%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV174^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n029.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 09:40:28 AM UTC 2026
% Result : Theorem 1.63s 1.55s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 86 ( 2 unt; 0 typ; 8 def)
% Number of atoms : 795 ( 258 equ; 0 cnn)
% Maximal formula atoms : 17 ( 9 avg)
% Number of connectives : 771 ( 161 ~; 155 |; 97 &; 317 @)
% ( 13 <=>; 25 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 107 ( 107 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 12 con; 0-2 aty)
% Number of variables : 166 ( 0 ^; 109 !; 57 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cP: ( a > $o ) > $o ).
thf(func_def_5,type,
sP0: a > $o ).
thf(func_def_6,type,
sP1: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_7,type,
sP2: ( a > $o ) > $o ).
thf(func_def_9,type,
sK4: a > $o ).
thf(func_def_10,type,
sK5: a > $o ).
thf(func_def_11,type,
sK6: ( a > $o ) > a ).
thf(func_def_12,type,
sK7: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_13,type,
sK8: a > a > $o ).
thf(func_def_14,type,
sK9: ( a > $o ) > a ).
thf(func_def_15,type,
sK10: a > $o ).
thf(func_def_17,type,
ph12:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK13: a ).
thf(f194,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f56,f61,f66,f74,f78,f83,f96,f102,f192]) ).
thf(f192,plain,
( spl11_2
| ~ spl11_3
| ~ spl11_4
| ~ spl11_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f191]) ).
thf(f191,plain,
( $false
| spl11_2
| ~ spl11_3
| ~ spl11_4
| ~ spl11_8 ),
inference(subsumption_resolution,[status(thm)],[f190,f151]) ).
thf(f151,plain,
( ( $true
= ( sK4 @ ( sK7 @ sK5 @ sK4 ) ) )
| ~ spl11_3 ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ( $true != $true )
| ( $true
= ( sK4 @ ( sK7 @ sK5 @ sK4 ) ) )
| ~ spl11_3 ),
inference(superposition,[status(thm)],[f40,f60]) ).
thf(f60,plain,
( ( $true
= ( sP1 @ sK5 @ sK4 ) )
| ~ spl11_3 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl11_3
<=> ( $true
= ( sP1 @ sK5 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition]) ).
thf(f40,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sP1 @ X1 @ X0 ) )
| ( $true
= ( X0 @ ( sK7 @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: a > $o,X1: a > $o] :
( ( ( $true
= ( X0 @ ( sK7 @ X1 @ X0 ) ) )
& ( $true
= ( X1 @ ( sK7 @ X1 @ X0 ) ) ) )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f22,f23]) ).
thf(f23,plain,
! [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( $true
= ( X1 @ X2 ) ) )
=> ( ( $true
= ( X0 @ ( sK7 @ X1 @ X0 ) ) )
& ( $true
= ( X1 @ ( sK7 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
! [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( $true
= ( X1 @ X2 ) ) )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
! [X11: a > $o,X10: a > $o] :
( ? [X12: a] :
( ( $true
= ( X11 @ X12 ) )
& ( $true
= ( X10 @ X12 ) ) )
| ( $true
!= ( sP1 @ X10 @ X11 ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X11: a > $o,X10: a > $o] :
( ? [X12: a] :
( ( $true
= ( X11 @ X12 ) )
& ( $true
= ( X10 @ X12 ) ) )
| ( $true
!= ( sP1 @ X10 @ X11 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f190,plain,
( ( $true
!= ( sK4 @ ( sK7 @ sK5 @ sK4 ) ) )
| spl11_2
| ~ spl11_3
| ~ spl11_4
| ~ spl11_8 ),
inference(trivial_inequality_removal,[status(thm)],[f187]) ).
thf(f187,plain,
( ( $true
!= ( sK4 @ ( sK7 @ sK5 @ sK4 ) ) )
| ( $true != $true )
| spl11_2
| ~ spl11_3
| ~ spl11_4
| ~ spl11_8 ),
inference(superposition,[status(thm)],[f176,f145]) ).
thf(f145,plain,
( ( $true
= ( sK5 @ ( sK7 @ sK5 @ sK4 ) ) )
| ~ spl11_3 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ( $true != $true )
| ( $true
= ( sK5 @ ( sK7 @ sK5 @ sK4 ) ) )
| ~ spl11_3 ),
inference(superposition,[status(thm)],[f39,f60]) ).
thf(f39,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sP1 @ X1 @ X0 ) )
| ( $true
= ( X1 @ ( sK7 @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f176,plain,
( ! [X0: a] :
( ( $true
!= ( sK5 @ X0 ) )
| ( $true
!= ( sK4 @ X0 ) ) )
| spl11_2
| ~ spl11_4
| ~ spl11_8 ),
inference(subsumption_resolution,[status(thm)],[f175,f55]) ).
thf(f55,plain,
( ( sK5 != sK4 )
| spl11_2 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl11_2
<=> ( sK5 = sK4 ) ),
introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition]) ).
thf(f175,plain,
( ! [X0: a] :
( ( $true
!= ( sK4 @ X0 ) )
| ( sK5 = sK4 )
| ( $true
!= ( sK5 @ X0 ) ) )
| ~ spl11_4
| ~ spl11_8 ),
inference(trivial_inequality_removal,[status(thm)],[f171]) ).
thf(f171,plain,
( ! [X0: a] :
( ( $true
!= ( sK5 @ X0 ) )
| ( sK5 = sK4 )
| ( $true != $true )
| ( $true
!= ( sK4 @ X0 ) ) )
| ~ spl11_4
| ~ spl11_8 ),
inference(superposition,[status(thm)],[f137,f82]) ).
thf(f82,plain,
( ( $true
= ( cP @ sK4 ) )
| ~ spl11_8 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f80,definition,
( spl11_8
<=> ( $true
= ( cP @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_8])],[avatar_definition]) ).
thf(f137,plain,
( ! [X0: a > $o,X1: a] :
( ( ( cP @ X0 )
!= $true )
| ( $true
!= ( sK5 @ X1 ) )
| ( sK5 = X0 )
| ( ( X0 @ X1 )
!= $true ) )
| ~ spl11_4 ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ! [X0: a > $o,X1: a] :
( ( ( X0 @ X1 )
!= $true )
| ( $true
!= ( sK5 @ X1 ) )
| ( sK5 = X0 )
| ( ( cP @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl11_4 ),
inference(superposition,[status(thm)],[f44,f65]) ).
thf(f65,plain,
( ( $true
= ( cP @ sK5 ) )
| ~ spl11_4 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl11_4
<=> ( $true
= ( cP @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_4])],[avatar_definition]) ).
thf(f44,plain,
! [X6: a > $o,X7: a,X5: a > $o] :
( ( ( cP @ X6 )
!= $true )
| ( X5 = X6 )
| ( ( cP @ X5 )
!= $true )
| ( $true
!= ( X6 @ X7 ) )
| ( $true
!= ( X5 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ! [X0: a > $o] :
( ( $true
= ( X0 @ ( sK9 @ X0 ) ) )
| ( ( cP @ X0 )
!= $true ) )
& ! [X2: a > $o] :
( ( ! [X4: a] :
( $true
!= ( sK10 @ X4 ) )
& ( $true
= ( cP @ sK10 ) ) )
| ( sP3 = $true )
| ( $true
= ( sP2 @ X2 ) ) )
& ! [X5: a > $o,X6: a > $o,X7: a] :
( ( $true
!= ( X6 @ X7 ) )
| ( $true
!= ( X5 @ X7 ) )
| ( ( cP @ X5 )
!= $true )
| ( ( cP @ X6 )
!= $true )
| ( X5 = X6 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f29,f31,f30]) ).
thf(f30,plain,
! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
= $true )
=> ( $true
= ( X0 @ ( sK9 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ? [X3: a > $o] :
( ! [X4: a] :
( $true
!= ( X3 @ X4 ) )
& ( ( cP @ X3 )
= $true ) )
=> ( ! [X4: a] :
( $true
!= ( sK10 @ X4 ) )
& ( $true
= ( cP @ sK10 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
= $true )
| ( ( cP @ X0 )
!= $true ) )
& ! [X2: a > $o] :
( ? [X3: a > $o] :
( ! [X4: a] :
( $true
!= ( X3 @ X4 ) )
& ( ( cP @ X3 )
= $true ) )
| ( sP3 = $true )
| ( $true
= ( sP2 @ X2 ) ) )
& ! [X5: a > $o,X6: a > $o,X7: a] :
( ( $true
!= ( X6 @ X7 ) )
| ( $true
!= ( X5 @ X7 ) )
| ( ( cP @ X5 )
!= $true )
| ( ( cP @ X6 )
!= $true )
| ( X5 = X6 ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
= $true )
| ( ( cP @ X0 )
!= $true ) )
& ! [X5: a > $o] :
( ? [X6: a > $o] :
( ! [X7: a] :
( $true
!= ( X6 @ X7 ) )
& ( ( cP @ X6 )
= $true ) )
| ( sP3 = $true )
| ( $true
= ( sP2 @ X5 ) ) )
& ! [X4: a > $o,X2: a > $o,X3: a] :
( ( $true
!= ( X2 @ X3 ) )
| ( $true
!= ( X4 @ X3 ) )
| ( $true
!= ( cP @ X4 ) )
| ( $true
!= ( cP @ X2 ) )
| ( X2 = X4 ) ) ),
inference(definition_folding,[status(thm)],[f7,f11,f10,f9,f8]) ).
