%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV386^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 09:41:08 AM UTC 2026
% Result : Theorem 1.24s 1.19s
% Output : Refutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 88 ( 1 unt; 0 typ; 7 def)
% Number of atoms : 532 ( 217 equ; 12 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 567 ( 196 ~; 185 |; 18 &; 149 @)
% ( 11 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 129 ( 34 ^; 76 !; 19 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
p: a > $o ).
thf(func_def_9,type,
sK0: a > a ).
thf(func_def_10,type,
sK1: a ).
thf(func_def_11,type,
sK2: a ).
thf(func_def_13,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK5: a > a ).
thf(func_def_15,type,
sK6: a > a ).
thf(func_def_16,type,
sK7: a ).
thf(func_def_17,type,
sK8: a > a ).
thf(f193,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f35,f39,f44,f98,f111,f154,f161,f191]) ).
thf(f191,plain,
( ~ spl3_1
| ~ spl3_4
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f190]) ).
thf(f190,plain,
( $false
| ~ spl3_1
| ~ spl3_4
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f181]) ).
thf(f181,plain,
( ( sK1 != sK1 )
| ( $true = $false )
| ~ spl3_1
| ~ spl3_4
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f179,f43]) ).
thf(f43,plain,
( ( ( p @ sK1 )
= $true )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl3_6
<=> ( ( p @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f179,plain,
( ! [X0: a] :
( ( ( p @ X0 )
= $false )
| ( sK1 != X0 ) )
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f178]) ).
thf(f178,plain,
( ! [X0: a] :
( ( X0 != X0 )
| ( ( p @ X0 )
= $false )
| ( sK1 != X0 ) )
| ~ spl3_1
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f165,f174]) ).
thf(f174,plain,
( ! [X0: a] :
( ( ( sK8 @ X0 )
= X0 )
| ( sK1 != X0 ) )
| ~ spl3_1
| ~ spl3_4 ),
inference(equality_factoring,[status(thm)],[f171]) ).
thf(f171,plain,
( ! [X0: a] :
( ( sK1
= ( sK8 @ X0 ) )
| ( ( sK8 @ X0 )
= X0 ) )
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
( ! [X0: a] :
( ( $true != $true )
| ( ( sK8 @ X0 )
= X0 )
| ( sK1
= ( sK8 @ X0 ) ) )
| ~ spl3_1
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f34,f166]) ).
thf(f166,plain,
( ! [X2: a] :
( ( ( p @ ( sK8 @ X2 ) )
= $true )
| ( ( sK8 @ X2 )
= X2 ) )
| ~ spl3_1 ),
inference(equality_proxy_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
( ! [X2: a] :
( ( ( X2
= ( sK8 @ X2 ) )
= $true )
| ( ( p @ ( sK8 @ X2 ) )
= $true ) )
| ~ spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f162]) ).
thf(f162,plain,
( ! [X2: a] :
( ( X2
= ( sK8 @ X2 ) )
!= ( p @ ( sK8 @ X2 ) ) )
| ~ spl3_1 ),
inference(negative_extensionality,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X2: a] :
( p
!= ( (=) @ X2 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl3_1
<=> ! [X2: a] :
( p
!= ( (=) @ X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f34,plain,
( ! [X4: a] :
( ( $true
!= ( p @ X4 ) )
| ( sK1 = X4 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl3_4
<=> ! [X4: a] :
( ( $true
!= ( p @ X4 ) )
| ( sK1 = X4 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f165,plain,
( ! [X2: a] :
( ( ( p @ ( sK8 @ X2 ) )
= $false )
| ( ( sK8 @ X2 )
!= X2 ) )
| ~ spl3_1 ),
inference(equality_proxy_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
( ! [X2: a] :
( ( ( X2
= ( sK8 @ X2 ) )
= $false )
| ( ( p @ ( sK8 @ X2 ) )
= $false ) )
| ~ spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f162]) ).
thf(f161,plain,
( ~ spl3_6
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f160]) ).
thf(f160,plain,
( $false
| ~ spl3_6
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $true != $true )
| ~ spl3_6
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f66,f43]) ).
thf(f66,plain,
( ! [X0: a] :
( ( p @ X0 )
!= $true )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f65,definition,
( spl3_8
<=> ! [X0: a] :
( ( p @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f154,plain,
( spl3_8
| ~ spl3_2
| ~ spl3_4
| ~ spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f153,f37,f33,f25,f65]) ).
thf(f25,definition,
( spl3_2
<=> ! [X0: a] :
( ( ( p @ ( sK0 @ X0 ) )
= $true )
| ( ( p @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f37,definition,
( spl3_5
<=> ! [X0: a] :
( ( ( p @ X0 )
!= $true )
| ( ( sK0 @ X0 )
!= X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f153,plain,
( ! [X0: a] :
( ( p @ X0 )
!= $true )
| ~ spl3_2
| ~ spl3_4
| ~ spl3_5 ),
inference(subsumption_resolution,[status(thm)],[f151,f34]) ).
thf(f151,plain,
( ! [X0: a] :
( ( ( p @ X0 )
!= $true )
| ( sK1 != X0 ) )
| ~ spl3_2
| ~ spl3_4
| ~ spl3_5 ),
inference(duplicate_literal_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ! [X0: a] :
( ( sK1 != X0 )
| ( ( p @ X0 )
!= $true )
| ( ( p @ X0 )
!= $true ) )
| ~ spl3_2
| ~ spl3_4
| ~ spl3_5 ),
inference(superposition,[status(thm)],[f38,f115]) ).
