%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV218^5 : 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 : n001.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 1.62s 1.31s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 3 unt; 0 typ; 6 def)
% Number of atoms : 563 ( 162 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 697 ( 110 ~; 117 |; 54 &; 386 @)
% ( 9 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 129 ( 0 ^; 87 !; 42 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cQ: a > a > $o ).
thf(func_def_5,type,
sK0: a > a > $o ).
thf(func_def_6,type,
sK1: a > a ).
thf(func_def_7,type,
sK2: a ).
thf(func_def_8,type,
sK3: a ).
thf(func_def_9,type,
sK4: a ).
thf(func_def_10,type,
sK5: a ).
thf(func_def_11,type,
sK6: a ).
thf(func_def_12,type,
sK7: a ).
thf(f290,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f38,f43,f48,f49,f54,f55,f67,f96,f289]) ).
thf(f289,plain,
( ~ spl8_2
| spl8_4
| ~ spl8_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f288]) ).
thf(f288,plain,
( $false
| ~ spl8_2
| spl8_4
| ~ spl8_6 ),
inference(subsumption_resolution,[status(thm)],[f280,f22]) ).
thf(f22,plain,
! [X1: a] :
( ( sK0 @ X1 @ X1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: a] :
( ( ( sK0 @ X1 @ ( sK1 @ X1 ) )
= $true )
& ( ( sK0 @ X1 @ X1 )
= $true )
& ! [X3: a] :
( ! [X4: a] :
( ( cQ @ X3 @ X4 )
= ( sK0 @ X1 @ X4 ) )
| ( ( sK0 @ X1 @ X3 )
!= $true ) ) )
& ( ( ( cQ @ sK2 @ sK2 )
!= $true )
| ( ( ( cQ @ sK4 @ sK3 )
= $true )
& ( $true
!= ( cQ @ sK3 @ sK4 ) ) )
| ( ( ( cQ @ sK5 @ sK7 )
= $true )
& ( ( cQ @ sK6 @ sK7 )
!= $true )
& ( ( cQ @ sK6 @ sK5 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f8,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > a > $o] :
! [X1: a] :
( ? [X2: a] :
( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X1 @ X1 )
= $true )
& ! [X3: a] :
( ! [X4: a] :
( ( X0 @ X1 @ X4 )
= ( cQ @ X3 @ X4 ) )
| ( ( X0 @ X1 @ X3 )
!= $true ) ) )
=> ! [X1: a] :
( ? [X2: a] :
( ( sK0 @ X1 @ X2 )
= $true )
& ( ( sK0 @ X1 @ X1 )
= $true )
& ! [X3: a] :
( ! [X4: a] :
( ( cQ @ X3 @ X4 )
= ( sK0 @ X1 @ X4 ) )
| ( ( sK0 @ X1 @ X3 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X1: a] :
( ? [X2: a] :
( ( sK0 @ X1 @ X2 )
= $true )
=> ( ( sK0 @ X1 @ ( sK1 @ X1 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X5: a] :
( ( cQ @ X5 @ X5 )
!= $true )
=> ( ( cQ @ sK2 @ sK2 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X6: a,X7: a] :
( ( ( cQ @ X7 @ X6 )
= $true )
& ( $true
!= ( cQ @ X6 @ X7 ) ) )
=> ( ( ( cQ @ sK4 @ sK3 )
= $true )
& ( $true
!= ( cQ @ sK3 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X8: a,X9: a,X10: a] :
( ( $true
= ( cQ @ X8 @ X10 ) )
& ( ( cQ @ X9 @ X10 )
!= $true )
& ( ( cQ @ X9 @ X8 )
= $true ) )
=> ( ( ( cQ @ sK5 @ sK7 )
= $true )
& ( ( cQ @ sK6 @ sK7 )
!= $true )
& ( ( cQ @ sK6 @ sK5 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X0: a > a > $o] :
! [X1: a] :
( ? [X2: a] :
( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X1 @ X1 )
= $true )
& ! [X3: a] :
( ! [X4: a] :
( ( X0 @ X1 @ X4 )
= ( cQ @ X3 @ X4 ) )
| ( ( X0 @ X1 @ X3 )
!= $true ) ) )
& ( ? [X5: a] :
( ( cQ @ X5 @ X5 )
!= $true )
| ? [X6: a,X7: a] :
( ( ( cQ @ X7 @ X6 )
= $true )
& ( $true
!= ( cQ @ X6 @ X7 ) ) )
| ? [X8: a,X9: a,X10: a] :
( ( $true
= ( cQ @ X8 @ X10 ) )
& ( ( cQ @ X9 @ X10 )
!= $true )
& ( ( cQ @ X9 @ X8 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X0: a > a > $o] :
! [X1: a] :
( ? [X2: a] :
( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X1 @ X1 )
= $true )
& ! [X3: a] :
( ! [X4: a] :
( ( X0 @ X1 @ X4 )
= ( cQ @ X3 @ X4 ) )
| ( ( X0 @ X1 @ X3 )
!= $true ) ) )
& ( ? [X7: a] :
( ( cQ @ X7 @ X7 )
!= $true )
| ? [X5: a,X6: a] :
( ( $true
= ( cQ @ X6 @ X5 ) )
& ( ( cQ @ X5 @ X6 )
!= $true ) )
| ? [X9: a,X10: a,X8: a] :
( ( ( cQ @ X9 @ X8 )
= $true )
& ( $true
!= ( cQ @ X10 @ X8 ) )
& ( $true
= ( cQ @ X10 @ X9 ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ? [X8: a,X10: a,X9: a] :
( ( $true
!= ( cQ @ X10 @ X8 ) )
& ( $true
= ( cQ @ X10 @ X9 ) )
& ( ( cQ @ X9 @ X8 )
= $true ) )
| ? [X7: a] :
( ( cQ @ X7 @ X7 )
!= $true )
| ? [X5: a,X6: a] :
( ( $true
= ( cQ @ X6 @ X5 ) )
& ( ( cQ @ X5 @ X6 )
!= $true ) ) )
& ? [X0: a > a > $o] :
! [X1: a] :
( ? [X2: a] :
( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X1 @ X1 )
