%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM768^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.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 : Wed Feb 25 09:24:39 AM UTC 2026
% Result : Theorem 8.97s 2.68s
% Output : Refutation 8.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of formulae : 117 ( 30 unt; 0 typ; 7 def)
% Number of atoms : 540 ( 245 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1814 ( 102 ~; 110 |; 0 &;1575 @)
% ( 7 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 12 con; 0-2 aty)
% Number of variables : 220 ( 71 ^; 149 !; 0 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
nat: $tType ).
thf(func_def_0,type,
frac: $tType ).
thf(func_def_1,type,
x: frac ).
thf(func_def_2,type,
y: frac ).
thf(func_def_3,type,
nat: $tType ).
thf(func_def_4,type,
some: ( nat > $o ) > $o ).
thf(func_def_5,type,
ts: nat > nat > nat ).
thf(func_def_6,type,
num: frac > nat ).
thf(func_def_7,type,
den: frac > nat ).
thf(func_def_8,type,
pl: nat > nat > nat ).
thf(func_def_10,type,
eq: frac > frac > $o ).
thf(func_def_11,type,
pf: frac > frac > frac ).
thf(func_def_12,type,
fr: nat > nat > frac ).
thf(func_def_13,type,
ind: ( nat > $o ) > nat ).
thf(func_def_14,type,
amone: ( nat > $o ) > $o ).
thf(func_def_22,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
sK2: nat > nat > nat ).
thf(func_def_24,type,
sK3: nat ).
thf(f1993,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f63,f113,f745,f1292,f1509,f1694,f1861,f1992]) ).
thf(f1992,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f1776,f1691,f1858]) ).
thf(f1858,definition,
( spl0_9
<=> ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f1691,definition,
( spl0_8
<=> ( ( ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) )
= ( ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f1776,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) )
| spl0_8 ),
inference(duplicate_literal_removal,[status(thm)],[f1775]) ).
thf(f1775,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) )
| ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) )
| spl0_8 ),
inference(equality_proxy_clausification,[status(thm)],[f1774]) ).
thf(f1774,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) )
| ( $true
= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) ) )
| spl0_8 ),
inference(equality_proxy_clausification,[status(thm)],[f1769]) ).
thf(f1769,plain,
( ( $true
= ( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
| ( $true
= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) ) )
| spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f1768]) ).
thf(f1768,plain,
( ( ( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
!= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) ) )
| spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1767]) ).
thf(f1767,plain,
( ( ( ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) )
@ sK3 )
!= ( ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
@ sK3 ) )
| spl0_8 ),
inference(negative_extensionality,[status(thm)],[f1693]) ).
thf(f1693,plain,
( ( ( ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) )
!= ( ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) )
| spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f1691]) ).
thf(f1861,plain,
( ~ spl0_9
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f1773,f1691,f1858]) ).
thf(f1773,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) )
| spl0_8 ),
inference(duplicate_literal_removal,[status(thm)],[f1772]) ).
thf(f1772,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) )
| ( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) )
| spl0_8 ),
inference(equality_proxy_clausification,[status(thm)],[f1771]) ).
thf(f1771,plain,
( ( $false
= ( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
| ( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) )
| spl0_8 ),
inference(equality_proxy_clausification,[status(thm)],[f1770]) ).
thf(f1770,plain,
( ( $false
= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 ) ) )
| ( $false
= ( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK3 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
| spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f1768]) ).
thf(f1694,plain,
( ~ spl0_8
| spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f1604,f1506,f60,f1691]) ).
thf(f60,definition,
( spl0_2
<=> ( $true
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f1506,definition,
( spl0_7
<=> ( $true
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f1604,plain,
( ( ( ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) )
!= ( ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) )
| spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1586]) ).
thf(f1586,plain,
( ( $true != $true )
| ( ( ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) )
!= ( ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) )
| spl0_2
| ~ spl0_7 ),
inference(constrained_superposition,[status(thm)],[f62,f1508]) ).
thf(f1508,plain,
( ( $true
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f1506]) ).
thf(f62,plain,
( ( $true
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f1509,plain,
( spl0_7
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f1382,f1289,f1506]) ).
thf(f1289,definition,
( spl0_6
<=> ( $true
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f1382,plain,
( ( $true
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f1359]) ).
thf(f1359,plain,
( ( $true
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) )
| ( $true != $true )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f74,f1291]) ).
thf(f1291,plain,
( ( $true
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f1289]) ).
thf(f74,plain,
! [X2: frac,X0: frac,X1: nat] :
( ( ( eq @ X2 @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) )
!= $true )
| ( ( eq @ X2 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: frac,X0: frac,X1: nat] :
( ( $true != $true )
| ( ( eq @ X2 @ X0 )
= $true )
| ( ( eq @ X2 @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f50,f48]) ).
thf(f48,plain,
! [X0: frac,X1: nat] :
( ( eq @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: frac,X1: nat] :
( ( eq @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: nat] : ( eq @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) @ X0 ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X1: frac,X4: nat] : ( eq @ ( fr @ ( ts @ ( num @ X1 ) @ X4 ) @ ( ts @ ( den @ X1 ) @ X4 ) ) @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz40a) ).
thf(f50,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X2 @ X1 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true )
| ( ( eq @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X2 )
!= $true )
| ( ( eq @ X2 @ X1 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
| ( ( eq @ X2 @ X1 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
=> ( ( ( eq @ X2 @ X1 )
= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X2 )
=> ( ( eq @ X2 @ X1 )
=> ( eq @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: frac,X3: frac,X2: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X2 @ X3 )
=> ( eq @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz39) ).
thf(f1292,plain,
( spl0_6
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f1217,f742,f1289]) ).
thf(f742,definition,
( spl0_4
<=> ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f1217,plain,
( ( $true
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f1212,f47]) ).
thf(f47,plain,
! [X0: nat,X1: nat] :
( ( ts @ X1 @ X0 )
= ( ts @ X0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: nat,X1: nat] :
( ( ts @ X1 @ X0 )
= ( ts @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X1: nat,X2: nat] :
( ( ts @ X1 @ X2 )
= ( ts @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz29) ).
thf(f1212,plain,
( ( $true
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
@ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1201]) ).
thf(f1201,plain,
( ( $true != $true )
| ( $true
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
@ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f908,f214]) ).
thf(f214,plain,
! [X2: nat,X0: frac,X1: frac] :
( $true
= ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ ( fr @ ( ts @ ( num @ X1 ) @ X2 ) @ ( ts @ ( den @ X1 ) @ X2 ) ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f202]) ).
thf(f202,plain,
! [X2: nat,X0: frac,X1: frac] :
( ( $true
= ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ ( fr @ ( ts @ ( num @ X1 ) @ X2 ) @ ( ts @ ( den @ X1 ) @ X2 ) ) @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f84,f44]) ).
thf(f44,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: frac] : ( eq @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz37) ).
thf(f84,plain,
! [X2: frac,X3: frac,X0: frac,X1: nat] :
( ( ( eq @ X2 @ X3 )
!= $true )
| ( $true
= ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) @ X3 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
! [X2: frac,X3: frac,X0: frac,X1: nat] :
( ( ( eq @ X2 @ X3 )
!= $true )
| ( $true != $true )
| ( $true
= ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) @ X3 ) ) ) ),
inference(superposition,[status(thm)],[f46,f49]) ).
thf(f49,plain,
! [X0: frac,X1: nat] :
( $true
= ( eq @ X0 @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: frac,X1: nat] :
( $true
= ( eq @ X0 @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: frac,X1: nat] : ( eq @ X0 @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: frac,X4: nat] : ( eq @ X1 @ ( fr @ ( ts @ ( num @ X1 ) @ X4 ) @ ( ts @ ( den @ X1 ) @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz40) ).
thf(f46,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ X3 ) )
| ( $true
= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) ) )
| ( ( eq @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
!= ( eq @ X0 @ X3 ) )
| ( $true
= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) ) )
| ( ( eq @ X1 @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) ) )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( $true
!= ( eq @ X0 @ X3 ) ) ),
inference(ennf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
= ( eq @ X0 @ X3 ) )
=> ( ( ( eq @ X1 @ X2 )
= $true )
=> ( $true
= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ X0 @ X3 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: frac,X3: frac,X0: frac,X2: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X3 @ X0 )
=> ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz56) ).
thf(f908,plain,
( ! [X0: nat,X1: frac] :
( ( $true
!= ( eq @ X1
@ ( pf @ ( fr @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X0 )
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ X0 ) ) ) )
| ( ( eq @ X1 @ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ X0 ) )
= $true ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f896]) ).
thf(f896,plain,
( ! [X0: nat,X1: frac] :
( ( $true
!= ( eq @ X1
@ ( pf @ ( fr @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X0 )
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ X0 ) ) ) )
| ( ( eq @ X1 @ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ X0 ) )
= $true )
| ( $true != $true ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f50,f818]) ).
thf(f818,plain,
( ! [X0: nat] :
( $true
= ( eq
@ ( pf @ ( fr @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X0 )
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
@ X0 ) )
@ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ X0 ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f53,f744]) ).
thf(f744,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f742]) ).
thf(f53,plain,
! [X2: nat,X0: nat,X1: nat] :
( $true
= ( eq @ ( pf @ ( fr @ X2 @ X1 ) @ ( fr @ X0 @ X1 ) ) @ ( fr @ ( pl @ X2 @ X0 ) @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat,X2: nat] :
( $true
= ( eq @ ( pf @ ( fr @ X2 @ X1 ) @ ( fr @ X0 @ X1 ) ) @ ( fr @ ( pl @ X2 @ X0 ) @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: nat,X1: nat,X2: nat] : ( eq @ ( pf @ ( fr @ X2 @ X1 ) @ ( fr @ X0 @ X1 ) ) @ ( fr @ ( pl @ X2 @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X6: nat,X4: nat,X5: nat] : ( eq @ ( pf @ ( fr @ X5 @ X4 ) @ ( fr @ X6 @ X4 ) ) @ ( fr @ ( pl @ X5 @ X6 ) @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz57) ).
thf(f745,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f692,f110,f742]) ).
thf(f110,definition,
( spl0_3
<=> ( $true
= ( some
@ ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f692,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) ) )
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f691,f609]) ).
thf(f609,plain,
( ! [X0: nat,X1: nat] :
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK2 @ X1 @ X0 ) ) )
| ( ( pl @ X0 @ ( sK2 @ X1 @ X0 ) )
!= X1 )
| ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f608]) ).
thf(f608,plain,
( ! [X0: nat,X1: nat] :
( ( $false
= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK2 @ X1 @ X0 ) ) ) )
| ( ( pl @ X0 @ ( sK2 @ X1 @ X0 ) )
!= X1 )
| ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f607]) ).
thf(f607,plain,
( ! [X0: nat,X1: nat] :
( ( ( ( pl @ X0 @ ( sK2 @ X1 @ X0 ) )
= X1 )
= $false )
| ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 )
| ( $false
= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK2 @ X1 @ X0 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f605]) ).
thf(f605,plain,
( ! [X0: nat,X1: nat] :
( ( ( ( pl @ X0 @ ( sK2 @ X1 @ X0 ) )
= X1 )
!= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK2 @ X1 @ X0 ) ) ) )
| ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f604]) ).
thf(f604,plain,
( ! [X0: nat,X1: nat] :
( ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 )
| ( ( ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) )
@ ( sK2 @ X1 @ X0 ) )
!= ( ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 )
@ ( sK2 @ X1 @ X0 ) ) ) )
| ~ spl0_3 ),
inference(negative_extensionality,[status(thm)],[f603]) ).
thf(f603,plain,
( ! [X0: nat,X1: nat] :
( ( ( ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) )
!= ( ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) ) )
| ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f602]) ).
thf(f602,plain,
( ! [X0: nat,X1: nat] :
( ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 )
| ( $true != $true )
| ( ( ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) )
!= ( ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f68,f112]) ).
thf(f112,plain,
( ( $true
= ( some
@ ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f110]) ).
thf(f68,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( some
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
| ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( some
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
| ( $true
= ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( some
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
| ( $true
= ( ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 )
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true
!= ( some
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
| ( $true
= ( ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 )
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) ) ) ),
inference(superposition,[status(thm)],[f43,f52]) ).
thf(f52,plain,
! [X0: nat,X1: nat] :
( $true
= ( amone
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( $true
= ( amone
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( amone
@ ^ [X2: nat] :
( ( pl @ X0 @ X2 )
= X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: nat,X1: nat] :
( amone
@ ^ [X3: nat] :
( ( pl @ X2 @ X3 )
= X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz8b) ).
thf(f43,plain,
! [X0: nat > $o] :
( ( $true
!= ( amone @ X0 ) )
| ( $true
!= ( some @ X0 ) )
| ( $true
= ( X0 @ ( ind @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: nat > $o] :
( ( $true
!= ( amone @ X0 ) )
| ( $true
!= ( some @ X0 ) )
| ( $true
= ( X0 @ ( ind @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: nat > $o] :
( ( $true
= ( X0 @ ( ind @ X0 ) ) )
| ( $true
!= ( some @ X0 ) )
| ( $true
!= ( amone @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: nat > $o] :
( ~ ( ( $true
= ( amone @ X0 ) )
=> ( $true
!= ( some @ X0 ) ) )
=> ( $true
= ( X0 @ ( ind @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: nat > $o] :
( ~ ( ( $true
= ( amone @ X0 ) )
=> ( $true
!= ( some @ X0 ) ) )
=> ( $true
= ( X0 @ ( ind @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: nat > $o] :
( ~ ( ( amone @ X0 )
=> ~ ( some @ X0 ) )
=> ( X0 @ ( ind @ X0 ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X7: nat > $o] :
( ~ ( ( amone @ X7 )
=> ~ ( some @ X7 ) )
=> ( X7 @ ( ind @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',oneax) ).
thf(f691,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) ) )
| ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK2 @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
| ~ spl0_3 ),
inference(equality_resolution,[status(thm)],[f663]) ).
thf(f663,plain,
( ! [X0: nat] :
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
!= X0 )
| ( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 )
= X0 ) ) )
= X0 )
| ( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK2 @ X0 @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
= X0 ) )
| ~ spl0_3 ),
inference(equality_factoring,[status(thm)],[f611]) ).
thf(f611,plain,
( ! [X0: nat,X1: nat] :
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK2 @ X1 @ X0 ) ) )
| ( ( pl @ X0 @ ( sK2 @ X1 @ X0 ) )
= X1 )
| ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f610]) ).
thf(f610,plain,
( ! [X0: nat,X1: nat] :
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK2 @ X1 @ X0 ) ) )
| ( ( ( pl @ X0 @ ( sK2 @ X1 @ X0 ) )
= X1 )
= $true )
| ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f606]) ).
thf(f606,plain,
( ! [X0: nat,X1: nat] :
( ( $true
= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK2 @ X1 @ X0 ) ) ) )
| ( ( pl @ X0
@ ( ind
@ ^ [Y0: nat] :
( ( pl @ X0 @ Y0 )
= X1 ) ) )
= X1 )
| ( ( ( pl @ X0 @ ( sK2 @ X1 @ X0 ) )
= X1 )
= $true ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f605]) ).
thf(f113,plain,
spl0_3,
inference(avatar_split_clause,[status(thm)],[f45,f110]) ).
thf(f45,plain,
( $true
= ( some
@ ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( some
@ ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
( some
@ ^ [X0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X0 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( some
@ ^ [X0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',m) ).
thf(f63,plain,
~ spl0_2,
inference(avatar_split_clause,[status(thm)],[f51,f60]) ).
thf(f51,plain,
( $true
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( $true
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
!= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [X0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,negated_conjecture,
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [X8: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X8 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f11,conjecture,
( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [X8: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X8 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz67c) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM768^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n021.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 11:13:38 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : NUM768^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.46 % Domain : Number Theory
% 0.19/0.46 % Problem : Landau theorem 67c
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English : eq (pf y (fr (ind (lambda t.ts (num x) (den y) = pl (ts (num y)
% 0.19/0.46 % (den x)) t)) (ts (den x) (den y)))) x
% 0.19/0.46
% 0.19/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.19/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.19/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : satz67c [Lan30]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % : Without extensionality : Theorem
% 0.19/0.46 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.60 v8.2.0, 0.62 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.71 v6.1.0, 1.00 v6.0.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v3.7.0
% 0.19/0.46 % Syntax : Number of formulae : 25 ( 5 unt; 14 typ; 0 def)
% 0.19/0.46 % Number of atoms : 19 ( 4 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 3 ( 1 avg)
% 0.19/0.46 % Number of connectives : 101 ( 2 ~; 0 |; 0 &; 93 @)
% 0.19/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 11 ( 7 avg)
% 0.19/0.46 % Number of types : 3 ( 2 usr)
% 0.19/0.46 % Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 13 ( 12 usr; 2 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 23 ( 3 ^; 20 !; 0 ?; 23 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments :
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(frac_type,type,
% 0.19/0.46 frac: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(x,type,
% 0.19/0.46 x: frac ).
