%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET582^5 : 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 : n031.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 09:31:48 AM UTC 2026
% Result : Theorem 1.47s 1.29s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 77 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 538 ( 156 equ; 0 cnn)
% Maximal formula atoms : 22 ( 6 avg)
% Number of connectives : 594 ( 158 ~; 150 |; 53 &; 209 @)
% ( 18 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 50 ( 12 ^; 29 !; 9 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_9,type,
sK0: a > $o ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_11,type,
sK2: a > $o ).
thf(func_def_13,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK5: a ).
thf(f108,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f54,f60,f66,f67,f70,f74,f85,f89,f99,f107]) ).
thf(f107,plain,
( ~ spl3_1
| ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f106]) ).
thf(f106,plain,
( $false
| ~ spl3_1
| ~ spl3_3
| ~ spl3_5 ),
inference(subsumption_resolution,[status(thm)],[f105,f48]) ).
thf(f48,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl3_3
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f105,plain,
( ( $true
!= ( sK1 @ sK5 ) )
| ~ spl3_1
| ~ spl3_5 ),
inference(subsumption_resolution,[status(thm)],[f104,f59]) ).
thf(f59,plain,
( ( ( sK2 @ sK5 )
= $true )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f57,definition,
( spl3_5
<=> ( ( sK2 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f104,plain,
( ( ( sK2 @ sK5 )
!= $true )
| ( $true
!= ( sK1 @ sK5 ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $true
!= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
!= $true )
| ( $true != $true )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f14,f40]) ).
thf(f40,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl3_1
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f14,plain,
! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( ( sK2 @ X3 )
!= $true )
| ( ( sK1 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X3: a] :
( ( ( ( ( ( sK1 @ X3 )
= $true )
| ( $true
= ( sK0 @ X3 ) ) )
& ( ( $true
!= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
!= $true ) ) )
| ( ( sK2 @ X3 )
!= $true ) )
& ( ( ( sK2 @ X3 )
= $true )
| ( ( ( $true
= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
!= $true ) )
& ( ( $true
!= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
= $true ) ) ) ) )
& ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
!= sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( ( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true ) )
& ( ( ( X0 @ X3 )
!= $true )
| ( ( X1 @ X3 )
!= $true ) ) )
| ( ( X2 @ X3 )
!= $true ) )
& ( ( ( X2 @ X3 )
= $true )
| ( ( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ( ( ( X0 @ X3 )
!= $true )
| ( ( X1 @ X3 )
= $true ) ) ) ) )
& ( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
!= X0 ) )
=> ( ! [X3: a] :
( ( ( ( ( ( sK1 @ X3 )
= $true )
| ( $true
= ( sK0 @ X3 ) ) )
& ( ( $true
!= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
!= $true ) ) )
| ( ( sK2 @ X3 )
!= $true ) )
& ( ( ( sK2 @ X3 )
= $true )
| ( ( ( $true
= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
!= $true ) )
& ( ( $true
!= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
= $true ) ) ) ) )
& ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
!= sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( ( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true ) )
& ( ( ( X0 @ X3 )
!= $true )
| ( ( X1 @ X3 )
!= $true ) ) )
| ( ( X2 @ X3 )
!= $true ) )
& ( ( ( X2 @ X3 )
= $true )
| ( ( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ( ( ( X0 @ X3 )
!= $true )
| ( ( X1 @ X3 )
= $true ) ) ) ) )
& ( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
!= X0 ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( ( X1 @ X3 )
= $true )
<=> ( ( X0 @ X3 )
!= $true ) )
<=> ( ( X2 @ X3 )
= $true ) )
& ( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
!= X0 ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( ( X1 @ X3 )
= $true )
<=> ( ( X0 @ X3 )
!= $true ) )
<=> ( ( X2 @ X3 )
= $true ) )
=> ( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X0 ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( ( X1 @ X3 )
= $true )
<=> ( ( X0 @ X3 )
!= $true ) )
<=> ( ( X2 @ X3 )
= $true ) )
=> ( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
<=> ~ ( X0 @ X3 ) )
<=> ( X2 @ X3 ) )
=> ( X0
= ( ^ [X4: a] :
( ( ( X1 @ X4 )
& ~ ( X2 @ X4 ) )
| ( ~ ( X1 @ X4 )
& ( X2 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
<=> ~ ( X0 @ X3 ) )
<=> ( X2 @ X3 ) )
=> ( X0
= ( ^ [X4: a] :
( ( ( X1 @ X4 )
& ~ ( X2 @ X4 ) )
| ( ~ ( X1 @ X4 )
& ( X2 @ X4 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
<=> ~ ( X0 @ X3 ) )
<=> ( X2 @ X3 ) )
=> ( X0
= ( ^ [X4: a] :
( ( ( X1 @ X4 )
& ~ ( X2 @ X4 ) )
| ( ~ ( X1 @ X4 )
& ( X2 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cG9SpI5O7T/DTF2THF_18676.p',cBOOL_PROP_25_pme) ).
