%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV189^5 : 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 : n016.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 09:40:30 AM UTC 2026
% Result : Theorem 1.30s 1.18s
% Output : Refutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 1 unt; 0 typ; 2 def)
% Number of atoms : 467 ( 120 equ; 0 cnn)
% Maximal formula atoms : 11 ( 11 avg)
% Number of connectives : 642 ( 50 ~; 50 |; 47 &; 359 @)
% ( 2 <=>; 92 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 193 ( 193 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 5 con; 0-2 aty)
% ( 42 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 172 ( 96 ^; 64 !; 12 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
cQ: ( b > $o ) > $o ).
thf(func_def_2,type,
cP: ( b > $o ) > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_12,type,
sK0: ( b > $o ) > $o ).
thf(func_def_13,type,
sK1: ( ( b > $o ) > $o ) > b > $o ).
thf(func_def_14,type,
sK2: ( ( b > $o ) > $o ) > b > $o ).
thf(func_def_16,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f48,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f29,f38,f47]) ).
thf(f47,plain,
( spl3_2
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f46,f26,f26]) ).
thf(f26,definition,
( spl3_2
<=> ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f46,plain,
( ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true != $true )
| ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| spl3_2 ),
inference(superposition,[status(thm)],[f14,f44]) ).
thf(f44,plain,
( ( $true
= ( cP @ ( sK2 @ sK0 ) ) )
| spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $true
= ( cP @ ( sK2 @ sK0 ) ) )
| ( $true != $true )
| spl3_2 ),
inference(superposition,[status(thm)],[f18,f40]) ).
thf(f40,plain,
( ( ( sK0 @ ( sK2 @ sK0 ) )
= $true )
| spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( sK0 @ ( sK2 @ sK0 ) )
= $true )
| ( $true != $true )
| spl3_2 ),
inference(superposition,[status(thm)],[f28,f15]) ).
thf(f15,plain,
! [X4: ( b > $o ) > $o] :
( ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X4 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true )
| ( $true
= ( X4 @ ( sK2 @ X4 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( $true
!= ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| ( $true
!= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) )
& ! [X1: b > $o] :
( ( ( ( cQ @ X1 )
= $true )
& ( ( cP @ X1 )
= $true ) )
| ( $true
!= ( sK0 @ X1 ) ) )
& ! [X2: ( b > $o ) > $o] :
( ( ( ( X2 @ ( sK1 @ X2 ) )
= $true )
& ( ( cQ @ ( sK1 @ X2 ) )
!= $true ) )
| ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X2 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) )
& ! [X4: ( b > $o ) > $o] :
( ( ( $true
= ( X4 @ ( sK2 @ X4 ) ) )
& ( ( cP @ ( sK2 @ X4 ) )
!= $true ) )
| ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X4 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: ( b > $o ) > $o] :
( ( ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
!= $true )
| ( $true
!= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) )
& ! [X1: b > $o] :
( ( ( ( cQ @ X1 )
= $true )
& ( ( cP @ X1 )
= $true ) )
| ( ( X0 @ X1 )
!= $true ) ) )
=> ( ( ( $true
!= ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| ( $true
!= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) )
& ! [X1: b > $o] :
( ( ( ( cQ @ X1 )
= $true )
& ( ( cP @ X1 )
= $true ) )
| ( $true
!= ( sK0 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X2: ( b > $o ) > $o] :
( ? [X3: b > $o] :
( ( ( X2 @ X3 )
= $true )
& ( ( cQ @ X3 )
!= $true ) )
=> ( ( ( X2 @ ( sK1 @ X2 ) )
= $true )
& ( ( cQ @ ( sK1 @ X2 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X4: ( b > $o ) > $o] :
( ? [X5: b > $o] :
( ( $true
= ( X4 @ X5 ) )
& ( ( cP @ X5 )
!= $true ) )
=> ( ( $true
= ( X4 @ ( sK2 @ X4 ) ) )
& ( ( cP @ ( sK2 @ X4 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X0: ( b > $o ) > $o] :
( ( ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
!= $true )
| ( $true
!= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) )
& ! [X1: b > $o] :
( ( ( ( cQ @ X1 )
= $true )
& ( ( cP @ X1 )
= $true ) )
| ( ( X0 @ X1 )
!= $true ) ) )
& ! [X2: ( b > $o ) > $o] :
( ? [X3: b > $o] :
( ( ( X2 @ X3 )
= $true )
& ( ( cQ @ X3 )
!= $true ) )
| ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X2 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) )
& ! [X4: ( b > $o ) > $o] :
( ? [X5: b > $o] :
( ( $true
= ( X4 @ X5 ) )
& ( ( cP @ X5 )
!= $true ) )
| ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X4 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ? [X4: ( b > $o ) > $o] :
( ( ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X4 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
!= $true )
| ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X4 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
!= $true ) )
& ! [X5: b > $o] :
( ( ( $true
= ( cQ @ X5 ) )
& ( ( cP @ X5 )
= $true ) )
| ( $true
!= ( X4 @ X5 ) ) ) )
& ! [X2: ( b > $o ) > $o] :
( ? [X3: b > $o] :
( ( ( X2 @ X3 )
= $true )
& ( ( cQ @ X3 )
!= $true ) )
| ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X2 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) )
& ! [X0: ( b > $o ) > $o] :
( ? [X1: b > $o] :
( ( ( X0 @ X1 )
= $true )
& ( ( cP @ X1 )
!= $true ) )
| ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X4: ( b > $o ) > $o] :
( ( ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X4 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
!= $true )
| ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X4 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
!= $true ) )
& ! [X5: b > $o] :
( ( ( $true
= ( cQ @ X5 ) )
& ( ( cP @ X5 )
= $true ) )
| ( $true
!= ( X4 @ X5 ) ) ) )
& ! [X0: ( b > $o ) > $o] :
( ? [X1: b > $o] :
( ( ( X0 @ X1 )
= $true )
& ( ( cP @ X1 )
!= $true ) )
| ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) )
& ! [X2: ( b > $o ) > $o] :
( ? [X3: b > $o] :
( ( ( X2 @ X3 )
= $true )
& ( ( cQ @ X3 )
!= $true ) )
| ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X2 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( ( X0 @ X1 )
= $true )
=> ( ( cP @ X1 )
= $true ) )
=> ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) )
& ! [X2: ( b > $o ) > $o] :
( ! [X3: b > $o] :
( ( ( X2 @ X3 )
= $true )
=> ( ( cQ @ X3 )
= $true ) )
=> ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X2 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) ) )
=> ! [X4: ( b > $o ) > $o] :
( ! [X5: b > $o] :
( ( $true
= ( X4 @ X5 ) )
=> ( ( $true
= ( cQ @ X5 ) )
& ( ( cP @ X5 )
= $true ) ) )
=> ( ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X4 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true )
& ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X4 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( ( X0 @ X1 )
= $true )
=> ( ( cP @ X1 )
= $true ) )
=> ( $true
= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) )
& ! [X4: ( b > $o ) > $o] :
( ! [X5: b > $o] :
( ( $true
= ( X4 @ X5 ) )
=> ( $true
= ( cQ @ X5 ) ) )
=> ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X4 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) ) )
=> ! [X8: ( b > $o ) > $o] :
( ! [X9: b > $o] :
( ( ( X8 @ X9 )
= $true )
=> ( ( $true
= ( cP @ X9 ) )
& ( ( cQ @ X9 )
= $true ) ) )
=> ( ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X8 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true )
& ( $true
= ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X8 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( cP @ X1 ) )
=> ( cP
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X0 @ X3 )
=> ( X3 @ X2 ) ) ) )
& ! [X4: ( b > $o ) > $o] :
( ! [X5: b > $o] :
( ( X4 @ X5 )
=> ( cQ @ X5 ) )
=> ( cQ
@ ^ [X6: b] :
! [X7: b > $o] :
( ( X4 @ X7 )
=> ( X7 @ X6 ) ) ) ) )
=> ! [X8: ( b > $o ) > $o] :
( ! [X9: b > $o] :
( ( X8 @ X9 )
=> ( ( cP @ X9 )
& ( cQ @ X9 ) ) )
=> ( ( cP
@ ^ [X10: b] :
! [X11: b > $o] :
( ( X8 @ X11 )
=> ( X11 @ X10 ) ) )
& ( cQ
@ ^ [X12: b] :
! [X13: b > $o] :
( ( X8 @ X13 )
=> ( X13 @ X12 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( cP @ X1 ) )
=> ( cP
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) )
& ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( cQ @ X1 ) )
=> ( cQ
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) ) )
=> ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( ( cP @ X1 )
& ( cQ @ X1 ) ) )
=> ( ( cP
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) )
& ( cQ
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( cP @ X1 ) )
=> ( cP
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) )
& ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( cQ @ X1 ) )
=> ( cQ
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) ) )
=> ! [X0: ( b > $o ) > $o] :
( ! [X1: b > $o] :
( ( X0 @ X1 )
=> ( ( cP @ X1 )
& ( cQ @ X1 ) ) )
=> ( ( cP
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) )
& ( cQ
@ ^ [X1: b] :
! [X2: b > $o] :
( ( X0 @ X2 )
=> ( X2 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5okUL5aFgV/DTF2THF_28980.p',cTHM567_pme) ).
