%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV019^5 : 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 : n015.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 09:40:04 AM UTC 2026
% Result : Theorem 1.50s 1.24s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 74 ( 3 unt; 0 typ; 6 def)
% Number of atoms : 567 ( 162 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 661 ( 110 ~; 117 |; 54 &; 350 @)
% ( 9 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 120 ( 0 ^; 78 !; 42 ?; 120 :)
% 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(f173,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f38,f43,f48,f53,f54,f55,f67,f160,f172]) ).
thf(f172,plain,
( ~ spl8_1
| spl8_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f171]) ).
thf(f171,plain,
( $false
| ~ spl8_1
| spl8_6 ),
inference(subsumption_resolution,[status(thm)],[f165,f21]) ).
thf(f21,plain,
! [X0: a] :
( ( sK0 @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: a] :
( ( ( sK0 @ X0 @ ( sK1 @ X0 ) )
= $true )
& ! [X3: a] :
( ( ( sK0 @ X0 @ X3 )
!= $true )
| ! [X4: a] :
( ( cQ @ X3 @ X4 )
= ( sK0 @ X0 @ X4 ) ) )
& ( ( sK0 @ X0 @ X0 )
= $true ) )
& ( ( ( cQ @ sK2 @ sK2 )
!= $true )
| ( ( ( cQ @ sK4 @ sK3 )
!= $true )
& ( ( cQ @ sK3 @ sK4 )
= $true ) )
| ( ( ( 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] :
( ? [X1: a > $o] :
( ? [X2: a] :
( ( X1 @ X2 )
= $true )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ! [X4: a] :
( ( X1 @ X4 )
= ( cQ @ X3 @ X4 ) ) )
& ( ( X1 @ X0 )
= $true ) )
=> ( ? [X2: a] :
( ( sK0 @ X0 @ X2 )
= $true )
& ! [X3: a] :
( ( ( sK0 @ X0 @ X3 )
!= $true )
| ! [X4: a] :
( ( cQ @ X3 @ X4 )
= ( sK0 @ X0 @ X4 ) ) )
& ( ( sK0 @ X0 @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: a] :
( ? [X2: a] :
( ( sK0 @ X0 @ X2 )
= $true )
=> ( ( sK0 @ X0 @ ( sK1 @ X0 ) )
= $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 )
& ( ( cQ @ X6 @ X7 )
= $true ) )
=> ( ( ( cQ @ sK4 @ sK3 )
!= $true )
& ( ( cQ @ sK3 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X8: a,X9: a,X10: a] :
( ( ( cQ @ X8 @ X10 )
= $true )
& ( ( 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] :
? [X1: a > $o] :
( ? [X2: a] :
( ( X1 @ X2 )
= $true )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ! [X4: a] :
( ( X1 @ X4 )
= ( cQ @ X3 @ X4 ) ) )
& ( ( X1 @ X0 )
= $true ) )
& ( ? [X5: a] :
( ( cQ @ X5 @ X5 )
!= $true )
| ? [X6: a,X7: a] :
( ( ( cQ @ X7 @ X6 )
!= $true )
& ( ( cQ @ X6 @ X7 )
= $true ) )
| ? [X8: a,X9: a,X10: a] :
( ( ( cQ @ X8 @ X10 )
= $true )
& ( ( cQ @ X9 @ X10 )
!= $true )
& ( ( cQ @ X9 @ X8 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: a] :
? [X1: a > $o] :
( ? [X4: a] :
( ( X1 @ X4 )
= $true )
& ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) )
& ( ( X1 @ X0 )
= $true ) )
& ( ? [X10: a] :
( ( cQ @ X10 @ X10 )
!= $true )
| ? [X6: a,X5: a] :
( ( ( cQ @ X5 @ X6 )
!= $true )
& ( ( cQ @ X6 @ X5 )
= $true ) )
| ? [X7: a,X9: a,X8: a] :
( ( ( cQ @ X7 @ X8 )
= $true )
& ( ( cQ @ X9 @ X8 )
!= $true )
& ( ( cQ @ X9 @ X7 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ? [X6: a,X5: a] :
( ( ( cQ @ X5 @ X6 )
!= $true )
& ( ( cQ @ X6 @ X5 )
= $true ) )
| ? [X7: a,X8: a,X9: a] :
( ( ( cQ @ X9 @ X8 )
!= $true )
& ( ( cQ @ X7 @ X8 )
= $true )
& ( ( cQ @ X9 @ X7 )
= $true ) )
| ? [X10: a] :
( ( cQ @ X10 @ X10 )
!= $true ) )
& ! [X0: a] :
? [X1: a > $o] :
( ? [X4: a] :
( ( X1 @ X4 )
= $true )
& ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) )
& ( ( X1 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a] :
? [X1: a > $o] :
( ? [X4: a] :
( ( X1 @ X4 )
= $true )
& ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) )
& ( ( X1 @ X0 )
= $true ) )
=> ( ! [X5: a,X6: a] :
( ( ( cQ @ X6 @ X5 )
= $true )
=> ( ( cQ @ X5 @ X6 )
= $true ) )
& ! [X7: a,X8: a,X9: a] :
( ( ( ( cQ @ X7 @ X8 )
= $true )
& ( ( cQ @ X9 @ X7 )
= $true ) )
=> ( ( cQ @ X9 @ X8 )
= $true ) )
& ! [X10: a] :
( ( cQ @ X10 @ X10 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( cQ @ X2 @ X3 )
<=> ( X1 @ X3 ) ) )
& ? [X4: a] : ( X1 @ X4 ) )
=> ( ! [X5: a,X6: a] :
( ( cQ @ X6 @ X5 )
=> ( cQ @ X5 @ X6 ) )
& ! [X7: a,X8: a,X9: a] :
( ( ( cQ @ X9 @ X7 )
& ( cQ @ X7 @ X8 ) )
=> ( cQ @ X9 @ X8 ) )
& ! [X10: a] : ( cQ @ X10 @ X10 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ! [X3: a] :
( ( X1 @ X3 )
=> ! [X4: a] :
( ( cQ @ X3 @ X4 )
<=> ( X1 @ X4 ) ) )
& ? [X2: a] : ( X1 @ X2 ) )
=> ( ! [X4: a,X0: a] :
( ( cQ @ X0 @ X4 )
=> ( cQ @ X4 @ X0 ) )
& ! [X4: a,X2: a,X0: a] :
( ( ( cQ @ X0 @ X4 )
& ( cQ @ X4 @ X2 ) )
=> ( cQ @ X0 @ X2 ) )
& ! [X0: a] : ( cQ @ X0 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ! [X3: a] :
( ( X1 @ X3 )
=> ! [X4: a] :
( ( cQ @ X3 @ X4 )
<=> ( X1 @ X4 ) ) )
& ? [X2: a] : ( X1 @ X2 ) )
=> ( ! [X4: a,X0: a] :
( ( cQ @ X0 @ X4 )
=> ( cQ @ X4 @ X0 ) )
& ! [X4: a,X2: a,X0: a] :
( ( ( cQ @ X0 @ X4 )
& ( cQ @ X4 @ X2 ) )
=> ( cQ @ X0 @ X2 ) )
& ! [X0: a] : ( cQ @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZOvkMvTezU/DTF2THF_8308.p',cTHM559_pme) ).
