TSTP Solution File: NUM768^1 by E---3.2.0
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%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : NUM768^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n024.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 : Mon Jun 24 12:38:21 EDT 2024
% Result : Theorem 0.39s 0.68s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 150 ( 34 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 825 ( 45 ~; 38 |; 2 &; 729 @)
% ( 2 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 125 ( 8 ^ 117 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
frac: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_22,type,
x: frac ).
thf(decl_23,type,
y: frac ).
thf(decl_24,type,
some: ( nat > $o ) > $o ).
thf(decl_25,type,
ts: nat > nat > nat ).
thf(decl_26,type,
num: frac > nat ).
thf(decl_27,type,
den: frac > nat ).
thf(decl_28,type,
pl: nat > nat > nat ).
thf(decl_29,type,
eq: frac > frac > $o ).
thf(decl_30,type,
pf: frac > frac > frac ).
thf(decl_31,type,
fr: nat > nat > frac ).
thf(decl_32,type,
ind: ( nat > $o ) > nat ).
thf(decl_33,type,
amone: ( nat > $o ) > $o ).
thf(decl_34,type,
epred1_0: nat > $o ).
thf(decl_35,type,
epred2_2: nat > nat > nat > $o ).
thf(decl_40,type,
esk5_2: nat > nat > nat ).
thf(satz8b,axiom,
! [X2: nat,X3: nat] :
( amone
@ ^ [X4: nat] :
( X2
= ( pl @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p',satz8b) ).
thf(satz29,axiom,
! [X2: nat,X3: nat] :
( ( ts @ X2 @ X3 )
= ( ts @ X3 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p',satz29) ).
thf(oneax,axiom,
! [X17: nat > $o] :
( ~ ( ( amone @ X17 )
=> ~ ( some @ X17 ) )
=> ( X17 @ ( ind @ X17 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p',oneax) ).
thf(satz57,axiom,
! [X15: nat,X16: nat,X13: nat] : ( eq @ ( pf @ ( fr @ X15 @ X13 ) @ ( fr @ X16 @ X13 ) ) @ ( fr @ ( pl @ X15 @ X16 ) @ X13 ) ),
file('/export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p',satz57) ).
thf(satz56,axiom,
! [X8: frac,X9: frac,X10: frac,X11: frac] :
( ( eq @ X8 @ X9 )
=> ( ( eq @ X10 @ X11 )
=> ( eq @ ( pf @ X8 @ X10 ) @ ( pf @ X9 @ X11 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p',satz56) ).
thf(satz37,axiom,
! [X14: frac] : ( eq @ X14 @ X14 ),
file('/export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p',satz37) ).
thf(satz40,axiom,
! [X12: frac,X13: nat] : ( eq @ X12 @ ( fr @ ( ts @ ( num @ X12 ) @ X13 ) @ ( ts @ ( den @ X12 ) @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p',satz40) ).
thf(m,axiom,
( some
@ ^ [X1: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p',m) ).
thf(satz67c,conjecture,
( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [X19: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X19 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
file('/export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p',satz67c) ).
thf(satz39,axiom,
! [X5: frac,X6: frac,X7: frac] :
( ( eq @ X5 @ X6 )
=> ( ( eq @ X6 @ X7 )
=> ( eq @ X5 @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p',satz39) ).
thf(satz40a,axiom,
! [X18: frac,X13: nat] : ( eq @ ( fr @ ( ts @ ( num @ X18 ) @ X13 ) @ ( ts @ ( den @ X18 ) @ X13 ) ) @ X18 ),
file('/export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p',satz40a) ).
thf(c_0_11,plain,
! [X2: nat,X3: nat] :
( amone
@ ^ [Z0: nat] :
( X2
= ( pl @ X3 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[satz8b]) ).
thf(c_0_12,plain,
! [X63: nat] :
( ( ~ ( epred1_0 @ X63 )
| ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X63 ) ) )
& ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X63 ) )
| ( epred1_0 @ X63 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).