% 0.19/0.46
% 0.19/0.46 thf(y,type,
% 0.19/0.46 y: frac ).
% 0.19/0.46
% 0.19/0.46 thf(nat_type,type,
% 0.19/0.46 nat: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(some,type,
% 0.19/0.46 some: ( nat > $o ) > $o ).
% 0.19/0.46
% 0.19/0.46 thf(ts,type,
% 0.19/0.46 ts: nat > nat > nat ).
% 0.19/0.46
% 0.19/0.46 thf(num,type,
% 0.19/0.46 num: frac > nat ).
% 0.19/0.46
% 0.19/0.46 thf(den,type,
% 0.19/0.46 den: frac > nat ).
% 0.19/0.46
% 0.19/0.46 thf(pl,type,
% 0.19/0.46 pl: nat > nat > nat ).
% 0.19/0.46
% 0.19/0.46 thf(m,axiom,
% 0.19/0.46 ( some
% 0.19/0.46 @ ^ [Xu: nat] :
% 0.19/0.46 ( ( ts @ ( num @ x ) @ ( den @ y ) )
% 0.19/0.46 = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xu ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(eq,type,
% 0.19/0.46 eq: frac > frac > $o ).
% 0.19/0.46
% 0.19/0.46 thf(pf,type,
% 0.19/0.46 pf: frac > frac > frac ).
% 0.19/0.46
% 0.19/0.46 thf(fr,type,
% 0.19/0.46 fr: nat > nat > frac ).
% 0.19/0.46
% 0.19/0.46 thf(ind,type,
% 0.19/0.46 ind: ( nat > $o ) > nat ).
% 0.19/0.46
% 0.19/0.46 thf(amone,type,
% 0.19/0.46 amone: ( nat > $o ) > $o ).
% 0.19/0.46
% 0.19/0.46 thf(satz8b,axiom,
% 0.19/0.46 ! [Xx: nat,Xy: nat] :
% 0.19/0.46 ( amone
% 0.19/0.46 @ ^ [Xz: nat] :
% 0.19/0.46 ( Xx
% 0.19/0.46 = ( pl @ Xy @ Xz ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz39,axiom,
% 0.19/0.46 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.19/0.46 ( ( eq @ Xx @ Xy )
% 0.19/0.46 => ( ( eq @ Xy @ Xz )
% 0.19/0.46 => ( eq @ Xx @ Xz ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz56,axiom,
% 0.19/0.46 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.19/0.46 ( ( eq @ Xx @ Xy )
% 0.19/0.46 => ( ( eq @ Xz @ Xu )
% 0.19/0.46 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz40,axiom,
% 0.19/0.46 ! [Xx: frac,Xn: nat] : ( eq @ Xx @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz37,axiom,
% 0.19/0.46 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz29,axiom,
% 0.19/0.46 ! [Xx: nat,Xy: nat] :
% 0.19/0.46 ( ( ts @ Xx @ Xy )
% 0.19/0.46 = ( ts @ Xy @ Xx ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz57,axiom,
% 0.19/0.46 ! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(oneax,axiom,
% 0.19/0.46 ! [Xp: nat > $o] :
% 0.19/0.46 ( ~ ( ( amone @ Xp )
% 0.19/0.46 => ~ ( some @ Xp ) )
% 0.19/0.46 => ( Xp @ ( ind @ Xp ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz40a,axiom,
% 0.19/0.46 ! [Xx: frac,Xn: nat] : ( eq @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) @ Xx ) ).
% 0.19/0.46
% 0.19/0.46 thf(satz67c,conjecture,
% 0.19/0.46 ( eq
% 0.19/0.46 @ ( pf @ y
% 0.19/0.46 @ ( fr
% 0.19/0.46 @ ( ind
% 0.19/0.46 @ ^ [Xt: nat] :
% 0.19/0.46 ( ( ts @ ( num @ x ) @ ( den @ y ) )
% 0.19/0.46 = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
% 0.19/0.46 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
% 0.19/0.46 @ x ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.70/1.31 ---- Embedded in THF ---
% 1.70/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.70/1.31 %%% Generated on Tue Feb 24 11:13:39 EST 2026
% 1.70/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.70/1.31 %%% Logic specification used:
% 1.70/1.31 %%% thf(spec, logic, $$dhol).
% 1.70/1.31
% 1.70/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2DTF13252.p
% See solution above
% 1.70/1.31 ------------------------
% 1.70/1.32 ---- Cleaned THF ---
% 1.70/1.32 thf(frac_type,type,
% 1.70/1.32 frac: $tType ).
% 1.70/1.32
% 1.70/1.32 thf(x,type,
% 1.70/1.32 x: frac ).
% 1.70/1.32
% 1.70/1.32 thf(y,type,
% 1.70/1.32 y: frac ).
% 1.70/1.32
% 1.70/1.32 thf(nat_type,type,
% 1.70/1.32 nat: $tType ).
% 1.70/1.32
% 1.70/1.32 thf(some,type,
% 1.70/1.32 some: ( nat > $o ) > $o ).
% 1.70/1.32
% 1.70/1.32 thf(ts,type,
% 1.70/1.32 ts: nat > nat > nat ).
% 1.70/1.32
% 1.70/1.32 thf(num,type,
% 1.70/1.32 num: frac > nat ).
% 1.70/1.32
% 1.70/1.32 thf(den,type,
% 1.70/1.32 den: frac > nat ).
% 1.70/1.32
% 1.70/1.32 thf(pl,type,
% 1.70/1.32 pl: nat > nat > nat ).
% 1.70/1.32
% 1.70/1.32 thf(m,axiom,
% 1.70/1.32 ( some
% 1.70/1.32 @ ^ [Xu: nat] :
% 1.70/1.32 ( ( ts @ ( num @ x ) @ ( den @ y ) )
% 1.70/1.32 = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xu ) ) ) ).
% 1.70/1.32
% 1.70/1.32 thf(eq,type,
% 1.70/1.32 eq: frac > frac > $o ).
% 1.70/1.32
% 1.70/1.32 thf(pf,type,
% 1.70/1.32 pf: frac > frac > frac ).
% 1.70/1.32
% 1.70/1.32 thf(fr,type,
% 1.70/1.32 fr: nat > nat > frac ).
% 1.70/1.32
% 1.70/1.32 thf(ind,type,
% 1.70/1.32 ind: ( nat > $o ) > nat ).
% 1.70/1.32
% 1.70/1.32 thf(amone,type,
% 1.70/1.32 amone: ( nat > $o ) > $o ).
% 1.70/1.32
% 1.70/1.32 thf(satz8b,axiom,
% 1.70/1.32 ! [Xx: nat,Xy: nat] :
% 1.70/1.32 ( amone
% 1.70/1.32 @ ^ [Xz: nat] :
% 1.70/1.32 ( Xx
% 1.70/1.32 = ( pl @ Xy @ Xz ) ) ) ).
% 1.70/1.32
% 1.70/1.32 thf(satz39,axiom,
% 1.70/1.32 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.70/1.32 ( ( eq @ Xx @ Xy )
% 1.70/1.32 => ( ( eq @ Xy @ Xz )
% 1.70/1.32 => ( eq @ Xx @ Xz ) ) ) ).
% 1.70/1.32
% 1.70/1.32 thf(satz56,axiom,
% 1.70/1.32 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.70/1.32 ( ( eq @ Xx @ Xy )
% 1.70/1.32 => ( ( eq @ Xz @ Xu )
% 1.70/1.32 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 1.70/1.32
% 1.70/1.32 thf(satz40,axiom,
% 1.70/1.32 ! [Xx: frac,Xn: nat] : ( eq @ Xx @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) ) ).
% 1.70/1.32
% 1.70/1.32 thf(satz37,axiom,
% 1.70/1.32 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 1.70/1.32
% 1.70/1.32 thf(satz29,axiom,
% 1.70/1.32 ! [Xx: nat,Xy: nat] :
% 1.70/1.32 ( ( ts @ Xx @ Xy )
% 1.70/1.32 = ( ts @ Xy @ Xx ) ) ).
% 1.70/1.32
% 1.70/1.32 thf(satz57,axiom,
% 1.70/1.32 ! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ) ).
% 1.70/1.32
% 1.70/1.32 thf(oneax,axiom,
% 1.70/1.32 ! [Xp: nat > $o] :
% 1.70/1.32 ( ~ ( ( amone @ Xp )
% 1.70/1.32 => ~ ( some @ Xp ) )
% 1.70/1.32 => ( Xp @ ( ind @ Xp ) ) ) ).
% 1.70/1.32
% 1.70/1.32 thf(satz40a,axiom,
% 1.70/1.32 ! [Xx: frac,Xn: nat] : ( eq @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) @ Xx ) ).
% 1.70/1.32
% 1.70/1.32 thf(satz67c,conjecture,
% 1.70/1.32 ( eq
% 1.70/1.32 @ ( pf @ y
% 1.70/1.32 @ ( fr
% 1.70/1.32 @ ( ind
% 1.70/1.32 @ ^ [Xt: nat] :
% 1.70/1.32 ( ( ts @ ( num @ x ) @ ( den @ y ) )
% 1.70/1.32 = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
% 1.70/1.32 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
% 1.70/1.32 @ x ) ).
% 1.70/1.32 ------------------------
% 1.70/1.34 % (13584)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/2Mi)
% 1.70/1.34 % (13584)Instruction limit reached!
% 1.70/1.34 % (13584)------------------------------
% 1.70/1.34 % (13584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.34 % (13584)Termination reason: Unknown
% 1.70/1.34 % (13584)Termination phase: shuffling
% 1.70/1.34
% 1.70/1.34 % (13584)Memory used [KB]: 1023
% 1.70/1.34 % (13584)Time elapsed: 0.002 s
% 1.70/1.34 % (13584)Instructions burned: 2 (million)
% 1.70/1.34 % (13584)------------------------------
% 1.70/1.34 % (13584)------------------------------
% 1.70/1.34 % (13582)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/27Mi)
% 1.70/1.34 % (13580)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/183Mi)
% 1.70/1.34 % (13581)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/4Mi)
% 1.70/1.34 % (13583)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/2Mi)
% 1.70/1.34 % (13585)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/275Mi)
% 1.70/1.34 % (13586)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/18Mi)
% 1.70/1.34 % (13583)Instruction limit reached!
% 1.70/1.34 % (13583)------------------------------
% 1.70/1.34 % (13583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.34 % (13583)Termination reason: Unknown
% 1.70/1.34 % (13583)Termination phase: shuffling
% 1.70/1.34
% 1.70/1.34 % (13583)Memory used [KB]: 1023
% 1.70/1.34 % (13583)Time elapsed: 0.003 s
% 1.70/1.34 % (13583)Instructions burned: 2 (million)
% 1.70/1.34 % (13583)------------------------------
% 1.70/1.34 % (13583)------------------------------
% 1.70/1.34 % (13581)Instruction limit reached!
% 1.70/1.34 % (13581)------------------------------
% 1.70/1.34 % (13581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.34 % (13581)Termination reason: Unknown
% 1.70/1.34 % (13581)Termination phase: Property scanning
% 1.70/1.34
% 1.70/1.34 % (13581)Memory used [KB]: 1023
% 1.70/1.34 % (13581)Time elapsed: 0.004 s
% 1.70/1.34 % (13581)Instructions burned: 4 (million)
% 1.70/1.34 % (13581)------------------------------
% 1.70/1.34 % (13581)------------------------------
% 1.70/1.35 % (13587)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/3Mi)
% 1.70/1.35 % (13587)Instruction limit reached!
% 1.70/1.35 % (13587)------------------------------
% 1.70/1.35 % (13587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.35 % (13587)Termination reason: Unknown
% 1.70/1.35 % (13587)Termination phase: Saturation
% 1.70/1.35
% 1.70/1.35 % (13587)Memory used [KB]: 1023
% 1.70/1.35 % (13587)Time elapsed: 0.002 s
% 1.70/1.35 % (13587)Instructions burned: 3 (million)
% 1.70/1.35 % (13587)------------------------------
% 1.70/1.35 % (13587)------------------------------
% 1.70/1.35 % (13582)Instruction limit reached!
% 1.70/1.35 % (13582)------------------------------
% 1.70/1.35 % (13582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.35 % (13582)Termination reason: Unknown
% 1.70/1.35 % (13582)Termination phase: Saturation
% 1.70/1.35
% 1.70/1.35 % (13582)Memory used [KB]: 5628
% 1.70/1.35 % (13582)Time elapsed: 0.012 s
% 1.70/1.35 % (13582)Instructions burned: 28 (million)
% 1.70/1.35 % (13582)------------------------------
% 1.70/1.35 % (13582)------------------------------
% 1.70/1.35 % (13586)Instruction limit reached!
% 1.70/1.35 % (13586)------------------------------
% 1.70/1.35 % (13586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.35 % (13586)Termination reason: Unknown
% 1.70/1.35 % (13586)Termination phase: Saturation
% 1.70/1.35
% 1.70/1.35 % (13586)Memory used [KB]: 5628
% 1.70/1.35 % (13586)Time elapsed: 0.014 s
% 1.70/1.35 % (13586)Instructions burned: 19 (million)
% 1.70/1.35 % (13586)------------------------------
% 1.70/1.35 % (13586)------------------------------
% 1.70/1.36 % (13590)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/3Mi)
% 1.70/1.36 % (13590)Instruction limit reached!
% 1.70/1.36 % (13590)------------------------------
% 1.70/1.36 % (13590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (13590)Termination reason: Unknown
% 1.70/1.36 % (13590)Termination phase: Saturation
% 1.70/1.36
% 1.70/1.36 % (13590)Memory used [KB]: 5500
% 1.70/1.36 % (13590)Time elapsed: 0.002 s
% 1.70/1.36 % (13590)Instructions burned: 3 (million)
% 1.70/1.36 % (13590)------------------------------
% 1.70/1.36 % (13590)------------------------------
% 1.70/1.36 % (13591)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/1041Mi)
% 1.70/1.36 % (13588)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/37Mi)
% 1.70/1.36 % (13589)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/15Mi)
% 1.70/1.37 % (13593)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/16Mi)
% 1.70/1.37 % (13589)Instruction limit reached!
% 1.70/1.37 % (13589)------------------------------
% 1.70/1.37 % (13589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.37 % (13589)Termination reason: Unknown
% 1.70/1.37 % (13589)Termination phase: Saturation
% 1.70/1.37
% 1.70/1.37 % (13589)Memory used [KB]: 5628
% 1.70/1.37 % (13589)Time elapsed: 0.011 s
% 1.70/1.37 % (13589)Instructions burned: 15 (million)
% 1.70/1.37 % (13589)------------------------------
% 1.70/1.37 % (13589)------------------------------
% 1.70/1.37 % (13593)Instruction limit reached!
% 1.70/1.37 % (13593)------------------------------
% 1.70/1.37 % (13593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.37 % (13593)Termination reason: Unknown
% 1.70/1.37 % (13593)Termination phase: Saturation
% 1.70/1.37
% 1.70/1.37 % (13593)Memory used [KB]: 5884
% 1.70/1.37 % (13593)Time elapsed: 0.007 s
% 1.70/1.37 % (13593)Instructions burned: 17 (million)
% 1.70/1.37 % (13593)------------------------------
% 1.70/1.37 % (13593)------------------------------
% 1.70/1.37 % (13592)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/7Mi)
% 1.70/1.38 % (13592)Instruction limit reached!
