%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV259^5 : 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:41 AM UTC 2026
% Result : Theorem 1.32s 1.17s
% Output : Refutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 401 ( 192 equ; 0 cnn)
% Maximal formula atoms : 36 ( 21 avg)
% Number of connectives : 602 ( 109 ~; 64 |; 117 &; 250 @)
% ( 0 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 177 ( 177 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 4 con; 0-2 aty)
% ( 0 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 234 ( 67 ^; 134 !; 33 ?; 234 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_10,type,
sK0: ( b > $o ) > $o ).
thf(func_def_11,type,
sK1: b ).
thf(func_def_12,type,
sK2: b > $o ).
thf(func_def_13,type,
sK3: b > $o ).
thf(func_def_14,type,
sK4: ( ( b > $o ) > $o ) > b > $o ).
thf(func_def_16,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f33,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f32,f17]) ).
thf(f17,plain,
( $true
= ( sK2 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: b > $o,X2: b > $o,X3: b > $o] :
( ( $true
= ( sK0 @ X1 ) )
| ( $true
!= ( sK0 @ X3 ) )
| ( $true
!= ( sK0 @ X2 ) )
| ( ( ^ [Y0: b] :
( ( X2 @ Y0 )
& ( X3 @ Y0 ) ) )
!= X1 ) )
& ! [X4: b > $o] :
( ( $true
= ( sK0 @ X4 ) )
| ( ( ^ [Y0: b] : ~ $false )
!= X4 ) )
& ! [X5: b > $o] :
( ( ( ^ [Y0: b] : $false )
!= X5 )
| ( $true
= ( sK0 @ X5 ) ) )
& ! [X9: b > $o] :
( ( ( ^ [Y0: b] :
~ ( sK3 @ Y0 ) )
!= X9 )
| ( $true
= ( sK0 @ X9 ) ) )
& ! [X10: b] :
( ( $true
= ( sK3 @ X10 ) )
| ( $true
!= ( sK2 @ X10 ) ) )
& ( $true
!= ( sK3 @ sK1 ) )
& ( $true
= ( sK2 @ sK1 ) )
& ! [X11: ( b > $o ) > $o,X12: b > $o] :
( ( $true
= ( sK0 @ X12 ) )
| ( ( $true
= ( X11 @ ( sK4 @ X11 ) ) )
& ( $true
!= ( sK0 @ ( sK4 @ X11 ) ) ) )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X11 @ Y1 ) ) ) )
!= X12 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: ( b > $o ) > $o] :
( ! [X1: b > $o,X2: b > $o,X3: b > $o] :
( ( ( X0 @ X1 )
= $true )
| ( $true
!= ( X0 @ X3 ) )
| ( ( X0 @ X2 )
!= $true )
| ( ( ^ [Y0: b] :
( ( X2 @ Y0 )
& ( X3 @ Y0 ) ) )
!= X1 ) )
& ! [X4: b > $o] :
( ( ( X0 @ X4 )
= $true )
| ( ( ^ [Y0: b] : ~ $false )
!= X4 ) )
& ! [X5: b > $o] :
( ( ( ^ [Y0: b] : $false )
!= X5 )
| ( ( X0 @ X5 )
= $true ) )
& ? [X6: b,X7: b > $o] :
( ? [X8: b > $o] :
( ! [X9: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X8 @ Y0 ) )
!= X9 )
| ( $true
= ( X0 @ X9 ) ) )
& ! [X10: b] :
( ( $true
= ( X8 @ X10 ) )
| ( $true
!= ( X7 @ X10 ) ) )
& ( $true
!= ( X8 @ X6 ) ) )
& ( ( X7 @ X6 )
= $true ) )
& ! [X11: ( b > $o ) > $o,X12: b > $o] :
( ( ( X0 @ X12 )
= $true )
| ? [X13: b > $o] :
( ( $true
= ( X11 @ X13 ) )
& ( $true
!= ( X0 @ X13 ) ) )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X11 @ Y1 ) ) ) )
!= X12 ) ) )
=> ( ! [X3: b > $o,X2: b > $o,X1: b > $o] :
( ( $true
= ( sK0 @ X1 ) )
| ( $true
!= ( sK0 @ X3 ) )
| ( $true
!= ( sK0 @ X2 ) )
| ( ( ^ [Y0: b] :
( ( X2 @ Y0 )
& ( X3 @ Y0 ) ) )
!= X1 ) )
& ! [X4: b > $o] :
( ( $true
= ( sK0 @ X4 ) )
| ( ( ^ [Y0: b] : ~ $false )
!= X4 ) )
& ! [X5: b > $o] :
( ( ( ^ [Y0: b] : $false )
!= X5 )
| ( $true
= ( sK0 @ X5 ) ) )
& ? [X7: b > $o,X6: b] :
( ? [X8: b > $o] :
( ! [X9: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X8 @ Y0 ) )
!= X9 )
| ( $true
= ( sK0 @ X9 ) ) )
& ! [X10: b] :
( ( $true
= ( X8 @ X10 ) )
| ( $true
!= ( X7 @ X10 ) ) )
& ( $true
!= ( X8 @ X6 ) ) )
& ( ( X7 @ X6 )
= $true ) )
& ! [X12: b > $o,X11: ( b > $o ) > $o] :
( ( $true
= ( sK0 @ X12 ) )
| ? [X13: b > $o] :
( ( $true
= ( X11 @ X13 ) )
& ( $true
!= ( sK0 @ X13 ) ) )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X11 @ Y1 ) ) ) )
!= X12 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X7: b > $o,X6: b] :
( ? [X8: b > $o] :