thf(f8,plain,
! [X8: a] :
( ( $true
= ( sP0 @ X8 ) )
<=> ? [X9: a > $o] :
( ( $true
= ( X9 @ X8 ) )
& ( $true
= ( cP @ X9 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f10,plain,
! [X5: a > $o] :
( ? [X8: a] :
( ( $true
= ( X5 @ X8 ) )
<~> ( $true
= ( sP0 @ X8 ) ) )
| ( $true
!= ( sP2 @ X5 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f11,plain,
( ? [X11: a > $o,X10: a > $o] :
( ( $true
= ( sP1 @ X10 @ X11 ) )
& ( X10 != X11 )
& ( $true
= ( cP @ X11 ) )
& ( $true
= ( cP @ X10 ) ) )
| ( sP3 != $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f7,plain,
( ! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
= $true )
| ( ( cP @ X0 )
!= $true ) )
& ! [X5: a > $o] :
( ? [X6: a > $o] :
( ! [X7: a] :
( $true
!= ( X6 @ X7 ) )
& ( ( cP @ X6 )
= $true ) )
| ? [X11: a > $o,X10: a > $o] :
( ? [X12: a] :
( ( $true
= ( X11 @ X12 ) )
& ( $true
= ( X10 @ X12 ) ) )
& ( X10 != X11 )
& ( $true
= ( cP @ X11 ) )
& ( $true
= ( cP @ X10 ) ) )
| ? [X8: a] :
( ( $true
= ( X5 @ X8 ) )
<~> ? [X9: a > $o] :
( ( $true
= ( X9 @ X8 ) )
& ( $true
= ( cP @ X9 ) ) ) ) )
& ! [X4: a > $o,X2: a > $o,X3: a] :
( ( $true
!= ( X2 @ X3 ) )
| ( $true
!= ( X4 @ X3 ) )
| ( $true
!= ( cP @ X4 ) )
| ( $true
!= ( cP @ X2 ) )
| ( X2 = X4 ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X5: a > $o] :
( ? [X6: a > $o] :
( ! [X7: a] :
( $true
!= ( X6 @ X7 ) )
& ( ( cP @ X6 )
= $true ) )
| ? [X11: a > $o,X10: a > $o] :
( ( X10 != X11 )
& ( $true
= ( cP @ X10 ) )
& ? [X12: a] :
( ( $true
= ( X11 @ X12 ) )
& ( $true
= ( X10 @ X12 ) ) )
& ( $true
= ( cP @ X11 ) ) )
| ? [X8: a] :
( ( $true
= ( X5 @ X8 ) )
<~> ? [X9: a > $o] :
( ( $true
= ( X9 @ X8 ) )
& ( $true
= ( cP @ X9 ) ) ) ) )
& ! [X3: a,X2: a > $o,X4: a > $o] :
( ( X2 = X4 )
| ( $true
!= ( X2 @ X3 ) )
| ( $true
!= ( cP @ X2 ) )
| ( $true
!= ( X4 @ X3 ) )
| ( $true
!= ( cP @ X4 ) ) )
& ! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
= $true )
| ( ( cP @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X3: a,X2: a > $o,X4: a > $o] :
( ( ( $true
= ( X2 @ X3 ) )
& ( $true
= ( cP @ X2 ) )
& ( $true
= ( X4 @ X3 ) )
& ( $true
= ( cP @ X4 ) ) )
=> ( X2 = X4 ) )
& ! [X0: a > $o] :
( ( ( cP @ X0 )
= $true )
=> ? [X1: a] :
( ( X0 @ X1 )
= $true ) ) )
=> ? [X5: a > $o] :
( ! [X6: a > $o] :
( ( ( cP @ X6 )
= $true )
=> ? [X7: a] :
( $true
= ( X6 @ X7 ) ) )
& ! [X11: a > $o,X10: a > $o] :
( ( ( $true
= ( cP @ X10 ) )
& ? [X12: a] :
( ( $true
= ( X11 @ X12 ) )
& ( $true
= ( X10 @ X12 ) ) )
& ( $true
= ( cP @ X11 ) ) )
=> ( X10 = X11 ) )
& ! [X8: a] :
( ( $true
= ( X5 @ X8 ) )
<=> ? [X9: a > $o] :
( ( $true
= ( X9 @ X8 ) )
& ( $true
= ( cP @ X9 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a > $o] :
( ( cP @ X0 )
=> ? [X1: a] : ( X0 @ X1 ) )
& ! [X2: a > $o,X3: a,X4: a > $o] :
( ( ( X4 @ X3 )
& ( X2 @ X3 )
& ( cP @ X4 )
& ( cP @ X2 ) )
=> ( X2 = X4 ) ) )
=> ? [X5: a > $o] :
( ! [X6: a > $o] :
( ( cP @ X6 )
=> ? [X7: a] : ( X6 @ X7 ) )
& ! [X8: a] :
( ( X5 @ X8 )
<=> ? [X9: a > $o] :
( ( X9 @ X8 )
& ( cP @ X9 ) ) )
& ! [X10: a > $o,X11: a > $o] :
( ( ( cP @ X11 )
& ? [X12: a] :
( ( X10 @ X12 )
& ( X11 @ X12 ) )
& ( cP @ X10 ) )
=> ( X10 = X11 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: a > $o] :
( ( cP @ X0 )
=> ? [X1: a] : ( X0 @ X1 ) )
& ! [X0: a > $o,X2: a,X3: a > $o] :
( ( ( X3 @ X2 )
& ( X0 @ X2 )
& ( cP @ X3 )
& ( cP @ X0 ) )
=> ( X0 = X3 ) ) )
=> ? [X4: a > $o] :
( ! [X5: a > $o] :
( ( cP @ X5 )
=> ? [X2: a] : ( X5 @ X2 ) )
& ! [X2: a] :
( ( X4 @ X2 )
<=> ? [X6: a > $o] :
( ( X6 @ X2 )
& ( cP @ X6 ) ) )
& ! [X8: a > $o,X7: a > $o] :
( ( ( cP @ X7 )
& ? [X2: a] :
( ( X8 @ X2 )
& ( X7 @ X2 ) )
& ( cP @ X8 ) )
=> ( X7 = X8 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: a > $o] :
( ( cP @ X0 )
=> ? [X1: a] : ( X0 @ X1 ) )
& ! [X0: a > $o,X2: a,X3: a > $o] :
( ( ( X3 @ X2 )
& ( X0 @ X2 )
& ( cP @ X3 )
& ( cP @ X0 ) )
=> ( X0 = X3 ) ) )
=> ? [X4: a > $o] :
( ! [X5: a > $o] :
( ( cP @ X5 )
=> ? [X2: a] : ( X5 @ X2 ) )
& ! [X2: a] :
( ( X4 @ X2 )
<=> ? [X6: a > $o] :
( ( X6 @ X2 )
& ( cP @ X6 ) ) )
& ! [X8: a > $o,X7: a > $o] :
( ( ( cP @ X7 )
& ? [X2: a] :
( ( X8 @ X2 )
& ( X7 @ X2 ) )
& ( cP @ X8 ) )
=> ( X7 = X8 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0UVNMSvSYe/DTF2THF_15857.p',cTHM555_pme) ).
thf(f102,plain,
( ~ spl11_5
| ~ spl11_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f101]) ).
thf(f101,plain,
( $false
| ~ spl11_5
| ~ spl11_7 ),
inference(subsumption_resolution,[status(thm)],[f99,f77]) ).
thf(f77,plain,
( ! [X4: a] :
( $true
!= ( sK10 @ X4 ) )
| ~ spl11_7 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f76,definition,
( spl11_7
<=> ! [X4: a] :
( $true
!= ( sK10 @ X4 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_7])],[avatar_definition]) ).
thf(f99,plain,
( ( ( sK10 @ ( sK9 @ sK10 ) )
= $true )
| ~ spl11_5 ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ( sK10 @ ( sK9 @ sK10 ) )
= $true )
| ( $true != $true )
| ~ spl11_5 ),
inference(superposition,[status(thm)],[f47,f70]) ).
thf(f70,plain,
( ( $true
= ( cP @ sK10 ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f68,definition,
( spl11_5
<=> ( $true
= ( cP @ sK10 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition]) ).
thf(f47,plain,
! [X0: a > $o] :
( ( ( cP @ X0 )
!= $true )
| ( $true
= ( X0 @ ( sK9 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f96,plain,
~ spl11_6,
inference(avatar_contradiction_clause,[status(thm)],[f95]) ).
thf(f95,plain,
( $false
| ~ spl11_6 ),
inference(subsumption_resolution,[status(thm)],[f94,f86]) ).
thf(f86,plain,
( ! [X0: a > $o] :
( ( $true
!= ( sP0 @ ( sK6 @ X0 ) ) )
| ( $true
!= ( X0 @ ( sK6 @ X0 ) ) ) )
| ~ spl11_6 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ! [X0: a > $o] :
( ( $true
!= ( sP0 @ ( sK6 @ X0 ) ) )
| ( $true
!= ( X0 @ ( sK6 @ X0 ) ) )
| ( $true != $true ) )
| ~ spl11_6 ),
inference(backward_demodulation,[status(thm)],[f38,f73]) ).
thf(f73,plain,
( ! [X2: a > $o] :
( $true
= ( sP2 @ X2 ) )
| ~ spl11_6 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f72,definition,
( spl11_6
<=> ! [X2: a > $o] :
( $true
= ( sP2 @ X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_6])],[avatar_definition]) ).
thf(f38,plain,
! [X0: a > $o] :
( ( $true
!= ( sP0 @ ( sK6 @ X0 ) ) )
| ( $true
!= ( sP2 @ X0 ) )
| ( $true
!= ( X0 @ ( sK6 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: a > $o] :
( ( ( ( $true
!= ( sP0 @ ( sK6 @ X0 ) ) )
| ( $true
!= ( X0 @ ( sK6 @ X0 ) ) ) )
& ( ( $true
= ( sP0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK6 @ X0 ) ) ) ) )
| ( $true
!= ( sP2 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f18,f19]) ).
thf(f19,plain,
! [X0: a > $o] :
( ? [X1: a] :
( ( ( $true
!= ( sP0 @ X1 ) )
| ( ( X0 @ X1 )
!= $true ) )
& ( ( $true
= ( sP0 @ X1 ) )
| ( ( X0 @ X1 )
= $true ) ) )
=> ( ( ( $true
!= ( sP0 @ ( sK6 @ X0 ) ) )
| ( $true
!= ( X0 @ ( sK6 @ X0 ) ) ) )
& ( ( $true
= ( sP0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK6 @ X0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
! [X0: a > $o] :
( ? [X1: a] :
( ( ( $true
!= ( sP0 @ X1 ) )
| ( ( X0 @ X1 )
!= $true ) )
& ( ( $true
= ( sP0 @ X1 ) )
| ( ( X0 @ X1 )
= $true ) ) )
| ( $true
!= ( sP2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
! [X5: a > $o] :
( ? [X8: a] :
( ( ( $true
!= ( sP0 @ X8 ) )
| ( $true
!= ( X5 @ X8 ) ) )
& ( ( $true
= ( sP0 @ X8 ) )
| ( $true
= ( X5 @ X8 ) ) ) )
| ( $true
!= ( sP2 @ X5 ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f94,plain,
( ( $true
= ( sP0 @ ( sK6 @ sP0 ) ) )
| ~ spl11_6 ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
( ( $true
= ( sP0 @ ( sK6 @ sP0 ) ) )
| ( $true != $true )
| ~ spl11_6 ),
inference(equality_factoring,[status(thm)],[f87]) ).