= $true )
& ! [X3: a] :
( ! [X4: a] :
( ( X0 @ X1 @ X4 )
= ( cQ @ X3 @ X4 ) )
| ( ( X0 @ X1 @ X3 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X0: a > a > $o] :
! [X1: a] :
( ? [X2: a] :
( ( X0 @ X1 @ X2 )
= $true )
& ! [X3: a] :
( ( ( X0 @ X1 @ X3 )
= $true )
=> ! [X4: a] :
( ( X0 @ X1 @ X4 )
= ( cQ @ X3 @ X4 ) ) )
& ( ( X0 @ X1 @ X1 )
= $true ) )
=> ( ! [X8: a,X10: a,X9: a] :
( ( ( $true
= ( cQ @ X10 @ X9 ) )
& ( ( cQ @ X9 @ X8 )
= $true ) )
=> ( $true
= ( cQ @ X10 @ X8 ) ) )
& ! [X7: a] :
( ( cQ @ X7 @ X7 )
= $true )
& ! [X6: a,X5: a] :
( ( $true
= ( cQ @ X6 @ X5 ) )
=> ( ( cQ @ X5 @ X6 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ? [X0: a > a > $o] :
! [X1: a] :
( ? [X2: a] : ( X0 @ X1 @ X2 )
& ! [X3: a] :
( ( X0 @ X1 @ X3 )
=> ! [X4: a] :
( ( X0 @ X1 @ X4 )
<=> ( cQ @ X3 @ X4 ) ) )
& ( X0 @ X1 @ X1 ) )
=> ( ! [X5: a,X6: a] :
( ( cQ @ X6 @ X5 )
=> ( cQ @ X5 @ X6 ) )
& ! [X7: a] : ( cQ @ X7 @ X7 )
& ! [X8: a,X9: a,X10: a] :
( ( ( cQ @ X9 @ X8 )
& ( cQ @ X10 @ X9 ) )
=> ( cQ @ X10 @ X8 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: a > a > $o] :
! [X1: a] :
( ? [X2: a] : ( X0 @ X1 @ X2 )
& ! [X3: a] :
( ( X0 @ X1 @ X3 )
=> ! [X4: a] :
( ( X0 @ X1 @ X4 )
<=> ( cQ @ X3 @ X4 ) ) )
& ( X0 @ X1 @ X1 ) )
=> ( ! [X4: a,X1: a] :
( ( cQ @ X1 @ X4 )
=> ( cQ @ X4 @ X1 ) )
& ! [X1: a] : ( cQ @ X1 @ X1 )
& ! [X2: a,X4: a,X1: a] :
( ( ( cQ @ X4 @ X2 )
& ( cQ @ X1 @ X4 ) )
=> ( cQ @ X1 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ? [X0: a > a > $o] :
! [X1: a] :
( ? [X2: a] : ( X0 @ X1 @ X2 )
& ! [X3: a] :
( ( X0 @ X1 @ X3 )
=> ! [X4: a] :
( ( X0 @ X1 @ X4 )
<=> ( cQ @ X3 @ X4 ) ) )
& ( X0 @ X1 @ X1 ) )
=> ( ! [X4: a,X1: a] :
( ( cQ @ X1 @ X4 )
=> ( cQ @ X4 @ X1 ) )
& ! [X1: a] : ( cQ @ X1 @ X1 )
& ! [X2: a,X4: a,X1: a] :
( ( ( cQ @ X4 @ X2 )
& ( cQ @ X1 @ X4 ) )
=> ( cQ @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xWQi9kz00I/DTF2THF_10347.p',cTHM559A_pme) ).
thf(f280,plain,
( ( ( sK0 @ sK6 @ sK6 )
!= $true )
| ~ spl8_2
| spl8_4
| ~ spl8_6 ),
inference(trivial_inequality_removal,[status(thm)],[f276]) ).
thf(f276,plain,
( ( $true = $false )
| ( ( sK0 @ sK6 @ sK6 )
!= $true )
| ~ spl8_2
| spl8_4
| ~ spl8_6 ),
inference(superposition,[status(thm)],[f178,f53]) ).
thf(f53,plain,
( ( ( cQ @ sK6 @ sK5 )
= $true )
| ~ spl8_6 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl8_6
<=> ( ( cQ @ sK6 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition]) ).
thf(f178,plain,
( ! [X0: a] :
( ( ( cQ @ X0 @ sK5 )
= $false )
| ( ( sK0 @ sK6 @ X0 )
!= $true ) )
| ~ spl8_2
| spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f176]) ).
thf(f176,plain,
( ! [X0: a] :
( ( ( sK0 @ sK6 @ X0 )
!= $true )
| ( ( cQ @ X0 @ sK5 )
= $false )
| ( $true != $true ) )
| ~ spl8_2
| spl8_4 ),
inference(superposition,[status(thm)],[f165,f25]) ).
thf(f25,plain,
! [X3: a,X1: a,X4: a] :
( ( ( sK0 @ X1 @ X4 )
= $true )
| ( ( cQ @ X3 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X3 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X3: a,X1: a,X4: a] :
( ( ( sK0 @ X1 @ X3 )
!= $true )
| ( ( cQ @ X3 @ X4 )
= ( sK0 @ X1 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f165,plain,
( ( ( sK0 @ sK6 @ sK5 )
!= $true )
| ~ spl8_2
| spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f161]) ).
thf(f161,plain,
( ( ( sK0 @ sK6 @ sK5 )
!= $true )
| ( $true != $true )
| ~ spl8_2
| spl8_4 ),
inference(superposition,[status(thm)],[f142,f22]) ).
thf(f142,plain,
( ! [X0: a] :
( ( ( sK0 @ X0 @ sK6 )
!= $true )
| ( ( sK0 @ X0 @ sK5 )
!= $true ) )
| ~ spl8_2
| spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ! [X0: a] :
( ( ( sK0 @ X0 @ sK5 )
!= $true )
| ( ( sK0 @ X0 @ sK6 )
!= $true )
| ( $true = $false ) )
| ~ spl8_2
| spl8_4 ),
inference(superposition,[status(thm)],[f110,f33]) ).
thf(f33,plain,
( ( ( cQ @ sK5 @ sK7 )
= $true )
| ~ spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl8_2
<=> ( ( cQ @ sK5 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f110,plain,
( ! [X0: a,X1: a] :
( ( ( cQ @ X0 @ sK7 )
= $false )
| ( ( sK0 @ X1 @ sK6 )
!= $true )
| ( $true
!= ( sK0 @ X1 @ X0 ) ) )
| spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true
!= ( sK0 @ X1 @ X0 ) )
| ( ( sK0 @ X1 @ sK6 )
!= $true )
| ( ( cQ @ X0 @ sK7 )
= $false ) )
| spl8_4 ),
inference(superposition,[status(thm)],[f42,f83]) ).