thf(f115,plain,
( ! [X0: a] :
( ( ( sK0 @ X0 )
= sK1 )
| ( ( p @ X0 )
!= $true ) )
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ! [X0: a] :
( ( ( p @ X0 )
!= $true )
| ( ( sK0 @ X0 )
= sK1 )
| ( $true != $true ) )
| ~ spl3_2
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f34,f26]) ).
thf(f26,plain,
( ! [X0: a] :
( ( ( p @ ( sK0 @ X0 ) )
= $true )
| ( ( p @ X0 )
!= $true ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f38,plain,
( ! [X0: a] :
( ( ( sK0 @ X0 )
!= X0 )
| ( ( p @ X0 )
!= $true ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f111,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f110]) ).
thf(f110,plain,
( $false
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(equality_resolution,[status(thm)],[f109]) ).
thf(f109,plain,
( ! [X0: a] : ( sK2 != X0 )
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(subsumption_resolution,[status(thm)],[f107,f48]) ).
thf(f48,plain,
( ! [X1: a] :
( ( ( p @ X1 )
= $true )
| ( sK2 != X1 ) )
| ~ spl3_3 ),
inference(equality_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ! [X1: a] :
( ( ( sK2 = X1 )
= $false )
| ( ( p @ X1 )
= $true ) )
| ~ spl3_3 ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ! [X1: a] :
( ( sK2 = X1 )
= ( p @ X1 ) )
| ~ spl3_3 ),
inference(argument_congruence,[status(thm)],[f31]) ).
thf(f31,plain,
( ( p
= ( (=) @ sK2 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl3_3
<=> ( p
= ( (=) @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f107,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( ( p @ X0 )
!= $true ) )
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(duplicate_literal_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( ( p @ X0 )
!= $true )
| ( ( p @ X0 )
!= $true ) )
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(superposition,[status(thm)],[f38,f104]) ).
thf(f104,plain,
( ! [X0: a] :
( ( ( sK0 @ X0 )
= sK2 )
| ( ( p @ X0 )
!= $true ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ! [X0: a] :
( ( $true = $false )
| ( ( sK0 @ X0 )
= sK2 )
| ( ( p @ X0 )
!= $true ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f26,f49]) ).
thf(f49,plain,
( ! [X1: a] :
( ( ( p @ X1 )
= $false )
| ( sK2 = X1 ) )
| ~ spl3_3 ),
inference(equality_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ! [X1: a] :
( ( ( p @ X1 )
= $false )
| ( ( sK2 = X1 )
= $true ) )
| ~ spl3_3 ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f98,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f97]) ).
thf(f97,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(equality_resolution,[status(thm)],[f96]) ).
thf(f96,plain,
( ! [X0: a] : ( sK2 != X0 )
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( X0 != X0 ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(duplicate_literal_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( X0 != X0 )
| ( sK2 != X0 ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f86,f91]) ).
thf(f91,plain,
( ! [X0: a] :
( ( ( sK6 @ X0 )
= X0 )
| ( sK2 != X0 ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( ( sK6 @ X0 )
= X0 )
| ( sK2 != sK2 ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f86,f88]) ).
thf(f88,plain,
( ! [X0: a] :
( ( sK2
= ( sK6 @ X0 ) )
| ( ( sK6 @ X0 )
= X0 ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(equality_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
( ! [X0: a] :
( ( ( X0
= ( sK6 @ X0 ) )
= $true )
| ( sK2
= ( sK6 @ X0 ) ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(equality_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( ! [X0: a] :
( ( ( sK2
= ( sK6 @ X0 ) )
= $true )
| ( ( X0
= ( sK6 @ X0 ) )
= $true ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ! [X0: a] :
( ( sK2
= ( sK6 @ X0 ) )
!= ( X0
= ( sK6 @ X0 ) ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(negative_extensionality,[status(thm)],[f71]) ).
thf(f71,plain,
( ! [X0: a] :
( ( (=) @ sK2 )
!= ( (=) @ X0 ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ! [X0: a] :
( ( p != p )
| ( ( (=) @ sK2 )
!= ( (=) @ X0 ) ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(constrained_superposition,[status(thm)],[f23,f31]) ).
thf(f86,plain,
( ! [X0: a] :
( ( sK2
!= ( sK6 @ X0 ) )
| ( ( sK6 @ X0 )
!= X0 ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(equality_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
( ! [X0: a] :
( ( ( sK6 @ X0 )
!= X0 )
| ( ( sK2
= ( sK6 @ X0 ) )
= $false ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(equality_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ! [X0: a] :
( ( ( X0
= ( sK6 @ X0 ) )
= $false )
| ( ( sK2
= ( sK6 @ X0 ) )
= $false ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f44,plain,
( spl3_6
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f17,f29,f41]) ).
thf(f17,plain,
( ( p
= ( (=) @ sK2 ) )
| ( ( p @ sK1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( p
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ sK2 ) )
| ( ( p @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ! [X0: a] :
( ( ( p @ X0 )
!= $true )
| ( ( ( sK0 @ X0 )
!= X0 )
& ( ( p @ ( sK0 @ X0 ) )
= $true ) ) )
| ! [X2: a] :
( p
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X2 ) ) )
& ( ( ( ( p @ sK1 )
= $true )
& ! [X4: a] :
( ( sK1 = X4 )
| ( $true
!= ( p @ X4 ) ) ) )
| ( p
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).