thf(f87,plain,
( ! [X0: a > $o] :
( ( $true
= ( sP0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK6 @ X0 ) ) ) )
| ~ spl11_6 ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
( ! [X0: a > $o] :
( ( $true
= ( X0 @ ( sK6 @ X0 ) ) )
| ( $true != $true )
| ( $true
= ( sP0 @ ( sK6 @ X0 ) ) ) )
| ~ spl11_6 ),
inference(backward_demodulation,[status(thm)],[f37,f73]) ).
thf(f37,plain,
! [X0: a > $o] :
( ( $true
!= ( sP2 @ X0 ) )
| ( $true
= ( sP0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK6 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f83,plain,
( ~ spl11_1
| spl11_8 ),
inference(avatar_split_clause,[status(thm)],[f34,f80,f49]) ).
thf(f49,definition,
( spl11_1
<=> ( sP3 = $true ) ),
introduced(definition,[new_symbols(naming,[spl11_1])],[avatar_definition]) ).
thf(f34,plain,
( ( $true
= ( cP @ sK4 ) )
| ( sP3 != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( $true
= ( sP1 @ sK5 @ sK4 ) )
& ( sK5 != sK4 )
& ( $true
= ( cP @ sK4 ) )
& ( $true
= ( cP @ sK5 ) ) )
| ( sP3 != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( $true
= ( sP1 @ X1 @ X0 ) )
& ( X0 != X1 )
& ( ( cP @ X0 )
= $true )
& ( $true
= ( cP @ X1 ) ) )
=> ( ( $true
= ( sP1 @ sK5 @ sK4 ) )
& ( sK5 != sK4 )
& ( $true
= ( cP @ sK4 ) )
& ( $true
= ( cP @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( $true
= ( sP1 @ X1 @ X0 ) )
& ( X0 != X1 )
& ( ( cP @ X0 )
= $true )
& ( $true
= ( cP @ X1 ) ) )
| ( sP3 != $true ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X11: a > $o,X10: a > $o] :
( ( $true
= ( sP1 @ X10 @ X11 ) )
& ( X10 != X11 )
& ( $true
= ( cP @ X11 ) )
& ( $true
= ( cP @ X10 ) ) )
| ( sP3 != $true ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
thf(f78,plain,
( spl11_6
| spl11_7
| spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f46,f49,f76,f72]) ).
thf(f46,plain,
! [X2: a > $o,X4: a] :
( ( $true
!= ( sK10 @ X4 ) )
| ( $true
= ( sP2 @ X2 ) )
| ( sP3 = $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f74,plain,
( spl11_1
| spl11_5
| spl11_6 ),
inference(avatar_split_clause,[status(thm)],[f45,f72,f68,f49]) ).
thf(f45,plain,
! [X2: a > $o] :
( ( sP3 = $true )
| ( $true
= ( cP @ sK10 ) )
| ( $true
= ( sP2 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f66,plain,
( spl11_4
| ~ spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f33,f49,f63]) ).
thf(f33,plain,
( ( $true
= ( cP @ sK5 ) )
| ( sP3 != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f61,plain,
( spl11_3
| ~ spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f36,f49,f58]) ).
thf(f36,plain,
( ( sP3 != $true )
| ( $true
= ( sP1 @ sK5 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f56,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f35,f53,f49]) ).
thf(f35,plain,
( ( sK5 != sK4 )
| ( sP3 != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV174^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n029.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 12:41:29 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
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SEV174^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.47 % Domain : Set Theory (Sets of sets)
% 0.20/0.47 % Problem : TPS problem from SETS-OF-SETS
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : tps_1049 [Bro09]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.60 v8.2.0, 0.62 v8.1.0, 0.82 v7.5.0, 0.71 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.20/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.20/0.47 % Number of atoms : 9 ( 2 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 9 ( 9 avg)
% 0.20/0.47 % Number of connectives : 31 ( 0 ~; 0 |; 10 &; 15 @)
% 0.20/0.47 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 13 ( 13 avg)
% 0.20/0.47 % Number of types : 2 ( 1 usr)
% 0.20/0.47 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.20/0.47 % Number of variables : 13 ( 0 ^; 8 !; 5 ?; 13 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(a_type,type,
% 0.20/0.47 a: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(cP,type,
% 0.20/0.47 cP: ( a > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(cTHM555_pme,conjecture,
% 0.20/0.47 ( ( ! [Xp: a > $o] :
% 0.20/0.47 ( ( cP @ Xp )
% 0.20/0.47 => ? [Xz: a] : ( Xp @ Xz ) )
% 0.20/0.47 & ! [Xx: a,Xp: a > $o,Xq: a > $o] :
% 0.20/0.47 ( ( ( cP @ Xp )
% 0.20/0.47 & ( cP @ Xq )
% 0.20/0.47 & ( Xp @ Xx )
% 0.20/0.47 & ( Xq @ Xx ) )
% 0.20/0.47 => ( Xp = Xq ) ) )
% 0.20/0.47 => ? [S: a > $o] :
% 0.20/0.47 ( ! [Xa: a > $o] :
% 0.20/0.47 ( ( cP @ Xa )
% 0.20/0.47 => ? [Xx: a] : ( Xa @ Xx ) )
% 0.20/0.47 & ! [Xx: a] :
% 0.20/0.47 ( ( S @ Xx )
% 0.20/0.47 <=> ? [S0: a > $o] :
% 0.20/0.47 ( ( cP @ S0 )
% 0.20/0.47 & ( S0 @ Xx ) ) )
% 0.20/0.47 & ! [Xb: a > $o,Xc: a > $o] :
% 0.20/0.47 ( ( ( cP @ Xb )
% 0.20/0.47 & ( cP @ Xc )
% 0.20/0.47 & ? [Xx: a] :
% 0.20/0.47 ( ( Xb @ Xx )
% 0.20/0.47 & ( Xc @ Xx ) ) )
% 0.20/0.47 => ( Xb = Xc ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.45/1.28 ---- Embedded in THF ---
% 1.45/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.28 %%% Generated on Tue Feb 24 12:41:30 EST 2026
% 1.45/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.28 %%% Logic specification used:
% 1.45/1.28 %%% thf(spec, logic, $$dhol).
% 1.45/1.28
% 1.45/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0UVNMSvSYe/DTF2DTF15857.p
% See solution above
% 1.45/1.28 ------------------------
% 1.45/1.29 ---- Cleaned THF ---
% 1.45/1.29 thf(a_type,type,
% 1.45/1.29 a: $tType ).
% 1.45/1.29
% 1.45/1.29 thf(cP,type,
% 1.45/1.29 cP: ( a > $o ) > $o ).
% 1.45/1.29
% 1.45/1.29 thf(cTHM555_pme,conjecture,
% 1.45/1.29 ( ( ! [Xp: a > $o] :
% 1.45/1.29 ( ( cP @ Xp )
% 1.45/1.29 => ? [Xz: a] : ( Xp @ Xz ) )
% 1.45/1.29 & ! [Xx: a,Xp: a > $o,Xq: a > $o] :
% 1.45/1.29 ( ( ( cP @ Xp )
% 1.45/1.29 & ( cP @ Xq )
% 1.45/1.29 & ( Xp @ Xx )
% 1.45/1.29 & ( Xq @ Xx ) )
% 1.45/1.29 => ( Xp = Xq ) ) )
% 1.45/1.29 => ? [S: a > $o] :
% 1.45/1.29 ( ! [Xa: a > $o] :
% 1.45/1.29 ( ( cP @ Xa )
% 1.45/1.29 => ? [Xx: a] : ( Xa @ Xx ) )
% 1.45/1.29 & ! [Xx: a] :
% 1.45/1.29 ( ( S @ Xx )
% 1.45/1.29 <=> ? [S0: a > $o] :
% 1.45/1.29 ( ( cP @ S0 )
% 1.45/1.29 & ( S0 @ Xx ) ) )
% 1.45/1.29 & ! [Xb: a > $o,Xc: a > $o] :
% 1.45/1.29 ( ( ( cP @ Xb )
% 1.45/1.29 & ( cP @ Xc )
% 1.45/1.29 & ? [Xx: a] :
% 1.45/1.29 ( ( Xb @ Xx )
% 1.45/1.29 & ( Xc @ Xx ) ) )
% 1.45/1.29 => ( Xb = Xc ) ) ) ) ).
% 1.45/1.29 ------------------------
% 1.63/1.30 % (16045)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/183Mi)
% 1.63/1.30 % (16049)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_15857 for (2999ds/2Mi)
% 1.63/1.30 % (16049)Instruction limit reached!
% 1.63/1.30 % (16049)------------------------------
% 1.63/1.30 % (16049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (16049)Termination reason: Unknown
% 1.63/1.30 % (16049)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (16049)Memory used [KB]: 5500
% 1.63/1.30 % (16049)Time elapsed: 0.002 s
% 1.63/1.30 % (16049)Instructions burned: 3 (million)
% 1.63/1.30 % (16049)------------------------------
% 1.63/1.30 % (16049)------------------------------
% 1.63/1.30 % (16051)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/18Mi)
% 1.63/1.31 % (16048)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/2Mi)
% 1.63/1.31 % (16050)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_15857 for (2999ds/275Mi)
% 1.63/1.31 % (16047)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_15857 for (2999ds/27Mi)
% 1.63/1.31 % (16048)Instruction limit reached!
% 1.63/1.31 % (16048)------------------------------
% 1.63/1.31 % (16048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (16051)Instruction limit reached!