thf(c_0_13,plain,
! [X52: nat,X53: nat] :
( ( ts @ X52 @ X53 )
= ( ts @ X53 @ X52 ) ),
inference(variable_rename,[status(thm)],[satz29]) ).
thf(c_0_14,plain,
! [X17: nat > $o] :
( ~ ( ( amone @ X17 )
=> ~ ( some @ X17 ) )
=> ( X17 @ ( ind @ X17 ) ) ),
inference(fof_simplification,[status(thm)],[oneax]) ).
thf(c_0_15,plain,
! [X40: nat,X41: nat] :
( amone
@ ^ [Z0: nat] :
( X40
= ( pl @ X41 @ Z0 ) ) ),
inference(variable_rename,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X61: nat,X1: nat,X2: nat] :
( ( epred2_2 @ X2 @ X1 @ X61 )
<=> ( X1
= ( pl @ X2 @ X61 ) ) ),
introduced(definition) ).
thf(c_0_17,plain,
! [X54: nat,X55: nat,X56: nat] : ( eq @ ( pf @ ( fr @ X54 @ X56 ) @ ( fr @ X55 @ X56 ) ) @ ( fr @ ( pl @ X54 @ X55 ) @ X56 ) ),
inference(variable_rename,[status(thm)],[satz57]) ).
thf(c_0_18,plain,
! [X1: nat] :
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X1 ) )
| ~ ( epred1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,plain,
! [X2: nat,X1: nat] :
( ( ts @ X1 @ X2 )
= ( ts @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_20,plain,
! [X45: frac,X46: frac,X47: frac,X48: frac] :
( ~ ( eq @ X45 @ X46 )
| ~ ( eq @ X47 @ X48 )
| ( eq @ ( pf @ X45 @ X47 ) @ ( pf @ X46 @ X48 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz56])])]) ).
thf(c_0_21,plain,
! [X51: frac] : ( eq @ X51 @ X51 ),
inference(variable_rename,[status(thm)],[satz37]) ).
thf(c_0_22,plain,
! [X49: frac,X50: nat] : ( eq @ X49 @ ( fr @ ( ts @ ( num @ X49 ) @ X50 ) @ ( ts @ ( den @ X49 ) @ X50 ) ) ),
inference(variable_rename,[status(thm)],[satz40]) ).
thf(c_0_23,plain,
! [X64: nat,X65: nat,X66: nat] :
( ( ~ ( epred2_2 @ X66 @ X65 @ X64 )
| ( X65
= ( pl @ X66 @ X64 ) ) )
& ( ( X65
!= ( pl @ X66 @ X64 ) )
| ( epred2_2 @ X66 @ X65 @ X64 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).
thf(c_0_24,plain,
! [X57: nat > $o] :
( ~ ( amone @ X57 )
| ~ ( some @ X57 )
| ( X57 @ ( ind @ X57 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
thf(c_0_25,plain,
! [X2: nat,X1: nat] :
( ( amone @ ( epred2_2 @ X2 @ X1 ) )
= $true ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_15]),c_0_16]) ).
thf(c_0_26,plain,
( some
@ ^ [Z0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_27,plain,
! [X60: nat] :
( ( epred1_0 @ X60 )
<=> ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X60 ) ) ),
introduced(definition) ).
thf(c_0_28,negated_conjecture,
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Z0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Z0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz67c])])]) ).
thf(c_0_29,plain,
! [X42: frac,X43: frac,X44: frac] :
( ~ ( eq @ X42 @ X43 )
| ~ ( eq @ X43 @ X44 )
| ( eq @ X42 @ X44 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz39])])]) ).
thf(c_0_30,plain,
! [X58: frac,X59: nat] : ( eq @ ( fr @ ( ts @ ( num @ X58 ) @ X59 ) @ ( ts @ ( den @ X58 ) @ X59 ) ) @ X58 ),
inference(variable_rename,[status(thm)],[satz40a]) ).