thf(f28,plain,
( ( $true
!= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f18,plain,
! [X1: b > $o] :
( ( $true
!= ( sK0 @ X1 ) )
| ( ( cP @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f14,plain,
! [X4: ( b > $o ) > $o] :
( ( ( cP @ ( sK2 @ X4 ) )
!= $true )
| ( ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X4 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f38,plain,
( spl3_1
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f37,f22,f22]) ).
thf(f22,definition,
( spl3_1
<=> ( $true
= ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f37,plain,
( ( $true
= ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true != $true )
| ( $true
= ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| spl3_1 ),
inference(superposition,[status(thm)],[f16,f35]) ).
thf(f35,plain,
( ( $true
= ( cQ @ ( sK1 @ sK0 ) ) )
| spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $true
= ( cQ @ ( sK1 @ sK0 ) ) )
| ( $true != $true )
| spl3_1 ),
inference(superposition,[status(thm)],[f19,f31]) ).
thf(f31,plain,
( ( ( sK0 @ ( sK1 @ sK0 ) )
= $true )
| spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true != $true )
| ( ( sK0 @ ( sK1 @ sK0 ) )
= $true )
| spl3_1 ),
inference(superposition,[status(thm)],[f24,f17]) ).
thf(f17,plain,
! [X2: ( b > $o ) > $o] :
( ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X2 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true )
| ( ( X2 @ ( sK1 @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f24,plain,
( ( $true
!= ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f19,plain,
! [X1: b > $o] :
( ( $true
!= ( sK0 @ X1 ) )
| ( ( cQ @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f16,plain,
! [X2: ( b > $o ) > $o] :
( ( ( cQ @ ( sK1 @ X2 ) )
!= $true )
| ( ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( X2 @ Y1 )
=> ( Y1 @ Y0 ) ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f29,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f20,f26,f22]) ).
thf(f20,plain,
( ( $true
!= ( cP
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) )
| ( $true
!= ( cQ
@ ^ [Y0: b] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( sK0 @ Y1 )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV189^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n016.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:42:06 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.43 ---- Original DTF file ---
% 0.16/0.43 thf(spec,logic,$$dhol).
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 % File : SEV189^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.43 % Domain : Set Theory (Sets of sets)
% 0.16/0.43 % Problem : TPS problem from CLOS-SYS-THMS
% 0.16/0.43 % Version : Especial.
% 0.16/0.43 % English :
% 0.16/0.43
% 0.16/0.43 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.43 % Source : [Bro09]
% 0.16/0.43 % Names : tps_1039 [Bro09]
% 0.16/0.43
% 0.16/0.43 % Status : Theorem
% 0.16/0.43 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v4.1.0, 0.33 v4.0.0
% 0.16/0.43 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.43 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.16/0.43 % Maximal formula atoms : 8 ( 8 avg)
% 0.16/0.43 % Number of connectives : 33 ( 0 ~; 0 |; 3 &; 19 @)
% 0.16/0.43 % ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% 0.16/0.43 % Maximal formula depth : 10 ( 10 avg)
% 0.16/0.43 % Number of types : 2 ( 1 usr)
% 0.16/0.43 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.16/0.43 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.16/0.43 % Number of variables : 14 ( 4 ^; 10 !; 0 ?; 14 :)
% 0.16/0.43 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.43
% 0.16/0.43 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.43 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.43 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.43 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 thf(b_type,type,
% 0.16/0.43 b: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(cQ,type,
% 0.16/0.43 cQ: ( b > $o ) > $o ).
% 0.16/0.43
% 0.16/0.43 thf(cP,type,
% 0.16/0.43 cP: ( b > $o ) > $o ).