( ! [X9: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X8 @ Y0 ) )
!= X9 )
| ( $true
= ( sK0 @ X9 ) ) )
& ! [X10: b] :
( ( $true
= ( X8 @ X10 ) )
| ( $true
!= ( X7 @ X10 ) ) )
& ( $true
!= ( X8 @ X6 ) ) )
& ( ( X7 @ X6 )
= $true ) )
=> ( ? [X8: b > $o] :
( ! [X9: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X8 @ Y0 ) )
!= X9 )
| ( $true
= ( sK0 @ X9 ) ) )
& ! [X10: b] :
( ( $true
= ( X8 @ X10 ) )
| ( $true
!= ( sK2 @ X10 ) ) )
& ( $true
!= ( X8 @ sK1 ) ) )
& ( $true
= ( sK2 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X8: b > $o] :
( ! [X9: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X8 @ Y0 ) )
!= X9 )
| ( $true
= ( sK0 @ X9 ) ) )
& ! [X10: b] :
( ( $true
= ( X8 @ X10 ) )
| ( $true
!= ( sK2 @ X10 ) ) )
& ( $true
!= ( X8 @ sK1 ) ) )
=> ( ! [X9: b > $o] :
( ( ( ^ [Y0: b] :
~ ( sK3 @ Y0 ) )
!= X9 )
| ( $true
= ( sK0 @ X9 ) ) )
& ! [X10: b] :
( ( $true
= ( sK3 @ X10 ) )
| ( $true
!= ( sK2 @ X10 ) ) )
& ( $true
!= ( sK3 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X11: ( b > $o ) > $o] :
( ? [X13: b > $o] :
( ( $true
= ( X11 @ X13 ) )
& ( $true
!= ( sK0 @ X13 ) ) )
=> ( ( $true
= ( X11 @ ( sK4 @ X11 ) ) )
& ( $true
!= ( sK0 @ ( sK4 @ X11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: ( b > $o ) > $o] :
( ! [X1: b > $o,X2: b > $o,X3: b > $o] :
( ( ( X0 @ X1 )
= $true )
| ( $true
!= ( X0 @ X3 ) )
| ( ( X0 @ X2 )
!= $true )
| ( ( ^ [Y0: b] :
( ( X2 @ Y0 )
& ( X3 @ Y0 ) ) )
!= X1 ) )
& ! [X4: b > $o] :
( ( ( X0 @ X4 )
= $true )
| ( ( ^ [Y0: b] : ~ $false )
!= X4 ) )
& ! [X5: b > $o] :
( ( ( ^ [Y0: b] : $false )
!= X5 )
| ( ( X0 @ X5 )
= $true ) )
& ? [X6: b,X7: b > $o] :
( ? [X8: b > $o] :
( ! [X9: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X8 @ Y0 ) )
!= X9 )
| ( $true
= ( X0 @ X9 ) ) )
& ! [X10: b] :
( ( $true
= ( X8 @ X10 ) )
| ( $true
!= ( X7 @ X10 ) ) )
& ( $true
!= ( X8 @ X6 ) ) )
& ( ( X7 @ X6 )
= $true ) )
& ! [X11: ( b > $o ) > $o,X12: b > $o] :
( ( ( X0 @ X12 )
= $true )
| ? [X13: b > $o] :
( ( $true
= ( X11 @ X13 ) )
& ( $true
!= ( X0 @ X13 ) ) )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X11 @ Y1 ) ) ) )
!= X12 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: ( b > $o ) > $o] :
( ! [X6: b > $o,X7: b > $o,X8: b > $o] :
( ( ( X0 @ X6 )
= $true )
| ( $true
!= ( X0 @ X8 ) )
| ( $true
!= ( X0 @ X7 ) )
| ( ( ^ [Y0: b] :
( ( X7 @ Y0 )
& ( X8 @ Y0 ) ) )
!= X6 ) )
& ! [X1: b > $o] :
( ( ( X0 @ X1 )
= $true )
| ( ( ^ [Y0: b] : ~ $false )
!= X1 ) )
& ! [X5: b > $o] :
( ( ( ^ [Y0: b] : $false )
!= X5 )
| ( ( X0 @ X5 )
= $true ) )
& ? [X9: b,X10: b > $o] :
( ? [X11: b > $o] :
( ! [X12: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X11 @ Y0 ) )
!= X12 )
| ( ( X0 @ X12 )
= $true ) )
& ! [X13: b] :
( ( $true
= ( X11 @ X13 ) )
| ( $true
!= ( X10 @ X13 ) ) )
& ( $true
!= ( X11 @ X9 ) ) )
& ( $true
= ( X10 @ X9 ) ) )
& ! [X2: ( b > $o ) > $o,X3: b > $o] :
( ( $true
= ( X0 @ X3 ) )
| ? [X4: b > $o] :
( ( $true
= ( X2 @ X4 ) )
& ( ( X0 @ X4 )
!= $true ) )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X2 @ Y1 ) ) ) )
!= X3 ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( b > $o ) > $o] :
( ? [X9: b,X10: b > $o] :
( ? [X11: b > $o] :
( ( $true
!= ( X11 @ X9 ) )
& ! [X13: b] :
( ( $true
= ( X11 @ X13 ) )
| ( $true
!= ( X10 @ X13 ) ) )
& ! [X12: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X11 @ Y0 ) )
!= X12 )
| ( ( X0 @ X12 )
= $true ) ) )
& ( $true
= ( X10 @ X9 ) ) )
& ! [X6: b > $o,X7: b > $o,X8: b > $o] :
( ( ( X0 @ X6 )
= $true )
| ( $true
!= ( X0 @ X8 ) )
| ( ( ^ [Y0: b] :
( ( X7 @ Y0 )
& ( X8 @ Y0 ) ) )
!= X6 )
| ( $true
!= ( X0 @ X7 ) ) )
& ! [X2: ( b > $o ) > $o,X3: b > $o] :
( ( $true
= ( X0 @ X3 ) )
| ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X2 @ Y1 ) ) ) )
!= X3 )
| ? [X4: b > $o] :
( ( $true
= ( X2 @ X4 ) )
& ( ( X0 @ X4 )