thf(f9,plain,
! [X0: a] :
( ? [X1: a] :
( ( X0 != X1 )
& ( ( p @ X1 )
= $true ) )
=> ( ( ( sK0 @ X0 )
!= X0 )
& ( ( p @ ( sK0 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: a] :
( ( $true
= ( p @ X3 ) )
& ! [X4: a] :
( ( X3 = X4 )
| ( $true
!= ( p @ X4 ) ) ) )
=> ( ( ( p @ sK1 )
= $true )
& ! [X4: a] :
( ( sK1 = X4 )
| ( $true
!= ( p @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X5: a] :
( p
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X5 ) )
=> ( p
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ( ! [X0: a] :
( ( ( p @ X0 )
!= $true )
| ? [X1: a] :
( ( X0 != X1 )
& ( ( p @ X1 )
= $true ) ) )
| ! [X2: a] :
( p
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X2 ) ) )
& ( ? [X3: a] :
( ( $true
= ( p @ X3 ) )
& ! [X4: a] :
( ( X3 = X4 )
| ( $true
!= ( p @ X4 ) ) ) )
| ? [X5: a] :
( p
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X5 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ! [X0: a] :
( ( ( p @ X0 )
!= $true )
| ? [X1: a] :
( ( X0 != X1 )
& ( ( p @ X1 )
= $true ) ) )
| ! [X2: a] :
( p
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X2 ) ) )
& ( ? [X0: a] :
( ( ( p @ X0 )
= $true )
& ! [X1: a] :
( ( X0 = X1 )
| ( ( p @ X1 )
!= $true ) ) )
| ? [X2: a] :
( p
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X2 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X2: a] :
( p
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X2 ) )
<~> ? [X0: a] :
( ( ( p @ X0 )
= $true )
& ! [X1: a] :
( ( X0 = X1 )
| ( ( p @ X1 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X0: a] :
( ( ( p @ X0 )
= $true )
& ! [X1: a] :
( ( ( p @ X1 )
= $true )
=> ( X0 = X1 ) ) )
<=> ? [X2: a] :
( p
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ? [X0: a] :
( ! [X1: a] :
( ( p @ X1 )
=> ( X0 = X1 ) )
& ( p @ X0 ) )
<=> ? [X2: a] :
( p
= ( ^ [X3: a,X4: a] : ( X3 = X4 )
@ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: a] :
( ! [X2: a] :
( ( p @ X2 )
=> ( X0 = X2 ) )
& ( p @ X0 ) )
<=> ? [X0: a] :
( p
= ( ^ [X1: a,X0: a] : ( X0 = X1 )
@ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ? [X0: a] :
( ! [X2: a] :
( ( p @ X2 )
=> ( X0 = X2 ) )
& ( p @ X0 ) )
<=> ? [X0: a] :
( p
= ( ^ [X1: a,X0: a] : ( X0 = X1 )
@ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.c6oRckkeWf/DTF2THF_11890.p',cTTTP5306A_pme) ).
thf(f39,plain,
( spl3_1
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f18,f37,f22]) ).
thf(f18,plain,
! [X2: a,X0: a] :
( ( ( p @ X0 )
!= $true )
| ( ( sK0 @ X0 )
!= X0 )
| ( p
!= ( (=) @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: a,X0: a] :
( ( p
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X2 ) )
| ( ( p @ X0 )
!= $true )
| ( ( sK0 @ X0 )
!= X0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f35,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f19,f33,f29]) ).
thf(f19,plain,
! [X4: a] :
( ( p
= ( (=) @ sK2 ) )
| ( $true
!= ( p @ X4 ) )
| ( sK1 = X4 ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
! [X4: a] :
( ( $true
!= ( p @ X4 ) )
| ( sK1 = X4 )
| ( p
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f27,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f20,f25,f22]) ).
thf(f20,plain,
! [X2: a,X0: a] :
( ( p
!= ( (=) @ X2 ) )
| ( ( p @ ( sK0 @ X0 ) )
= $true )
| ( ( p @ X0 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: a,X0: a] :
( ( ( p @ X0 )
!= $true )
| ( ( p @ ( sK0 @ X0 ) )
= $true )
| ( p
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV386^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n003.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:45:55 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.43 ---- Original DTF file ---
% 0.16/0.43 thf(spec,logic,$$dhol).
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 % File : SEV386^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.43 % Domain : Set Theory
% 0.16/0.43 % Problem : TPS problem TTTP5306A
% 0.16/0.43 % Version : Especial.
% 0.16/0.43 % English :
% 0.16/0.43
% 0.16/0.43 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.43 % Source : [Bro09]
% 0.16/0.43 % Names : tps_0467 [Bro09]
% 0.16/0.43 % : TTTP5306A [TPS]
% 0.16/0.43
% 0.16/0.43 % Status : Theorem
% 0.16/0.43 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.16/0.43 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.16/0.43 % Number of atoms : 6 ( 3 equ; 0 cnn)
% 0.16/0.43 % Maximal formula atoms : 4 ( 6 avg)
% 0.16/0.43 % Number of connectives : 6 ( 0 ~; 0 |; 1 &; 3 @)
% 0.16/0.43 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.43 % Maximal formula depth : 7 ( 7 avg)
% 0.16/0.43 % Number of types : 2 ( 1 usr)
% 0.16/0.43 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.16/0.43 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.16/0.43 % Number of variables : 5 ( 2 ^; 1 !; 2 ?; 5 :)
% 0.16/0.43 % SPC : TH0_THM_EQU_NAR
% 0.16/0.43
% 0.16/0.43 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.43 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.43 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.43 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.43 % : Polymorphic definitions expanded.
