%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV123^5 : 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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:20 AM UTC 2026
% Result : Theorem 1.62s 1.41s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 923 ( 322 equ; 0 cnn)
% Maximal formula atoms : 22 ( 16 avg)
% Number of connectives : 1536 ( 104 ~; 189 |; 103 &; 984 @)
% ( 0 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 374 ( 374 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 5 con; 0-5 aty)
% ( 70 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 390 ( 113 ^; 210 !; 67 ?; 390 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_11,type,
sK0: ( a > a > $o ) > $o ).
thf(func_def_12,type,
sK1: a ).
thf(func_def_13,type,
sK2: a ).
thf(func_def_14,type,
sK3: ( a > a > $o ) > $o ).
thf(func_def_15,type,
sK4: a > a > $o ).
thf(func_def_16,type,
sK5: ( a > a > $o ) > a ).
thf(func_def_17,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_18,type,
sK7: ( a > a > $o ) > a > a > $o ).
thf(func_def_19,type,
sK8: ( a > a > $o ) > a > a > $o ).
thf(func_def_21,type,
ph10:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
sK11: a > ( a > a > $o ) > a > a > a > $o ).
thf(func_def_25,type,
sK12: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_26,type,
sK13: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(f399,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f398,f20]) ).
thf(f20,plain,
( ( sK4 @ sK1 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
= ( sK0 @ sK4 ) )
& ! [X5: a,X6: a] :
( ! [X7: a > a > $o] :
( ( $true
!= ( sK3 @ X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( $true
= ( sK4 @ X5 @ X6 ) ) )
& ( ( sK4 @ sK1 @ sK2 )
!= $true )
& ! [X8: a > a > $o] :
( ( ( ( sK7 @ X8 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK8 @ X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
& ( $true
= ( sK3 @ ( sK8 @ X8 ) ) )
& ( ( sK7 @ X8 @ ( sK6 @ X8 ) @ ( sK5 @ X8 ) )
= $true )
& ( ( X8 @ ( sK6 @ X8 ) @ ( sK5 @ X8 ) )
!= $true ) )
| ( ( sK0 @ X8 )
!= $true )
| ( $true
= ( X8 @ sK1 @ sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f9,f14,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ? [X4: a > a > $o] :
( ( ( X0 @ X4 )
= $true )
& ! [X5: a,X6: a] :
( ! [X7: a > a > $o] :
( ( $true
!= ( X3 @ X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( ( X4 @ X5 @ X6 )
= $true ) )
& ( $true
!= ( X4 @ X1 @ X2 ) ) )
& ! [X8: a > a > $o] :
( ? [X9: a,X10: a] :
( ? [X11: a > a > $o] :
( ? [X12: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X12 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X11 )
& ( ( X3 @ X12 )
= $true ) )
& ( $true
= ( X11 @ X10 @ X9 ) ) )
& ( $true
!= ( X8 @ X10 @ X9 ) ) )
| ( ( X0 @ X8 )
!= $true )
| ( ( X8 @ X1 @ X2 )
= $true ) ) )
=> ( ? [X4: a > a > $o] :
( ( $true
= ( sK0 @ X4 ) )
& ! [X6: a,X5: a] :
( ! [X7: a > a > $o] :
( ( $true
!= ( sK3 @ X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( ( X4 @ X5 @ X6 )
= $true ) )
& ( ( X4 @ sK1 @ sK2 )
!= $true ) )
& ! [X8: a > a > $o] :
( ? [X10: a,X9: a] :
( ? [X11: a > a > $o] :
( ? [X12: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X12 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X11 )
& ( ( sK3 @ X12 )
= $true ) )
& ( $true
= ( X11 @ X10 @ X9 ) ) )
& ( $true
!= ( X8 @ X10 @ X9 ) ) )
| ( ( sK0 @ X8 )
!= $true )
| ( $true
= ( X8 @ sK1 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X4: a > a > $o] :
( ( $true
= ( sK0 @ X4 ) )
& ! [X6: a,X5: a] :
( ! [X7: a > a > $o] :
( ( $true
!= ( sK3 @ X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( ( X4 @ X5 @ X6 )
= $true ) )
& ( ( X4 @ sK1 @ sK2 )
!= $true ) )
=> ( ( $true
= ( sK0 @ sK4 ) )
& ! [X6: a,X5: a] :
( ! [X7: a > a > $o] :
( ( $true
!= ( sK3 @ X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( $true
= ( sK4 @ X5 @ X6 ) ) )
& ( ( sK4 @ sK1 @ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X8: a > a > $o] :
( ? [X10: a,X9: a] :
( ? [X11: a > a > $o] :
( ? [X12: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X12 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X11 )
& ( ( sK3 @ X12 )
= $true ) )
& ( $true
= ( X11 @ X10 @ X9 ) ) )
& ( $true
!= ( X8 @ X10 @ X9 ) ) )
=> ( ? [X11: a > a > $o] :
( ? [X12: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X12 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X11 )
& ( ( sK3 @ X12 )
= $true ) )
& ( $true
= ( X11 @ ( sK6 @ X8 ) @ ( sK5 @ X8 ) ) ) )
& ( ( X8 @ ( sK6 @ X8 ) @ ( sK5 @ X8 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X8: a > a > $o] :
( ? [X11: a > a > $o] :
( ? [X12: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X12 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X11 )
& ( ( sK3 @ X12 )
= $true ) )
& ( $true
= ( X11 @ ( sK6 @ X8 ) @ ( sK5 @ X8 ) ) ) )
=> ( ? [X12: a > a > $o] :
( ( ( sK7 @ X8 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X12 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
& ( ( sK3 @ X12 )
= $true ) )
& ( ( sK7 @ X8 @ ( sK6 @ X8 ) @ ( sK5 @ X8 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
! [X8: a > a > $o] :
( ? [X12: a > a > $o] :
( ( ( sK7 @ X8 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X12 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
& ( ( sK3 @ X12 )
= $true ) )
=> ( ( ( sK7 @ X8 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK8 @ X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
& ( $true
= ( sK3 @ ( sK8 @ X8 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ? [X4: a > a > $o] :
( ( ( X0 @ X4 )
= $true )
& ! [X5: a,X6: a] :
( ! [X7: a > a > $o] :
( ( $true
!= ( X3 @ X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( ( X4 @ X5 @ X6 )
= $true ) )
& ( $true
!= ( X4 @ X1 @ X2 ) ) )
& ! [X8: a > a > $o] :
( ? [X9: a,X10: a] :
( ? [X11: a > a > $o] :
( ? [X12: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X12 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X11 )
& ( ( X3 @ X12 )
= $true ) )
& ( $true
= ( X11 @ X10 @ X9 ) ) )
& ( $true
!= ( X8 @ X10 @ X9 ) ) )
| ( ( X0 @ X8 )
!= $true )
| ( ( X8 @ X1 @ X2 )
= $true ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ? [X9: a > a > $o] :
( ( $true
= ( X0 @ X9 ) )
& ! [X10: a,X11: a] :
( ! [X12: a > a > $o] :
( ( ( X3 @ X12 )
!= $true )
| ( $true
!= ( X12 @ X10 @ X11 ) ) )
| ( $true
= ( X9 @ X10 @ X11 ) ) )
& ( ( X9 @ X1 @ X2 )
!= $true ) )
& ! [X4: a > a > $o] :
( ? [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 )
& ( $true
= ( X3 @ X8 ) ) )
& ( $true
= ( X7 @ X6 @ X5 ) ) )
& ( ( X4 @ X6 @ X5 )
!= $true ) )
| ( ( X0 @ X4 )
!= $true )
| ( $true
= ( X4 @ X1 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ? [X9: a > a > $o] :
( ( ( X9 @ X1 @ X2 )
!= $true )
& ( $true
= ( X0 @ X9 ) )
& ! [X10: a,X11: a] :
( ! [X12: a > a > $o] :
( ( ( X3 @ X12 )
!= $true )
| ( $true
!= ( X12 @ X10 @ X11 ) ) )
| ( $true
= ( X9 @ X10 @ X11 ) ) ) )
& ! [X4: a > a > $o] :
( ( $true
= ( X4 @ X1 @ X2 ) )
| ( ( X0 @ X4 )
!= $true )
| ? [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 )
& ( $true
= ( X3 @ X8 ) ) )
& ( $true
= ( X7 @ X6 @ X5 ) ) )
& ( ( X4 @ X6 @ X5 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ( ( ( X0 @ X4 )
= $true )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 )
& ( $true
= ( X3 @ X8 ) ) )
& ( $true
= ( X7 @ X6 @ X5 ) ) )
=> ( ( X4 @ X6 @ X5 )
= $true ) ) )
=> ( $true
= ( X4 @ X1 @ X2 ) ) )
=> ! [X9: a > a > $o] :
( ( ( $true
= ( X0 @ X9 ) )
& ! [X10: a,X11: a] :
( ? [X12: a > a > $o] :
( ( ( X3 @ X12 )
= $true )
& ( $true
= ( X12 @ X10 @ X11 ) ) )
=> ( $true
= ( X9 @ X10 @ X11 ) ) ) )
=> ( ( X9 @ X1 @ X2 )
= $true ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ( ( ( X0 @ X4 )
= $true )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X7 )
& ( $true
= ( X3 @ X8 ) ) )
& ( $true
= ( X7 @ X6 @ X5 ) ) )
=> ( ( X4 @ X6 @ X5 )
= $true ) ) )
=> ( $true
= ( X4 @ X1 @ X2 ) ) )
=> ! [X14: a > a > $o] :
( ( ! [X15: a,X16: a] :
( ? [X17: a > a > $o] :
( ( ( X3 @ X17 )
= $true )
& ( ( X17 @ X15 @ X16 )
= $true ) )
=> ( $true
= ( X14 @ X15 @ X16 ) ) )
& ( $true
= ( X0 @ X14 ) ) )
=> ( $true
= ( X14 @ X1 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X7 @ X6 @ X5 )
& ? [X8: a > a > $o] :
( ( X3 @ X8 )
& ( ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ( X0 @ X11 )
& ! [X12: a,X13: a] :
( ( X8 @ X13 @ X12 )
=> ( X11 @ X13 @ X12 ) ) )
=> ( X11 @ X9 @ X10 ) ) )
= X7 ) ) )
=> ( X4 @ X6 @ X5 ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ! [X14: a > a > $o] :
( ( ! [X15: a,X16: a] :
( ? [X17: a > a > $o] :
( ( X3 @ X17 )
& ( X17 @ X15 @ X16 ) )
=> ( X14 @ X15 @ X16 ) )
& ( X0 @ X14 ) )
=> ( X14 @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > a > $o ) > $o,X2: a,X3: a,X1: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ( X7 @ X5 @ X6 )
& ? [X8: a > a > $o] :
( ( X1 @ X8 )
& ( ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ( X0 @ X11 )
& ! [X13: a,X12: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) ) )
=> ( X11 @ X9 @ X10 ) ) )
= X7 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X1 @ X7 )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > a > $o ) > $o,X2: a,X3: a,X1: ( a > a > $o ) > $o] :
( ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ( X7 @ X5 @ X6 )
& ? [X8: a > a > $o] :
( ( X1 @ X8 )
& ( ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ( X0 @ X11 )
& ! [X13: a,X12: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) ) )
=> ( X11 @ X9 @ X10 ) ) )
= X7 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X1 @ X7 )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4bWiOwifAS/DTF2THF_5504.p',cTHM254_B_pme) ).
