%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV222^5 : 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 : n028.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 09:40:35 AM UTC 2026
% Result : Theorem 1.31s 1.14s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 1 unt; 0 typ; 7 def)
% Number of atoms : 622 ( 188 equ; 0 cnn)
% Maximal formula atoms : 24 ( 8 avg)
% Number of connectives : 606 ( 123 ~; 179 |; 43 &; 234 @)
% ( 12 <=>; 14 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 114 ( 30 ^; 54 !; 30 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cZ: a > $o ).
thf(func_def_2,type,
cW: ( a > $o ) > $o ).
thf(func_def_9,type,
sK0: a ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_11,type,
sK2: a > $o ).
thf(func_def_12,type,
sK3: a > $o ).
thf(func_def_15,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f107,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f38,f43,f52,f53,f59,f63,f64,f65,f66,f91,f102,f106]) ).
thf(f106,plain,
( spl4_1
| ~ spl4_4
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
| spl4_1
| ~ spl4_4
| ~ spl4_7 ),
inference(subsumption_resolution,[status(thm)],[f104,f33]) ).
thf(f33,plain,
( ( ( sK1 @ sK0 )
!= $true )
| spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl4_1
<=> ( ( sK1 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f104,plain,
( ( ( sK1 @ sK0 )
= $true )
| ~ spl4_4
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f103]) ).
thf(f103,plain,
( ( ( sK1 @ sK0 )
= $true )
| ( $true != $true )
| ~ spl4_4
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f62,f47]) ).
thf(f47,plain,
( ( ( cW @ sK1 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl4_4
<=> ( ( cW @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f62,plain,
( ! [X4: a > $o] :
( ( $true
!= ( cW @ X4 ) )
| ( ( X4 @ sK0 )
= $true ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl4_7
<=> ! [X4: a > $o] :
( ( $true
!= ( cW @ X4 ) )
| ( ( X4 @ sK0 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition]) ).
thf(f102,plain,
( ~ spl4_2
| ~ spl4_5
| spl4_6
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f101]) ).
thf(f101,plain,
( $false
| ~ spl4_2
| ~ spl4_5
| spl4_6
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_5
| spl4_6
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f96,f94]) ).
thf(f94,plain,
( ( ( sK3 @ sK0 )
= $false )
| ~ spl4_2
| spl4_6 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $true != $true )
| ( ( sK3 @ sK0 )
= $false )
| ~ spl4_2
| spl4_6 ),
inference(superposition,[status(thm)],[f58,f73]) ).
thf(f73,plain,
( ! [X1: a] :
( ( $true
= ( sK2 @ X1 ) )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ! [X1: a] :
( ( ( ( sK3 @ X1 )
| ( cZ @ X1 ) )
= $false )
| ( $true
= ( sK2 @ X1 ) ) )
| ~ spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
| ( cZ @ X1 ) )
= ( sK2 @ X1 ) )
| ~ spl4_2 ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( cZ @ Y0 ) )
@ X1 )
= ( sK2 @ X1 ) )
| ~ spl4_2 ),
inference(argument_congruence,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( cZ @ Y0 ) ) )
= sK2 )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl4_2
<=> ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( cZ @ Y0 ) ) )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f58,plain,
( ( $true
!= ( sK2 @ sK0 ) )
| spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl4_6
<=> ( $true
= ( sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f96,plain,
( ( $true
= ( sK3 @ sK0 ) )
| ~ spl4_5
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ( $true
= ( sK3 @ sK0 ) )
| ( $true != $true )
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f62,f51]) ).
thf(f51,plain,
( ( ( cW @ sK3 )
= $true )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl4_5
<=> ( ( cW @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f91,plain,
( ~ spl4_2
| ~ spl4_3
| spl4_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f90]) ).
thf(f90,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| spl4_6 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_3
| spl4_6 ),
inference(superposition,[status(thm)],[f41,f85]) ).
thf(f85,plain,
( ( ( cZ @ sK0 )
= $false )
| ~ spl4_2
| spl4_6 ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
( ( ( cZ @ sK0 )
= $false )
| ( $true != $true )
| ~ spl4_2
| spl4_6 ),
inference(superposition,[status(thm)],[f58,f72]) ).
thf(f72,plain,
( ! [X1: a] :
( ( $true
= ( sK2 @ X1 ) )
| ( ( cZ @ X1 )
= $false ) )
| ~ spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f41,plain,
( ( ( cZ @ sK0 )
= $true )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl4_3
<=> ( ( cZ @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f66,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f19,f56,f40]) ).
thf(f19,plain,
( ( $true
!= ( sK2 @ sK0 ) )
| ( ( cZ @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ( ( sK1 @ sK0 )
!= $true )
& ( ( cW @ sK1 )
= $true )
& ( ( cZ @ sK0 )
!= $true ) )
| ( ( $true
!= ( sK2 @ sK0 ) )
& ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( cZ @ Y0 ) ) )
= sK2 )
& ( ( cW @ sK3 )
= $true ) ) )
& ( ! [X4: a > $o] :
( ( ( X4 @ sK0 )
= $true )
| ( $true
!= ( cW @ X4 ) ) )
| ( ( cZ @ sK0 )
= $true )
| ! [X5: a > $o] :
( ( $true
= ( X5 @ sK0 ) )
| ! [X6: a > $o] :
( ( ( ^ [Y0: a] :
( ( X6 @ Y0 )
| ( cZ @ Y0 ) ) )
!= X5 )
| ( $true
!= ( cW @ X6 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f14,f13,f12,f11]) ).