thf(f165,plain,
( ( ( sK0 @ sK3 @ sK3 )
!= $true )
| ~ spl8_1
| spl8_6 ),
inference(trivial_inequality_removal,[status(thm)],[f161]) ).
thf(f161,plain,
( ( ( sK0 @ sK3 @ sK3 )
!= $true )
| ( $false = $true )
| ~ spl8_1
| spl8_6 ),
inference(superposition,[status(thm)],[f29,f81]) ).
thf(f81,plain,
( ! [X0: a] :
( ( ( cQ @ X0 @ sK4 )
= $false )
| ( ( sK0 @ sK3 @ X0 )
!= $true ) )
| spl8_6 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ! [X0: a] :
( ( ( cQ @ X0 @ sK4 )
= $false )
| ( ( sK0 @ sK3 @ X0 )
!= $true )
| ( $true != $true ) )
| spl8_6 ),
inference(superposition,[status(thm)],[f71,f25]) ).
thf(f25,plain,
! [X3: a,X0: a,X4: a] :
( ( ( sK0 @ X0 @ X4 )
= $true )
| ( ( cQ @ X3 @ X4 )
= $false )
| ( ( sK0 @ X0 @ X3 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X3: a,X0: a,X4: a] :
( ( ( sK0 @ X0 @ X3 )
!= $true )
| ( ( cQ @ X3 @ X4 )
= ( sK0 @ X0 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f71,plain,
( ( ( sK0 @ sK3 @ sK4 )
!= $true )
| spl8_6 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( sK0 @ sK3 @ sK4 )
!= $true )
| ( $true != $true )
| spl8_6 ),
inference(superposition,[status(thm)],[f52,f62]) ).
thf(f62,plain,
! [X0: a,X1: a] :
( ( ( cQ @ X1 @ X0 )
= $true )
| ( ( sK0 @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: a,X1: a] :
( ( ( sK0 @ X0 @ X1 )
!= $true )
| ( ( cQ @ X1 @ X0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f21,f24]) ).
thf(f24,plain,
! [X3: a,X0: a,X4: a] :
( ( $false
= ( sK0 @ X0 @ X4 ) )
| ( ( sK0 @ X0 @ X3 )
!= $true )
| ( ( cQ @ X3 @ X4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f52,plain,
( ( ( cQ @ sK4 @ sK3 )
!= $true )
| spl8_6 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl8_6
<=> ( ( cQ @ sK4 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition]) ).
thf(f29,plain,
( ( ( cQ @ sK3 @ sK4 )
= $true )
| ~ spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl8_1
<=> ( ( cQ @ sK3 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f160,plain,
( spl8_2
| ~ spl8_4
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f159]) ).
thf(f159,plain,
( $false
| spl8_2
| ~ spl8_4
| ~ spl8_5 ),
inference(subsumption_resolution,[status(thm)],[f153,f21]) ).
thf(f153,plain,
( ( ( sK0 @ sK6 @ sK6 )
!= $true )
| spl8_2
| ~ spl8_4
| ~ spl8_5 ),
inference(trivial_inequality_removal,[status(thm)],[f152]) ).
thf(f152,plain,
( ( $false = $true )
| ( ( sK0 @ sK6 @ sK6 )
!= $true )
| spl8_2
| ~ spl8_4
| ~ spl8_5 ),
inference(superposition,[status(thm)],[f47,f148]) ).
thf(f148,plain,
( ! [X0: a] :
( ( ( cQ @ X0 @ sK5 )
= $false )
| ( ( sK0 @ sK6 @ X0 )
!= $true ) )
| spl8_2
| ~ spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f146]) ).
thf(f146,plain,
( ! [X0: a] :
( ( ( sK0 @ sK6 @ X0 )
!= $true )
| ( $true != $true )
| ( ( cQ @ X0 @ sK5 )
= $false ) )
| spl8_2
| ~ spl8_4 ),
inference(superposition,[status(thm)],[f144,f25]) ).
thf(f144,plain,
( ( ( sK0 @ sK6 @ sK5 )
!= $true )
| spl8_2
| ~ spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ( ( sK0 @ sK6 @ sK5 )
!= $true )
| ( $false = $true )
| spl8_2
| ~ spl8_4 ),
inference(superposition,[status(thm)],[f99,f42]) ).
thf(f42,plain,
( ( ( cQ @ sK5 @ sK7 )
= $true )
| ~ spl8_4 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl8_4
<=> ( ( cQ @ sK5 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).
thf(f99,plain,
( ! [X0: a] :
( ( $false
= ( cQ @ X0 @ sK7 ) )
| ( ( sK0 @ sK6 @ X0 )
!= $true ) )
| spl8_2 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ! [X0: a] :
( ( $false
= ( cQ @ X0 @ sK7 ) )
| ( $true != $true )
| ( ( sK0 @ sK6 @ X0 )
!= $true ) )
| spl8_2 ),
inference(superposition,[status(thm)],[f95,f25]) ).