thf(f398,plain,
( ( sK4 @ sK1 @ sK2 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f397,f22]) ).
thf(f22,plain,
( $true
= ( sK0 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f397,plain,
( ( $true
!= ( sK0 @ sK4 ) )
| ( ( sK4 @ sK1 @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f396]) ).
thf(f396,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK4 ) )
| ( ( sK4 @ sK1 @ sK2 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f388]) ).
thf(f388,plain,
( ( $true != $true )
| ( ( sK4 @ sK1 @ sK2 )
= $true )
| ( ( sK4 @ sK1 @ sK2 )
= $true )
| ( $true
!= ( sK0 @ sK4 ) )
| ( $true
!= ( sK0 @ sK4 ) ) ),
inference(superposition,[status(thm)],[f16,f357]) ).
thf(f357,plain,
! [X0: a > a > $o] :
( ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) )
| ( ( sK0 @ X0 )
!= $true )
| ( ( X0 @ sK1 @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f356]) ).
thf(f356,plain,
! [X0: a > a > $o] :
( ( $true = $false )
| ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) )
| ( ( sK0 @ X0 )
!= $true )
| ( ( X0 @ sK1 @ sK2 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f346]) ).
thf(f346,plain,
! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
!= $true )
| ( ( sK0 @ X0 )
!= $true )
| ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( $true = $false )
| ( ( X0 @ sK1 @ sK2 )
= $true ) ),
inference(superposition,[status(thm)],[f343,f17]) ).
thf(f17,plain,
! [X8: a > a > $o] :
( ( ( sK7 @ X8 @ ( sK6 @ X8 ) @ ( sK5 @ X8 ) )
= $true )
| ( ( sK0 @ X8 )
!= $true )
| ( $true
= ( X8 @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f343,plain,
! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK7 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( ( sK0 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f342]) ).
thf(f342,plain,
! [X2: a,X0: a > a > $o,X1: a] :
( ( $false != $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
!= $true )
| ( ( sK7 @ X0 @ X1 @ X2 )
= $false )
| ( ( X0 @ sK1 @ sK2 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f337]) ).
thf(f337,plain,
! [X2: a,X0: a > a > $o,X1: a] :
( ( ( X0 @ sK1 @ sK2 )
= $true )
| ( ( sK7 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false != $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
!= $true ) ),
inference(equality_factoring,[status(thm)],[f328]) ).
thf(f328,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK7 @ X0 @ X3 @ X4 )
= $false )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK7 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X0 )
!= $true )
| ( $true
= ( sK4 @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f327]) ).
thf(f327,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true = $false )
| ( ( sK0 @ X0 )
!= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK7 @ X0 @ X3 @ X4 )
= $false )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( ( sK7 @ X0 @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f326,f22]) ).
thf(f326,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( ( sK7 @ X0 @ X3 @ X4 )
= $false )
| ( ( sK0 @ X0 )
!= $true )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( ( sK7 @ X0 @ X1 @ X2 )
= $false ) ),
inference(subsumption_resolution,[status(thm)],[f314,f18]) ).
thf(f18,plain,
! [X8: a > a > $o] :
( ( $true
= ( sK3 @ ( sK8 @ X8 ) ) )
| ( ( sK0 @ X8 )
!= $true )
| ( $true
= ( X8 @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f314,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true
!= ( sK3 @ ( sK8 @ X0 ) ) )
| ( ( sK7 @ X0 @ X3 @ X4 )
= $false )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( ( sK0 @ X0 )
!= $true )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK7 @ X0 @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f313]) ).
thf(f313,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK7 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X0 )
!= $true )
| ( $true != $true )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( ( sK7 @ X0 @ X3 @ X4 )
= $false )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $true
!= ( sK3 @ ( sK8 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f309]) ).
thf(f309,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK0 @ X0 )
!= $true )
| ( $true != $true )
| ( ( sK0 @ X0 )
!= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( $true
!= ( sK3 @ ( sK8 @ X0 ) ) )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( ( sK7 @ X0 @ X3 @ X4 )
= $false )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( ( sK7 @ X0 @ X1 @ X2 )
= $false ) ),
inference(superposition,[status(thm)],[f270,f176]) ).
thf(f176,plain,
! [X10: a,X11: a > a > $o,X8: a > a > $o,X9: a] :
( ( ( sK8 @ X8 @ ( sK12 @ X8 @ X11 ) @ ( sK13 @ X8 @ X11 ) )
= $true )
| ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( ( sK0 @ X8 )
!= $true )
| ( $false
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( ( X11 @ X9 @ X10 )
= $true )
| ( ( sK0 @ X11 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f174]) ).
thf(f174,plain,
! [X10: a,X11: a > a > $o,X8: a > a > $o,X9: a] :
( ( $false
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( ( X11 @ X9 @ X10 )
= $true )
| ( ( sK0 @ X11 )
= $false )
| ( ( ( sK8 @ X8 @ ( sK12 @ X8 @ X11 ) @ ( sK13 @ X8 @ X11 ) )
=> ( X11 @ ( sK12 @ X8 @ X11 ) @ ( sK13 @ X8 @ X11 ) ) )
= $false )
| ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( ( sK0 @ X8 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f173]) ).
thf(f173,plain,
! [X10: a,X11: a > a > $o,X8: a > a > $o,X9: a] :
( ( ( ^ [Y0: a] :
( ( sK8 @ X8 @ ( sK12 @ X8 @ X11 ) @ Y0 )
=> ( X11 @ ( sK12 @ X8 @ X11 ) @ Y0 ) )
@ ( sK13 @ X8 @ X11 ) )
= $false )
| ( ( sK0 @ X11 )
= $false )
| ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( ( X11 @ X9 @ X10 )
= $true )
| ( $false
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( ( sK0 @ X8 )
!= $true ) ),
inference(sigma_clausification,[status(thm)],[f172]) ).
thf(f172,plain,
! [X10: a,X11: a > a > $o,X8: a > a > $o,X9: a] :
( ( $false
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK8 @ X8 @ ( sK12 @ X8 @ X11 ) @ Y0 )
=> ( X11 @ ( sK12 @ X8 @ X11 ) @ Y0 ) ) ) )
| ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( ( X11 @ X9 @ X10 )
= $true )
| ( ( sK0 @ X11 )
= $false )
| ( ( sK0 @ X8 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f171]) ).