thf(f11,plain,
( ? [X0: a] :
( ( ( ? [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
& ( ( cW @ X1 )
= $true ) )
& ( ( cZ @ X0 )
!= $true ) )
| ? [X2: a > $o] :
( ( ( X2 @ X0 )
!= $true )
& ? [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( X3 @ Y0 )
| ( cZ @ Y0 ) ) )
= X2 )
& ( ( cW @ X3 )
= $true ) ) ) )
& ( ! [X4: a > $o] :
( ( ( X4 @ X0 )
= $true )
| ( $true
!= ( cW @ X4 ) ) )
| ( ( cZ @ X0 )
= $true )
| ! [X5: a > $o] :
( ( ( X5 @ X0 )
= $true )
| ! [X6: a > $o] :
( ( ( ^ [Y0: a] :
( ( X6 @ Y0 )
| ( cZ @ Y0 ) ) )
!= X5 )
| ( $true
!= ( cW @ X6 ) ) ) ) ) )
=> ( ( ( ? [X1: a > $o] :
( ( ( X1 @ sK0 )
!= $true )
& ( ( cW @ X1 )
= $true ) )
& ( ( cZ @ sK0 )
!= $true ) )
| ? [X2: a > $o] :
( ( ( X2 @ sK0 )
!= $true )
& ? [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( X3 @ Y0 )
| ( cZ @ Y0 ) ) )
= X2 )
& ( ( cW @ X3 )
= $true ) ) ) )
& ( ! [X4: a > $o] :
( ( ( X4 @ sK0 )
= $true )
| ( $true
!= ( cW @ X4 ) ) )
| ( ( cZ @ sK0 )
= $true )
| ! [X5: a > $o] :
( ( $true
= ( X5 @ sK0 ) )
| ! [X6: a > $o] :
( ( ( ^ [Y0: a] :
( ( X6 @ Y0 )
| ( cZ @ Y0 ) ) )
!= X5 )
| ( $true
!= ( cW @ X6 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X1: a > $o] :
( ( ( X1 @ sK0 )
!= $true )
& ( ( cW @ X1 )
= $true ) )
=> ( ( ( sK1 @ sK0 )
!= $true )
& ( ( cW @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X2: a > $o] :
( ( ( X2 @ sK0 )
!= $true )
& ? [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( X3 @ Y0 )
| ( cZ @ Y0 ) ) )
= X2 )
& ( ( cW @ X3 )
= $true ) ) )
=> ( ( $true
!= ( sK2 @ sK0 ) )
& ? [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( X3 @ Y0 )
| ( cZ @ Y0 ) ) )
= sK2 )
& ( ( cW @ X3 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( X3 @ Y0 )
| ( cZ @ Y0 ) ) )
= sK2 )
& ( ( cW @ X3 )
= $true ) )
=> ( ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( cZ @ Y0 ) ) )
= sK2 )
& ( ( cW @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: a] :
( ( ( ? [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
& ( ( cW @ X1 )
= $true ) )
& ( ( cZ @ X0 )
!= $true ) )
| ? [X2: a > $o] :
( ( ( X2 @ X0 )
!= $true )
& ? [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( X3 @ Y0 )
| ( cZ @ Y0 ) ) )
= X2 )
& ( ( cW @ X3 )
= $true ) ) ) )
& ( ! [X4: a > $o] :
( ( ( X4 @ X0 )
= $true )
| ( $true
!= ( cW @ X4 ) ) )
| ( ( cZ @ X0 )
= $true )
| ! [X5: a > $o] :
( ( ( X5 @ X0 )
= $true )
| ! [X6: a > $o] :
( ( ( ^ [Y0: a] :
( ( X6 @ Y0 )
| ( cZ @ Y0 ) ) )
!= X5 )
| ( $true
!= ( cW @ X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: a] :
( ( ( ? [X3: a > $o] :
( ( ( X3 @ X0 )
!= $true )
& ( ( cW @ X3 )
= $true ) )
& ( ( cZ @ X0 )
!= $true ) )
| ? [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
& ? [X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
| ( cZ @ Y0 ) ) )
= X1 )
& ( ( cW @ X2 )
= $true ) ) ) )
& ( ! [X3: a > $o] :
( ( ( X3 @ X0 )
= $true )
| ( ( cW @ X3 )
!= $true ) )
| ( ( cZ @ X0 )
= $true )
| ! [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
| ! [X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
| ( cZ @ Y0 ) ) )
!= X1 )
| ( ( cW @ X2 )
!= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a] :
( ( ( ? [X3: a > $o] :
( ( ( X3 @ X0 )
!= $true )
& ( ( cW @ X3 )
= $true ) )
& ( ( cZ @ X0 )
!= $true ) )
| ? [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
& ? [X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
| ( cZ @ Y0 ) ) )
= X1 )
& ( ( cW @ X2 )
= $true ) ) ) )
& ( ! [X3: a > $o] :
( ( ( X3 @ X0 )
= $true )
| ( ( cW @ X3 )
!= $true ) )
| ( ( cZ @ X0 )
= $true )
| ! [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
| ! [X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
| ( cZ @ Y0 ) ) )
!= X1 )
| ( ( cW @ X2 )
!= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a] :
( ! [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
| ! [X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
| ( cZ @ Y0 ) ) )
!= X1 )
| ( ( cW @ X2 )
!= $true ) ) )
<~> ( ! [X3: a > $o] :
( ( ( X3 @ X0 )
= $true )
| ( ( cW @ X3 )
!= $true ) )
| ( ( cZ @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a] :
( ( ! [X3: a > $o] :
( ( ( cW @ X3 )
= $true )
=> ( ( X3 @ X0 )
= $true ) )
| ( ( cZ @ X0 )
= $true ) )
<=> ! [X1: a > $o] :
( ? [X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
| ( cZ @ Y0 ) ) )
= X1 )
& ( ( cW @ X2 )
= $true ) )
=> ( ( X1 @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ! [X1: a > $o] :
( ? [X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
| ( cZ @ Y0 ) ) )
= X1 )
& ( ( cW @ X2 )
= $true ) )
=> ( ( X1 @ X0 )
= $true ) )
<=> ( ( ( cZ @ X0 )
= $true )
| ! [X4: a > $o] :
( ( $true
= ( cW @ X4 ) )
=> ( ( X4 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ! [X1: a > $o] :
( ? [X2: a > $o] :
( ( cW @ X2 )
& ( X1
= ( ^ [X3: a] :
( ( cZ @ X3 )
| ( X2 @ X3 ) ) ) ) )
=> ( X1 @ X0 ) )
<=> ( ( cZ @ X0 )
| ! [X4: a > $o] :
( ( cW @ X4 )
=> ( X4 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ! [X1: a > $o] :
( ? [X2: a > $o] :
( ( cW @ X2 )
& ( X1
= ( ^ [X3: a] :
( ( cZ @ X3 )
| ( X2 @ X3 ) ) ) ) )
=> ( X1 @ X0 ) )
<=> ( ( cZ @ X0 )
| ! [X1: a > $o] :
( ( cW @ X1 )
=> ( X1 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ! [X1: a > $o] :
( ? [X2: a > $o] :
( ( cW @ X2 )
& ( X1
= ( ^ [X3: a] :
( ( cZ @ X3 )
| ( X2 @ X3 ) ) ) ) )
=> ( X1 @ X0 ) )
<=> ( ( cZ @ X0 )
| ! [X1: a > $o] :
( ( cW @ X1 )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RWL32k4e2A/DTF2THF_26339.p',cTHM60_pme) ).