thf(c_0_31,plain,
! [X1: nat,X3: nat,X2: nat] : ( eq @ ( pf @ ( fr @ X1 @ X2 ) @ ( fr @ X3 @ X2 ) ) @ ( fr @ ( pl @ X1 @ X3 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_32,plain,
! [X1: nat] :
( ( ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ X1 )
= ( ts @ ( den @ y ) @ ( num @ x ) ) )
| ~ ( epred1_0 @ X1 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).
thf(c_0_33,plain,
! [X5: frac,X6: frac,X7: frac,X8: frac] :
( ( eq @ ( pf @ X5 @ X7 ) @ ( pf @ X6 @ X8 ) )
| ~ ( eq @ X5 @ X6 )
| ~ ( eq @ X7 @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_34,plain,
! [X5: frac] : ( eq @ X5 @ X5 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_35,plain,
! [X5: frac,X1: nat] : ( eq @ X5 @ ( fr @ ( ts @ ( num @ X5 ) @ X1 ) @ ( ts @ ( den @ X5 ) @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_36,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( X2
= ( pl @ X1 @ X3 ) )
| ~ ( epred2_2 @ X1 @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_37,plain,
! [X17: nat > $o] :
( ( X17 @ ( ind @ X17 ) )
| ~ ( amone @ X17 )
| ~ ( some @ X17 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_38,plain,
! [X1: nat,X2: nat] : ( amone @ ( epred2_2 @ X1 @ X2 ) ),
inference(cn,[status(thm)],[c_0_25]) ).
thf(c_0_39,plain,
( ( some @ epred1_0 )
= $true ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_26]),c_0_27]) ).
thf(c_0_40,negated_conjecture,
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Z0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Z0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
inference(fof_nnf,[status(thm)],[c_0_28]) ).
thf(c_0_41,plain,
! [X5: frac,X6: frac,X7: frac] :
( ( eq @ X5 @ X7 )
| ~ ( eq @ X5 @ X6 )
| ~ ( eq @ X6 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_42,plain,
! [X1: nat,X5: frac] : ( eq @ ( fr @ ( ts @ ( num @ X5 ) @ X1 ) @ ( ts @ ( den @ X5 ) @ X1 ) ) @ X5 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_43,plain,
! [X1: nat,X2: nat] :
( ( eq @ ( pf @ ( fr @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ X1 ) @ ( fr @ X2 @ X1 ) ) @ ( fr @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ X1 ) )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_44,plain,
! [X5: frac,X6: frac,X7: frac] :
( ( eq @ ( pf @ X5 @ X6 ) @ ( pf @ X7 @ X6 ) )
| ~ ( eq @ X5 @ X7 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_45,plain,
! [X5: frac,X1: nat] : ( eq @ X5 @ ( fr @ ( ts @ X1 @ ( num @ X5 ) ) @ ( ts @ ( den @ X5 ) @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_35,c_0_19]) ).
thf(c_0_46,plain,
! [X1: nat,X2: nat] :
( ( ( pl @ X1 @ ( ind @ ( epred2_2 @ X1 @ X2 ) ) )
= X2 )
| ~ ( some @ ( epred2_2 @ X1 @ X2 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
thf(c_0_47,plain,
some @ epred1_0,
inference(cn,[status(thm)],[c_0_39]) ).
thf(c_0_48,negated_conjecture,
( ( eq @ ( pf @ y @ ( fr @ ( ind @ ( epred2_2 @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) @ x )
!= $true ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_40]),c_0_16]) ).
thf(c_0_49,plain,
! [X6: frac,X5: frac,X1: nat] :
( ( eq @ X5 @ X6 )
| ~ ( eq @ X5 @ ( fr @ ( ts @ ( num @ X6 ) @ X1 ) @ ( ts @ ( den @ X6 ) @ X1 ) ) ) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_50,plain,
! [X1: nat,X5: frac,X2: nat] :
( ( eq @ X5 @ ( fr @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ X1 ) )
| ~ ( eq @ X5 @ ( pf @ ( fr @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ X1 ) @ ( fr @ X2 @ X1 ) ) )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_43]) ).