% 1.70/1.38 % (13592)------------------------------
% 1.70/1.38 % (13592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (13592)Termination reason: Unknown
% 1.70/1.38 % (13592)Termination phase: Saturation
% 1.70/1.38
% 1.70/1.38 % (13592)Memory used [KB]: 1023
% 1.70/1.38 % (13592)Time elapsed: 0.006 s
% 1.70/1.38 % (13592)Instructions burned: 7 (million)
% 1.70/1.38 % (13592)------------------------------
% 1.70/1.38 % (13592)------------------------------
% 1.70/1.38 % (13595)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/3Mi)
% 1.70/1.38 % (13595)Instruction limit reached!
% 1.70/1.38 % (13595)------------------------------
% 1.70/1.38 % (13595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (13595)Termination reason: Unknown
% 1.70/1.38 % (13595)Termination phase: Equality resolution with deletion
% 1.70/1.38
% 1.70/1.38 % (13595)Memory used [KB]: 1023
% 1.70/1.38 % (13595)Time elapsed: 0.002 s
% 1.70/1.38 % (13595)Instructions burned: 4 (million)
% 1.70/1.38 % (13595)------------------------------
% 1.70/1.38 % (13595)------------------------------
% 1.70/1.38 % (13588)Instruction limit reached!
% 1.70/1.38 % (13588)------------------------------
% 1.70/1.38 % (13588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (13588)Termination reason: Unknown
% 1.70/1.38 % (13588)Termination phase: Saturation
% 1.70/1.38
% 1.70/1.38 % (13588)Memory used [KB]: 6140
% 1.70/1.38 % (13588)Time elapsed: 0.023 s
% 1.70/1.38 % (13588)Instructions burned: 38 (million)
% 1.70/1.38 % (13588)------------------------------
% 1.70/1.38 % (13588)------------------------------
% 1.70/1.39 % (13594)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/3Mi)
% 1.70/1.39 % (13594)Instruction limit reached!
% 1.70/1.39 % (13594)------------------------------
% 1.70/1.39 % (13594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (13594)Termination reason: Unknown
% 1.70/1.39 % (13594)Termination phase: Twee Goal Transformation
% 1.70/1.39
% 1.70/1.39 % (13594)Memory used [KB]: 1023
% 1.70/1.39 % (13594)Time elapsed: 0.004 s
% 1.70/1.39 % (13594)Instructions burned: 4 (million)
% 1.70/1.39 % (13594)------------------------------
% 1.70/1.39 % (13594)------------------------------
% 1.70/1.39 % (13597)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/3Mi)
% 1.70/1.39 % (13597)Instruction limit reached!
% 1.70/1.39 % (13597)------------------------------
% 1.70/1.39 % (13597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (13597)Termination reason: Unknown
% 1.70/1.39 % (13597)Termination phase: Property scanning
% 1.70/1.39
% 1.70/1.39 % (13597)Memory used [KB]: 1023
% 1.70/1.39 % (13597)Time elapsed: 0.002 s
% 1.70/1.39 % (13597)Instructions burned: 4 (million)
% 1.70/1.39 % (13597)------------------------------
% 1.70/1.39 % (13597)------------------------------
% 1.70/1.39 % (13596)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/7Mi)
% 1.74/1.40 % (13596)Refutation not found, incomplete strategy
% 1.74/1.40 % (13596)------------------------------
% 1.74/1.40 % (13596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.40 % (13596)Termination reason: Refutation not found, incomplete strategy
% 1.74/1.40
% 1.74/1.40
% 1.74/1.40 % (13596)Memory used [KB]: 5500
% 1.74/1.40 % (13596)Time elapsed: 0.005 s
% 1.74/1.40 % (13596)Instructions burned: 6 (million)
% 1.74/1.40 % (13596)------------------------------
% 1.74/1.40 % (13596)------------------------------
% 1.74/1.40 % (13598)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/4Mi)
% 1.74/1.40 % (13600)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/710Mi)
% 1.74/1.40 % (13598)Instruction limit reached!
% 1.74/1.40 % (13598)------------------------------
% 1.74/1.40 % (13598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.40 % (13598)Termination reason: Unknown
% 1.74/1.40 % (13598)Termination phase: Saturation
% 1.74/1.40
% 1.74/1.40 % (13598)Memory used [KB]: 5500
% 1.74/1.40 % (13598)Time elapsed: 0.004 s
% 1.74/1.40 % (13598)Instructions burned: 4 (million)
% 1.74/1.40 % (13598)------------------------------
% 1.74/1.40 % (13598)------------------------------
% 1.74/1.41 % (13599)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/18Mi)
% 1.74/1.41 % (13601)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/6Mi)
% 1.74/1.41 % (13601)Instruction limit reached!
% 1.74/1.41 % (13601)------------------------------
% 1.74/1.41 % (13601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.41 % (13601)Termination reason: Unknown
% 1.74/1.41 % (13601)Termination phase: Saturation
% 1.74/1.41
% 1.74/1.41 % (13601)Memory used [KB]: 5628
% 1.74/1.41 % (13601)Time elapsed: 0.004 s
% 1.74/1.41 % (13601)Instructions burned: 7 (million)
% 1.74/1.41 % (13601)------------------------------
% 1.74/1.41 % (13601)------------------------------
% 1.74/1.42 % (13599)Instruction limit reached!
% 1.74/1.42 % (13599)------------------------------
% 1.74/1.42 % (13599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.42 % (13599)Termination reason: Unknown
% 1.74/1.42 % (13599)Termination phase: Saturation
% 1.74/1.42
% 1.74/1.42 % (13599)Memory used [KB]: 5628
% 1.74/1.42 % (13599)Time elapsed: 0.013 s
% 1.74/1.42 % (13599)Instructions burned: 18 (million)
% 1.74/1.42 % (13599)------------------------------
% 1.74/1.42 % (13599)------------------------------
% 1.74/1.42 % (13602)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/902Mi)
% 1.74/1.42 % (13580)Instruction limit reached!
% 1.74/1.42 % (13580)------------------------------
% 1.74/1.42 % (13580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.42 % (13580)Termination reason: Unknown
% 1.74/1.42 % (13580)Termination phase: Saturation
% 1.74/1.42
% 1.74/1.42 % (13580)Memory used [KB]: 6780
% 1.74/1.42 % (13580)Time elapsed: 0.080 s
% 1.74/1.42 % (13580)Instructions burned: 184 (million)
% 1.74/1.42 % (13580)------------------------------
% 1.74/1.42 % (13580)------------------------------
% 1.74/1.42 % (13603)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/21Mi)
% 1.74/1.43 % (13603)Instruction limit reached!
% 1.74/1.43 % (13603)------------------------------
% 1.74/1.43 % (13603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.43 % (13603)Termination reason: Unknown
% 1.74/1.43 % (13603)Termination phase: Saturation
% 1.74/1.43
% 1.74/1.43 % (13603)Memory used [KB]: 5628
% 1.74/1.43 % (13603)Time elapsed: 0.010 s
% 1.74/1.43 % (13603)Instructions burned: 22 (million)
% 1.74/1.43 % (13603)------------------------------
% 1.74/1.43 % (13603)------------------------------
% 1.74/1.43 % (13605)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/6Mi)
% 1.74/1.43 % (13605)Instruction limit reached!
% 1.74/1.43 % (13605)------------------------------
% 1.74/1.43 % (13605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.43 % (13605)Termination reason: Unknown
% 1.74/1.43 % (13605)Termination phase: Saturation
% 1.74/1.43
% 1.74/1.43 % (13605)Memory used [KB]: 5500
% 1.74/1.43 % (13605)Time elapsed: 0.004 s
% 1.74/1.43 % (13605)Instructions burned: 7 (million)
% 1.74/1.43 % (13605)------------------------------
% 1.74/1.43 % (13605)------------------------------
% 1.74/1.44 % (13604)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/5Mi)
% 1.74/1.44 % (13604)Instruction limit reached!
% 1.74/1.44 % (13604)------------------------------
% 1.74/1.44 % (13604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.44 % (13604)Termination reason: Unknown
% 1.74/1.44 % (13604)Termination phase: Saturation
% 1.74/1.44
% 1.74/1.44 % (13604)Memory used [KB]: 5500
% 1.74/1.44 % (13604)Time elapsed: 0.005 s
% 1.74/1.44 % (13604)Instructions burned: 5 (million)
% 1.74/1.44 % (13604)------------------------------
% 1.74/1.44 % (13604)------------------------------
% 1.74/1.44 % (13606)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/377Mi)
% 1.74/1.44 % (13607)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_13252 for (2999ds/779Mi)
% 1.74/1.45 % (13608)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_13252 for (2998ds/19Mi)
% 1.74/1.46 % (13608)Instruction limit reached!
% 1.74/1.46 % (13608)------------------------------
% 1.74/1.46 % (13608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.46 % (13608)Termination reason: Unknown
% 1.74/1.46 % (13608)Termination phase: Saturation
% 1.74/1.46
% 1.74/1.46 % (13608)Memory used [KB]: 5628
% 1.74/1.46 % (13608)Time elapsed: 0.009 s
% 1.74/1.46 % (13608)Instructions burned: 20 (million)
% 1.74/1.46 % (13608)------------------------------
% 1.74/1.46 % (13608)------------------------------
% 1.74/1.47 % (13609)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13252 for (2998ds/879Mi)
% 1.74/1.47 % (13585)Instruction limit reached!
% 1.74/1.47 % (13585)------------------------------
% 1.74/1.47 % (13585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (13585)Termination reason: Unknown
% 1.74/1.47 % (13585)Termination phase: Saturation
% 1.74/1.47
% 1.74/1.47 % (13585)Memory used [KB]: 5884
% 1.74/1.47 % (13585)Time elapsed: 0.131 s
% 1.74/1.47 % (13585)Instructions burned: 276 (million)
% 1.74/1.47 % (13585)------------------------------
% 1.74/1.47 % (13585)------------------------------
% 1.74/1.48 % (13610)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13252 for (2998ds/17Mi)
% 1.74/1.49 % (13610)Instruction limit reached!
% 1.74/1.49 % (13610)------------------------------
% 1.74/1.49 % (13610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.49 % (13610)Termination reason: Unknown
% 1.74/1.49 % (13610)Termination phase: Saturation
% 1.74/1.49
% 1.74/1.49 % (13610)Memory used [KB]: 5756
% 1.74/1.49 % (13610)Time elapsed: 0.008 s
% 1.74/1.49 % (13610)Instructions burned: 17 (million)
% 1.74/1.49 % (13610)------------------------------
% 1.74/1.49 % (13610)------------------------------
% 1.74/1.50 % (13611)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13252 for (2998ds/3Mi)
% 1.74/1.50 % (13611)Instruction limit reached!
% 1.74/1.50 % (13611)------------------------------
% 1.74/1.50 % (13611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.50 % (13611)Termination reason: Unknown
% 1.74/1.50 % (13611)Termination phase: Property scanning
% 1.74/1.50
% 1.74/1.50 % (13611)Memory used [KB]: 1023
% 1.74/1.50 % (13611)Time elapsed: 0.003 s
% 1.74/1.50 % (13611)Instructions burned: 4 (million)
% 1.74/1.50 % (13611)------------------------------
% 1.74/1.50 % (13611)------------------------------
% 1.74/1.51 % (13612)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13252 for (2998ds/30Mi)
% 1.74/1.52 % (13612)Instruction limit reached!
% 1.74/1.52 % (13612)------------------------------
% 1.74/1.52 % (13612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.52 % (13612)Termination reason: Unknown
% 1.74/1.52 % (13612)Termination phase: Saturation
% 1.74/1.52
% 1.74/1.52 % (13612)Memory used [KB]: 5628
% 1.74/1.52 % (13612)Time elapsed: 0.012 s
% 1.74/1.52 % (13612)Instructions burned: 30 (million)
% 1.74/1.52 % (13612)------------------------------
% 1.74/1.52 % (13612)------------------------------
% 1.74/1.53 % (13613)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13252 for (2998ds/127Mi)
% 1.74/1.56 % (13606)Instruction limit reached!
% 1.74/1.56 % (13606)------------------------------
% 1.74/1.56 % (13606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.56 % (13606)Termination reason: Unknown
% 1.74/1.56 % (13606)Termination phase: Saturation
% 1.74/1.56
% 1.74/1.56 % (13606)Memory used [KB]: 6268
% 1.74/1.56 % (13606)Time elapsed: 0.119 s
% 1.74/1.56 % (13606)Instructions burned: 378 (million)
% 1.74/1.56 % (13606)------------------------------
% 1.74/1.56 % (13606)------------------------------
% 1.74/1.57 % (13614)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13252 for (2997ds/100Mi)
% 1.74/1.57 % (13613)Instruction limit reached!
% 1.74/1.57 % (13613)------------------------------
% 1.74/1.57 % (13613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.57 % (13613)Termination reason: Unknown
% 1.74/1.57 % (13613)Termination phase: Saturation
% 1.74/1.57
% 1.74/1.57 % (13613)Memory used [KB]: 5756
% 1.74/1.57 % (13613)Time elapsed: 0.044 s
% 1.74/1.57 % (13613)Instructions burned: 129 (million)
% 1.74/1.57 % (13613)------------------------------
% 1.74/1.57 % (13613)------------------------------
% 1.74/1.58 % (13615)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_13252 for (2997ds/3Mi)
% 1.74/1.58 % (13615)Instruction limit reached!
% 1.74/1.58 % (13615)------------------------------
% 1.74/1.58 % (13615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.58 % (13615)Termination reason: Unknown
% 1.74/1.58 % (13615)Termination phase: Saturation
% 1.74/1.58
% 1.74/1.58 % (13615)Memory used [KB]: 5500
% 1.74/1.58 % (13615)Time elapsed: 0.003 s
% 1.74/1.58 % (13615)Instructions burned: 4 (million)
% 1.74/1.58 % (13615)------------------------------
% 1.74/1.58 % (13615)------------------------------
% 1.74/1.59 % (13616)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_13252 for (2997ds/20Mi)
% 1.74/1.60 % (13614)Instruction limit reached!
% 1.74/1.60 % (13614)------------------------------
% 1.74/1.60 % (13614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.60 % (13614)Termination reason: Unknown
% 1.74/1.60 % (13614)Termination phase: Saturation
% 1.74/1.60
% 1.74/1.60 % (13614)Memory used [KB]: 5884
% 1.74/1.60 % (13614)Time elapsed: 0.034 s
% 1.74/1.60 % (13614)Instructions burned: 102 (million)
% 1.74/1.60 % (13614)------------------------------
% 1.74/1.60 % (13614)------------------------------
% 1.74/1.60 % (13616)Instruction limit reached!
% 1.74/1.60 % (13616)------------------------------
% 1.74/1.60 % (13616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.60 % (13616)Termination reason: Unknown
% 1.74/1.60 % (13616)Termination phase: Saturation
% 1.74/1.60
% 1.74/1.60 % (13616)Memory used [KB]: 5628
% 1.74/1.60 % (13616)Time elapsed: 0.009 s
% 1.74/1.60 % (13616)Instructions burned: 21 (million)
% 1.74/1.60 % (13616)------------------------------
% 1.74/1.60 % (13616)------------------------------
% 1.74/1.61 % (13617)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_13252 for (2997ds/86Mi)
% 1.74/1.61 % (13618)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_13252 for (2997ds/107Mi)
% 1.74/1.62 % (13600)Instruction limit reached!
% 1.74/1.62 % (13600)------------------------------
% 1.74/1.62 % (13600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.62 % (13600)Termination reason: Unknown
% 1.74/1.62 % (13600)Termination phase: Saturation
% 1.74/1.62
% 1.74/1.62 % (13600)Memory used [KB]: 7547
% 1.74/1.62 % (13600)Time elapsed: 0.217 s
% 1.74/1.62 % (13600)Instructions burned: 711 (million)
% 1.74/1.62 % (13600)------------------------------
% 1.74/1.62 % (13600)------------------------------
% 1.74/1.63 % (13619)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_13252 for (2997ds/39Mi)
% 1.74/1.64 % (13617)Instruction limit reached!