thf(f65,plain,
( spl4_4
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f35,f45]) ).
thf(f21,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( cZ @ Y0 ) ) )
= sK2 )
| ( ( cW @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f64,plain,
( ~ spl4_6
| spl4_4 ),
inference(avatar_split_clause,[status(thm)],[f22,f45,f56]) ).
thf(f22,plain,
( ( $true
!= ( sK2 @ sK0 ) )
| ( ( cW @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f63,plain,
( spl4_7
| spl4_3
| spl4_7 ),
inference(avatar_split_clause,[status(thm)],[f29,f61,f40,f61]) ).
thf(f29,plain,
! [X6: a > $o,X4: a > $o] :
( ( $true
!= ( cW @ X6 ) )
| ( ( cZ @ sK0 )
= $true )
| ( $true
!= ( cW @ X4 ) )
| ( ( X4 @ sK0 )
= $true )
| ( $true
= ( X6 @ sK0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X6: a > $o,X4: a > $o] :
( ( ( cZ @ sK0 )
= $true )
| ( ( X4 @ sK0 )
= $true )
| ( ( cZ @ sK0 )
= $true )
| ( $true
!= ( cW @ X4 ) )
| ( $true
!= ( cW @ X6 ) )
| ( $true
= ( X6 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X6: a > $o,X4: a > $o] :
( ( ( cZ @ sK0 )
= $true )
| ( $true
!= ( cW @ X4 ) )
| ( ( ( X6 @ sK0 )
| ( cZ @ sK0 ) )
= $true )
| ( $true
!= ( cW @ X6 ) )
| ( ( X4 @ sK0 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X6: a > $o,X4: a > $o] :
( ( $true
!= ( cW @ X6 ) )
| ( ( X4 @ sK0 )
= $true )
| ( ( ^ [Y0: a] :
( ( X6 @ Y0 )
| ( cZ @ Y0 ) )
@ sK0 )
= $true )
| ( ( cZ @ sK0 )
= $true )
| ( $true
!= ( cW @ X4 ) ) ),
inference(equality_resolution,[status(thm)],[f16]) ).
thf(f16,plain,
! [X6: a > $o,X4: a > $o,X5: a > $o] :
( ( ( X4 @ sK0 )
= $true )
| ( $true
!= ( cW @ X4 ) )
| ( ( cZ @ sK0 )
= $true )
| ( $true
= ( X5 @ sK0 ) )
| ( ( ^ [Y0: a] :
( ( X6 @ Y0 )
| ( cZ @ Y0 ) ) )
!= X5 )
| ( $true
!= ( cW @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f59,plain,
( ~ spl4_6
| ~ spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f25,f31,f56]) ).
thf(f25,plain,
( ( ( sK1 @ sK0 )
!= $true )
| ( $true
!= ( sK2 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f53,plain,
( ~ spl4_1
| spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f23,f49,f31]) ).
thf(f23,plain,
( ( ( sK1 @ sK0 )
!= $true )
| ( ( cW @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f52,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f20,f49,f45]) ).
thf(f20,plain,
( ( ( cW @ sK3 )
= $true )
| ( ( cW @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f43,plain,
( spl4_2
| ~ spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f18,f40,f35]) ).
thf(f18,plain,
( ( ( cZ @ sK0 )
!= $true )
| ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( cZ @ Y0 ) ) )
= sK2 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f38,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f24,f35,f31]) ).
thf(f24,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( cZ @ Y0 ) ) )
= sK2 )
| ( ( sK1 @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV222^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n028.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 12:42:12 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.41 ---- Original DTF file ---
% 0.16/0.41 thf(spec,logic,$$dhol).
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 % File : SEV222^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.41 % Domain : Set Theory (Sets of sets)
% 0.16/0.41 % Problem : TPS problem THM60
% 0.16/0.41 % Version : Especial.
% 0.16/0.41 % English :
% 0.16/0.41
% 0.16/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.41 % Source : [Bro09]
% 0.16/0.41 % Names : tps_0460 [Bro09]
% 0.16/0.41 % : THM60 [TPS]
% 0.16/0.41
% 0.16/0.41 % Status : Theorem
% 0.16/0.41 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.16/0.41 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.41 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.16/0.41 % Maximal formula atoms : 4 ( 5 avg)
% 0.16/0.41 % Number of connectives : 13 ( 0 ~; 2 |; 1 &; 7 @)
% 0.16/0.41 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.41 % Maximal formula depth : 8 ( 8 avg)
% 0.16/0.41 % Number of types : 2 ( 1 usr)
% 0.16/0.41 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.16/0.41 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.16/0.41 % Number of variables : 5 ( 1 ^; 3 !; 1 ?; 5 :)
% 0.16/0.41 % SPC : TH0_THM_EQU_NAR
% 0.16/0.41
% 0.16/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.41 % : Polymorphic definitions expanded.
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 thf(a_type,type,
% 0.16/0.41 a: $tType ).
% 0.16/0.41
% 0.16/0.41 thf(cZ,type,
% 0.16/0.41 cZ: a > $o ).
% 0.16/0.41
% 0.16/0.41 thf(cW,type,
% 0.16/0.41 cW: ( a > $o ) > $o ).