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 thf(a_type,type,
% 0.16/0.43 a: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(p,type,
% 0.16/0.43 p: a > $o ).
% 0.16/0.43
% 0.16/0.43 thf(cTTTP5306A_pme,conjecture,
% 0.16/0.43 ( ? [Xy: a] :
% 0.16/0.43 ( p
% 0.16/0.43 = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
% 0.16/0.43 @ Xy ) )
% 0.16/0.43 <=> ? [Xy: a] :
% 0.16/0.43 ( ( p @ Xy )
% 0.16/0.43 & ! [Xz: a] :
% 0.16/0.43 ( ( p @ Xz )
% 0.16/0.43 => ( Xy = Xz ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 ------------------------
% 1.24/1.16 ---- Embedded in THF ---
% 1.24/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.24/1.16 %%% Generated on Tue Feb 24 12:45:56 EST 2026
% 1.24/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.24/1.16 %%% Logic specification used:
% 1.24/1.16 %%% thf(spec, logic, $$dhol).
% 1.24/1.16
% 1.24/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.c6oRckkeWf/DTF2DTF11890.p
% See solution above
% 1.24/1.16 ------------------------
% 1.24/1.17 ---- Cleaned THF ---
% 1.24/1.17 thf(a_type,type,
% 1.24/1.17 a: $tType ).
% 1.24/1.17
% 1.24/1.17 thf(p,type,
% 1.24/1.17 p: a > $o ).
% 1.24/1.17
% 1.24/1.17 thf(cTTTP5306A_pme,conjecture,
% 1.24/1.17 ( ? [Xy: a] :
% 1.24/1.17 ( p
% 1.24/1.17 = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
% 1.24/1.17 @ Xy ) )
% 1.24/1.17 <=> ? [Xy: a] :
% 1.24/1.17 ( ( p @ Xy )
% 1.24/1.17 & ! [Xz: a] :
% 1.24/1.17 ( ( p @ Xz )
% 1.24/1.17 => ( Xy = Xz ) ) ) ) ).
% 1.24/1.17 ------------------------
% 1.24/1.18 % (11987)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11890 for (3000ds/183Mi)
% 1.24/1.19 % (11987)First to succeed.
% 1.24/1.19 % (11991)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_11890 for (3000ds/2Mi)
% 1.24/1.19 % (11993)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11890 for (3000ds/18Mi)
% 1.24/1.19 % (11989)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_11890 for (3000ds/27Mi)
% 1.24/1.19 % (11992)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_11890 for (3000ds/275Mi)
% 1.24/1.19 % (11990)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11890 for (3000ds/2Mi)
% 1.24/1.19 % (11988)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_11890 for (3000ds/4Mi)
% 1.24/1.19 % (11991)Instruction limit reached!
% 1.24/1.19 % (11991)------------------------------
% 1.24/1.19 % (11991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.24/1.19 % (11991)Termination reason: Unknown
% 1.24/1.19 % (11991)Termination phase: Saturation
% 1.24/1.19
% 1.24/1.19 % (11991)Memory used [KB]: 5500
% 1.24/1.19 % (11991)Time elapsed: 0.003 s
% 1.24/1.19 % (11991)Instructions burned: 2 (million)
% 1.24/1.19 % (11991)------------------------------
% 1.24/1.19 % (11991)------------------------------
% 1.24/1.19 % (11987)Refutation found. Thanks to Tanya!
% 1.24/1.19 % SZS status Theorem for DTF2THF_11890
% 1.24/1.19 % SZS output start Proof for DTF2THF_11890
% 1.24/1.19 thf(type_def_5, type, a: $tType).
% 1.24/1.19 thf(func_def_0, type, a: $tType).
% 1.24/1.19 thf(func_def_1, type, p: a > $o).
% 1.24/1.19 thf(func_def_9, type, sK0: a > a).
% 1.24/1.19 thf(func_def_10, type, sK1: a).
% 1.24/1.19 thf(func_def_11, type, sK2: a).
% 1.24/1.19 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.24/1.19 thf(func_def_14, type, sK5: a > a).
% 1.24/1.19 thf(func_def_15, type, sK6: a > a).
% 1.24/1.19 thf(func_def_16, type, sK7: a).
% 1.24/1.19 thf(func_def_17, type, sK8: a > a).
% 1.24/1.19 thf(f193,plain,(
% 1.24/1.19 $false),
% 1.24/1.19 inference(avatar_sat_refutation,[status(thm)],[f27,f35,f39,f44,f98,f111,f154,f161,f191])).
% 1.24/1.19 thf(f191,plain,(
% 1.24/1.19 ~spl3_1 | ~spl3_4 | ~spl3_6),
% 1.24/1.19 inference(avatar_contradiction_clause,[status(thm)],[f190])).
% 1.24/1.19 thf(f190,plain,(
% 1.24/1.19 $false | (~spl3_1 | ~spl3_4 | ~spl3_6)),
% 1.24/1.19 inference(trivial_inequality_removal,[status(thm)],[f181])).
% 1.24/1.19 thf(f181,plain,(
% 1.24/1.19 (sK1 != sK1) | ($true = $false) | (~spl3_1 | ~spl3_4 | ~spl3_6)),
% 1.24/1.19 inference(superposition,[status(thm)],[f179,f43])).