thf(f171,plain,
! [X10: a,X11: a > a > $o,X8: a > a > $o,X9: a] :
( ( ( sK0 @ X11 )
= $false )
| ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( $false
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( ( X11 @ X9 @ X10 )
= $true )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK8 @ X8 @ Y0 @ Y1 )
=> ( X11 @ Y0 @ Y1 ) ) )
@ ( sK12 @ X8 @ X11 ) )
= $false )
| ( ( sK0 @ X8 )
!= $true ) ),
inference(sigma_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
! [X10: a,X11: a > a > $o,X8: a > a > $o,X9: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK8 @ X8 @ Y0 @ Y1 )
=> ( X11 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $false
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( ( sK0 @ X11 )
= $false )
| ( ( X11 @ X9 @ X10 )
= $true )
| ( ( sK0 @ X8 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
! [X10: a,X11: a > a > $o,X8: a > a > $o,X9: a] :
( ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK8 @ X8 @ Y0 @ Y1 )
=> ( X11 @ Y0 @ Y1 ) ) ) )
& ( sK0 @ X11 ) ) )
| ( ( X11 @ X9 @ X10 )
= $true )
| ( $false
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( ( sK0 @ X8 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
! [X10: a,X11: a > a > $o,X8: a > a > $o,X9: a] :
( ( ( sK0 @ X8 )
!= $true )
| ( $false
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK8 @ X8 @ Y0 @ Y1 )
=> ( X11 @ Y0 @ Y1 ) ) ) )
& ( sK0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f167]) ).
thf(f167,plain,
! [X10: a,X11: a > a > $o,X8: a > a > $o,X9: a] :
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK8 @ X8 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK0 @ Y0 ) )
=> ( Y0 @ X9 @ X10 ) )
@ X11 )
= $true )
| ( ( sK0 @ X8 )
!= $true )
| ( $false
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( $true
= ( X8 @ sK1 @ sK2 ) ) ),
inference(pi_clausification,[status(thm)],[f154]) ).
thf(f154,plain,
! [X10: a,X8: a > a > $o,X9: a] :
( ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( ( sK0 @ X8 )
!= $true )
| ( $false
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK8 @ X8 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK0 @ Y0 ) )
=> ( Y0 @ X9 @ X10 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f153]) ).
thf(f153,plain,
! [X10: a,X8: a > a > $o,X9: a] :
( ( ( sK0 @ X8 )
!= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK8 @ X8 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK0 @ Y0 ) )
=> ( Y0 @ X9 @ X10 ) ) )
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( $true
= ( X8 @ sK1 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f152]) ).
thf(f152,plain,
! [X10: a,X8: a > a > $o,X9: a] :
( ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( ( sK0 @ X8 )
!= $true )
| ( ( sK7 @ X8 @ X9 @ X10 )
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK8 @ X8 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK0 @ Y1 ) )
=> ( Y1 @ X9 @ Y0 ) ) )
@ X10 ) ) ),
inference(argument_congruence,[status(thm)],[f106]) ).
thf(f106,plain,
! [X8: a > a > $o,X9: a] :
( ( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK8 @ X8 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK0 @ Y1 ) )
=> ( Y1 @ X9 @ Y0 ) ) ) )
= ( sK7 @ X8 @ X9 ) )
| ( ( sK0 @ X8 )
!= $true )
| ( $true
= ( X8 @ sK1 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
! [X8: a > a > $o,X9: a] :
( ( ( sK0 @ X8 )
!= $true )
| ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK8 @ X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X9 )
= ( sK7 @ X8 @ X9 ) ) ),
inference(argument_congruence,[status(thm)],[f19]) ).
thf(f19,plain,
! [X8: a > a > $o] :
( ( ( sK7 @ X8 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK8 @ X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( ( sK0 @ X8 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f270,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( X1 @ ( sK12 @ X0 @ sK4 ) @ ( sK13 @ X0 @ sK4 ) )
!= $true )
| ( $true
!= ( sK3 @ X1 ) )
| ( ( sK0 @ X0 )
!= $true )
| ( ( sK4 @ X2 @ X3 )
= $true )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( ( sK7 @ X0 @ X2 @ X3 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f269]) ).
thf(f269,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK7 @ X0 @ X2 @ X3 )
= $false )
| ( ( X1 @ ( sK12 @ X0 @ sK4 ) @ ( sK13 @ X0 @ sK4 ) )
!= $true )
| ( ( sK4 @ X2 @ X3 )
= $true )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( $true = $false )
| ( ( sK0 @ X0 )
!= $true )
| ( $true
!= ( sK3 @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f256,f22]) ).
thf(f256,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK4 @ X2 @ X3 )
= $true )
| ( $true
!= ( sK3 @ X1 ) )
| ( ( X1 @ ( sK12 @ X0 @ sK4 ) @ ( sK13 @ X0 @ sK4 ) )
!= $true )
| ( ( sK0 @ X0 )
!= $true )
| ( ( sK7 @ X0 @ X2 @ X3 )
= $false )
| ( ( X0 @ sK1 @ sK2 )
= $true )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f239]) ).
thf(f239,plain,
! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( X0 @ sK1 @ sK2 )
= $true )
| ( ( sK7 @ X0 @ X2 @ X3 )
= $false )
| ( ( X1 @ ( sK12 @ X0 @ sK4 ) @ ( sK13 @ X0 @ sK4 ) )
!= $true )
| ( $true
!= ( sK3 @ X1 ) )
| ( ( sK4 @ X2 @ X3 )
= $true )
| ( $false
= ( sK0 @ sK4 ) )
| ( $true = $false )
| ( ( sK0 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f21,f175]) ).
thf(f175,plain,
! [X10: a,X11: a > a > $o,X8: a > a > $o,X9: a] :
( ( ( X11 @ ( sK12 @ X8 @ X11 ) @ ( sK13 @ X8 @ X11 ) )
= $false )
| ( $true
= ( X8 @ sK1 @ sK2 ) )
| ( $false
= ( sK7 @ X8 @ X9 @ X10 ) )
| ( ( sK0 @ X11 )
= $false )
| ( ( sK0 @ X8 )
!= $true )
| ( ( X11 @ X9 @ X10 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f174]) ).
thf(f21,plain,
! [X6: a,X7: a > a > $o,X5: a] :
( ( $true
= ( sK4 @ X5 @ X6 ) )
| ( $true
!= ( sK3 @ X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f16,plain,
! [X8: a > a > $o] :
( ( ( X8 @ ( sK6 @ X8 ) @ ( sK5 @ X8 ) )
!= $true )
| ( ( sK0 @ X8 )
!= $true )
| ( $true
= ( X8 @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV123^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n001.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 12:41:35 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEV123^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Set Theory (Relations)
% 0.16/0.39 % Problem : TPS problem from SETS-OF-RELNS-THMS
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_1077 [Bro09]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.11 v9.1.0, 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.20 v4.1.0, 0.33 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.16/0.39 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 1 ( 1 avg)
% 0.16/0.39 % Number of connectives : 36 ( 0 ~; 0 |; 6 &; 23 @)
% 0.16/0.39 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 17 ( 17 avg)
% 0.16/0.39 % Number of types : 2 ( 1 usr)
% 0.16/0.39 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.39 % Number of variables : 18 ( 2 ^; 13 !; 3 ?; 18 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(a_type,type,
% 0.16/0.39 a: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(cTHM254_B_pme,conjecture,
% 0.16/0.39 ! [PROP: ( a > a > $o ) > $o,S: ( a > a > $o ) > $o,Xx: a,Xy: a] :
% 0.16/0.39 ( ! [Xp: a > a > $o] :
% 0.16/0.39 ( ( ! [Xx0: a,Xy0: a] :
% 0.16/0.39 ( ? [R: a > a > $o] :
% 0.16/0.39 ( ? [Q: a > a > $o] :
% 0.16/0.39 ( ( S @ Q )
% 0.16/0.39 & ( R
% 0.16/0.39 = ( ^ [Xx1: a,Xy1: a] :
% 0.16/0.39 ! [Xp0: a > a > $o] :
% 0.16/0.39 ( ( ! [Xx2: a,Xy2: a] :
% 0.16/0.39 ( ( Q @ Xx2 @ Xy2 )
% 0.16/0.39 => ( Xp0 @ Xx2 @ Xy2 ) )
% 0.16/0.39 & ( PROP @ Xp0 ) )
% 0.16/0.39 => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) )
% 0.16/0.39 & ( R @ Xx0 @ Xy0 ) )
% 0.16/0.39 => ( Xp @ Xx0 @ Xy0 ) )
% 0.16/0.39 & ( PROP @ Xp ) )
% 0.16/0.39 => ( Xp @ Xx @ Xy ) )
% 0.16/0.39 => ! [Xp: a > a > $o] :
% 0.16/0.39 ( ( ! [Xx0: a,Xy0: a] :
% 0.16/0.39 ( ? [R: a > a > $o] :
% 0.16/0.39 ( ( S @ R )
% 0.16/0.39 & ( R @ Xx0 @ Xy0 ) )
% 0.16/0.39 => ( Xp @ Xx0 @ Xy0 ) )
% 0.16/0.39 & ( PROP @ Xp ) )
% 0.16/0.39 => ( Xp @ Xx @ Xy ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.56/1.33 ---- Embedded in THF ---
% 1.56/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.33 %%% Generated on Tue Feb 24 12:41:36 EST 2026
% 1.56/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.33 %%% Logic specification used:
% 1.56/1.33 %%% thf(spec, logic, $$dhol).