% 1.63/1.31 % (16051)------------------------------
% 1.63/1.31 % (16051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (16051)Termination reason: Unknown
% 1.63/1.31 % (16051)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (16051)Memory used [KB]: 5628
% 1.63/1.31 % (16051)Time elapsed: 0.008 s
% 1.63/1.31 % (16051)Instructions burned: 19 (million)
% 1.63/1.31 % (16051)------------------------------
% 1.63/1.31 % (16051)------------------------------
% 1.63/1.31 % (16048)Termination reason: Unknown
% 1.63/1.31 % (16048)Termination phase: Preprocessing 3
% 1.63/1.31
% 1.63/1.31 % (16048)Memory used [KB]: 1023
% 1.63/1.31 % (16048)Time elapsed: 0.003 s
% 1.63/1.31 % (16048)Instructions burned: 2 (million)
% 1.63/1.31 % (16048)------------------------------
% 1.63/1.31 % (16048)------------------------------
% 1.63/1.31 % (16052)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/3Mi)
% 1.63/1.31 % (16052)Instruction limit reached!
% 1.63/1.31 % (16052)------------------------------
% 1.63/1.31 % (16052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (16052)Termination reason: Unknown
% 1.63/1.31 % (16052)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (16052)Memory used [KB]: 5500
% 1.63/1.31 % (16052)Time elapsed: 0.002 s
% 1.63/1.31 % (16052)Instructions burned: 3 (million)
% 1.63/1.31 % (16052)------------------------------
% 1.63/1.31 % (16052)------------------------------
% 1.63/1.32 % (16046)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_15857 for (2999ds/4Mi)
% 1.63/1.32 % (16046)Instruction limit reached!
% 1.63/1.32 % (16046)------------------------------
% 1.63/1.32 % (16046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (16046)Termination reason: Unknown
% 1.63/1.32 % (16046)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (16046)Memory used [KB]: 5500
% 1.63/1.32 % (16046)Time elapsed: 0.004 s
% 1.63/1.32 % (16046)Instructions burned: 4 (million)
% 1.63/1.32 % (16046)------------------------------
% 1.63/1.32 % (16046)------------------------------
% 1.63/1.32 % (16047)Refutation not found, incomplete strategy
% 1.63/1.32 % (16047)------------------------------
% 1.63/1.32 % (16047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (16047)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.32
% 1.63/1.32
% 1.63/1.32 % (16047)Memory used [KB]: 5628
% 1.63/1.32 % (16047)Time elapsed: 0.011 s
% 1.63/1.32 % (16047)Instructions burned: 12 (million)
% 1.63/1.32 % (16047)------------------------------
% 1.63/1.32 % (16047)------------------------------
% 1.63/1.32 % (16053)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_15857 for (2999ds/37Mi)
% 1.63/1.32 % (16055)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_15857 for (2999ds/3Mi)
% 1.63/1.33 % (16055)Instruction limit reached!
% 1.63/1.33 % (16055)------------------------------
% 1.63/1.33 % (16055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (16055)Termination reason: Unknown
% 1.63/1.33 % (16055)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (16055)Memory used [KB]: 5500
% 1.63/1.33 % (16055)Time elapsed: 0.003 s
% 1.63/1.33 % (16055)Instructions burned: 5 (million)
% 1.63/1.33 % (16055)------------------------------
% 1.63/1.33 % (16055)------------------------------
% 1.63/1.33 % (16054)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_15857 for (2999ds/15Mi)
% 1.63/1.33 % (16056)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_15857 for (2999ds/1041Mi)
% 1.63/1.33 % (16053)Instruction limit reached!
% 1.63/1.33 % (16053)------------------------------
% 1.63/1.33 % (16053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (16053)Termination reason: Unknown
% 1.63/1.33 % (16053)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (16053)Memory used [KB]: 6012
% 1.63/1.33 % (16053)Time elapsed: 0.014 s
% 1.63/1.33 % (16053)Instructions burned: 40 (million)
% 1.63/1.33 % (16053)------------------------------
% 1.63/1.33 % (16053)------------------------------
% 1.63/1.33 % (16058)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/16Mi)
% 1.63/1.34 % (16057)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/7Mi)
% 1.63/1.34 % (16054)Instruction limit reached!
% 1.63/1.34 % (16054)------------------------------
% 1.63/1.34 % (16054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (16054)Termination reason: Unknown
% 1.63/1.34 % (16054)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (16054)Memory used [KB]: 5628
% 1.63/1.34 % (16054)Time elapsed: 0.012 s
% 1.63/1.34 % (16054)Instructions burned: 15 (million)
% 1.63/1.34 % (16054)------------------------------
% 1.63/1.34 % (16054)------------------------------
% 1.63/1.34 % (16058)Instruction limit reached!
% 1.63/1.34 % (16058)------------------------------
% 1.63/1.34 % (16058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (16058)Termination reason: Unknown
% 1.63/1.34 % (16058)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (16058)Memory used [KB]: 5628
% 1.63/1.34 % (16058)Time elapsed: 0.009 s
% 1.63/1.34 % (16058)Instructions burned: 17 (million)
% 1.63/1.34 % (16058)------------------------------
% 1.63/1.34 % (16058)------------------------------
% 1.63/1.34 % (16057)Instruction limit reached!
% 1.63/1.34 % (16057)------------------------------
% 1.63/1.34 % (16057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (16057)Termination reason: Unknown
% 1.63/1.34 % (16057)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (16057)Memory used [KB]: 1023
% 1.63/1.34 % (16057)Time elapsed: 0.007 s
% 1.63/1.34 % (16057)Instructions burned: 8 (million)
% 1.63/1.34 % (16057)------------------------------
% 1.63/1.34 % (16057)------------------------------
% 1.63/1.34 % (16059)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_15857 for (2999ds/3Mi)
% 1.63/1.34 % (16059)Instruction limit reached!
% 1.63/1.34 % (16059)------------------------------
% 1.63/1.34 % (16059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (16059)Termination reason: Unknown
% 1.63/1.34 % (16059)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.35 % (16059)Memory used [KB]: 5500
% 1.63/1.35 % (16059)Time elapsed: 0.003 s
% 1.63/1.35 % (16059)Instructions burned: 4 (million)
% 1.63/1.35 % (16059)------------------------------
% 1.63/1.35 % (16059)------------------------------
% 1.63/1.35 % (16045)Instruction limit reached!
% 1.63/1.35 % (16045)------------------------------
% 1.63/1.35 % (16045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (16045)Termination reason: Unknown
% 1.63/1.35 % (16045)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (16045)Memory used [KB]: 6652
% 1.63/1.35 % (16045)Time elapsed: 0.047 s
% 1.63/1.35 % (16045)Instructions burned: 183 (million)
% 1.63/1.35 % (16045)------------------------------
% 1.63/1.35 % (16045)------------------------------
% 1.63/1.35 % (16061)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/7Mi)
% 1.63/1.36 % (16063)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/4Mi)
% 1.63/1.36 % (16061)Refutation not found, incomplete strategy
% 1.63/1.36 % (16061)------------------------------
% 1.63/1.36 % (16061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (16061)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.36
% 1.63/1.36
% 1.63/1.36 % (16061)Memory used [KB]: 5500
% 1.63/1.36 % (16061)Time elapsed: 0.002 s
% 1.63/1.36 % (16061)Instructions burned: 3 (million)
% 1.63/1.36 % (16061)------------------------------
% 1.63/1.36 % (16061)------------------------------
% 1.63/1.36 % (16060)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_15857 for (2999ds/3Mi)
% 1.63/1.36 % (16064)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/18Mi)
% 1.63/1.36 % (16063)Instruction limit reached!
% 1.63/1.36 % (16063)------------------------------
% 1.63/1.36 % (16063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (16063)Termination reason: Unknown
% 1.63/1.36 % (16063)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (16063)Memory used [KB]: 5500
% 1.63/1.36 % (16063)Time elapsed: 0.004 s
% 1.63/1.36 % (16063)Instructions burned: 6 (million)
% 1.63/1.36 % (16063)------------------------------
% 1.63/1.36 % (16063)------------------------------
% 1.63/1.36 % (16060)Instruction limit reached!
% 1.63/1.36 % (16060)------------------------------
% 1.63/1.36 % (16060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (16060)Termination reason: Unknown
% 1.63/1.36 % (16060)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (16060)Memory used [KB]: 1023
% 1.63/1.36 % (16060)Time elapsed: 0.004 s
% 1.63/1.36 % (16060)Instructions burned: 4 (million)
% 1.63/1.36 % (16060)------------------------------
% 1.63/1.36 % (16060)------------------------------
% 1.63/1.36 % (16062)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/3Mi)
% 1.63/1.36 % (16062)Instruction limit reached!
% 1.63/1.36 % (16062)------------------------------
% 1.63/1.36 % (16062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (16062)Termination reason: Unknown
% 1.63/1.36 % (16062)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (16062)Memory used [KB]: 5500
% 1.63/1.36 % (16062)Time elapsed: 0.004 s
% 1.63/1.36 % (16062)Instructions burned: 4 (million)
% 1.63/1.36 % (16062)------------------------------
% 1.63/1.36 % (16062)------------------------------
% 1.63/1.36 % (16064)Instruction limit reached!
% 1.63/1.36 % (16064)------------------------------
% 1.63/1.36 % (16064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (16064)Termination reason: Unknown
% 1.63/1.36 % (16064)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (16064)Memory used [KB]: 5628
% 1.63/1.36 % (16064)Time elapsed: 0.007 s
% 1.63/1.36 % (16064)Instructions burned: 18 (million)
% 1.63/1.36 % (16064)------------------------------
% 1.63/1.36 % (16064)------------------------------
% 1.63/1.37 % (16065)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/710Mi)
% 1.63/1.37 % (16066)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/6Mi)
% 1.63/1.37 % (16066)Instruction limit reached!
