%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV086^5 : 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 : n018.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 09:40:15 AM UTC 2026
% Result : Theorem 1.45s 1.22s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 86 ( 2 unt; 0 typ; 12 def)
% Number of atoms : 666 ( 279 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 674 ( 108 ~; 91 |; 46 &; 402 @)
% ( 15 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 415 ( 415 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 14 con; 0-2 aty)
% Number of variables : 348 ( 254 ^; 50 !; 44 ?; 348 :)
% 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 > $o ).
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 ).
thf(func_def_11,type,
sK8: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_13,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f207,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f64,f101,f112,f141,f146,f151,f152,f180,f189,f198,f200,f203,f204]) ).
thf(f204,plain,
( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
!= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f203,plain,
( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $false
!= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) )
| ( $false
!= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
!= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f200,plain,
( ( $false
!= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) )
| ( $false
!= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
!= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f198,plain,
( spl9_17
| spl9_18
| ~ spl9_4 ),
inference(avatar_split_clause,[status(thm)],[f168,f61,f195,f191]) ).
thf(f191,definition,
( spl9_17
<=> ( $false
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_17])],[avatar_definition]) ).
thf(f195,definition,
( spl9_18
<=> ( $false
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_18])],[avatar_definition]) ).
thf(f61,definition,
( spl9_4
<=> ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_4])],[avatar_definition]) ).
thf(f168,plain,
( ( $false
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_4 ),
inference(binary_proxy_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
( ( ( sK5
@ ^ [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 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_4 ),
inference(trivial_inequality_removal,[status(thm)],[f164]) ).
thf(f164,plain,
( ( $true != $true )
| ( ( sK5
@ ^ [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 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_4 ),
inference(superposition,[status(thm)],[f27,f63]) ).
thf(f63,plain,
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_4 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f27,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sK5 @ X0 @ ( sK7 @ X0 ) )
!= ( sK6 @ X0 @ ( sK7 @ X0 ) ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( ( sK5 @ X0 @ ( sK7 @ X0 ) )
!= ( sK6 @ X0 @ ( sK7 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK5 @ X0 ) @ ( sK6 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f15,f17,f16]) ).
thf(f16,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ? [X3: $i] :
( ( X2 @ X3 )
!= ( X1 @ X3 ) )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
=> ( ? [X3: $i] :
( ( sK6 @ X0 @ X3 )
!= ( sK5 @ X0 @ X3 ) )
& ( $true
= ( X0 @ ( sK5 @ X0 ) @ ( sK6 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X3: $i] :
( ( sK6 @ X0 @ X3 )
!= ( sK5 @ X0 @ X3 ) )
=> ( ( sK5 @ X0 @ ( sK7 @ X0 ) )
!= ( sK6 @ X0 @ ( sK7 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ? [X3: $i] :
( ( X2 @ X3 )
!= ( X1 @ X3 ) )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ? [X3: $i] :
( ( X2 @ X3 )
!= ( X1 @ X3 ) )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
| ( ( sP0 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f189,plain,
( spl9_15
| spl9_16
| ~ spl9_4 ),
inference(avatar_split_clause,[status(thm)],[f167,f61,f186,f182]) ).
thf(f182,definition,
( spl9_15
<=> ( $true
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_15])],[avatar_definition]) ).
thf(f186,definition,
( spl9_16
<=> ( $true
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_16])],[avatar_definition]) ).
thf(f167,plain,
( ( $true
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK7
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_4 ),
inference(binary_proxy_clausification,[status(thm)],[f166]) ).
thf(f180,plain,
( spl9_14
| ~ spl9_4 ),
inference(avatar_split_clause,[status(thm)],[f171,f61,f176]) ).
thf(f176,definition,
( spl9_14
<=> ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_14])],[avatar_definition]) ).
thf(f171,plain,
( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_4 ),
inference(equality_proxy_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
( ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_4 ),
inference(beta_eta_normalization,[status(thm)],[f169]) ).
thf(f169,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_4 ),
inference(trivial_inequality_removal,[status(thm)],[f163]) ).
thf(f163,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true != $true )
| ~ spl9_4 ),
inference(superposition,[status(thm)],[f25,f63]) ).
thf(f25,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f152,plain,
( ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( sK3
@ ^ [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 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f151,plain,
( spl9_12
| ~ spl9_3 ),
inference(avatar_split_clause,[status(thm)],[f130,f57,f148]) ).
thf(f148,definition,
( spl9_12
<=> ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_12])],[avatar_definition]) ).
thf(f57,definition,
( spl9_3
<=> ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition]) ).
thf(f130,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_3 ),
inference(equality_proxy_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
( ( $true
= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_3 ),
inference(beta_eta_normalization,[status(thm)],[f128]) ).
thf(f128,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl9_3 ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ~ spl9_3 ),
inference(superposition,[status(thm)],[f22,f59]) ).
