%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV158^5 : 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 : n008.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 09:40:26 AM UTC 2026
% Result : Theorem 1.61s 1.34s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 79 ( 4 unt; 0 typ; 11 def)
% Number of atoms : 632 ( 284 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 644 ( 98 ~; 85 |; 46 &; 392 @)
% ( 11 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 398 ( 398 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 13 con; 0-2 aty)
% Number of variables : 332 ( 238 ^; 50 !; 44 ?; 332 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sP0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $o ).
thf(func_def_4,type,
sP1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $o ).
thf(func_def_5,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_6,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_7,type,
sK4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i ).
thf(func_def_8,type,
sK5: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_9,type,
sK6: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_10,type,
sK7: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_11,type,
sK8: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_13,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f192,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f55,f112,f121,f130,f148,f153,f158,f185,f186,f187,f189,f190]) ).
thf(f190,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $false
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f189,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $false
!= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $false
!= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f187,plain,
( ( $false
!= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $false
!= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f186,plain,
( ( ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f185,plain,
( spl9_22
| spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f180,f48,f182]) ).
thf(f182,definition,
( spl9_22
<=> ( $false
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_22])],[avatar_definition]) ).
thf(f48,definition,
( spl9_1
<=> ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition]) ).
thf(f180,plain,
( ( $false
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f179]) ).
thf(f179,plain,
( ( $true != $true )
| ( $false
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| spl9_1 ),
inference(fool_paramodulation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $true
!= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| spl9_1 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f158,plain,
( ~ spl9_16
| ~ spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f137,f48,f155]) ).
thf(f155,definition,
( spl9_16
<=> ( ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_16])],[avatar_definition]) ).
thf(f137,plain,
( ( ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_1 ),
inference(equality_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( ( ( ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ~ spl9_1 ),
inference(beta_eta_normalization,[status(thm)],[f135]) ).
thf(f135,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ~ spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( $true != $true )
| ~ spl9_1 ),
inference(superposition,[status(thm)],[f26,f50]) ).
thf(f50,plain,
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_1 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f26,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( sP0 @ X0 ) )
| ( ( X0 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( ( X0 @ ( sK5 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
& ( ( X0 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK7 @ X0 ) @ ( sK5 @ X0 ) )
= $true ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f16,f17]) ).
thf(f17,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X1 )
= $true ) )
=> ( ( ( X0 @ ( sK5 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
& ( ( X0 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK7 @ X0 ) @ ( sK5 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X1 )
= $true ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X1 )
= $true ) )
| ( $true
!= ( sP0 @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f153,plain,
( spl9_15
| ~ spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f140,f48,f150]) ).
thf(f150,definition,
( spl9_15
<=> ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_15])],[avatar_definition]) ).
thf(f140,plain,
( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_1 ),
inference(equality_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
( ( ( ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl9_1 ),
inference(beta_eta_normalization,[status(thm)],[f138]) ).
thf(f138,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f134]) ).
thf(f134,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( $true != $true )
| ~ spl9_1 ),
inference(superposition,[status(thm)],[f27,f50]) ).
thf(f27,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( sP0 @ X0 ) )
| ( ( X0 @ ( sK5 @ X0 ) @ ( sK6 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f148,plain,
( spl9_14
| ~ spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f143,f48,f145]) ).
thf(f145,definition,
( spl9_14
<=> ( ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_14])],[avatar_definition]) ).
thf(f143,plain,
( ( ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_1 ),
inference(equality_proxy_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
( ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl9_1 ),
inference(beta_eta_normalization,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f133]) ).
thf(f133,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl9_1 ),
inference(superposition,[status(thm)],[f25,f50]) ).
thf(f25,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( sP0 @ X0 ) )
| ( ( X0 @ ( sK7 @ X0 ) @ ( sK5 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f130,plain,
( spl9_12
| spl9_13
| ~ spl9_2 ),
inference(avatar_split_clause,[status(thm)],[f100,f52,f127,f123]) ).
thf(f123,definition,
( spl9_12
<=> ( $false
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_12])],[avatar_definition]) ).
thf(f127,definition,
( spl9_13
<=> ( $false
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_13])],[avatar_definition]) ).
thf(f52,definition,
( spl9_2
<=> ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition]) ).
thf(f100,plain,
( ( $false
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_2 ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_2 ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true != $true )
| ~ spl9_2 ),
inference(superposition,[status(thm)],[f22,f54]) ).