thf(f83,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( $true
= ( cQ @ X3 @ X1 ) )
| ( ( cQ @ X2 @ X1 )
= $false )
| ( ( sK0 @ X0 @ X3 )
!= $true )
| ( ( sK0 @ X0 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( ( sK0 @ X0 @ X2 )
!= $true )
| ( ( cQ @ X2 @ X1 )
= $false )
| ( $true
= ( cQ @ X3 @ X1 ) )
| ( $true = $false )
| ( ( sK0 @ X0 @ X3 )
!= $true ) ),
inference(superposition,[status(thm)],[f25,f24]) ).
thf(f24,plain,
! [X3: a,X1: a,X4: a] :
( ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X3 )
!= $true )
| ( ( cQ @ X3 @ X4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f42,plain,
( ( ( cQ @ sK6 @ sK7 )
!= $true )
| spl8_4 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl8_4
<=> ( ( cQ @ sK6 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).
thf(f96,plain,
( ~ spl8_3
| spl8_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f95]) ).
thf(f95,plain,
( $false
| ~ spl8_3
| spl8_5 ),
inference(subsumption_resolution,[status(thm)],[f90,f22]) ).
thf(f90,plain,
( ( ( sK0 @ sK4 @ sK4 )
!= $true )
| ~ spl8_3
| spl8_5 ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( ( sK0 @ sK4 @ sK4 )
!= $true )
| ( $true = $false )
| ~ spl8_3
| spl8_5 ),
inference(superposition,[status(thm)],[f84,f37]) ).
thf(f37,plain,
( ( ( cQ @ sK4 @ sK3 )
= $true )
| ~ spl8_3 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl8_3
<=> ( ( cQ @ sK4 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f84,plain,
( ! [X0: a] :
( ( ( cQ @ X0 @ sK3 )
= $false )
| ( $true
!= ( sK0 @ sK4 @ X0 ) ) )
| spl8_5 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true
!= ( sK0 @ sK4 @ X0 ) )
| ( ( cQ @ X0 @ sK3 )
= $false ) )
| spl8_5 ),
inference(superposition,[status(thm)],[f69,f25]) ).
thf(f69,plain,
( ( ( sK0 @ sK4 @ sK3 )
!= $true )
| spl8_5 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $true != $true )
| ( ( sK0 @ sK4 @ sK3 )
!= $true )
| spl8_5 ),
inference(superposition,[status(thm)],[f47,f62]) ).
thf(f62,plain,
! [X0: a,X1: a] :
( ( $true
= ( cQ @ X1 @ X0 ) )
| ( ( sK0 @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: a,X1: a] :
( ( ( sK0 @ X0 @ X1 )
!= $true )
| ( $true = $false )
| ( $true
= ( cQ @ X1 @ X0 ) ) ),
inference(superposition,[status(thm)],[f22,f24]) ).
thf(f47,plain,
( ( $true
!= ( cQ @ sK3 @ sK4 ) )
| spl8_5 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl8_5
<=> ( $true
= ( cQ @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition]) ).
thf(f67,plain,
spl8_1,
inference(avatar_contradiction_clause,[status(thm)],[f66]) ).
thf(f66,plain,
( $false
| spl8_1 ),
inference(subsumption_resolution,[status(thm)],[f65,f22]) ).
thf(f65,plain,
( ( ( sK0 @ sK2 @ sK2 )
!= $true )
| spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( sK0 @ sK2 @ sK2 )
!= $true )
| ( $true != $true )
| spl8_1 ),
inference(superposition,[status(thm)],[f29,f62]) ).
thf(f29,plain,
( ( ( cQ @ sK2 @ sK2 )
!= $true )
| spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl8_1
<=> ( ( cQ @ sK2 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f55,plain,
( spl8_3
| ~ spl8_1
| spl8_6 ),
inference(avatar_split_clause,[status(thm)],[f18,f51,f27,f35]) ).
thf(f18,plain,
( ( ( cQ @ sK6 @ sK5 )
= $true )
| ( ( cQ @ sK2 @ sK2 )
!= $true )
| ( ( cQ @ sK4 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f54,plain,
( ~ spl8_5
| spl8_6
| ~ spl8_1 ),
inference(avatar_split_clause,[status(thm)],[f15,f27,f51,f45]) ).
thf(f15,plain,
( ( $true
!= ( cQ @ sK3 @ sK4 ) )
| ( ( cQ @ sK6 @ sK5 )
= $true )
| ( ( cQ @ sK2 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f49,plain,
( ~ spl8_1
| ~ spl8_5
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f17,f31,f45,f27]) ).
thf(f17,plain,
( ( $true
!= ( cQ @ sK3 @ sK4 ) )
| ( ( cQ @ sK5 @ sK7 )
= $true )
| ( ( cQ @ sK2 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f48,plain,
( ~ spl8_5
| ~ spl8_1
| ~ spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f16,f40,f27,f45]) ).
thf(f16,plain,
( ( ( cQ @ sK2 @ sK2 )
!= $true )
| ( ( cQ @ sK6 @ sK7 )
!= $true )
| ( $true
!= ( cQ @ sK3 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f43,plain,
( ~ spl8_1
| ~ spl8_4
| spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f19,f35,f40,f27]) ).
thf(f19,plain,
( ( ( cQ @ sK4 @ sK3 )
= $true )
| ( ( cQ @ sK6 @ sK7 )
!= $true )
| ( ( cQ @ sK2 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f38,plain,
( ~ spl8_1
| spl8_2
| spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f20,f35,f31,f27]) ).
thf(f20,plain,
( ( ( cQ @ sK4 @ sK3 )
= $true )
| ( ( cQ @ sK2 @ sK2 )
!= $true )
| ( ( cQ @ sK5 @ sK7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV218^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:42:50 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.48 ---- Original DTF file ---
% 0.26/0.48 thf(spec,logic,$$dhol).
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 % File : SEV218^5 : TPTP v9.2.1. Released v4.0.0.
% 0.26/0.48 % Domain : Set Theory (Sets of sets)
% 0.26/0.48 % Problem : TPS problem from CHOICE-COVER-THMS
% 0.26/0.48 % Version : Especial.