% 1.56/1.33
% 1.56/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4bWiOwifAS/DTF2DTF5504.p
% See solution above
% 1.56/1.33 ------------------------
% 1.56/1.34 ---- Cleaned THF ---
% 1.56/1.34 thf(a_type,type,
% 1.56/1.34 a: $tType ).
% 1.56/1.34
% 1.56/1.34 thf(cTHM254_B_pme,conjecture,
% 1.56/1.34 ! [PROP: ( a > a > $o ) > $o,S: ( a > a > $o ) > $o,Xx: a,Xy: a] :
% 1.56/1.34 ( ! [Xp: a > a > $o] :
% 1.56/1.34 ( ( ! [Xx0: a,Xy0: a] :
% 1.56/1.34 ( ? [R: a > a > $o] :
% 1.56/1.34 ( ? [Q: a > a > $o] :
% 1.56/1.34 ( ( S @ Q )
% 1.56/1.34 & ( R
% 1.56/1.34 = ( ^ [Xx1: a,Xy1: a] :
% 1.56/1.34 ! [Xp0: a > a > $o] :
% 1.56/1.34 ( ( ! [Xx2: a,Xy2: a] :
% 1.56/1.34 ( ( Q @ Xx2 @ Xy2 )
% 1.56/1.34 => ( Xp0 @ Xx2 @ Xy2 ) )
% 1.56/1.34 & ( PROP @ Xp0 ) )
% 1.56/1.34 => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) )
% 1.56/1.34 & ( R @ Xx0 @ Xy0 ) )
% 1.56/1.34 => ( Xp @ Xx0 @ Xy0 ) )
% 1.56/1.34 & ( PROP @ Xp ) )
% 1.56/1.34 => ( Xp @ Xx @ Xy ) )
% 1.56/1.34 => ! [Xp: a > a > $o] :
% 1.56/1.34 ( ( ! [Xx0: a,Xy0: a] :
% 1.56/1.34 ( ? [R: a > a > $o] :
% 1.56/1.34 ( ( S @ R )
% 1.56/1.34 & ( R @ Xx0 @ Xy0 ) )
% 1.56/1.34 => ( Xp @ Xx0 @ Xy0 ) )
% 1.56/1.34 & ( PROP @ Xp ) )
% 1.56/1.34 => ( Xp @ Xx @ Xy ) ) ) ).
% 1.56/1.34 ------------------------
% 1.56/1.36 % (5603)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_5504 for (2999ds/4Mi)
% 1.56/1.36 % (5608)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5504 for (2999ds/18Mi)
% 1.56/1.36 % (5605)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5504 for (2999ds/2Mi)
% 1.56/1.36 % (5606)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_5504 for (2999ds/2Mi)
% 1.56/1.36 % (5604)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_5504 for (2999ds/27Mi)
% 1.56/1.36 % (5607)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_5504 for (2999ds/275Mi)
% 1.56/1.36 % (5602)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5504 for (2999ds/183Mi)
% 1.56/1.36 % (5605)Instruction limit reached!
% 1.56/1.36 % (5605)------------------------------
% 1.56/1.36 % (5605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (5605)Termination reason: Unknown
% 1.56/1.36 % (5606)Instruction limit reached!
% 1.56/1.36 % (5606)------------------------------
% 1.56/1.36 % (5606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (5606)Termination reason: Unknown
% 1.56/1.36 % (5606)Termination phase: Property scanning
% 1.56/1.36
% 1.56/1.36 % (5606)Memory used [KB]: 1023
% 1.56/1.36 % (5606)Time elapsed: 0.003 s
% 1.56/1.36 % (5606)Instructions burned: 3 (million)
% 1.56/1.36 % (5606)------------------------------
% 1.56/1.36 % (5606)------------------------------
% 1.56/1.36 % (5605)Termination phase: Preprocessing 3
% 1.56/1.36
% 1.56/1.36 % (5605)Memory used [KB]: 1023
% 1.56/1.36 % (5605)Time elapsed: 0.003 s
% 1.56/1.36 % (5605)Instructions burned: 2 (million)
% 1.56/1.36 % (5605)------------------------------
% 1.56/1.36 % (5605)------------------------------
% 1.56/1.36 % (5603)Instruction limit reached!
% 1.56/1.36 % (5603)------------------------------
% 1.56/1.36 % (5603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (5603)Termination reason: Unknown
% 1.56/1.36 % (5603)Termination phase: Saturation
% 1.56/1.36
% 1.56/1.36 % (5603)Memory used [KB]: 5500
% 1.56/1.36 % (5603)Time elapsed: 0.004 s
% 1.56/1.36 % (5603)Instructions burned: 4 (million)
% 1.56/1.36 % (5603)------------------------------
% 1.56/1.36 % (5603)------------------------------
% 1.56/1.37 % (5608)Instruction limit reached!
% 1.56/1.37 % (5608)------------------------------
% 1.56/1.37 % (5608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (5608)Termination reason: Unknown
% 1.56/1.37 % (5608)Termination phase: Saturation
% 1.56/1.37
% 1.56/1.37 % (5608)Memory used [KB]: 5628
% 1.56/1.37 % (5608)Time elapsed: 0.012 s
% 1.56/1.37 % (5608)Instructions burned: 19 (million)
% 1.56/1.37 % (5608)------------------------------
% 1.56/1.37 % (5608)------------------------------
% 1.56/1.38 % (5604)Instruction limit reached!
% 1.56/1.38 % (5604)------------------------------
% 1.56/1.38 % (5604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.38 % (5604)Termination reason: Unknown
% 1.56/1.38 % (5604)Termination phase: Saturation
% 1.56/1.38
% 1.56/1.38 % (5604)Memory used [KB]: 5756
% 1.56/1.38 % (5604)Time elapsed: 0.017 s
% 1.56/1.38 % (5604)Instructions burned: 28 (million)
% 1.56/1.38 % (5604)------------------------------
% 1.56/1.38 % (5604)------------------------------
% 1.56/1.38 % (5609)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5504 for (2999ds/3Mi)
% 1.56/1.38 % (5610)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_5504 for (2999ds/37Mi)
% 1.56/1.38 % (5611)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_5504 for (2999ds/15Mi)
% 1.56/1.38 % (5609)Instruction limit reached!
% 1.56/1.38 % (5609)------------------------------
% 1.56/1.38 % (5609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.38 % (5609)Termination reason: Unknown
% 1.56/1.38 % (5609)Termination phase: Saturation
% 1.56/1.38
% 1.56/1.38 % (5609)Memory used [KB]: 1023
% 1.56/1.38 % (5609)Time elapsed: 0.003 s
% 1.56/1.38 % (5609)Instructions burned: 3 (million)
% 1.56/1.38 % (5609)------------------------------
% 1.56/1.38 % (5609)------------------------------
% 1.56/1.39 % (5611)Instruction limit reached!
% 1.56/1.39 % (5611)------------------------------
% 1.56/1.39 % (5611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.39 % (5611)Termination reason: Unknown
% 1.56/1.39 % (5611)Termination phase: Saturation
% 1.56/1.39
% 1.56/1.39 % (5611)Memory used [KB]: 5756
% 1.56/1.39 % (5611)Time elapsed: 0.010 s
% 1.56/1.39 % (5611)Instructions burned: 15 (million)
% 1.56/1.39 % (5611)------------------------------
% 1.56/1.39 % (5611)------------------------------
% 1.56/1.39 % (5612)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5504 for (2999ds/3Mi)
% 1.56/1.39 % (5612)Instruction limit reached!
% 1.56/1.39 % (5612)------------------------------
% 1.56/1.39 % (5612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.39 % (5612)Termination reason: Unknown
% 1.56/1.39 % (5612)Termination phase: Saturation
% 1.56/1.39
% 1.56/1.39 % (5612)Memory used [KB]: 1023
% 1.56/1.39 % (5612)Time elapsed: 0.003 s
% 1.56/1.39 % (5612)Instructions burned: 3 (million)
% 1.56/1.39 % (5612)------------------------------
% 1.56/1.39 % (5612)------------------------------
% 1.56/1.39 % (5613)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_5504 for (2999ds/1041Mi)
% 1.56/1.40 % (5614)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5504 for (2999ds/7Mi)
% 1.56/1.40 % (5610)Instruction limit reached!
% 1.56/1.40 % (5610)------------------------------
% 1.56/1.40 % (5610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.40 % (5610)Termination reason: Unknown
% 1.56/1.40 % (5610)Termination phase: Saturation
% 1.56/1.40
% 1.56/1.40 % (5610)Memory used [KB]: 6012
% 1.56/1.40 % (5610)Time elapsed: 0.019 s
% 1.56/1.40 % (5610)Instructions burned: 38 (million)
% 1.56/1.40 % (5610)------------------------------
% 1.56/1.40 % (5610)------------------------------
% 1.62/1.40 % (5614)Instruction limit reached!