thf(f54,plain,
( ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_2 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f22,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
!= $true )
| ( ( sK3 @ X0 @ ( sK4 @ X0 ) )
!= ( sK2 @ X0 @ ( sK4 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) )
= $true )
& ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) )
& ( ( sK3 @ X0 @ ( sK4 @ X0 ) )
!= ( sK2 @ X0 @ ( sK4 @ X0 ) ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f12,f14,f13]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ( $true
= ( X0 @ X2 @ X1 ) )
& ( ( X0 @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( X1 @ X3 )
!= ( X2 @ X3 ) ) )
=> ( ( ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) )
= $true )
& ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) )
& ? [X3: $i] :
( ( sK2 @ X0 @ X3 )
!= ( sK3 @ X0 @ X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X3: $i] :
( ( sK2 @ X0 @ X3 )
!= ( sK3 @ X0 @ X3 ) )
=> ( ( sK3 @ X0 @ ( sK4 @ X0 ) )
!= ( sK2 @ X0 @ ( sK4 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ( $true
= ( X0 @ X2 @ X1 ) )
& ( ( X0 @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( X1 @ X3 )
!= ( X2 @ X3 ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X6: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X6 )
= $true )
& ( ( X0 @ X6 @ X5 )
= $true )
& ? [X7: $i] :
( ( X5 @ X7 )
!= ( X6 @ X7 ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X6: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X6 )
= $true )
& ( ( X0 @ X6 @ X5 )
= $true )
& ? [X7: $i] :
( ( X5 @ X7 )
!= ( X6 @ X7 ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f121,plain,
( spl9_10
| spl9_11
| ~ spl9_2 ),
inference(avatar_split_clause,[status(thm)],[f99,f52,f118,f114]) ).
thf(f114,definition,
( spl9_10
<=> ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_10])],[avatar_definition]) ).
thf(f118,definition,
( spl9_11
<=> ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_11])],[avatar_definition]) ).
thf(f99,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl9_2 ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f112,plain,
( spl9_9
| ~ spl9_2 ),
inference(avatar_split_clause,[status(thm)],[f103,f52,f108]) ).
thf(f108,definition,
( spl9_9
<=> ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_9])],[avatar_definition]) ).
thf(f103,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_2 ),
inference(equality_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
( ( $true
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_2 ),
inference(beta_eta_normalization,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_2 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_2 ),
inference(superposition,[status(thm)],[f23,f54]) ).
thf(f23,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
!= $true )
| ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f55,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[status(thm)],[f41,f52,f48]) ).
thf(f41,plain,
( ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true != $true )
| ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK8
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK8 @ X0 ) @ ( sK8 @ X0 ) )
!= $true )
| ( $true
= ( sP0 @ X0 ) )
| ( ( sP1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
= $true )
| ( ( X0 @ ( sK8 @ X0 ) @ ( sK8 @ X0 ) )
!= $true )
| ( $true
= ( sP0 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f19,f20]) ).
thf(f20,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
=> ( ( X0 @ ( sK8 @ X0 ) @ ( sK8 @ X0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
= $true )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true )
| ( $true
= ( sP0 @ X0 ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
= $true )
| ? [X4: $i > $o] :
( $true
!= ( X0 @ X4 @ X4 ) )
| ( $true
= ( sP0 @ X0 ) ) ),
inference(definition_folding,[status(thm)],[f7,f9,f8]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X6: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X6 )
= $true )
& ( ( X0 @ X6 @ X5 )
= $true )
& ? [X7: $i] :
( ( X5 @ X7 )
!= ( X6 @ X7 ) ) )
| ? [X4: $i > $o] :
( $true
!= ( X0 @ X4 @ X4 ) )
| ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X6: $i > $o,X5: $i > $o] :
( ? [X7: $i] :
( ( X5 @ X7 )
!= ( X6 @ X7 ) )
& ( ( X0 @ X6 @ X5 )
= $true )
& ( ( X0 @ X5 @ X6 )
= $true ) )
| ? [X1: $i > $o,X3: $i > $o,X2: $i > $o] :
( ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X3 @ X1 )
= $true ) )
| ? [X4: $i > $o] :
( $true
!= ( X0 @ X4 @ X4 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X6: $i > $o,X5: $i > $o] :
( ( ( ( X0 @ X6 @ X5 )
= $true )
& ( ( X0 @ X5 @ X6 )
= $true ) )
=> ! [X7: $i] :
( ( X5 @ X7 )
= ( X6 @ X7 ) ) )
& ! [X1: $i > $o,X3: $i > $o,X2: $i > $o] :
( ( ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X3 @ X1 )
= $true ) )
=> ( ( X0 @ X3 @ X2 )
= $true ) )
& ! [X4: $i > $o] :
( $true
= ( X0 @ X4 @ X4 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X3 @ X2 ) )
& ! [X4: $i > $o] : ( X0 @ X4 @ X4 )
& ! [X5: $i > $o,X6: $i > $o] :
( ( ( X0 @ X6 @ X5 )
& ( X0 @ X5 @ X6 ) )
=> ! [X7: $i] :
( ( X5 @ X7 )
= ( X6 @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X2: $i > $o,X3: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ! [X4: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ! [X1: $i] :
( ( X4 @ X1 )
= ( X5 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X2: $i > $o,X3: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ! [X4: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ! [X1: $i] :
( ( X4 @ X1 )
= ( X5 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0TI39aXRn2/DTF2THF_8828.p',cTHM120I_1_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV158^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:41:09 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SEV158^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.45 % Domain : Set Theory (Relations)
% 0.29/0.45 % Problem : TPS problem THM120I-1
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_0502 [Bro09]
% 0.29/0.45 % : THM120I-1 [TPS]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.54 v8.1.0, 0.64 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.40 v5.2.0, 0.60 v5.1.0, 0.80 v4.1.0, 0.67 v4.0.0
% 0.29/0.45 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.29/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.29/0.45 % Number of connectives : 20 ( 0 ~; 0 |; 4 &; 14 @)
% 0.29/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 11 ( 11 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.45 % Number of variables : 8 ( 0 ^; 7 !; 1 ?; 8 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 % : Polymorphic definitions expanded.