% 0.26/0.48 % English :
% 0.26/0.48
% 0.26/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.48 % Source : [Bro09]
% 0.26/0.48 % Names : tps_1007 [Bro09]
% 0.26/0.48
% 0.26/0.48 % Status : Theorem
% 0.26/0.48 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.33 v4.0.0
% 0.26/0.48 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.26/0.48 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.26/0.48 % Maximal formula atoms : 7 ( 7 avg)
% 0.26/0.48 % Number of connectives : 32 ( 0 ~; 0 |; 5 &; 22 @)
% 0.26/0.48 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.26/0.48 % Maximal formula depth : 12 ( 12 avg)
% 0.26/0.48 % Number of types : 2 ( 1 usr)
% 0.26/0.48 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.26/0.48 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.26/0.48 % Number of variables : 11 ( 0 ^; 9 !; 2 ?; 11 :)
% 0.26/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.26/0.48
% 0.26/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.26/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.26/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.26/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 thf(a_type,type,
% 0.26/0.48 a: $tType ).
% 0.26/0.48
% 0.26/0.48 thf(cQ,type,
% 0.26/0.48 cQ: a > a > $o ).
% 0.26/0.48
% 0.26/0.48 thf(cTHM559A_pme,conjecture,
% 0.26/0.48 ( ? [Xf: a > a > $o] :
% 0.26/0.48 ! [Xx: a] :
% 0.26/0.48 ( ? [Xz: a] : ( Xf @ Xx @ Xz )
% 0.26/0.48 & ! [Xx_0: a] :
% 0.26/0.48 ( ( Xf @ Xx @ Xx_0 )
% 0.26/0.48 => ! [Xy: a] :
% 0.26/0.48 ( ( Xf @ Xx @ Xy )
% 0.26/0.48 <=> ( cQ @ Xx_0 @ Xy ) ) )
% 0.26/0.48 & ( Xf @ Xx @ Xx ) )
% 0.26/0.48 => ( ! [Xx: a] : ( cQ @ Xx @ Xx )
% 0.26/0.48 & ! [Xx: a,Xy: a] :
% 0.26/0.48 ( ( cQ @ Xx @ Xy )
% 0.26/0.48 => ( cQ @ Xy @ Xx ) )
% 0.26/0.48 & ! [Xx: a,Xy: a,Xz: a] :
% 0.26/0.48 ( ( ( cQ @ Xx @ Xy )
% 0.26/0.48 & ( cQ @ Xy @ Xz ) )
% 0.26/0.48 => ( cQ @ Xx @ Xz ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 ------------------------
% 1.45/1.27 ---- Embedded in THF ---
% 1.45/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.27 %%% Generated on Tue Feb 24 12:42:51 EST 2026
% 1.45/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.27 %%% Logic specification used:
% 1.45/1.27 %%% thf(spec, logic, $$dhol).
% 1.45/1.27
% 1.45/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.xWQi9kz00I/DTF2DTF10347.p
% See solution above
% 1.45/1.27 ------------------------
% 1.45/1.28 ---- Cleaned THF ---
% 1.45/1.28 thf(a_type,type,
% 1.45/1.28 a: $tType ).
% 1.45/1.28
% 1.45/1.28 thf(cQ,type,
% 1.45/1.28 cQ: a > a > $o ).
% 1.45/1.28
% 1.45/1.28 thf(cTHM559A_pme,conjecture,
% 1.45/1.28 ( ? [Xf: a > a > $o] :
% 1.45/1.28 ! [Xx: a] :
% 1.45/1.28 ( ? [Xz: a] : ( Xf @ Xx @ Xz )
% 1.45/1.28 & ! [Xx_0: a] :
% 1.45/1.28 ( ( Xf @ Xx @ Xx_0 )
% 1.45/1.28 => ! [Xy: a] :
% 1.45/1.28 ( ( Xf @ Xx @ Xy )
% 1.45/1.28 <=> ( cQ @ Xx_0 @ Xy ) ) )
% 1.45/1.28 & ( Xf @ Xx @ Xx ) )
% 1.45/1.28 => ( ! [Xx: a] : ( cQ @ Xx @ Xx )
% 1.45/1.28 & ! [Xx: a,Xy: a] :
% 1.45/1.28 ( ( cQ @ Xx @ Xy )
% 1.45/1.28 => ( cQ @ Xy @ Xx ) )
% 1.45/1.28 & ! [Xx: a,Xy: a,Xz: a] :
% 1.45/1.28 ( ( ( cQ @ Xx @ Xy )
% 1.45/1.28 & ( cQ @ Xy @ Xz ) )
% 1.45/1.28 => ( cQ @ Xx @ Xz ) ) ) ) ).
% 1.45/1.28 ------------------------
% 1.62/1.30 % (10624)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_10347 for (2999ds/275Mi)
% 1.62/1.30 % (10620)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_10347 for (2999ds/4Mi)
% 1.62/1.30 % (10620)Instruction limit reached!
% 1.62/1.30 % (10620)------------------------------
% 1.62/1.30 % (10620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (10620)Termination reason: Unknown
% 1.62/1.30 % (10620)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (10620)Memory used [KB]: 5500
% 1.62/1.30 % (10620)Time elapsed: 0.003 s
% 1.62/1.30 % (10620)Instructions burned: 4 (million)
% 1.62/1.30 % (10620)------------------------------
% 1.62/1.30 % (10620)------------------------------
% 1.62/1.30 % (10622)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10347 for (2999ds/2Mi)
% 1.62/1.30 % (10621)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_10347 for (2999ds/27Mi)
% 1.62/1.30 % (10623)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_10347 for (2999ds/2Mi)
% 1.62/1.30 % (10619)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10347 for (2999ds/183Mi)
% 1.62/1.30 % (10625)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10347 for (2999ds/18Mi)
% 1.62/1.31 % (10622)Instruction limit reached!
% 1.62/1.31 % (10622)------------------------------
% 1.62/1.31 % (10622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (10622)Termination reason: Unknown
% 1.62/1.31 % (10622)Termination phase: Preprocessing 3
% 1.62/1.31
% 1.62/1.31 % (10622)Memory used [KB]: 895
% 1.62/1.31 % (10622)Time elapsed: 0.003 s
% 1.62/1.31 % (10622)Instructions burned: 2 (million)
% 1.62/1.31 % (10622)------------------------------
% 1.62/1.31 % (10622)------------------------------
% 1.62/1.31 % (10623)Instruction limit reached!