thf(f99,plain,
( ~ spl3_3
| ~ spl3_4
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f98]) ).
thf(f98,plain,
( $false
| ~ spl3_3
| ~ spl3_4
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $false = $true )
| ~ spl3_3
| ~ spl3_4
| ~ spl3_6 ),
inference(forward_demodulation,[status(thm)],[f96,f53]) ).
thf(f53,plain,
( ( ( sK2 @ sK5 )
= $false )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl3_4
<=> ( ( sK2 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f96,plain,
( ( ( sK2 @ sK5 )
= $true )
| ~ spl3_3
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( $false = $true )
| ~ spl3_3
| ~ spl3_6 ),
inference(forward_demodulation,[status(thm)],[f94,f65]) ).
thf(f65,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl3_6
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f94,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true != $true )
| ( ( sK2 @ sK5 )
= $true )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f13,f48]) ).
thf(f13,plain,
! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK2 @ X3 )
= $true )
| ( $true
= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f89,plain,
( ~ spl3_1
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f88]) ).
thf(f88,plain,
( $false
| ~ spl3_1
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_6 ),
inference(forward_demodulation,[status(thm)],[f40,f65]) ).
thf(f85,plain,
( ~ spl3_2
| ~ spl3_5
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f84]) ).
thf(f84,plain,
( $false
| ~ spl3_2
| ~ spl3_5
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_5
| ~ spl3_6 ),
inference(forward_demodulation,[status(thm)],[f82,f44]) ).
thf(f44,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl3_2
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f82,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl3_5
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $false = $true )
| ( $true
= ( sK1 @ sK5 ) )
| ~ spl3_5
| ~ spl3_6 ),
inference(forward_demodulation,[status(thm)],[f80,f65]) ).
thf(f80,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK1 @ sK5 ) )
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ~ spl3_5 ),
inference(superposition,[status(thm)],[f15,f59]) ).
thf(f15,plain,
! [X3: a] :
( ( ( sK2 @ X3 )
!= $true )
| ( ( sK1 @ X3 )
= $true )
| ( $true
= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f74,plain,
( ~ spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f73]) ).
thf(f73,plain,
( $false
| ~ spl3_4
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $false = $true )
| ~ spl3_4
| ~ spl3_5 ),
inference(forward_demodulation,[status(thm)],[f59,f53]) ).
thf(f70,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f69]) ).
thf(f69,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[status(thm)],[f48,f44]) ).
thf(f67,plain,
( spl3_3
| spl3_4
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f23,f63,f51,f46]) ).
thf(f23,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ~ ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $false
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( sK0 @ sK5 )
!= ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( sK0 @ sK5 )
!= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f66,plain,
( spl3_5
| spl3_6
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f25,f42,f63,f57]) ).
thf(f25,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $true )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ~ ( sK2 @ sK5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ~ ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f60,plain,
( spl3_5
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f55,f46,f57]) ).
thf(f55,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(subsumption_resolution,[status(thm)],[f29,f12]) ).
thf(f12,plain,
! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
= $true )
| ( ( sK2 @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f29,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ~ ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true
= ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) ) )
| ( $true
= ( ~ ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ( ( sK2 @ sK5 )
& ~ ( sK1 @ sK5 ) )
| ( ~ ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f54,plain,
( spl3_4
| spl3_2
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f35,f38,f42,f51]) ).
thf(f35,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( ~ ( sK2 @ sK5 ) )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( ~ ( sK1 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( ~ ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $true
= ( ~ ( sK2 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( ( ~ ( sK1 @ sK5 ) )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET582^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n031.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:00:33 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SET582^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : TPS problem BOOL-PROP-25
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : Trybulec's 25th Boolean property of sets
% 0.29/0.46
% 0.29/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.29/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0255 [Bro09]
% 0.29/0.46 % : BOOL-PROP-25 [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.29/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.29/0.46 % Number of connectives : 16 ( 3 ~; 1 |; 2 &; 7 @)
% 0.29/0.46 % ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.46 % Number of variables : 5 ( 1 ^; 4 !; 0 ?; 5 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 % : Polymorphic definitions expanded.