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(cTHM120I_1_pme,conjecture,
% 0.29/0.45 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.29/0.45 ( ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 0.29/0.45 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.29/0.45 ( ( ( R @ Xx @ Xy )
% 0.29/0.45 & ( R @ Xy @ Xz ) )
% 0.29/0.45 => ( R @ Xx @ Xz ) )
% 0.29/0.45 & ! [X: $i > $o,Y: $i > $o] :
% 0.29/0.45 ( ( ( R @ X @ Y )
% 0.29/0.45 & ( R @ Y @ X ) )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ( ( X @ Xx )
% 0.29/0.45 = ( Y @ Xx ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.45/1.27 ---- Embedded in THF ---
% 1.45/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.27 %%% Generated on Tue Feb 24 12:41:10 EST 2026
% 1.45/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.27 %%% Logic specification used:
% 1.45/1.27 %%% thf(spec, logic, $$dhol).
% 1.45/1.27
% 1.45/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0TI39aXRn2/DTF2DTF8828.p
% See solution above
% 1.45/1.27 ------------------------
% 1.45/1.28 ---- Cleaned THF ---
% 1.45/1.28 thf(cTHM120I_1_pme,conjecture,
% 1.45/1.28 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 1.45/1.28 ( ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 1.45/1.28 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.45/1.28 ( ( ( R @ Xx @ Xy )
% 1.45/1.28 & ( R @ Xy @ Xz ) )
% 1.45/1.28 => ( R @ Xx @ Xz ) )
% 1.45/1.28 & ! [X: $i > $o,Y: $i > $o] :
% 1.45/1.28 ( ( ( R @ X @ Y )
% 1.45/1.28 & ( R @ Y @ X ) )
% 1.45/1.28 => ! [Xx: $i] :
% 1.45/1.28 ( ( X @ Xx )
% 1.45/1.28 = ( Y @ Xx ) ) ) ) ).
% 1.45/1.28 ------------------------
% 1.61/1.30 % (8931)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_8828 for (2999ds/275Mi)
% 1.61/1.30 % (8928)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_8828 for (2999ds/27Mi)
% 1.61/1.30 % (8928)Refutation not found, incomplete strategy
% 1.61/1.30 % (8928)------------------------------
% 1.61/1.30 % (8928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (8928)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.30
% 1.61/1.30
% 1.61/1.30 % (8928)Memory used [KB]: 5500
% 1.61/1.30 % (8928)Time elapsed: 0.003 s
% 1.61/1.30 % (8928)Instructions burned: 5 (million)
% 1.61/1.30 % (8928)------------------------------
% 1.61/1.30 % (8928)------------------------------
% 1.61/1.30 % (8926)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8828 for (2999ds/183Mi)
% 1.61/1.31 % (8927)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_8828 for (2999ds/4Mi)
% 1.61/1.31 % (8929)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8828 for (2999ds/2Mi)
% 1.61/1.31 % (8930)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_8828 for (2999ds/2Mi)
% 1.61/1.31 % (8931)Refutation not found, incomplete strategy
% 1.61/1.31 % (8931)------------------------------
% 1.61/1.31 % (8931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (8931)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.31
% 1.61/1.31
% 1.61/1.31 % (8931)Memory used [KB]: 5628
% 1.61/1.31 % (8931)Time elapsed: 0.009 s
% 1.61/1.31 % (8931)Instructions burned: 23 (million)
% 1.61/1.31 % (8931)------------------------------
% 1.61/1.31 % (8931)------------------------------
% 1.61/1.31 % (8932)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8828 for (2999ds/18Mi)
% 1.61/1.31 % (8929)Instruction limit reached!
% 1.61/1.31 % (8929)------------------------------
% 1.61/1.31 % (8929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (8929)Termination reason: Unknown
% 1.61/1.31 % (8929)Termination phase: Property scanning
% 1.61/1.31 % (8930)Instruction limit reached!