!= $true ) ) )
& ! [X5: b > $o] :
( ( ( ^ [Y0: b] : $false )
!= X5 )
| ( ( X0 @ X5 )
= $true ) )
& ! [X1: b > $o] :
( ( ( X0 @ X1 )
= $true )
| ( ( ^ [Y0: b] : ~ $false )
!= X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: ( b > $o ) > $o] :
( ( ! [X6: b > $o,X7: b > $o,X8: b > $o] :
( ( ( $true
= ( X0 @ X8 ) )
& ( ( ^ [Y0: b] :
( ( X7 @ Y0 )
& ( X8 @ Y0 ) ) )
= X6 )
& ( $true
= ( X0 @ X7 ) ) )
=> ( ( X0 @ X6 )
= $true ) )
& ! [X2: ( b > $o ) > $o,X3: b > $o] :
( ( ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X2 @ Y1 ) ) ) )
= X3 )
& ! [X4: b > $o] :
( ( $true
= ( X2 @ X4 ) )
=> ( ( X0 @ X4 )
= $true ) ) )
=> ( $true
= ( X0 @ X3 ) ) )
& ! [X5: b > $o] :
( ( ( ^ [Y0: b] : $false )
= X5 )
=> ( ( X0 @ X5 )
= $true ) )
& ! [X1: b > $o] :
( ( ( ^ [Y0: b] : ~ $false )
= X1 )
=> ( ( X0 @ X1 )
= $true ) ) )
=> ! [X9: b,X10: b > $o] :
( ( $true
= ( X10 @ X9 ) )
=> ! [X11: b > $o] :
( ( ! [X13: b] :
( ( $true
= ( X10 @ X13 ) )
=> ( $true
= ( X11 @ X13 ) ) )
& ! [X12: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X11 @ Y0 ) )
= X12 )
=> ( ( X0 @ X12 )
= $true ) ) )
=> ( $true
= ( X11 @ X9 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( b > $o ) > $o] :
( ( ! [X1: b > $o] :
( ( ( ^ [Y0: b] : ~ $false )
= X1 )
=> ( ( X0 @ X1 )
= $true ) )
& ! [X3: ( b > $o ) > $o,X4: b > $o] :
( ( ! [X5: b > $o] :
( ( $true
= ( X3 @ X5 ) )
=> ( ( X0 @ X5 )
= $true ) )
& ( ( ^ [Y0: b] :
( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1 @ Y0 )
& ( X3 @ Y1 ) ) ) )
= X4 ) )
=> ( ( X0 @ X4 )
= $true ) )
& ! [X8: b > $o] :
( ( ( ^ [Y0: b] : $false )
= X8 )
=> ( $true
= ( X0 @ X8 ) ) )
& ! [X10: b > $o,X11: b > $o,X12: b > $o] :
( ( ( $true
= ( X0 @ X11 ) )
& ( ( X0 @ X12 )
= $true )
& ( ( ^ [Y0: b] :
( ( X11 @ Y0 )
& ( X12 @ Y0 ) ) )
= X10 ) )
=> ( $true
= ( X0 @ X10 ) ) ) )
=> ! [X14: b,X15: b > $o] :
( ( ( X15 @ X14 )
= $true )
=> ! [X16: b > $o] :
( ( ! [X17: b > $o] :
( ( ( ^ [Y0: b] :
~ ( X16 @ Y0 ) )
= X17 )
=> ( ( X0 @ X17 )
= $true ) )
& ! [X19: b] :
( ( $true
= ( X15 @ X19 ) )
=> ( $true
= ( X16 @ X19 ) ) ) )
=> ( $true
= ( X16 @ X14 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( b > $o ) > $o] :
( ( ! [X1: b > $o] :
( ( ( ^ [X2: b] : ~ $false )
= X1 )
=> ( X0 @ X1 ) )
& ! [X3: ( b > $o ) > $o,X4: b > $o] :
( ( ! [X5: b > $o] :
( ( X3 @ X5 )
=> ( X0 @ X5 ) )
& ( ( ^ [X6: b] :
? [X7: b > $o] :
( ( X3 @ X7 )
& ( X7 @ X6 ) ) )
= X4 ) )
=> ( X0 @ X4 ) )
& ! [X8: b > $o] :
( ( X8
= ( ^ [X9: b] : $false ) )
=> ( X0 @ X8 ) )
& ! [X10: b > $o,X11: b > $o,X12: b > $o] :
( ( ( X0 @ X11 )
& ( X0 @ X12 )
& ( X10
= ( ^ [X13: b] :
( ( X12 @ X13 )
& ( X11 @ X13 ) ) ) ) )
=> ( X0 @ X10 ) ) )
=> ! [X14: b,X15: b > $o] :
( ( X15 @ X14 )
=> ! [X16: b > $o] :
( ( ! [X17: b > $o] :
( ( X17
= ( ^ [X18: b] :
~ ( X16 @ X18 ) ) )
=> ( X0 @ X17 ) )
& ! [X19: b] :
( ( X15 @ X19 )
=> ( X16 @ X19 ) ) )
=> ( X16 @ X14 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( b > $o ) > $o] :
( ( ! [X1: b > $o] :
( ( ( ^ [X2: b] : ~ $false )
= X1 )
=> ( X0 @ X1 ) )
& ! [X3: ( b > $o ) > $o,X1: b > $o] :
( ( ! [X2: b > $o] :
( ( X3 @ X2 )
=> ( X0 @ X2 ) )
& ( ( ^ [X2: b] :
? [X4: b > $o] :
( ( X3 @ X4 )
& ( X4 @ X2 ) ) )
= X1 ) )
=> ( X0 @ X1 ) )
& ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( X0 @ X1 ) )
& ! [X4: b > $o,X6: b > $o,X5: b > $o] :
( ( ( X0 @ X6 )
& ( X0 @ X5 )
& ( X4
= ( ^ [X2: b] :
( ( X5 @ X2 )
& ( X6 @ X2 ) ) ) ) )
=> ( X0 @ X4 ) ) )
=> ! [X2: b,X7: b > $o] :
( ( X7 @ X2 )
=> ! [X4: b > $o] :
( ( ! [X1: b > $o] :
( ( X1
= ( ^ [X8: b] :
~ ( X4 @ X8 ) ) )
=> ( X0 @ X1 ) )
& ! [X8: b] :
( ( X7 @ X8 )
=> ( X4 @ X8 ) ) )
=> ( X4 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( b > $o ) > $o] :
( ( ! [X1: b > $o] :
( ( ( ^ [X2: b] : ~ $false )
= X1 )
=> ( X0 @ X1 ) )
