%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU975^5 : 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 : n022.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 09:37:53 AM UTC 2026
% Result : Theorem 1.69s 1.37s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 3 unt; 0 typ; 4 def)
% Number of atoms : 629 ( 331 equ; 0 cnn)
% Maximal formula atoms : 29 ( 11 avg)
% Number of connectives : 1528 ( 165 ~; 149 |; 149 &;1009 @)
% ( 14 <=>; 40 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 190 ( 0 ^; 141 !; 49 ?; 190 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cR: a > a ).
thf(func_def_2,type,
cP: a > a > a ).
thf(func_def_3,type,
cL: a > a ).
thf(func_def_4,type,
cZ: a ).
thf(func_def_8,type,
sK0: a ).
thf(func_def_9,type,
sK1: a ).
thf(func_def_10,type,
sK2: ( a > $o ) > a ).
thf(func_def_11,type,
sK3: ( a > $o ) > a ).
thf(func_def_12,type,
sK4: a > $o ).
thf(func_def_13,type,
sK5: ( a > $o ) > a ).
thf(func_def_14,type,
sK6: ( a > $o ) > a ).
thf(func_def_17,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f478,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f108,f132,f445,f469,f477]) ).
thf(f477,plain,
spl7_3,
inference(avatar_contradiction_clause,[status(thm)],[f476]) ).
thf(f476,plain,
( $false
| spl7_3 ),
inference(subsumption_resolution,[status(thm)],[f475,f23]) ).
thf(f23,plain,
( ( sK4 @ ( cP @ sK0 @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: a] :
( ( ( cZ != X0 )
| ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
!= X0 ) )
& ( ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
= X0 )
| ( cZ = X0 ) ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 )
& ! [X5: a > $o] :
( ( ( ( ( X5 @ ( cP @ ( cL @ ( sK2 @ X5 ) ) @ ( cL @ ( sK3 @ X5 ) ) ) )
!= $true )
| ( $true
!= ( X5 @ ( cP @ ( cR @ ( sK2 @ X5 ) ) @ ( cR @ ( sK3 @ X5 ) ) ) ) )
| ( ( cZ
= ( sK3 @ X5 ) )
& ( cZ
!= ( sK2 @ X5 ) ) ) )
& ( ( X5 @ ( cP @ ( sK2 @ X5 ) @ ( sK3 @ X5 ) ) )
= $true ) )
| ( ( X5 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true ) )
& ( ( sK4 @ ( cP @ sK0 @ sK1 ) )
= $true )
& ! [X9: a,X10: a] :
( ( ( sK4 @ ( cP @ X9 @ X10 ) )
!= $true )
| ( ( ( sK4 @ ( cP @ ( cL @ X9 ) @ ( cL @ X10 ) ) )
= $true )
& ( ( cZ != X10 )
| ( cZ = X9 ) )
& ( ( sK4 @ ( cP @ ( cR @ X9 ) @ ( cR @ X10 ) ) )
= $true ) ) )
& ! [X11: a > $o] :
( ( ( ( X11 @ ( cP @ ( sK6 @ X11 ) @ ( sK5 @ X11 ) ) )
= $true )