% 0.16/0.41
% 0.16/0.41 thf(cTHM60_pme,conjecture,
% 0.16/0.41 ! [Xx: a] :
% 0.16/0.41 ( ( ! [S: a > $o] :
% 0.16/0.41 ( ( cW @ S )
% 0.16/0.41 => ( S @ Xx ) )
% 0.16/0.41 | ( cZ @ Xx ) )
% 0.16/0.41 <=> ! [S: a > $o] :
% 0.16/0.41 ( ? [Xt: a > $o] :
% 0.16/0.41 ( ( cW @ Xt )
% 0.16/0.41 & ( S
% 0.16/0.41 = ( ^ [Xz: a] :
% 0.16/0.41 ( ( cZ @ Xz )
% 0.16/0.41 | ( Xt @ Xz ) ) ) ) )
% 0.16/0.41 => ( S @ Xx ) ) ) ).
% 0.16/0.41
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 ------------------------
% 1.11/1.11 ---- Embedded in THF ---
% 1.11/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.11/1.11 %%% Generated on Tue Feb 24 12:42:12 EST 2026
% 1.11/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 1.11/1.11 %%% Logic specification used:
% 1.11/1.11 %%% thf(spec, logic, $$dhol).
% 1.11/1.11
% 1.11/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RWL32k4e2A/DTF2DTF26339.p
% See solution above
% 1.11/1.11 ------------------------
% 1.31/1.12 ---- Cleaned THF ---
% 1.31/1.12 thf(a_type,type,
% 1.31/1.12 a: $tType ).
% 1.31/1.12
% 1.31/1.12 thf(cZ,type,
% 1.31/1.12 cZ: a > $o ).
% 1.31/1.12
% 1.31/1.12 thf(cW,type,
% 1.31/1.12 cW: ( a > $o ) > $o ).
% 1.31/1.12
% 1.31/1.12 thf(cTHM60_pme,conjecture,
% 1.31/1.12 ! [Xx: a] :
% 1.31/1.12 ( ( ! [S: a > $o] :
% 1.31/1.12 ( ( cW @ S )
% 1.31/1.12 => ( S @ Xx ) )
% 1.31/1.12 | ( cZ @ Xx ) )
% 1.31/1.12 <=> ! [S: a > $o] :
% 1.31/1.12 ( ? [Xt: a > $o] :
% 1.31/1.12 ( ( cW @ Xt )
% 1.31/1.12 & ( S
% 1.31/1.12 = ( ^ [Xz: a] :
% 1.31/1.12 ( ( cZ @ Xz )
% 1.31/1.12 | ( Xt @ Xz ) ) ) ) )
% 1.31/1.12 => ( S @ Xx ) ) ) ).
% 1.31/1.12 ------------------------
% 1.31/1.14 % (26443)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26339 for (3000ds/183Mi)
% 1.31/1.14 % (26444)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_26339 for (3000ds/4Mi)
% 1.31/1.14 % (26445)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_26339 for (3000ds/27Mi)
% 1.31/1.14 % (26448)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_26339 for (3000ds/275Mi)
% 1.31/1.14 % (26446)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26339 for (3000ds/2Mi)
% 1.31/1.14 % (26447)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_26339 for (3000ds/2Mi)
% 1.31/1.14 % (26449)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26339 for (3000ds/18Mi)
% 1.31/1.14 % (26446)Instruction limit reached!
% 1.31/1.14 % (26446)------------------------------
% 1.31/1.14 % (26446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.14 % (26446)Termination reason: Unknown
% 1.31/1.14 % (26446)Termination phase: Property scanning
% 1.31/1.14
% 1.31/1.14 % (26446)Memory used [KB]: 895
% 1.31/1.14 % (26446)Time elapsed: 0.002 s
% 1.31/1.14 % (26446)Instructions burned: 2 (million)
% 1.31/1.14 % (26446)------------------------------
% 1.31/1.14 % (26446)------------------------------
% 1.31/1.14 % (26447)Refutation not found, incomplete strategy
% 1.31/1.14 % (26447)------------------------------
% 1.31/1.14 % (26447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.14 % (26447)Termination reason: Refutation not found, incomplete strategy
% 1.31/1.14
% 1.31/1.14
% 1.31/1.14 % (26447)Memory used [KB]: 5500
% 1.31/1.14 % (26447)Time elapsed: 0.003 s
% 1.31/1.14 % (26447)Instructions burned: 1 (million)
% 1.31/1.14 % (26447)------------------------------
% 1.31/1.14 % (26447)------------------------------
% 1.31/1.14 % (26444)Instruction limit reached!
% 1.31/1.14 % (26444)------------------------------
% 1.31/1.14 % (26444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.14 % (26443)First to succeed.
% 1.31/1.14 % (26444)Termination reason: Unknown
% 1.31/1.14 % (26444)Termination phase: Saturation
% 1.31/1.14
% 1.31/1.14 % (26444)Memory used [KB]: 5500
% 1.31/1.14 % (26444)Time elapsed: 0.004 s
% 1.31/1.14 % (26444)Instructions burned: 5 (million)
% 1.31/1.14 % (26444)------------------------------
% 1.31/1.14 % (26444)------------------------------
% 1.31/1.14 % (26445)Also succeeded, but the first one will report.
% 1.31/1.14 % (26448)Also succeeded, but the first one will report.
% 1.31/1.14 % (26443)Refutation found. Thanks to Tanya!
% 1.31/1.14 % SZS status Theorem for DTF2THF_26339
% 1.31/1.14 % SZS output start Proof for DTF2THF_26339
% 1.31/1.14 thf(type_def_5, type, a: $tType).
% 1.31/1.14 thf(func_def_0, type, a: $tType).
% 1.31/1.14 thf(func_def_1, type, cZ: a > $o).
% 1.31/1.14 thf(func_def_2, type, cW: (a > $o) > $o).
% 1.31/1.14 thf(func_def_9, type, sK0: a).
% 1.31/1.14 thf(func_def_10, type, sK1: a > $o).
% 1.31/1.14 thf(func_def_11, type, sK2: a > $o).
% 1.31/1.14 thf(func_def_12, type, sK3: a > $o).