% 1.61/1.31 % (8930)------------------------------
% 1.61/1.31 % (8930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (8930)Termination reason: Unknown
% 1.61/1.31 % (8930)Termination phase: Property scanning
% 1.61/1.31
% 1.61/1.31 % (8930)Memory used [KB]: 895
% 1.61/1.31 % (8930)Time elapsed: 0.003 s
% 1.61/1.31 % (8930)Instructions burned: 2 (million)
% 1.61/1.31 % (8930)------------------------------
% 1.61/1.31 % (8930)------------------------------
% 1.61/1.31
% 1.61/1.31 % (8929)Memory used [KB]: 895
% 1.61/1.31 % (8929)Time elapsed: 0.003 s
% 1.61/1.31 % (8929)Instructions burned: 2 (million)
% 1.61/1.31 % (8929)------------------------------
% 1.61/1.31 % (8929)------------------------------
% 1.61/1.31 % (8927)Instruction limit reached!
% 1.61/1.31 % (8927)------------------------------
% 1.61/1.31 % (8927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (8927)Termination reason: Unknown
% 1.61/1.31 % (8927)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (8927)Memory used [KB]: 5500
% 1.61/1.31 % (8927)Time elapsed: 0.005 s
% 1.61/1.31 % (8927)Instructions burned: 4 (million)
% 1.61/1.31 % (8927)------------------------------
% 1.61/1.31 % (8927)------------------------------
% 1.61/1.31 % (8933)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8828 for (2999ds/3Mi)
% 1.61/1.31 % (8933)Instruction limit reached!
% 1.61/1.31 % (8933)------------------------------
% 1.61/1.31 % (8933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (8933)Termination reason: Unknown
% 1.61/1.31 % (8933)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (8933)Memory used [KB]: 5500
% 1.61/1.31 % (8933)Time elapsed: 0.003 s
% 1.61/1.31 % (8933)Instructions burned: 3 (million)
% 1.61/1.31 % (8933)------------------------------
% 1.61/1.31 % (8933)------------------------------
% 1.61/1.31 % (8934)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_8828 for (2999ds/37Mi)
% 1.61/1.32 % (8932)Instruction limit reached!
% 1.61/1.32 % (8932)------------------------------
% 1.61/1.32 % (8932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (8932)Termination reason: Unknown
% 1.61/1.32 % (8932)Termination phase: Saturation
% 1.61/1.32
% 1.61/1.32 % (8932)Memory used [KB]: 5628
% 1.61/1.32 % (8932)Time elapsed: 0.013 s
% 1.61/1.32 % (8932)Instructions burned: 19 (million)
% 1.61/1.32 % (8932)------------------------------
% 1.61/1.32 % (8932)------------------------------
% 1.61/1.32 % (8938)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8828 for (2999ds/7Mi)
% 1.61/1.32 % (8936)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_8828 for (2999ds/3Mi)
% 1.61/1.32 % (8935)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_8828 for (2999ds/15Mi)
% 1.61/1.32 % (8936)Instruction limit reached!
% 1.61/1.32 % (8936)------------------------------
% 1.61/1.32 % (8936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (8936)Termination reason: Unknown
% 1.61/1.32 % (8936)Termination phase: Saturation
% 1.61/1.32
% 1.61/1.32 % (8936)Memory used [KB]: 5500
% 1.61/1.32 % (8936)Time elapsed: 0.003 s
% 1.61/1.32 % (8936)Instructions burned: 3 (million)
% 1.61/1.32 % (8936)------------------------------
% 1.61/1.32 % (8936)------------------------------
% 1.61/1.33 % (8938)Instruction limit reached!
% 1.61/1.33 % (8938)------------------------------
% 1.61/1.33 % (8938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (8938)Termination reason: Unknown
% 1.61/1.33 % (8938)Termination phase: Saturation
% 1.61/1.33
% 1.61/1.33 % (8938)Memory used [KB]: 1023
% 1.61/1.33 % (8938)Time elapsed: 0.005 s
% 1.61/1.33 % (8938)Instructions burned: 9 (million)
% 1.61/1.33 % (8937)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_8828 for (2999ds/1041Mi)
% 1.61/1.33 % (8938)------------------------------
% 1.61/1.33 % (8938)------------------------------
% 1.61/1.33 % (8934)Instruction limit reached!
% 1.61/1.33 % (8934)------------------------------
% 1.61/1.33 % (8934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (8934)Termination reason: Unknown
% 1.61/1.33 % (8934)Termination phase: Saturation
% 1.61/1.33
% 1.61/1.33 % (8934)Memory used [KB]: 6012
% 1.61/1.33 % (8934)Time elapsed: 0.012 s
% 1.61/1.33 % (8934)Instructions burned: 40 (million)
% 1.61/1.33 % (8934)------------------------------
% 1.61/1.33 % (8934)------------------------------
% 1.61/1.33 % (8935)First to succeed.