% 1.62/1.31 % (10623)------------------------------
% 1.62/1.31 % (10623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (10623)Termination reason: Unknown
% 1.62/1.31 % (10623)Termination phase: Property scanning
% 1.62/1.31
% 1.62/1.31 % (10623)Memory used [KB]: 895
% 1.62/1.31 % (10623)Time elapsed: 0.003 s
% 1.62/1.31 % (10623)Instructions burned: 2 (million)
% 1.62/1.31 % (10623)------------------------------
% 1.62/1.31 % (10623)------------------------------
% 1.62/1.31 % (10626)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10347 for (2999ds/3Mi)
% 1.62/1.31 % (10626)Instruction limit reached!
% 1.62/1.31 % (10626)------------------------------
% 1.62/1.31 % (10626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (10626)Termination reason: Unknown
% 1.62/1.31 % (10626)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (10626)Memory used [KB]: 5500
% 1.62/1.31 % (10626)Time elapsed: 0.003 s
% 1.62/1.31 % (10626)Instructions burned: 3 (million)
% 1.62/1.31 % (10626)------------------------------
% 1.62/1.31 % (10626)------------------------------
% 1.62/1.31 % (10624)First to succeed.
% 1.62/1.31 % (10624)Refutation found. Thanks to Tanya!
% 1.62/1.31 % SZS status Theorem for DTF2THF_10347
% 1.62/1.31 % SZS output start Proof for DTF2THF_10347
% 1.62/1.31 thf(type_def_5, type, a: $tType).
% 1.62/1.31 thf(func_def_0, type, a: $tType).
% 1.62/1.31 thf(func_def_1, type, cQ: a > a > $o).
% 1.62/1.31 thf(func_def_5, type, sK0: a > a > $o).
% 1.62/1.31 thf(func_def_6, type, sK1: a > a).
% 1.62/1.31 thf(func_def_7, type, sK2: a).
% 1.62/1.31 thf(func_def_8, type, sK3: a).
% 1.62/1.31 thf(func_def_9, type, sK4: a).
% 1.62/1.31 thf(func_def_10, type, sK5: a).
% 1.62/1.31 thf(func_def_11, type, sK6: a).
% 1.62/1.31 thf(func_def_12, type, sK7: a).
% 1.62/1.31 thf(f290,plain,(
% 1.62/1.31 $false),
% 1.62/1.31 inference(avatar_sat_refutation,[status(thm)],[f38,f43,f48,f49,f54,f55,f67,f96,f289])).
% 1.62/1.31 thf(f289,plain,(
% 1.62/1.31 ~spl8_2 | spl8_4 | ~spl8_6),
% 1.62/1.31 inference(avatar_contradiction_clause,[status(thm)],[f288])).
% 1.62/1.31 thf(f288,plain,(
% 1.62/1.31 $false | (~spl8_2 | spl8_4 | ~spl8_6)),
% 1.62/1.31 inference(subsumption_resolution,[status(thm)],[f280,f22])).
% 1.62/1.31 thf(f22,plain,(
% 1.62/1.31 ( ! [X1 : a] : (((sK0 @ X1 @ X1) = $true)) )),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.31 thf(f14,plain,(
% 1.62/1.31 ! [X1 : a] : (((sK0 @ X1 @ (sK1 @ X1)) = $true) & ((sK0 @ X1 @ X1) = $true) & ! [X3 : a] : (! [X4 : a] : ((cQ @ X3 @ X4) = (sK0 @ X1 @ X4)) | ((sK0 @ X1 @ X3) != $true))) & (((cQ @ sK2 @ sK2) != $true) | (((cQ @ sK4 @ sK3) = $true) & ($true != (cQ @ sK3 @ sK4))) | (((cQ @ sK5 @ sK7) = $true) & ((cQ @ sK6 @ sK7) != $true) & ((cQ @ sK6 @ sK5) = $true)))),
% 1.62/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f8,f13,f12,f11,f10,f9])).
% 1.62/1.31 thf(f9,plain,(
% 1.62/1.31 ? [X0 : a > a > $o] : ! [X1 : a] : (? [X2 : a] : ((X0 @ X1 @ X2) = $true) & ((X0 @ X1 @ X1) = $true) & ! [X3 : a] : (! [X4 : a] : ((X0 @ X1 @ X4) = (cQ @ X3 @ X4)) | ((X0 @ X1 @ X3) != $true))) => ! [X1 : a] : (? [X2 : a] : ((sK0 @ X1 @ X2) = $true) & ((sK0 @ X1 @ X1) = $true) & ! [X3 : a] : (! [X4 : a] : ((cQ @ X3 @ X4) = (sK0 @ X1 @ X4)) | ((sK0 @ X1 @ X3) != $true)))),
% 1.62/1.31 introduced(definition,[],[choice_axiom])).
% 1.62/1.31 thf(f10,plain,(
% 1.62/1.31 ! [X1 : a] : (? [X2 : a] : ((sK0 @ X1 @ X2) = $true) => ((sK0 @ X1 @ (sK1 @ X1)) = $true))),
% 1.62/1.31 introduced(definition,[],[choice_axiom])).
% 1.62/1.31 thf(f11,plain,(
% 1.62/1.31 ? [X5 : a] : ((cQ @ X5 @ X5) != $true) => ((cQ @ sK2 @ sK2) != $true)),
% 1.62/1.31 introduced(definition,[],[choice_axiom])).
% 1.62/1.31 thf(f12,plain,(
% 1.62/1.31 ? [X6 : a,X7 : a] : (((cQ @ X7 @ X6) = $true) & ($true != (cQ @ X6 @ X7))) => (((cQ @ sK4 @ sK3) = $true) & ($true != (cQ @ sK3 @ sK4)))),
% 1.62/1.31 introduced(definition,[],[choice_axiom])).
% 1.62/1.31 thf(f13,plain,(
% 1.62/1.31 ? [X8 : a,X9 : a,X10 : a] : (($true = (cQ @ X8 @ X10)) & ((cQ @ X9 @ X10) != $true) & ((cQ @ X9 @ X8) = $true)) => (((cQ @ sK5 @ sK7) = $true) & ((cQ @ sK6 @ sK7) != $true) & ((cQ @ sK6 @ sK5) = $true))),
% 1.62/1.31 introduced(definition,[],[choice_axiom])).