thf(f59,plain,
( ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_3 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f22,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
!= $true )
| ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( $true
= ( X0 @ ( sK4 @ X0 ) @ ( sK3 @ X0 ) ) )
& ( $true
!= ( X0 @ ( sK4 @ X0 ) @ ( sK2 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f12,f13]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( $true
= ( X0 @ X3 @ X2 ) )
& ( $true
!= ( X0 @ X3 @ X1 ) )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
=> ( ( $true
= ( X0 @ ( sK4 @ X0 ) @ ( sK3 @ X0 ) ) )
& ( $true
!= ( X0 @ ( sK4 @ X0 ) @ ( sK2 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( $true
= ( X0 @ X3 @ X2 ) )
& ( $true
!= ( X0 @ X3 @ X1 ) )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X4: $i > $o,X6: $i > $o,X5: $i > $o] :
( ( $true
= ( X0 @ X5 @ X6 ) )
& ( ( X0 @ X5 @ X4 )
!= $true )
& ( $true
= ( X0 @ X6 @ X4 ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X4: $i > $o,X6: $i > $o,X5: $i > $o] :
( ( $true
= ( X0 @ X5 @ X6 ) )
& ( ( X0 @ X5 @ X4 )
!= $true )
& ( $true
= ( X0 @ X6 @ X4 ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f146,plain,
( ~ spl9_11
| ~ spl9_3 ),
inference(avatar_split_clause,[status(thm)],[f133,f57,f143]) ).
thf(f143,definition,
( spl9_11
<=> ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_11])],[avatar_definition]) ).
thf(f133,plain,
( ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_3 ),
inference(equality_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ~ spl9_3 ),
inference(beta_eta_normalization,[status(thm)],[f131]) ).
thf(f131,plain,
( ( $true
!= ( ^ [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 ) ) ) )
| ~ spl9_3 ),
inference(trivial_inequality_removal,[status(thm)],[f127]) ).
thf(f127,plain,
( ( $true != $true )
| ( $true
!= ( ^ [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 ) ) ) )
| ~ spl9_3 ),
inference(superposition,[status(thm)],[f23,f59]) ).
thf(f23,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( X0 @ ( sK4 @ X0 ) @ ( sK2 @ X0 ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f141,plain,
( spl9_10
| ~ spl9_3 ),
inference(avatar_split_clause,[status(thm)],[f136,f57,f138]) ).
thf(f138,definition,
( spl9_10
<=> ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_10])],[avatar_definition]) ).
thf(f136,plain,
( ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl9_3 ),
inference(equality_proxy_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $true
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl9_3 ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,plain,
( ( $true
= ( ^ [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 ) ) ) )
| ~ spl9_3 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true != $true )
| ( $true
= ( ^ [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 ) ) ) )
| ~ spl9_3 ),
inference(superposition,[status(thm)],[f24,f59]) ).
thf(f24,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0 @ ( sK4 @ X0 ) @ ( sK3 @ X0 ) ) )
| ( ( sP1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f112,plain,
( spl9_9
| spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f107,f48,f109]) ).
thf(f109,definition,
( spl9_9
<=> ( $false
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) ) ),
introduced(definition,[new_symbols(naming,[spl9_9])],[avatar_definition]) ).
thf(f48,definition,
( spl9_1
<=> ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) ) ),
introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition]) ).
thf(f107,plain,
( ( $false
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) )
| spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $false
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) )
| ( $true != $true )
| spl9_1 ),
inference(fool_paramodulation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $true
!= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) )
| spl9_1 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f101,plain,
~ spl9_1,
inference(avatar_contradiction_clause,[status(thm)],[f100]) ).
thf(f100,plain,
( $false
| ~ spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true != $true )
| ~ spl9_1 ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : $true
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) ) )
| ~ spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $true != $true )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : $true
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) ) )
| ~ spl9_1 ),
inference(superposition,[status(thm)],[f23,f50]) ).
thf(f50,plain,
( ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : $true ) )
| ~ spl9_1 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f64,plain,
( spl9_3
| spl9_4 ),
inference(avatar_split_clause,[status(thm)],[f42,f61,f57]) ).
thf(f42,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)],[f41]) ).