% 0.29/0.46 % :
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(a_type,type,
% 0.29/0.46 a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(cBOOL_PROP_25_pme,conjecture,
% 0.29/0.46 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.29/0.46 ( ! [Xx: a] :
% 0.29/0.46 ( ( ~ ( X @ Xx )
% 0.29/0.46 <=> ( Y @ Xx ) )
% 0.29/0.46 <=> ( Z @ Xx ) )
% 0.29/0.46 => ( X
% 0.29/0.46 = ( ^ [Xz: a] :
% 0.29/0.46 ( ( ( Y @ Xz )
% 0.29/0.46 & ~ ( Z @ Xz ) )
% 0.29/0.46 | ( ( Z @ Xz )
% 0.29/0.46 & ~ ( Y @ Xz ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 12:00:34 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cG9SpI5O7T/DTF2DTF18676.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(a_type,type,
% 1.47/1.27 a: $tType ).
% 1.47/1.27
% 1.47/1.27 thf(cBOOL_PROP_25_pme,conjecture,
% 1.47/1.27 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.47/1.27 ( ! [Xx: a] :
% 1.47/1.27 ( ( ~ ( X @ Xx )
% 1.47/1.27 <=> ( Y @ Xx ) )
% 1.47/1.27 <=> ( Z @ Xx ) )
% 1.47/1.27 => ( X
% 1.47/1.27 = ( ^ [Xz: a] :
% 1.47/1.27 ( ( ( Y @ Xz )
% 1.47/1.27 & ~ ( Z @ Xz ) )
% 1.47/1.27 | ( ( Z @ Xz )
% 1.47/1.27 & ~ ( Y @ Xz ) ) ) ) ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.28 % (18983)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18676 for (2999ds/18Mi)
% 1.47/1.29 % (18983)First to succeed.
% 1.47/1.29 % (18978)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_18676 for (2999ds/4Mi)
% 1.47/1.29 % (18983)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_18676
% 1.47/1.29 % SZS output start Proof for DTF2THF_18676
% 1.47/1.29 thf(type_def_5, type, a: $tType).
% 1.47/1.29 thf(func_def_0, type, a: $tType).
% 1.47/1.29 thf(func_def_9, type, sK0: a > $o).
% 1.47/1.29 thf(func_def_10, type, sK1: a > $o).
% 1.47/1.29 thf(func_def_11, type, sK2: a > $o).
% 1.47/1.29 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.47/1.29 thf(func_def_14, type, sK5: a).
% 1.47/1.29 thf(f108,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(avatar_sat_refutation,[status(thm)],[f54,f60,f66,f67,f70,f74,f85,f89,f99,f107])).
% 1.47/1.29 thf(f107,plain,(
% 1.47/1.29 ~spl3_1 | ~spl3_3 | ~spl3_5),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f106])).
% 1.47/1.29 thf(f106,plain,(
% 1.47/1.29 $false | (~spl3_1 | ~spl3_3 | ~spl3_5)),
% 1.47/1.29 inference(subsumption_resolution,[status(thm)],[f105,f48])).
% 1.47/1.29 thf(f48,plain,(
% 1.47/1.29 ($true = (sK1 @ sK5)) | ~spl3_3),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.47/1.29 thf(f46,definition,(
% 1.47/1.29 spl3_3 <=> ($true = (sK1 @ sK5))),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.47/1.29 thf(f105,plain,(
% 1.47/1.29 ($true != (sK1 @ sK5)) | (~spl3_1 | ~spl3_5)),
% 1.47/1.29 inference(subsumption_resolution,[status(thm)],[f104,f59])).
% 1.47/1.29 thf(f59,plain,(
% 1.47/1.29 ((sK2 @ sK5) = $true) | ~spl3_5),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.47/1.29 thf(f57,definition,(
% 1.47/1.29 spl3_5 <=> ((sK2 @ sK5) = $true)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.47/1.29 thf(f104,plain,(
% 1.47/1.29 ((sK2 @ sK5) != $true) | ($true != (sK1 @ sK5)) | ~spl3_1),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.47/1.29 thf(f101,plain,(
% 1.47/1.29 ($true != (sK1 @ sK5)) | ((sK2 @ sK5) != $true) | ($true != $true) | ~spl3_1),
% 1.47/1.29 inference(superposition,[status(thm)],[f14,f40])).