% 0.16/0.43
% 0.16/0.43 thf(cTHM567_pme,conjecture,
% 0.16/0.43 ( ( ! [S: ( b > $o ) > $o] :
% 0.16/0.43 ( ! [Xx: b > $o] :
% 0.16/0.43 ( ( S @ Xx )
% 0.16/0.43 => ( cP @ Xx ) )
% 0.16/0.43 => ( cP
% 0.16/0.43 @ ^ [Xx: b] :
% 0.16/0.43 ! [S0: b > $o] :
% 0.16/0.43 ( ( S @ S0 )
% 0.16/0.43 => ( S0 @ Xx ) ) ) )
% 0.16/0.43 & ! [S: ( b > $o ) > $o] :
% 0.16/0.43 ( ! [Xx: b > $o] :
% 0.16/0.43 ( ( S @ Xx )
% 0.16/0.43 => ( cQ @ Xx ) )
% 0.16/0.43 => ( cQ
% 0.16/0.43 @ ^ [Xx: b] :
% 0.16/0.43 ! [S0: b > $o] :
% 0.16/0.43 ( ( S @ S0 )
% 0.16/0.43 => ( S0 @ Xx ) ) ) ) )
% 0.16/0.43 => ! [S: ( b > $o ) > $o] :
% 0.16/0.43 ( ! [Xx: b > $o] :
% 0.16/0.43 ( ( S @ Xx )
% 0.16/0.43 => ( ( cP @ Xx )
% 0.16/0.43 & ( cQ @ Xx ) ) )
% 0.16/0.43 => ( ( cP
% 0.16/0.43 @ ^ [Xx: b] :
% 0.16/0.43 ! [S0: b > $o] :
% 0.16/0.43 ( ( S @ S0 )
% 0.16/0.43 => ( S0 @ Xx ) ) )
% 0.16/0.43 & ( cQ
% 0.16/0.43 @ ^ [Xx: b] :
% 0.16/0.43 ! [S0: b > $o] :
% 0.16/0.43 ( ( S @ S0 )
% 0.16/0.43 => ( S0 @ Xx ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 ------------------------
% 1.30/1.15 ---- Embedded in THF ---
% 1.30/1.15 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.30/1.15 %%% Generated on Tue Feb 24 12:42:06 EST 2026
% 1.30/1.15 %%% using '$$dhol' embedding, version 1.3.0.
% 1.30/1.15 %%% Logic specification used:
% 1.30/1.15 %%% thf(spec, logic, $$dhol).
% 1.30/1.15
% 1.30/1.15 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5okUL5aFgV/DTF2DTF28980.p
% See solution above
% 1.30/1.15 ------------------------
% 1.30/1.15 ---- Cleaned THF ---
% 1.30/1.16 thf(b_type,type,
% 1.30/1.16 b: $tType ).
% 1.30/1.16
% 1.30/1.16 thf(cQ,type,
% 1.30/1.16 cQ: ( b > $o ) > $o ).
% 1.30/1.16
% 1.30/1.16 thf(cP,type,
% 1.30/1.16 cP: ( b > $o ) > $o ).
% 1.30/1.16
% 1.30/1.16 thf(cTHM567_pme,conjecture,
% 1.30/1.16 ( ( ! [S: ( b > $o ) > $o] :
% 1.30/1.16 ( ! [Xx: b > $o] :
% 1.30/1.16 ( ( S @ Xx )
% 1.30/1.16 => ( cP @ Xx ) )
% 1.30/1.16 => ( cP
% 1.30/1.16 @ ^ [Xx: b] :
% 1.30/1.16 ! [S0: b > $o] :
% 1.30/1.16 ( ( S @ S0 )
% 1.30/1.16 => ( S0 @ Xx ) ) ) )
% 1.30/1.16 & ! [S: ( b > $o ) > $o] :
% 1.30/1.16 ( ! [Xx: b > $o] :
% 1.30/1.16 ( ( S @ Xx )
% 1.30/1.16 => ( cQ @ Xx ) )
% 1.30/1.16 => ( cQ
% 1.30/1.16 @ ^ [Xx: b] :
% 1.30/1.16 ! [S0: b > $o] :
% 1.30/1.16 ( ( S @ S0 )
% 1.30/1.16 => ( S0 @ Xx ) ) ) ) )
% 1.30/1.16 => ! [S: ( b > $o ) > $o] :
% 1.30/1.16 ( ! [Xx: b > $o] :
% 1.30/1.16 ( ( S @ Xx )
% 1.30/1.16 => ( ( cP @ Xx )
% 1.30/1.16 & ( cQ @ Xx ) ) )
% 1.30/1.16 => ( ( cP
% 1.30/1.16 @ ^ [Xx: b] :
% 1.30/1.16 ! [S0: b > $o] :
% 1.30/1.16 ( ( S @ S0 )
% 1.30/1.16 => ( S0 @ Xx ) ) )
% 1.30/1.16 & ( cQ
% 1.30/1.16 @ ^ [Xx: b] :
% 1.30/1.16 ! [S0: b > $o] :
% 1.30/1.16 ( ( S @ S0 )
% 1.30/1.16 => ( S0 @ Xx ) ) ) ) ) ) ).
% 1.30/1.16 ------------------------
% 1.30/1.17 % (29077)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28980 for (2999ds/183Mi)
% 1.30/1.17 % (29079)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_28980 for (2999ds/27Mi)
% 1.30/1.17 % (29078)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_28980 for (2999ds/4Mi)
% 1.30/1.17 % (29080)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28980 for (2999ds/2Mi)
% 1.30/1.17 % (29081)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_28980 for (2999ds/2Mi)
% 1.30/1.17 % (29082)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_28980 for (2999ds/275Mi)
% 1.30/1.17 % (29083)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28980 for (2999ds/18Mi)
% 1.30/1.18 % (29081)Instruction limit reached!