% 1.31/1.14 thf(func_def_15, type, ph5: !>[X0: $tType]:(X0)).
% 1.31/1.14 thf(f107,plain,(
% 1.31/1.14 $false),
% 1.31/1.14 inference(avatar_sat_refutation,[status(thm)],[f38,f43,f52,f53,f59,f63,f64,f65,f66,f91,f102,f106])).
% 1.31/1.14 thf(f106,plain,(
% 1.31/1.14 spl4_1 | ~spl4_4 | ~spl4_7),
% 1.31/1.14 inference(avatar_contradiction_clause,[status(thm)],[f105])).
% 1.31/1.14 thf(f105,plain,(
% 1.31/1.14 $false | (spl4_1 | ~spl4_4 | ~spl4_7)),
% 1.31/1.14 inference(subsumption_resolution,[status(thm)],[f104,f33])).
% 1.31/1.14 thf(f33,plain,(
% 1.31/1.14 ((sK1 @ sK0) != $true) | spl4_1),
% 1.31/1.14 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.31/1.14 thf(f31,definition,(
% 1.31/1.14 spl4_1 <=> ((sK1 @ sK0) = $true)),
% 1.31/1.14 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.31/1.14 thf(f104,plain,(
% 1.31/1.14 ((sK1 @ sK0) = $true) | (~spl4_4 | ~spl4_7)),
% 1.31/1.14 inference(trivial_inequality_removal,[status(thm)],[f103])).
% 1.31/1.14 thf(f103,plain,(
% 1.31/1.14 ((sK1 @ sK0) = $true) | ($true != $true) | (~spl4_4 | ~spl4_7)),
% 1.31/1.14 inference(superposition,[status(thm)],[f62,f47])).
% 1.31/1.14 thf(f47,plain,(
% 1.31/1.14 ((cW @ sK1) = $true) | ~spl4_4),
% 1.31/1.14 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.31/1.14 thf(f45,definition,(
% 1.31/1.14 spl4_4 <=> ((cW @ sK1) = $true)),
% 1.31/1.14 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.31/1.14 thf(f62,plain,(
% 1.31/1.14 ( ! [X4 : a > $o] : (($true != (cW @ X4)) | ((X4 @ sK0) = $true)) ) | ~spl4_7),
% 1.31/1.14 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.31/1.14 thf(f61,definition,(
% 1.31/1.14 spl4_7 <=> ! [X4 : a > $o] : (($true != (cW @ X4)) | ((X4 @ sK0) = $true))),
% 1.31/1.14 introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition])).
% 1.31/1.14 thf(f102,plain,(
% 1.31/1.14 ~spl4_2 | ~spl4_5 | spl4_6 | ~spl4_7),
% 1.31/1.14 inference(avatar_contradiction_clause,[status(thm)],[f101])).
% 1.31/1.14 thf(f101,plain,(
% 1.31/1.14 $false | (~spl4_2 | ~spl4_5 | spl4_6 | ~spl4_7)),
% 1.31/1.14 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.31/1.14 thf(f98,plain,(
% 1.31/1.14 ($true = $false) | (~spl4_2 | ~spl4_5 | spl4_6 | ~spl4_7)),
% 1.31/1.14 inference(superposition,[status(thm)],[f96,f94])).
% 1.31/1.14 thf(f94,plain,(
% 1.31/1.14 ((sK3 @ sK0) = $false) | (~spl4_2 | spl4_6)),
% 1.31/1.14 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.31/1.14 thf(f93,plain,(
% 1.31/1.14 ($true != $true) | ((sK3 @ sK0) = $false) | (~spl4_2 | spl4_6)),
% 1.31/1.14 inference(superposition,[status(thm)],[f58,f73])).
% 1.31/1.14 thf(f73,plain,(
% 1.31/1.14 ( ! [X1 : a] : (($true = (sK2 @ X1)) | ((sK3 @ X1) = $false)) ) | ~spl4_2),
% 1.31/1.14 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.31/1.14 thf(f71,plain,(
% 1.31/1.14 ( ! [X1 : a] : ((((sK3 @ X1) | (cZ @ X1)) = $false) | ($true = (sK2 @ X1))) ) | ~spl4_2),
% 1.31/1.14 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.31/1.14 thf(f69,plain,(
% 1.31/1.14 ( ! [X1 : a] : ((((sK3 @ X1) | (cZ @ X1)) = (sK2 @ X1))) ) | ~spl4_2),
% 1.31/1.14 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.31/1.14 thf(f67,plain,(
% 1.31/1.14 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK3 @ Y0) | (cZ @ Y0))) @ X1) = (sK2 @ X1))) ) | ~spl4_2),
% 1.31/1.14 inference(argument_congruence,[status(thm)],[f37])).
% 1.31/1.14 thf(f37,plain,(
% 1.31/1.14 ((^[Y0 : a]: ((sK3 @ Y0) | (cZ @ Y0))) = sK2) | ~spl4_2),
% 1.31/1.14 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.31/1.14 thf(f35,definition,(
% 1.31/1.14 spl4_2 <=> ((^[Y0 : a]: ((sK3 @ Y0) | (cZ @ Y0))) = sK2)),
% 1.31/1.14 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.31/1.14 thf(f58,plain,(
% 1.31/1.14 ($true != (sK2 @ sK0)) | spl4_6),
% 1.31/1.14 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.31/1.14 thf(f56,definition,(
% 1.31/1.14 spl4_6 <=> ($true = (sK2 @ sK0))),
% 1.31/1.14 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.31/1.14 thf(f96,plain,(
% 1.31/1.14 ($true = (sK3 @ sK0)) | (~spl4_5 | ~spl4_7)),
% 1.31/1.14 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.31/1.14 thf(f95,plain,(
% 1.31/1.14 ($true = (sK3 @ sK0)) | ($true != $true) | (~spl4_5 | ~spl4_7)),
% 1.31/1.14 inference(superposition,[status(thm)],[f62,f51])).