% 1.47/1.29 thf(f40,plain,(
% 1.47/1.29 ((sK0 @ sK5) = $true) | ~spl3_1),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.47/1.29 thf(f38,definition,(
% 1.47/1.29 spl3_1 <=> ((sK0 @ sK5) = $true)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.47/1.29 thf(f14,plain,(
% 1.47/1.29 ( ! [X3 : a] : (($true != (sK0 @ X3)) | ((sK2 @ X3) != $true) | ((sK1 @ X3) != $true)) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.29 thf(f10,plain,(
% 1.47/1.29 ! [X3 : a] : ((((((sK1 @ X3) = $true) | ($true = (sK0 @ X3))) & (($true != (sK0 @ X3)) | ((sK1 @ X3) != $true))) | ((sK2 @ X3) != $true)) & (((sK2 @ X3) = $true) | ((($true = (sK0 @ X3)) | ((sK1 @ X3) != $true)) & (($true != (sK0 @ X3)) | ((sK1 @ X3) = $true))))) & ((^[Y0 : a]: (((sK2 @ Y0) & (~ (sK1 @ Y0))) | ((~ (sK2 @ Y0)) & (sK1 @ Y0)))) != sK0)),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9])).
% 1.47/1.29 thf(f9,plain,(
% 1.47/1.29 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : ((((((X1 @ X3) = $true) | ((X0 @ X3) = $true)) & (((X0 @ X3) != $true) | ((X1 @ X3) != $true))) | ((X2 @ X3) != $true)) & (((X2 @ X3) = $true) | ((((X0 @ X3) = $true) | ((X1 @ X3) != $true)) & (((X0 @ X3) != $true) | ((X1 @ X3) = $true))))) & ((^[Y0 : a]: (((X2 @ Y0) & (~ (X1 @ Y0))) | ((~ (X2 @ Y0)) & (X1 @ Y0)))) != X0)) => (! [X3 : a] : ((((((sK1 @ X3) = $true) | ($true = (sK0 @ X3))) & (($true != (sK0 @ X3)) | ((sK1 @ X3) != $true))) | ((sK2 @ X3) != $true)) & (((sK2 @ X3) = $true) | ((($true = (sK0 @ X3)) | ((sK1 @ X3) != $true)) & (($true != (sK0 @ X3)) | ((sK1 @ X3) = $true))))) & ((^[Y0 : a]: (((sK2 @ Y0) & (~ (sK1 @ Y0))) | ((~ (sK2 @ Y0)) & (sK1 @ Y0)))) != sK0))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : ((((((X1 @ X3) = $true) | ((X0 @ X3) = $true)) & (((X0 @ X3) != $true) | ((X1 @ X3) != $true))) | ((X2 @ X3) != $true)) & (((X2 @ X3) = $true) | ((((X0 @ X3) = $true) | ((X1 @ X3) != $true)) & (((X0 @ X3) != $true) | ((X1 @ X3) = $true))))) & ((^[Y0 : a]: (((X2 @ Y0) & (~ (X1 @ Y0))) | ((~ (X2 @ Y0)) & (X1 @ Y0)))) != X0))),
% 1.47/1.29 inference(nnf_transformation,[status(thm)],[f7])).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : ((((X1 @ X3) = $true) <=> ((X0 @ X3) != $true)) <=> ((X2 @ X3) = $true)) & ((^[Y0 : a]: (((X2 @ Y0) & (~ (X1 @ Y0))) | ((~ (X2 @ Y0)) & (X1 @ Y0)))) != X0))),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f6])).
% 1.47/1.29 thf(f6,plain,(
% 1.47/1.29 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : ((((X1 @ X3) = $true) <=> ((X0 @ X3) != $true)) <=> ((X2 @ X3) = $true)) => ((^[Y0 : a]: (((X2 @ Y0) & (~ (X1 @ Y0))) | ((~ (X2 @ Y0)) & (X1 @ Y0)))) = X0))),
% 1.47/1.29 inference(flattening,[status(thm)],[f5])).