thf(f41,plain,
( ( $true != $true )
| ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( sP0
@ ^ [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 ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true
= ( sP0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( sP1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( ^ [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 ) ),
inference(primitive_instantiation,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( X0 @ ( sK8 @ X0 ) @ ( sK8 @ X0 ) ) )
| ( ( sP0 @ X0 )
= $true )
| ( ( sP1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
= $true )
| ( ( sP0 @ X0 )
= $true )
| ( $true
!= ( X0 @ ( sK8 @ X0 ) @ ( sK8 @ 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 )
=> ( $true
!= ( X0 @ ( sK8 @ X0 ) @ ( sK8 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
= $true )
| ( ( sP0 @ X0 )
= $true )
| ? [X1: $i > $o] :
( ( X0 @ X1 @ X1 )
!= $true ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( sP1 @ X0 )
= $true )
| ( ( sP0 @ X0 )
= $true )
| ? [X7: $i > $o] :
( $true
!= ( X0 @ X7 @ X7 ) ) ),
inference(definition_folding,[status(thm)],[f7,f9,f8]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X4: $i > $o,X6: $i > $o,X5: $i > $o] :
( ( $true
= ( X0 @ X5 @ X6 ) )
& ( ( X0 @ X5 @ X4 )
!= $true )
& ( $true
= ( X0 @ X6 @ X4 ) ) )
| ? [X1: $i > $o,X2: $i > $o] :
( ? [X3: $i] :
( ( X2 @ X3 )
!= ( X1 @ X3 ) )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
| ? [X7: $i > $o] :
( $true
!= ( X0 @ X7 @ X7 ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X1: $i > $o] :
( ? [X3: $i] :
( ( X2 @ X3 )
!= ( X1 @ X3 ) )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
| ? [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X5 @ X4 )
!= $true )
& ( $true
= ( X0 @ X5 @ X6 ) )
& ( $true
= ( X0 @ X6 @ X4 ) ) )
| ? [X7: $i > $o] :
( $true
!= ( X0 @ X7 @ X7 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X2: $i > $o,X1: $i > $o] :
( ( ( ( X0 @ X1 @ X2 )
= $true )
& ( $true
= ( X0 @ X2 @ X1 ) ) )
=> ! [X3: $i] :
( ( X2 @ X3 )
= ( X1 @ X3 ) ) )
& ! [X6: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ( $true
= ( X0 @ X5 @ X6 ) )
& ( $true
= ( X0 @ X6 @ X4 ) ) )
=> ( ( X0 @ X5 @ X4 )
= $true ) )
& ! [X7: $i > $o] :
( $true
= ( X0 @ X7 @ X7 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) ) )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( X0 @ X6 @ X4 )
& ( X0 @ X5 @ X6 ) )
=> ( X0 @ X5 @ X4 ) )
& ! [X7: $i > $o] : ( X0 @ X7 @ X7 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X4: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ! [X1: $i] :
( ( X4 @ X1 )
<=> ( X5 @ X1 ) ) )
& ! [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X1: $i > $o] : ( X0 @ X1 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X4: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ! [X1: $i] :
( ( X4 @ X1 )
<=> ( X5 @ X1 ) ) )
& ! [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X1: $i > $o] : ( X0 @ X1 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.uzHxZy6aoe/DTF2THF_26391.p',cTHM120I_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV086^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:39:46 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEV086^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Set Theory (Relations)
% 0.19/0.45 % Problem : TPS problem from RELN-THMS
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0918 [Bro09]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.33 v7.5.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.50 v6.4.0, 0.43 v6.3.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.25 v5.2.0, 0.50 v5.1.0, 0.75 v4.1.0, 0.67 v4.0.0
% 0.19/0.45 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.19/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.19/0.45 % Number of connectives : 21 ( 0 ~; 0 |; 4 &; 14 @)
% 0.19/0.45 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 11 ( 11 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.45 % Number of variables : 8 ( 0 ^; 7 !; 1 ?; 8 :)
% 0.19/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(cTHM120I_pme,conjecture,
% 0.19/0.45 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.19/0.45 ( ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 0.19/0.45 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.19/0.45 ( ( ( R @ Xx @ Xy )
% 0.19/0.45 & ( R @ Xy @ Xz ) )
% 0.19/0.45 => ( R @ Xx @ Xz ) )
% 0.19/0.45 & ! [X: $i > $o,Y: $i > $o] :
% 0.19/0.45 ( ( ( R @ X @ Y )
% 0.19/0.45 & ( R @ Y @ X ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( X @ Xx )
% 0.19/0.45 <=> ( Y @ Xx ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.37/1.17 ---- Embedded in THF ---
% 1.37/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.17 %%% Generated on Tue Feb 24 12:39:46 EST 2026
% 1.37/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.17 %%% Logic specification used:
% 1.37/1.17 %%% thf(spec, logic, $$dhol).
% 1.37/1.17
% 1.37/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.uzHxZy6aoe/DTF2DTF26391.p
% See solution above
% 1.37/1.17 ------------------------
% 1.37/1.17 ---- Cleaned THF ---
% 1.37/1.18 thf(cTHM120I_pme,conjecture,
% 1.37/1.18 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 1.37/1.18 ( ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 1.37/1.18 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.37/1.18 ( ( ( R @ Xx @ Xy )
% 1.37/1.18 & ( R @ Xy @ Xz ) )
% 1.37/1.18 => ( R @ Xx @ Xz ) )
% 1.37/1.18 & ! [X: $i > $o,Y: $i > $o] :
% 1.37/1.18 ( ( ( R @ X @ Y )
% 1.37/1.18 & ( R @ Y @ X ) )
% 1.37/1.18 => ! [Xx: $i] :
% 1.37/1.18 ( ( X @ Xx )
% 1.37/1.18 <=> ( Y @ Xx ) ) ) ) ).
% 1.37/1.18 ------------------------
% 1.37/1.19 % (26491)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26391 for (3000ds/2Mi)
% 1.37/1.19 % (26488)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26391 for (3000ds/183Mi)
% 1.37/1.19 % (26491)Instruction limit reached!
% 1.37/1.19 % (26491)------------------------------
% 1.37/1.19 % (26491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.19 % (26491)Termination reason: Unknown
% 1.37/1.19 % (26491)Termination phase: Saturation
% 1.37/1.19
% 1.37/1.19 % (26491)Memory used [KB]: 5500
% 1.37/1.19 % (26491)Time elapsed: 0.002 s
% 1.37/1.19 % (26491)Instructions burned: 2 (million)
% 1.37/1.19 % (26491)------------------------------
% 1.37/1.19 % (26491)------------------------------
% 1.37/1.19 % (26492)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_26391 for (3000ds/2Mi)
% 1.37/1.19 % (26493)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_26391 for (3000ds/275Mi)
% 1.37/1.19 % (26494)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26391 for (3000ds/18Mi)
% 1.37/1.19 % (26492)Instruction limit reached!