% 1.61/1.33 % (8939)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8828 for (2999ds/16Mi)
% 1.61/1.34 % (8935)Refutation found. Thanks to Tanya!
% 1.61/1.34 % SZS status Theorem for DTF2THF_8828
% 1.61/1.34 % SZS output start Proof for DTF2THF_8828
% 1.61/1.34 thf(func_def_3, type, sP0: (($i > $o) > ($i > $o) > $o) > $o).
% 1.61/1.34 thf(func_def_4, type, sP1: (($i > $o) > ($i > $o) > $o) > $o).
% 1.61/1.34 thf(func_def_5, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.61/1.34 thf(func_def_6, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.61/1.34 thf(func_def_7, type, sK4: (($i > $o) > ($i > $o) > $o) > $i).
% 1.61/1.34 thf(func_def_8, type, sK5: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.61/1.34 thf(func_def_9, type, sK6: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.61/1.34 thf(func_def_10, type, sK7: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.61/1.34 thf(func_def_11, type, sK8: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.61/1.34 thf(func_def_13, type, ph10: !>[X0: $tType]:(X0)).
% 1.61/1.34 thf(f192,plain,(
% 1.61/1.34 $false),
% 1.61/1.34 inference(avatar_sat_refutation,[status(thm)],[f55,f112,f121,f130,f148,f153,f158,f185,f186,f187,f189,f190])).
% 1.61/1.34 thf(f190,plain,(
% 1.61/1.34 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($false != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.61/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.61/1.34 thf(f189,plain,(
% 1.61/1.34 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($false != (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($false != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.61/1.34 thf(f187,plain,(
% 1.61/1.34 ($false != (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($false != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.61/1.34 thf(f186,plain,(
% 1.61/1.34 ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.61/1.34 thf(f185,plain,(
% 1.61/1.34 spl9_22 | spl9_1),
% 1.61/1.34 inference(avatar_split_clause,[status(thm)],[f180,f48,f182])).
% 1.61/1.34 thf(f182,definition,(
% 1.61/1.34 spl9_22 <=> ($false = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl9_22])],[avatar_definition])).
% 1.61/1.34 thf(f48,definition,(
% 1.61/1.34 spl9_1 <=> ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition])).
% 1.61/1.34 thf(f180,plain,(
% 1.61/1.34 ($false = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | spl9_1),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f179])).
% 1.61/1.34 thf(f179,plain,(
% 1.61/1.34 ($true != $true) | ($false = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | spl9_1),
% 1.61/1.34 inference(fool_paramodulation,[status(thm)],[f49])).
% 1.61/1.34 thf(f49,plain,(
% 1.61/1.34 ($true != (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | spl9_1),
% 1.61/1.34 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.61/1.34 thf(f158,plain,(
% 1.61/1.34 ~spl9_16 | ~spl9_1),
% 1.61/1.34 inference(avatar_split_clause,[status(thm)],[f137,f48,f155])).
% 1.61/1.34 thf(f155,definition,(
% 1.61/1.34 spl9_16 <=> ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl9_16])],[avatar_definition])).
% 1.61/1.34 thf(f137,plain,(
% 1.61/1.34 ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_1),
% 1.61/1.34 inference(equality_proxy_clausification,[status(thm)],[f136])).
% 1.61/1.34 thf(f136,plain,(
% 1.61/1.34 (((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl9_1),
% 1.61/1.34 inference(beta_eta_normalization,[status(thm)],[f135])).
% 1.61/1.34 thf(f135,plain,(
% 1.61/1.34 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl9_1),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.61/1.34 thf(f132,plain,(
% 1.61/1.34 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ($true != $true) | ~spl9_1),
% 1.61/1.34 inference(superposition,[status(thm)],[f26,f50])).
% 1.61/1.34 thf(f50,plain,(
% 1.61/1.34 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_1),
% 1.61/1.34 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.61/1.34 thf(f26,plain,(
% 1.61/1.34 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (sP0 @ X0)) | ((X0 @ (sK7 @ X0) @ (sK6 @ X0)) != $true)) )),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f18])).
% 1.61/1.34 thf(f18,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((X0 @ (sK5 @ X0) @ (sK6 @ X0)) = $true) & ((X0 @ (sK7 @ X0) @ (sK6 @ X0)) != $true) & ((X0 @ (sK7 @ X0) @ (sK5 @ X0)) = $true)) | ($true != (sP0 @ X0)))),
% 1.61/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f16,f17])).