& ! [X3: ( b > $o ) > $o,X1: b > $o] :
( ( ! [X2: b > $o] :
( ( X3 @ X2 )
=> ( X0 @ X2 ) )
& ( ( ^ [X2: b] :
? [X4: b > $o] :
( ( X3 @ X4 )
& ( X4 @ X2 ) ) )
= X1 ) )
=> ( X0 @ X1 ) )
& ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( X0 @ X1 ) )
& ! [X4: b > $o,X6: b > $o,X5: b > $o] :
( ( ( X0 @ X6 )
& ( X0 @ X5 )
& ( X4
= ( ^ [X2: b] :
( ( X5 @ X2 )
& ( X6 @ X2 ) ) ) ) )
=> ( X0 @ X4 ) ) )
=> ! [X2: b,X7: b > $o] :
( ( X7 @ X2 )
=> ! [X4: b > $o] :
( ( ! [X1: b > $o] :
( ( X1
= ( ^ [X8: b] :
~ ( X4 @ X8 ) ) )
=> ( X0 @ X1 ) )
& ! [X8: b] :
( ( X7 @ X8 )
=> ( X4 @ X8 ) ) )
=> ( X4 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yiSk3ZtPsE/DTF2THF_32037.p',cCLOSURE_THM0_pme) ).
thf(f32,plain,
( $true
!= ( sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $true
!= ( sK2 @ sK1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f18,f19]) ).
thf(f19,plain,
! [X10: b] :
( ( $true
= ( sK3 @ X10 ) )
| ( $true
!= ( sK2 @ X10 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f18,plain,
( $true
!= ( sK3 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV259^5 : 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
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 12:42:40 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SEV259^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.42 % Domain : Set Theory (Sets of sets)
% 0.16/0.42 % Problem : TPS problem CLOSURE-THM0
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English :
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro09]
% 0.16/0.42 % Names : tps_0339 [Bro09]
% 0.16/0.42 % : CLOSURE-THM0 [TPS]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.16/0.42 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.16/0.42 % Number of atoms : 7 ( 5 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 5 ( 7 avg)
% 0.16/0.42 % Number of connectives : 39 ( 2 ~; 0 |; 9 &; 18 @)
% 0.16/0.42 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 13 ( 13 avg)
% 0.16/0.42 % Number of types : 2 ( 1 usr)
% 0.16/0.42 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.16/0.42 % Number of variables : 20 ( 5 ^; 14 !; 1 ?; 20 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.42 % : Polymorphic definitions expanded.
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(b_type,type,
% 0.16/0.42 b: $tType ).
% 0.16/0.42
% 0.16/0.42 thf(cCLOSURE_THM0_pme,conjecture,
% 0.16/0.42 ! [S: ( b > $o ) > $o] :
% 0.16/0.42 ( ( ! [R: b > $o] :
% 0.16/0.42 ( ( R
% 0.16/0.42 = ( ^ [Xx: b] : $false ) )
% 0.16/0.42 => ( S @ R ) )
% 0.16/0.42 & ! [R: b > $o] :
% 0.16/0.42 ( ( R
% 0.16/0.42 = ( ^ [Xx: b] : ~ $false ) )
% 0.16/0.42 => ( S @ R ) )
% 0.16/0.42 & ! [K: ( b > $o ) > $o,R: b > $o] :
% 0.16/0.42 ( ( ! [Xx: b > $o] :
% 0.16/0.42 ( ( K @ Xx )
% 0.16/0.42 => ( S @ Xx ) )
% 0.16/0.42 & ( R
% 0.16/0.42 = ( ^ [Xx: b] :
% 0.16/0.42 ? [S0: b > $o] :
% 0.16/0.42 ( ( K @ S0 )
% 0.16/0.42 & ( S0 @ Xx ) ) ) ) )
% 0.16/0.42 => ( S @ R ) )
% 0.16/0.42 & ! [Y: b > $o,Z: b > $o,S0: b > $o] :
% 0.16/0.42 ( ( ( S @ Y )
% 0.16/0.42 & ( S @ Z )
% 0.16/0.42 & ( S0
% 0.16/0.42 = ( ^ [Xx: b] :
% 0.16/0.42 ( ( Y @ Xx )
% 0.16/0.42 & ( Z @ Xx ) ) ) ) )
% 0.16/0.42 => ( S @ S0 ) ) )
% 0.16/0.42 => ! [W: b > $o,Xx: b] :
% 0.16/0.42 ( ( W @ Xx )
% 0.16/0.42 => ! [S0: b > $o] :
% 0.16/0.42 ( ( ! [Xx0: b] :
% 0.16/0.42 ( ( W @ Xx0 )
% 0.16/0.42 => ( S0 @ Xx0 ) )
% 0.16/0.42 & ! [R: b > $o] :
% 0.16/0.42 ( ( R
% 0.16/0.42 = ( ^ [Xx0: b] :
% 0.16/0.42 ~ ( S0 @ Xx0 ) ) )
% 0.16/0.42 => ( S @ R ) ) )
% 0.16/0.42 => ( S0 @ Xx ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.32/1.14 ---- Embedded in THF ---
% 1.32/1.15 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.32/1.15 %%% Generated on Tue Feb 24 12:42:41 EST 2026
% 1.32/1.15 %%% using '$$dhol' embedding, version 1.3.0.