% 1.24/1.19 thf(f43,plain,(
% 1.24/1.19 ((p @ sK1) = $true) | ~spl3_6),
% 1.24/1.19 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.24/1.19 thf(f41,definition,(
% 1.24/1.19 spl3_6 <=> ((p @ sK1) = $true)),
% 1.24/1.19 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.24/1.19 thf(f179,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((p @ X0) = $false) | (sK1 != X0)) ) | (~spl3_1 | ~spl3_4)),
% 1.24/1.19 inference(trivial_inequality_removal,[status(thm)],[f178])).
% 1.24/1.19 thf(f178,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((X0 != X0) | ((p @ X0) = $false) | (sK1 != X0)) ) | (~spl3_1 | ~spl3_4)),
% 1.24/1.19 inference(superposition,[status(thm)],[f165,f174])).
% 1.24/1.19 thf(f174,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((sK8 @ X0) = X0) | (sK1 != X0)) ) | (~spl3_1 | ~spl3_4)),
% 1.24/1.19 inference(equality_factoring,[status(thm)],[f171])).
% 1.24/1.19 thf(f171,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((sK1 = (sK8 @ X0)) | ((sK8 @ X0) = X0)) ) | (~spl3_1 | ~spl3_4)),
% 1.24/1.19 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.24/1.19 thf(f170,plain,(
% 1.24/1.19 ( ! [X0 : a] : (($true != $true) | ((sK8 @ X0) = X0) | (sK1 = (sK8 @ X0))) ) | (~spl3_1 | ~spl3_4)),
% 1.24/1.19 inference(superposition,[status(thm)],[f34,f166])).
% 1.24/1.19 thf(f166,plain,(
% 1.24/1.19 ( ! [X2 : a] : (((p @ (sK8 @ X2)) = $true) | ((sK8 @ X2) = X2)) ) | ~spl3_1),
% 1.24/1.19 inference(equality_proxy_clausification,[status(thm)],[f163])).
% 1.24/1.19 thf(f163,plain,(
% 1.24/1.19 ( ! [X2 : a] : (((X2 = (sK8 @ X2)) = $true) | ((p @ (sK8 @ X2)) = $true)) ) | ~spl3_1),
% 1.24/1.19 inference(binary_proxy_clausification,[status(thm)],[f162])).
% 1.24/1.19 thf(f162,plain,(
% 1.24/1.19 ( ! [X2 : a] : (((X2 = (sK8 @ X2)) != (p @ (sK8 @ X2)))) ) | ~spl3_1),
% 1.24/1.19 inference(negative_extensionality,[status(thm)],[f23])).
% 1.24/1.19 thf(f23,plain,(
% 1.24/1.19 ( ! [X2 : a] : ((p != (= @ X2))) ) | ~spl3_1),
% 1.24/1.19 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.24/1.19 thf(f22,definition,(
% 1.24/1.19 spl3_1 <=> ! [X2 : a] : (p != (= @ X2))),
% 1.24/1.19 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.24/1.19 thf(f34,plain,(
% 1.24/1.19 ( ! [X4 : a] : (($true != (p @ X4)) | (sK1 = X4)) ) | ~spl3_4),
% 1.24/1.19 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.24/1.19 thf(f33,definition,(
% 1.24/1.19 spl3_4 <=> ! [X4 : a] : (($true != (p @ X4)) | (sK1 = X4))),
% 1.24/1.19 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.24/1.19 thf(f165,plain,(
% 1.24/1.19 ( ! [X2 : a] : (((p @ (sK8 @ X2)) = $false) | ((sK8 @ X2) != X2)) ) | ~spl3_1),
% 1.24/1.19 inference(equality_proxy_clausification,[status(thm)],[f164])).
% 1.24/1.19 thf(f164,plain,(
% 1.24/1.19 ( ! [X2 : a] : (((X2 = (sK8 @ X2)) = $false) | ((p @ (sK8 @ X2)) = $false)) ) | ~spl3_1),
% 1.24/1.19 inference(binary_proxy_clausification,[status(thm)],[f162])).
% 1.24/1.19 thf(f161,plain,(
% 1.24/1.19 ~spl3_6 | ~spl3_8),
% 1.24/1.19 inference(avatar_contradiction_clause,[status(thm)],[f160])).
% 1.24/1.19 thf(f160,plain,(
% 1.24/1.19 $false | (~spl3_6 | ~spl3_8)),
% 1.24/1.19 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 1.24/1.19 thf(f156,plain,(
% 1.24/1.19 ($true != $true) | (~spl3_6 | ~spl3_8)),
% 1.24/1.19 inference(superposition,[status(thm)],[f66,f43])).
% 1.24/1.19 thf(f66,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((p @ X0) != $true)) ) | ~spl3_8),
% 1.24/1.19 inference(avatar_component_clause,[status(thm)],[f65])).
% 1.24/1.19 thf(f65,definition,(
% 1.24/1.19 spl3_8 <=> ! [X0 : a] : ((p @ X0) != $true)),
% 1.24/1.19 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 1.24/1.19 thf(f154,plain,(
% 1.24/1.19 spl3_8 | ~spl3_2 | ~spl3_4 | ~spl3_5),
% 1.24/1.19 inference(avatar_split_clause,[status(thm)],[f153,f37,f33,f25,f65])).