% 1.62/1.40 % (5614)------------------------------
% 1.62/1.40 % (5614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.40 % (5614)Termination reason: Unknown
% 1.62/1.40 % (5614)Termination phase: Saturation
% 1.62/1.40
% 1.62/1.40 % (5614)Memory used [KB]: 1023
% 1.62/1.40 % (5614)Time elapsed: 0.005 s
% 1.62/1.40 % (5614)Instructions burned: 7 (million)
% 1.62/1.40 % (5614)------------------------------
% 1.62/1.40 % (5614)------------------------------
% 1.62/1.40 % (5607)First to succeed.
% 1.62/1.40 % (5615)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5504 for (2999ds/16Mi)
% 1.62/1.41 % (5616)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_5504 for (2999ds/3Mi)
% 1.62/1.41 % (5616)Instruction limit reached!
% 1.62/1.41 % (5616)------------------------------
% 1.62/1.41 % (5616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.41 % (5616)Termination reason: Unknown
% 1.62/1.41 % (5616)Termination phase: Twee Goal Transformation
% 1.62/1.41
% 1.62/1.41 % (5616)Memory used [KB]: 1023
% 1.62/1.41 % (5616)Time elapsed: 0.003 s
% 1.62/1.41 % (5616)Instructions burned: 3 (million)
% 1.62/1.41 % (5616)------------------------------
% 1.62/1.41 % (5616)------------------------------
% 1.62/1.41 % (5607)Refutation found. Thanks to Tanya!
% 1.62/1.41 % SZS status Theorem for DTF2THF_5504
% 1.62/1.41 % SZS output start Proof for DTF2THF_5504
% 1.62/1.41 thf(type_def_5, type, a: $tType).
% 1.62/1.41 thf(func_def_0, type, a: $tType).
% 1.62/1.41 thf(func_def_11, type, sK0: (a > a > $o) > $o).
% 1.62/1.41 thf(func_def_12, type, sK1: a).
% 1.62/1.41 thf(func_def_13, type, sK2: a).
% 1.62/1.41 thf(func_def_14, type, sK3: (a > a > $o) > $o).
% 1.62/1.41 thf(func_def_15, type, sK4: a > a > $o).
% 1.62/1.41 thf(func_def_16, type, sK5: (a > a > $o) > a).
% 1.62/1.41 thf(func_def_17, type, sK6: (a > a > $o) > a).
% 1.62/1.41 thf(func_def_18, type, sK7: (a > a > $o) > a > a > $o).
% 1.62/1.41 thf(func_def_19, type, sK8: (a > a > $o) > a > a > $o).
% 1.62/1.41 thf(func_def_21, type, ph10: !>[X0: $tType]:(X0)).
% 1.62/1.41 thf(func_def_24, type, sK11: a > (a > a > $o) > a > a > a > $o).
% 1.62/1.41 thf(func_def_25, type, sK12: (a > a > $o) > (a > a > $o) > a).
% 1.62/1.41 thf(func_def_26, type, sK13: (a > a > $o) > (a > a > $o) > a).
% 1.62/1.41 thf(f399,plain,(
% 1.62/1.41 $false),
% 1.62/1.41 inference(subsumption_resolution,[status(thm)],[f398,f20])).
% 1.62/1.41 thf(f20,plain,(
% 1.62/1.41 ((sK4 @ sK1 @ sK2) != $true)),
% 1.62/1.41 inference(cnf_transformation,[status(thm)],[f15])).
% 1.62/1.41 thf(f15,plain,(
% 1.62/1.41 (($true = (sK0 @ sK4)) & ! [X5 : a,X6 : a] : (! [X7 : a > a > $o] : (($true != (sK3 @ X7)) | ((X7 @ X5 @ X6) != $true)) | ($true = (sK4 @ X5 @ X6))) & ((sK4 @ sK1 @ sK2) != $true)) & ! [X8 : a > a > $o] : ((((((sK7 @ X8) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK8 @ X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1)))))))) & ($true = (sK3 @ (sK8 @ X8)))) & ((sK7 @ X8 @ (sK6 @ X8) @ (sK5 @ X8)) = $true)) & ((X8 @ (sK6 @ X8) @ (sK5 @ X8)) != $true)) | ((sK0 @ X8) != $true) | ($true = (X8 @ sK1 @ sK2)))),
% 1.62/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f9,f14,f13,f12,f11,f10])).
% 1.62/1.41 thf(f10,plain,(
% 1.62/1.41 ? [X0 : (a > a > $o) > $o,X1 : a,X2 : a,X3 : (a > a > $o) > $o] : (? [X4 : a > a > $o] : (((X0 @ X4) = $true) & ! [X5 : a,X6 : a] : (! [X7 : a > a > $o] : (($true != (X3 @ X7)) | ((X7 @ X5 @ X6) != $true)) | ((X4 @ X5 @ X6) = $true)) & ($true != (X4 @ X1 @ X2))) & ! [X8 : a > a > $o] : (? [X9 : a,X10 : a] : (? [X11 : a > a > $o] : (? [X12 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (X0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X11) & ((X3 @ X12) = $true)) & ($true = (X11 @ X10 @ X9))) & ($true != (X8 @ X10 @ X9))) | ((X0 @ X8) != $true) | ((X8 @ X1 @ X2) = $true))) => (? [X4 : a > a > $o] : (($true = (sK0 @ X4)) & ! [X6 : a,X5 : a] : (! [X7 : a > a > $o] : (($true != (sK3 @ X7)) | ((X7 @ X5 @ X6) != $true)) | ((X4 @ X5 @ X6) = $true)) & ((X4 @ sK1 @ sK2) != $true)) & ! [X8 : a > a > $o] : (? [X10 : a,X9 : a] : (? [X11 : a > a > $o] : (? [X12 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X11) & ((sK3 @ X12) = $true)) & ($true = (X11 @ X10 @ X9))) & ($true != (X8 @ X10 @ X9))) | ((sK0 @ X8) != $true) | ($true = (X8 @ sK1 @ sK2))))),
% 1.62/1.41 introduced(definition,[],[choice_axiom])).
% 1.62/1.41 thf(f11,plain,(
% 1.62/1.41 ? [X4 : a > a > $o] : (($true = (sK0 @ X4)) & ! [X6 : a,X5 : a] : (! [X7 : a > a > $o] : (($true != (sK3 @ X7)) | ((X7 @ X5 @ X6) != $true)) | ((X4 @ X5 @ X6) = $true)) & ((X4 @ sK1 @ sK2) != $true)) => (($true = (sK0 @ sK4)) & ! [X6 : a,X5 : a] : (! [X7 : a > a > $o] : (($true != (sK3 @ X7)) | ((X7 @ X5 @ X6) != $true)) | ($true = (sK4 @ X5 @ X6))) & ((sK4 @ sK1 @ sK2) != $true))),
% 1.62/1.41 introduced(definition,[],[choice_axiom])).
% 1.62/1.41 thf(f12,plain,(
% 1.62/1.41 ! [X8 : a > a > $o] : (? [X10 : a,X9 : a] : (? [X11 : a > a > $o] : (? [X12 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X11) & ((sK3 @ X12) = $true)) & ($true = (X11 @ X10 @ X9))) & ($true != (X8 @ X10 @ X9))) => (? [X11 : a > a > $o] : (? [X12 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X11) & ((sK3 @ X12) = $true)) & ($true = (X11 @ (sK6 @ X8) @ (sK5 @ X8)))) & ((X8 @ (sK6 @ X8) @ (sK5 @ X8)) != $true)))),
% 1.62/1.41 introduced(definition,[],[choice_axiom])).
% 1.62/1.41 thf(f13,plain,(
% 1.62/1.41 ! [X8 : a > a > $o] : (? [X11 : a > a > $o] : (? [X12 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X11) & ((sK3 @ X12) = $true)) & ($true = (X11 @ (sK6 @ X8) @ (sK5 @ X8)))) => (? [X12 : a > a > $o] : (((sK7 @ X8) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1)))))))) & ((sK3 @ X12) = $true)) & ((sK7 @ X8 @ (sK6 @ X8) @ (sK5 @ X8)) = $true)))),
% 1.62/1.41 introduced(definition,[],[choice_axiom])).
% 1.62/1.41 thf(f14,plain,(
% 1.62/1.41 ! [X8 : a > a > $o] : (? [X12 : a > a > $o] : (((sK7 @ X8) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1)))))))) & ((sK3 @ X12) = $true)) => (((sK7 @ X8) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK8 @ X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1)))))))) & ($true = (sK3 @ (sK8 @ X8)))))),
% 1.62/1.41 introduced(definition,[],[choice_axiom])).
% 1.62/1.41 thf(f9,plain,(
% 1.62/1.41 ? [X0 : (a > a > $o) > $o,X1 : a,X2 : a,X3 : (a > a > $o) > $o] : (? [X4 : a > a > $o] : (((X0 @ X4) = $true) & ! [X5 : a,X6 : a] : (! [X7 : a > a > $o] : (($true != (X3 @ X7)) | ((X7 @ X5 @ X6) != $true)) | ((X4 @ X5 @ X6) = $true)) & ($true != (X4 @ X1 @ X2))) & ! [X8 : a > a > $o] : (? [X9 : a,X10 : a] : (? [X11 : a > a > $o] : (? [X12 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (X0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X11) & ((X3 @ X12) = $true)) & ($true = (X11 @ X10 @ X9))) & ($true != (X8 @ X10 @ X9))) | ((X0 @ X8) != $true) | ((X8 @ X1 @ X2) = $true)))),
% 1.62/1.41 inference(rectify,[status(thm)],[f8])).