& ( ( ( X11 @ ( cP @ ( cL @ ( sK6 @ X11 ) ) @ ( cL @ ( sK5 @ X11 ) ) ) )
!= $true )
| ( ( X11 @ ( cP @ ( cR @ ( sK6 @ X11 ) ) @ ( cR @ ( sK5 @ X11 ) ) ) )
!= $true )
| ( ( ( cZ
!= ( sK6 @ X11 ) )
| ( cZ
!= ( sK5 @ X11 ) ) )
& ( ( cZ
= ( sK6 @ X11 ) )
| ( cZ
= ( sK5 @ X11 ) ) ) ) ) )
| ! [X14: a,X15: a] :
( ( ( X11 @ ( cP @ X14 @ X15 ) )
!= $true )
| ( X14 = X15 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X16: a,X17: a] :
( ( cR @ ( cP @ X16 @ X17 ) )
= X17 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f9,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X3: a,X4: a] :
( ! [X5: a > $o] :
( ? [X6: a,X7: a] :
( ( ( ( X5 @ ( cP @ ( cL @ X6 ) @ ( cL @ X7 ) ) )
!= $true )
| ( ( X5 @ ( cP @ ( cR @ X6 ) @ ( cR @ X7 ) ) )
!= $true )
| ( ( cZ = X7 )
& ( cZ != X6 ) ) )
& ( ( X5 @ ( cP @ X6 @ X7 ) )
= $true ) )
| ( ( X5 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) )
!= $true ) )
& ? [X8: a > $o] :
( ( ( X8 @ ( cP @ X3 @ X4 ) )
= $true )
& ! [X9: a,X10: a] :
( ( ( X8 @ ( cP @ X9 @ X10 ) )
!= $true )
| ( ( ( X8 @ ( cP @ ( cL @ X9 ) @ ( cL @ X10 ) ) )
= $true )
& ( ( cZ != X10 )
| ( cZ = X9 ) )
& ( ( X8 @ ( cP @ ( cR @ X9 ) @ ( cR @ X10 ) ) )
= $true ) ) ) ) )
=> ( ! [X5: a > $o] :
( ? [X6: a,X7: a] :
( ( ( ( X5 @ ( cP @ ( cL @ X6 ) @ ( cL @ X7 ) ) )
!= $true )
| ( ( X5 @ ( cP @ ( cR @ X6 ) @ ( cR @ X7 ) ) )
!= $true )
| ( ( cZ = X7 )
& ( cZ != X6 ) ) )
& ( ( X5 @ ( cP @ X6 @ X7 ) )
= $true ) )
| ( ( X5 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true ) )
& ? [X8: a > $o] :
( ( $true
= ( X8 @ ( cP @ sK0 @ sK1 ) ) )
& ! [X9: a,X10: a] :
( ( ( X8 @ ( cP @ X9 @ X10 ) )
!= $true )
| ( ( ( X8 @ ( cP @ ( cL @ X9 ) @ ( cL @ X10 ) ) )
= $true )
& ( ( cZ != X10 )
| ( cZ = X9 ) )
& ( ( X8 @ ( cP @ ( cR @ X9 ) @ ( cR @ X10 ) ) )
= $true ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X5: a > $o] :
( ? [X6: a,X7: a] :
( ( ( ( X5 @ ( cP @ ( cL @ X6 ) @ ( cL @ X7 ) ) )
!= $true )
| ( ( X5 @ ( cP @ ( cR @ X6 ) @ ( cR @ X7 ) ) )
!= $true )
| ( ( cZ = X7 )
& ( cZ != X6 ) ) )
& ( ( X5 @ ( cP @ X6 @ X7 ) )
= $true ) )
=> ( ( ( ( X5 @ ( cP @ ( cL @ ( sK2 @ X5 ) ) @ ( cL @ ( sK3 @ X5 ) ) ) )
!= $true )
| ( $true
!= ( X5 @ ( cP @ ( cR @ ( sK2 @ X5 ) ) @ ( cR @ ( sK3 @ X5 ) ) ) ) )
| ( ( cZ
= ( sK3 @ X5 ) )
& ( cZ
!= ( sK2 @ X5 ) ) ) )
& ( ( X5 @ ( cP @ ( sK2 @ X5 ) @ ( sK3 @ X5 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X8: a > $o] :