% 1.61/1.34 thf(f17,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) = $true) & ((X0 @ X3 @ X2) != $true) & ((X0 @ X3 @ X1) = $true)) => (((X0 @ (sK5 @ X0) @ (sK6 @ X0)) = $true) & ((X0 @ (sK7 @ X0) @ (sK6 @ X0)) != $true) & ((X0 @ (sK7 @ X0) @ (sK5 @ X0)) = $true)))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f16,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) = $true) & ((X0 @ X3 @ X2) != $true) & ((X0 @ X3 @ X1) = $true)) | ($true != (sP0 @ X0)))),
% 1.61/1.34 inference(nnf_transformation,[status(thm)],[f8])).
% 1.61/1.34 thf(f8,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) = $true) & ((X0 @ X3 @ X2) != $true) & ((X0 @ X3 @ X1) = $true)) | ~($true = (sP0 @ X0)))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.61/1.34 thf(f153,plain,(
% 1.61/1.34 spl9_15 | ~spl9_1),
% 1.61/1.34 inference(avatar_split_clause,[status(thm)],[f140,f48,f150])).
% 1.61/1.34 thf(f150,definition,(
% 1.61/1.34 spl9_15 <=> ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl9_15])],[avatar_definition])).
% 1.61/1.34 thf(f140,plain,(
% 1.61/1.34 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_1),
% 1.61/1.34 inference(equality_proxy_clausification,[status(thm)],[f139])).
% 1.61/1.34 thf(f139,plain,(
% 1.61/1.34 (((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_1),
% 1.61/1.34 inference(beta_eta_normalization,[status(thm)],[f138])).
% 1.61/1.34 thf(f138,plain,(
% 1.61/1.34 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_1),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f134])).
% 1.61/1.34 thf(f134,plain,(
% 1.61/1.34 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ($true != $true) | ~spl9_1),
% 1.61/1.34 inference(superposition,[status(thm)],[f27,f50])).
% 1.61/1.34 thf(f27,plain,(
% 1.61/1.34 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (sP0 @ X0)) | ((X0 @ (sK5 @ X0) @ (sK6 @ X0)) = $true)) )),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f18])).
% 1.61/1.34 thf(f148,plain,(
% 1.61/1.34 spl9_14 | ~spl9_1),
% 1.61/1.34 inference(avatar_split_clause,[status(thm)],[f143,f48,f145])).
% 1.61/1.34 thf(f145,definition,(
% 1.61/1.34 spl9_14 <=> ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl9_14])],[avatar_definition])).
% 1.61/1.34 thf(f143,plain,(
% 1.61/1.34 ((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_1),
% 1.61/1.34 inference(equality_proxy_clausification,[status(thm)],[f142])).
% 1.61/1.34 thf(f142,plain,(
% 1.61/1.34 (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_1),
% 1.61/1.34 inference(beta_eta_normalization,[status(thm)],[f141])).
% 1.61/1.34 thf(f141,plain,(
% 1.61/1.34 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_1),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f133])).
% 1.61/1.34 thf(f133,plain,(
% 1.61/1.34 ($true != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_1),
% 1.61/1.34 inference(superposition,[status(thm)],[f25,f50])).
% 1.61/1.34 thf(f25,plain,(
% 1.61/1.34 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (sP0 @ X0)) | ((X0 @ (sK7 @ X0) @ (sK5 @ X0)) = $true)) )),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f18])).
% 1.61/1.34 thf(f130,plain,(
% 1.61/1.34 spl9_12 | spl9_13 | ~spl9_2),
% 1.61/1.34 inference(avatar_split_clause,[status(thm)],[f100,f52,f127,f123])).
% 1.61/1.34 thf(f123,definition,(
% 1.61/1.34 spl9_12 <=> ($false = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl9_12])],[avatar_definition])).
% 1.61/1.34 thf(f127,definition,(
% 1.61/1.34 spl9_13 <=> ($false = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl9_13])],[avatar_definition])).
% 1.61/1.34 thf(f52,definition,(
% 1.61/1.34 spl9_2 <=> ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition])).
% 1.61/1.34 thf(f100,plain,(
% 1.61/1.34 ($false = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2),
% 1.61/1.34 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.61/1.34 thf(f98,plain,(
% 1.61/1.34 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.61/1.34 thf(f95,plain,(
% 1.61/1.34 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != $true) | ~spl9_2),
% 1.61/1.34 inference(superposition,[status(thm)],[f22,f54])).
% 1.61/1.34 thf(f54,plain,(
% 1.61/1.34 ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_2),
% 1.61/1.34 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.61/1.34 thf(f22,plain,(
% 1.61/1.34 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) != $true) | ((sK3 @ X0 @ (sK4 @ X0)) != (sK2 @ X0 @ (sK4 @ X0)))) )),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f15])).