thf(f95,plain,
( ( ( sK0 @ sK6 @ sK7 )
!= $true )
| spl8_2 ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $true != $true )
| ( ( sK0 @ sK6 @ sK7 )
!= $true )
| spl8_2 ),
inference(superposition,[status(thm)],[f85,f21]) ).
thf(f85,plain,
( ! [X0: a] :
( ( ( sK0 @ sK7 @ X0 )
!= $true )
| ( ( sK0 @ sK6 @ X0 )
!= $true ) )
| spl8_2 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ! [X0: a] :
( ( ( sK0 @ sK6 @ X0 )
!= $true )
| ( ( sK0 @ sK7 @ X0 )
!= $true )
| ( $false = $true ) )
| spl8_2 ),
inference(superposition,[status(thm)],[f62,f78]) ).
thf(f78,plain,
( ! [X0: a] :
( ( ( cQ @ X0 @ sK6 )
= $false )
| ( ( sK0 @ sK7 @ X0 )
!= $true ) )
| spl8_2 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ! [X0: a] :
( ( ( sK0 @ sK7 @ X0 )
!= $true )
| ( $true != $true )
| ( ( cQ @ X0 @ sK6 )
= $false ) )
| spl8_2 ),
inference(superposition,[status(thm)],[f69,f25]) ).
thf(f69,plain,
( ( ( sK0 @ sK7 @ sK6 )
!= $true )
| spl8_2 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( sK0 @ sK7 @ sK6 )
!= $true )
| ( $true != $true )
| spl8_2 ),
inference(superposition,[status(thm)],[f33,f62]) ).
thf(f33,plain,
( ( ( cQ @ sK6 @ sK7 )
!= $true )
| spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl8_2
<=> ( ( cQ @ sK6 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f47,plain,
( ( ( cQ @ sK6 @ sK5 )
= $true )
| ~ spl8_5 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl8_5
<=> ( ( cQ @ sK6 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition]) ).
thf(f67,plain,
spl8_3,
inference(avatar_contradiction_clause,[status(thm)],[f66]) ).
thf(f66,plain,
( $false
| spl8_3 ),
inference(subsumption_resolution,[status(thm)],[f65,f21]) ).
thf(f65,plain,
( ( ( sK0 @ sK2 @ sK2 )
!= $true )
| spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( sK0 @ sK2 @ sK2 )
!= $true )
| ( $true != $true )
| spl8_3 ),
inference(superposition,[status(thm)],[f37,f62]) ).
thf(f37,plain,
( ( ( cQ @ sK2 @ sK2 )
!= $true )
| spl8_3 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl8_3
<=> ( ( cQ @ sK2 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f55,plain,
( spl8_4
| ~ spl8_6
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f20,f35,f50,f40]) ).
thf(f20,plain,
( ( ( cQ @ sK2 @ sK2 )
!= $true )
| ( ( cQ @ sK4 @ sK3 )
!= $true )
| ( ( cQ @ sK5 @ sK7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f54,plain,
( ~ spl8_3
| ~ spl8_2
| ~ spl8_6 ),
inference(avatar_split_clause,[status(thm)],[f19,f50,f31,f35]) ).
thf(f19,plain,
( ( ( cQ @ sK2 @ sK2 )
!= $true )
| ( ( cQ @ sK6 @ sK7 )
!= $true )
| ( ( cQ @ sK4 @ sK3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f53,plain,
( ~ spl8_6
| spl8_5
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f18,f35,f45,f50]) ).
thf(f18,plain,
( ( ( cQ @ sK6 @ sK5 )
= $true )
| ( ( cQ @ sK4 @ sK3 )
!= $true )
| ( ( cQ @ sK2 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f48,plain,
( spl8_1
| ~ spl8_3
| spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f15,f45,f35,f27]) ).
thf(f15,plain,
( ( ( cQ @ sK2 @ sK2 )
!= $true )
| ( ( cQ @ sK3 @ sK4 )
= $true )
| ( ( cQ @ sK6 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f43,plain,
( spl8_4
| spl8_1
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f17,f35,f27,f40]) ).
thf(f17,plain,
( ( ( cQ @ sK5 @ sK7 )
= $true )
| ( ( cQ @ sK2 @ sK2 )
!= $true )
| ( ( cQ @ sK3 @ sK4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f38,plain,
( spl8_1
| ~ spl8_2
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f16,f35,f31,f27]) ).
thf(f16,plain,
( ( ( cQ @ sK3 @ sK4 )
= $true )
| ( ( cQ @ sK2 @ sK2 )
!= $true )
| ( ( cQ @ sK6 @ sK7 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV019^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n015.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 12:39:01 EST 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.43 thf(spec,logic,$$dhol).
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 % File : SEV019^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.43 % Domain : Set Theory (Relations)
% 0.15/0.43 % Problem : TPS problem from EQUIVALENCE-RELATIONS-THMS
% 0.15/0.43 % Version : Especial.
% 0.15/0.43 % English :
% 0.15/0.43
% 0.15/0.43 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.43 % Source : [Bro09]
% 0.15/0.43 % Names : tps_0993 [Bro09]
% 0.15/0.43
% 0.15/0.43 % Status : Theorem
% 0.15/0.43 % 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
% 0.15/0.43 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.15/0.43 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.15/0.43 % Maximal formula atoms : 7 ( 7 avg)
% 0.15/0.43 % Number of connectives : 28 ( 0 ~; 0 |; 5 &; 18 @)
% 0.15/0.43 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.15/0.43 % Maximal formula depth : 12 ( 12 avg)
% 0.15/0.43 % Number of types : 2 ( 1 usr)
% 0.15/0.43 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.15/0.43 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.15/0.43 % Number of variables : 11 ( 0 ^; 9 !; 2 ?; 11 :)
% 0.15/0.43 % SPC : TH0_THM_NEQ_NAR
% 0.15/0.43
% 0.15/0.43 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.43 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.43 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.43 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 thf(a_type,type,
% 0.15/0.43 a: $tType ).
% 0.15/0.43
% 0.15/0.43 thf(cQ,type,
% 0.15/0.43 cQ: a > a > $o ).