% 1.32/1.15 %%% Logic specification used:
% 1.32/1.15 %%% thf(spec, logic, $$dhol).
% 1.32/1.15
% 1.32/1.15 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.yiSk3ZtPsE/DTF2DTF32037.p
% See solution above
% 1.32/1.15 ------------------------
% 1.32/1.15 ---- Cleaned THF ---
% 1.32/1.15 thf(b_type,type,
% 1.32/1.15 b: $tType ).
% 1.32/1.15
% 1.32/1.15 thf(cCLOSURE_THM0_pme,conjecture,
% 1.32/1.15 ! [S: ( b > $o ) > $o] :
% 1.32/1.15 ( ( ! [R: b > $o] :
% 1.32/1.15 ( ( R
% 1.32/1.15 = ( ^ [Xx: b] : $false ) )
% 1.32/1.15 => ( S @ R ) )
% 1.32/1.15 & ! [R: b > $o] :
% 1.32/1.15 ( ( R
% 1.32/1.15 = ( ^ [Xx: b] : ~ $false ) )
% 1.32/1.15 => ( S @ R ) )
% 1.32/1.15 & ! [K: ( b > $o ) > $o,R: b > $o] :
% 1.32/1.15 ( ( ! [Xx: b > $o] :
% 1.32/1.15 ( ( K @ Xx )
% 1.32/1.15 => ( S @ Xx ) )
% 1.32/1.15 & ( R
% 1.32/1.15 = ( ^ [Xx: b] :
% 1.32/1.15 ? [S0: b > $o] :
% 1.32/1.15 ( ( K @ S0 )
% 1.32/1.15 & ( S0 @ Xx ) ) ) ) )
% 1.32/1.15 => ( S @ R ) )
% 1.32/1.15 & ! [Y: b > $o,Z: b > $o,S0: b > $o] :
% 1.32/1.15 ( ( ( S @ Y )
% 1.32/1.15 & ( S @ Z )
% 1.32/1.15 & ( S0
% 1.32/1.15 = ( ^ [Xx: b] :
% 1.32/1.15 ( ( Y @ Xx )
% 1.32/1.15 & ( Z @ Xx ) ) ) ) )
% 1.32/1.15 => ( S @ S0 ) ) )
% 1.32/1.15 => ! [W: b > $o,Xx: b] :
% 1.32/1.15 ( ( W @ Xx )
% 1.32/1.15 => ! [S0: b > $o] :
% 1.32/1.15 ( ( ! [Xx0: b] :
% 1.32/1.15 ( ( W @ Xx0 )
% 1.32/1.15 => ( S0 @ Xx0 ) )
% 1.32/1.15 & ! [R: b > $o] :
% 1.32/1.15 ( ( R
% 1.32/1.15 = ( ^ [Xx0: b] :
% 1.32/1.15 ~ ( S0 @ Xx0 ) ) )
% 1.32/1.15 => ( S @ R ) ) )
% 1.32/1.15 => ( S0 @ Xx ) ) ) ) ).
% 1.32/1.15 ------------------------
% 1.32/1.17 % (32135)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32037 for (3000ds/183Mi)
% 1.32/1.17 % (32135)First to succeed.
% 1.32/1.17 % (32135)Refutation found. Thanks to Tanya!
% 1.32/1.17 % SZS status Theorem for DTF2THF_32037
% 1.32/1.17 % SZS output start Proof for DTF2THF_32037
% 1.32/1.17 thf(type_def_5, type, b: $tType).
% 1.32/1.17 thf(func_def_0, type, b: $tType).
% 1.32/1.17 thf(func_def_10, type, sK0: (b > $o) > $o).
% 1.32/1.17 thf(func_def_11, type, sK1: b).
% 1.32/1.17 thf(func_def_12, type, sK2: b > $o).
% 1.32/1.17 thf(func_def_13, type, sK3: b > $o).
% 1.32/1.17 thf(func_def_14, type, sK4: ((b > $o) > $o) > b > $o).
% 1.32/1.17 thf(func_def_16, type, ph6: !>[X0: $tType]:(X0)).
% 1.32/1.17 thf(f33,plain,(
% 1.32/1.17 $false),
% 1.32/1.17 inference(subsumption_resolution,[status(thm)],[f32,f17])).
% 1.32/1.17 thf(f17,plain,(
% 1.32/1.17 ($true = (sK2 @ sK1))),
% 1.32/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.32/1.17 thf(f14,plain,(
% 1.32/1.17 ! [X1 : b > $o,X2 : b > $o,X3 : b > $o] : (($true = (sK0 @ X1)) | ($true != (sK0 @ X3)) | ($true != (sK0 @ X2)) | ((^[Y0 : b]: ((X2 @ Y0) & (X3 @ Y0))) != X1)) & ! [X4 : b > $o] : (($true = (sK0 @ X4)) | ((^[Y0 : b]: (~ $false)) != X4)) & ! [X5 : b > $o] : (((^[Y0 : b]: ($false)) != X5) | ($true = (sK0 @ X5))) & ((! [X9 : b > $o] : (((^[Y0 : b]: (~ (sK3 @ Y0))) != X9) | ($true = (sK0 @ X9))) & ! [X10 : b] : (($true = (sK3 @ X10)) | ($true != (sK2 @ X10))) & ($true != (sK3 @ sK1))) & ($true = (sK2 @ sK1))) & ! [X11 : (b > $o) > $o,X12 : b > $o] : (($true = (sK0 @ X12)) | (($true = (X11 @ (sK4 @ X11))) & ($true != (sK0 @ (sK4 @ X11)))) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X11 @ Y1))))) != X12))),
% 1.32/1.17 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f13,f12,f11,f10])).