% 1.62/1.41 thf(f8,plain,(
% 1.62/1.41 ? [X0 : (a > a > $o) > $o,X1 : a,X2 : a,X3 : (a > a > $o) > $o] : (? [X9 : a > a > $o] : (($true = (X0 @ X9)) & ! [X10 : a,X11 : a] : (! [X12 : a > a > $o] : (((X3 @ X12) != $true) | ($true != (X12 @ X10 @ X11))) | ($true = (X9 @ X10 @ X11))) & ((X9 @ X1 @ X2) != $true)) & ! [X4 : a > a > $o] : (? [X5 : a,X6 : a] : (? [X7 : a > a > $o] : (? [X8 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (X0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X7) & ($true = (X3 @ X8))) & ($true = (X7 @ X6 @ X5))) & ((X4 @ X6 @ X5) != $true)) | ((X0 @ X4) != $true) | ($true = (X4 @ X1 @ X2))))),
% 1.62/1.41 inference(flattening,[status(thm)],[f7])).
% 1.62/1.41 thf(f7,plain,(
% 1.62/1.41 ? [X0 : (a > a > $o) > $o,X1 : a,X2 : a,X3 : (a > a > $o) > $o] : (? [X9 : a > a > $o] : (((X9 @ X1 @ X2) != $true) & (($true = (X0 @ X9)) & ! [X10 : a,X11 : a] : (! [X12 : a > a > $o] : (((X3 @ X12) != $true) | ($true != (X12 @ X10 @ X11))) | ($true = (X9 @ X10 @ X11))))) & ! [X4 : a > a > $o] : (($true = (X4 @ X1 @ X2)) | (((X0 @ X4) != $true) | ? [X5 : a,X6 : a] : (? [X7 : a > a > $o] : (? [X8 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (X0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X7) & ($true = (X3 @ X8))) & ($true = (X7 @ X6 @ X5))) & ((X4 @ X6 @ X5) != $true)))))),
% 1.62/1.41 inference(ennf_transformation,[status(thm)],[f6])).
% 1.62/1.41 thf(f6,plain,(
% 1.62/1.41 ~! [X0 : (a > a > $o) > $o,X1 : a,X2 : a,X3 : (a > a > $o) > $o] : (! [X4 : a > a > $o] : ((((X0 @ X4) = $true) & ! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : (? [X8 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (X0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X7) & ($true = (X3 @ X8))) & ($true = (X7 @ X6 @ X5))) => ((X4 @ X6 @ X5) = $true))) => ($true = (X4 @ X1 @ X2))) => ! [X9 : a > a > $o] : ((($true = (X0 @ X9)) & ! [X10 : a,X11 : a] : (? [X12 : a > a > $o] : (((X3 @ X12) = $true) & ($true = (X12 @ X10 @ X11))) => ($true = (X9 @ X10 @ X11)))) => ((X9 @ X1 @ X2) = $true)))),
% 1.62/1.41 inference(rectify,[status(thm)],[f5])).
% 1.62/1.41 thf(f5,plain,(
% 1.62/1.41 ~! [X0 : (a > a > $o) > $o,X1 : a,X2 : a,X3 : (a > a > $o) > $o] : (! [X4 : a > a > $o] : ((((X0 @ X4) = $true) & ! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : (? [X8 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (X0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X7) & ($true = (X3 @ X8))) & ($true = (X7 @ X6 @ X5))) => ((X4 @ X6 @ X5) = $true))) => ($true = (X4 @ X1 @ X2))) => ! [X14 : a > a > $o] : ((! [X15 : a,X16 : a] : (? [X17 : a > a > $o] : (((X3 @ X17) = $true) & ((X17 @ X15 @ X16) = $true)) => ($true = (X14 @ X15 @ X16))) & ($true = (X0 @ X14))) => ($true = (X14 @ X1 @ X2))))),
% 1.62/1.41 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.41 thf(f4,plain,(
% 1.62/1.41 ~! [X0 : (a > a > $o) > $o,X1 : a,X2 : a,X3 : (a > a > $o) > $o] : (! [X4 : a > a > $o] : (((X0 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : ((X7 @ X6 @ X5) & ? [X8 : a > a > $o] : ((X3 @ X8) & ((^[X9 : a, X10 : a] : (! [X11 : a > a > $o] : (((X0 @ X11) & ! [X12 : a,X13 : a] : ((X8 @ X13 @ X12) => (X11 @ X13 @ X12))) => (X11 @ X9 @ X10)))) = X7))) => (X4 @ X6 @ X5))) => (X4 @ X1 @ X2)) => ! [X14 : a > a > $o] : ((! [X15 : a,X16 : a] : (? [X17 : a > a > $o] : ((X3 @ X17) & (X17 @ X15 @ X16)) => (X14 @ X15 @ X16)) & (X0 @ X14)) => (X14 @ X1 @ X2)))),
% 1.62/1.41 inference(rectify,[status(thm)],[f2])).
% 1.62/1.41 thf(f2,negated_conjecture,(
% 1.62/1.41 ~! [X0 : (a > a > $o) > $o,X2 : a,X3 : a,X1 : (a > a > $o) > $o] : (! [X4 : a > a > $o] : (((X0 @ X4) & ! [X6 : a,X5 : a] : (? [X7 : a > a > $o] : ((X7 @ X5 @ X6) & ? [X8 : a > a > $o] : ((X1 @ X8) & ((^[X9 : a, X10 : a] : (! [X11 : a > a > $o] : (((X0 @ X11) & ! [X13 : a,X12 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13))) => (X11 @ X9 @ X10)))) = X7))) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : ((X1 @ X7) & (X7 @ X5 @ X6)) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))),
% 1.62/1.41 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.41 thf(f1,conjecture,(
% 1.62/1.41 ! [X0 : (a > a > $o) > $o,X2 : a,X3 : a,X1 : (a > a > $o) > $o] : (! [X4 : a > a > $o] : (((X0 @ X4) & ! [X6 : a,X5 : a] : (? [X7 : a > a > $o] : ((X7 @ X5 @ X6) & ? [X8 : a > a > $o] : ((X1 @ X8) & ((^[X9 : a, X10 : a] : (! [X11 : a > a > $o] : (((X0 @ X11) & ! [X13 : a,X12 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13))) => (X11 @ X9 @ X10)))) = X7))) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : ((X1 @ X7) & (X7 @ X5 @ X6)) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))),
% 1.62/1.41 file('/export/starexec/sandbox/tmp/tmp.4bWiOwifAS/DTF2THF_5504.p',cTHM254_B_pme)).
% 1.62/1.41 thf(f398,plain,(
% 1.62/1.41 ((sK4 @ sK1 @ sK2) = $true)),
% 1.62/1.41 inference(subsumption_resolution,[status(thm)],[f397,f22])).
% 1.62/1.41 thf(f22,plain,(
% 1.62/1.41 ($true = (sK0 @ sK4))),
% 1.62/1.41 inference(cnf_transformation,[status(thm)],[f15])).
% 1.62/1.41 thf(f397,plain,(
% 1.62/1.41 ($true != (sK0 @ sK4)) | ((sK4 @ sK1 @ sK2) = $true)),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f396])).
% 1.62/1.41 thf(f396,plain,(
% 1.62/1.41 ($true != $true) | ($true != (sK0 @ sK4)) | ((sK4 @ sK1 @ sK2) = $true)),
% 1.62/1.41 inference(duplicate_literal_removal,[status(thm)],[f388])).
% 1.62/1.41 thf(f388,plain,(
% 1.62/1.41 ($true != $true) | ((sK4 @ sK1 @ sK2) = $true) | ((sK4 @ sK1 @ sK2) = $true) | ($true != (sK0 @ sK4)) | ($true != (sK0 @ sK4))),
% 1.62/1.41 inference(superposition,[status(thm)],[f16,f357])).
% 1.62/1.41 thf(f357,plain,(
% 1.62/1.41 ( ! [X0 : a > a > $o] : (($true = (sK4 @ (sK6 @ X0) @ (sK5 @ X0))) | ((sK0 @ X0) != $true) | ((X0 @ sK1 @ sK2) = $true)) )),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f356])).
% 1.62/1.41 thf(f356,plain,(
% 1.62/1.41 ( ! [X0 : a > a > $o] : (($true = $false) | ($true = (sK4 @ (sK6 @ X0) @ (sK5 @ X0))) | ((sK0 @ X0) != $true) | ((X0 @ sK1 @ sK2) = $true)) )),
% 1.62/1.41 inference(duplicate_literal_removal,[status(thm)],[f346])).