% 1.74/1.64 % (13617)------------------------------
% 1.74/1.64 % (13617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.64 % (13617)Termination reason: Unknown
% 1.74/1.64 % (13617)Termination phase: Saturation
% 1.74/1.64
% 1.74/1.64 % (13617)Memory used [KB]: 5756
% 1.74/1.64 % (13617)Time elapsed: 0.029 s
% 1.74/1.64 % (13617)Instructions burned: 87 (million)
% 1.74/1.64 % (13617)------------------------------
% 1.74/1.64 % (13617)------------------------------
% 1.74/1.64 % (13619)Instruction limit reached!
% 1.74/1.64 % (13619)------------------------------
% 1.74/1.64 % (13619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.64 % (13619)Termination reason: Unknown
% 1.74/1.64 % (13619)Termination phase: Saturation
% 1.74/1.64
% 1.74/1.64 % (13619)Memory used [KB]: 5756
% 1.74/1.64 % (13619)Time elapsed: 0.013 s
% 1.74/1.64 % (13619)Instructions burned: 39 (million)
% 1.74/1.64 % (13619)------------------------------
% 1.74/1.64 % (13619)------------------------------
% 1.74/1.65 % (13620)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_13252 for (2997ds/448Mi)
% 1.74/1.65 % (13618)Instruction limit reached!
% 1.74/1.65 % (13618)------------------------------
% 1.74/1.65 % (13618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.65 % (13618)Termination reason: Unknown
% 1.74/1.65 % (13618)Termination phase: Saturation
% 1.74/1.65
% 1.74/1.65 % (13618)Memory used [KB]: 6012
% 1.74/1.65 % (13618)Time elapsed: 0.038 s
% 1.74/1.65 % (13618)Instructions burned: 108 (million)
% 1.74/1.65 % (13618)------------------------------
% 1.74/1.65 % (13618)------------------------------
% 1.74/1.65 % (13621)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_13252 for (2997ds/46Mi)
% 1.74/1.66 % (13622)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_13252 for (2996ds/98Mi)
% 1.74/1.66 % (13621)Instruction limit reached!
% 1.74/1.66 % (13621)------------------------------
% 1.74/1.66 % (13621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.66 % (13621)Termination reason: Unknown
% 1.74/1.66 % (13621)Termination phase: Saturation
% 1.74/1.66
% 1.74/1.66 % (13621)Memory used [KB]: 5884
% 1.74/1.66 % (13621)Time elapsed: 0.039 s
% 1.74/1.66 % (13621)Instructions burned: 47 (million)
% 1.74/1.66 % (13621)------------------------------
% 1.74/1.66 % (13621)------------------------------
% 1.74/1.67 % (13591)Instruction limit reached!
% 1.74/1.67 % (13591)------------------------------
% 1.74/1.67 % (13591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.67 % (13591)Termination reason: Unknown
% 1.74/1.67 % (13591)Termination phase: Saturation
% 1.74/1.67
% 1.74/1.67 % (13591)Memory used [KB]: 7931
% 1.74/1.67 % (13591)Time elapsed: 0.313 s
% 1.74/1.67 % (13591)Instructions burned: 1044 (million)
% 1.74/1.67 % (13591)------------------------------
% 1.74/1.67 % (13591)------------------------------
% 1.74/1.67 % (13623)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_13252 for (2996ds/507Mi)
% 1.74/1.68 % (13624)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_13252 for (2996ds/149Mi)
% 1.74/1.69 % (13607)Instruction limit reached!
% 1.74/1.69 % (13607)------------------------------
% 1.74/1.69 % (13607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.69 % (13607)Termination reason: Unknown
% 1.74/1.69 % (13607)Termination phase: Saturation
% 1.74/1.69
% 1.74/1.69 % (13607)Memory used [KB]: 6268
% 1.74/1.69 % (13607)Time elapsed: 0.247 s
% 1.74/1.69 % (13607)Instructions burned: 781 (million)
% 1.74/1.69 % (13607)------------------------------
% 1.74/1.69 % (13607)------------------------------
% 1.74/1.69 % (13622)Instruction limit reached!
% 1.74/1.69 % (13622)------------------------------
% 1.74/1.69 % (13622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.69 % (13622)Termination reason: Unknown
% 1.74/1.69 % (13622)Termination phase: Saturation
% 1.74/1.69
% 1.74/1.69 % (13622)Memory used [KB]: 1407
% 1.74/1.69 % (13622)Time elapsed: 0.057 s
% 1.74/1.69 % (13622)Instructions burned: 100 (million)
% 1.74/1.69 % (13622)------------------------------
% 1.74/1.69 % (13622)------------------------------
% 1.74/1.70 % (13625)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_13252 for (2996ds/39Mi)
% 1.74/1.70 % (13626)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_13252 for (2996ds/6Mi)
% 1.74/1.70 % (13626)Instruction limit reached!
% 1.74/1.70 % (13626)------------------------------
% 1.74/1.70 % (13626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.70 % (13626)Termination reason: Unknown
% 1.74/1.70 % (13626)Termination phase: Saturation
% 1.74/1.70
% 1.74/1.70 % (13626)Memory used [KB]: 9978
% 1.74/1.70 % (13626)Time elapsed: 0.004 s
% 1.74/1.70 % (13626)Instructions burned: 6 (million)
% 1.74/1.70 % (13626)------------------------------
% 1.74/1.70 % (13626)------------------------------
% 1.74/1.71 % (13602)Instruction limit reached!
% 1.74/1.71 % (13602)------------------------------
% 1.74/1.71 % (13602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.71 % (13602)Termination reason: Unknown
% 1.74/1.71 % (13602)Termination phase: Saturation
% 1.74/1.71
% 1.74/1.71 % (13602)Memory used [KB]: 6012
% 1.74/1.71 % (13602)Time elapsed: 0.292 s
% 1.74/1.71 % (13602)Instructions burned: 903 (million)
% 1.74/1.71 % (13602)------------------------------
% 1.74/1.71 % (13602)------------------------------
% 1.74/1.71 % (13625)Instruction limit reached!
% 1.74/1.71 % (13625)------------------------------
% 1.74/1.71 % (13625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.71 % (13625)Termination reason: Unknown
% 1.74/1.71 % (13625)Termination phase: Saturation
% 1.74/1.71
% 1.74/1.71 % (13625)Memory used [KB]: 5628
% 1.74/1.71 % (13625)Time elapsed: 0.015 s
% 1.74/1.71 % (13625)Instructions burned: 39 (million)
% 1.74/1.71 % (13625)------------------------------
% 1.74/1.71 % (13625)------------------------------
% 1.74/1.71 % (13627)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_13252 for (2996ds/1087Mi)
% 1.74/1.72 % (13628)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_13252 for (2996ds/47Mi)
% 1.74/1.72 % (13629)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_13252 for (2996ds/44Mi)
% 1.74/1.73 % (13624)Instruction limit reached!
% 1.74/1.73 % (13624)------------------------------
% 1.74/1.73 % (13624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.73 % (13624)Termination reason: Unknown
% 1.74/1.73 % (13624)Termination phase: Saturation
% 1.74/1.73
% 1.74/1.73 % (13624)Memory used [KB]: 6140
% 1.74/1.73 % (13624)Time elapsed: 0.050 s
% 1.74/1.73 % (13624)Instructions burned: 149 (million)
% 1.74/1.73 % (13624)------------------------------
% 1.74/1.73 % (13624)------------------------------
% 1.74/1.74 % (13628)Instruction limit reached!
% 1.74/1.74 % (13628)------------------------------
% 1.74/1.74 % (13628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.74 % (13628)Termination reason: Unknown
% 1.74/1.74 % (13628)Termination phase: Saturation
% 1.74/1.74
% 1.74/1.74 % (13628)Memory used [KB]: 5756
% 1.74/1.74 % (13628)Time elapsed: 0.018 s
% 1.74/1.74 % (13628)Instructions burned: 48 (million)
% 1.74/1.74 % (13628)------------------------------
% 1.74/1.74 % (13628)------------------------------
% 1.74/1.74 % (13629)Instruction limit reached!
% 1.74/1.74 % (13629)------------------------------
% 1.74/1.74 % (13629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.74 % (13629)Termination reason: Unknown
% 1.74/1.74 % (13629)Termination phase: Saturation
% 1.74/1.74
% 1.74/1.74 % (13629)Memory used [KB]: 1279
% 1.74/1.74 % (13629)Time elapsed: 0.016 s
% 1.74/1.74 % (13629)Instructions burned: 45 (million)
% 1.74/1.74 % (13629)------------------------------
% 1.74/1.74 % (13629)------------------------------
% 1.74/1.74 % (13630)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_13252 for (2996ds/432Mi)
% 1.74/1.74 % (13632)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/31Mi)
% 1.74/1.75 % (13631)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/62Mi)
% 1.74/1.76 % (13632)Instruction limit reached!
% 1.74/1.76 % (13632)------------------------------
% 1.74/1.76 % (13632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.76 % (13632)Termination reason: Unknown
% 1.74/1.76 % (13632)Termination phase: Saturation
% 1.74/1.76
% 1.74/1.76 % (13632)Memory used [KB]: 5628
% 1.74/1.76 % (13632)Time elapsed: 0.011 s
% 1.74/1.76 % (13632)Instructions burned: 32 (million)
% 1.74/1.76 % (13632)------------------------------
% 1.74/1.76 % (13632)------------------------------
% 1.74/1.76 % (13609)Instruction limit reached!
% 1.74/1.76 % (13609)------------------------------
% 1.74/1.76 % (13609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.76 % (13609)Termination reason: Unknown
% 1.74/1.76 % (13609)Termination phase: Saturation
% 1.74/1.76
% 1.74/1.76 % (13609)Memory used [KB]: 7803
% 1.74/1.76 % (13609)Time elapsed: 0.287 s
% 1.74/1.76 % (13609)Instructions burned: 881 (million)
% 1.74/1.76 % (13609)------------------------------
% 1.74/1.76 % (13609)------------------------------
% 1.74/1.76 % (13633)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/96Mi)
% 1.74/1.77 % (13634)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/453Mi)
% 1.74/1.78 % (13620)Instruction limit reached!
% 1.74/1.78 % (13620)------------------------------
% 1.74/1.78 % (13620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.78 % (13620)Termination reason: Unknown
% 1.74/1.78 % (13620)Termination phase: Saturation
% 1.74/1.78
% 1.74/1.78 % (13620)Memory used [KB]: 6140
% 1.74/1.78 % (13620)Time elapsed: 0.160 s
% 1.74/1.78 % (13620)Instructions burned: 451 (million)
% 1.74/1.78 % (13620)------------------------------
% 1.74/1.78 % (13620)------------------------------
% 1.74/1.79 % (13631)Instruction limit reached!
% 1.74/1.79 % (13631)------------------------------
% 1.74/1.79 % (13631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.79 % (13631)Termination reason: Unknown
% 1.74/1.79 % (13631)Termination phase: Saturation
% 1.74/1.79
% 1.74/1.79 % (13631)Memory used [KB]: 6012
% 1.74/1.79 % (13631)Time elapsed: 0.038 s
% 1.74/1.79 % (13631)Instructions burned: 63 (million)
% 1.74/1.79 % (13631)------------------------------
% 1.74/1.79 % (13631)------------------------------
% 1.74/1.79 % (13635)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/71Mi)
% 1.74/1.79 % (13633)Instruction limit reached!
% 1.74/1.79 % (13633)------------------------------
% 1.74/1.79 % (13633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.79 % (13633)Termination reason: Unknown
% 1.74/1.79 % (13633)Termination phase: Saturation
% 1.74/1.79
% 1.74/1.79 % (13633)Memory used [KB]: 5756
% 1.74/1.79 % (13633)Time elapsed: 0.031 s
% 1.74/1.79 % (13633)Instructions burned: 98 (million)
% 1.74/1.79 % (13633)------------------------------
% 1.74/1.79 % (13633)------------------------------
% 1.74/1.80 % (13637)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/11Mi)
% 1.74/1.81 % (13636)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/83Mi)
% 1.74/1.81 % (13637)Instruction limit reached!
% 1.74/1.81 % (13637)------------------------------
% 1.74/1.81 % (13637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.81 % (13637)Termination reason: Unknown
% 1.74/1.81 % (13637)Termination phase: Saturation
% 1.74/1.81
% 1.74/1.81 % (13637)Memory used [KB]: 5628
% 1.74/1.81 % (13637)Time elapsed: 0.005 s
% 1.74/1.81 % (13637)Instructions burned: 13 (million)
% 1.74/1.81 % (13637)------------------------------
% 1.74/1.81 % (13637)------------------------------
% 1.74/1.82 % (13635)Instruction limit reached!
% 1.74/1.82 % (13635)------------------------------
% 1.74/1.82 % (13635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.82 % (13635)Termination reason: Unknown
% 1.74/1.82 % (13635)Termination phase: Saturation
% 1.74/1.82
% 1.74/1.82 % (13635)Memory used [KB]: 5884
% 1.74/1.82 % (13635)Time elapsed: 0.024 s
% 1.74/1.82 % (13635)Instructions burned: 73 (million)
% 1.74/1.82 % (13635)------------------------------
% 1.74/1.82 % (13635)------------------------------
% 1.74/1.82 % (13638)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/41Mi)
% 1.74/1.82 % (13623)Instruction limit reached!
% 1.74/1.82 % (13623)------------------------------
% 1.74/1.82 % (13623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.82 % (13623)Termination reason: Unknown
% 1.74/1.82 % (13623)Termination phase: Saturation
% 1.74/1.82
% 1.74/1.82 % (13623)Memory used [KB]: 6396
% 1.74/1.82 % (13623)Time elapsed: 0.148 s
% 1.74/1.82 % (13623)Instructions burned: 508 (million)
% 1.74/1.82 % (13623)------------------------------
% 1.74/1.82 % (13623)------------------------------
% 1.74/1.83 % (13639)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/6Mi)
% 1.74/1.83 % (13639)Instruction limit reached!
% 1.74/1.83 % (13639)------------------------------
% 1.74/1.83 % (13639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.83 % (13639)Termination reason: Unknown
% 1.74/1.83 % (13639)Termination phase: Saturation
% 1.74/1.83
% 1.74/1.83 % (13639)Memory used [KB]: 5500
% 1.74/1.83 % (13639)Time elapsed: 0.003 s
% 1.74/1.83 % (13639)Instructions burned: 6 (million)
% 1.74/1.83 % (13639)------------------------------
% 1.74/1.83 % (13639)------------------------------
% 1.74/1.83 % (13638)Instruction limit reached!
% 1.74/1.83 % (13638)------------------------------
% 1.74/1.83 % (13638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.83 % (13638)Termination reason: Unknown
% 1.74/1.83 % (13638)Termination phase: Saturation
% 1.74/1.83
% 1.74/1.83 % (13638)Memory used [KB]: 5756
% 1.74/1.83 % (13638)Time elapsed: 0.014 s
% 1.74/1.83 % (13638)Instructions burned: 41 (million)
% 1.74/1.83 % (13638)------------------------------
% 1.74/1.83 % (13638)------------------------------
% 1.74/1.83 % (13640)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/150Mi)
% 1.74/1.84 % (13641)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/343Mi)
% 1.74/1.84 % (13642)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_13252 for (2995ds/109Mi)
% 1.74/1.85 % (13636)Instruction limit reached!
% 1.74/1.85 % (13636)------------------------------
% 1.74/1.85 % (13636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.85 % (13636)Termination reason: Unknown
% 1.74/1.85 % (13636)Termination phase: Saturation
% 1.74/1.85
% 1.74/1.85 % (13636)Memory used [KB]: 5756
% 1.74/1.85 % (13636)Time elapsed: 0.042 s
% 1.74/1.85 % (13636)Instructions burned: 84 (million)
% 1.74/1.85 % (13636)------------------------------
% 1.74/1.85 % (13636)------------------------------
% 1.74/1.86 % (13643)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_13252 for (2994ds/253Mi)
% 1.74/1.86 % (13630)Instruction limit reached!
% 1.74/1.86 % (13630)------------------------------
% 1.74/1.86 % (13630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.86 % (13630)Termination reason: Unknown
% 1.74/1.86 % (13630)Termination phase: Saturation
% 1.74/1.86
% 1.74/1.86 % (13630)Memory used [KB]: 3198
% 1.74/1.86 % (13630)Time elapsed: 0.127 s
% 1.74/1.86 % (13630)Instructions burned: 433 (million)
% 1.74/1.86 % (13630)------------------------------
% 1.74/1.86 % (13630)------------------------------
% 1.74/1.87 % (13644)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_13252 for (2994ds/140Mi)
% 1.74/1.87 % (13642)Instruction limit reached!