% 1.63/1.37 % (16066)------------------------------
% 1.63/1.37 % (16066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (16066)Termination reason: Unknown
% 1.63/1.37 % (16066)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (16066)Memory used [KB]: 5500
% 1.63/1.37 % (16066)Time elapsed: 0.004 s
% 1.63/1.37 % (16066)Instructions burned: 6 (million)
% 1.63/1.37 % (16066)------------------------------
% 1.63/1.37 % (16066)------------------------------
% 1.63/1.37 % (16069)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/5Mi)
% 1.63/1.38 % (16067)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_15857 for (2999ds/902Mi)
% 1.63/1.38 % (16069)Instruction limit reached!
% 1.63/1.38 % (16069)------------------------------
% 1.63/1.38 % (16069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (16069)Termination reason: Unknown
% 1.63/1.38 % (16069)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (16069)Memory used [KB]: 5500
% 1.63/1.38 % (16069)Time elapsed: 0.003 s
% 1.63/1.38 % (16069)Instructions burned: 6 (million)
% 1.63/1.38 % (16069)------------------------------
% 1.63/1.38 % (16069)------------------------------
% 1.63/1.38 % (16068)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_15857 for (2999ds/21Mi)
% 1.63/1.38 % (16070)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_15857 for (2999ds/6Mi)
% 1.63/1.38 % (16070)Instruction limit reached!
% 1.63/1.38 % (16070)------------------------------
% 1.63/1.38 % (16070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (16070)Termination reason: Unknown
% 1.63/1.38 % (16070)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (16070)Memory used [KB]: 5500
% 1.63/1.38 % (16070)Time elapsed: 0.004 s
% 1.63/1.38 % (16070)Instructions burned: 8 (million)
% 1.63/1.38 % (16070)------------------------------
% 1.63/1.38 % (16070)------------------------------
% 1.63/1.39 % (16071)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15857 for (2999ds/377Mi)
% 1.63/1.39 % (16068)Instruction limit reached!
% 1.63/1.39 % (16068)------------------------------
% 1.63/1.39 % (16068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.39 % (16068)Termination reason: Unknown
% 1.63/1.39 % (16068)Termination phase: Saturation
% 1.63/1.39
% 1.63/1.39 % (16068)Memory used [KB]: 5756
% 1.63/1.39 % (16068)Time elapsed: 0.012 s
% 1.63/1.39 % (16068)Instructions burned: 23 (million)
% 1.63/1.39 % (16068)------------------------------
% 1.63/1.39 % (16068)------------------------------
% 1.63/1.39 % (16072)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_15857 for (2999ds/779Mi)
% 1.63/1.40 % (16073)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_15857 for (2999ds/19Mi)
% 1.63/1.41 % (16073)Instruction limit reached!
% 1.63/1.41 % (16073)------------------------------
% 1.63/1.41 % (16073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.41 % (16073)Termination reason: Unknown
% 1.63/1.41 % (16073)Termination phase: Saturation
% 1.63/1.41
% 1.63/1.41 % (16073)Memory used [KB]: 5628
% 1.63/1.41 % (16073)Time elapsed: 0.008 s
% 1.63/1.41 % (16073)Instructions burned: 20 (million)
% 1.63/1.41 % (16073)------------------------------
% 1.63/1.41 % (16073)------------------------------
% 1.63/1.42 % (16074)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_15857 for (2998ds/879Mi)
% 1.63/1.42 % (16074)Refutation not found, incomplete strategy
% 1.63/1.42 % (16074)------------------------------
% 1.63/1.42 % (16074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.42 % (16074)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.42
% 1.63/1.42
% 1.63/1.42 % (16074)Memory used [KB]: 5628
% 1.63/1.42 % (16074)Time elapsed: 0.005 s
% 1.63/1.42 % (16074)Instructions burned: 10 (million)
% 1.63/1.42 % (16074)------------------------------
% 1.63/1.42 % (16074)------------------------------
% 1.63/1.43 % (16077)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_15857 for (2998ds/17Mi)
% 1.63/1.44 % (16077)Instruction limit reached!
% 1.63/1.44 % (16077)------------------------------
% 1.63/1.44 % (16077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (16077)Termination reason: Unknown
% 1.63/1.44 % (16077)Termination phase: Saturation
% 1.63/1.44
% 1.63/1.44 % (16077)Memory used [KB]: 5628
% 1.63/1.44 % (16077)Time elapsed: 0.012 s
% 1.63/1.44 % (16077)Instructions burned: 18 (million)
% 1.63/1.44 % (16077)------------------------------
% 1.63/1.44 % (16077)------------------------------
% 1.63/1.45 % (16050)Instruction limit reached!
% 1.63/1.45 % (16050)------------------------------
% 1.63/1.45 % (16050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.45 % (16050)Termination reason: Unknown
% 1.63/1.45 % (16050)Termination phase: Saturation
% 1.63/1.45
% 1.63/1.45 % (16050)Memory used [KB]: 6012
% 1.63/1.45 % (16050)Time elapsed: 0.140 s
% 1.63/1.45 % (16050)Instructions burned: 277 (million)
% 1.63/1.45 % (16050)------------------------------
% 1.63/1.45 % (16050)------------------------------
% 1.63/1.45 % (16090)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15857 for (2998ds/3Mi)
% 1.63/1.45 % (16090)Instruction limit reached!
% 1.63/1.45 % (16090)------------------------------
% 1.63/1.45 % (16090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.45 % (16090)Termination reason: Unknown
% 1.63/1.45 % (16090)Termination phase: Saturation
% 1.63/1.45
% 1.63/1.45 % (16090)Memory used [KB]: 1023
% 1.63/1.45 % (16090)Time elapsed: 0.002 s
% 1.63/1.45 % (16090)Instructions burned: 3 (million)
% 1.63/1.45 % (16090)------------------------------
% 1.63/1.45 % (16090)------------------------------
% 1.63/1.46 % (16092)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_15857 for (2998ds/30Mi)
% 1.63/1.46 % (16093)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_15857 for (2998ds/127Mi)
% 1.63/1.47 % (16092)Instruction limit reached!
% 1.63/1.47 % (16092)------------------------------
% 1.63/1.47 % (16092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.47 % (16092)Termination reason: Unknown
% 1.63/1.47 % (16092)Termination phase: Saturation
% 1.63/1.47
% 1.63/1.47 % (16092)Memory used [KB]: 5756
% 1.63/1.47 % (16092)Time elapsed: 0.013 s
% 1.63/1.47 % (16092)Instructions burned: 32 (million)
% 1.63/1.47 % (16092)------------------------------
% 1.63/1.47 % (16092)------------------------------
% 1.63/1.48 % (16094)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_15857 for (2998ds/100Mi)
% 1.63/1.52 % (16094)Instruction limit reached!
% 1.63/1.52 % (16094)------------------------------
% 1.63/1.52 % (16094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.52 % (16094)Termination reason: Unknown
% 1.63/1.52 % (16094)Termination phase: Saturation
% 1.63/1.52
% 1.63/1.52 % (16094)Memory used [KB]: 5884
% 1.63/1.52 % (16094)Time elapsed: 0.037 s
% 1.63/1.52 % (16094)Instructions burned: 100 (million)
% 1.63/1.52 % (16094)------------------------------
% 1.63/1.52 % (16094)------------------------------
% 1.63/1.52 % (16093)Instruction limit reached!
% 1.63/1.52 % (16093)------------------------------
% 1.63/1.52 % (16093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.52 % (16093)Termination reason: Unknown
% 1.63/1.52 % (16093)Termination phase: Saturation
% 1.63/1.52
% 1.63/1.52 % (16093)Memory used [KB]: 6140
% 1.63/1.52 % (16093)Time elapsed: 0.056 s
% 1.63/1.52 % (16093)Instructions burned: 128 (million)
% 1.63/1.52 % (16093)------------------------------
% 1.63/1.52 % (16093)------------------------------
% 1.63/1.52 % (16071)Instruction limit reached!
% 1.63/1.52 % (16071)------------------------------
% 1.63/1.52 % (16071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.52 % (16071)Termination reason: Unknown
% 1.63/1.52 % (16071)Termination phase: Saturation
% 1.63/1.52
% 1.63/1.52 % (16071)Memory used [KB]: 6780
% 1.63/1.52 % (16071)Time elapsed: 0.136 s
% 1.63/1.52 % (16071)Instructions burned: 379 (million)
% 1.63/1.52 % (16071)------------------------------
% 1.63/1.52 % (16071)------------------------------
% 1.63/1.53 % (16095)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_15857 for (2997ds/3Mi)
% 1.63/1.53 % (16095)Instruction limit reached!
% 1.63/1.53 % (16095)------------------------------
% 1.63/1.53 % (16095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.53 % (16095)Termination reason: Unknown
% 1.63/1.53 % (16095)Termination phase: Saturation
% 1.63/1.53
% 1.63/1.53 % (16095)Memory used [KB]: 5500
% 1.63/1.53 % (16095)Time elapsed: 0.003 s
% 1.63/1.53 % (16095)Instructions burned: 3 (million)
% 1.63/1.53 % (16095)------------------------------
% 1.63/1.53 % (16095)------------------------------
% 1.63/1.53 % (16096)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_15857 for (2997ds/20Mi)
% 1.63/1.53 % (16097)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_15857 for (2997ds/86Mi)
% 1.63/1.54 % (16098)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_15857 for (2997ds/107Mi)
% 1.63/1.54 % (16096)Instruction limit reached!
% 1.63/1.54 % (16096)------------------------------
% 1.63/1.54 % (16096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.54 % (16096)Termination reason: Unknown
% 1.63/1.54 % (16096)Termination phase: Saturation
% 1.63/1.54
% 1.63/1.54 % (16096)Memory used [KB]: 5628
% 1.63/1.54 % (16096)Time elapsed: 0.014 s
% 1.63/1.54 % (16096)Instructions burned: 20 (million)
% 1.63/1.54 % (16096)------------------------------
% 1.63/1.54 % (16096)------------------------------
% 1.63/1.54 % (16098)First to succeed.
% 1.63/1.55 % (16098)Refutation found. Thanks to Tanya!
% 1.63/1.55 % SZS status Theorem for DTF2THF_15857
% 1.63/1.55 % SZS output start Proof for DTF2THF_15857
% 1.63/1.55 thf(type_def_5, type, a: $tType).