% 1.37/1.19 % (26492)------------------------------
% 1.37/1.19 % (26492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.19 % (26492)Termination reason: Unknown
% 1.37/1.19 % (26492)Termination phase: Saturation
% 1.37/1.19
% 1.37/1.19 % (26492)Memory used [KB]: 5500
% 1.37/1.19 % (26492)Time elapsed: 0.003 s
% 1.37/1.19 % (26492)Instructions burned: 2 (million)
% 1.37/1.19 % (26492)------------------------------
% 1.37/1.19 % (26492)------------------------------
% 1.45/1.20 % (26495)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26391 for (2999ds/3Mi)
% 1.45/1.20 % (26495)Instruction limit reached!
% 1.45/1.20 % (26495)------------------------------
% 1.45/1.20 % (26495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.20 % (26495)Termination reason: Unknown
% 1.45/1.20 % (26495)Termination phase: Saturation
% 1.45/1.20
% 1.45/1.20 % (26495)Memory used [KB]: 5500
% 1.45/1.20 % (26495)Time elapsed: 0.002 s
% 1.45/1.20 % (26495)Instructions burned: 3 (million)
% 1.45/1.20 % (26495)------------------------------
% 1.45/1.20 % (26495)------------------------------
% 1.45/1.20 % (26489)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_26391 for (3000ds/4Mi)
% 1.45/1.20 % (26489)Instruction limit reached!
% 1.45/1.20 % (26489)------------------------------
% 1.45/1.20 % (26489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.20 % (26489)Termination reason: Unknown
% 1.45/1.20 % (26489)Termination phase: Saturation
% 1.45/1.20
% 1.45/1.20 % (26489)Memory used [KB]: 5500
% 1.45/1.20 % (26489)Time elapsed: 0.004 s
% 1.45/1.20 % (26489)Instructions burned: 6 (million)
% 1.45/1.20 % (26489)------------------------------
% 1.45/1.20 % (26489)------------------------------
% 1.45/1.20 % (26494)Instruction limit reached!
% 1.45/1.20 % (26494)------------------------------
% 1.45/1.20 % (26494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.20 % (26494)Termination reason: Unknown
% 1.45/1.20 % (26494)Termination phase: Saturation
% 1.45/1.20
% 1.45/1.20 % (26494)Memory used [KB]: 5628
% 1.45/1.20 % (26494)Time elapsed: 0.011 s
% 1.45/1.20 % (26494)Instructions burned: 19 (million)
% 1.45/1.20 % (26494)------------------------------
% 1.45/1.20 % (26494)------------------------------
% 1.45/1.21 % (26493)Refutation not found, incomplete strategy
% 1.45/1.21 % (26493)------------------------------
% 1.45/1.21 % (26493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.21 % (26493)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.21
% 1.45/1.21
% 1.45/1.21 % (26493)Memory used [KB]: 5628
% 1.45/1.21 % (26493)Time elapsed: 0.013 s
% 1.45/1.21 % (26493)Instructions burned: 23 (million)
% 1.45/1.21 % (26493)------------------------------
% 1.45/1.21 % (26493)------------------------------
% 1.45/1.21 % (26497)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_26391 for (2999ds/15Mi)
% 1.45/1.21 % (26490)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_26391 for (3000ds/27Mi)
% 1.45/1.21 % (26496)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_26391 for (2999ds/37Mi)
% 1.45/1.21 % (26497)First to succeed.
% 1.45/1.21 % (26498)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_26391 for (2999ds/3Mi)
% 1.45/1.21 % (26498)Instruction limit reached!
% 1.45/1.21 % (26498)------------------------------
% 1.45/1.21 % (26498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.21 % (26498)Termination reason: Unknown
% 1.45/1.21 % (26498)Termination phase: Saturation
% 1.45/1.21
% 1.45/1.21 % (26498)Memory used [KB]: 5500
% 1.45/1.21 % (26498)Time elapsed: 0.003 s
% 1.45/1.21 % (26498)Instructions burned: 3 (million)
% 1.45/1.21 % (26498)------------------------------
% 1.45/1.21 % (26498)------------------------------
% 1.45/1.21 % (26490)Refutation not found, incomplete strategy
% 1.45/1.21 % (26490)------------------------------
% 1.45/1.21 % (26490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.21 % (26490)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.21
% 1.45/1.21
% 1.45/1.21 % (26490)Memory used [KB]: 5500
% 1.45/1.21 % (26490)Time elapsed: 0.009 s
% 1.45/1.21 % (26490)Instructions burned: 6 (million)
% 1.45/1.21 % (26490)------------------------------
% 1.45/1.21 % (26490)------------------------------
% 1.45/1.22 % (26497)Refutation found. Thanks to Tanya!
% 1.45/1.22 % SZS status Theorem for DTF2THF_26391
% 1.45/1.22 % SZS output start Proof for DTF2THF_26391
% 1.45/1.22 thf(func_def_3, type, sP0: (($i > $o) > ($i > $o) > $o) > $o).