% 1.74/1.87 % (13642)------------------------------
% 1.74/1.87 % (13642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.87 % (13642)Termination reason: Unknown
% 1.74/1.87 % (13642)Termination phase: Saturation
% 1.74/1.87
% 1.74/1.87 % (13642)Memory used [KB]: 6012
% 1.74/1.87 % (13642)Time elapsed: 0.036 s
% 1.74/1.87 % (13642)Instructions burned: 110 (million)
% 1.74/1.87 % (13642)------------------------------
% 1.74/1.87 % (13642)------------------------------
% 1.74/1.88 % (13640)Instruction limit reached!
% 1.74/1.88 % (13640)------------------------------
% 1.74/1.88 % (13640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.88 % (13640)Termination reason: Unknown
% 1.74/1.88 % (13640)Termination phase: Saturation
% 1.74/1.88
% 1.74/1.88 % (13640)Memory used [KB]: 5884
% 1.74/1.88 % (13640)Time elapsed: 0.048 s
% 1.74/1.88 % (13640)Instructions burned: 151 (million)
% 1.74/1.88 % (13640)------------------------------
% 1.74/1.88 % (13640)------------------------------
% 1.74/1.88 % (13645)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_13252 for (2994ds/614Mi)
% 1.74/1.89 % (13646)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_13252 for (2994ds/202Mi)
% 1.74/1.90 % (13634)Instruction limit reached!
% 1.74/1.90 % (13634)------------------------------
% 1.74/1.90 % (13634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.90 % (13634)Termination reason: Unknown
% 1.74/1.90 % (13634)Termination phase: Saturation
% 1.74/1.90
% 1.74/1.90 % (13634)Memory used [KB]: 6396
% 1.74/1.90 % (13634)Time elapsed: 0.134 s
% 1.74/1.90 % (13634)Instructions burned: 453 (million)
% 1.74/1.90 % (13634)------------------------------
% 1.74/1.90 % (13634)------------------------------
% 1.74/1.91 % (13647)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_13252 for (2994ds/339Mi)
% 1.74/1.92 % (13644)Instruction limit reached!
% 1.74/1.92 % (13644)------------------------------
% 1.74/1.92 % (13644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.92 % (13644)Termination reason: Unknown
% 1.74/1.92 % (13644)Termination phase: Saturation
% 1.74/1.92
% 1.74/1.92 % (13644)Memory used [KB]: 6140
% 1.74/1.92 % (13644)Time elapsed: 0.046 s
% 1.74/1.92 % (13644)Instructions burned: 142 (million)
% 1.74/1.92 % (13644)------------------------------
% 1.74/1.92 % (13644)------------------------------
% 1.74/1.93 % (13648)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_13252 for (2994ds/283Mi)
% 1.74/1.94 % (13643)Instruction limit reached!
% 1.74/1.94 % (13643)------------------------------
% 1.74/1.94 % (13643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.94 % (13643)Termination reason: Unknown
% 1.74/1.94 % (13643)Termination phase: Saturation
% 1.74/1.94
% 1.74/1.94 % (13643)Memory used [KB]: 6012
% 1.74/1.94 % (13643)Time elapsed: 0.081 s
% 1.74/1.94 % (13643)Instructions burned: 254 (million)
% 1.74/1.94 % (13643)------------------------------
% 1.74/1.94 % (13643)------------------------------
% 1.74/1.95 % (13649)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_13252 for (2994ds/134Mi)
% 1.74/1.95 % (13641)Instruction limit reached!
% 1.74/1.95 % (13641)------------------------------
% 1.74/1.95 % (13641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.95 % (13641)Termination reason: Unknown
% 1.74/1.95 % (13641)Termination phase: Saturation
% 1.74/1.95
% 1.74/1.95 % (13641)Memory used [KB]: 6780
% 1.74/1.95 % (13641)Time elapsed: 0.110 s
% 1.74/1.95 % (13641)Instructions burned: 344 (million)
% 1.74/1.95 % (13641)------------------------------
% 1.74/1.95 % (13641)------------------------------
% 1.74/1.95 % (13646)Instruction limit reached!
% 1.74/1.95 % (13646)------------------------------
% 1.74/1.95 % (13646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.95 % (13646)Termination reason: Unknown
% 1.74/1.95 % (13646)Termination phase: Saturation
% 1.74/1.95
% 1.74/1.95 % (13646)Memory used [KB]: 6012
% 1.74/1.95 % (13646)Time elapsed: 0.062 s
% 1.74/1.95 % (13646)Instructions burned: 205 (million)
% 1.74/1.95 % (13646)------------------------------
% 1.74/1.95 % (13646)------------------------------
% 1.74/1.96 % (13650)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_13252 for (2993ds/298Mi)
% 1.74/1.96 % (13651)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_13252 for (2993ds/192Mi)
% 1.74/1.99 % (13649)Instruction limit reached!
% 1.74/1.99 % (13649)------------------------------
% 1.74/1.99 % (13649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.99 % (13649)Termination reason: Unknown
% 1.74/1.99 % (13649)Termination phase: Saturation
% 1.74/1.99
% 1.74/1.99 % (13649)Memory used [KB]: 6140
% 1.74/1.99 % (13649)Time elapsed: 0.046 s
% 1.74/1.99 % (13649)Instructions burned: 135 (million)
% 1.74/1.99 % (13649)------------------------------
% 1.74/1.99 % (13649)------------------------------
% 1.74/2.00 % (13652)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_13252 for (2993ds/258Mi)
% 1.74/2.01 % (13648)Instruction limit reached!
% 1.74/2.01 % (13648)------------------------------
% 1.74/2.01 % (13648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/2.01 % (13648)Termination reason: Unknown
% 1.74/2.01 % (13648)Termination phase: Saturation
% 1.74/2.01
% 1.74/2.01 % (13648)Memory used [KB]: 6908
% 1.74/2.01 % (13648)Time elapsed: 0.080 s
% 1.74/2.01 % (13648)Instructions burned: 283 (million)
% 1.74/2.01 % (13648)------------------------------
% 1.74/2.01 % (13648)------------------------------
% 1.74/2.01 % (13647)Instruction limit reached!
% 1.74/2.01 % (13647)------------------------------
% 1.74/2.01 % (13647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/2.01 % (13647)Termination reason: Unknown
% 1.74/2.01 % (13647)Termination phase: Saturation
% 1.74/2.01
% 1.74/2.01 % (13647)Memory used [KB]: 6012
% 1.74/2.01 % (13647)Time elapsed: 0.101 s
% 1.74/2.01 % (13647)Instructions burned: 341 (million)
% 1.74/2.01 % (13647)------------------------------
% 1.74/2.01 % (13647)------------------------------
% 6.48/2.01 % (13651)Instruction limit reached!
% 6.48/2.01 % (13651)------------------------------
% 6.48/2.01 % (13651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.01 % (13651)Termination reason: Unknown
% 6.48/2.01 % (13651)Termination phase: Saturation
% 6.48/2.01
% 6.48/2.01 % (13651)Memory used [KB]: 6396
% 6.48/2.01 % (13651)Time elapsed: 0.057 s
% 6.48/2.01 % (13651)Instructions burned: 194 (million)
% 6.48/2.01 % (13651)------------------------------
% 6.48/2.01 % (13651)------------------------------
% 6.48/2.02 % (13653)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_13252 for (2993ds/90Mi)
% 6.48/2.02 % (13654)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_13252 for (2993ds/231Mi)
% 6.48/2.02 % (13655)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_13252 for (2993ds/458Mi)
% 6.48/2.03 % (13627)Instruction limit reached!
% 6.48/2.03 % (13627)------------------------------
% 6.48/2.03 % (13627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.03 % (13627)Termination reason: Unknown
% 6.48/2.03 % (13627)Termination phase: Saturation
% 6.48/2.03
% 6.48/2.03 % (13627)Memory used [KB]: 6396
% 6.48/2.03 % (13627)Time elapsed: 0.318 s
% 6.48/2.03 % (13627)Instructions burned: 1087 (million)
% 6.48/2.03 % (13627)------------------------------
% 6.48/2.03 % (13627)------------------------------
% 6.48/2.04 % (13656)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_13252 for (2993ds/31Mi)
% 6.48/2.05 % (13653)Instruction limit reached!
% 6.48/2.05 % (13653)------------------------------
% 6.48/2.05 % (13653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.05 % (13653)Termination reason: Unknown
% 6.48/2.05 % (13653)Termination phase: Saturation
% 6.48/2.05
% 6.48/2.05 % (13653)Memory used [KB]: 6012
% 6.48/2.05 % (13653)Time elapsed: 0.031 s
% 6.48/2.05 % (13653)Instructions burned: 91 (million)
% 6.48/2.05 % (13653)------------------------------
% 6.48/2.05 % (13653)------------------------------
% 6.48/2.05 % (13656)Instruction limit reached!
% 6.48/2.05 % (13656)------------------------------
% 6.48/2.05 % (13656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.05 % (13656)Termination reason: Unknown
% 6.48/2.05 % (13656)Termination phase: Saturation
% 6.48/2.05
% 6.48/2.05 % (13656)Memory used [KB]: 5628
% 6.48/2.05 % (13656)Time elapsed: 0.012 s
% 6.48/2.05 % (13656)Instructions burned: 32 (million)
% 6.48/2.05 % (13656)------------------------------
% 6.48/2.05 % (13656)------------------------------
% 6.48/2.05 % (13657)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_13252 for (2992ds/297Mi)
% 6.48/2.06 % (13658)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_13252 for (2992ds/987Mi)
% 6.48/2.07 % (13645)Instruction limit reached!
% 6.48/2.07 % (13645)------------------------------
% 6.48/2.07 % (13645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.07 % (13645)Termination reason: Unknown
% 6.48/2.07 % (13645)Termination phase: Saturation
% 6.48/2.07
% 6.48/2.07 % (13645)Memory used [KB]: 6652
% 6.48/2.07 % (13645)Time elapsed: 0.187 s
% 6.48/2.07 % (13645)Instructions burned: 617 (million)
% 6.48/2.07 % (13645)------------------------------
% 6.48/2.07 % (13645)------------------------------
% 6.48/2.08 % (13650)Instruction limit reached!
% 6.48/2.08 % (13650)------------------------------
% 6.48/2.08 % (13650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.08 % (13650)Termination reason: Unknown
% 6.48/2.08 % (13650)Termination phase: Saturation
% 6.48/2.08
% 6.48/2.08 % (13650)Memory used [KB]: 6268
% 6.48/2.08 % (13650)Time elapsed: 0.123 s
% 6.48/2.08 % (13650)Instructions burned: 300 (million)
% 6.48/2.08 % (13650)------------------------------
% 6.48/2.08 % (13650)------------------------------
% 6.48/2.08 % (13659)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_13252 for (2992ds/182Mi)
% 6.48/2.08 % (13652)Instruction limit reached!
% 6.48/2.08 % (13652)------------------------------
% 6.48/2.08 % (13652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.08 % (13652)Termination reason: Unknown
% 6.48/2.08 % (13652)Termination phase: Saturation
% 6.48/2.08
% 6.48/2.08 % (13652)Memory used [KB]: 5884
% 6.48/2.08 % (13652)Time elapsed: 0.083 s
% 6.48/2.08 % (13652)Instructions burned: 260 (million)
% 6.48/2.08 % (13652)------------------------------
% 6.48/2.08 % (13652)------------------------------
% 6.48/2.09 % (13660)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_13252 for (2992ds/182Mi)
% 6.48/2.09 % (13654)Instruction limit reached!
% 6.48/2.09 % (13654)------------------------------
% 6.48/2.09 % (13654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.09 % (13654)Termination reason: Unknown
% 6.48/2.09 % (13654)Termination phase: Saturation
% 6.48/2.09
% 6.48/2.09 % (13654)Memory used [KB]: 6396
% 6.48/2.09 % (13654)Time elapsed: 0.073 s
% 6.48/2.09 % (13654)Instructions burned: 231 (million)
% 6.48/2.09 % (13654)------------------------------
% 6.48/2.09 % (13654)------------------------------
% 6.48/2.09 % (13661)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_13252 for (2992ds/154Mi)
% 6.48/2.09 % (13661)Refutation not found, incomplete strategy
% 6.48/2.09 % (13661)------------------------------
% 6.48/2.09 % (13661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.09 % (13661)Termination reason: Refutation not found, incomplete strategy
% 6.48/2.09
% 6.48/2.09
% 6.48/2.09 % (13661)Memory used [KB]: 5628
% 6.48/2.09 % (13661)Time elapsed: 0.004 s
% 6.48/2.09 % (13661)Instructions burned: 7 (million)
% 6.48/2.09 % (13661)------------------------------
% 6.48/2.09 % (13661)------------------------------
% 6.48/2.10 % (13662)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_13252 for (2992ds/79Mi)
% 6.48/2.10 % (13663)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_13252 for (2992ds/216Mi)
% 6.90/2.12 % (13662)Instruction limit reached!
% 6.90/2.12 % (13662)------------------------------
% 6.90/2.12 % (13662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.12 % (13662)Termination reason: Unknown
% 6.90/2.12 % (13662)Termination phase: Saturation
% 6.90/2.12
% 6.90/2.12 % (13662)Memory used [KB]: 5756
% 6.90/2.12 % (13662)Time elapsed: 0.046 s
% 6.90/2.12 % (13662)Instructions burned: 80 (million)
% 6.90/2.12 % (13662)------------------------------
% 6.90/2.12 % (13662)------------------------------
% 6.90/2.13 % (13664)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_13252 for (2992ds/114Mi)
% 6.90/2.13 % (13659)Instruction limit reached!
% 6.90/2.13 % (13659)------------------------------
% 6.90/2.13 % (13659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.13 % (13659)Termination reason: Unknown
% 6.90/2.13 % (13659)Termination phase: Saturation
% 6.90/2.13
% 6.90/2.13 % (13659)Memory used [KB]: 6140
% 6.90/2.13 % (13659)Time elapsed: 0.078 s
% 6.90/2.13 % (13659)Instructions burned: 184 (million)
% 6.90/2.13 % (13659)------------------------------
% 6.90/2.13 % (13659)------------------------------
% 6.90/2.14 % (13657)Instruction limit reached!
% 6.90/2.14 % (13657)------------------------------
% 6.90/2.14 % (13657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.14 % (13657)Termination reason: Unknown
% 6.90/2.14 % (13657)Termination phase: Saturation
% 6.90/2.14
% 6.90/2.14 % (13657)Memory used [KB]: 6524
% 6.90/2.14 % (13657)Time elapsed: 0.090 s
% 6.90/2.14 % (13657)Instructions burned: 298 (million)
% 6.90/2.14 % (13657)------------------------------
% 6.90/2.14 % (13657)------------------------------
% 6.90/2.14 % (13665)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_13252 for (2991ds/922Mi)
% 6.90/2.15 % (13660)Instruction limit reached!
% 6.90/2.15 % (13660)------------------------------
% 6.90/2.15 % (13660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.15 % (13660)Termination reason: Unknown
% 6.90/2.15 % (13660)Termination phase: Saturation
% 6.90/2.15
% 6.90/2.15 % (13660)Memory used [KB]: 5884
% 6.90/2.15 % (13660)Time elapsed: 0.080 s
% 6.90/2.15 % (13660)Instructions burned: 182 (million)
% 6.90/2.15 % (13660)------------------------------
% 6.90/2.15 % (13660)------------------------------
% 6.90/2.15 % (13666)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_13252 for (2991ds/182Mi)
% 6.90/2.15 % (13655)Instruction limit reached!