% 1.47/1.29 thf(f5,plain,(
% 1.47/1.29 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : ((((X1 @ X3) = $true) <=> ~((X0 @ X3) = $true)) <=> ((X2 @ X3) = $true)) => ((^[Y0 : a]: (((X2 @ Y0) & (~ (X1 @ Y0))) | ((~ (X2 @ Y0)) & (X1 @ Y0)))) = X0))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.29 thf(f4,plain,(
% 1.47/1.29 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X1 @ X3) <=> ~(X0 @ X3)) <=> (X2 @ X3)) => (X0 = (^[X4 : a] : (((X1 @ X4) & ~(X2 @ X4)) | (~(X1 @ X4) & (X2 @ X4))))))),
% 1.47/1.29 inference(rectify,[status(thm)],[f2])).
% 1.47/1.29 thf(f2,negated_conjecture,(
% 1.47/1.29 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X1 @ X3) <=> ~(X0 @ X3)) <=> (X2 @ X3)) => (X0 = (^[X4 : a] : (((X1 @ X4) & ~(X2 @ X4)) | (~(X1 @ X4) & (X2 @ X4))))))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.29 thf(f1,conjecture,(
% 1.47/1.29 ! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X1 @ X3) <=> ~(X0 @ X3)) <=> (X2 @ X3)) => (X0 = (^[X4 : a] : (((X1 @ X4) & ~(X2 @ X4)) | (~(X1 @ X4) & (X2 @ X4))))))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.cG9SpI5O7T/DTF2THF_18676.p',cBOOL_PROP_25_pme)).
% 1.47/1.29 thf(f99,plain,(
% 1.47/1.29 ~spl3_3 | ~spl3_4 | ~spl3_6),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f98])).
% 1.47/1.29 thf(f98,plain,(
% 1.47/1.29 $false | (~spl3_3 | ~spl3_4 | ~spl3_6)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.47/1.29 thf(f97,plain,(
% 1.47/1.29 ($false = $true) | (~spl3_3 | ~spl3_4 | ~spl3_6)),
% 1.47/1.29 inference(forward_demodulation,[status(thm)],[f96,f53])).
% 1.47/1.29 thf(f53,plain,(
% 1.47/1.29 ((sK2 @ sK5) = $false) | ~spl3_4),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.47/1.29 thf(f51,definition,(
% 1.47/1.29 spl3_4 <=> ((sK2 @ sK5) = $false)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.47/1.29 thf(f96,plain,(
% 1.47/1.29 ((sK2 @ sK5) = $true) | (~spl3_3 | ~spl3_6)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.47/1.29 thf(f95,plain,(
% 1.47/1.29 ((sK2 @ sK5) = $true) | ($false = $true) | (~spl3_3 | ~spl3_6)),
% 1.47/1.29 inference(forward_demodulation,[status(thm)],[f94,f65])).
% 1.47/1.29 thf(f65,plain,(
% 1.47/1.29 ($false = (sK0 @ sK5)) | ~spl3_6),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.47/1.29 thf(f63,definition,(
% 1.47/1.29 spl3_6 <=> ($false = (sK0 @ sK5))),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.47/1.29 thf(f94,plain,(
% 1.47/1.29 ((sK2 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ~spl3_3),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.47/1.29 thf(f93,plain,(
% 1.47/1.29 ((sK0 @ sK5) = $true) | ($true != $true) | ((sK2 @ sK5) = $true) | ~spl3_3),
% 1.47/1.29 inference(superposition,[status(thm)],[f13,f48])).
% 1.47/1.29 thf(f13,plain,(
% 1.47/1.29 ( ! [X3 : a] : (((sK1 @ X3) != $true) | ((sK2 @ X3) = $true) | ($true = (sK0 @ X3))) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.29 thf(f89,plain,(
% 1.47/1.29 ~spl3_1 | ~spl3_6),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f88])).
% 1.47/1.29 thf(f88,plain,(
% 1.47/1.29 $false | (~spl3_1 | ~spl3_6)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.47/1.29 thf(f87,plain,(
% 1.47/1.29 ($false = $true) | (~spl3_1 | ~spl3_6)),
% 1.47/1.29 inference(forward_demodulation,[status(thm)],[f40,f65])).
% 1.47/1.29 thf(f85,plain,(
% 1.47/1.29 ~spl3_2 | ~spl3_5 | ~spl3_6),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f84])).