% 1.61/1.34 thf(f15,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((X0 @ (sK3 @ X0) @ (sK2 @ X0)) = $true) & ($true = (X0 @ (sK2 @ X0) @ (sK3 @ X0))) & ((sK3 @ X0 @ (sK4 @ X0)) != (sK2 @ X0 @ (sK4 @ X0)))) | ((sP1 @ X0) != $true))),
% 1.61/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f12,f14,f13])).
% 1.61/1.34 thf(f13,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (($true = (X0 @ X2 @ X1)) & ((X0 @ X1 @ X2) = $true) & ? [X3 : $i] : ((X1 @ X3) != (X2 @ X3))) => (((X0 @ (sK3 @ X0) @ (sK2 @ X0)) = $true) & ($true = (X0 @ (sK2 @ X0) @ (sK3 @ X0))) & ? [X3 : $i] : ((sK2 @ X0 @ X3) != (sK3 @ X0 @ X3))))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f14,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X3 : $i] : ((sK2 @ X0 @ X3) != (sK3 @ X0 @ X3)) => ((sK3 @ X0 @ (sK4 @ X0)) != (sK2 @ X0 @ (sK4 @ X0))))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f12,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (($true = (X0 @ X2 @ X1)) & ((X0 @ X1 @ X2) = $true) & ? [X3 : $i] : ((X1 @ X3) != (X2 @ X3))) | ((sP1 @ X0) != $true))),
% 1.61/1.34 inference(rectify,[status(thm)],[f11])).
% 1.61/1.34 thf(f11,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X6) = $true) & ((X0 @ X6 @ X5) = $true) & ? [X7 : $i] : ((X5 @ X7) != (X6 @ X7))) | ((sP1 @ X0) != $true))),
% 1.61/1.34 inference(nnf_transformation,[status(thm)],[f9])).
% 1.61/1.34 thf(f9,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X6) = $true) & ((X0 @ X6 @ X5) = $true) & ? [X7 : $i] : ((X5 @ X7) != (X6 @ X7))) | ~((sP1 @ X0) = $true))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.61/1.34 thf(f121,plain,(
% 1.61/1.34 spl9_10 | spl9_11 | ~spl9_2),
% 1.61/1.34 inference(avatar_split_clause,[status(thm)],[f99,f52,f118,f114])).
% 1.61/1.34 thf(f114,definition,(
% 1.61/1.34 spl9_10 <=> ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true)),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl9_10])],[avatar_definition])).
% 1.61/1.34 thf(f118,definition,(
% 1.61/1.34 spl9_11 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true)),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl9_11])],[avatar_definition])).
% 1.61/1.34 thf(f99,plain,(
% 1.61/1.34 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_2),
% 1.61/1.34 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.61/1.34 thf(f112,plain,(
% 1.61/1.34 spl9_9 | ~spl9_2),
% 1.61/1.34 inference(avatar_split_clause,[status(thm)],[f103,f52,f108])).
% 1.61/1.34 thf(f108,definition,(
% 1.61/1.34 spl9_9 <=> ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 introduced(definition,[new_symbols(naming,[spl9_9])],[avatar_definition])).
% 1.61/1.34 thf(f103,plain,(
% 1.61/1.34 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_2),
% 1.61/1.34 inference(equality_proxy_clausification,[status(thm)],[f102])).
% 1.61/1.34 thf(f102,plain,(
% 1.61/1.34 ($true = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2),
% 1.61/1.34 inference(beta_eta_normalization,[status(thm)],[f101])).
% 1.61/1.34 thf(f101,plain,(
% 1.61/1.34 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.61/1.34 thf(f97,plain,(
% 1.61/1.34 ($true != $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2),
% 1.61/1.34 inference(superposition,[status(thm)],[f23,f54])).
% 1.61/1.34 thf(f23,plain,(
% 1.61/1.34 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) != $true) | ($true = (X0 @ (sK2 @ X0) @ (sK3 @ X0)))) )),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f15])).
% 1.61/1.34 thf(f55,plain,(
% 1.61/1.34 spl9_1 | spl9_2),
% 1.61/1.34 inference(avatar_split_clause,[status(thm)],[f41,f52,f48])).
% 1.61/1.34 thf(f41,plain,(
% 1.61/1.34 ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.61/1.34 thf(f40,plain,(
% 1.61/1.34 ($true != $true) | ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 inference(boolean_simplification,[status(thm)],[f39])).
% 1.61/1.34 thf(f39,plain,(
% 1.61/1.34 (((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.61/1.34 thf(f30,plain,(
% 1.61/1.34 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.61/1.34 inference(primitive_instantiation,[status(thm)],[f28])).
% 1.61/1.34 thf(f28,plain,(
% 1.61/1.34 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK8 @ X0) @ (sK8 @ X0)) != $true) | ($true = (sP0 @ X0)) | ((sP1 @ X0) = $true)) )),
% 1.61/1.34 inference(cnf_transformation,[status(thm)],[f21])).