% 1.24/1.19 thf(f25,definition,(
% 1.24/1.19 spl3_2 <=> ! [X0 : a] : (((p @ (sK0 @ X0)) = $true) | ((p @ X0) != $true))),
% 1.24/1.19 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.24/1.19 thf(f37,definition,(
% 1.24/1.19 spl3_5 <=> ! [X0 : a] : (((p @ X0) != $true) | ((sK0 @ X0) != X0))),
% 1.24/1.19 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.24/1.19 thf(f153,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((p @ X0) != $true)) ) | (~spl3_2 | ~spl3_4 | ~spl3_5)),
% 1.24/1.19 inference(subsumption_resolution,[status(thm)],[f151,f34])).
% 1.24/1.19 thf(f151,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((p @ X0) != $true) | (sK1 != X0)) ) | (~spl3_2 | ~spl3_4 | ~spl3_5)),
% 1.24/1.19 inference(duplicate_literal_removal,[status(thm)],[f150])).
% 1.24/1.19 thf(f150,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((sK1 != X0) | ((p @ X0) != $true) | ((p @ X0) != $true)) ) | (~spl3_2 | ~spl3_4 | ~spl3_5)),
% 1.24/1.19 inference(superposition,[status(thm)],[f38,f115])).
% 1.24/1.19 thf(f115,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((sK0 @ X0) = sK1) | ((p @ X0) != $true)) ) | (~spl3_2 | ~spl3_4)),
% 1.24/1.19 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.24/1.19 thf(f112,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((p @ X0) != $true) | ((sK0 @ X0) = sK1) | ($true != $true)) ) | (~spl3_2 | ~spl3_4)),
% 1.24/1.19 inference(superposition,[status(thm)],[f34,f26])).
% 1.24/1.19 thf(f26,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((p @ (sK0 @ X0)) = $true) | ((p @ X0) != $true)) ) | ~spl3_2),
% 1.24/1.19 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.24/1.19 thf(f38,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((sK0 @ X0) != X0) | ((p @ X0) != $true)) ) | ~spl3_5),
% 1.24/1.19 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.24/1.19 thf(f111,plain,(
% 1.24/1.19 ~spl3_2 | ~spl3_3 | ~spl3_5),
% 1.24/1.19 inference(avatar_contradiction_clause,[status(thm)],[f110])).
% 1.24/1.19 thf(f110,plain,(
% 1.24/1.19 $false | (~spl3_2 | ~spl3_3 | ~spl3_5)),
% 1.24/1.19 inference(equality_resolution,[status(thm)],[f109])).
% 1.24/1.19 thf(f109,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((sK2 != X0)) ) | (~spl3_2 | ~spl3_3 | ~spl3_5)),
% 1.24/1.19 inference(subsumption_resolution,[status(thm)],[f107,f48])).
% 1.24/1.19 thf(f48,plain,(
% 1.24/1.19 ( ! [X1 : a] : (((p @ X1) = $true) | (sK2 != X1)) ) | ~spl3_3),
% 1.24/1.19 inference(equality_proxy_clausification,[status(thm)],[f47])).
% 1.24/1.19 thf(f47,plain,(
% 1.24/1.19 ( ! [X1 : a] : (((sK2 = X1) = $false) | ((p @ X1) = $true)) ) | ~spl3_3),
% 1.24/1.19 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.24/1.19 thf(f45,plain,(
% 1.24/1.19 ( ! [X1 : a] : (((sK2 = X1) = (p @ X1))) ) | ~spl3_3),
% 1.24/1.19 inference(argument_congruence,[status(thm)],[f31])).
% 1.24/1.19 thf(f31,plain,(
% 1.24/1.19 (p = (= @ sK2)) | ~spl3_3),
% 1.24/1.19 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.24/1.19 thf(f29,definition,(
% 1.24/1.19 spl3_3 <=> (p = (= @ sK2))),
% 1.24/1.19 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.24/1.19 thf(f107,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((sK2 != X0) | ((p @ X0) != $true)) ) | (~spl3_2 | ~spl3_3 | ~spl3_5)),
% 1.24/1.19 inference(duplicate_literal_removal,[status(thm)],[f106])).
% 1.24/1.19 thf(f106,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((sK2 != X0) | ((p @ X0) != $true) | ((p @ X0) != $true)) ) | (~spl3_2 | ~spl3_3 | ~spl3_5)),
% 1.24/1.19 inference(superposition,[status(thm)],[f38,f104])).
% 1.24/1.19 thf(f104,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((sK0 @ X0) = sK2) | ((p @ X0) != $true)) ) | (~spl3_2 | ~spl3_3)),
% 1.24/1.19 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.24/1.19 thf(f101,plain,(
% 1.24/1.19 ( ! [X0 : a] : (($true = $false) | ((sK0 @ X0) = sK2) | ((p @ X0) != $true)) ) | (~spl3_2 | ~spl3_3)),
% 1.24/1.19 inference(superposition,[status(thm)],[f26,f49])).
% 1.24/1.19 thf(f49,plain,(
% 1.24/1.19 ( ! [X1 : a] : (((p @ X1) = $false) | (sK2 = X1)) ) | ~spl3_3),
% 1.24/1.19 inference(equality_proxy_clausification,[status(thm)],[f46])).
% 1.24/1.19 thf(f46,plain,(
% 1.24/1.19 ( ! [X1 : a] : (((p @ X1) = $false) | ((sK2 = X1) = $true)) ) | ~spl3_3),
% 1.24/1.19 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.24/1.19 thf(f98,plain,(
% 1.24/1.19 ~spl3_1 | ~spl3_3),
% 1.24/1.19 inference(avatar_contradiction_clause,[status(thm)],[f97])).