% 1.30/1.18 % (29081)------------------------------
% 1.30/1.18 % (29081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.18 % (29081)Termination reason: Unknown
% 1.30/1.18 % (29081)Termination phase: Property scanning
% 1.30/1.18
% 1.30/1.18 % (29081)Memory used [KB]: 895
% 1.30/1.18 % (29081)Time elapsed: 0.002 s
% 1.30/1.18 % (29081)Instructions burned: 2 (million)
% 1.30/1.18 % (29081)------------------------------
% 1.30/1.18 % (29081)------------------------------
% 1.30/1.18 % (29080)Instruction limit reached!
% 1.30/1.18 % (29080)------------------------------
% 1.30/1.18 % (29080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.18 % (29080)Termination reason: Unknown
% 1.30/1.18 % (29080)Termination phase: Saturation
% 1.30/1.18
% 1.30/1.18 % (29080)Memory used [KB]: 5500
% 1.30/1.18 % (29080)Time elapsed: 0.003 s
% 1.30/1.18 % (29080)Instructions burned: 3 (million)
% 1.30/1.18 % (29080)------------------------------
% 1.30/1.18 % (29080)------------------------------
% 1.30/1.18 % (29078)Instruction limit reached!
% 1.30/1.18 % (29078)------------------------------
% 1.30/1.18 % (29078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.18 % (29078)Termination reason: Unknown
% 1.30/1.18 % (29078)Termination phase: Saturation
% 1.30/1.18
% 1.30/1.18 % (29078)Memory used [KB]: 5500
% 1.30/1.18 % (29078)Time elapsed: 0.004 s
% 1.30/1.18 % (29078)Instructions burned: 4 (million)
% 1.30/1.18 % (29078)------------------------------
% 1.30/1.18 % (29078)------------------------------
% 1.30/1.18 % (29079)First to succeed.
% 1.30/1.18 % (29082)Also succeeded, but the first one will report.
% 1.30/1.18 % (29079)Refutation found. Thanks to Tanya!
% 1.30/1.18 % SZS status Theorem for DTF2THF_28980
% 1.30/1.18 % SZS output start Proof for DTF2THF_28980
% 1.30/1.18 thf(type_def_5, type, b: $tType).
% 1.30/1.18 thf(func_def_0, type, b: $tType).
% 1.30/1.18 thf(func_def_1, type, cQ: (b > $o) > $o).
% 1.30/1.18 thf(func_def_2, type, cP: (b > $o) > $o).
% 1.30/1.18 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.30/1.18 thf(func_def_12, type, sK0: (b > $o) > $o).
% 1.30/1.18 thf(func_def_13, type, sK1: ((b > $o) > $o) > b > $o).
% 1.30/1.18 thf(func_def_14, type, sK2: ((b > $o) > $o) > b > $o).
% 1.30/1.18 thf(func_def_16, type, ph4: !>[X0: $tType]:(X0)).
% 1.30/1.18 thf(f48,plain,(
% 1.30/1.18 $false),
% 1.30/1.18 inference(avatar_sat_refutation,[status(thm)],[f29,f38,f47])).
% 1.30/1.18 thf(f47,plain,(
% 1.30/1.18 spl3_2 | spl3_2),
% 1.30/1.18 inference(avatar_split_clause,[status(thm)],[f46,f26,f26])).
% 1.30/1.18 thf(f26,definition,(
% 1.30/1.18 spl3_2 <=> ($true = (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0)))))))),
% 1.30/1.18 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.30/1.18 thf(f46,plain,(
% 1.30/1.18 ($true = (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))) | spl3_2),
% 1.30/1.18 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.30/1.18 thf(f45,plain,(
% 1.30/1.18 ($true != $true) | ($true = (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))) | spl3_2),
% 1.30/1.18 inference(superposition,[status(thm)],[f14,f44])).
% 1.30/1.18 thf(f44,plain,(
% 1.30/1.18 ($true = (cP @ (sK2 @ sK0))) | spl3_2),
% 1.30/1.18 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.30/1.18 thf(f42,plain,(
% 1.30/1.18 ($true = (cP @ (sK2 @ sK0))) | ($true != $true) | spl3_2),
% 1.30/1.18 inference(superposition,[status(thm)],[f18,f40])).