% 0.15/0.43
% 0.15/0.43 thf(cTHM559_pme,conjecture,
% 0.15/0.43 ( ! [Xx: a] :
% 0.15/0.43 ? [Xp: a > $o] :
% 0.15/0.43 ( ? [Xz: a] : ( Xp @ Xz )
% 0.15/0.43 & ! [Xx0: a] :
% 0.15/0.43 ( ( Xp @ Xx0 )
% 0.15/0.43 => ! [Xy: a] :
% 0.15/0.43 ( ( Xp @ Xy )
% 0.15/0.43 <=> ( cQ @ Xx0 @ Xy ) ) )
% 0.15/0.43 & ( Xp @ Xx ) )
% 0.15/0.43 => ( ! [Xx: a] : ( cQ @ Xx @ Xx )
% 0.15/0.43 & ! [Xx: a,Xy: a] :
% 0.15/0.43 ( ( cQ @ Xx @ Xy )
% 0.15/0.43 => ( cQ @ Xy @ Xx ) )
% 0.15/0.43 & ! [Xx: a,Xy: a,Xz: a] :
% 0.15/0.43 ( ( ( cQ @ Xx @ Xy )
% 0.15/0.43 & ( cQ @ Xy @ Xz ) )
% 0.15/0.43 => ( cQ @ Xx @ Xz ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 ------------------------
% 1.50/1.20 ---- Embedded in THF ---
% 1.50/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.20 %%% Generated on Tue Feb 24 12:39:02 EST 2026
% 1.50/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.20 %%% Logic specification used:
% 1.50/1.20 %%% thf(spec, logic, $$dhol).
% 1.50/1.20
% 1.50/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ZOvkMvTezU/DTF2DTF8308.p
% See solution above
% 1.50/1.20 ------------------------
% 1.50/1.21 ---- Cleaned THF ---
% 1.50/1.21 thf(a_type,type,
% 1.50/1.21 a: $tType ).
% 1.50/1.21
% 1.50/1.21 thf(cQ,type,
% 1.50/1.21 cQ: a > a > $o ).
% 1.50/1.21
% 1.50/1.21 thf(cTHM559_pme,conjecture,
% 1.50/1.21 ( ! [Xx: a] :
% 1.50/1.21 ? [Xp: a > $o] :
% 1.50/1.21 ( ? [Xz: a] : ( Xp @ Xz )
% 1.50/1.21 & ! [Xx0: a] :
% 1.50/1.21 ( ( Xp @ Xx0 )
% 1.50/1.21 => ! [Xy: a] :
% 1.50/1.21 ( ( Xp @ Xy )
% 1.50/1.21 <=> ( cQ @ Xx0 @ Xy ) ) )
% 1.50/1.21 & ( Xp @ Xx ) )
% 1.50/1.21 => ( ! [Xx: a] : ( cQ @ Xx @ Xx )
% 1.50/1.21 & ! [Xx: a,Xy: a] :
% 1.50/1.21 ( ( cQ @ Xx @ Xy )
% 1.50/1.21 => ( cQ @ Xy @ Xx ) )
% 1.50/1.21 & ! [Xx: a,Xy: a,Xz: a] :
% 1.50/1.21 ( ( ( cQ @ Xx @ Xy )
% 1.50/1.21 & ( cQ @ Xy @ Xz ) )
% 1.50/1.21 => ( cQ @ Xx @ Xz ) ) ) ) ).
% 1.50/1.21 ------------------------
% 1.50/1.23 % (8526)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_8308 for (2999ds/4Mi)
% 1.50/1.23 % (8525)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8308 for (2999ds/183Mi)
% 1.50/1.23 % (8526)Instruction limit reached!
% 1.50/1.23 % (8526)------------------------------
% 1.50/1.23 % (8526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (8526)Termination reason: Unknown
% 1.50/1.23 % (8526)Termination phase: Saturation
% 1.50/1.23
% 1.50/1.23 % (8526)Memory used [KB]: 5500
% 1.50/1.23 % (8526)Time elapsed: 0.003 s
% 1.50/1.23 % (8526)Instructions burned: 4 (million)
% 1.50/1.23 % (8526)------------------------------
% 1.50/1.23 % (8526)------------------------------
% 1.50/1.24 % (8525)First to succeed.
% 1.50/1.24 % (8527)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_8308 for (2999ds/27Mi)
% 1.50/1.24 % (8528)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8308 for (2999ds/2Mi)
% 1.50/1.24 % (8529)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_8308 for (2999ds/2Mi)
% 1.50/1.24 % (8530)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_8308 for (2999ds/275Mi)
% 1.50/1.24 % (8531)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8308 for (2999ds/18Mi)
% 1.50/1.24 % (8528)Instruction limit reached!
% 1.50/1.24 % (8528)------------------------------
% 1.50/1.24 % (8528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (8528)Termination reason: Unknown
% 1.50/1.24 % (8528)Termination phase: Preprocessing 3
% 1.50/1.24
% 1.50/1.24 % (8528)Memory used [KB]: 895
% 1.50/1.24 % (8528)Time elapsed: 0.003 s
% 1.50/1.24 % (8528)Instructions burned: 2 (million)
% 1.50/1.24 % (8528)------------------------------
% 1.50/1.24 % (8528)------------------------------
% 1.50/1.24 % (8529)Instruction limit reached!
% 1.50/1.24 % (8529)------------------------------
% 1.50/1.24 % (8529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (8529)Termination reason: Unknown
% 1.50/1.24 % (8529)Termination phase: Property scanning
% 1.50/1.24
% 1.50/1.24 % (8529)Memory used [KB]: 895
% 1.50/1.24 % (8529)Time elapsed: 0.003 s
% 1.50/1.24 % (8529)Instructions burned: 2 (million)
% 1.50/1.24 % (8529)------------------------------
% 1.50/1.24 % (8529)------------------------------
% 1.50/1.24 % (8525)Refutation found. Thanks to Tanya!
% 1.50/1.24 % SZS status Theorem for DTF2THF_8308
% 1.50/1.24 % SZS output start Proof for DTF2THF_8308
% 1.50/1.24 thf(type_def_5, type, a: $tType).
% 1.50/1.24 thf(func_def_0, type, a: $tType).
% 1.50/1.24 thf(func_def_1, type, cQ: a > a > $o).