% 1.47/1.29 thf(f84,plain,(
% 1.47/1.29 $false | (~spl3_2 | ~spl3_5 | ~spl3_6)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.47/1.29 thf(f83,plain,(
% 1.47/1.29 ($false = $true) | (~spl3_2 | ~spl3_5 | ~spl3_6)),
% 1.47/1.29 inference(forward_demodulation,[status(thm)],[f82,f44])).
% 1.47/1.29 thf(f44,plain,(
% 1.47/1.29 ($false = (sK1 @ sK5)) | ~spl3_2),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.47/1.29 thf(f42,definition,(
% 1.47/1.29 spl3_2 <=> ($false = (sK1 @ sK5))),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.47/1.29 thf(f82,plain,(
% 1.47/1.29 ($true = (sK1 @ sK5)) | (~spl3_5 | ~spl3_6)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.47/1.29 thf(f81,plain,(
% 1.47/1.29 ($false = $true) | ($true = (sK1 @ sK5)) | (~spl3_5 | ~spl3_6)),
% 1.47/1.29 inference(forward_demodulation,[status(thm)],[f80,f65])).
% 1.47/1.29 thf(f80,plain,(
% 1.47/1.29 ((sK0 @ sK5) = $true) | ($true = (sK1 @ sK5)) | ~spl3_5),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.47/1.29 thf(f79,plain,(
% 1.47/1.29 ($true != $true) | ($true = (sK1 @ sK5)) | ((sK0 @ sK5) = $true) | ~spl3_5),
% 1.47/1.29 inference(superposition,[status(thm)],[f15,f59])).
% 1.47/1.29 thf(f15,plain,(
% 1.47/1.29 ( ! [X3 : a] : (((sK2 @ X3) != $true) | ((sK1 @ X3) = $true) | ($true = (sK0 @ X3))) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.29 thf(f74,plain,(
% 1.47/1.29 ~spl3_4 | ~spl3_5),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f73])).
% 1.47/1.29 thf(f73,plain,(
% 1.47/1.29 $false | (~spl3_4 | ~spl3_5)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.47/1.29 thf(f72,plain,(
% 1.47/1.29 ($false = $true) | (~spl3_4 | ~spl3_5)),
% 1.47/1.29 inference(forward_demodulation,[status(thm)],[f59,f53])).
% 1.47/1.29 thf(f70,plain,(
% 1.47/1.29 ~spl3_2 | ~spl3_3),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f69])).
% 1.47/1.29 thf(f69,plain,(
% 1.47/1.29 $false | (~spl3_2 | ~spl3_3)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.47/1.29 thf(f68,plain,(
% 1.47/1.29 ($false = $true) | (~spl3_2 | ~spl3_3)),
% 1.47/1.29 inference(forward_demodulation,[status(thm)],[f48,f44])).
% 1.47/1.29 thf(f67,plain,(
% 1.47/1.29 spl3_3 | spl3_4 | spl3_6),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f23,f63,f51,f46])).
% 1.47/1.29 thf(f23,plain,(
% 1.47/1.29 ($false = (sK0 @ sK5)) | ((sK2 @ sK5) = $false) | ($true = (sK1 @ sK5))),
% 1.47/1.29 inference(not_proxy_clausification,[status(thm)],[f22])).
% 1.47/1.29 thf(f22,plain,(
% 1.47/1.29 ((sK2 @ sK5) = $false) | ($false = (sK0 @ sK5)) | ($false = (~ (sK1 @ sK5)))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.47/1.29 thf(f21,plain,(
% 1.47/1.29 ($false = ((sK2 @ sK5) & (~ (sK1 @ sK5)))) | ($false = (sK0 @ sK5))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.47/1.29 thf(f19,plain,(
% 1.47/1.29 ($false = (sK0 @ sK5)) | ($false = (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((~ (sK2 @ sK5)) & (sK1 @ sK5))))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.47/1.29 thf(f17,plain,(
% 1.47/1.29 ((sK0 @ sK5) != (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((~ (sK2 @ sK5)) & (sK1 @ sK5))))),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.47/1.29 thf(f16,plain,(
% 1.47/1.29 ((sK0 @ sK5) != ((^[Y0 : a]: (((sK2 @ Y0) & (~ (sK1 @ Y0))) | ((~ (sK2 @ Y0)) & (sK1 @ Y0)))) @ sK5))),
% 1.47/1.29 inference(negative_extensionality,[status(thm)],[f11])).