% 1.45/1.22 thf(func_def_4, type, sP1: (($i > $o) > ($i > $o) > $o) > $o).
% 1.45/1.22 thf(func_def_5, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.45/1.22 thf(func_def_6, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.45/1.22 thf(func_def_7, type, sK4: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.45/1.22 thf(func_def_8, type, sK5: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.45/1.22 thf(func_def_9, type, sK6: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.45/1.22 thf(func_def_10, type, sK7: (($i > $o) > ($i > $o) > $o) > $i).
% 1.45/1.22 thf(func_def_11, type, sK8: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.45/1.22 thf(func_def_13, type, ph10: !>[X0: $tType]:(X0)).
% 1.45/1.22 thf(f207,plain,(
% 1.45/1.22 $false),
% 1.45/1.22 inference(avatar_sat_refutation,[status(thm)],[f64,f101,f112,f141,f146,f151,f152,f180,f189,f198,f200,f203,f204])).
% 1.45/1.22 thf(f204,plain,(
% 1.45/1.22 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.45/1.22 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.45/1.22 thf(f203,plain,(
% 1.45/1.22 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($false != (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | ($false != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))),
% 1.45/1.22 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.45/1.22 thf(f200,plain,(
% 1.45/1.22 ($false != (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | ($false != (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))),
% 1.45/1.22 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.45/1.22 thf(f198,plain,(
% 1.45/1.22 spl9_17 | spl9_18 | ~spl9_4),
% 1.45/1.22 inference(avatar_split_clause,[status(thm)],[f168,f61,f195,f191])).
% 1.45/1.22 thf(f191,definition,(
% 1.45/1.22 spl9_17 <=> ($false = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_17])],[avatar_definition])).
% 1.45/1.22 thf(f195,definition,(
% 1.45/1.22 spl9_18 <=> ($false = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_18])],[avatar_definition])).
% 1.45/1.22 thf(f61,definition,(
% 1.45/1.22 spl9_4 <=> ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_4])],[avatar_definition])).
% 1.45/1.22 thf(f168,plain,(
% 1.45/1.22 ($false = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_4),
% 1.45/1.22 inference(binary_proxy_clausification,[status(thm)],[f166])).
% 1.45/1.22 thf(f166,plain,(
% 1.45/1.22 ((sK5 @ (^[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)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_4),
% 1.45/1.22 inference(trivial_inequality_removal,[status(thm)],[f164])).
% 1.45/1.22 thf(f164,plain,(
% 1.45/1.22 ($true != $true) | ((sK5 @ (^[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)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_4),
% 1.45/1.22 inference(superposition,[status(thm)],[f27,f63])).
% 1.45/1.22 thf(f63,plain,(
% 1.45/1.22 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_4),
% 1.45/1.22 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.45/1.22 thf(f27,plain,(
% 1.45/1.22 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sK5 @ X0 @ (sK7 @ X0)) != (sK6 @ X0 @ (sK7 @ X0))) | ((sP0 @ X0) != $true)) )),
% 1.45/1.22 inference(cnf_transformation,[status(thm)],[f18])).
% 1.45/1.22 thf(f18,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((sK5 @ X0 @ (sK7 @ X0)) != (sK6 @ X0 @ (sK7 @ X0))) & ($true = (X0 @ (sK5 @ X0) @ (sK6 @ X0))) & ($true = (X0 @ (sK6 @ X0) @ (sK5 @ X0)))) | ((sP0 @ X0) != $true))),
% 1.45/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f15,f17,f16])).
% 1.45/1.22 thf(f16,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (? [X3 : $i] : ((X2 @ X3) != (X1 @ X3)) & ((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X2 @ X1))) => (? [X3 : $i] : ((sK6 @ X0 @ X3) != (sK5 @ X0 @ X3)) & ($true = (X0 @ (sK5 @ X0) @ (sK6 @ X0))) & ($true = (X0 @ (sK6 @ X0) @ (sK5 @ X0)))))),
% 1.45/1.22 introduced(definition,[],[choice_axiom])).
% 1.45/1.22 thf(f17,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X3 : $i] : ((sK6 @ X0 @ X3) != (sK5 @ X0 @ X3)) => ((sK5 @ X0 @ (sK7 @ X0)) != (sK6 @ X0 @ (sK7 @ X0))))),
% 1.45/1.22 introduced(definition,[],[choice_axiom])).
% 1.45/1.22 thf(f15,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (? [X3 : $i] : ((X2 @ X3) != (X1 @ X3)) & ((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X2 @ X1))) | ((sP0 @ X0) != $true))),
% 1.45/1.22 inference(nnf_transformation,[status(thm)],[f8])).
% 1.45/1.22 thf(f8,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (? [X3 : $i] : ((X2 @ X3) != (X1 @ X3)) & ((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X2 @ X1))) | ~((sP0 @ X0) = $true))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.45/1.22 thf(f189,plain,(
% 1.45/1.22 spl9_15 | spl9_16 | ~spl9_4),
% 1.45/1.22 inference(avatar_split_clause,[status(thm)],[f167,f61,f186,f182])).
% 1.45/1.22 thf(f182,definition,(
% 1.45/1.22 spl9_15 <=> ($true = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_15])],[avatar_definition])).