thf(c_0_51,plain,
! [X1: nat,X5: frac,X6: frac] : ( eq @ ( pf @ X5 @ X6 ) @ ( pf @ ( fr @ ( ts @ X1 @ ( num @ X5 ) ) @ ( ts @ ( den @ X5 ) @ X1 ) ) @ X6 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_52,plain,
! [X1: nat,X2: nat] :
( ( ( pl @ X1 @ ( ind @ ( epred2_2 @ X1 @ X2 ) ) )
= X2 )
| ( ( epred2_2 @ X1 @ X2 )
!= epred1_0 ) ),
inference(ext_sup,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_53,negated_conjecture,
~ ( eq @ ( pf @ y @ ( fr @ ( ind @ ( epred2_2 @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) @ x ),
inference(cn,[status(thm)],[c_0_48]) ).
thf(c_0_54,plain,
! [X6: frac,X5: frac,X1: nat] :
( ( eq @ X5 @ X6 )
| ~ ( eq @ X5 @ ( fr @ ( ts @ X1 @ ( num @ X6 ) ) @ ( ts @ ( den @ X6 ) @ X1 ) ) ) ),
inference(spm,[status(thm)],[c_0_49,c_0_19]) ).
thf(c_0_55,plain,
! [X1: nat] :
( ( eq @ ( pf @ y @ ( fr @ X1 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) @ ( fr @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
| ~ ( epred1_0 @ X1 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_19]),c_0_19]) ).
thf(c_0_56,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( epred2_2 @ X2 @ X1 @ X3 )
| ( X1
!= ( pl @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_57,plain,
! [X1: nat] :
( ( epred1_0 @ X1 )
| ( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_58,plain,
! [X1: nat,X2: nat] :
( ( ( pl @ X1 @ ( ind @ ( epred2_2 @ X1 @ X2 ) ) )
= X2 )
| ( ( epred2_2 @ X1 @ X2 @ ( esk5_2 @ X1 @ X2 ) )
<~> ( epred1_0 @ ( esk5_2 @ X1 @ X2 ) ) ) ),
inference(neg_ext,[status(thm)],[c_0_52]) ).
thf(c_0_59,negated_conjecture,
~ ( eq @ ( pf @ y @ ( fr @ ( ind @ ( epred2_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) @ x ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_19]),c_0_19]) ).
thf(c_0_60,plain,
! [X1: nat] :
( ( eq @ ( pf @ y @ ( fr @ X1 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) @ x )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_61,plain,
! [X1: nat,X2: nat] : ( epred2_2 @ X1 @ ( pl @ X1 @ X2 ) @ X2 ),
inference(er,[status(thm)],[c_0_56]) ).
thf(c_0_62,plain,
! [X1: nat] :
( ( epred1_0 @ X1 )
| ( ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ X1 )
!= ( ts @ ( den @ y ) @ ( num @ x ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_19]),c_0_19]) ).
thf(c_0_63,plain,
! [X1: nat,X2: nat] :
( ( ( pl @ X1 @ ( ind @ ( epred2_2 @ X1 @ X2 ) ) )
= X2 )
| ( epred2_2 @ X1 @ X2 @ ( esk5_2 @ X1 @ X2 ) )
| ( epred1_0 @ ( esk5_2 @ X1 @ X2 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_58]) ).
thf(c_0_64,negated_conjecture,
~ ( epred1_0 @ ( ind @ ( epred2_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ) ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_65,plain,
! [X1: nat] :
( ( epred2_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ X1 )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_32]) ).
thf(c_0_66,plain,
epred2_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ ( esk5_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63])]),c_0_64]),c_0_65]) ).
thf(c_0_67,plain,
( ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( esk5_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ) )
= ( ts @ ( den @ y ) @ ( num @ x ) ) ),
inference(spm,[status(thm)],[c_0_36,c_0_66]) ).