% 1.62/1.31 thf(f8,plain,(
% 1.62/1.31 ? [X0 : a > a > $o] : ! [X1 : a] : (? [X2 : a] : ((X0 @ X1 @ X2) = $true) & ((X0 @ X1 @ X1) = $true) & ! [X3 : a] : (! [X4 : a] : ((X0 @ X1 @ X4) = (cQ @ X3 @ X4)) | ((X0 @ X1 @ X3) != $true))) & (? [X5 : a] : ((cQ @ X5 @ X5) != $true) | ? [X6 : a,X7 : a] : (((cQ @ X7 @ X6) = $true) & ($true != (cQ @ X6 @ X7))) | ? [X8 : a,X9 : a,X10 : a] : (($true = (cQ @ X8 @ X10)) & ((cQ @ X9 @ X10) != $true) & ((cQ @ X9 @ X8) = $true)))),
% 1.62/1.31 inference(rectify,[status(thm)],[f7])).
% 1.62/1.31 thf(f7,plain,(
% 1.62/1.31 ? [X0 : a > a > $o] : ! [X1 : a] : (? [X2 : a] : ((X0 @ X1 @ X2) = $true) & ((X0 @ X1 @ X1) = $true) & ! [X3 : a] : (! [X4 : a] : ((X0 @ X1 @ X4) = (cQ @ X3 @ X4)) | ((X0 @ X1 @ X3) != $true))) & (? [X7 : a] : ((cQ @ X7 @ X7) != $true) | ? [X5 : a,X6 : a] : (($true = (cQ @ X6 @ X5)) & ((cQ @ X5 @ X6) != $true)) | ? [X9 : a,X10 : a,X8 : a] : (((cQ @ X9 @ X8) = $true) & ($true != (cQ @ X10 @ X8)) & ($true = (cQ @ X10 @ X9))))),
% 1.62/1.31 inference(flattening,[status(thm)],[f6])).
% 1.62/1.31 thf(f6,plain,(
% 1.62/1.31 (? [X8 : a,X10 : a,X9 : a] : (($true != (cQ @ X10 @ X8)) & (($true = (cQ @ X10 @ X9)) & ((cQ @ X9 @ X8) = $true))) | ? [X7 : a] : ((cQ @ X7 @ X7) != $true) | ? [X5 : a,X6 : a] : (($true = (cQ @ X6 @ X5)) & ((cQ @ X5 @ X6) != $true))) & ? [X0 : a > a > $o] : ! [X1 : a] : (? [X2 : a] : ((X0 @ X1 @ X2) = $true) & ((X0 @ X1 @ X1) = $true) & ! [X3 : a] : (! [X4 : a] : ((X0 @ X1 @ X4) = (cQ @ X3 @ X4)) | ((X0 @ X1 @ X3) != $true)))),
% 1.62/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.62/1.31 thf(f5,plain,(
% 1.62/1.31 ~(? [X0 : a > a > $o] : ! [X1 : a] : (? [X2 : a] : ((X0 @ X1 @ X2) = $true) & ! [X3 : a] : (((X0 @ X1 @ X3) = $true) => ! [X4 : a] : ((X0 @ X1 @ X4) = (cQ @ X3 @ X4))) & ((X0 @ X1 @ X1) = $true)) => (! [X8 : a,X10 : a,X9 : a] : ((($true = (cQ @ X10 @ X9)) & ((cQ @ X9 @ X8) = $true)) => ($true = (cQ @ X10 @ X8))) & ! [X7 : a] : ((cQ @ X7 @ X7) = $true) & ! [X6 : a,X5 : a] : (($true = (cQ @ X6 @ X5)) => ((cQ @ X5 @ X6) = $true))))),
% 1.62/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.31 thf(f4,plain,(
% 1.62/1.31 ~(? [X0 : a > a > $o] : ! [X1 : a] : (? [X2 : a] : (X0 @ X1 @ X2) & ! [X3 : a] : ((X0 @ X1 @ X3) => ! [X4 : a] : ((X0 @ X1 @ X4) <=> (cQ @ X3 @ X4))) & (X0 @ X1 @ X1)) => (! [X5 : a,X6 : a] : ((cQ @ X6 @ X5) => (cQ @ X5 @ X6)) & ! [X7 : a] : (cQ @ X7 @ X7) & ! [X8 : a,X9 : a,X10 : a] : (((cQ @ X9 @ X8) & (cQ @ X10 @ X9)) => (cQ @ X10 @ X8))))),
% 1.62/1.31 inference(rectify,[status(thm)],[f2])).
% 1.62/1.31 thf(f2,negated_conjecture,(
% 1.62/1.31 ~(? [X0 : a > a > $o] : ! [X1 : a] : (? [X2 : a] : (X0 @ X1 @ X2) & ! [X3 : a] : ((X0 @ X1 @ X3) => ! [X4 : a] : ((X0 @ X1 @ X4) <=> (cQ @ X3 @ X4))) & (X0 @ X1 @ X1)) => (! [X4 : a,X1 : a] : ((cQ @ X1 @ X4) => (cQ @ X4 @ X1)) & ! [X1 : a] : (cQ @ X1 @ X1) & ! [X2 : a,X4 : a,X1 : a] : (((cQ @ X4 @ X2) & (cQ @ X1 @ X4)) => (cQ @ X1 @ X2))))),
% 1.62/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.31 thf(f1,conjecture,(
% 1.62/1.31 ? [X0 : a > a > $o] : ! [X1 : a] : (? [X2 : a] : (X0 @ X1 @ X2) & ! [X3 : a] : ((X0 @ X1 @ X3) => ! [X4 : a] : ((X0 @ X1 @ X4) <=> (cQ @ X3 @ X4))) & (X0 @ X1 @ X1)) => (! [X4 : a,X1 : a] : ((cQ @ X1 @ X4) => (cQ @ X4 @ X1)) & ! [X1 : a] : (cQ @ X1 @ X1) & ! [X2 : a,X4 : a,X1 : a] : (((cQ @ X4 @ X2) & (cQ @ X1 @ X4)) => (cQ @ X1 @ X2)))),
% 1.62/1.31 file('/export/starexec/sandbox2/tmp/tmp.xWQi9kz00I/DTF2THF_10347.p',cTHM559A_pme)).
% 1.62/1.31 thf(f280,plain,(
% 1.62/1.31 ((sK0 @ sK6 @ sK6) != $true) | (~spl8_2 | spl8_4 | ~spl8_6)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f276])).