% 6.90/2.15 % (13655)------------------------------
% 6.90/2.15 % (13655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.15 % (13655)Termination reason: Unknown
% 6.90/2.15 % (13655)Termination phase: Saturation
% 6.90/2.15
% 6.90/2.15 % (13655)Memory used [KB]: 6524
% 6.90/2.15 % (13655)Time elapsed: 0.133 s
% 6.90/2.15 % (13655)Instructions burned: 460 (million)
% 6.90/2.15 % (13655)------------------------------
% 6.90/2.15 % (13655)------------------------------
% 6.90/2.15 % (13667)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_13252 for (2991ds/164Mi)
% 6.90/2.16 % (13667)Refutation not found, incomplete strategy
% 6.90/2.16 % (13667)------------------------------
% 6.90/2.16 % (13667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.16 % (13667)Termination reason: Refutation not found, incomplete strategy
% 6.90/2.16
% 6.90/2.16
% 6.90/2.16 % (13667)Memory used [KB]: 1151
% 6.90/2.16 % (13667)Time elapsed: 0.008 s
% 6.90/2.16 % (13667)Instructions burned: 22 (million)
% 6.90/2.16 % (13667)------------------------------
% 6.90/2.16 % (13667)------------------------------
% 6.90/2.16 % (13668)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_13252 for (2991ds/50Mi)
% 6.90/2.17 % (13664)Instruction limit reached!
% 6.90/2.17 % (13664)------------------------------
% 6.90/2.17 % (13664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.17 % (13664)Termination reason: Unknown
% 6.90/2.17 % (13664)Termination phase: Saturation
% 6.90/2.17
% 6.90/2.17 % (13664)Memory used [KB]: 6012
% 6.90/2.17 % (13664)Time elapsed: 0.036 s
% 6.90/2.17 % (13664)Instructions burned: 117 (million)
% 6.90/2.17 % (13664)------------------------------
% 6.90/2.17 % (13664)------------------------------
% 6.90/2.17 % (13669)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_13252 for (2991ds/368Mi)
% 6.90/2.17 % (13663)Instruction limit reached!
% 6.90/2.17 % (13663)------------------------------
% 6.90/2.17 % (13663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.17 % (13663)Termination reason: Unknown
% 6.90/2.17 % (13663)Termination phase: Saturation
% 6.90/2.17
% 6.90/2.17 % (13663)Memory used [KB]: 6268
% 6.90/2.17 % (13663)Time elapsed: 0.094 s
% 6.90/2.17 % (13663)Instructions burned: 217 (million)
% 6.90/2.17 % (13663)------------------------------
% 6.90/2.17 % (13663)------------------------------
% 6.90/2.18 % (13670)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_13252 for (2991ds/1021Mi)
% 6.90/2.18 % (13668)Instruction limit reached!
% 6.90/2.18 % (13668)------------------------------
% 6.90/2.18 % (13668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.18 % (13668)Termination reason: Unknown
% 6.90/2.18 % (13668)Termination phase: Saturation
% 6.90/2.18
% 6.90/2.18 % (13668)Memory used [KB]: 10490
% 6.90/2.18 % (13668)Time elapsed: 0.018 s
% 6.90/2.18 % (13668)Instructions burned: 52 (million)
% 6.90/2.18 % (13668)------------------------------
% 6.90/2.18 % (13668)------------------------------
% 6.90/2.19 % (13671)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_13252 for (2991ds/267Mi)
% 6.90/2.19 % (13672)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_13252 for (2991ds/204Mi)
% 7.47/2.20 % (13666)Instruction limit reached!
% 7.47/2.20 % (13666)------------------------------
% 7.47/2.20 % (13666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.20 % (13666)Termination reason: Unknown
% 7.47/2.20 % (13666)Termination phase: Saturation
% 7.47/2.20
% 7.47/2.20 % (13666)Memory used [KB]: 5628
% 7.47/2.20 % (13666)Time elapsed: 0.050 s
% 7.47/2.20 % (13666)Instructions burned: 182 (million)
% 7.47/2.20 % (13666)------------------------------
% 7.47/2.20 % (13666)------------------------------
% 7.47/2.21 % (13673)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_13252 for (2991ds/26Mi)
% 7.47/2.22 % (13673)Instruction limit reached!
% 7.47/2.22 % (13673)------------------------------
% 7.47/2.22 % (13673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.22 % (13673)Termination reason: Unknown
% 7.47/2.22 % (13673)Termination phase: Saturation
% 7.47/2.22
% 7.47/2.22 % (13673)Memory used [KB]: 5628
% 7.47/2.22 % (13673)Time elapsed: 0.009 s
% 7.47/2.22 % (13673)Instructions burned: 27 (million)
% 7.47/2.22 % (13673)------------------------------
% 7.47/2.22 % (13673)------------------------------
% 7.47/2.23 % (13674)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_13252 for (2991ds/53Mi)
% 7.47/2.24 % (13674)Instruction limit reached!
% 7.47/2.24 % (13674)------------------------------
% 7.47/2.24 % (13674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.24 % (13674)Termination reason: Unknown
% 7.47/2.24 % (13674)Termination phase: Saturation
% 7.47/2.24
% 7.47/2.24 % (13674)Memory used [KB]: 6140
% 7.47/2.24 % (13674)Time elapsed: 0.017 s
% 7.47/2.24 % (13674)Instructions burned: 53 (million)
% 7.47/2.24 % (13674)------------------------------
% 7.47/2.24 % (13674)------------------------------
% 7.47/2.25 % (13672)Instruction limit reached!
% 7.47/2.25 % (13672)------------------------------
% 7.47/2.25 % (13672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.25 % (13672)Termination reason: Unknown
% 7.47/2.25 % (13672)Termination phase: Saturation
% 7.47/2.25
% 7.47/2.25 % (13672)Memory used [KB]: 6012
% 7.47/2.25 % (13672)Time elapsed: 0.063 s
% 7.47/2.25 % (13672)Instructions burned: 205 (million)
% 7.47/2.25 % (13672)------------------------------
% 7.47/2.25 % (13672)------------------------------
% 7.47/2.25 % (13675)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_13252 for (2990ds/4436Mi)
% 7.47/2.26 % (13676)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_13252 for (2990ds/1539Mi)
% 7.47/2.27 % (13671)Instruction limit reached!
% 7.47/2.27 % (13671)------------------------------
% 7.47/2.27 % (13671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.27 % (13671)Termination reason: Unknown
% 7.47/2.27 % (13671)Termination phase: Saturation
% 7.47/2.27
% 7.47/2.27 % (13671)Memory used [KB]: 6396
% 7.47/2.27 % (13671)Time elapsed: 0.086 s
% 7.47/2.27 % (13671)Instructions burned: 269 (million)
% 7.47/2.27 % (13671)------------------------------
% 7.47/2.27 % (13671)------------------------------
% 7.47/2.28 % (13677)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_13252 for (2990ds/408Mi)
% 7.47/2.28 % (13677)Refutation not found, incomplete strategy
% 7.47/2.28 % (13677)------------------------------
% 7.47/2.28 % (13677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.28 % (13677)Termination reason: Refutation not found, incomplete strategy
% 7.47/2.28
% 7.47/2.28
% 7.47/2.28 % (13677)Memory used [KB]: 5500
% 7.47/2.28 % (13677)Time elapsed: 0.002 s
% 7.47/2.28 % (13677)Instructions burned: 4 (million)
% 7.47/2.28 % (13677)------------------------------
% 7.47/2.28 % (13677)------------------------------
% 7.47/2.28 % (13669)Instruction limit reached!
% 7.47/2.28 % (13669)------------------------------
% 7.47/2.28 % (13669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.28 % (13669)Termination reason: Unknown
% 7.47/2.28 % (13669)Termination phase: Saturation
% 7.47/2.28
% 7.47/2.28 % (13669)Memory used [KB]: 6268
% 7.47/2.28 % (13669)Time elapsed: 0.112 s
% 7.47/2.28 % (13669)Instructions burned: 369 (million)
% 7.47/2.28 % (13669)------------------------------
% 7.47/2.28 % (13669)------------------------------
% 7.47/2.29 % (13678)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_13252 for (2990ds/5205Mi)
% 7.47/2.29 % (13679)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_13252 for (2990ds/1913Mi)
% 7.88/2.35 % (13658)Instruction limit reached!
% 7.88/2.35 % (13658)------------------------------
% 7.88/2.35 % (13658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.88/2.35 % (13658)Termination reason: Unknown
% 7.88/2.35 % (13658)Termination phase: Saturation
% 7.88/2.35
% 7.88/2.35 % (13658)Memory used [KB]: 7803
% 7.88/2.35 % (13658)Time elapsed: 0.290 s
% 7.88/2.35 % (13658)Instructions burned: 987 (million)
% 7.88/2.35 % (13658)------------------------------
% 7.88/2.35 % (13658)------------------------------
% 7.88/2.36 % (13680)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_13252 for (2989ds/4350Mi)
% 8.18/2.41 % (13665)Instruction limit reached!
% 8.18/2.41 % (13665)------------------------------
% 8.18/2.41 % (13665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.41 % (13665)Termination reason: Unknown
% 8.18/2.41 % (13665)Termination phase: Saturation
% 8.18/2.41
% 8.18/2.41 % (13665)Memory used [KB]: 6268
% 8.18/2.41 % (13665)Time elapsed: 0.265 s
% 8.18/2.41 % (13665)Instructions burned: 923 (million)
% 8.18/2.41 % (13665)------------------------------
% 8.18/2.41 % (13665)------------------------------
% 8.18/2.42 % (13681)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_13252 for (2989ds/68Mi)
% 8.18/2.44 % (13681)Instruction limit reached!
% 8.18/2.44 % (13681)------------------------------
% 8.18/2.44 % (13681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.44 % (13681)Termination reason: Unknown
% 8.18/2.44 % (13681)Termination phase: Saturation
% 8.18/2.44
% 8.18/2.44 % (13681)Memory used [KB]: 5884
% 8.18/2.44 % (13681)Time elapsed: 0.023 s
% 8.18/2.44 % (13681)Instructions burned: 70 (million)
% 8.18/2.44 % (13681)------------------------------
% 8.18/2.44 % (13681)------------------------------
% 8.18/2.45 % (13682)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_13252 for (2988ds/358Mi)
% 8.18/2.48 % (13670)Instruction limit reached!
% 8.18/2.48 % (13670)------------------------------
% 8.18/2.48 % (13670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.48 % (13670)Termination reason: Unknown
% 8.18/2.48 % (13670)Termination phase: Saturation
% 8.18/2.48
% 8.18/2.48 % (13670)Memory used [KB]: 6652
% 8.18/2.48 % (13670)Time elapsed: 0.303 s
% 8.18/2.48 % (13670)Instructions burned: 1024 (million)
% 8.18/2.48 % (13670)------------------------------
% 8.18/2.48 % (13670)------------------------------
% 8.18/2.49 % (13683)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_13252 for (2988ds/31Mi)
% 8.80/2.50 % (13683)Instruction limit reached!
% 8.80/2.50 % (13683)------------------------------
% 8.80/2.50 % (13683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.50 % (13683)Termination reason: Unknown
% 8.80/2.50 % (13683)Termination phase: Saturation
% 8.80/2.50
% 8.80/2.50 % (13683)Memory used [KB]: 5628
% 8.80/2.50 % (13683)Time elapsed: 0.011 s
% 8.80/2.50 % (13683)Instructions burned: 32 (million)
% 8.80/2.50 % (13683)------------------------------
% 8.80/2.50 % (13683)------------------------------
% 8.80/2.51 % (13684)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_13252 for (2988ds/279Mi)
% 8.80/2.51 % (13684)Refutation not found, incomplete strategy
% 8.80/2.51 % (13684)------------------------------
% 8.80/2.51 % (13684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.51 % (13684)Termination reason: Refutation not found, incomplete strategy
% 8.80/2.51
% 8.80/2.51
% 8.80/2.51 % (13684)Memory used [KB]: 5500
% 8.80/2.51 % (13684)Time elapsed: 0.003 s
% 8.80/2.51 % (13684)Instructions burned: 6 (million)
% 8.80/2.51 % (13684)------------------------------
% 8.80/2.51 % (13684)------------------------------
% 8.80/2.52 % (13685)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_13252 for (2988ds/258Mi)
% 8.80/2.56 % (13682)Instruction limit reached!
% 8.80/2.56 % (13682)------------------------------
% 8.80/2.56 % (13682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.56 % (13682)Termination reason: Unknown
% 8.80/2.56 % (13682)Termination phase: Saturation
% 8.80/2.56
% 8.80/2.56 % (13682)Memory used [KB]: 6140
% 8.80/2.56 % (13682)Time elapsed: 0.111 s
% 8.80/2.56 % (13682)Instructions burned: 360 (million)
% 8.80/2.56 % (13682)------------------------------
% 8.80/2.56 % (13682)------------------------------
% 8.80/2.57 % (13686)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_13252 for (2987ds/26Mi)
% 8.80/2.58 % (13686)Instruction limit reached!
% 8.80/2.58 % (13686)------------------------------
% 8.80/2.58 % (13686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.58 % (13686)Termination reason: Unknown
% 8.80/2.58 % (13686)Termination phase: Saturation
% 8.80/2.58
% 8.80/2.58 % (13686)Memory used [KB]: 5628
% 8.80/2.58 % (13686)Time elapsed: 0.010 s
% 8.80/2.58 % (13686)Instructions burned: 29 (million)
% 8.80/2.58 % (13686)------------------------------
% 8.80/2.58 % (13686)------------------------------
% 8.80/2.59 % (13687)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_13252 for (2987ds/995Mi)
% 8.97/2.60 % (13685)Instruction limit reached!
% 8.97/2.60 % (13685)------------------------------
% 8.97/2.60 % (13685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.97/2.60 % (13685)Termination reason: Unknown
% 8.97/2.60 % (13685)Termination phase: Saturation
% 8.97/2.60
% 8.97/2.60 % (13685)Memory used [KB]: 6524
% 8.97/2.60 % (13685)Time elapsed: 0.083 s
% 8.97/2.60 % (13685)Instructions burned: 258 (million)
% 8.97/2.60 % (13685)------------------------------
% 8.97/2.60 % (13685)------------------------------
% 8.97/2.61 % (13688)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_13252 for (2987ds/373Mi)
% 8.97/2.68 % (13676)First to succeed.
% 8.97/2.68 % (13676)Refutation found. Thanks to Tanya!
% 8.97/2.68 % SZS status Theorem for DTF2THF_13252
% 8.97/2.68 % SZS output start Proof for DTF2THF_13252
% 8.97/2.68 thf(type_def_5, type, frac: $tType).
% 8.97/2.68 thf(type_def_6, type, nat: $tType).
% 8.97/2.68 thf(func_def_0, type, frac: $tType).
% 8.97/2.68 thf(func_def_1, type, x: frac).
% 8.97/2.68 thf(func_def_2, type, y: frac).
% 8.97/2.68 thf(func_def_3, type, nat: $tType).
% 8.97/2.68 thf(func_def_4, type, some: (nat > $o) > $o).
% 8.97/2.68 thf(func_def_5, type, ts: nat > nat > nat).
% 8.97/2.68 thf(func_def_6, type, num: frac > nat).
% 8.97/2.68 thf(func_def_7, type, den: frac > nat).
% 8.97/2.68 thf(func_def_8, type, pl: nat > nat > nat).
% 8.97/2.68 thf(func_def_10, type, eq: frac > frac > $o).
% 8.97/2.68 thf(func_def_11, type, pf: frac > frac > frac).
% 8.97/2.68 thf(func_def_12, type, fr: nat > nat > frac).
% 8.97/2.68 thf(func_def_13, type, ind: (nat > $o) > nat).
% 8.97/2.68 thf(func_def_14, type, amone: (nat > $o) > $o).
% 8.97/2.68 thf(func_def_22, type, ph1: !>[X0: $tType]:(X0)).
% 8.97/2.68 thf(func_def_23, type, sK2: nat > nat > nat).
% 8.97/2.68 thf(func_def_24, type, sK3: nat).
% 8.97/2.68 thf(f1993,plain,(
% 8.97/2.68 $false),
% 8.97/2.68 inference(avatar_sat_refutation,[status(thm)],[f63,f113,f745,f1292,f1509,f1694,f1861,f1992])).
% 8.97/2.68 thf(f1992,plain,(
% 8.97/2.68 spl0_9 | spl0_8),
% 8.97/2.68 inference(avatar_split_clause,[status(thm)],[f1776,f1691,f1858])).