( ( $true
= ( X8 @ ( cP @ sK0 @ sK1 ) ) )
& ! [X9: a,X10: a] :
( ( ( X8 @ ( cP @ X9 @ X10 ) )
!= $true )
| ( ( ( X8 @ ( cP @ ( cL @ X9 ) @ ( cL @ X10 ) ) )
= $true )
& ( ( cZ != X10 )
| ( cZ = X9 ) )
& ( ( X8 @ ( cP @ ( cR @ X9 ) @ ( cR @ X10 ) ) )
= $true ) ) ) )
=> ( ( ( sK4 @ ( cP @ sK0 @ sK1 ) )
= $true )
& ! [X10: a,X9: a] :
( ( ( sK4 @ ( cP @ X9 @ X10 ) )
!= $true )
| ( ( ( sK4 @ ( cP @ ( cL @ X9 ) @ ( cL @ X10 ) ) )
= $true )
& ( ( cZ != X10 )
| ( cZ = X9 ) )
& ( ( sK4 @ ( cP @ ( cR @ X9 ) @ ( cR @ X10 ) ) )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X11: a > $o] :
( ? [X12: a,X13: a] :
( ( ( X11 @ ( cP @ X13 @ X12 ) )
= $true )
& ( ( ( X11 @ ( cP @ ( cL @ X13 ) @ ( cL @ X12 ) ) )
!= $true )
| ( ( X11 @ ( cP @ ( cR @ X13 ) @ ( cR @ X12 ) ) )
!= $true )
| ( ( ( cZ != X13 )
| ( cZ != X12 ) )
& ( ( cZ = X13 )
| ( cZ = X12 ) ) ) ) )
=> ( ( ( X11 @ ( cP @ ( sK6 @ X11 ) @ ( sK5 @ X11 ) ) )
= $true )
& ( ( ( X11 @ ( cP @ ( cL @ ( sK6 @ X11 ) ) @ ( cL @ ( sK5 @ X11 ) ) ) )
!= $true )
| ( ( X11 @ ( cP @ ( cR @ ( sK6 @ X11 ) ) @ ( cR @ ( sK5 @ X11 ) ) ) )
!= $true )
| ( ( ( cZ
!= ( sK6 @ X11 ) )
| ( cZ
!= ( sK5 @ X11 ) ) )
& ( ( cZ
= ( sK6 @ X11 ) )
| ( cZ
= ( sK5 @ X11 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: a] :
( ( ( cZ != X0 )
| ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
!= X0 ) )
& ( ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
= X0 )
| ( cZ = X0 ) ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 )
& ? [X3: a,X4: a] :
( ! [X5: a > $o] :
( ? [X6: a,X7: a] :
( ( ( ( X5 @ ( cP @ ( cL @ X6 ) @ ( cL @ X7 ) ) )
!= $true )
| ( ( X5 @ ( cP @ ( cR @ X6 ) @ ( cR @ X7 ) ) )
!= $true )
| ( ( cZ = X7 )
& ( cZ != X6 ) ) )
& ( ( X5 @ ( cP @ X6 @ X7 ) )
= $true ) )
| ( ( X5 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) )
!= $true ) )
& ? [X8: a > $o] :
( ( ( X8 @ ( cP @ X3 @ X4 ) )
= $true )
& ! [X9: a,X10: a] :
( ( ( X8 @ ( cP @ X9 @ X10 ) )
!= $true )
| ( ( ( X8 @ ( cP @ ( cL @ X9 ) @ ( cL @ X10 ) ) )
= $true )
& ( ( cZ != X10 )
| ( cZ = X9 ) )
& ( ( X8 @ ( cP @ ( cR @ X9 ) @ ( cR @ X10 ) ) )
= $true ) ) ) ) )
& ! [X11: a > $o] :
( ? [X12: a,X13: a] :
( ( ( X11 @ ( cP @ X13 @ X12 ) )
= $true )
& ( ( ( X11 @ ( cP @ ( cL @ X13 ) @ ( cL @ X12 ) ) )
!= $true )
| ( ( X11 @ ( cP @ ( cR @ X13 ) @ ( cR @ X12 ) ) )
!= $true )
| ( ( ( cZ != X13 )
| ( cZ != X12 ) )
& ( ( cZ = X13 )