% 1.45/1.22 thf(f186,definition,(
% 1.45/1.22 spl9_16 <=> ($true = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_16])],[avatar_definition])).
% 1.45/1.22 thf(f167,plain,(
% 1.45/1.22 ($true = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_4),
% 1.45/1.22 inference(binary_proxy_clausification,[status(thm)],[f166])).
% 1.45/1.22 thf(f180,plain,(
% 1.45/1.22 spl9_14 | ~spl9_4),
% 1.45/1.22 inference(avatar_split_clause,[status(thm)],[f171,f61,f176])).
% 1.45/1.22 thf(f176,definition,(
% 1.45/1.22 spl9_14 <=> ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_14])],[avatar_definition])).
% 1.45/1.22 thf(f171,plain,(
% 1.45/1.22 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_4),
% 1.45/1.22 inference(equality_proxy_clausification,[status(thm)],[f170])).
% 1.45/1.22 thf(f170,plain,(
% 1.45/1.22 ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_4),
% 1.45/1.22 inference(beta_eta_normalization,[status(thm)],[f169])).
% 1.45/1.22 thf(f169,plain,(
% 1.45/1.22 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_4),
% 1.45/1.22 inference(trivial_inequality_removal,[status(thm)],[f163])).
% 1.45/1.22 thf(f163,plain,(
% 1.45/1.22 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != $true) | ~spl9_4),
% 1.45/1.22 inference(superposition,[status(thm)],[f25,f63])).
% 1.45/1.22 thf(f25,plain,(
% 1.45/1.22 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (X0 @ (sK6 @ X0) @ (sK5 @ X0))) | ((sP0 @ X0) != $true)) )),
% 1.45/1.22 inference(cnf_transformation,[status(thm)],[f18])).
% 1.45/1.22 thf(f152,plain,(
% 1.45/1.22 ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK3 @ (^[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))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.45/1.22 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.45/1.22 thf(f151,plain,(
% 1.45/1.22 spl9_12 | ~spl9_3),
% 1.45/1.22 inference(avatar_split_clause,[status(thm)],[f130,f57,f148])).
% 1.45/1.22 thf(f148,definition,(
% 1.45/1.22 spl9_12 <=> ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_12])],[avatar_definition])).
% 1.45/1.22 thf(f57,definition,(
% 1.45/1.22 spl9_3 <=> ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition])).
% 1.45/1.22 thf(f130,plain,(
% 1.45/1.22 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_3),
% 1.45/1.22 inference(equality_proxy_clausification,[status(thm)],[f129])).
% 1.45/1.22 thf(f129,plain,(
% 1.45/1.22 ($true = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_3),
% 1.45/1.22 inference(beta_eta_normalization,[status(thm)],[f128])).
% 1.45/1.22 thf(f128,plain,(
% 1.45/1.22 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_3),
% 1.45/1.22 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.45/1.22 thf(f126,plain,(
% 1.45/1.22 ($true != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_3),
% 1.45/1.22 inference(superposition,[status(thm)],[f22,f59])).
% 1.45/1.22 thf(f59,plain,(
% 1.45/1.22 ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_3),
% 1.45/1.22 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.45/1.22 thf(f22,plain,(
% 1.45/1.22 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) != $true) | ($true = (X0 @ (sK3 @ X0) @ (sK2 @ X0)))) )),
% 1.45/1.22 inference(cnf_transformation,[status(thm)],[f14])).
% 1.45/1.22 thf(f14,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((($true = (X0 @ (sK4 @ X0) @ (sK3 @ X0))) & ($true != (X0 @ (sK4 @ X0) @ (sK2 @ X0))) & ($true = (X0 @ (sK3 @ X0) @ (sK2 @ X0)))) | ((sP1 @ X0) != $true))),
% 1.45/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f12,f13])).
% 1.45/1.22 thf(f13,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (($true = (X0 @ X3 @ X2)) & ($true != (X0 @ X3 @ X1)) & ($true = (X0 @ X2 @ X1))) => (($true = (X0 @ (sK4 @ X0) @ (sK3 @ X0))) & ($true != (X0 @ (sK4 @ X0) @ (sK2 @ X0))) & ($true = (X0 @ (sK3 @ X0) @ (sK2 @ X0)))))),
% 1.45/1.22 introduced(definition,[],[choice_axiom])).
% 1.45/1.22 thf(f12,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (($true = (X0 @ X3 @ X2)) & ($true != (X0 @ X3 @ X1)) & ($true = (X0 @ X2 @ X1))) | ((sP1 @ X0) != $true))),
% 1.45/1.22 inference(rectify,[status(thm)],[f11])).
% 1.45/1.22 thf(f11,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X4 : $i > $o,X6 : $i > $o,X5 : $i > $o] : (($true = (X0 @ X5 @ X6)) & ((X0 @ X5 @ X4) != $true) & ($true = (X0 @ X6 @ X4))) | ((sP1 @ X0) != $true))),
% 1.45/1.22 inference(nnf_transformation,[status(thm)],[f9])).
% 1.45/1.22 thf(f9,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X4 : $i > $o,X6 : $i > $o,X5 : $i > $o] : (($true = (X0 @ X5 @ X6)) & ((X0 @ X5 @ X4) != $true) & ($true = (X0 @ X6 @ X4))) | ~((sP1 @ X0) = $true))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.45/1.22 thf(f146,plain,(
% 1.45/1.22 ~spl9_11 | ~spl9_3),
% 1.45/1.22 inference(avatar_split_clause,[status(thm)],[f133,f57,f143])).