% 1.62/1.31 thf(f276,plain,(
% 1.62/1.31 ($true = $false) | ((sK0 @ sK6 @ sK6) != $true) | (~spl8_2 | spl8_4 | ~spl8_6)),
% 1.62/1.31 inference(superposition,[status(thm)],[f178,f53])).
% 1.62/1.31 thf(f53,plain,(
% 1.62/1.31 ((cQ @ sK6 @ sK5) = $true) | ~spl8_6),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.62/1.31 thf(f51,definition,(
% 1.62/1.31 spl8_6 <=> ((cQ @ sK6 @ sK5) = $true)),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition])).
% 1.62/1.31 thf(f178,plain,(
% 1.62/1.31 ( ! [X0 : a] : (((cQ @ X0 @ sK5) = $false) | ((sK0 @ sK6 @ X0) != $true)) ) | (~spl8_2 | spl8_4)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f176])).
% 1.62/1.31 thf(f176,plain,(
% 1.62/1.31 ( ! [X0 : a] : (((sK0 @ sK6 @ X0) != $true) | ((cQ @ X0 @ sK5) = $false) | ($true != $true)) ) | (~spl8_2 | spl8_4)),
% 1.62/1.31 inference(superposition,[status(thm)],[f165,f25])).
% 1.62/1.31 thf(f25,plain,(
% 1.62/1.31 ( ! [X3 : a,X1 : a,X4 : a] : (((sK0 @ X1 @ X4) = $true) | ((cQ @ X3 @ X4) = $false) | ((sK0 @ X1 @ X3) != $true)) )),
% 1.62/1.31 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.62/1.31 thf(f21,plain,(
% 1.62/1.31 ( ! [X3 : a,X1 : a,X4 : a] : (((sK0 @ X1 @ X3) != $true) | ((cQ @ X3 @ X4) = (sK0 @ X1 @ X4))) )),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.31 thf(f165,plain,(
% 1.62/1.31 ((sK0 @ sK6 @ sK5) != $true) | (~spl8_2 | spl8_4)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f161])).
% 1.62/1.31 thf(f161,plain,(
% 1.62/1.31 ((sK0 @ sK6 @ sK5) != $true) | ($true != $true) | (~spl8_2 | spl8_4)),
% 1.62/1.31 inference(superposition,[status(thm)],[f142,f22])).
% 1.62/1.31 thf(f142,plain,(
% 1.62/1.31 ( ! [X0 : a] : (((sK0 @ X0 @ sK6) != $true) | ((sK0 @ X0 @ sK5) != $true)) ) | (~spl8_2 | spl8_4)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.62/1.31 thf(f131,plain,(
% 1.62/1.31 ( ! [X0 : a] : (((sK0 @ X0 @ sK5) != $true) | ((sK0 @ X0 @ sK6) != $true) | ($true = $false)) ) | (~spl8_2 | spl8_4)),
% 1.62/1.31 inference(superposition,[status(thm)],[f110,f33])).
% 1.62/1.31 thf(f33,plain,(
% 1.62/1.31 ((cQ @ sK5 @ sK7) = $true) | ~spl8_2),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.62/1.31 thf(f31,definition,(
% 1.62/1.31 spl8_2 <=> ((cQ @ sK5 @ sK7) = $true)),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.62/1.31 thf(f110,plain,(
% 1.62/1.31 ( ! [X0 : a,X1 : a] : (((cQ @ X0 @ sK7) = $false) | ((sK0 @ X1 @ sK6) != $true) | ($true != (sK0 @ X1 @ X0))) ) | spl8_4),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.62/1.31 thf(f106,plain,(
% 1.62/1.31 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true != (sK0 @ X1 @ X0)) | ((sK0 @ X1 @ sK6) != $true) | ((cQ @ X0 @ sK7) = $false)) ) | spl8_4),
% 1.62/1.31 inference(superposition,[status(thm)],[f42,f83])).
% 1.62/1.31 thf(f83,plain,(
% 1.62/1.31 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : (($true = (cQ @ X3 @ X1)) | ((cQ @ X2 @ X1) = $false) | ((sK0 @ X0 @ X3) != $true) | ((sK0 @ X0 @ X2) != $true)) )),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.62/1.31 thf(f79,plain,(
% 1.62/1.31 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : (((sK0 @ X0 @ X2) != $true) | ((cQ @ X2 @ X1) = $false) | ($true = (cQ @ X3 @ X1)) | ($true = $false) | ((sK0 @ X0 @ X3) != $true)) )),
% 1.62/1.31 inference(superposition,[status(thm)],[f25,f24])).
% 1.62/1.31 thf(f24,plain,(
% 1.62/1.31 ( ! [X3 : a,X1 : a,X4 : a] : (((sK0 @ X1 @ X4) = $false) | ((sK0 @ X1 @ X3) != $true) | ((cQ @ X3 @ X4) = $true)) )),
% 1.62/1.31 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.62/1.31 thf(f42,plain,(
% 1.62/1.31 ((cQ @ sK6 @ sK7) != $true) | spl8_4),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.62/1.31 thf(f40,definition,(
% 1.62/1.31 spl8_4 <=> ((cQ @ sK6 @ sK7) = $true)),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 1.62/1.31 thf(f96,plain,(
% 1.62/1.31 ~spl8_3 | spl8_5),
% 1.62/1.31 inference(avatar_contradiction_clause,[status(thm)],[f95])).
% 1.62/1.31 thf(f95,plain,(
% 1.62/1.31 $false | (~spl8_3 | spl8_5)),
% 1.62/1.31 inference(subsumption_resolution,[status(thm)],[f90,f22])).
% 1.62/1.31 thf(f90,plain,(
% 1.62/1.31 ((sK0 @ sK4 @ sK4) != $true) | (~spl8_3 | spl8_5)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.62/1.31 thf(f86,plain,(
% 1.62/1.31 ((sK0 @ sK4 @ sK4) != $true) | ($true = $false) | (~spl8_3 | spl8_5)),
% 1.62/1.31 inference(superposition,[status(thm)],[f84,f37])).