% 1.30/1.18 thf(f40,plain,(
% 1.30/1.18 ((sK0 @ (sK2 @ sK0)) = $true) | spl3_2),
% 1.30/1.18 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.30/1.18 thf(f39,plain,(
% 1.30/1.18 ((sK0 @ (sK2 @ sK0)) = $true) | ($true != $true) | spl3_2),
% 1.30/1.18 inference(superposition,[status(thm)],[f28,f15])).
% 1.30/1.18 thf(f15,plain,(
% 1.30/1.18 ( ! [X4 : (b > $o) > $o] : (((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))) = $true) | ($true = (X4 @ (sK2 @ X4)))) )),
% 1.30/1.18 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.18 thf(f13,plain,(
% 1.30/1.18 ((($true != (cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))) | ($true != (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0)))))))) & ! [X1 : b > $o] : ((((cQ @ X1) = $true) & ((cP @ X1) = $true)) | ($true != (sK0 @ X1)))) & ! [X2 : (b > $o) > $o] : ((((X2 @ (sK1 @ X2)) = $true) & ((cQ @ (sK1 @ X2)) != $true)) | ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))) = $true)) & ! [X4 : (b > $o) > $o] : ((($true = (X4 @ (sK2 @ X4))) & ((cP @ (sK2 @ X4)) != $true)) | ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))) = $true))),
% 1.30/1.18 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10])).
% 1.30/1.18 thf(f10,plain,(
% 1.30/1.18 ? [X0 : (b > $o) > $o] : ((((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))) != $true) | ($true != (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) & ! [X1 : b > $o] : ((((cQ @ X1) = $true) & ((cP @ X1) = $true)) | ((X0 @ X1) != $true))) => ((($true != (cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))) | ($true != (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0)))))))) & ! [X1 : b > $o] : ((((cQ @ X1) = $true) & ((cP @ X1) = $true)) | ($true != (sK0 @ X1))))),
% 1.30/1.18 introduced(definition,[],[choice_axiom])).
% 1.30/1.18 thf(f11,plain,(
% 1.30/1.18 ! [X2 : (b > $o) > $o] : (? [X3 : b > $o] : (((X2 @ X3) = $true) & ((cQ @ X3) != $true)) => (((X2 @ (sK1 @ X2)) = $true) & ((cQ @ (sK1 @ X2)) != $true)))),
% 1.30/1.18 introduced(definition,[],[choice_axiom])).
% 1.30/1.18 thf(f12,plain,(
% 1.30/1.18 ! [X4 : (b > $o) > $o] : (? [X5 : b > $o] : (($true = (X4 @ X5)) & ((cP @ X5) != $true)) => (($true = (X4 @ (sK2 @ X4))) & ((cP @ (sK2 @ X4)) != $true)))),
% 1.30/1.18 introduced(definition,[],[choice_axiom])).
% 1.30/1.18 thf(f9,plain,(
% 1.30/1.18 ? [X0 : (b > $o) > $o] : ((((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))) != $true) | ($true != (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) & ! [X1 : b > $o] : ((((cQ @ X1) = $true) & ((cP @ X1) = $true)) | ((X0 @ X1) != $true))) & ! [X2 : (b > $o) > $o] : (? [X3 : b > $o] : (((X2 @ X3) = $true) & ((cQ @ X3) != $true)) | ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))) = $true)) & ! [X4 : (b > $o) > $o] : (? [X5 : b > $o] : (($true = (X4 @ X5)) & ((cP @ X5) != $true)) | ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))) = $true))),
% 1.30/1.18 inference(rectify,[status(thm)],[f8])).
% 1.30/1.18 thf(f8,plain,(
% 1.30/1.18 ? [X4 : (b > $o) > $o] : ((((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))) != $true) | ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))) != $true)) & ! [X5 : b > $o] : ((($true = (cQ @ X5)) & ((cP @ X5) = $true)) | ($true != (X4 @ X5)))) & ! [X2 : (b > $o) > $o] : (? [X3 : b > $o] : (((X2 @ X3) = $true) & ((cQ @ X3) != $true)) | ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))) = $true)) & ! [X0 : (b > $o) > $o] : (? [X1 : b > $o] : (((X0 @ X1) = $true) & ((cP @ X1) != $true)) | ($true = (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0))))))))),
% 1.30/1.18 inference(flattening,[status(thm)],[f7])).
% 1.30/1.18 thf(f7,plain,(
% 1.30/1.18 ? [X4 : (b > $o) > $o] : ((((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))) != $true) | ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))) != $true)) & ! [X5 : b > $o] : ((($true = (cQ @ X5)) & ((cP @ X5) = $true)) | ($true != (X4 @ X5)))) & (! [X0 : (b > $o) > $o] : (? [X1 : b > $o] : (((X0 @ X1) = $true) & ((cP @ X1) != $true)) | ($true = (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) & ! [X2 : (b > $o) > $o] : (? [X3 : b > $o] : (((X2 @ X3) = $true) & ((cQ @ X3) != $true)) | ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))) = $true)))),
% 1.30/1.18 inference(ennf_transformation,[status(thm)],[f6])).