% 1.62/1.41 thf(f346,plain,(
% 1.62/1.41 ( ! [X0 : a > a > $o] : (((sK0 @ X0) != $true) | ((sK0 @ X0) != $true) | ($true = (sK4 @ (sK6 @ X0) @ (sK5 @ X0))) | ((X0 @ sK1 @ sK2) = $true) | ($true = $false) | ((X0 @ sK1 @ sK2) = $true)) )),
% 1.62/1.41 inference(superposition,[status(thm)],[f343,f17])).
% 1.62/1.41 thf(f17,plain,(
% 1.62/1.41 ( ! [X8 : a > a > $o] : (((sK7 @ X8 @ (sK6 @ X8) @ (sK5 @ X8)) = $true) | ((sK0 @ X8) != $true) | ($true = (X8 @ sK1 @ sK2))) )),
% 1.62/1.41 inference(cnf_transformation,[status(thm)],[f15])).
% 1.62/1.41 thf(f343,plain,(
% 1.62/1.41 ( ! [X2 : a,X0 : a > a > $o,X1 : a] : (((sK7 @ X0 @ X1 @ X2) = $false) | ($true = (sK4 @ X1 @ X2)) | ((X0 @ sK1 @ sK2) = $true) | ((sK0 @ X0) != $true)) )),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f342])).
% 1.62/1.41 thf(f342,plain,(
% 1.62/1.41 ( ! [X2 : a,X0 : a > a > $o,X1 : a] : (($false != $false) | ($true = (sK4 @ X1 @ X2)) | ((sK0 @ X0) != $true) | ((sK7 @ X0 @ X1 @ X2) = $false) | ((X0 @ sK1 @ sK2) = $true)) )),
% 1.62/1.41 inference(duplicate_literal_removal,[status(thm)],[f337])).
% 1.62/1.41 thf(f337,plain,(
% 1.62/1.41 ( ! [X2 : a,X0 : a > a > $o,X1 : a] : (((X0 @ sK1 @ sK2) = $true) | ((sK7 @ X0 @ X1 @ X2) = $false) | ($true = (sK4 @ X1 @ X2)) | ($false != $false) | ($true = (sK4 @ X1 @ X2)) | ((sK0 @ X0) != $true)) )),
% 1.62/1.41 inference(equality_factoring,[status(thm)],[f328])).
% 1.62/1.41 thf(f328,plain,(
% 1.62/1.41 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a,X4 : a] : (((sK7 @ X0 @ X3 @ X4) = $false) | ((X0 @ sK1 @ sK2) = $true) | ($true = (sK4 @ X1 @ X2)) | ((sK7 @ X0 @ X1 @ X2) = $false) | ((sK0 @ X0) != $true) | ($true = (sK4 @ X3 @ X4))) )),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f327])).
% 1.62/1.41 thf(f327,plain,(
% 1.62/1.41 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a,X4 : a] : (($true = $false) | ((sK0 @ X0) != $true) | ($true = (sK4 @ X1 @ X2)) | ((sK7 @ X0 @ X3 @ X4) = $false) | ((X0 @ sK1 @ sK2) = $true) | ($true = (sK4 @ X3 @ X4)) | ((sK7 @ X0 @ X1 @ X2) = $false)) )),
% 1.62/1.41 inference(forward_demodulation,[status(thm)],[f326,f22])).
% 1.62/1.41 thf(f326,plain,(
% 1.62/1.41 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a,X4 : a] : (($true = (sK4 @ X1 @ X2)) | ($false = (sK0 @ sK4)) | ((sK7 @ X0 @ X3 @ X4) = $false) | ((sK0 @ X0) != $true) | ((X0 @ sK1 @ sK2) = $true) | ($true = (sK4 @ X3 @ X4)) | ((sK7 @ X0 @ X1 @ X2) = $false)) )),
% 1.62/1.41 inference(subsumption_resolution,[status(thm)],[f314,f18])).
% 1.62/1.41 thf(f18,plain,(
% 1.62/1.41 ( ! [X8 : a > a > $o] : (($true = (sK3 @ (sK8 @ X8))) | ((sK0 @ X8) != $true) | ($true = (X8 @ sK1 @ sK2))) )),
% 1.62/1.41 inference(cnf_transformation,[status(thm)],[f15])).
% 1.62/1.41 thf(f314,plain,(
% 1.62/1.41 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a,X4 : a] : (($true != (sK3 @ (sK8 @ X0))) | ((sK7 @ X0 @ X3 @ X4) = $false) | ((X0 @ sK1 @ sK2) = $true) | ((sK0 @ X0) != $true) | ($true = (sK4 @ X3 @ X4)) | ($false = (sK0 @ sK4)) | ($true = (sK4 @ X1 @ X2)) | ((sK7 @ X0 @ X1 @ X2) = $false)) )),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f313])).
% 1.62/1.41 thf(f313,plain,(
% 1.62/1.41 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a,X4 : a] : (((sK7 @ X0 @ X1 @ X2) = $false) | ((sK0 @ X0) != $true) | ($true != $true) | ((X0 @ sK1 @ sK2) = $true) | ((sK7 @ X0 @ X3 @ X4) = $false) | ($true = (sK4 @ X3 @ X4)) | ($false = (sK0 @ sK4)) | ($true = (sK4 @ X1 @ X2)) | ($true != (sK3 @ (sK8 @ X0)))) )),
% 1.62/1.41 inference(duplicate_literal_removal,[status(thm)],[f309])).
% 1.62/1.41 thf(f309,plain,(
% 1.62/1.41 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a,X4 : a] : (((sK0 @ X0) != $true) | ($true != $true) | ((sK0 @ X0) != $true) | ($true = (sK4 @ X1 @ X2)) | ($false = (sK0 @ sK4)) | ($true != (sK3 @ (sK8 @ X0))) | ((X0 @ sK1 @ sK2) = $true) | ((X0 @ sK1 @ sK2) = $true) | ((sK7 @ X0 @ X3 @ X4) = $false) | ($true = (sK4 @ X3 @ X4)) | ((sK7 @ X0 @ X1 @ X2) = $false)) )),
% 1.62/1.41 inference(superposition,[status(thm)],[f270,f176])).
% 1.62/1.41 thf(f176,plain,(
% 1.62/1.41 ( ! [X10 : a,X11 : a > a > $o,X8 : a > a > $o,X9 : a] : (((sK8 @ X8 @ (sK12 @ X8 @ X11) @ (sK13 @ X8 @ X11)) = $true) | ($true = (X8 @ sK1 @ sK2)) | ((sK0 @ X8) != $true) | ($false = (sK7 @ X8 @ X9 @ X10)) | ((X11 @ X9 @ X10) = $true) | ((sK0 @ X11) = $false)) )),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f174])).
% 1.62/1.41 thf(f174,plain,(
% 1.62/1.41 ( ! [X10 : a,X11 : a > a > $o,X8 : a > a > $o,X9 : a] : (($false = (sK7 @ X8 @ X9 @ X10)) | ((X11 @ X9 @ X10) = $true) | ((sK0 @ X11) = $false) | (((sK8 @ X8 @ (sK12 @ X8 @ X11) @ (sK13 @ X8 @ X11)) => (X11 @ (sK12 @ X8 @ X11) @ (sK13 @ X8 @ X11))) = $false) | ($true = (X8 @ sK1 @ sK2)) | ((sK0 @ X8) != $true)) )),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f173])).
% 1.62/1.41 thf(f173,plain,(
% 1.62/1.41 ( ! [X10 : a,X11 : a > a > $o,X8 : a > a > $o,X9 : a] : ((((^[Y0 : a]: ((sK8 @ X8 @ (sK12 @ X8 @ X11) @ Y0) => (X11 @ (sK12 @ X8 @ X11) @ Y0))) @ (sK13 @ X8 @ X11)) = $false) | ((sK0 @ X11) = $false) | ($true = (X8 @ sK1 @ sK2)) | ((X11 @ X9 @ X10) = $true) | ($false = (sK7 @ X8 @ X9 @ X10)) | ((sK0 @ X8) != $true)) )),
% 1.62/1.41 inference(sigma_clausification,[status(thm)],[f172])).
% 1.62/1.41 thf(f172,plain,(
% 1.62/1.41 ( ! [X10 : a,X11 : a > a > $o,X8 : a > a > $o,X9 : a] : (($false = (sK7 @ X8 @ X9 @ X10)) | ($false = (!! @ a @ (^[Y0 : a]: ((sK8 @ X8 @ (sK12 @ X8 @ X11) @ Y0) => (X11 @ (sK12 @ X8 @ X11) @ Y0))))) | ($true = (X8 @ sK1 @ sK2)) | ((X11 @ X9 @ X10) = $true) | ((sK0 @ X11) = $false) | ((sK0 @ X8) != $true)) )),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f171])).
% 1.62/1.41 thf(f171,plain,(
% 1.62/1.41 ( ! [X10 : a,X11 : a > a > $o,X8 : a > a > $o,X9 : a] : (((sK0 @ X11) = $false) | ($true = (X8 @ sK1 @ sK2)) | ($false = (sK7 @ X8 @ X9 @ X10)) | ((X11 @ X9 @ X10) = $true) | (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK8 @ X8 @ Y0 @ Y1) => (X11 @ Y0 @ Y1))))) @ (sK12 @ X8 @ X11)) = $false) | ((sK0 @ X8) != $true)) )),
% 1.62/1.41 inference(sigma_clausification,[status(thm)],[f170])).