thf(c_0_68,plain,
! [X1: nat,X2: nat] :
( ( ( pl @ X1 @ ( ind @ ( epred2_2 @ X1 @ X2 ) ) )
= X2 )
| ~ ( epred2_2 @ X1 @ X2 @ ( esk5_2 @ X1 @ X2 ) )
| ~ ( epred1_0 @ ( esk5_2 @ X1 @ X2 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_58]) ).
thf(c_0_69,plain,
epred1_0 @ ( esk5_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ),
inference(spm,[status(thm)],[c_0_62,c_0_67]) ).
thf(c_0_70,plain,
( ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ind @ ( epred2_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ) ) )
= ( ts @ ( den @ y ) @ ( num @ x ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_66])]) ).
thf(c_0_71,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_70]),c_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : NUM768^1 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Jun 22 19:53:09 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.39/0.54 Running higher-order theorem proving
% 0.39/0.54 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.yZZZy5OV87/E---3.1_4390.p
% 0.39/0.68 # Version: 3.2.0-ho
% 0.39/0.68 # partial match(1): HSSSSMSSSSMCSSA
% 0.39/0.68 # Preprocessing class: HSMSSMSSSSMCSSA.
% 0.39/0.68 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.39/0.68 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.39/0.68 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.39/0.68 # Starting new_bool_3 with 300s (1) cores
% 0.39/0.68 # Starting new_bool_1 with 300s (1) cores
% 0.39/0.68 # ho_unfolding_3 with pid 4468 completed with status 0
% 0.39/0.68 # Result found by ho_unfolding_3
% 0.39/0.68 # partial match(1): HSSSSMSSSSMCSSA
% 0.39/0.68 # Preprocessing class: HSMSSMSSSSMCSSA.
% 0.39/0.68 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.39/0.68 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.39/0.68 # No SInE strategy applied
% 0.39/0.68 # Search class: HHUSM-FFSF21-DSSFFFBN
% 0.39/0.68 # partial match(4): FHUSM-FFSF21-DFFFFFNN
% 0.39/0.68 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.39/0.68 # Starting G-E--_041_C18_F1_PI_AE_Q4_CS_SP_S0Y with 541s (1) cores
% 0.39/0.68 # Starting ho_unfolding_3 with 151s (1) cores
% 0.39/0.68 # Starting new_bool_3 with 271s (1) cores
% 0.39/0.68 # Starting U----_206d_02_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.39/0.68 # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.39/0.68 # new_bool_3 with pid 4476 completed with status 0
% 0.39/0.68 # Result found by new_bool_3
% 0.39/0.68 # partial match(1): HSSSSMSSSSMCSSA
% 0.39/0.68 # Preprocessing class: HSMSSMSSSSMCSSA.
% 0.39/0.68 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.39/0.68 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.39/0.68 # No SInE strategy applied
% 0.39/0.68 # Search class: HHUSM-FFSF21-DSSFFFBN
% 0.39/0.68 # partial match(4): FHUSM-FFSF21-DFFFFFNN
% 0.39/0.68 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.39/0.68 # Starting G-E--_041_C18_F1_PI_AE_Q4_CS_SP_S0Y with 541s (1) cores
% 0.39/0.68 # Starting ho_unfolding_3 with 151s (1) cores
% 0.39/0.68 # Starting new_bool_3 with 271s (1) cores
% 0.39/0.68 # Preprocessing time : 0.001 s
% 0.39/0.68 # Presaturation interreduction done
% 0.39/0.68
% 0.39/0.68 # Proof found!