% 1.30/1.18 thf(f6,plain,(
% 1.30/1.18 ~((! [X0 : (b > $o) > $o] : (! [X1 : b > $o] : (((X0 @ X1) = $true) => ((cP @ X1) = $true)) => ($true = (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) & ! [X2 : (b > $o) > $o] : (! [X3 : b > $o] : (((X2 @ X3) = $true) => ((cQ @ X3) = $true)) => ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))) = $true))) => ! [X4 : (b > $o) > $o] : (! [X5 : b > $o] : (($true = (X4 @ X5)) => (($true = (cQ @ X5)) & ((cP @ X5) = $true))) => (((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))) = $true) & ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))) = $true))))),
% 1.30/1.18 inference(rectify,[status(thm)],[f5])).
% 1.30/1.18 thf(f5,plain,(
% 1.30/1.18 ~((! [X0 : (b > $o) > $o] : (! [X1 : b > $o] : (((X0 @ X1) = $true) => ((cP @ X1) = $true)) => ($true = (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) & ! [X4 : (b > $o) > $o] : (! [X5 : b > $o] : (($true = (X4 @ X5)) => ($true = (cQ @ X5))) => ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))) = $true))) => ! [X8 : (b > $o) > $o] : (! [X9 : b > $o] : (((X8 @ X9) = $true) => (($true = (cP @ X9)) & ((cQ @ X9) = $true))) => (((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X8 @ Y1) => (Y1 @ Y0)))))) = $true) & ($true = (cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X8 @ Y1) => (Y1 @ Y0))))))))))),
% 1.30/1.18 inference(fool_elimination,[status(thm)],[f4])).
% 1.30/1.18 thf(f4,plain,(
% 1.30/1.18 ~((! [X0 : (b > $o) > $o] : (! [X1 : b > $o] : ((X0 @ X1) => (cP @ X1)) => (cP @ (^[X2 : b] : (! [X3 : b > $o] : ((X0 @ X3) => (X3 @ X2)))))) & ! [X4 : (b > $o) > $o] : (! [X5 : b > $o] : ((X4 @ X5) => (cQ @ X5)) => (cQ @ (^[X6 : b] : (! [X7 : b > $o] : ((X4 @ X7) => (X7 @ X6))))))) => ! [X8 : (b > $o) > $o] : (! [X9 : b > $o] : ((X8 @ X9) => ((cP @ X9) & (cQ @ X9))) => ((cP @ (^[X10 : b] : (! [X11 : b > $o] : ((X8 @ X11) => (X11 @ X10))))) & (cQ @ (^[X12 : b] : (! [X13 : b > $o] : ((X8 @ X13) => (X13 @ X12))))))))),
% 1.30/1.18 inference(rectify,[status(thm)],[f2])).
% 1.30/1.18 thf(f2,negated_conjecture,(
% 1.30/1.18 ~((! [X0 : (b > $o) > $o] : (! [X1 : b > $o] : ((X0 @ X1) => (cP @ X1)) => (cP @ (^[X1 : b] : (! [X2 : b > $o] : ((X0 @ X2) => (X2 @ X1)))))) & ! [X0 : (b > $o) > $o] : (! [X1 : b > $o] : ((X0 @ X1) => (cQ @ X1)) => (cQ @ (^[X1 : b] : (! [X2 : b > $o] : ((X0 @ X2) => (X2 @ X1))))))) => ! [X0 : (b > $o) > $o] : (! [X1 : b > $o] : ((X0 @ X1) => ((cP @ X1) & (cQ @ X1))) => ((cP @ (^[X1 : b] : (! [X2 : b > $o] : ((X0 @ X2) => (X2 @ X1))))) & (cQ @ (^[X1 : b] : (! [X2 : b > $o] : ((X0 @ X2) => (X2 @ X1))))))))),
% 1.30/1.18 inference(negated_conjecture,[status(cth)],[f1])).