% 1.63/1.55 thf(func_def_0, type, a: $tType).
% 1.63/1.55 thf(func_def_1, type, cP: (a > $o) > $o).
% 1.63/1.55 thf(func_def_5, type, sP0: a > $o).
% 1.63/1.55 thf(func_def_6, type, sP1: (a > $o) > (a > $o) > $o).
% 1.63/1.55 thf(func_def_7, type, sP2: (a > $o) > $o).
% 1.63/1.55 thf(func_def_9, type, sK4: a > $o).
% 1.63/1.55 thf(func_def_10, type, sK5: a > $o).
% 1.63/1.55 thf(func_def_11, type, sK6: (a > $o) > a).
% 1.63/1.55 thf(func_def_12, type, sK7: (a > $o) > (a > $o) > a).
% 1.63/1.55 thf(func_def_13, type, sK8: a > a > $o).
% 1.63/1.55 thf(func_def_14, type, sK9: (a > $o) > a).
% 1.63/1.55 thf(func_def_15, type, sK10: a > $o).
% 1.63/1.55 thf(func_def_17, type, ph12: !>[X0: $tType]:(X0)).
% 1.63/1.55 thf(func_def_18, type, sK13: a).
% 1.63/1.55 thf(f194,plain,(
% 1.63/1.55 $false),
% 1.63/1.55 inference(avatar_sat_refutation,[status(thm)],[f56,f61,f66,f74,f78,f83,f96,f102,f192])).
% 1.63/1.55 thf(f192,plain,(
% 1.63/1.55 spl11_2 | ~spl11_3 | ~spl11_4 | ~spl11_8),
% 1.63/1.55 inference(avatar_contradiction_clause,[status(thm)],[f191])).
% 1.63/1.55 thf(f191,plain,(
% 1.63/1.55 $false | (spl11_2 | ~spl11_3 | ~spl11_4 | ~spl11_8)),
% 1.63/1.55 inference(subsumption_resolution,[status(thm)],[f190,f151])).
% 1.63/1.55 thf(f151,plain,(
% 1.63/1.55 ($true = (sK4 @ (sK7 @ sK5 @ sK4))) | ~spl11_3),
% 1.63/1.55 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.63/1.55 thf(f150,plain,(
% 1.63/1.55 ($true != $true) | ($true = (sK4 @ (sK7 @ sK5 @ sK4))) | ~spl11_3),
% 1.63/1.55 inference(superposition,[status(thm)],[f40,f60])).
% 1.63/1.55 thf(f60,plain,(
% 1.63/1.55 ($true = (sP1 @ sK5 @ sK4)) | ~spl11_3),
% 1.63/1.55 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.63/1.55 thf(f58,definition,(
% 1.63/1.55 spl11_3 <=> ($true = (sP1 @ sK5 @ sK4))),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition])).
% 1.63/1.55 thf(f40,plain,(
% 1.63/1.55 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sP1 @ X1 @ X0)) | ($true = (X0 @ (sK7 @ X1 @ X0)))) )),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.55 thf(f24,plain,(
% 1.63/1.55 ! [X0 : a > $o,X1 : a > $o] : ((($true = (X0 @ (sK7 @ X1 @ X0))) & ($true = (X1 @ (sK7 @ X1 @ X0)))) | ($true != (sP1 @ X1 @ X0)))),
% 1.63/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f22,f23])).
% 1.63/1.55 thf(f23,plain,(
% 1.63/1.55 ! [X0 : a > $o,X1 : a > $o] : (? [X2 : a] : (((X0 @ X2) = $true) & ($true = (X1 @ X2))) => (($true = (X0 @ (sK7 @ X1 @ X0))) & ($true = (X1 @ (sK7 @ X1 @ X0)))))),
% 1.63/1.55 introduced(definition,[],[choice_axiom])).
% 1.63/1.55 thf(f22,plain,(
% 1.63/1.55 ! [X0 : a > $o,X1 : a > $o] : (? [X2 : a] : (((X0 @ X2) = $true) & ($true = (X1 @ X2))) | ($true != (sP1 @ X1 @ X0)))),
% 1.63/1.55 inference(rectify,[status(thm)],[f21])).
% 1.63/1.55 thf(f21,plain,(
% 1.63/1.55 ! [X11 : a > $o,X10 : a > $o] : (? [X12 : a] : (($true = (X11 @ X12)) & ($true = (X10 @ X12))) | ($true != (sP1 @ X10 @ X11)))),
% 1.63/1.55 inference(nnf_transformation,[status(thm)],[f9])).
% 1.63/1.55 thf(f9,plain,(
% 1.63/1.55 ! [X11 : a > $o,X10 : a > $o] : (? [X12 : a] : (($true = (X11 @ X12)) & ($true = (X10 @ X12))) | ~($true = (sP1 @ X10 @ X11)))),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.63/1.55 thf(f190,plain,(
% 1.63/1.55 ($true != (sK4 @ (sK7 @ sK5 @ sK4))) | (spl11_2 | ~spl11_3 | ~spl11_4 | ~spl11_8)),
% 1.63/1.55 inference(trivial_inequality_removal,[status(thm)],[f187])).
% 1.63/1.55 thf(f187,plain,(
% 1.63/1.55 ($true != (sK4 @ (sK7 @ sK5 @ sK4))) | ($true != $true) | (spl11_2 | ~spl11_3 | ~spl11_4 | ~spl11_8)),
% 1.63/1.55 inference(superposition,[status(thm)],[f176,f145])).
% 1.63/1.55 thf(f145,plain,(
% 1.63/1.55 ($true = (sK5 @ (sK7 @ sK5 @ sK4))) | ~spl11_3),
% 1.63/1.55 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.63/1.55 thf(f144,plain,(
% 1.63/1.55 ($true != $true) | ($true = (sK5 @ (sK7 @ sK5 @ sK4))) | ~spl11_3),
% 1.63/1.55 inference(superposition,[status(thm)],[f39,f60])).
% 1.63/1.55 thf(f39,plain,(
% 1.63/1.55 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sP1 @ X1 @ X0)) | ($true = (X1 @ (sK7 @ X1 @ X0)))) )),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f24])).
% 1.63/1.55 thf(f176,plain,(
% 1.63/1.55 ( ! [X0 : a] : (($true != (sK5 @ X0)) | ($true != (sK4 @ X0))) ) | (spl11_2 | ~spl11_4 | ~spl11_8)),
% 1.63/1.55 inference(subsumption_resolution,[status(thm)],[f175,f55])).
% 1.63/1.55 thf(f55,plain,(
% 1.63/1.55 (sK5 != sK4) | spl11_2),
% 1.63/1.55 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.63/1.55 thf(f53,definition,(
% 1.63/1.55 spl11_2 <=> (sK5 = sK4)),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition])).
% 1.63/1.55 thf(f175,plain,(
% 1.63/1.55 ( ! [X0 : a] : (($true != (sK4 @ X0)) | (sK5 = sK4) | ($true != (sK5 @ X0))) ) | (~spl11_4 | ~spl11_8)),
% 1.63/1.55 inference(trivial_inequality_removal,[status(thm)],[f171])).
% 1.63/1.55 thf(f171,plain,(
% 1.63/1.55 ( ! [X0 : a] : (($true != (sK5 @ X0)) | (sK5 = sK4) | ($true != $true) | ($true != (sK4 @ X0))) ) | (~spl11_4 | ~spl11_8)),
% 1.63/1.55 inference(superposition,[status(thm)],[f137,f82])).
% 1.63/1.55 thf(f82,plain,(
% 1.63/1.55 ($true = (cP @ sK4)) | ~spl11_8),
% 1.63/1.55 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.63/1.55 thf(f80,definition,(
% 1.63/1.55 spl11_8 <=> ($true = (cP @ sK4))),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[spl11_8])],[avatar_definition])).
% 1.63/1.55 thf(f137,plain,(
% 1.63/1.55 ( ! [X0 : a > $o,X1 : a] : (((cP @ X0) != $true) | ($true != (sK5 @ X1)) | (sK5 = X0) | ((X0 @ X1) != $true)) ) | ~spl11_4),
% 1.63/1.55 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.63/1.55 thf(f135,plain,(
% 1.63/1.55 ( ! [X0 : a > $o,X1 : a] : (((X0 @ X1) != $true) | ($true != (sK5 @ X1)) | (sK5 = X0) | ((cP @ X0) != $true) | ($true != $true)) ) | ~spl11_4),
% 1.63/1.55 inference(superposition,[status(thm)],[f44,f65])).
% 1.63/1.55 thf(f65,plain,(
% 1.63/1.55 ($true = (cP @ sK5)) | ~spl11_4),
% 1.63/1.55 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.63/1.55 thf(f63,definition,(
% 1.63/1.55 spl11_4 <=> ($true = (cP @ sK5))),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[spl11_4])],[avatar_definition])).
% 1.63/1.55 thf(f44,plain,(
% 1.63/1.55 ( ! [X6 : a > $o,X7 : a,X5 : a > $o] : (((cP @ X6) != $true) | (X5 = X6) | ((cP @ X5) != $true) | ($true != (X6 @ X7)) | ($true != (X5 @ X7))) )),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f32])).
% 1.63/1.55 thf(f32,plain,(
% 1.63/1.55 ! [X0 : a > $o] : (($true = (X0 @ (sK9 @ X0))) | ((cP @ X0) != $true)) & ! [X2 : a > $o] : ((! [X4 : a] : ($true != (sK10 @ X4)) & ($true = (cP @ sK10))) | (sP3 = $true) | ($true = (sP2 @ X2))) & ! [X5 : a > $o,X6 : a > $o,X7 : a] : (($true != (X6 @ X7)) | ($true != (X5 @ X7)) | ((cP @ X5) != $true) | ((cP @ X6) != $true) | (X5 = X6))),
% 1.63/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f29,f31,f30])).
% 1.63/1.55 thf(f30,plain,(
% 1.63/1.55 ! [X0 : a > $o] : (? [X1 : a] : ((X0 @ X1) = $true) => ($true = (X0 @ (sK9 @ X0))))),
% 1.63/1.55 introduced(definition,[],[choice_axiom])).