% 1.32/1.17 thf(f10,plain,(
% 1.32/1.17 ? [X0 : (b > $o) > $o] : (! [X1 : b > $o,X2 : b > $o,X3 : b > $o] : (((X0 @ X1) = $true) | ($true != (X0 @ X3)) | ((X0 @ X2) != $true) | ((^[Y0 : b]: ((X2 @ Y0) & (X3 @ Y0))) != X1)) & ! [X4 : b > $o] : (((X0 @ X4) = $true) | ((^[Y0 : b]: (~ $false)) != X4)) & ! [X5 : b > $o] : (((^[Y0 : b]: ($false)) != X5) | ((X0 @ X5) = $true)) & ? [X6 : b,X7 : b > $o] : (? [X8 : b > $o] : (! [X9 : b > $o] : (((^[Y0 : b]: (~ (X8 @ Y0))) != X9) | ($true = (X0 @ X9))) & ! [X10 : b] : (($true = (X8 @ X10)) | ($true != (X7 @ X10))) & ($true != (X8 @ X6))) & ((X7 @ X6) = $true)) & ! [X11 : (b > $o) > $o,X12 : b > $o] : (((X0 @ X12) = $true) | ? [X13 : b > $o] : (($true = (X11 @ X13)) & ($true != (X0 @ X13))) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X11 @ Y1))))) != X12))) => (! [X3 : b > $o,X2 : b > $o,X1 : b > $o] : (($true = (sK0 @ X1)) | ($true != (sK0 @ X3)) | ($true != (sK0 @ X2)) | ((^[Y0 : b]: ((X2 @ Y0) & (X3 @ Y0))) != X1)) & ! [X4 : b > $o] : (($true = (sK0 @ X4)) | ((^[Y0 : b]: (~ $false)) != X4)) & ! [X5 : b > $o] : (((^[Y0 : b]: ($false)) != X5) | ($true = (sK0 @ X5))) & ? [X7 : b > $o,X6 : b] : (? [X8 : b > $o] : (! [X9 : b > $o] : (((^[Y0 : b]: (~ (X8 @ Y0))) != X9) | ($true = (sK0 @ X9))) & ! [X10 : b] : (($true = (X8 @ X10)) | ($true != (X7 @ X10))) & ($true != (X8 @ X6))) & ((X7 @ X6) = $true)) & ! [X12 : b > $o,X11 : (b > $o) > $o] : (($true = (sK0 @ X12)) | ? [X13 : b > $o] : (($true = (X11 @ X13)) & ($true != (sK0 @ X13))) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X11 @ Y1))))) != X12)))),
% 1.32/1.17 introduced(definition,[],[choice_axiom])).
% 1.32/1.17 thf(f11,plain,(
% 1.32/1.17 ? [X7 : b > $o,X6 : b] : (? [X8 : b > $o] : (! [X9 : b > $o] : (((^[Y0 : b]: (~ (X8 @ Y0))) != X9) | ($true = (sK0 @ X9))) & ! [X10 : b] : (($true = (X8 @ X10)) | ($true != (X7 @ X10))) & ($true != (X8 @ X6))) & ((X7 @ X6) = $true)) => (? [X8 : b > $o] : (! [X9 : b > $o] : (((^[Y0 : b]: (~ (X8 @ Y0))) != X9) | ($true = (sK0 @ X9))) & ! [X10 : b] : (($true = (X8 @ X10)) | ($true != (sK2 @ X10))) & ($true != (X8 @ sK1))) & ($true = (sK2 @ sK1)))),
% 1.32/1.17 introduced(definition,[],[choice_axiom])).
% 1.32/1.17 thf(f12,plain,(
% 1.32/1.17 ? [X8 : b > $o] : (! [X9 : b > $o] : (((^[Y0 : b]: (~ (X8 @ Y0))) != X9) | ($true = (sK0 @ X9))) & ! [X10 : b] : (($true = (X8 @ X10)) | ($true != (sK2 @ X10))) & ($true != (X8 @ sK1))) => (! [X9 : b > $o] : (((^[Y0 : b]: (~ (sK3 @ Y0))) != X9) | ($true = (sK0 @ X9))) & ! [X10 : b] : (($true = (sK3 @ X10)) | ($true != (sK2 @ X10))) & ($true != (sK3 @ sK1)))),
% 1.32/1.17 introduced(definition,[],[choice_axiom])).
% 1.32/1.17 thf(f13,plain,(
% 1.32/1.17 ! [X11 : (b > $o) > $o] : (? [X13 : b > $o] : (($true = (X11 @ X13)) & ($true != (sK0 @ X13))) => (($true = (X11 @ (sK4 @ X11))) & ($true != (sK0 @ (sK4 @ X11)))))),
% 1.32/1.17 introduced(definition,[],[choice_axiom])).
% 1.32/1.17 thf(f9,plain,(
% 1.32/1.17 ? [X0 : (b > $o) > $o] : (! [X1 : b > $o,X2 : b > $o,X3 : b > $o] : (((X0 @ X1) = $true) | ($true != (X0 @ X3)) | ((X0 @ X2) != $true) | ((^[Y0 : b]: ((X2 @ Y0) & (X3 @ Y0))) != X1)) & ! [X4 : b > $o] : (((X0 @ X4) = $true) | ((^[Y0 : b]: (~ $false)) != X4)) & ! [X5 : b > $o] : (((^[Y0 : b]: ($false)) != X5) | ((X0 @ X5) = $true)) & ? [X6 : b,X7 : b > $o] : (? [X8 : b > $o] : (! [X9 : b > $o] : (((^[Y0 : b]: (~ (X8 @ Y0))) != X9) | ($true = (X0 @ X9))) & ! [X10 : b] : (($true = (X8 @ X10)) | ($true != (X7 @ X10))) & ($true != (X8 @ X6))) & ((X7 @ X6) = $true)) & ! [X11 : (b > $o) > $o,X12 : b > $o] : (((X0 @ X12) = $true) | ? [X13 : b > $o] : (($true = (X11 @ X13)) & ($true != (X0 @ X13))) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X11 @ Y1))))) != X12)))),
% 1.32/1.17 inference(rectify,[status(thm)],[f8])).