% 1.47/1.29 thf(f11,plain,(
% 1.47/1.29 ((^[Y0 : a]: (((sK2 @ Y0) & (~ (sK1 @ Y0))) | ((~ (sK2 @ Y0)) & (sK1 @ Y0)))) != sK0)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.29 thf(f66,plain,(
% 1.47/1.29 spl3_5 | spl3_6 | spl3_2),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f25,f42,f63,f57])).
% 1.47/1.29 thf(f25,plain,(
% 1.47/1.29 ($false = (sK0 @ sK5)) | ((sK2 @ sK5) = $true) | ($false = (sK1 @ sK5))),
% 1.47/1.29 inference(not_proxy_clausification,[status(thm)],[f24])).
% 1.47/1.29 thf(f24,plain,(
% 1.47/1.29 ($false = (sK0 @ sK5)) | ($false = (sK1 @ sK5)) | ((~ (sK2 @ sK5)) = $false)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.47/1.29 thf(f20,plain,(
% 1.47/1.29 ($false = (sK0 @ sK5)) | ($false = ((~ (sK2 @ sK5)) & (sK1 @ sK5)))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.47/1.29 thf(f60,plain,(
% 1.47/1.29 spl3_5 | spl3_3),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f55,f46,f57])).
% 1.47/1.29 thf(f55,plain,(
% 1.47/1.29 ((sK2 @ sK5) = $true) | ($true = (sK1 @ sK5))),
% 1.47/1.29 inference(subsumption_resolution,[status(thm)],[f29,f12])).
% 1.47/1.29 thf(f12,plain,(
% 1.47/1.29 ( ! [X3 : a] : (($true != (sK0 @ X3)) | ((sK1 @ X3) = $true) | ((sK2 @ X3) = $true)) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.29 thf(f29,plain,(
% 1.47/1.29 ($true = (sK1 @ sK5)) | ((sK2 @ sK5) = $true) | ((sK0 @ sK5) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.47/1.29 thf(f28,plain,(
% 1.47/1.29 ((sK0 @ sK5) = $true) | ($true = ((~ (sK2 @ sK5)) & (sK1 @ sK5))) | ((sK2 @ sK5) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.47/1.29 thf(f26,plain,(
% 1.47/1.29 ($true = ((sK2 @ sK5) & (~ (sK1 @ sK5)))) | ($true = ((~ (sK2 @ sK5)) & (sK1 @ sK5))) | ((sK0 @ sK5) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.47/1.29 thf(f18,plain,(
% 1.47/1.29 ((sK0 @ sK5) = $true) | ($true = (((sK2 @ sK5) & (~ (sK1 @ sK5))) | ((~ (sK2 @ sK5)) & (sK1 @ sK5))))),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.47/1.29 thf(f54,plain,(
% 1.47/1.29 spl3_4 | spl3_2 | spl3_1),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f35,f38,f42,f51])).
% 1.47/1.29 thf(f35,plain,(
% 1.47/1.29 ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $true) | ((sK2 @ sK5) = $false)),
% 1.47/1.29 inference(not_proxy_clausification,[status(thm)],[f34])).
% 1.47/1.29 thf(f34,plain,(
% 1.47/1.29 ((~ (sK2 @ sK5)) = $true) | ($false = (sK1 @ sK5)) | ((sK0 @ sK5) = $true)),
% 1.47/1.29 inference(not_proxy_clausification,[status(thm)],[f33])).
% 1.47/1.29 thf(f33,plain,(
% 1.47/1.29 ((~ (sK1 @ sK5)) = $true) | ((sK0 @ sK5) = $true) | ((~ (sK2 @ sK5)) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.47/1.29 thf(f27,plain,(
% 1.47/1.29 ($true = ((~ (sK2 @ sK5)) & (sK1 @ sK5))) | ((~ (sK1 @ sK5)) = $true) | ((sK0 @ sK5) = $true)),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.47/1.29 % SZS output end Proof for DTF2THF_18676
% 1.47/1.29 % (18983)------------------------------
% 1.47/1.29 % (18983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (18983)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (18983)Memory used [KB]: 5500
% 1.47/1.29 % (18983)Time elapsed: 0.005 s
% 1.47/1.29 % (18983)Instructions burned: 6 (million)
% 1.47/1.29 % (18983)------------------------------
% 1.47/1.29 % (18983)------------------------------
% 1.47/1.29 % (18976)Success in time 0.015 s
%------------------------------------------------------------------------------