% 1.63/1.55 thf(f31,plain,(
% 1.63/1.55 ? [X3 : a > $o] : (! [X4 : a] : ($true != (X3 @ X4)) & ((cP @ X3) = $true)) => (! [X4 : a] : ($true != (sK10 @ X4)) & ($true = (cP @ sK10)))),
% 1.63/1.55 introduced(definition,[],[choice_axiom])).
% 1.63/1.55 thf(f29,plain,(
% 1.63/1.55 ! [X0 : a > $o] : (? [X1 : a] : ((X0 @ X1) = $true) | ((cP @ X0) != $true)) & ! [X2 : a > $o] : (? [X3 : a > $o] : (! [X4 : a] : ($true != (X3 @ X4)) & ((cP @ X3) = $true)) | (sP3 = $true) | ($true = (sP2 @ X2))) & ! [X5 : a > $o,X6 : a > $o,X7 : a] : (($true != (X6 @ X7)) | ($true != (X5 @ X7)) | ((cP @ X5) != $true) | ((cP @ X6) != $true) | (X5 = X6))),
% 1.63/1.55 inference(rectify,[status(thm)],[f12])).
% 1.63/1.55 thf(f12,plain,(
% 1.63/1.55 ! [X0 : a > $o] : (? [X1 : a] : ((X0 @ X1) = $true) | ((cP @ X0) != $true)) & ! [X5 : a > $o] : (? [X6 : a > $o] : (! [X7 : a] : ($true != (X6 @ X7)) & ((cP @ X6) = $true)) | (sP3 = $true) | ($true = (sP2 @ X5))) & ! [X4 : a > $o,X2 : a > $o,X3 : a] : (($true != (X2 @ X3)) | ($true != (X4 @ X3)) | ($true != (cP @ X4)) | ($true != (cP @ X2)) | (X2 = X4))),
% 1.63/1.55 inference(definition_folding,[status(thm)],[f7,f11,f10,f9,f8])).
% 1.63/1.55 thf(f8,plain,(
% 1.63/1.55 ! [X8 : a] : (($true = (sP0 @ X8)) <=> ? [X9 : a > $o] : (($true = (X9 @ X8)) & ($true = (cP @ X9))))),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.63/1.55 thf(f10,plain,(
% 1.63/1.55 ! [X5 : a > $o] : (? [X8 : a] : (($true = (X5 @ X8)) <~> ($true = (sP0 @ X8))) | ~($true = (sP2 @ X5)))),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.63/1.55 thf(f11,plain,(
% 1.63/1.55 ? [X11 : a > $o,X10 : a > $o] : (($true = (sP1 @ X10 @ X11)) & (X10 != X11) & ($true = (cP @ X11)) & ($true = (cP @ X10))) | ~(sP3 = $true)),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.63/1.55 thf(f7,plain,(
% 1.63/1.55 ! [X0 : a > $o] : (? [X1 : a] : ((X0 @ X1) = $true) | ((cP @ X0) != $true)) & ! [X5 : a > $o] : (? [X6 : a > $o] : (! [X7 : a] : ($true != (X6 @ X7)) & ((cP @ X6) = $true)) | ? [X11 : a > $o,X10 : a > $o] : (? [X12 : a] : (($true = (X11 @ X12)) & ($true = (X10 @ X12))) & (X10 != X11) & ($true = (cP @ X11)) & ($true = (cP @ X10))) | ? [X8 : a] : (($true = (X5 @ X8)) <~> ? [X9 : a > $o] : (($true = (X9 @ X8)) & ($true = (cP @ X9))))) & ! [X4 : a > $o,X2 : a > $o,X3 : a] : (($true != (X2 @ X3)) | ($true != (X4 @ X3)) | ($true != (cP @ X4)) | ($true != (cP @ X2)) | (X2 = X4))),
% 1.63/1.55 inference(flattening,[status(thm)],[f6])).
% 1.63/1.55 thf(f6,plain,(
% 1.63/1.55 ! [X5 : a > $o] : (? [X6 : a > $o] : (! [X7 : a] : ($true != (X6 @ X7)) & ((cP @ X6) = $true)) | ? [X11 : a > $o,X10 : a > $o] : ((X10 != X11) & (($true = (cP @ X10)) & ? [X12 : a] : (($true = (X11 @ X12)) & ($true = (X10 @ X12))) & ($true = (cP @ X11)))) | ? [X8 : a] : (($true = (X5 @ X8)) <~> ? [X9 : a > $o] : (($true = (X9 @ X8)) & ($true = (cP @ X9))))) & (! [X3 : a,X2 : a > $o,X4 : a > $o] : ((X2 = X4) | (($true != (X2 @ X3)) | ($true != (cP @ X2)) | ($true != (X4 @ X3)) | ($true != (cP @ X4)))) & ! [X0 : a > $o] : (? [X1 : a] : ((X0 @ X1) = $true) | ((cP @ X0) != $true)))),
% 1.63/1.55 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.55 thf(f5,plain,(
% 1.63/1.55 ~((! [X3 : a,X2 : a > $o,X4 : a > $o] : ((($true = (X2 @ X3)) & ($true = (cP @ X2)) & ($true = (X4 @ X3)) & ($true = (cP @ X4))) => (X2 = X4)) & ! [X0 : a > $o] : (((cP @ X0) = $true) => ? [X1 : a] : ((X0 @ X1) = $true))) => ? [X5 : a > $o] : (! [X6 : a > $o] : (((cP @ X6) = $true) => ? [X7 : a] : ($true = (X6 @ X7))) & ! [X11 : a > $o,X10 : a > $o] : ((($true = (cP @ X10)) & ? [X12 : a] : (($true = (X11 @ X12)) & ($true = (X10 @ X12))) & ($true = (cP @ X11))) => (X10 = X11)) & ! [X8 : a] : (($true = (X5 @ X8)) <=> ? [X9 : a > $o] : (($true = (X9 @ X8)) & ($true = (cP @ X9))))))),
% 1.63/1.55 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.55 thf(f4,plain,(
% 1.63/1.55 ~((! [X0 : a > $o] : ((cP @ X0) => ? [X1 : a] : (X0 @ X1)) & ! [X2 : a > $o,X3 : a,X4 : a > $o] : (((X4 @ X3) & (X2 @ X3) & (cP @ X4) & (cP @ X2)) => (X2 = X4))) => ? [X5 : a > $o] : (! [X6 : a > $o] : ((cP @ X6) => ? [X7 : a] : (X6 @ X7)) & ! [X8 : a] : ((X5 @ X8) <=> ? [X9 : a > $o] : ((X9 @ X8) & (cP @ X9))) & ! [X10 : a > $o,X11 : a > $o] : (((cP @ X11) & ? [X12 : a] : ((X10 @ X12) & (X11 @ X12)) & (cP @ X10)) => (X10 = X11))))),
% 1.63/1.55 inference(rectify,[status(thm)],[f2])).
% 1.63/1.55 thf(f2,negated_conjecture,(
% 1.63/1.55 ~((! [X0 : a > $o] : ((cP @ X0) => ? [X1 : a] : (X0 @ X1)) & ! [X0 : a > $o,X2 : a,X3 : a > $o] : (((X3 @ X2) & (X0 @ X2) & (cP @ X3) & (cP @ X0)) => (X0 = X3))) => ? [X4 : a > $o] : (! [X5 : a > $o] : ((cP @ X5) => ? [X2 : a] : (X5 @ X2)) & ! [X2 : a] : ((X4 @ X2) <=> ? [X6 : a > $o] : ((X6 @ X2) & (cP @ X6))) & ! [X8 : a > $o,X7 : a > $o] : (((cP @ X7) & ? [X2 : a] : ((X8 @ X2) & (X7 @ X2)) & (cP @ X8)) => (X7 = X8))))),
% 1.63/1.55 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.55 thf(f1,conjecture,(
% 1.63/1.55 (! [X0 : a > $o] : ((cP @ X0) => ? [X1 : a] : (X0 @ X1)) & ! [X0 : a > $o,X2 : a,X3 : a > $o] : (((X3 @ X2) & (X0 @ X2) & (cP @ X3) & (cP @ X0)) => (X0 = X3))) => ? [X4 : a > $o] : (! [X5 : a > $o] : ((cP @ X5) => ? [X2 : a] : (X5 @ X2)) & ! [X2 : a] : ((X4 @ X2) <=> ? [X6 : a > $o] : ((X6 @ X2) & (cP @ X6))) & ! [X8 : a > $o,X7 : a > $o] : (((cP @ X7) & ? [X2 : a] : ((X8 @ X2) & (X7 @ X2)) & (cP @ X8)) => (X7 = X8)))),
% 1.63/1.55 file('/export/starexec/sandbox/tmp/tmp.0UVNMSvSYe/DTF2THF_15857.p',cTHM555_pme)).
% 1.63/1.55 thf(f102,plain,(
% 1.63/1.55 ~spl11_5 | ~spl11_7),
% 1.63/1.55 inference(avatar_contradiction_clause,[status(thm)],[f101])).
% 1.63/1.55 thf(f101,plain,(
% 1.63/1.55 $false | (~spl11_5 | ~spl11_7)),
% 1.63/1.55 inference(subsumption_resolution,[status(thm)],[f99,f77])).
% 1.63/1.55 thf(f77,plain,(
% 1.63/1.55 ( ! [X4 : a] : (($true != (sK10 @ X4))) ) | ~spl11_7),
% 1.63/1.55 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.63/1.55 thf(f76,definition,(
% 1.63/1.55 spl11_7 <=> ! [X4 : a] : ($true != (sK10 @ X4))),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[spl11_7])],[avatar_definition])).
% 1.63/1.55 thf(f99,plain,(
% 1.63/1.55 ((sK10 @ (sK9 @ sK10)) = $true) | ~spl11_5),
% 1.63/1.55 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.63/1.55 thf(f98,plain,(
% 1.63/1.55 ((sK10 @ (sK9 @ sK10)) = $true) | ($true != $true) | ~spl11_5),
% 1.63/1.55 inference(superposition,[status(thm)],[f47,f70])).