% 1.32/1.17 thf(f8,plain,(
% 1.32/1.17 ? [X0 : (b > $o) > $o] : (! [X6 : b > $o,X7 : b > $o,X8 : b > $o] : (((X0 @ X6) = $true) | ($true != (X0 @ X8)) | ($true != (X0 @ X7)) | ((^[Y0 : b]: ((X7 @ Y0) & (X8 @ Y0))) != X6)) & ! [X1 : b > $o] : (((X0 @ X1) = $true) | ((^[Y0 : b]: (~ $false)) != X1)) & ! [X5 : b > $o] : (((^[Y0 : b]: ($false)) != X5) | ((X0 @ X5) = $true)) & ? [X9 : b,X10 : b > $o] : (? [X11 : b > $o] : (! [X12 : b > $o] : (((^[Y0 : b]: (~ (X11 @ Y0))) != X12) | ((X0 @ X12) = $true)) & ! [X13 : b] : (($true = (X11 @ X13)) | ($true != (X10 @ X13))) & ($true != (X11 @ X9))) & ($true = (X10 @ X9))) & ! [X2 : (b > $o) > $o,X3 : b > $o] : (($true = (X0 @ X3)) | ? [X4 : b > $o] : (($true = (X2 @ X4)) & ((X0 @ X4) != $true)) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X2 @ Y1))))) != X3)))),
% 1.32/1.17 inference(flattening,[status(thm)],[f7])).
% 1.32/1.17 thf(f7,plain,(
% 1.32/1.17 ? [X0 : (b > $o) > $o] : (? [X9 : b,X10 : b > $o] : (? [X11 : b > $o] : (($true != (X11 @ X9)) & (! [X13 : b] : (($true = (X11 @ X13)) | ($true != (X10 @ X13))) & ! [X12 : b > $o] : (((^[Y0 : b]: (~ (X11 @ Y0))) != X12) | ((X0 @ X12) = $true)))) & ($true = (X10 @ X9))) & (! [X6 : b > $o,X7 : b > $o,X8 : b > $o] : (((X0 @ X6) = $true) | (($true != (X0 @ X8)) | ((^[Y0 : b]: ((X7 @ Y0) & (X8 @ Y0))) != X6) | ($true != (X0 @ X7)))) & ! [X2 : (b > $o) > $o,X3 : b > $o] : (($true = (X0 @ X3)) | (((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X2 @ Y1))))) != X3) | ? [X4 : b > $o] : (($true = (X2 @ X4)) & ((X0 @ X4) != $true)))) & ! [X5 : b > $o] : (((^[Y0 : b]: ($false)) != X5) | ((X0 @ X5) = $true)) & ! [X1 : b > $o] : (((X0 @ X1) = $true) | ((^[Y0 : b]: (~ $false)) != X1))))),
% 1.32/1.17 inference(ennf_transformation,[status(thm)],[f6])).
% 1.32/1.17 thf(f6,plain,(
% 1.32/1.17 ~! [X0 : (b > $o) > $o] : ((! [X6 : b > $o,X7 : b > $o,X8 : b > $o] : ((($true = (X0 @ X8)) & ((^[Y0 : b]: ((X7 @ Y0) & (X8 @ Y0))) = X6) & ($true = (X0 @ X7))) => ((X0 @ X6) = $true)) & ! [X2 : (b > $o) > $o,X3 : b > $o] : ((((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X2 @ Y1))))) = X3) & ! [X4 : b > $o] : (($true = (X2 @ X4)) => ((X0 @ X4) = $true))) => ($true = (X0 @ X3))) & ! [X5 : b > $o] : (((^[Y0 : b]: ($false)) = X5) => ((X0 @ X5) = $true)) & ! [X1 : b > $o] : (((^[Y0 : b]: (~ $false)) = X1) => ((X0 @ X1) = $true))) => ! [X9 : b,X10 : b > $o] : (($true = (X10 @ X9)) => ! [X11 : b > $o] : ((! [X13 : b] : (($true = (X10 @ X13)) => ($true = (X11 @ X13))) & ! [X12 : b > $o] : (((^[Y0 : b]: (~ (X11 @ Y0))) = X12) => ((X0 @ X12) = $true))) => ($true = (X11 @ X9)))))),
% 1.32/1.17 inference(rectify,[status(thm)],[f5])).
% 1.32/1.17 thf(f5,plain,(
% 1.32/1.17 ~! [X0 : (b > $o) > $o] : ((! [X1 : b > $o] : (((^[Y0 : b]: (~ $false)) = X1) => ((X0 @ X1) = $true)) & ! [X3 : (b > $o) > $o,X4 : b > $o] : ((! [X5 : b > $o] : (($true = (X3 @ X5)) => ((X0 @ X5) = $true)) & ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X3 @ Y1))))) = X4)) => ((X0 @ X4) = $true)) & ! [X8 : b > $o] : (((^[Y0 : b]: ($false)) = X8) => ($true = (X0 @ X8))) & ! [X10 : b > $o,X11 : b > $o,X12 : b > $o] : ((($true = (X0 @ X11)) & ((X0 @ X12) = $true) & ((^[Y0 : b]: ((X11 @ Y0) & (X12 @ Y0))) = X10)) => ($true = (X0 @ X10)))) => ! [X14 : b,X15 : b > $o] : (((X15 @ X14) = $true) => ! [X16 : b > $o] : ((! [X17 : b > $o] : (((^[Y0 : b]: (~ (X16 @ Y0))) = X17) => ((X0 @ X17) = $true)) & ! [X19 : b] : (($true = (X15 @ X19)) => ($true = (X16 @ X19)))) => ($true = (X16 @ X14)))))),
% 1.32/1.17 inference(fool_elimination,[status(thm)],[f4])).