% 1.50/1.24 thf(func_def_5, type, sK0: a > a > $o).
% 1.50/1.24 thf(func_def_6, type, sK1: a > a).
% 1.50/1.24 thf(func_def_7, type, sK2: a).
% 1.50/1.24 thf(func_def_8, type, sK3: a).
% 1.50/1.24 thf(func_def_9, type, sK4: a).
% 1.50/1.24 thf(func_def_10, type, sK5: a).
% 1.50/1.24 thf(func_def_11, type, sK6: a).
% 1.50/1.24 thf(func_def_12, type, sK7: a).
% 1.50/1.24 thf(f173,plain,(
% 1.50/1.24 $false),
% 1.50/1.24 inference(avatar_sat_refutation,[status(thm)],[f38,f43,f48,f53,f54,f55,f67,f160,f172])).
% 1.50/1.24 thf(f172,plain,(
% 1.50/1.24 ~spl8_1 | spl8_6),
% 1.50/1.24 inference(avatar_contradiction_clause,[status(thm)],[f171])).
% 1.50/1.24 thf(f171,plain,(
% 1.50/1.24 $false | (~spl8_1 | spl8_6)),
% 1.50/1.24 inference(subsumption_resolution,[status(thm)],[f165,f21])).
% 1.50/1.24 thf(f21,plain,(
% 1.50/1.24 ( ! [X0 : a] : (((sK0 @ X0 @ X0) = $true)) )),
% 1.50/1.24 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.24 thf(f14,plain,(
% 1.50/1.24 ! [X0 : a] : (((sK0 @ X0 @ (sK1 @ X0)) = $true) & ! [X3 : a] : (((sK0 @ X0 @ X3) != $true) | ! [X4 : a] : ((cQ @ X3 @ X4) = (sK0 @ X0 @ X4))) & ((sK0 @ X0 @ X0) = $true)) & (((cQ @ sK2 @ sK2) != $true) | (((cQ @ sK4 @ sK3) != $true) & ((cQ @ sK3 @ sK4) = $true)) | (((cQ @ sK5 @ sK7) = $true) & ((cQ @ sK6 @ sK7) != $true) & ((cQ @ sK6 @ sK5) = $true)))),
% 1.50/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f8,f13,f12,f11,f10,f9])).
% 1.50/1.24 thf(f9,plain,(
% 1.50/1.24 ! [X0 : a] : (? [X1 : a > $o] : (? [X2 : a] : ((X1 @ X2) = $true) & ! [X3 : a] : (((X1 @ X3) != $true) | ! [X4 : a] : ((X1 @ X4) = (cQ @ X3 @ X4))) & ((X1 @ X0) = $true)) => (? [X2 : a] : ((sK0 @ X0 @ X2) = $true) & ! [X3 : a] : (((sK0 @ X0 @ X3) != $true) | ! [X4 : a] : ((cQ @ X3 @ X4) = (sK0 @ X0 @ X4))) & ((sK0 @ X0 @ X0) = $true)))),
% 1.50/1.24 introduced(definition,[],[choice_axiom])).
% 1.50/1.24 thf(f10,plain,(
% 1.50/1.24 ! [X0 : a] : (? [X2 : a] : ((sK0 @ X0 @ X2) = $true) => ((sK0 @ X0 @ (sK1 @ X0)) = $true))),
% 1.50/1.24 introduced(definition,[],[choice_axiom])).
% 1.50/1.24 thf(f11,plain,(
% 1.50/1.24 ? [X5 : a] : ((cQ @ X5 @ X5) != $true) => ((cQ @ sK2 @ sK2) != $true)),
% 1.50/1.24 introduced(definition,[],[choice_axiom])).
% 1.50/1.24 thf(f12,plain,(
% 1.50/1.24 ? [X6 : a,X7 : a] : (((cQ @ X7 @ X6) != $true) & ((cQ @ X6 @ X7) = $true)) => (((cQ @ sK4 @ sK3) != $true) & ((cQ @ sK3 @ sK4) = $true))),
% 1.50/1.24 introduced(definition,[],[choice_axiom])).
% 1.50/1.24 thf(f13,plain,(
% 1.50/1.24 ? [X8 : a,X9 : a,X10 : a] : (((cQ @ X8 @ X10) = $true) & ((cQ @ X9 @ X10) != $true) & ((cQ @ X9 @ X8) = $true)) => (((cQ @ sK5 @ sK7) = $true) & ((cQ @ sK6 @ sK7) != $true) & ((cQ @ sK6 @ sK5) = $true))),
% 1.50/1.24 introduced(definition,[],[choice_axiom])).
% 1.50/1.24 thf(f8,plain,(
% 1.50/1.24 ! [X0 : a] : ? [X1 : a > $o] : (? [X2 : a] : ((X1 @ X2) = $true) & ! [X3 : a] : (((X1 @ X3) != $true) | ! [X4 : a] : ((X1 @ X4) = (cQ @ X3 @ X4))) & ((X1 @ X0) = $true)) & (? [X5 : a] : ((cQ @ X5 @ X5) != $true) | ? [X6 : a,X7 : a] : (((cQ @ X7 @ X6) != $true) & ((cQ @ X6 @ X7) = $true)) | ? [X8 : a,X9 : a,X10 : a] : (((cQ @ X8 @ X10) = $true) & ((cQ @ X9 @ X10) != $true) & ((cQ @ X9 @ X8) = $true)))),
% 1.50/1.24 inference(rectify,[status(thm)],[f7])).
% 1.50/1.24 thf(f7,plain,(
% 1.50/1.24 ! [X0 : a] : ? [X1 : a > $o] : (? [X4 : a] : ((X1 @ X4) = $true) & ! [X2 : a] : (((X1 @ X2) != $true) | ! [X3 : a] : ((X1 @ X3) = (cQ @ X2 @ X3))) & ((X1 @ X0) = $true)) & (? [X10 : a] : ((cQ @ X10 @ X10) != $true) | ? [X6 : a,X5 : a] : (((cQ @ X5 @ X6) != $true) & ((cQ @ X6 @ X5) = $true)) | ? [X7 : a,X9 : a,X8 : a] : (((cQ @ X7 @ X8) = $true) & ((cQ @ X9 @ X8) != $true) & ((cQ @ X9 @ X7) = $true)))),
% 1.50/1.24 inference(flattening,[status(thm)],[f6])).
