]) ).
cnf(c_0_151,plain,
( ~ int_less(int_zero,X1)
| ~ int_less(X2,int_zero)
| ~ int_leq(X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_138]),c_0_20]) ).
cnf(c_0_152,negated_conjecture,
( n = esk3_0
| int_leq(esk5_0,n)
| ~ int_less(n,esk2_0) ),
inference(spm,[status(thm)],[c_0_139,c_0_97]) ).
cnf(c_0_153,negated_conjecture,
( n = esk3_0
| ~ int_leq(int_one,n)
| ~ int_leq(n,esk2_0) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_154,hypothesis,
( ~ int_leq(esk2_0,n)
| ~ int_leq(int_one,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_108]),c_0_109]),c_0_143]),c_0_130]) ).
cnf(c_0_155,negated_conjecture,
( n = esk3_0
| esk5_0 = int_one
| ~ int_leq(esk5_0,int_one) ),
inference(spm,[status(thm)],[c_0_35,c_0_144]) ).
cnf(c_0_156,negated_conjecture,
( esk5_0 = int_one
| n = esk3_0
| int_leq(int_one,n)
| int_leq(esk5_0,int_one) ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_157,plain,
( ~ int_less(int_zero,X1)
| ~ int_less(X1,X2)
| ~ int_leq(X2,int_zero) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_147]),c_0_20]) ).
cnf(c_0_158,negated_conjecture,
( a(X1,X1) = real_one
| int_leq(int_one,esk3_0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,esk5_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_121]),c_0_149]) ).
cnf(c_0_159,negated_conjecture,
( a(X1,X1) = real_one
| int_leq(int_one,esk2_0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,esk5_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_106]),c_0_115]) ).
cnf(c_0_160,negated_conjecture,
( int_leq(esk5_0,n)
| ~ int_less(int_zero,esk2_0)
| ~ int_less(X1,int_zero)
| ~ int_leq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_97]) ).
cnf(c_0_161,plain,
( X1 = X2
| int_leq(int_one,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_28]) ).
cnf(c_0_162,negated_conjecture,
( n = esk3_0
| int_leq(esk2_0,n)
| int_leq(esk5_0,n) ),
inference(spm,[status(thm)],[c_0_152,c_0_38]) ).
cnf(c_0_163,negated_conjecture,
( n = esk3_0
| ~ int_leq(int_one,n) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_74]),c_0_154]) ).
cnf(c_0_164,negated_conjecture,
( esk5_0 = int_one
| n = esk3_0
| int_leq(int_one,n) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_165,plain,
( ~ int_less(X1,X2)
| ~ int_leq(X2,int_zero)
| ~ int_leq(int_one,X1) ),
inference(spm,[status(thm)],[c_0_157,c_0_66]) ).
cnf(c_0_166,negated_conjecture,
( int_less(esk2_0,esk3_0)
| int_leq(int_one,esk3_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_158]),c_0_76])]),c_0_109]),c_0_149]) ).
cnf(c_0_167,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_128,c_0_159]),c_0_76])]),c_0_109]),c_0_115]) ).
cnf(c_0_168,plain,
( ~ int_less(X1,int_zero)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_66]) ).
cnf(c_0_169,negated_conjecture,
( int_leq(esk5_0,n)
| ~ int_less(X1,int_zero)
| ~ int_leq(esk3_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_66]),c_0_106]) ).
cnf(c_0_170,negated_conjecture,
( n = esk3_0
| esk5_0 = X1
| int_leq(int_one,X1)
| ~ int_leq(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_161,c_0_144]) ).
cnf(c_0_171,negated_conjecture,
( n = esk3_0
| int_leq(esk5_0,n) ),
inference(spm,[status(thm)],[c_0_143,c_0_162]) ).
cnf(c_0_172,negated_conjecture,
( esk5_0 = int_one
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_173,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_165,c_0_166]),c_0_167])]),c_0_119]) ).
cnf(c_0_174,plain,
( X1 = int_zero
| int_less(X2,int_zero)
| int_leq(int_one,X1)
| ~ int_less(X2,X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_119]) ).
cnf(c_0_175,plain,
( int_leq(int_zero,X1)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,X1) ),
inference(spm,[status(thm)],[c_0_168,c_0_38]) ).
cnf(c_0_176,negated_conjecture,
( X1 = int_zero
| int_leq(esk5_0,n)
| ~ int_leq(esk3_0,X1)
| ~ int_leq(X1,int_zero) ),
inference(spm,[status(thm)],[c_0_169,c_0_28]) ).