% 1.32/1.17 thf(f4,plain,(
% 1.32/1.17 ~! [X0 : (b > $o) > $o] : ((! [X1 : b > $o] : (((^[X2 : b] : (~$false)) = X1) => (X0 @ X1)) & ! [X3 : (b > $o) > $o,X4 : b > $o] : ((! [X5 : b > $o] : ((X3 @ X5) => (X0 @ X5)) & ((^[X6 : b] : (? [X7 : b > $o] : ((X3 @ X7) & (X7 @ X6)))) = X4)) => (X0 @ X4)) & ! [X8 : b > $o] : ((X8 = (^[X9 : b] : ($false))) => (X0 @ X8)) & ! [X10 : b > $o,X11 : b > $o,X12 : b > $o] : (((X0 @ X11) & (X0 @ X12) & (X10 = (^[X13 : b] : ((X12 @ X13) & (X11 @ X13))))) => (X0 @ X10))) => ! [X14 : b,X15 : b > $o] : ((X15 @ X14) => ! [X16 : b > $o] : ((! [X17 : b > $o] : ((X17 = (^[X18 : b] : (~(X16 @ X18)))) => (X0 @ X17)) & ! [X19 : b] : ((X15 @ X19) => (X16 @ X19))) => (X16 @ X14))))),
% 1.32/1.17 inference(rectify,[status(thm)],[f2])).
% 1.32/1.17 thf(f2,negated_conjecture,(
% 1.32/1.17 ~! [X0 : (b > $o) > $o] : ((! [X1 : b > $o] : (((^[X2 : b] : (~$false)) = X1) => (X0 @ X1)) & ! [X3 : (b > $o) > $o,X1 : b > $o] : ((! [X2 : b > $o] : ((X3 @ X2) => (X0 @ X2)) & ((^[X2 : b] : (? [X4 : b > $o] : ((X3 @ X4) & (X4 @ X2)))) = X1)) => (X0 @ X1)) & ! [X1 : b > $o] : ((X1 = (^[X2 : b] : ($false))) => (X0 @ X1)) & ! [X4 : b > $o,X6 : b > $o,X5 : b > $o] : (((X0 @ X6) & (X0 @ X5) & (X4 = (^[X2 : b] : ((X5 @ X2) & (X6 @ X2))))) => (X0 @ X4))) => ! [X2 : b,X7 : b > $o] : ((X7 @ X2) => ! [X4 : b > $o] : ((! [X1 : b > $o] : ((X1 = (^[X8 : b] : (~(X4 @ X8)))) => (X0 @ X1)) & ! [X8 : b] : ((X7 @ X8) => (X4 @ X8))) => (X4 @ X2))))),
% 1.32/1.17 inference(negated_conjecture,[status(cth)],[f1])).
% 1.32/1.17 thf(f1,conjecture,(
% 1.32/1.17 ! [X0 : (b > $o) > $o] : ((! [X1 : b > $o] : (((^[X2 : b] : (~$false)) = X1) => (X0 @ X1)) & ! [X3 : (b > $o) > $o,X1 : b > $o] : ((! [X2 : b > $o] : ((X3 @ X2) => (X0 @ X2)) & ((^[X2 : b] : (? [X4 : b > $o] : ((X3 @ X4) & (X4 @ X2)))) = X1)) => (X0 @ X1)) & ! [X1 : b > $o] : ((X1 = (^[X2 : b] : ($false))) => (X0 @ X1)) & ! [X4 : b > $o,X6 : b > $o,X5 : b > $o] : (((X0 @ X6) & (X0 @ X5) & (X4 = (^[X2 : b] : ((X5 @ X2) & (X6 @ X2))))) => (X0 @ X4))) => ! [X2 : b,X7 : b > $o] : ((X7 @ X2) => ! [X4 : b > $o] : ((! [X1 : b > $o] : ((X1 = (^[X8 : b] : (~(X4 @ X8)))) => (X0 @ X1)) & ! [X8 : b] : ((X7 @ X8) => (X4 @ X8))) => (X4 @ X2))))),
% 1.32/1.17 file('/export/starexec/sandbox/tmp/tmp.yiSk3ZtPsE/DTF2THF_32037.p',cCLOSURE_THM0_pme)).
% 1.32/1.17 thf(f32,plain,(
% 1.32/1.17 ($true != (sK2 @ sK1))),
% 1.32/1.17 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.32/1.17 thf(f31,plain,(
% 1.32/1.17 ($true != (sK2 @ sK1)) | ($true != $true)),
% 1.32/1.17 inference(superposition,[status(thm)],[f18,f19])).
% 1.32/1.17 thf(f19,plain,(
% 1.32/1.17 ( ! [X10 : b] : (($true = (sK3 @ X10)) | ($true != (sK2 @ X10))) )),
% 1.32/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.32/1.17 thf(f18,plain,(
% 1.32/1.17 ($true != (sK3 @ sK1))),
% 1.32/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.32/1.17 % SZS output end Proof for DTF2THF_32037
% 1.32/1.17 % (32135)------------------------------
% 1.32/1.17 % (32135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.17 % (32135)Termination reason: Refutation
% 1.32/1.17
% 1.32/1.17 % (32135)Memory used [KB]: 5500
% 1.32/1.17 % (32135)Time elapsed: 0.004 s
% 1.32/1.17 % (32135)Instructions burned: 4 (million)
% 1.32/1.17 % (32135)------------------------------
% 1.32/1.17 % (32135)------------------------------
% 1.32/1.17 % (32134)Success in time 0.013 s
%------------------------------------------------------------------------------