% 1.31/1.14 thf(f51,plain,(
% 1.31/1.14 ((cW @ sK3) = $true) | ~spl4_5),
% 1.31/1.14 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.31/1.14 thf(f49,definition,(
% 1.31/1.14 spl4_5 <=> ((cW @ sK3) = $true)),
% 1.31/1.14 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.31/1.14 thf(f91,plain,(
% 1.31/1.14 ~spl4_2 | ~spl4_3 | spl4_6),
% 1.31/1.14 inference(avatar_contradiction_clause,[status(thm)],[f90])).
% 1.31/1.14 thf(f90,plain,(
% 1.31/1.14 $false | (~spl4_2 | ~spl4_3 | spl4_6)),
% 1.31/1.14 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.31/1.14 thf(f87,plain,(
% 1.31/1.14 ($true = $false) | (~spl4_2 | ~spl4_3 | spl4_6)),
% 1.31/1.14 inference(superposition,[status(thm)],[f41,f85])).
% 1.31/1.14 thf(f85,plain,(
% 1.31/1.14 ((cZ @ sK0) = $false) | (~spl4_2 | spl4_6)),
% 1.31/1.14 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.31/1.14 thf(f84,plain,(
% 1.31/1.14 ((cZ @ sK0) = $false) | ($true != $true) | (~spl4_2 | spl4_6)),
% 1.31/1.14 inference(superposition,[status(thm)],[f58,f72])).
% 1.31/1.14 thf(f72,plain,(
% 1.31/1.14 ( ! [X1 : a] : (($true = (sK2 @ X1)) | ((cZ @ X1) = $false)) ) | ~spl4_2),
% 1.31/1.14 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.31/1.14 thf(f41,plain,(
% 1.31/1.14 ((cZ @ sK0) = $true) | ~spl4_3),
% 1.31/1.14 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.31/1.14 thf(f40,definition,(
% 1.31/1.14 spl4_3 <=> ((cZ @ sK0) = $true)),
% 1.31/1.14 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.31/1.14 thf(f66,plain,(
% 1.31/1.14 ~spl4_3 | ~spl4_6),
% 1.31/1.14 inference(avatar_split_clause,[status(thm)],[f19,f56,f40])).
% 1.31/1.14 thf(f19,plain,(
% 1.31/1.14 ($true != (sK2 @ sK0)) | ((cZ @ sK0) != $true)),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.31/1.14 thf(f15,plain,(
% 1.31/1.14 (((((sK1 @ sK0) != $true) & ((cW @ sK1) = $true)) & ((cZ @ sK0) != $true)) | (($true != (sK2 @ sK0)) & (((^[Y0 : a]: ((sK3 @ Y0) | (cZ @ Y0))) = sK2) & ((cW @ sK3) = $true)))) & (! [X4 : a > $o] : (((X4 @ sK0) = $true) | ($true != (cW @ X4))) | ((cZ @ sK0) = $true) | ! [X5 : a > $o] : (($true = (X5 @ sK0)) | ! [X6 : a > $o] : (((^[Y0 : a]: ((X6 @ Y0) | (cZ @ Y0))) != X5) | ($true != (cW @ X6)))))),
% 1.31/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f14,f13,f12,f11])).
% 1.31/1.14 thf(f11,plain,(
% 1.31/1.14 ? [X0 : a] : (((? [X1 : a > $o] : (((X1 @ X0) != $true) & ((cW @ X1) = $true)) & ((cZ @ X0) != $true)) | ? [X2 : a > $o] : (((X2 @ X0) != $true) & ? [X3 : a > $o] : (((^[Y0 : a]: ((X3 @ Y0) | (cZ @ Y0))) = X2) & ((cW @ X3) = $true)))) & (! [X4 : a > $o] : (((X4 @ X0) = $true) | ($true != (cW @ X4))) | ((cZ @ X0) = $true) | ! [X5 : a > $o] : (((X5 @ X0) = $true) | ! [X6 : a > $o] : (((^[Y0 : a]: ((X6 @ Y0) | (cZ @ Y0))) != X5) | ($true != (cW @ X6)))))) => (((? [X1 : a > $o] : (((X1 @ sK0) != $true) & ((cW @ X1) = $true)) & ((cZ @ sK0) != $true)) | ? [X2 : a > $o] : (((X2 @ sK0) != $true) & ? [X3 : a > $o] : (((^[Y0 : a]: ((X3 @ Y0) | (cZ @ Y0))) = X2) & ((cW @ X3) = $true)))) & (! [X4 : a > $o] : (((X4 @ sK0) = $true) | ($true != (cW @ X4))) | ((cZ @ sK0) = $true) | ! [X5 : a > $o] : (($true = (X5 @ sK0)) | ! [X6 : a > $o] : (((^[Y0 : a]: ((X6 @ Y0) | (cZ @ Y0))) != X5) | ($true != (cW @ X6))))))),
% 1.31/1.14 introduced(definition,[],[choice_axiom])).
% 1.31/1.14 thf(f12,plain,(
% 1.31/1.14 ? [X1 : a > $o] : (((X1 @ sK0) != $true) & ((cW @ X1) = $true)) => (((sK1 @ sK0) != $true) & ((cW @ sK1) = $true))),
% 1.31/1.14 introduced(definition,[],[choice_axiom])).
% 1.31/1.14 thf(f13,plain,(
% 1.31/1.14 ? [X2 : a > $o] : (((X2 @ sK0) != $true) & ? [X3 : a > $o] : (((^[Y0 : a]: ((X3 @ Y0) | (cZ @ Y0))) = X2) & ((cW @ X3) = $true))) => (($true != (sK2 @ sK0)) & ? [X3 : a > $o] : (((^[Y0 : a]: ((X3 @ Y0) | (cZ @ Y0))) = sK2) & ((cW @ X3) = $true)))),
% 1.31/1.14 introduced(definition,[],[choice_axiom])).
% 1.31/1.14 thf(f14,plain,(
% 1.31/1.14 ? [X3 : a > $o] : (((^[Y0 : a]: ((X3 @ Y0) | (cZ @ Y0))) = sK2) & ((cW @ X3) = $true)) => (((^[Y0 : a]: ((sK3 @ Y0) | (cZ @ Y0))) = sK2) & ((cW @ sK3) = $true))),
% 1.31/1.14 introduced(definition,[],[choice_axiom])).