cnf(c_0_177,negated_conjecture,
( n = esk5_0
| n = esk3_0
| int_leq(int_one,n) ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_178,hypothesis,
( esk5_0 = int_one
| ~ int_leq(esk2_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_172]),c_0_173])]) ).
cnf(c_0_179,negated_conjecture,
( int_leq(esk2_0,esk3_0)
| ~ int_leq(int_one,n) ),
inference(spm,[status(thm)],[c_0_69,c_0_125]) ).
cnf(c_0_180,plain,
( X1 = int_zero
| X2 = X1
| int_less(X2,int_zero)
| int_leq(int_one,X1)
| ~ int_leq(X2,X1) ),
inference(spm,[status(thm)],[c_0_174,c_0_28]) ).
cnf(c_0_181,negated_conjecture,
( n = esk3_0
| int_leq(int_zero,X1)
| ~ int_leq(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_175,c_0_144]) ).
cnf(c_0_182,negated_conjecture,
( int_zero = n
| int_leq(esk5_0,n)
| ~ int_leq(n,int_zero) ),
inference(spm,[status(thm)],[c_0_176,c_0_96]) ).
cnf(c_0_183,negated_conjecture,
( n = esk5_0
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_163,c_0_177]) ).
cnf(c_0_184,negated_conjecture,
( esk5_0 = int_one
| ~ int_leq(int_one,n) ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_185,negated_conjecture,
( n = esk3_0
| X1 = int_zero
| int_leq(int_one,X1)
| ~ int_leq(esk5_0,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_20]) ).
cnf(c_0_186,negated_conjecture,
( int_zero = n
| int_leq(int_one,n)
| int_leq(esk5_0,n) ),
inference(spm,[status(thm)],[c_0_182,c_0_119]) ).
cnf(c_0_187,hypothesis,
( n = esk5_0
| ~ int_leq(esk2_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_183]),c_0_173])]) ).
cnf(c_0_188,negated_conjecture,
esk5_0 = int_one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_172]),c_0_173])]) ).
cnf(c_0_189,negated_conjecture,
( int_zero = n
| n = esk3_0
| int_leq(int_one,n) ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_190,hypothesis,
( n = int_one
| ~ int_leq(esk2_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_191,negated_conjecture,
( n = esk5_0
| esk3_0 != esk5_0 ),
inference(ef,[status(thm)],[c_0_183]) ).
cnf(c_0_192,negated_conjecture,
( int_zero = n
| n = esk3_0 ),
inference(spm,[status(thm)],[c_0_163,c_0_189]) ).
cnf(c_0_193,negated_conjecture,
( n = int_one
| ~ int_leq(int_one,n) ),
inference(spm,[status(thm)],[c_0_190,c_0_179]) ).
cnf(c_0_194,negated_conjecture,
( n = esk3_0
| n = int_one ),
inference(rw,[status(thm)],[c_0_183,c_0_188]) ).
cnf(c_0_195,negated_conjecture,
( n = int_one
| esk3_0 != int_one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_191,c_0_188]),c_0_188]) ).
cnf(c_0_196,negated_conjecture,
( n = esk3_0
| int_less(n,int_one) ),
inference(spm,[status(thm)],[c_0_133,c_0_192]) ).
cnf(c_0_197,negated_conjecture,
n = int_one,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_173])]),c_0_195]) ).
cnf(c_0_198,negated_conjecture,
( ~ int_less(esk3_0,esk2_0)
| ~ int_leq(int_one,n) ),
inference(spm,[status(thm)],[c_0_27,c_0_125]) ).
cnf(c_0_199,negated_conjecture,
esk3_0 = int_one,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_197]),c_0_197]),c_0_20]) ).
cnf(c_0_200,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_198,c_0_197]),c_0_76])]),c_0_199]) ).
cnf(c_0_201,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_154,c_0_197]),c_0_197]),c_0_76])]) ).
cnf(c_0_202,negated_conjecture,
esk2_0 = int_one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_28]),c_0_167])]) ).
cnf(c_0_203,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_202]),c_0_76])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV492+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 10:27:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.61 start to proof: theBenchmark
% 17.02/17.16 % Version : CSE_E---1.5
% 17.02/17.16 % Problem : theBenchmark.p
% 17.02/17.16 % Proof found
% 17.02/17.16 % SZS status Theorem for theBenchmark.p
% 17.02/17.16 % SZS output start Proof
% See solution above
% 17.02/17.17 % Total time : 16.539000 s
% 17.02/17.17 % SZS output end Proof
% 17.02/17.17 % Total time : 16.543000 s
%------------------------------------------------------------------------------