% 1.45/1.22 thf(f143,definition,(
% 1.45/1.22 spl9_11 <=> ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_11])],[avatar_definition])).
% 1.45/1.22 thf(f133,plain,(
% 1.45/1.22 ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_3),
% 1.45/1.22 inference(equality_proxy_clausification,[status(thm)],[f132])).
% 1.45/1.22 thf(f132,plain,(
% 1.45/1.22 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl9_3),
% 1.45/1.22 inference(beta_eta_normalization,[status(thm)],[f131])).
% 1.45/1.22 thf(f131,plain,(
% 1.45/1.22 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_3),
% 1.45/1.22 inference(trivial_inequality_removal,[status(thm)],[f127])).
% 1.45/1.22 thf(f127,plain,(
% 1.45/1.22 ($true != $true) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_3),
% 1.45/1.22 inference(superposition,[status(thm)],[f23,f59])).
% 1.45/1.22 thf(f23,plain,(
% 1.45/1.22 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (X0 @ (sK4 @ X0) @ (sK2 @ X0))) | ((sP1 @ X0) != $true)) )),
% 1.45/1.22 inference(cnf_transformation,[status(thm)],[f14])).
% 1.45/1.22 thf(f141,plain,(
% 1.45/1.22 spl9_10 | ~spl9_3),
% 1.45/1.22 inference(avatar_split_clause,[status(thm)],[f136,f57,f138])).
% 1.45/1.22 thf(f138,definition,(
% 1.45/1.22 spl9_10 <=> ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_10])],[avatar_definition])).
% 1.45/1.22 thf(f136,plain,(
% 1.45/1.22 ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_3),
% 1.45/1.22 inference(equality_proxy_clausification,[status(thm)],[f135])).
% 1.45/1.22 thf(f135,plain,(
% 1.45/1.22 ($true = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_3),
% 1.45/1.22 inference(beta_eta_normalization,[status(thm)],[f134])).
% 1.45/1.22 thf(f134,plain,(
% 1.45/1.22 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_3),
% 1.45/1.22 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.45/1.22 thf(f125,plain,(
% 1.45/1.22 ($true != $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_3),
% 1.45/1.22 inference(superposition,[status(thm)],[f24,f59])).
% 1.45/1.22 thf(f24,plain,(
% 1.45/1.22 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (X0 @ (sK4 @ X0) @ (sK3 @ X0))) | ((sP1 @ X0) != $true)) )),
% 1.45/1.22 inference(cnf_transformation,[status(thm)],[f14])).
% 1.45/1.22 thf(f112,plain,(
% 1.45/1.22 spl9_9 | spl9_1),
% 1.45/1.22 inference(avatar_split_clause,[status(thm)],[f107,f48,f109])).
% 1.45/1.22 thf(f109,definition,(
% 1.45/1.22 spl9_9 <=> ($false = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_9])],[avatar_definition])).
% 1.45/1.22 thf(f48,definition,(
% 1.45/1.22 spl9_1 <=> ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))),
% 1.45/1.22 introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition])).
% 1.45/1.22 thf(f107,plain,(
% 1.45/1.22 ($false = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | spl9_1),
% 1.45/1.22 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.45/1.22 thf(f106,plain,(
% 1.45/1.22 ($false = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | ($true != $true) | spl9_1),
% 1.45/1.22 inference(fool_paramodulation,[status(thm)],[f49])).
% 1.45/1.22 thf(f49,plain,(
% 1.45/1.22 ($true != (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | spl9_1),
% 1.45/1.22 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.45/1.22 thf(f101,plain,(
% 1.45/1.22 ~spl9_1),
% 1.45/1.22 inference(avatar_contradiction_clause,[status(thm)],[f100])).
% 1.45/1.22 thf(f100,plain,(
% 1.45/1.22 $false | ~spl9_1),
% 1.45/1.22 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.45/1.22 thf(f99,plain,(
% 1.45/1.22 ($true != $true) | ~spl9_1),
% 1.45/1.22 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.45/1.22 thf(f98,plain,(
% 1.45/1.22 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))) | ~spl9_1),
% 1.45/1.22 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.45/1.22 thf(f97,plain,(
% 1.45/1.22 ($true != $true) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))) | ~spl9_1),
% 1.45/1.22 inference(superposition,[status(thm)],[f23,f50])).
% 1.45/1.22 thf(f50,plain,(
% 1.45/1.22 ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | ~spl9_1),
% 1.45/1.22 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.45/1.22 thf(f64,plain,(
% 1.45/1.22 spl9_3 | spl9_4),
% 1.45/1.22 inference(avatar_split_clause,[status(thm)],[f42,f61,f57])).
% 1.45/1.22 thf(f42,plain,(
% 1.45/1.22 ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.45/1.22 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.45/1.22 thf(f41,plain,(
% 1.45/1.22 ($true != $true) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.45/1.22 inference(boolean_simplification,[status(thm)],[f40])).