% 1.62/1.41 thf(f170,plain,(
% 1.62/1.41 ( ! [X10 : a,X11 : a > a > $o,X8 : a > a > $o,X9 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK8 @ X8 @ Y0 @ Y1) => (X11 @ Y0 @ Y1)))))) = $false) | ($false = (sK7 @ X8 @ X9 @ X10)) | ($true = (X8 @ sK1 @ sK2)) | ((sK0 @ X11) = $false) | ((X11 @ X9 @ X10) = $true) | ((sK0 @ X8) != $true)) )),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f169])).
% 1.62/1.41 thf(f169,plain,(
% 1.62/1.41 ( ! [X10 : a,X11 : a > a > $o,X8 : a > a > $o,X9 : a] : (($true = (X8 @ sK1 @ sK2)) | ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK8 @ X8 @ Y0 @ Y1) => (X11 @ Y0 @ Y1)))))) & (sK0 @ X11))) | ((X11 @ X9 @ X10) = $true) | ($false = (sK7 @ X8 @ X9 @ X10)) | ((sK0 @ X8) != $true)) )),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f168])).
% 1.62/1.41 thf(f168,plain,(
% 1.62/1.41 ( ! [X10 : a,X11 : a > a > $o,X8 : a > a > $o,X9 : a] : (((sK0 @ X8) != $true) | ($false = (sK7 @ X8 @ X9 @ X10)) | ($true = (X8 @ sK1 @ sK2)) | ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK8 @ X8 @ Y0 @ Y1) => (X11 @ Y0 @ Y1)))))) & (sK0 @ X11)) => (X11 @ X9 @ X10)))) )),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f167])).
% 1.62/1.41 thf(f167,plain,(
% 1.62/1.41 ( ! [X10 : a,X11 : a > a > $o,X8 : a > a > $o,X9 : a] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK8 @ X8 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK0 @ Y0)) => (Y0 @ X9 @ X10))) @ X11) = $true) | ((sK0 @ X8) != $true) | ($false = (sK7 @ X8 @ X9 @ X10)) | ($true = (X8 @ sK1 @ sK2))) )),
% 1.62/1.41 inference(pi_clausification,[status(thm)],[f154])).
% 1.62/1.41 thf(f154,plain,(
% 1.62/1.41 ( ! [X10 : a,X8 : a > a > $o,X9 : a] : (($true = (X8 @ sK1 @ sK2)) | ((sK0 @ X8) != $true) | ($false = (sK7 @ X8 @ X9 @ X10)) | ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK8 @ X8 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK0 @ Y0)) => (Y0 @ X9 @ X10)))) = $true)) )),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f153])).
% 1.62/1.41 thf(f153,plain,(
% 1.62/1.41 ( ! [X10 : a,X8 : a > a > $o,X9 : a] : (((sK0 @ X8) != $true) | ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK8 @ X8 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK0 @ Y0)) => (Y0 @ X9 @ X10)))) = (sK7 @ X8 @ X9 @ X10)) | ($true = (X8 @ sK1 @ sK2))) )),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f152])).
% 1.62/1.41 thf(f152,plain,(
% 1.62/1.41 ( ! [X10 : a,X8 : a > a > $o,X9 : a] : (($true = (X8 @ sK1 @ sK2)) | ((sK0 @ X8) != $true) | ((sK7 @ X8 @ X9 @ X10) = ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK8 @ X8 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (sK0 @ Y1)) => (Y1 @ X9 @ Y0))))) @ X10))) )),
% 1.62/1.41 inference(argument_congruence,[status(thm)],[f106])).
% 1.62/1.41 thf(f106,plain,(
% 1.62/1.41 ( ! [X8 : a > a > $o,X9 : a] : (((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK8 @ X8 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (sK0 @ Y1)) => (Y1 @ X9 @ Y0))))) = (sK7 @ X8 @ X9)) | ((sK0 @ X8) != $true) | ($true = (X8 @ sK1 @ sK2))) )),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f105])).
% 1.62/1.41 thf(f105,plain,(
% 1.62/1.41 ( ! [X8 : a > a > $o,X9 : a] : (((sK0 @ X8) != $true) | ($true = (X8 @ sK1 @ sK2)) | (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK8 @ X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) @ X9) = (sK7 @ X8 @ X9))) )),
% 1.62/1.41 inference(argument_congruence,[status(thm)],[f19])).
% 1.62/1.41 thf(f19,plain,(
% 1.62/1.41 ( ! [X8 : a > a > $o] : (((sK7 @ X8) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK8 @ X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1)))))))) | ($true = (X8 @ sK1 @ sK2)) | ((sK0 @ X8) != $true)) )),
% 1.62/1.41 inference(cnf_transformation,[status(thm)],[f15])).
% 1.62/1.41 thf(f270,plain,(
% 1.62/1.41 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (((X1 @ (sK12 @ X0 @ sK4) @ (sK13 @ X0 @ sK4)) != $true) | ($true != (sK3 @ X1)) | ((sK0 @ X0) != $true) | ((sK4 @ X2 @ X3) = $true) | ((X0 @ sK1 @ sK2) = $true) | ((sK7 @ X0 @ X2 @ X3) = $false)) )),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f269])).
% 1.62/1.41 thf(f269,plain,(
% 1.62/1.41 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (((sK7 @ X0 @ X2 @ X3) = $false) | ((X1 @ (sK12 @ X0 @ sK4) @ (sK13 @ X0 @ sK4)) != $true) | ((sK4 @ X2 @ X3) = $true) | ((X0 @ sK1 @ sK2) = $true) | ($true = $false) | ((sK0 @ X0) != $true) | ($true != (sK3 @ X1))) )),
% 1.62/1.41 inference(forward_demodulation,[status(thm)],[f256,f22])).
% 1.62/1.41 thf(f256,plain,(
% 1.62/1.41 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (((sK4 @ X2 @ X3) = $true) | ($true != (sK3 @ X1)) | ((X1 @ (sK12 @ X0 @ sK4) @ (sK13 @ X0 @ sK4)) != $true) | ((sK0 @ X0) != $true) | ((sK7 @ X0 @ X2 @ X3) = $false) | ((X0 @ sK1 @ sK2) = $true) | ($false = (sK0 @ sK4))) )),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f239])).
% 1.62/1.41 thf(f239,plain,(
% 1.62/1.41 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (((X0 @ sK1 @ sK2) = $true) | ((sK7 @ X0 @ X2 @ X3) = $false) | ((X1 @ (sK12 @ X0 @ sK4) @ (sK13 @ X0 @ sK4)) != $true) | ($true != (sK3 @ X1)) | ((sK4 @ X2 @ X3) = $true) | ($false = (sK0 @ sK4)) | ($true = $false) | ((sK0 @ X0) != $true)) )),
% 1.62/1.41 inference(superposition,[status(thm)],[f21,f175])).
% 1.62/1.41 thf(f175,plain,(
% 1.62/1.41 ( ! [X10 : a,X11 : a > a > $o,X8 : a > a > $o,X9 : a] : (((X11 @ (sK12 @ X8 @ X11) @ (sK13 @ X8 @ X11)) = $false) | ($true = (X8 @ sK1 @ sK2)) | ($false = (sK7 @ X8 @ X9 @ X10)) | ((sK0 @ X11) = $false) | ((sK0 @ X8) != $true) | ((X11 @ X9 @ X10) = $true)) )),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f174])).
% 1.62/1.41 thf(f21,plain,(
% 1.62/1.41 ( ! [X6 : a,X7 : a > a > $o,X5 : a] : (($true = (sK4 @ X5 @ X6)) | ($true != (sK3 @ X7)) | ((X7 @ X5 @ X6) != $true)) )),
% 1.62/1.41 inference(cnf_transformation,[status(thm)],[f15])).
% 1.62/1.41 thf(f16,plain,(
% 1.62/1.41 ( ! [X8 : a > a > $o] : (((X8 @ (sK6 @ X8) @ (sK5 @ X8)) != $true) | ((sK0 @ X8) != $true) | ($true = (X8 @ sK1 @ sK2))) )),
% 1.62/1.41 inference(cnf_transformation,[status(thm)],[f15])).
% 1.62/1.41 % SZS output end Proof for DTF2THF_5504
% 1.62/1.41 % (5607)------------------------------
% 1.62/1.41 % (5607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.41 % (5607)Termination reason: Refutation
% 1.62/1.41
% 1.62/1.41 % (5607)Memory used [KB]: 5884
% 1.62/1.41 % (5607)Time elapsed: 0.047 s
% 1.62/1.41 % (5607)Instructions burned: 82 (million)
% 1.62/1.41 % (5607)------------------------------
% 1.62/1.41 % (5607)------------------------------
% 1.62/1.41 % (5601)Success in time 0.05 s
%------------------------------------------------------------------------------