% 1.50/1.24 thf(f6,plain,(
% 1.50/1.24 (? [X6 : a,X5 : a] : (((cQ @ X5 @ X6) != $true) & ((cQ @ X6 @ X5) = $true)) | ? [X7 : a,X8 : a,X9 : a] : (((cQ @ X9 @ X8) != $true) & (((cQ @ X7 @ X8) = $true) & ((cQ @ X9 @ X7) = $true))) | ? [X10 : a] : ((cQ @ X10 @ X10) != $true)) & ! [X0 : a] : ? [X1 : a > $o] : (? [X4 : a] : ((X1 @ X4) = $true) & ! [X2 : a] : (((X1 @ X2) != $true) | ! [X3 : a] : ((X1 @ X3) = (cQ @ X2 @ X3))) & ((X1 @ X0) = $true))),
% 1.50/1.24 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.24 thf(f5,plain,(
% 1.50/1.24 ~(! [X0 : a] : ? [X1 : a > $o] : (? [X4 : a] : ((X1 @ X4) = $true) & ! [X2 : a] : (((X1 @ X2) = $true) => ! [X3 : a] : ((X1 @ X3) = (cQ @ X2 @ X3))) & ((X1 @ X0) = $true)) => (! [X5 : a,X6 : a] : (((cQ @ X6 @ X5) = $true) => ((cQ @ X5 @ X6) = $true)) & ! [X7 : a,X8 : a,X9 : a] : ((((cQ @ X7 @ X8) = $true) & ((cQ @ X9 @ X7) = $true)) => ((cQ @ X9 @ X8) = $true)) & ! [X10 : a] : ((cQ @ X10 @ X10) = $true)))),
% 1.50/1.24 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.24 thf(f4,plain,(
% 1.50/1.24 ~(! [X0 : a] : ? [X1 : a > $o] : ((X1 @ X0) & ! [X2 : a] : ((X1 @ X2) => ! [X3 : a] : ((cQ @ X2 @ X3) <=> (X1 @ X3))) & ? [X4 : a] : (X1 @ X4)) => (! [X5 : a,X6 : a] : ((cQ @ X6 @ X5) => (cQ @ X5 @ X6)) & ! [X7 : a,X8 : a,X9 : a] : (((cQ @ X9 @ X7) & (cQ @ X7 @ X8)) => (cQ @ X9 @ X8)) & ! [X10 : a] : (cQ @ X10 @ X10)))),
% 1.50/1.24 inference(rectify,[status(thm)],[f2])).
% 1.50/1.24 thf(f2,negated_conjecture,(
% 1.50/1.24 ~(! [X0 : a] : ? [X1 : a > $o] : ((X1 @ X0) & ! [X3 : a] : ((X1 @ X3) => ! [X4 : a] : ((cQ @ X3 @ X4) <=> (X1 @ X4))) & ? [X2 : a] : (X1 @ X2)) => (! [X4 : a,X0 : a] : ((cQ @ X0 @ X4) => (cQ @ X4 @ X0)) & ! [X4 : a,X2 : a,X0 : a] : (((cQ @ X0 @ X4) & (cQ @ X4 @ X2)) => (cQ @ X0 @ X2)) & ! [X0 : a] : (cQ @ X0 @ X0)))),
% 1.50/1.24 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.24 thf(f1,conjecture,(
% 1.50/1.24 ! [X0 : a] : ? [X1 : a > $o] : ((X1 @ X0) & ! [X3 : a] : ((X1 @ X3) => ! [X4 : a] : ((cQ @ X3 @ X4) <=> (X1 @ X4))) & ? [X2 : a] : (X1 @ X2)) => (! [X4 : a,X0 : a] : ((cQ @ X0 @ X4) => (cQ @ X4 @ X0)) & ! [X4 : a,X2 : a,X0 : a] : (((cQ @ X0 @ X4) & (cQ @ X4 @ X2)) => (cQ @ X0 @ X2)) & ! [X0 : a] : (cQ @ X0 @ X0))),
% 1.50/1.24 file('/export/starexec/sandbox2/tmp/tmp.ZOvkMvTezU/DTF2THF_8308.p',cTHM559_pme)).
% 1.50/1.24 thf(f165,plain,(
% 1.50/1.24 ((sK0 @ sK3 @ sK3) != $true) | (~spl8_1 | spl8_6)),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f161])).
% 1.50/1.24 thf(f161,plain,(
% 1.50/1.24 ((sK0 @ sK3 @ sK3) != $true) | ($false = $true) | (~spl8_1 | spl8_6)),
% 1.50/1.24 inference(superposition,[status(thm)],[f29,f81])).
% 1.50/1.24 thf(f81,plain,(
% 1.50/1.24 ( ! [X0 : a] : (((cQ @ X0 @ sK4) = $false) | ((sK0 @ sK3 @ X0) != $true)) ) | spl8_6),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.50/1.24 thf(f77,plain,(
% 1.50/1.24 ( ! [X0 : a] : (((cQ @ X0 @ sK4) = $false) | ((sK0 @ sK3 @ X0) != $true) | ($true != $true)) ) | spl8_6),
% 1.50/1.24 inference(superposition,[status(thm)],[f71,f25])).
% 1.50/1.24 thf(f25,plain,(
% 1.50/1.24 ( ! [X3 : a,X0 : a,X4 : a] : (((sK0 @ X0 @ X4) = $true) | ((cQ @ X3 @ X4) = $false) | ((sK0 @ X0 @ X3) != $true)) )),
% 1.50/1.24 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.50/1.24 thf(f22,plain,(
% 1.50/1.24 ( ! [X3 : a,X0 : a,X4 : a] : (((sK0 @ X0 @ X3) != $true) | ((cQ @ X3 @ X4) = (sK0 @ X0 @ X4))) )),
% 1.50/1.24 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.24 thf(f71,plain,(
% 1.50/1.24 ((sK0 @ sK3 @ sK4) != $true) | spl8_6),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.50/1.24 thf(f70,plain,(
% 1.50/1.24 ((sK0 @ sK3 @ sK4) != $true) | ($true != $true) | spl8_6),
% 1.50/1.24 inference(superposition,[status(thm)],[f52,f62])).