% 1.63/1.55 thf(f70,plain,(
% 1.63/1.55 ($true = (cP @ sK10)) | ~spl11_5),
% 1.63/1.55 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.63/1.55 thf(f68,definition,(
% 1.63/1.55 spl11_5 <=> ($true = (cP @ sK10))),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition])).
% 1.63/1.55 thf(f47,plain,(
% 1.63/1.55 ( ! [X0 : a > $o] : (((cP @ X0) != $true) | ($true = (X0 @ (sK9 @ X0)))) )),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f32])).
% 1.63/1.55 thf(f96,plain,(
% 1.63/1.55 ~spl11_6),
% 1.63/1.55 inference(avatar_contradiction_clause,[status(thm)],[f95])).
% 1.63/1.55 thf(f95,plain,(
% 1.63/1.55 $false | ~spl11_6),
% 1.63/1.55 inference(subsumption_resolution,[status(thm)],[f94,f86])).
% 1.63/1.55 thf(f86,plain,(
% 1.63/1.55 ( ! [X0 : a > $o] : (($true != (sP0 @ (sK6 @ X0))) | ($true != (X0 @ (sK6 @ X0)))) ) | ~spl11_6),
% 1.63/1.55 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.63/1.55 thf(f85,plain,(
% 1.63/1.55 ( ! [X0 : a > $o] : (($true != (sP0 @ (sK6 @ X0))) | ($true != (X0 @ (sK6 @ X0))) | ($true != $true)) ) | ~spl11_6),
% 1.63/1.55 inference(backward_demodulation,[status(thm)],[f38,f73])).
% 1.63/1.55 thf(f73,plain,(
% 1.63/1.55 ( ! [X2 : a > $o] : (($true = (sP2 @ X2))) ) | ~spl11_6),
% 1.63/1.55 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.63/1.55 thf(f72,definition,(
% 1.63/1.55 spl11_6 <=> ! [X2 : a > $o] : ($true = (sP2 @ X2))),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[spl11_6])],[avatar_definition])).
% 1.63/1.55 thf(f38,plain,(
% 1.63/1.55 ( ! [X0 : a > $o] : (($true != (sP0 @ (sK6 @ X0))) | ($true != (sP2 @ X0)) | ($true != (X0 @ (sK6 @ X0)))) )),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f20])).
% 1.63/1.55 thf(f20,plain,(
% 1.63/1.55 ! [X0 : a > $o] : (((($true != (sP0 @ (sK6 @ X0))) | ($true != (X0 @ (sK6 @ X0)))) & (($true = (sP0 @ (sK6 @ X0))) | ($true = (X0 @ (sK6 @ X0))))) | ($true != (sP2 @ X0)))),
% 1.63/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f18,f19])).
% 1.63/1.55 thf(f19,plain,(
% 1.63/1.55 ! [X0 : a > $o] : (? [X1 : a] : ((($true != (sP0 @ X1)) | ((X0 @ X1) != $true)) & (($true = (sP0 @ X1)) | ((X0 @ X1) = $true))) => ((($true != (sP0 @ (sK6 @ X0))) | ($true != (X0 @ (sK6 @ X0)))) & (($true = (sP0 @ (sK6 @ X0))) | ($true = (X0 @ (sK6 @ X0))))))),
% 1.63/1.55 introduced(definition,[],[choice_axiom])).
% 1.63/1.55 thf(f18,plain,(
% 1.63/1.55 ! [X0 : a > $o] : (? [X1 : a] : ((($true != (sP0 @ X1)) | ((X0 @ X1) != $true)) & (($true = (sP0 @ X1)) | ((X0 @ X1) = $true))) | ($true != (sP2 @ X0)))),
% 1.63/1.55 inference(rectify,[status(thm)],[f17])).
% 1.63/1.55 thf(f17,plain,(
% 1.63/1.55 ! [X5 : a > $o] : (? [X8 : a] : ((($true != (sP0 @ X8)) | ($true != (X5 @ X8))) & (($true = (sP0 @ X8)) | ($true = (X5 @ X8)))) | ($true != (sP2 @ X5)))),
% 1.63/1.55 inference(nnf_transformation,[status(thm)],[f10])).
% 1.63/1.55 thf(f94,plain,(
% 1.63/1.55 ($true = (sP0 @ (sK6 @ sP0))) | ~spl11_6),
% 1.63/1.55 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.63/1.55 thf(f91,plain,(
% 1.63/1.55 ($true = (sP0 @ (sK6 @ sP0))) | ($true != $true) | ~spl11_6),
% 1.63/1.55 inference(equality_factoring,[status(thm)],[f87])).
% 1.63/1.55 thf(f87,plain,(
% 1.63/1.55 ( ! [X0 : a > $o] : (($true = (sP0 @ (sK6 @ X0))) | ($true = (X0 @ (sK6 @ X0)))) ) | ~spl11_6),
% 1.63/1.55 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.63/1.55 thf(f84,plain,(
% 1.63/1.55 ( ! [X0 : a > $o] : (($true = (X0 @ (sK6 @ X0))) | ($true != $true) | ($true = (sP0 @ (sK6 @ X0)))) ) | ~spl11_6),
% 1.63/1.55 inference(backward_demodulation,[status(thm)],[f37,f73])).
% 1.63/1.55 thf(f37,plain,(
% 1.63/1.55 ( ! [X0 : a > $o] : (($true != (sP2 @ X0)) | ($true = (sP0 @ (sK6 @ X0))) | ($true = (X0 @ (sK6 @ X0)))) )),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f20])).
% 1.63/1.55 thf(f83,plain,(
% 1.63/1.55 ~spl11_1 | spl11_8),
% 1.63/1.55 inference(avatar_split_clause,[status(thm)],[f34,f80,f49])).
% 1.63/1.55 thf(f49,definition,(
% 1.63/1.55 spl11_1 <=> (sP3 = $true)),
% 1.63/1.55 introduced(definition,[new_symbols(naming,[spl11_1])],[avatar_definition])).
% 1.63/1.55 thf(f34,plain,(
% 1.63/1.55 ($true = (cP @ sK4)) | (sP3 != $true)),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.55 thf(f16,plain,(
% 1.63/1.55 (($true = (sP1 @ sK5 @ sK4)) & (sK5 != sK4) & ($true = (cP @ sK4)) & ($true = (cP @ sK5))) | (sP3 != $true)),
% 1.63/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f14,f15])).
% 1.63/1.55 thf(f15,plain,(
% 1.63/1.55 ? [X0 : a > $o,X1 : a > $o] : (($true = (sP1 @ X1 @ X0)) & (X0 != X1) & ((cP @ X0) = $true) & ($true = (cP @ X1))) => (($true = (sP1 @ sK5 @ sK4)) & (sK5 != sK4) & ($true = (cP @ sK4)) & ($true = (cP @ sK5)))),
% 1.63/1.55 introduced(definition,[],[choice_axiom])).
% 1.63/1.55 thf(f14,plain,(
% 1.63/1.55 ? [X0 : a > $o,X1 : a > $o] : (($true = (sP1 @ X1 @ X0)) & (X0 != X1) & ((cP @ X0) = $true) & ($true = (cP @ X1))) | (sP3 != $true)),
% 1.63/1.55 inference(rectify,[status(thm)],[f13])).
% 1.63/1.55 thf(f13,plain,(
% 1.63/1.55 ? [X11 : a > $o,X10 : a > $o] : (($true = (sP1 @ X10 @ X11)) & (X10 != X11) & ($true = (cP @ X11)) & ($true = (cP @ X10))) | (sP3 != $true)),
% 1.63/1.55 inference(nnf_transformation,[status(thm)],[f11])).
% 1.63/1.55 thf(f78,plain,(
% 1.63/1.55 spl11_6 | spl11_7 | spl11_1),
% 1.63/1.55 inference(avatar_split_clause,[status(thm)],[f46,f49,f76,f72])).
% 1.63/1.55 thf(f46,plain,(
% 1.63/1.55 ( ! [X2 : a > $o,X4 : a] : (($true != (sK10 @ X4)) | ($true = (sP2 @ X2)) | (sP3 = $true)) )),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f32])).
% 1.63/1.55 thf(f74,plain,(
% 1.63/1.55 spl11_1 | spl11_5 | spl11_6),
% 1.63/1.55 inference(avatar_split_clause,[status(thm)],[f45,f72,f68,f49])).
% 1.63/1.55 thf(f45,plain,(
% 1.63/1.55 ( ! [X2 : a > $o] : ((sP3 = $true) | ($true = (cP @ sK10)) | ($true = (sP2 @ X2))) )),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f32])).
% 1.63/1.55 thf(f66,plain,(
% 1.63/1.55 spl11_4 | ~spl11_1),
% 1.63/1.55 inference(avatar_split_clause,[status(thm)],[f33,f49,f63])).
% 1.63/1.55 thf(f33,plain,(
% 1.63/1.55 ($true = (cP @ sK5)) | (sP3 != $true)),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.55 thf(f61,plain,(
% 1.63/1.55 spl11_3 | ~spl11_1),
% 1.63/1.55 inference(avatar_split_clause,[status(thm)],[f36,f49,f58])).
% 1.63/1.55 thf(f36,plain,(
% 1.63/1.55 (sP3 != $true) | ($true = (sP1 @ sK5 @ sK4))),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.55 thf(f56,plain,(
% 1.63/1.55 ~spl11_1 | ~spl11_2),
% 1.63/1.55 inference(avatar_split_clause,[status(thm)],[f35,f53,f49])).
% 1.63/1.55 thf(f35,plain,(
% 1.63/1.55 (sK5 != sK4) | (sP3 != $true)),
% 1.63/1.55 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.55 % SZS output end Proof for DTF2THF_15857
% 1.63/1.55 % (16098)------------------------------
% 1.63/1.55 % (16098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.55 % (16098)Termination reason: Refutation
% 1.63/1.55
% 1.63/1.55 % (16098)Memory used [KB]: 5628
% 1.63/1.55 % (16098)Time elapsed: 0.010 s
% 1.63/1.55 % (16098)Instructions burned: 16 (million)
% 1.63/1.55 % (16098)------------------------------
% 1.63/1.55 % (16098)------------------------------
% 1.63/1.55 % (16044)Success in time 0.248 s
%------------------------------------------------------------------------------