% 1.24/1.19 thf(f97,plain,(
% 1.24/1.19 $false | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(equality_resolution,[status(thm)],[f96])).
% 1.24/1.19 thf(f96,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((sK2 != X0)) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.24/1.19 thf(f95,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((sK2 != X0) | (X0 != X0)) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(duplicate_literal_removal,[status(thm)],[f94])).
% 1.24/1.19 thf(f94,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((sK2 != X0) | (X0 != X0) | (sK2 != X0)) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(superposition,[status(thm)],[f86,f91])).
% 1.24/1.19 thf(f91,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((sK6 @ X0) = X0) | (sK2 != X0)) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.24/1.19 thf(f89,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((sK2 != X0) | ((sK6 @ X0) = X0) | (sK2 != sK2)) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(superposition,[status(thm)],[f86,f88])).
% 1.24/1.19 thf(f88,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((sK2 = (sK6 @ X0)) | ((sK6 @ X0) = X0)) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(equality_proxy_clausification,[status(thm)],[f87])).
% 1.24/1.19 thf(f87,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((X0 = (sK6 @ X0)) = $true) | (sK2 = (sK6 @ X0))) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(equality_proxy_clausification,[status(thm)],[f83])).
% 1.24/1.19 thf(f83,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((sK2 = (sK6 @ X0)) = $true) | ((X0 = (sK6 @ X0)) = $true)) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.24/1.19 thf(f80,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((sK2 = (sK6 @ X0)) != (X0 = (sK6 @ X0)))) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(negative_extensionality,[status(thm)],[f71])).
% 1.24/1.19 thf(f71,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((= @ sK2) != (= @ X0))) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.24/1.19 thf(f70,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((p != p) | ((= @ sK2) != (= @ X0))) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(constrained_superposition,[status(thm)],[f23,f31])).
% 1.24/1.19 thf(f86,plain,(
% 1.24/1.19 ( ! [X0 : a] : ((sK2 != (sK6 @ X0)) | ((sK6 @ X0) != X0)) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(equality_proxy_clausification,[status(thm)],[f85])).
% 1.24/1.19 thf(f85,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((sK6 @ X0) != X0) | ((sK2 = (sK6 @ X0)) = $false)) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(equality_proxy_clausification,[status(thm)],[f84])).
% 1.24/1.19 thf(f84,plain,(
% 1.24/1.19 ( ! [X0 : a] : (((X0 = (sK6 @ X0)) = $false) | ((sK2 = (sK6 @ X0)) = $false)) ) | (~spl3_1 | ~spl3_3)),
% 1.24/1.19 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.24/1.19 thf(f44,plain,(
% 1.24/1.19 spl3_6 | spl3_3),
% 1.24/1.19 inference(avatar_split_clause,[status(thm)],[f17,f29,f41])).
% 1.24/1.19 thf(f17,plain,(
% 1.24/1.19 (p = (= @ sK2)) | ((p @ sK1) = $true)),
% 1.24/1.19 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.24/1.19 thf(f14,plain,(
% 1.24/1.19 (p = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ sK2)) | ((p @ sK1) = $true)),
% 1.24/1.19 inference(cnf_transformation,[status(thm)],[f12])).
% 1.24/1.19 thf(f12,plain,(
% 1.24/1.19 (! [X0 : a] : (((p @ X0) != $true) | (((sK0 @ X0) != X0) & ((p @ (sK0 @ X0)) = $true))) | ! [X2 : a] : (p != ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X2))) & ((((p @ sK1) = $true) & ! [X4 : a] : ((sK1 = X4) | ($true != (p @ X4)))) | (p = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ sK2)))),
% 1.24/1.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9])).
% 1.24/1.19 thf(f9,plain,(
% 1.24/1.19 ! [X0 : a] : (? [X1 : a] : ((X0 != X1) & ((p @ X1) = $true)) => (((sK0 @ X0) != X0) & ((p @ (sK0 @ X0)) = $true)))),
% 1.24/1.19 introduced(definition,[],[choice_axiom])).
% 1.24/1.19 thf(f10,plain,(
% 1.24/1.19 ? [X3 : a] : (($true = (p @ X3)) & ! [X4 : a] : ((X3 = X4) | ($true != (p @ X4)))) => (((p @ sK1) = $true) & ! [X4 : a] : ((sK1 = X4) | ($true != (p @ X4))))),
% 1.24/1.19 introduced(definition,[],[choice_axiom])).
% 1.24/1.19 thf(f11,plain,(
% 1.24/1.19 ? [X5 : a] : (p = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X5)) => (p = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ sK2))),
% 1.24/1.19 introduced(definition,[],[choice_axiom])).
% 1.24/1.19 thf(f8,plain,(
% 1.24/1.19 (! [X0 : a] : (((p @ X0) != $true) | ? [X1 : a] : ((X0 != X1) & ((p @ X1) = $true))) | ! [X2 : a] : (p != ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X2))) & (? [X3 : a] : (($true = (p @ X3)) & ! [X4 : a] : ((X3 = X4) | ($true != (p @ X4)))) | ? [X5 : a] : (p = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X5)))),
% 1.24/1.19 inference(rectify,[status(thm)],[f7])).