% 1.50/1.24 thf(f62,plain,(
% 1.50/1.24 ( ! [X0 : a,X1 : a] : (((cQ @ X1 @ X0) = $true) | ((sK0 @ X0 @ X1) != $true)) )),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.50/1.24 thf(f58,plain,(
% 1.50/1.24 ( ! [X0 : a,X1 : a] : (((sK0 @ X0 @ X1) != $true) | ((cQ @ X1 @ X0) = $true) | ($false = $true)) )),
% 1.50/1.24 inference(superposition,[status(thm)],[f21,f24])).
% 1.50/1.24 thf(f24,plain,(
% 1.50/1.24 ( ! [X3 : a,X0 : a,X4 : a] : (($false = (sK0 @ X0 @ X4)) | ((sK0 @ X0 @ X3) != $true) | ((cQ @ X3 @ X4) = $true)) )),
% 1.50/1.24 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.50/1.24 thf(f52,plain,(
% 1.50/1.24 ((cQ @ sK4 @ sK3) != $true) | spl8_6),
% 1.50/1.24 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.50/1.24 thf(f50,definition,(
% 1.50/1.24 spl8_6 <=> ((cQ @ sK4 @ sK3) = $true)),
% 1.50/1.24 introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition])).
% 1.50/1.24 thf(f29,plain,(
% 1.50/1.24 ((cQ @ sK3 @ sK4) = $true) | ~spl8_1),
% 1.50/1.24 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.50/1.24 thf(f27,definition,(
% 1.50/1.24 spl8_1 <=> ((cQ @ sK3 @ sK4) = $true)),
% 1.50/1.24 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.50/1.24 thf(f160,plain,(
% 1.50/1.24 spl8_2 | ~spl8_4 | ~spl8_5),
% 1.50/1.24 inference(avatar_contradiction_clause,[status(thm)],[f159])).
% 1.50/1.24 thf(f159,plain,(
% 1.50/1.24 $false | (spl8_2 | ~spl8_4 | ~spl8_5)),
% 1.50/1.24 inference(subsumption_resolution,[status(thm)],[f153,f21])).
% 1.50/1.24 thf(f153,plain,(
% 1.50/1.24 ((sK0 @ sK6 @ sK6) != $true) | (spl8_2 | ~spl8_4 | ~spl8_5)),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f152])).
% 1.50/1.24 thf(f152,plain,(
% 1.50/1.24 ($false = $true) | ((sK0 @ sK6 @ sK6) != $true) | (spl8_2 | ~spl8_4 | ~spl8_5)),
% 1.50/1.24 inference(superposition,[status(thm)],[f47,f148])).
% 1.50/1.24 thf(f148,plain,(
% 1.50/1.24 ( ! [X0 : a] : (((cQ @ X0 @ sK5) = $false) | ((sK0 @ sK6 @ X0) != $true)) ) | (spl8_2 | ~spl8_4)),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f146])).
% 1.50/1.24 thf(f146,plain,(
% 1.50/1.24 ( ! [X0 : a] : (((sK0 @ sK6 @ X0) != $true) | ($true != $true) | ((cQ @ X0 @ sK5) = $false)) ) | (spl8_2 | ~spl8_4)),
% 1.50/1.24 inference(superposition,[status(thm)],[f144,f25])).
% 1.50/1.24 thf(f144,plain,(
% 1.50/1.24 ((sK0 @ sK6 @ sK5) != $true) | (spl8_2 | ~spl8_4)),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.50/1.24 thf(f138,plain,(
% 1.50/1.24 ((sK0 @ sK6 @ sK5) != $true) | ($false = $true) | (spl8_2 | ~spl8_4)),
% 1.50/1.24 inference(superposition,[status(thm)],[f99,f42])).
% 1.50/1.24 thf(f42,plain,(
% 1.50/1.24 ((cQ @ sK5 @ sK7) = $true) | ~spl8_4),
% 1.50/1.24 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.50/1.24 thf(f40,definition,(
% 1.50/1.24 spl8_4 <=> ((cQ @ sK5 @ sK7) = $true)),
% 1.50/1.24 introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 1.50/1.24 thf(f99,plain,(
% 1.50/1.24 ( ! [X0 : a] : (($false = (cQ @ X0 @ sK7)) | ((sK0 @ sK6 @ X0) != $true)) ) | spl8_2),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.50/1.24 thf(f97,plain,(
% 1.50/1.24 ( ! [X0 : a] : (($false = (cQ @ X0 @ sK7)) | ($true != $true) | ((sK0 @ sK6 @ X0) != $true)) ) | spl8_2),
% 1.50/1.24 inference(superposition,[status(thm)],[f95,f25])).
% 1.50/1.24 thf(f95,plain,(
% 1.50/1.24 ((sK0 @ sK6 @ sK7) != $true) | spl8_2),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.50/1.24 thf(f90,plain,(
% 1.50/1.24 ($true != $true) | ((sK0 @ sK6 @ sK7) != $true) | spl8_2),
% 1.50/1.24 inference(superposition,[status(thm)],[f85,f21])).
% 1.50/1.24 thf(f85,plain,(
% 1.50/1.24 ( ! [X0 : a] : (((sK0 @ sK7 @ X0) != $true) | ((sK0 @ sK6 @ X0) != $true)) ) | spl8_2),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.50/1.24 thf(f83,plain,(
% 1.50/1.24 ( ! [X0 : a] : (((sK0 @ sK6 @ X0) != $true) | ((sK0 @ sK7 @ X0) != $true) | ($false = $true)) ) | spl8_2),
% 1.50/1.24 inference(superposition,[status(thm)],[f62,f78])).
% 1.50/1.24 thf(f78,plain,(
% 1.50/1.24 ( ! [X0 : a] : (((cQ @ X0 @ sK6) = $false) | ((sK0 @ sK7 @ X0) != $true)) ) | spl8_2),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.50/1.24 thf(f76,plain,(
% 1.50/1.24 ( ! [X0 : a] : (((sK0 @ sK7 @ X0) != $true) | ($true != $true) | ((cQ @ X0 @ sK6) = $false)) ) | spl8_2),
% 1.50/1.24 inference(superposition,[status(thm)],[f69,f25])).