% 1.31/1.14 thf(f10,plain,(
% 1.31/1.14 ? [X0 : a] : (((? [X1 : a > $o] : (((X1 @ X0) != $true) & ((cW @ X1) = $true)) & ((cZ @ X0) != $true)) | ? [X2 : a > $o] : (((X2 @ X0) != $true) & ? [X3 : a > $o] : (((^[Y0 : a]: ((X3 @ Y0) | (cZ @ Y0))) = X2) & ((cW @ X3) = $true)))) & (! [X4 : a > $o] : (((X4 @ X0) = $true) | ($true != (cW @ X4))) | ((cZ @ X0) = $true) | ! [X5 : a > $o] : (((X5 @ X0) = $true) | ! [X6 : a > $o] : (((^[Y0 : a]: ((X6 @ Y0) | (cZ @ Y0))) != X5) | ($true != (cW @ X6))))))),
% 1.31/1.14 inference(rectify,[status(thm)],[f9])).
% 1.31/1.14 thf(f9,plain,(
% 1.31/1.14 ? [X0 : a] : (((? [X3 : a > $o] : (((X3 @ X0) != $true) & ((cW @ X3) = $true)) & ((cZ @ X0) != $true)) | ? [X1 : a > $o] : (((X1 @ X0) != $true) & ? [X2 : a > $o] : (((^[Y0 : a]: ((X2 @ Y0) | (cZ @ Y0))) = X1) & ((cW @ X2) = $true)))) & (! [X3 : a > $o] : (((X3 @ X0) = $true) | ((cW @ X3) != $true)) | ((cZ @ X0) = $true) | ! [X1 : a > $o] : (((X1 @ X0) = $true) | ! [X2 : a > $o] : (((^[Y0 : a]: ((X2 @ Y0) | (cZ @ Y0))) != X1) | ((cW @ X2) != $true)))))),
% 1.31/1.14 inference(flattening,[status(thm)],[f8])).
% 1.31/1.14 thf(f8,plain,(
% 1.31/1.14 ? [X0 : a] : (((? [X3 : a > $o] : (((X3 @ X0) != $true) & ((cW @ X3) = $true)) & ((cZ @ X0) != $true)) | ? [X1 : a > $o] : (((X1 @ X0) != $true) & ? [X2 : a > $o] : (((^[Y0 : a]: ((X2 @ Y0) | (cZ @ Y0))) = X1) & ((cW @ X2) = $true)))) & ((! [X3 : a > $o] : (((X3 @ X0) = $true) | ((cW @ X3) != $true)) | ((cZ @ X0) = $true)) | ! [X1 : a > $o] : (((X1 @ X0) = $true) | ! [X2 : a > $o] : (((^[Y0 : a]: ((X2 @ Y0) | (cZ @ Y0))) != X1) | ((cW @ X2) != $true)))))),
% 1.31/1.14 inference(nnf_transformation,[status(thm)],[f7])).
% 1.31/1.14 thf(f7,plain,(
% 1.31/1.14 ? [X0 : a] : (! [X1 : a > $o] : (((X1 @ X0) = $true) | ! [X2 : a > $o] : (((^[Y0 : a]: ((X2 @ Y0) | (cZ @ Y0))) != X1) | ((cW @ X2) != $true))) <~> (! [X3 : a > $o] : (((X3 @ X0) = $true) | ((cW @ X3) != $true)) | ((cZ @ X0) = $true)))),
% 1.31/1.14 inference(ennf_transformation,[status(thm)],[f6])).
% 1.31/1.14 thf(f6,plain,(
% 1.31/1.14 ~! [X0 : a] : ((! [X3 : a > $o] : (((cW @ X3) = $true) => ((X3 @ X0) = $true)) | ((cZ @ X0) = $true)) <=> ! [X1 : a > $o] : (? [X2 : a > $o] : (((^[Y0 : a]: ((X2 @ Y0) | (cZ @ Y0))) = X1) & ((cW @ X2) = $true)) => ((X1 @ X0) = $true)))),
% 1.31/1.14 inference(rectify,[status(thm)],[f5])).
% 1.31/1.14 thf(f5,plain,(
% 1.31/1.14 ~! [X0 : a] : (! [X1 : a > $o] : (? [X2 : a > $o] : (((^[Y0 : a]: ((X2 @ Y0) | (cZ @ Y0))) = X1) & ((cW @ X2) = $true)) => ((X1 @ X0) = $true)) <=> (((cZ @ X0) = $true) | ! [X4 : a > $o] : (($true = (cW @ X4)) => ((X4 @ X0) = $true))))),
% 1.31/1.14 inference(fool_elimination,[status(thm)],[f4])).
% 1.31/1.14 thf(f4,plain,(
% 1.31/1.14 ~! [X0 : a] : (! [X1 : a > $o] : (? [X2 : a > $o] : ((cW @ X2) & (X1 = (^[X3 : a] : ((cZ @ X3) | (X2 @ X3))))) => (X1 @ X0)) <=> ((cZ @ X0) | ! [X4 : a > $o] : ((cW @ X4) => (X4 @ X0))))),
% 1.31/1.14 inference(rectify,[status(thm)],[f2])).
% 1.31/1.14 thf(f2,negated_conjecture,(
% 1.31/1.14 ~! [X0 : a] : (! [X1 : a > $o] : (? [X2 : a > $o] : ((cW @ X2) & (X1 = (^[X3 : a] : ((cZ @ X3) | (X2 @ X3))))) => (X1 @ X0)) <=> ((cZ @ X0) | ! [X1 : a > $o] : ((cW @ X1) => (X1 @ X0))))),
% 1.31/1.14 inference(negated_conjecture,[status(cth)],[f1])).
% 1.31/1.14 thf(f1,conjecture,(
% 1.31/1.14 ! [X0 : a] : (! [X1 : a > $o] : (? [X2 : a > $o] : ((cW @ X2) & (X1 = (^[X3 : a] : ((cZ @ X3) | (X2 @ X3))))) => (X1 @ X0)) <=> ((cZ @ X0) | ! [X1 : a > $o] : ((cW @ X1) => (X1 @ X0))))),
% 1.31/1.14 file('/export/starexec/sandbox/tmp/tmp.RWL32k4e2A/DTF2THF_26339.p',cTHM60_pme)).