% 1.30/1.18 thf(f1,conjecture,(
% 1.30/1.18 (! [X0 : (b > $o) > $o] : (! [X1 : b > $o] : ((X0 @ X1) => (cP @ X1)) => (cP @ (^[X1 : b] : (! [X2 : b > $o] : ((X0 @ X2) => (X2 @ X1)))))) & ! [X0 : (b > $o) > $o] : (! [X1 : b > $o] : ((X0 @ X1) => (cQ @ X1)) => (cQ @ (^[X1 : b] : (! [X2 : b > $o] : ((X0 @ X2) => (X2 @ X1))))))) => ! [X0 : (b > $o) > $o] : (! [X1 : b > $o] : ((X0 @ X1) => ((cP @ X1) & (cQ @ X1))) => ((cP @ (^[X1 : b] : (! [X2 : b > $o] : ((X0 @ X2) => (X2 @ X1))))) & (cQ @ (^[X1 : b] : (! [X2 : b > $o] : ((X0 @ X2) => (X2 @ X1)))))))),
% 1.30/1.18 file('/export/starexec/sandbox/tmp/tmp.5okUL5aFgV/DTF2THF_28980.p',cTHM567_pme)).
% 1.30/1.18 thf(f28,plain,(
% 1.30/1.18 ($true != (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))) | spl3_2),
% 1.30/1.18 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.30/1.18 thf(f18,plain,(
% 1.30/1.18 ( ! [X1 : b > $o] : (($true != (sK0 @ X1)) | ((cP @ X1) = $true)) )),
% 1.30/1.18 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.18 thf(f14,plain,(
% 1.30/1.18 ( ! [X4 : (b > $o) > $o] : (((cP @ (sK2 @ X4)) != $true) | ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))) = $true)) )),
% 1.30/1.18 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.18 thf(f38,plain,(
% 1.30/1.18 spl3_1 | spl3_1),
% 1.30/1.18 inference(avatar_split_clause,[status(thm)],[f37,f22,f22])).
% 1.30/1.18 thf(f22,definition,(
% 1.30/1.18 spl3_1 <=> ($true = (cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0)))))))),
% 1.30/1.18 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.30/1.18 thf(f37,plain,(
% 1.30/1.18 ($true = (cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))) | spl3_1),
% 1.30/1.18 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.30/1.18 thf(f36,plain,(
% 1.30/1.18 ($true != $true) | ($true = (cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))) | spl3_1),
% 1.30/1.18 inference(superposition,[status(thm)],[f16,f35])).
% 1.30/1.18 thf(f35,plain,(
% 1.30/1.18 ($true = (cQ @ (sK1 @ sK0))) | spl3_1),
% 1.30/1.18 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.30/1.18 thf(f32,plain,(
% 1.30/1.18 ($true = (cQ @ (sK1 @ sK0))) | ($true != $true) | spl3_1),
% 1.30/1.18 inference(superposition,[status(thm)],[f19,f31])).
% 1.30/1.18 thf(f31,plain,(
% 1.30/1.18 ((sK0 @ (sK1 @ sK0)) = $true) | spl3_1),
% 1.30/1.18 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.30/1.18 thf(f30,plain,(
% 1.30/1.18 ($true != $true) | ((sK0 @ (sK1 @ sK0)) = $true) | spl3_1),
% 1.30/1.18 inference(superposition,[status(thm)],[f24,f17])).
% 1.30/1.18 thf(f17,plain,(
% 1.30/1.18 ( ! [X2 : (b > $o) > $o] : (((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))) = $true) | ((X2 @ (sK1 @ X2)) = $true)) )),
% 1.30/1.18 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.18 thf(f24,plain,(
% 1.30/1.18 ($true != (cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))) | spl3_1),
% 1.30/1.18 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.30/1.18 thf(f19,plain,(
% 1.30/1.18 ( ! [X1 : b > $o] : (($true != (sK0 @ X1)) | ((cQ @ X1) = $true)) )),
% 1.30/1.18 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.18 thf(f16,plain,(
% 1.30/1.18 ( ! [X2 : (b > $o) > $o] : (((cQ @ (sK1 @ X2)) != $true) | ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))) = $true)) )),
% 1.30/1.18 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.18 thf(f29,plain,(
% 1.30/1.18 ~spl3_1 | ~spl3_2),
% 1.30/1.18 inference(avatar_split_clause,[status(thm)],[f20,f26,f22])).
% 1.30/1.18 thf(f20,plain,(
% 1.30/1.18 ($true != (cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))) | ($true != (cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0)))))))),
% 1.30/1.18 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.18 % SZS output end Proof for DTF2THF_28980
% 1.30/1.18 % (29079)------------------------------
% 1.30/1.18 % (29079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.18 % (29079)Termination reason: Refutation
% 1.30/1.18
% 1.30/1.18 % (29079)Memory used [KB]: 5500
% 1.30/1.18 % (29079)Time elapsed: 0.007 s
% 1.30/1.18 % (29079)Instructions burned: 6 (million)
% 1.30/1.18 % (29079)------------------------------
% 1.30/1.18 % (29079)------------------------------
% 1.30/1.18 % (29076)Success in time 0.021 s
%------------------------------------------------------------------------------