% 1.45/1.22 thf(f40,plain,(
% 1.45/1.22 ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true = (sP0 @ (^[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)))))) != $true)),
% 1.45/1.22 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.45/1.22 thf(f30,plain,(
% 1.45/1.22 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | (((^[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)))))) != $true)),
% 1.45/1.22 inference(primitive_instantiation,[status(thm)],[f28])).
% 1.45/1.22 thf(f28,plain,(
% 1.45/1.22 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (X0 @ (sK8 @ X0) @ (sK8 @ X0))) | ((sP0 @ X0) = $true) | ((sP1 @ X0) = $true)) )),
% 1.45/1.22 inference(cnf_transformation,[status(thm)],[f21])).
% 1.45/1.22 thf(f21,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) = $true) | ((sP0 @ X0) = $true) | ($true != (X0 @ (sK8 @ X0) @ (sK8 @ X0))))),
% 1.45/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f19,f20])).
% 1.45/1.22 thf(f20,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) => ($true != (X0 @ (sK8 @ X0) @ (sK8 @ X0))))),
% 1.45/1.22 introduced(definition,[],[choice_axiom])).
% 1.45/1.22 thf(f19,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) = $true) | ((sP0 @ X0) = $true) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true))),
% 1.45/1.22 inference(rectify,[status(thm)],[f10])).
% 1.45/1.22 thf(f10,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP1 @ X0) = $true) | ((sP0 @ X0) = $true) | ? [X7 : $i > $o] : ($true != (X0 @ X7 @ X7)))),
% 1.45/1.22 inference(definition_folding,[status(thm)],[f7,f9,f8])).
% 1.45/1.22 thf(f7,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X4 : $i > $o,X6 : $i > $o,X5 : $i > $o] : (($true = (X0 @ X5 @ X6)) & ((X0 @ X5 @ X4) != $true) & ($true = (X0 @ X6 @ X4))) | ? [X1 : $i > $o,X2 : $i > $o] : (? [X3 : $i] : ((X2 @ X3) != (X1 @ X3)) & ((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X2 @ X1))) | ? [X7 : $i > $o] : ($true != (X0 @ X7 @ X7)))),
% 1.45/1.22 inference(flattening,[status(thm)],[f6])).
% 1.45/1.22 thf(f6,plain,(
% 1.45/1.22 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X1 : $i > $o] : (? [X3 : $i] : ((X2 @ X3) != (X1 @ X3)) & (((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X2 @ X1)))) | ? [X6 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (((X0 @ X5 @ X4) != $true) & (($true = (X0 @ X5 @ X6)) & ($true = (X0 @ X6 @ X4)))) | ? [X7 : $i > $o] : ($true != (X0 @ X7 @ X7)))),
% 1.45/1.22 inference(ennf_transformation,[status(thm)],[f5])).
% 1.45/1.22 thf(f5,plain,(
% 1.45/1.22 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X2 : $i > $o,X1 : $i > $o] : ((((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X2 @ X1))) => ! [X3 : $i] : ((X2 @ X3) = (X1 @ X3))) & ! [X6 : $i > $o,X5 : $i > $o,X4 : $i > $o] : ((($true = (X0 @ X5 @ X6)) & ($true = (X0 @ X6 @ X4))) => ((X0 @ X5 @ X4) = $true)) & ! [X7 : $i > $o] : ($true = (X0 @ X7 @ X7)))),
% 1.45/1.22 inference(fool_elimination,[status(thm)],[f4])).
% 1.45/1.22 thf(f4,plain,(
% 1.45/1.22 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X2)) => ! [X3 : $i] : ((X1 @ X3) <=> (X2 @ X3))) & ! [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (((X0 @ X6 @ X4) & (X0 @ X5 @ X6)) => (X0 @ X5 @ X4)) & ! [X7 : $i > $o] : (X0 @ X7 @ X7))),
% 1.45/1.22 inference(rectify,[status(thm)],[f2])).
% 1.45/1.22 thf(f2,negated_conjecture,(
% 1.45/1.22 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X4 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => ! [X1 : $i] : ((X4 @ X1) <=> (X5 @ X1))) & ! [X3 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X1 : $i > $o] : (X0 @ X1 @ X1))),
% 1.45/1.22 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/1.22 thf(f1,conjecture,(
% 1.45/1.22 ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X4 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => ! [X1 : $i] : ((X4 @ X1) <=> (X5 @ X1))) & ! [X3 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X1 : $i > $o] : (X0 @ X1 @ X1))),
% 1.45/1.22 file('/export/starexec/sandbox/tmp/tmp.uzHxZy6aoe/DTF2THF_26391.p',cTHM120I_pme)).
% 1.45/1.22 % SZS output end Proof for DTF2THF_26391
% 1.45/1.22 % (26497)------------------------------
% 1.45/1.22 % (26497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.22 % (26497)Termination reason: Refutation
% 1.45/1.22
% 1.45/1.22 % (26497)Memory used [KB]: 5756
% 1.45/1.22 % (26497)Time elapsed: 0.007 s
% 1.45/1.22 % (26497)Instructions burned: 12 (million)
% 1.45/1.22 % (26497)------------------------------
% 1.45/1.22 % (26497)------------------------------
% 1.45/1.22 % (26487)Success in time 0.031 s
%------------------------------------------------------------------------------