% 0.39/0.68 # SZS status Theorem
% 0.39/0.68 # SZS output start CNFRefutation
% See solution above
% 0.39/0.68 # Parsed axioms : 25
% 0.39/0.68 # Removed by relevancy pruning/SinE : 0
% 0.39/0.68 # Initial clauses : 29
% 0.39/0.68 # Removed in clause preprocessing : 14
% 0.39/0.68 # Initial clauses in saturation : 15
% 0.39/0.68 # Processed clauses : 574
% 0.39/0.68 # ...of these trivial : 51
% 0.39/0.68 # ...subsumed : 238
% 0.39/0.68 # ...remaining for further processing : 285
% 0.39/0.68 # Other redundant clauses eliminated : 2
% 0.39/0.68 # Clauses deleted for lack of memory : 0
% 0.39/0.68 # Backward-subsumed : 6
% 0.39/0.68 # Backward-rewritten : 1
% 0.39/0.68 # Generated clauses : 5391
% 0.39/0.68 # ...of the previous two non-redundant : 4909
% 0.39/0.68 # ...aggressively subsumed : 0
% 0.39/0.68 # Contextual simplify-reflections : 1
% 0.39/0.68 # Paramodulations : 5327
% 0.39/0.68 # Factorizations : 0
% 0.39/0.68 # NegExts : 13
% 0.39/0.68 # Equation resolutions : 3
% 0.39/0.68 # Disequality decompositions : 0
% 0.39/0.68 # Total rewrite steps : 597
% 0.39/0.68 # ...of those cached : 524
% 0.39/0.68 # Propositional unsat checks : 0
% 0.39/0.68 # Propositional check models : 0
% 0.39/0.68 # Propositional check unsatisfiable : 0
% 0.39/0.68 # Propositional clauses : 0
% 0.39/0.68 # Propositional clauses after purity: 0
% 0.39/0.68 # Propositional unsat core size : 0
% 0.39/0.68 # Propositional preprocessing time : 0.000
% 0.39/0.68 # Propositional encoding time : 0.000
% 0.39/0.68 # Propositional solver time : 0.000
% 0.39/0.68 # Success case prop preproc time : 0.000
% 0.39/0.68 # Success case prop encoding time : 0.000
% 0.39/0.68 # Success case prop solver time : 0.000
% 0.39/0.68 # Current number of processed clauses : 250
% 0.39/0.68 # Positive orientable unit clauses : 71
% 0.39/0.68 # Positive unorientable unit clauses: 1
% 0.39/0.68 # Negative unit clauses : 2
% 0.39/0.68 # Non-unit-clauses : 176
% 0.39/0.68 # Current number of unprocessed clauses: 4357
% 0.39/0.68 # ...number of literals in the above : 5781
% 0.39/0.68 # Current number of archived formulas : 0
% 0.39/0.68 # Current number of archived clauses : 34
% 0.39/0.68 # Clause-clause subsumption calls (NU) : 6907
% 0.39/0.68 # Rec. Clause-clause subsumption calls : 5769
% 0.39/0.68 # Non-unit clause-clause subsumptions : 245
% 0.39/0.68 # Unit Clause-clause subsumption calls : 234
% 0.39/0.68 # Rewrite failures with RHS unbound : 0
% 0.39/0.68 # BW rewrite match attempts : 591
% 0.39/0.68 # BW rewrite match successes : 4
% 0.39/0.68 # Condensation attempts : 0
% 0.39/0.68 # Condensation successes : 0
% 0.39/0.68 # Termbank termtop insertions : 210201
% 0.39/0.68 # Search garbage collected termcells : 204
% 0.39/0.68
% 0.39/0.68 # -------------------------------------------------
% 0.39/0.68 # User time : 0.122 s
% 0.39/0.68 # System time : 0.005 s
% 0.39/0.68 # Total time : 0.127 s
% 0.39/0.68 # Maximum resident set size: 1948 pages
% 0.39/0.68
% 0.39/0.68 # -------------------------------------------------
% 0.39/0.68 # User time : 0.595 s
% 0.39/0.68 # System time : 0.028 s
% 0.39/0.68 # Total time : 0.623 s
% 0.39/0.68 # Maximum resident set size: 1744 pages
% 0.39/0.68 % E---3.1 exiting
% 0.39/0.69 % E exiting
%------------------------------------------------------------------------------