% 1.61/1.34 thf(f21,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) = $true) | ((X0 @ (sK8 @ X0) @ (sK8 @ X0)) != $true) | ($true = (sP0 @ X0)))),
% 1.61/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f19,f20])).
% 1.61/1.34 thf(f20,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) => ((X0 @ (sK8 @ X0) @ (sK8 @ X0)) != $true))),
% 1.61/1.34 introduced(definition,[],[choice_axiom])).
% 1.61/1.34 thf(f19,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) = $true) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) | ($true = (sP0 @ X0)))),
% 1.61/1.34 inference(rectify,[status(thm)],[f10])).
% 1.61/1.34 thf(f10,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) = $true) | ? [X4 : $i > $o] : ($true != (X0 @ X4 @ X4)) | ($true = (sP0 @ X0)))),
% 1.61/1.34 inference(definition_folding,[status(thm)],[f7,f9,f8])).
% 1.61/1.34 thf(f7,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X6) = $true) & ((X0 @ X6 @ X5) = $true) & ? [X7 : $i] : ((X5 @ X7) != (X6 @ X7))) | ? [X4 : $i > $o] : ($true != (X0 @ X4 @ X4)) | ? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) = $true) & ((X0 @ X3 @ X2) != $true) & ((X0 @ X3 @ X1) = $true)))),
% 1.61/1.34 inference(flattening,[status(thm)],[f6])).
% 1.61/1.34 thf(f6,plain,(
% 1.61/1.34 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X5 : $i > $o] : (? [X7 : $i] : ((X5 @ X7) != (X6 @ X7)) & (((X0 @ X6 @ X5) = $true) & ((X0 @ X5 @ X6) = $true))) | ? [X1 : $i > $o,X3 : $i > $o,X2 : $i > $o] : (((X0 @ X3 @ X2) != $true) & (((X0 @ X1 @ X2) = $true) & ((X0 @ X3 @ X1) = $true))) | ? [X4 : $i > $o] : ($true != (X0 @ X4 @ X4)))),
% 1.61/1.34 inference(ennf_transformation,[status(thm)],[f5])).
% 1.61/1.34 thf(f5,plain,(
% 1.61/1.34 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X6 : $i > $o,X5 : $i > $o] : ((((X0 @ X6 @ X5) = $true) & ((X0 @ X5 @ X6) = $true)) => ! [X7 : $i] : ((X5 @ X7) = (X6 @ X7))) & ! [X1 : $i > $o,X3 : $i > $o,X2 : $i > $o] : ((((X0 @ X1 @ X2) = $true) & ((X0 @ X3 @ X1) = $true)) => ((X0 @ X3 @ X2) = $true)) & ! [X4 : $i > $o] : ($true = (X0 @ X4 @ X4)))),
% 1.61/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 1.61/1.34 thf(f4,plain,(
% 1.61/1.34 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X1) & (X0 @ X1 @ X2)) => (X0 @ X3 @ X2)) & ! [X4 : $i > $o] : (X0 @ X4 @ X4) & ! [X5 : $i > $o,X6 : $i > $o] : (((X0 @ X6 @ X5) & (X0 @ X5 @ X6)) => ! [X7 : $i] : ((X5 @ X7) = (X6 @ X7))))),
% 1.61/1.34 inference(rectify,[status(thm)],[f2])).
% 1.61/1.34 thf(f2,negated_conjecture,(
% 1.61/1.34 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X2 : $i > $o,X3 : $i > $o,X1 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X1 : $i > $o] : (X0 @ X1 @ X1) & ! [X4 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => ! [X1 : $i] : ((X4 @ X1) = (X5 @ X1))))),
% 1.61/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.34 thf(f1,conjecture,(
% 1.61/1.34 ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X2 : $i > $o,X3 : $i > $o,X1 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X1 : $i > $o] : (X0 @ X1 @ X1) & ! [X4 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => ! [X1 : $i] : ((X4 @ X1) = (X5 @ X1))))),
% 1.61/1.34 file('/export/starexec/sandbox/tmp/tmp.0TI39aXRn2/DTF2THF_8828.p',cTHM120I_1_pme)).
% 1.61/1.34 % SZS output end Proof for DTF2THF_8828
% 1.61/1.34 % (8935)------------------------------
% 1.61/1.34 % (8935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.34 % (8935)Termination reason: Refutation
% 1.61/1.34
% 1.61/1.34 % (8935)Memory used [KB]: 5756
% 1.61/1.34 % (8935)Time elapsed: 0.033 s
% 1.61/1.34 % (8935)Instructions burned: 11 (million)
% 1.61/1.34 % (8935)------------------------------
% 1.61/1.34 % (8935)------------------------------
% 1.61/1.34 % (8925)Success in time 0.054 s
%------------------------------------------------------------------------------