% 1.24/1.19 thf(f7,plain,(
% 1.24/1.19 (! [X0 : a] : (((p @ X0) != $true) | ? [X1 : a] : ((X0 != X1) & ((p @ X1) = $true))) | ! [X2 : a] : (p != ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X2))) & (? [X0 : a] : (((p @ X0) = $true) & ! [X1 : a] : ((X0 = X1) | ((p @ X1) != $true))) | ? [X2 : a] : (p = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X2)))),
% 1.24/1.19 inference(nnf_transformation,[status(thm)],[f6])).
% 1.24/1.19 thf(f6,plain,(
% 1.24/1.19 ? [X2 : a] : (p = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X2)) <~> ? [X0 : a] : (((p @ X0) = $true) & ! [X1 : a] : ((X0 = X1) | ((p @ X1) != $true)))),
% 1.24/1.19 inference(ennf_transformation,[status(thm)],[f5])).
% 1.24/1.19 thf(f5,plain,(
% 1.24/1.19 ~(? [X0 : a] : (((p @ X0) = $true) & ! [X1 : a] : (((p @ X1) = $true) => (X0 = X1))) <=> ? [X2 : a] : (p = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X2)))),
% 1.24/1.19 inference(fool_elimination,[status(thm)],[f4])).
% 1.24/1.19 thf(f4,plain,(
% 1.24/1.19 ~(? [X0 : a] : (! [X1 : a] : ((p @ X1) => (X0 = X1)) & (p @ X0)) <=> ? [X2 : a] : (p = ((^[X3 : a, X4 : a] : ((X3 = X4))) @ X2)))),
% 1.24/1.19 inference(rectify,[status(thm)],[f2])).
% 1.24/1.19 thf(f2,negated_conjecture,(
% 1.24/1.19 ~(? [X0 : a] : (! [X2 : a] : ((p @ X2) => (X0 = X2)) & (p @ X0)) <=> ? [X0 : a] : (p = ((^[X1 : a, X0 : a] : ((X0 = X1))) @ X0)))),
% 1.24/1.19 inference(negated_conjecture,[status(cth)],[f1])).
% 1.24/1.19 thf(f1,conjecture,(
% 1.24/1.19 ? [X0 : a] : (! [X2 : a] : ((p @ X2) => (X0 = X2)) & (p @ X0)) <=> ? [X0 : a] : (p = ((^[X1 : a, X0 : a] : ((X0 = X1))) @ X0))),
% 1.24/1.19 file('/export/starexec/sandbox2/tmp/tmp.c6oRckkeWf/DTF2THF_11890.p',cTTTP5306A_pme)).
% 1.24/1.19 thf(f39,plain,(
% 1.24/1.19 spl3_1 | spl3_5),
% 1.24/1.19 inference(avatar_split_clause,[status(thm)],[f18,f37,f22])).
% 1.24/1.19 thf(f18,plain,(
% 1.24/1.19 ( ! [X2 : a,X0 : a] : (((p @ X0) != $true) | ((sK0 @ X0) != X0) | (p != (= @ X2))) )),
% 1.24/1.19 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.24/1.19 thf(f16,plain,(
% 1.24/1.19 ( ! [X2 : a,X0 : a] : ((p != ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X2)) | ((p @ X0) != $true) | ((sK0 @ X0) != X0)) )),
% 1.24/1.19 inference(cnf_transformation,[status(thm)],[f12])).
% 1.24/1.19 thf(f35,plain,(
% 1.24/1.19 spl3_3 | spl3_4),
% 1.24/1.19 inference(avatar_split_clause,[status(thm)],[f19,f33,f29])).
% 1.24/1.19 thf(f19,plain,(
% 1.24/1.19 ( ! [X4 : a] : ((p = (= @ sK2)) | ($true != (p @ X4)) | (sK1 = X4)) )),
% 1.24/1.19 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.24/1.19 thf(f13,plain,(
% 1.24/1.19 ( ! [X4 : a] : (($true != (p @ X4)) | (sK1 = X4) | (p = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ sK2))) )),
% 1.24/1.19 inference(cnf_transformation,[status(thm)],[f12])).
% 1.24/1.19 thf(f27,plain,(
% 1.24/1.19 spl3_1 | spl3_2),
% 1.24/1.19 inference(avatar_split_clause,[status(thm)],[f20,f25,f22])).
% 1.24/1.19 thf(f20,plain,(
% 1.24/1.19 ( ! [X2 : a,X0 : a] : ((p != (= @ X2)) | ((p @ (sK0 @ X0)) = $true) | ((p @ X0) != $true)) )),
% 1.24/1.19 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.24/1.19 thf(f15,plain,(
% 1.24/1.19 ( ! [X2 : a,X0 : a] : (((p @ X0) != $true) | ((p @ (sK0 @ X0)) = $true) | (p != ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ X2))) )),
% 1.24/1.19 inference(cnf_transformation,[status(thm)],[f12])).
% 1.24/1.19 % SZS output end Proof for DTF2THF_11890
% 1.24/1.19 % (11987)------------------------------
% 1.24/1.19 % (11987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.24/1.19 % (11987)Termination reason: Refutation
% 1.24/1.19
% 1.24/1.19 % (11987)Memory used [KB]: 5628
% 1.24/1.19 % (11987)Time elapsed: 0.008 s
% 1.24/1.19 % (11987)Instructions burned: 11 (million)
% 1.24/1.19 % (11987)------------------------------
% 1.24/1.19 % (11987)------------------------------
% 1.24/1.19 % (11986)Success in time 0.016 s
%------------------------------------------------------------------------------