% 1.31/1.14 thf(f65,plain,(
% 1.31/1.14 spl4_4 | spl4_2),
% 1.31/1.14 inference(avatar_split_clause,[status(thm)],[f21,f35,f45])).
% 1.31/1.14 thf(f21,plain,(
% 1.31/1.14 ((^[Y0 : a]: ((sK3 @ Y0) | (cZ @ Y0))) = sK2) | ((cW @ sK1) = $true)),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.31/1.14 thf(f64,plain,(
% 1.31/1.14 ~spl4_6 | spl4_4),
% 1.31/1.14 inference(avatar_split_clause,[status(thm)],[f22,f45,f56])).
% 1.31/1.14 thf(f22,plain,(
% 1.31/1.14 ($true != (sK2 @ sK0)) | ((cW @ sK1) = $true)),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.31/1.14 thf(f63,plain,(
% 1.31/1.14 spl4_7 | spl4_3 | spl4_7),
% 1.31/1.14 inference(avatar_split_clause,[status(thm)],[f29,f61,f40,f61])).
% 1.31/1.14 thf(f29,plain,(
% 1.31/1.14 ( ! [X6 : a > $o,X4 : a > $o] : (($true != (cW @ X6)) | ((cZ @ sK0) = $true) | ($true != (cW @ X4)) | ((X4 @ sK0) = $true) | ($true = (X6 @ sK0))) )),
% 1.31/1.14 inference(duplicate_literal_removal,[status(thm)],[f28])).
% 1.31/1.14 thf(f28,plain,(
% 1.31/1.14 ( ! [X6 : a > $o,X4 : a > $o] : (((cZ @ sK0) = $true) | ((X4 @ sK0) = $true) | ((cZ @ sK0) = $true) | ($true != (cW @ X4)) | ($true != (cW @ X6)) | ($true = (X6 @ sK0))) )),
% 1.31/1.14 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.31/1.14 thf(f27,plain,(
% 1.31/1.14 ( ! [X6 : a > $o,X4 : a > $o] : (((cZ @ sK0) = $true) | ($true != (cW @ X4)) | (((X6 @ sK0) | (cZ @ sK0)) = $true) | ($true != (cW @ X6)) | ((X4 @ sK0) = $true)) )),
% 1.31/1.14 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.31/1.14 thf(f26,plain,(
% 1.31/1.14 ( ! [X6 : a > $o,X4 : a > $o] : (($true != (cW @ X6)) | ((X4 @ sK0) = $true) | (((^[Y0 : a]: ((X6 @ Y0) | (cZ @ Y0))) @ sK0) = $true) | ((cZ @ sK0) = $true) | ($true != (cW @ X4))) )),
% 1.31/1.14 inference(equality_resolution,[status(thm)],[f16])).
% 1.31/1.14 thf(f16,plain,(
% 1.31/1.14 ( ! [X6 : a > $o,X4 : a > $o,X5 : a > $o] : (((X4 @ sK0) = $true) | ($true != (cW @ X4)) | ((cZ @ sK0) = $true) | ($true = (X5 @ sK0)) | ((^[Y0 : a]: ((X6 @ Y0) | (cZ @ Y0))) != X5) | ($true != (cW @ X6))) )),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.31/1.14 thf(f59,plain,(
% 1.31/1.14 ~spl4_6 | ~spl4_1),
% 1.31/1.14 inference(avatar_split_clause,[status(thm)],[f25,f31,f56])).
% 1.31/1.14 thf(f25,plain,(
% 1.31/1.14 ((sK1 @ sK0) != $true) | ($true != (sK2 @ sK0))),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.31/1.14 thf(f53,plain,(
% 1.31/1.14 ~spl4_1 | spl4_5),
% 1.31/1.14 inference(avatar_split_clause,[status(thm)],[f23,f49,f31])).
% 1.31/1.14 thf(f23,plain,(
% 1.31/1.14 ((sK1 @ sK0) != $true) | ((cW @ sK3) = $true)),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.31/1.14 thf(f52,plain,(
% 1.31/1.14 spl4_4 | spl4_5),
% 1.31/1.14 inference(avatar_split_clause,[status(thm)],[f20,f49,f45])).
% 1.31/1.14 thf(f20,plain,(
% 1.31/1.14 ((cW @ sK3) = $true) | ((cW @ sK1) = $true)),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.31/1.14 thf(f43,plain,(
% 1.31/1.14 spl4_2 | ~spl4_3),
% 1.31/1.14 inference(avatar_split_clause,[status(thm)],[f18,f40,f35])).
% 1.31/1.14 thf(f18,plain,(
% 1.31/1.14 ((cZ @ sK0) != $true) | ((^[Y0 : a]: ((sK3 @ Y0) | (cZ @ Y0))) = sK2)),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.31/1.14 thf(f38,plain,(
% 1.31/1.14 ~spl4_1 | spl4_2),
% 1.31/1.14 inference(avatar_split_clause,[status(thm)],[f24,f35,f31])).
% 1.31/1.14 thf(f24,plain,(
% 1.31/1.14 ((^[Y0 : a]: ((sK3 @ Y0) | (cZ @ Y0))) = sK2) | ((sK1 @ sK0) != $true)),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.31/1.14 % SZS output end Proof for DTF2THF_26339
% 1.31/1.14 % (26443)------------------------------
% 1.31/1.14 % (26443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.14 % (26443)Termination reason: Refutation
% 1.31/1.14
% 1.31/1.14 % (26443)Memory used [KB]: 5500
% 1.31/1.14 % (26443)Time elapsed: 0.006 s
% 1.31/1.14 % (26443)Instructions burned: 6 (million)
% 1.31/1.14 % (26443)------------------------------
% 1.31/1.14 % (26443)------------------------------
% 1.31/1.14 % (26442)Success in time 0.019 s
%------------------------------------------------------------------------------