% 1.62/1.31 thf(f37,plain,(
% 1.62/1.31 ((cQ @ sK4 @ sK3) = $true) | ~spl8_3),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.62/1.31 thf(f35,definition,(
% 1.62/1.31 spl8_3 <=> ((cQ @ sK4 @ sK3) = $true)),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 1.62/1.31 thf(f84,plain,(
% 1.62/1.31 ( ! [X0 : a] : (((cQ @ X0 @ sK3) = $false) | ($true != (sK0 @ sK4 @ X0))) ) | spl8_5),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.62/1.31 thf(f81,plain,(
% 1.62/1.31 ( ! [X0 : a] : (($true != $true) | ($true != (sK0 @ sK4 @ X0)) | ((cQ @ X0 @ sK3) = $false)) ) | spl8_5),
% 1.62/1.31 inference(superposition,[status(thm)],[f69,f25])).
% 1.62/1.31 thf(f69,plain,(
% 1.62/1.31 ((sK0 @ sK4 @ sK3) != $true) | spl8_5),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.62/1.31 thf(f68,plain,(
% 1.62/1.31 ($true != $true) | ((sK0 @ sK4 @ sK3) != $true) | spl8_5),
% 1.62/1.31 inference(superposition,[status(thm)],[f47,f62])).
% 1.62/1.31 thf(f62,plain,(
% 1.62/1.31 ( ! [X0 : a,X1 : a] : (($true = (cQ @ X1 @ X0)) | ((sK0 @ X0 @ X1) != $true)) )),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.62/1.31 thf(f58,plain,(
% 1.62/1.31 ( ! [X0 : a,X1 : a] : (((sK0 @ X0 @ X1) != $true) | ($true = $false) | ($true = (cQ @ X1 @ X0))) )),
% 1.62/1.31 inference(superposition,[status(thm)],[f22,f24])).
% 1.62/1.31 thf(f47,plain,(
% 1.62/1.31 ($true != (cQ @ sK3 @ sK4)) | spl8_5),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.62/1.31 thf(f45,definition,(
% 1.62/1.31 spl8_5 <=> ($true = (cQ @ sK3 @ sK4))),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition])).
% 1.62/1.31 thf(f67,plain,(
% 1.62/1.31 spl8_1),
% 1.62/1.31 inference(avatar_contradiction_clause,[status(thm)],[f66])).
% 1.62/1.31 thf(f66,plain,(
% 1.62/1.31 $false | spl8_1),
% 1.62/1.31 inference(subsumption_resolution,[status(thm)],[f65,f22])).
% 1.62/1.31 thf(f65,plain,(
% 1.62/1.31 ((sK0 @ sK2 @ sK2) != $true) | spl8_1),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.62/1.31 thf(f64,plain,(
% 1.62/1.31 ((sK0 @ sK2 @ sK2) != $true) | ($true != $true) | spl8_1),
% 1.62/1.31 inference(superposition,[status(thm)],[f29,f62])).
% 1.62/1.31 thf(f29,plain,(
% 1.62/1.31 ((cQ @ sK2 @ sK2) != $true) | spl8_1),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.62/1.31 thf(f27,definition,(
% 1.62/1.31 spl8_1 <=> ((cQ @ sK2 @ sK2) = $true)),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.62/1.31 thf(f55,plain,(
% 1.62/1.31 spl8_3 | ~spl8_1 | spl8_6),
% 1.62/1.31 inference(avatar_split_clause,[status(thm)],[f18,f51,f27,f35])).
% 1.62/1.31 thf(f18,plain,(
% 1.62/1.31 ((cQ @ sK6 @ sK5) = $true) | ((cQ @ sK2 @ sK2) != $true) | ((cQ @ sK4 @ sK3) = $true)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.31 thf(f54,plain,(
% 1.62/1.31 ~spl8_5 | spl8_6 | ~spl8_1),
% 1.62/1.31 inference(avatar_split_clause,[status(thm)],[f15,f27,f51,f45])).
% 1.62/1.31 thf(f15,plain,(
% 1.62/1.31 ($true != (cQ @ sK3 @ sK4)) | ((cQ @ sK6 @ sK5) = $true) | ((cQ @ sK2 @ sK2) != $true)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.31 thf(f49,plain,(
% 1.62/1.31 ~spl8_1 | ~spl8_5 | spl8_2),
% 1.62/1.31 inference(avatar_split_clause,[status(thm)],[f17,f31,f45,f27])).
% 1.62/1.31 thf(f17,plain,(
% 1.62/1.31 ($true != (cQ @ sK3 @ sK4)) | ((cQ @ sK5 @ sK7) = $true) | ((cQ @ sK2 @ sK2) != $true)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.31 thf(f48,plain,(
% 1.62/1.31 ~spl8_5 | ~spl8_1 | ~spl8_4),
% 1.62/1.31 inference(avatar_split_clause,[status(thm)],[f16,f40,f27,f45])).
% 1.62/1.31 thf(f16,plain,(
% 1.62/1.31 ((cQ @ sK2 @ sK2) != $true) | ((cQ @ sK6 @ sK7) != $true) | ($true != (cQ @ sK3 @ sK4))),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.31 thf(f43,plain,(
% 1.62/1.31 ~spl8_1 | ~spl8_4 | spl8_3),
% 1.62/1.31 inference(avatar_split_clause,[status(thm)],[f19,f35,f40,f27])).
% 1.62/1.31 thf(f19,plain,(
% 1.62/1.31 ((cQ @ sK4 @ sK3) = $true) | ((cQ @ sK6 @ sK7) != $true) | ((cQ @ sK2 @ sK2) != $true)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.31 thf(f38,plain,(
% 1.62/1.31 ~spl8_1 | spl8_2 | spl8_3),
% 1.62/1.31 inference(avatar_split_clause,[status(thm)],[f20,f35,f31,f27])).
% 1.62/1.31 thf(f20,plain,(
% 1.62/1.31 ((cQ @ sK4 @ sK3) = $true) | ((cQ @ sK2 @ sK2) != $true) | ((cQ @ sK5 @ sK7) = $true)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.31 % SZS output end Proof for DTF2THF_10347
% 1.62/1.31 % (10624)------------------------------
% 1.62/1.31 % (10624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (10624)Termination reason: Refutation
% 1.62/1.31
% 1.62/1.31 % (10624)Memory used [KB]: 5628
% 1.62/1.31 % (10624)Time elapsed: 0.017 s
% 1.62/1.31 % (10624)Instructions burned: 43 (million)
% 1.62/1.31 % (10624)------------------------------
% 1.62/1.31 % (10624)------------------------------
% 1.62/1.31 % (10618)Success in time 0.027 s
%------------------------------------------------------------------------------