% 8.97/2.68 thf(f1858,definition,(
% 8.97/2.68 spl0_9 <=> ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3))),
% 8.97/2.68 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 8.97/2.68 thf(f1691,definition,(
% 8.97/2.68 spl0_8 <=> ((^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0))) = (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y)))))),
% 8.97/2.68 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 8.97/2.68 thf(f1776,plain,(
% 8.97/2.68 ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3)) | spl0_8),
% 8.97/2.68 inference(duplicate_literal_removal,[status(thm)],[f1775])).
% 8.97/2.68 thf(f1775,plain,(
% 8.97/2.68 ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3)) | ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3)) | spl0_8),
% 8.97/2.68 inference(equality_proxy_clausification,[status(thm)],[f1774])).
% 8.97/2.68 thf(f1774,plain,(
% 8.97/2.68 ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3)) | ($true = ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3))) | spl0_8),
% 8.97/2.68 inference(equality_proxy_clausification,[status(thm)],[f1769])).
% 8.97/2.68 thf(f1769,plain,(
% 8.97/2.68 ($true = ((pl @ (ts @ (num @ y) @ (den @ x)) @ sK3) = (ts @ (num @ x) @ (den @ y)))) | ($true = ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3))) | spl0_8),
% 8.97/2.68 inference(binary_proxy_clausification,[status(thm)],[f1768])).
% 8.97/2.68 thf(f1768,plain,(
% 8.97/2.68 (((pl @ (ts @ (num @ y) @ (den @ x)) @ sK3) = (ts @ (num @ x) @ (den @ y))) != ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3))) | spl0_8),
% 8.97/2.68 inference(beta_eta_normalization,[status(thm)],[f1767])).
% 8.97/2.68 thf(f1767,plain,(
% 8.97/2.68 (((^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0))) @ sK3) != ((^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y)))) @ sK3)) | spl0_8),
% 8.97/2.68 inference(negative_extensionality,[status(thm)],[f1693])).
% 8.97/2.68 thf(f1693,plain,(
% 8.97/2.68 ((^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0))) != (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) | spl0_8),
% 8.97/2.68 inference(avatar_component_clause,[status(thm)],[f1691])).
% 8.97/2.68 thf(f1861,plain,(
% 8.97/2.68 ~spl0_9 | spl0_8),
% 8.97/2.68 inference(avatar_split_clause,[status(thm)],[f1773,f1691,f1858])).
% 8.97/2.68 thf(f1773,plain,(
% 8.97/2.68 ((ts @ (num @ x) @ (den @ y)) != (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3)) | spl0_8),
% 8.97/2.68 inference(duplicate_literal_removal,[status(thm)],[f1772])).
% 8.97/2.68 thf(f1772,plain,(
% 8.97/2.68 ((ts @ (num @ x) @ (den @ y)) != (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3)) | ((ts @ (num @ x) @ (den @ y)) != (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3)) | spl0_8),
% 8.97/2.68 inference(equality_proxy_clausification,[status(thm)],[f1771])).
% 8.97/2.68 thf(f1771,plain,(
% 8.97/2.68 ($false = ((pl @ (ts @ (num @ y) @ (den @ x)) @ sK3) = (ts @ (num @ x) @ (den @ y)))) | ((ts @ (num @ x) @ (den @ y)) != (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3)) | spl0_8),
% 8.97/2.68 inference(equality_proxy_clausification,[status(thm)],[f1770])).
% 8.97/2.68 thf(f1770,plain,(
% 8.97/2.68 ($false = ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK3))) | ($false = ((pl @ (ts @ (num @ y) @ (den @ x)) @ sK3) = (ts @ (num @ x) @ (den @ y)))) | spl0_8),
% 8.97/2.68 inference(binary_proxy_clausification,[status(thm)],[f1768])).
% 8.97/2.68 thf(f1694,plain,(
% 8.97/2.68 ~spl0_8 | spl0_2 | ~spl0_7),
% 8.97/2.68 inference(avatar_split_clause,[status(thm)],[f1604,f1506,f60,f1691])).
% 8.97/2.68 thf(f60,definition,(
% 8.97/2.68 spl0_2 <=> ($true = (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0)))) @ (ts @ (den @ x) @ (den @ y)))) @ x))),
% 8.97/2.68 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 8.97/2.68 thf(f1506,definition,(
% 8.97/2.68 spl0_7 <=> ($true = (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ (ts @ (den @ x) @ (den @ y)))) @ x))),
% 8.97/2.68 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 8.97/2.68 thf(f1604,plain,(
% 8.97/2.68 ((^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0))) != (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) | (spl0_2 | ~spl0_7)),
% 8.97/2.68 inference(trivial_inequality_removal,[status(thm)],[f1586])).
% 8.97/2.68 thf(f1586,plain,(
% 8.97/2.68 ($true != $true) | ((^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0))) != (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) | (spl0_2 | ~spl0_7)),
% 8.97/2.68 inference(constrained_superposition,[status(thm)],[f62,f1508])).
% 8.97/2.68 thf(f1508,plain,(
% 8.97/2.68 ($true = (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ (ts @ (den @ x) @ (den @ y)))) @ x)) | ~spl0_7),
% 8.97/2.68 inference(avatar_component_clause,[status(thm)],[f1506])).
% 8.97/2.68 thf(f62,plain,(
% 8.97/2.68 ($true != (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0)))) @ (ts @ (den @ x) @ (den @ y)))) @ x)) | spl0_2),
% 8.97/2.68 inference(avatar_component_clause,[status(thm)],[f60])).
% 8.97/2.68 thf(f1509,plain,(
% 8.97/2.68 spl0_7 | ~spl0_6),
% 8.97/2.68 inference(avatar_split_clause,[status(thm)],[f1382,f1289,f1506])).
% 8.97/2.68 thf(f1289,definition,(
% 8.97/2.68 spl0_6 <=> ($true = (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ (ts @ (den @ x) @ (den @ y)))) @ (fr @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (den @ x) @ (den @ y)))))),
% 8.97/2.68 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 8.97/2.68 thf(f1382,plain,(
% 8.97/2.68 ($true = (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ (ts @ (den @ x) @ (den @ y)))) @ x)) | ~spl0_6),
% 8.97/2.68 inference(trivial_inequality_removal,[status(thm)],[f1359])).
% 8.97/2.68 thf(f1359,plain,(
% 8.97/2.68 ($true = (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ (ts @ (den @ x) @ (den @ y)))) @ x)) | ($true != $true) | ~spl0_6),
% 8.97/2.68 inference(superposition,[status(thm)],[f74,f1291])).
% 8.97/2.68 thf(f1291,plain,(
% 8.97/2.68 ($true = (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ (ts @ (den @ x) @ (den @ y)))) @ (fr @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (den @ x) @ (den @ y))))) | ~spl0_6),
% 8.97/2.68 inference(avatar_component_clause,[status(thm)],[f1289])).
% 8.97/2.68 thf(f74,plain,(
% 8.97/2.68 ( ! [X2 : frac,X0 : frac,X1 : nat] : (((eq @ X2 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1))) != $true) | ((eq @ X2 @ X0) = $true)) )),
% 8.97/2.68 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 8.97/2.68 thf(f73,plain,(
% 8.97/2.68 ( ! [X2 : frac,X0 : frac,X1 : nat] : (($true != $true) | ((eq @ X2 @ X0) = $true) | ((eq @ X2 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1))) != $true)) )),
% 8.97/2.68 inference(superposition,[status(thm)],[f50,f48])).
% 8.97/2.68 thf(f48,plain,(
% 8.97/2.68 ( ! [X0 : frac,X1 : nat] : (((eq @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)) @ X0) = $true)) )),
% 8.97/2.68 inference(cnf_transformation,[status(thm)],[f23])).
% 8.97/2.68 thf(f23,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : nat] : ((eq @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)) @ X0) = $true)),
% 8.97/2.68 inference(fool_elimination,[status(thm)],[f22])).
% 8.97/2.68 thf(f22,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : nat] : (eq @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)) @ X0)),
% 8.97/2.68 inference(rectify,[status(thm)],[f10])).
% 8.97/2.68 thf(f10,axiom,(
% 8.97/2.68 ! [X1 : frac,X4 : nat] : (eq @ (fr @ (ts @ (num @ X1) @ X4) @ (ts @ (den @ X1) @ X4)) @ X1)),
% 8.97/2.68 file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz40a)).
% 8.97/2.68 thf(f50,plain,(
% 8.97/2.68 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ X2 @ X1) != $true) | ((eq @ X0 @ X1) = $true) | ((eq @ X0 @ X2) != $true)) )),
% 8.97/2.68 inference(cnf_transformation,[status(thm)],[f42])).
% 8.97/2.68 thf(f42,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : frac,X2 : frac] : (((eq @ X0 @ X2) != $true) | ((eq @ X2 @ X1) != $true) | ((eq @ X0 @ X1) = $true))),
% 8.97/2.68 inference(flattening,[status(thm)],[f41])).
% 8.97/2.68 thf(f41,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : frac,X2 : frac] : ((((eq @ X0 @ X1) = $true) | ((eq @ X2 @ X1) != $true)) | ((eq @ X0 @ X2) != $true))),
% 8.97/2.68 inference(ennf_transformation,[status(thm)],[f29])).
% 8.97/2.68 thf(f29,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : frac,X2 : frac] : (((eq @ X0 @ X2) = $true) => (((eq @ X2 @ X1) = $true) => ((eq @ X0 @ X1) = $true)))),
% 8.97/2.68 inference(fool_elimination,[status(thm)],[f28])).
% 8.97/2.68 thf(f28,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X0 @ X2) => ((eq @ X2 @ X1) => (eq @ X0 @ X1)))),
% 8.97/2.68 inference(rectify,[status(thm)],[f3])).
% 8.97/2.68 thf(f3,axiom,(
% 8.97/2.68 ! [X1 : frac,X3 : frac,X2 : frac] : ((eq @ X1 @ X2) => ((eq @ X2 @ X3) => (eq @ X1 @ X3)))),
% 8.97/2.68 file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz39)).
% 8.97/2.68 thf(f1292,plain,(
% 8.97/2.68 spl0_6 | ~spl0_4),
% 8.97/2.68 inference(avatar_split_clause,[status(thm)],[f1217,f742,f1289])).
% 8.97/2.68 thf(f742,definition,(
% 8.97/2.68 spl0_4 <=> ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y)))))))),
% 8.97/2.68 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 8.97/2.68 thf(f1217,plain,(
% 8.97/2.68 ($true = (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ (ts @ (den @ x) @ (den @ y)))) @ (fr @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (den @ x) @ (den @ y))))) | ~spl0_4),
% 8.97/2.68 inference(forward_demodulation,[status(thm)],[f1212,f47])).
% 8.97/2.68 thf(f47,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (((ts @ X1 @ X0) = (ts @ X0 @ X1))) )),
% 8.97/2.68 inference(cnf_transformation,[status(thm)],[f34])).
% 8.97/2.68 thf(f34,plain,(
% 8.97/2.68 ! [X0 : nat,X1 : nat] : ((ts @ X1 @ X0) = (ts @ X0 @ X1))),
% 8.97/2.68 inference(rectify,[status(thm)],[f7])).
% 8.97/2.68 thf(f7,axiom,(
% 8.97/2.68 ! [X1 : nat,X2 : nat] : ((ts @ X1 @ X2) = (ts @ X2 @ X1))),
% 8.97/2.68 file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz29)).
% 8.97/2.68 thf(f1212,plain,(
% 8.97/2.68 ($true = (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ (ts @ (den @ y) @ (den @ x)))) @ (fr @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (den @ y) @ (den @ x))))) | ~spl0_4),
% 8.97/2.68 inference(trivial_inequality_removal,[status(thm)],[f1201])).
% 8.97/2.68 thf(f1201,plain,(
% 8.97/2.68 ($true != $true) | ($true = (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ (ts @ (den @ y) @ (den @ x)))) @ (fr @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (den @ y) @ (den @ x))))) | ~spl0_4),
% 8.97/2.68 inference(superposition,[status(thm)],[f908,f214])).
% 8.97/2.68 thf(f214,plain,(
% 8.97/2.68 ( ! [X2 : nat,X0 : frac,X1 : frac] : (($true = (eq @ (pf @ X1 @ X0) @ (pf @ (fr @ (ts @ (num @ X1) @ X2) @ (ts @ (den @ X1) @ X2)) @ X0)))) )),
% 8.97/2.68 inference(trivial_inequality_removal,[status(thm)],[f202])).
% 8.97/2.68 thf(f202,plain,(
% 8.97/2.68 ( ! [X2 : nat,X0 : frac,X1 : frac] : (($true = (eq @ (pf @ X1 @ X0) @ (pf @ (fr @ (ts @ (num @ X1) @ X2) @ (ts @ (den @ X1) @ X2)) @ X0))) | ($true != $true)) )),
% 8.97/2.68 inference(superposition,[status(thm)],[f84,f44])).
% 8.97/2.68 thf(f44,plain,(
% 8.97/2.68 ( ! [X0 : frac] : (((eq @ X0 @ X0) = $true)) )),
% 8.97/2.68 inference(cnf_transformation,[status(thm)],[f17])).
% 8.97/2.68 thf(f17,plain,(
% 8.97/2.68 ! [X0 : frac] : ((eq @ X0 @ X0) = $true)),
% 8.97/2.68 inference(fool_elimination,[status(thm)],[f16])).
% 8.97/2.68 thf(f16,plain,(
% 8.97/2.68 ! [X0 : frac] : (eq @ X0 @ X0)),
% 8.97/2.68 inference(rectify,[status(thm)],[f6])).
% 8.97/2.68 thf(f6,axiom,(
% 8.97/2.68 ! [X1 : frac] : (eq @ X1 @ X1)),
% 8.97/2.68 file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz37)).
% 8.97/2.68 thf(f84,plain,(
% 8.97/2.68 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : nat] : (((eq @ X2 @ X3) != $true) | ($true = (eq @ (pf @ X0 @ X2) @ (pf @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)) @ X3)))) )),
% 8.97/2.68 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 8.97/2.68 thf(f82,plain,(
% 8.97/2.68 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : nat] : (((eq @ X2 @ X3) != $true) | ($true != $true) | ($true = (eq @ (pf @ X0 @ X2) @ (pf @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)) @ X3)))) )),
% 8.97/2.68 inference(superposition,[status(thm)],[f46,f49])).
% 8.97/2.68 thf(f49,plain,(
% 8.97/2.68 ( ! [X0 : frac,X1 : nat] : (($true = (eq @ X0 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1))))) )),
% 8.97/2.68 inference(cnf_transformation,[status(thm)],[f19])).
% 8.97/2.68 thf(f19,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : nat] : ($true = (eq @ X0 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1))))),
% 8.97/2.68 inference(fool_elimination,[status(thm)],[f18])).
% 8.97/2.68 thf(f18,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : nat] : (eq @ X0 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)))),
% 8.97/2.68 inference(rectify,[status(thm)],[f5])).
% 8.97/2.68 thf(f5,axiom,(
% 8.97/2.68 ! [X1 : frac,X4 : nat] : (eq @ X1 @ (fr @ (ts @ (num @ X1) @ X4) @ (ts @ (den @ X1) @ X4)))),
% 8.97/2.68 file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz40)).
% 8.97/2.68 thf(f46,plain,(
% 8.97/2.68 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != (eq @ X0 @ X3)) | ($true = (eq @ (pf @ X0 @ X1) @ (pf @ X3 @ X2))) | ((eq @ X1 @ X2) != $true)) )),
% 8.97/2.68 inference(cnf_transformation,[status(thm)],[f40])).
% 8.97/2.68 thf(f40,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true != (eq @ X0 @ X3)) | ($true = (eq @ (pf @ X0 @ X1) @ (pf @ X3 @ X2))) | ((eq @ X1 @ X2) != $true))),
% 8.97/2.68 inference(flattening,[status(thm)],[f39])).
% 8.97/2.68 thf(f39,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((($true = (eq @ (pf @ X0 @ X1) @ (pf @ X3 @ X2))) | ((eq @ X1 @ X2) != $true)) | ($true != (eq @ X0 @ X3)))),
% 8.97/2.68 inference(ennf_transformation,[status(thm)],[f31])).