% 1.50/1.24 thf(f69,plain,(
% 1.50/1.24 ((sK0 @ sK7 @ sK6) != $true) | spl8_2),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.50/1.24 thf(f68,plain,(
% 1.50/1.24 ((sK0 @ sK7 @ sK6) != $true) | ($true != $true) | spl8_2),
% 1.50/1.24 inference(superposition,[status(thm)],[f33,f62])).
% 1.50/1.24 thf(f33,plain,(
% 1.50/1.24 ((cQ @ sK6 @ sK7) != $true) | spl8_2),
% 1.50/1.24 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.50/1.24 thf(f31,definition,(
% 1.50/1.24 spl8_2 <=> ((cQ @ sK6 @ sK7) = $true)),
% 1.50/1.24 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.50/1.24 thf(f47,plain,(
% 1.50/1.24 ((cQ @ sK6 @ sK5) = $true) | ~spl8_5),
% 1.50/1.24 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.50/1.24 thf(f45,definition,(
% 1.50/1.24 spl8_5 <=> ((cQ @ sK6 @ sK5) = $true)),
% 1.50/1.24 introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition])).
% 1.50/1.24 thf(f67,plain,(
% 1.50/1.24 spl8_3),
% 1.50/1.24 inference(avatar_contradiction_clause,[status(thm)],[f66])).
% 1.50/1.24 thf(f66,plain,(
% 1.50/1.24 $false | spl8_3),
% 1.50/1.24 inference(subsumption_resolution,[status(thm)],[f65,f21])).
% 1.50/1.24 thf(f65,plain,(
% 1.50/1.24 ((sK0 @ sK2 @ sK2) != $true) | spl8_3),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.50/1.24 thf(f64,plain,(
% 1.50/1.24 ((sK0 @ sK2 @ sK2) != $true) | ($true != $true) | spl8_3),
% 1.50/1.24 inference(superposition,[status(thm)],[f37,f62])).
% 1.50/1.24 thf(f37,plain,(
% 1.50/1.24 ((cQ @ sK2 @ sK2) != $true) | spl8_3),
% 1.50/1.24 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.50/1.24 thf(f35,definition,(
% 1.50/1.24 spl8_3 <=> ((cQ @ sK2 @ sK2) = $true)),
% 1.50/1.24 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 1.50/1.24 thf(f55,plain,(
% 1.50/1.24 spl8_4 | ~spl8_6 | ~spl8_3),
% 1.50/1.24 inference(avatar_split_clause,[status(thm)],[f20,f35,f50,f40])).
% 1.50/1.24 thf(f20,plain,(
% 1.50/1.24 ((cQ @ sK2 @ sK2) != $true) | ((cQ @ sK4 @ sK3) != $true) | ((cQ @ sK5 @ sK7) = $true)),
% 1.50/1.24 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.24 thf(f54,plain,(
% 1.50/1.24 ~spl8_3 | ~spl8_2 | ~spl8_6),
% 1.50/1.24 inference(avatar_split_clause,[status(thm)],[f19,f50,f31,f35])).
% 1.50/1.24 thf(f19,plain,(
% 1.50/1.24 ((cQ @ sK2 @ sK2) != $true) | ((cQ @ sK6 @ sK7) != $true) | ((cQ @ sK4 @ sK3) != $true)),
% 1.50/1.24 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.24 thf(f53,plain,(
% 1.50/1.24 ~spl8_6 | spl8_5 | ~spl8_3),
% 1.50/1.24 inference(avatar_split_clause,[status(thm)],[f18,f35,f45,f50])).
% 1.50/1.24 thf(f18,plain,(
% 1.50/1.24 ((cQ @ sK6 @ sK5) = $true) | ((cQ @ sK4 @ sK3) != $true) | ((cQ @ sK2 @ sK2) != $true)),
% 1.50/1.24 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.24 thf(f48,plain,(
% 1.50/1.24 spl8_1 | ~spl8_3 | spl8_5),
% 1.50/1.24 inference(avatar_split_clause,[status(thm)],[f15,f45,f35,f27])).
% 1.50/1.24 thf(f15,plain,(
% 1.50/1.24 ((cQ @ sK2 @ sK2) != $true) | ((cQ @ sK3 @ sK4) = $true) | ((cQ @ sK6 @ sK5) = $true)),
% 1.50/1.24 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.24 thf(f43,plain,(
% 1.50/1.24 spl8_4 | spl8_1 | ~spl8_3),
% 1.50/1.24 inference(avatar_split_clause,[status(thm)],[f17,f35,f27,f40])).
% 1.50/1.24 thf(f17,plain,(
% 1.50/1.24 ((cQ @ sK5 @ sK7) = $true) | ((cQ @ sK2 @ sK2) != $true) | ((cQ @ sK3 @ sK4) = $true)),
% 1.50/1.24 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.24 thf(f38,plain,(
% 1.50/1.24 spl8_1 | ~spl8_2 | ~spl8_3),
% 1.50/1.24 inference(avatar_split_clause,[status(thm)],[f16,f35,f31,f27])).
% 1.50/1.24 thf(f16,plain,(
% 1.50/1.24 ((cQ @ sK3 @ sK4) = $true) | ((cQ @ sK2 @ sK2) != $true) | ((cQ @ sK6 @ sK7) != $true)),
% 1.50/1.24 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.24 % SZS output end Proof for DTF2THF_8308
% 1.50/1.24 % (8525)------------------------------
% 1.50/1.24 % (8525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (8525)Termination reason: Refutation
% 1.50/1.24
% 1.50/1.24 % (8525)Memory used [KB]: 5628
% 1.50/1.24 % (8525)Time elapsed: 0.009 s
% 1.50/1.24 % (8525)Instructions burned: 18 (million)
% 1.50/1.24 % (8525)------------------------------
% 1.50/1.24 % (8525)------------------------------
% 1.50/1.24 % (8524)Success in time 0.019 s
%------------------------------------------------------------------------------