% 8.97/2.68 thf(f31,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true = (eq @ X0 @ X3)) => (((eq @ X1 @ X2) = $true) => ($true = (eq @ (pf @ X0 @ X1) @ (pf @ X3 @ X2)))))),
% 8.97/2.68 inference(fool_elimination,[status(thm)],[f30])).
% 8.97/2.68 thf(f30,plain,(
% 8.97/2.68 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X3) => ((eq @ X1 @ X2) => (eq @ (pf @ X0 @ X1) @ (pf @ X3 @ X2))))),
% 8.97/2.68 inference(rectify,[status(thm)],[f4])).
% 8.97/2.68 thf(f4,axiom,(
% 8.97/2.68 ! [X1 : frac,X3 : frac,X0 : frac,X2 : frac] : ((eq @ X1 @ X2) => ((eq @ X3 @ X0) => (eq @ (pf @ X1 @ X3) @ (pf @ X2 @ X0))))),
% 8.97/2.68 file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz56)).
% 8.97/2.68 thf(f908,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : frac] : (($true != (eq @ X1 @ (pf @ (fr @ (ts @ (num @ y) @ (den @ x)) @ X0) @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ X0)))) | ((eq @ X1 @ (fr @ (ts @ (num @ x) @ (den @ y)) @ X0)) = $true)) ) | ~spl0_4),
% 8.97/2.68 inference(trivial_inequality_removal,[status(thm)],[f896])).
% 8.97/2.68 thf(f896,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : frac] : (($true != (eq @ X1 @ (pf @ (fr @ (ts @ (num @ y) @ (den @ x)) @ X0) @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ X0)))) | ((eq @ X1 @ (fr @ (ts @ (num @ x) @ (den @ y)) @ X0)) = $true) | ($true != $true)) ) | ~spl0_4),
% 8.97/2.68 inference(superposition,[status(thm)],[f50,f818])).
% 8.97/2.68 thf(f818,plain,(
% 8.97/2.68 ( ! [X0 : nat] : (($true = (eq @ (pf @ (fr @ (ts @ (num @ y) @ (den @ x)) @ X0) @ (fr @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))) @ X0)) @ (fr @ (ts @ (num @ x) @ (den @ y)) @ X0)))) ) | ~spl0_4),
% 8.97/2.68 inference(superposition,[status(thm)],[f53,f744])).
% 8.97/2.68 thf(f744,plain,(
% 8.97/2.68 ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))))) | ~spl0_4),
% 8.97/2.68 inference(avatar_component_clause,[status(thm)],[f742])).
% 8.97/2.68 thf(f53,plain,(
% 8.97/2.68 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = (eq @ (pf @ (fr @ X2 @ X1) @ (fr @ X0 @ X1)) @ (fr @ (pl @ X2 @ X0) @ X1)))) )),
% 8.97/2.68 inference(cnf_transformation,[status(thm)],[f21])).
% 8.97/2.68 thf(f21,plain,(
% 8.97/2.68 ! [X0 : nat,X1 : nat,X2 : nat] : ($true = (eq @ (pf @ (fr @ X2 @ X1) @ (fr @ X0 @ X1)) @ (fr @ (pl @ X2 @ X0) @ X1)))),
% 8.97/2.68 inference(fool_elimination,[status(thm)],[f20])).
% 8.97/2.68 thf(f20,plain,(
% 8.97/2.68 ! [X0 : nat,X1 : nat,X2 : nat] : (eq @ (pf @ (fr @ X2 @ X1) @ (fr @ X0 @ X1)) @ (fr @ (pl @ X2 @ X0) @ X1))),
% 8.97/2.68 inference(rectify,[status(thm)],[f8])).
% 8.97/2.68 thf(f8,axiom,(
% 8.97/2.68 ! [X6 : nat,X4 : nat,X5 : nat] : (eq @ (pf @ (fr @ X5 @ X4) @ (fr @ X6 @ X4)) @ (fr @ (pl @ X5 @ X6) @ X4))),
% 8.97/2.68 file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz57)).
% 8.97/2.68 thf(f745,plain,(
% 8.97/2.68 spl0_4 | ~spl0_3),
% 8.97/2.68 inference(avatar_split_clause,[status(thm)],[f692,f110,f742])).
% 8.97/2.68 thf(f110,definition,(
% 8.97/2.68 spl0_3 <=> ($true = (some @ (^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0)))))),
% 8.97/2.68 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 8.97/2.68 thf(f692,plain,(
% 8.97/2.68 ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))))) | ~spl0_3),
% 8.97/2.68 inference(subsumption_resolution,[status(thm)],[f691,f609])).
% 8.97/2.68 thf(f609,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (((ts @ (num @ x) @ (den @ y)) != (pl @ (ts @ (num @ y) @ (den @ x)) @ (sK2 @ X1 @ X0))) | ((pl @ X0 @ (sK2 @ X1 @ X0)) != X1) | ((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1)) ) | ~spl0_3),
% 8.97/2.68 inference(equality_proxy_clausification,[status(thm)],[f608])).
% 8.97/2.68 thf(f608,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (($false = ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ (sK2 @ X1 @ X0)))) | ((pl @ X0 @ (sK2 @ X1 @ X0)) != X1) | ((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1)) ) | ~spl0_3),
% 8.97/2.68 inference(equality_proxy_clausification,[status(thm)],[f607])).
% 8.97/2.68 thf(f607,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : ((((pl @ X0 @ (sK2 @ X1 @ X0)) = X1) = $false) | ((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1) | ($false = ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ (sK2 @ X1 @ X0))))) ) | ~spl0_3),
% 8.97/2.68 inference(binary_proxy_clausification,[status(thm)],[f605])).
% 8.97/2.68 thf(f605,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : ((((pl @ X0 @ (sK2 @ X1 @ X0)) = X1) != ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ (sK2 @ X1 @ X0)))) | ((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1)) ) | ~spl0_3),
% 8.97/2.68 inference(beta_eta_normalization,[status(thm)],[f604])).
% 8.97/2.68 thf(f604,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1) | (((^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0))) @ (sK2 @ X1 @ X0)) != ((^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)) @ (sK2 @ X1 @ X0)))) ) | ~spl0_3),
% 8.97/2.68 inference(negative_extensionality,[status(thm)],[f603])).
% 8.97/2.68 thf(f603,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (((^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)) != (^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0)))) | ((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1)) ) | ~spl0_3),
% 8.97/2.68 inference(trivial_inequality_removal,[status(thm)],[f602])).
% 8.97/2.68 thf(f602,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1) | ($true != $true) | ((^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)) != (^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0))))) ) | ~spl0_3),
% 8.97/2.68 inference(constrained_superposition,[status(thm)],[f68,f112])).
% 8.97/2.68 thf(f112,plain,(
% 8.97/2.68 ($true = (some @ (^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0))))) | ~spl0_3),
% 8.97/2.68 inference(avatar_component_clause,[status(thm)],[f110])).
% 8.97/2.68 thf(f68,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (($true != (some @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) | ((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1)) )),
% 8.97/2.68 inference(equality_proxy_clausification,[status(thm)],[f67])).
% 8.97/2.68 thf(f67,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (($true != (some @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) | ($true = ((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1))) )),
% 8.97/2.68 inference(beta_eta_normalization,[status(thm)],[f66])).
% 8.97/2.68 thf(f66,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (($true != (some @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) | ($true = ((^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)) @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))))) )),
% 8.97/2.68 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 8.97/2.68 thf(f65,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != (some @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) | ($true = ((^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)) @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))))) )),
% 8.97/2.68 inference(superposition,[status(thm)],[f43,f52])).
% 8.97/2.68 thf(f52,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (($true = (amone @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1))))) )),
% 8.97/2.68 inference(cnf_transformation,[status(thm)],[f15])).
% 8.97/2.68 thf(f15,plain,(
% 8.97/2.68 ! [X0 : nat,X1 : nat] : ($true = (amone @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1))))),
% 8.97/2.68 inference(fool_elimination,[status(thm)],[f14])).
% 8.97/2.68 thf(f14,plain,(
% 8.97/2.68 ! [X0 : nat,X1 : nat] : (amone @ (^[X2 : nat] : (((pl @ X0 @ X2) = X1))))),
% 8.97/2.68 inference(rectify,[status(thm)],[f2])).
% 8.97/2.68 thf(f2,axiom,(
% 8.97/2.68 ! [X2 : nat,X1 : nat] : (amone @ (^[X3 : nat] : (((pl @ X2 @ X3) = X1))))),
% 8.97/2.68 file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz8b)).
% 8.97/2.68 thf(f43,plain,(
% 8.97/2.68 ( ! [X0 : nat > $o] : (($true != (amone @ X0)) | ($true != (some @ X0)) | ($true = (X0 @ (ind @ X0)))) )),
% 8.97/2.68 inference(cnf_transformation,[status(thm)],[f38])).
% 8.97/2.68 thf(f38,plain,(
% 8.97/2.68 ! [X0 : nat > $o] : (($true != (amone @ X0)) | ($true != (some @ X0)) | ($true = (X0 @ (ind @ X0))))),
% 8.97/2.68 inference(flattening,[status(thm)],[f37])).
% 8.97/2.68 thf(f37,plain,(
% 8.97/2.68 ! [X0 : nat > $o] : (($true = (X0 @ (ind @ X0))) | (($true != (some @ X0)) | ($true != (amone @ X0))))),
% 8.97/2.68 inference(ennf_transformation,[status(thm)],[f36])).
% 8.97/2.68 thf(f36,plain,(
% 8.97/2.68 ! [X0 : nat > $o] : (~(($true = (amone @ X0)) => ($true != (some @ X0))) => ($true = (X0 @ (ind @ X0))))),
% 8.97/2.68 inference(flattening,[status(thm)],[f33])).
% 8.97/2.68 thf(f33,plain,(
% 8.97/2.68 ! [X0 : nat > $o] : (~(($true = (amone @ X0)) => ~($true = (some @ X0))) => ($true = (X0 @ (ind @ X0))))),
% 8.97/2.68 inference(fool_elimination,[status(thm)],[f32])).
% 8.97/2.68 thf(f32,plain,(
% 8.97/2.68 ! [X0 : nat > $o] : (~((amone @ X0) => ~(some @ X0)) => (X0 @ (ind @ X0)))),
% 8.97/2.68 inference(rectify,[status(thm)],[f9])).
% 8.97/2.68 thf(f9,axiom,(
% 8.97/2.68 ! [X7 : nat > $o] : (~((amone @ X7) => ~(some @ X7)) => (X7 @ (ind @ X7)))),
% 8.97/2.68 file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',oneax)).
% 8.97/2.68 thf(f691,plain,(
% 8.97/2.68 ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = (ts @ (num @ x) @ (den @ y))))))) | ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ (sK2 @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))))) | ~spl0_3),
% 8.97/2.68 inference(equality_resolution,[status(thm)],[f663])).
% 8.97/2.68 thf(f663,plain,(
% 8.97/2.68 ( ! [X0 : nat] : (((ts @ (num @ x) @ (den @ y)) != X0) | ((pl @ (ts @ (num @ y) @ (den @ x)) @ (ind @ (^[Y0 : nat]: ((pl @ (ts @ (num @ y) @ (den @ x)) @ Y0) = X0)))) = X0) | ((pl @ (ts @ (num @ y) @ (den @ x)) @ (sK2 @ X0 @ (ts @ (num @ y) @ (den @ x)))) = X0)) ) | ~spl0_3),
% 8.97/2.68 inference(equality_factoring,[status(thm)],[f611])).
% 8.97/2.68 thf(f611,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ (sK2 @ X1 @ X0))) | ((pl @ X0 @ (sK2 @ X1 @ X0)) = X1) | ((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1)) ) | ~spl0_3),
% 8.97/2.68 inference(equality_proxy_clausification,[status(thm)],[f610])).
% 8.97/2.68 thf(f610,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ (sK2 @ X1 @ X0))) | (((pl @ X0 @ (sK2 @ X1 @ X0)) = X1) = $true) | ((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1)) ) | ~spl0_3),
% 8.97/2.68 inference(equality_proxy_clausification,[status(thm)],[f606])).
% 8.97/2.68 thf(f606,plain,(
% 8.97/2.68 ( ! [X0 : nat,X1 : nat] : (($true = ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ (sK2 @ X1 @ X0)))) | ((pl @ X0 @ (ind @ (^[Y0 : nat]: ((pl @ X0 @ Y0) = X1)))) = X1) | (((pl @ X0 @ (sK2 @ X1 @ X0)) = X1) = $true)) ) | ~spl0_3),
% 8.97/2.68 inference(binary_proxy_clausification,[status(thm)],[f605])).
% 8.97/2.68 thf(f113,plain,(
% 8.97/2.68 spl0_3),
% 8.97/2.68 inference(avatar_split_clause,[status(thm)],[f45,f110])).
% 8.97/2.68 thf(f45,plain,(
% 8.97/2.68 ($true = (some @ (^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0)))))),
% 8.97/2.68 inference(cnf_transformation,[status(thm)],[f25])).
% 8.97/2.68 thf(f25,plain,(
% 8.97/2.68 ($true = (some @ (^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0)))))),
% 8.97/2.68 inference(fool_elimination,[status(thm)],[f24])).
% 8.97/2.68 thf(f24,plain,(
% 8.97/2.68 (some @ (^[X0 : nat] : (((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ X0)))))),
% 8.97/2.68 inference(rectify,[status(thm)],[f1])).
% 8.97/2.68 thf(f1,axiom,(
% 8.97/2.68 (some @ (^[X0 : nat] : (((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ X0)))))),
% 8.97/2.68 file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',m)).
% 8.97/2.68 thf(f63,plain,(
% 8.97/2.68 ~spl0_2),
% 8.97/2.68 inference(avatar_split_clause,[status(thm)],[f51,f60])).
% 8.97/2.68 thf(f51,plain,(
% 8.97/2.68 ($true != (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0)))) @ (ts @ (den @ x) @ (den @ y)))) @ x))),
% 8.97/2.68 inference(cnf_transformation,[status(thm)],[f35])).
% 8.97/2.68 thf(f35,plain,(
% 8.97/2.68 ($true != (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0)))) @ (ts @ (den @ x) @ (den @ y)))) @ x))),
% 8.97/2.68 inference(flattening,[status(thm)],[f27])).
% 8.97/2.68 thf(f27,plain,(
% 8.97/2.68 ~($true = (eq @ (pf @ y @ (fr @ (ind @ (^[Y0 : nat]: ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ Y0)))) @ (ts @ (den @ x) @ (den @ y)))) @ x))),
% 8.97/2.68 inference(fool_elimination,[status(thm)],[f26])).
% 8.97/2.68 thf(f26,plain,(
% 8.97/2.68 ~(eq @ (pf @ y @ (fr @ (ind @ (^[X0 : nat] : (((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ X0))))) @ (ts @ (den @ x) @ (den @ y)))) @ x)),
% 8.97/2.68 inference(rectify,[status(thm)],[f12])).
% 8.97/2.68 thf(f12,negated_conjecture,(
% 8.97/2.68 ~(eq @ (pf @ y @ (fr @ (ind @ (^[X8 : nat] : (((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ X8))))) @ (ts @ (den @ x) @ (den @ y)))) @ x)),
% 8.97/2.68 inference(negated_conjecture,[status(cth)],[f11])).
% 8.97/2.68 thf(f11,conjecture,(
% 8.97/2.68 (eq @ (pf @ y @ (fr @ (ind @ (^[X8 : nat] : (((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ X8))))) @ (ts @ (den @ x) @ (den @ y)))) @ x)),
% 8.97/2.68 file('/export/starexec/sandbox/tmp/tmp.qa7tL2SBjR/DTF2THF_13252.p',satz67c)).
% 8.97/2.68 % SZS output end Proof for DTF2THF_13252
% 8.97/2.68 % (13676)------------------------------
% 8.97/2.68 % (13676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.97/2.68 % (13676)Termination reason: Refutation
% 8.97/2.68
% 8.97/2.68 % (13676)Memory used [KB]: 7419
% 8.97/2.68 % (13676)Time elapsed: 0.419 s
% 8.97/2.68 % (13676)Instructions burned: 1381 (million)
% 8.97/2.68 % (13676)------------------------------
% 8.97/2.68 % (13676)------------------------------
% 8.97/2.68 % (13579)Success in time 1.344 s
%------------------------------------------------------------------------------