| ( cZ = X12 ) ) ) ) )
| ! [X14: a,X15: a] :
( ( ( X11 @ ( cP @ X14 @ X15 ) )
!= $true )
| ( X14 = X15 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X16: a,X17: a] :
( ( cR @ ( cP @ X16 @ X17 ) )
= X17 ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X9: a] :
( ( ( cZ != X9 )
| ( ( cP @ ( cL @ X9 ) @ ( cR @ X9 ) )
!= X9 ) )
& ( ( ( cP @ ( cL @ X9 ) @ ( cR @ X9 ) )
= X9 )
| ( cZ = X9 ) ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ? [X10: a,X11: a] :
( ! [X15: a > $o] :
( ? [X17: a,X16: a] :
( ( ( $true
!= ( X15 @ ( cP @ ( cL @ X17 ) @ ( cL @ X16 ) ) ) )
| ( ( X15 @ ( cP @ ( cR @ X17 ) @ ( cR @ X16 ) ) )
!= $true )
| ( ( cZ = X16 )
& ( cZ != X17 ) ) )
& ( ( X15 @ ( cP @ X17 @ X16 ) )
= $true ) )
| ( ( X15 @ ( cP @ ( cL @ X10 ) @ ( cL @ X11 ) ) )
!= $true ) )
& ? [X12: a > $o] :
( ( $true
= ( X12 @ ( cP @ X10 @ X11 ) ) )
& ! [X14: a,X13: a] :
( ( ( X12 @ ( cP @ X14 @ X13 ) )
!= $true )
| ( ( ( X12 @ ( cP @ ( cL @ X14 ) @ ( cL @ X13 ) ) )
= $true )
& ( ( cZ != X13 )
| ( cZ = X14 ) )
& ( $true
= ( X12 @ ( cP @ ( cR @ X14 ) @ ( cR @ X13 ) ) ) ) ) ) ) )
& ! [X2: a > $o] :
( ? [X3: a,X4: a] :
( ( ( X2 @ ( cP @ X4 @ X3 ) )
= $true )
& ( ( $true
!= ( X2 @ ( cP @ ( cL @ X4 ) @ ( cL @ X3 ) ) ) )
| ( ( X2 @ ( cP @ ( cR @ X4 ) @ ( cR @ X3 ) ) )
!= $true )
| ( ( ( cZ != X4 )
| ( cZ != X3 ) )
& ( ( cZ = X4 )
| ( cZ = X3 ) ) ) ) )
| ! [X6: a,X5: a] :
( ( ( X2 @ ( cP @ X6 @ X5 ) )
!= $true )
| ( X5 = X6 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X8: a,X7: a] :
( ( cR @ ( cP @ X8 @ X7 ) )
= X7 ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X9: a] :
( ( cZ != X9 )
<=> ( ( cP @ ( cL @ X9 ) @ ( cR @ X9 ) )
= X9 ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ? [X10: a,X11: a] :
( ! [X15: a > $o] :
( ? [X17: a,X16: a] :
( ( ( $true
!= ( X15 @ ( cP @ ( cL @ X17 ) @ ( cL @ X16 ) ) ) )
| ( ( X15 @ ( cP @ ( cR @ X17 ) @ ( cR @ X16 ) ) )
!= $true )
| ( ( cZ = X16 )
& ( cZ != X17 ) ) )
& ( ( X15 @ ( cP @ X17 @ X16 ) )
= $true ) )
| ( ( X15 @ ( cP @ ( cL @ X10 ) @ ( cL @ X11 ) ) )
!= $true ) )
& ? [X12: a > $o] :
( ( $true
= ( X12 @ ( cP @ X10 @ X11 ) ) )
& ! [X14: a,X13: a] :
( ( ( X12 @ ( cP @ X14 @ X13 ) )
!= $true )
| ( ( ( X12 @ ( cP @ ( cL @ X14 ) @ ( cL @ X13 ) ) )
= $true )
& ( ( cZ != X13 )
| ( cZ = X14 ) )
& ( $true
= ( X12 @ ( cP @ ( cR @ X14 ) @ ( cR @ X13 ) ) ) ) ) ) ) )
& ! [X2: a > $o] :
( ? [X3: a,X4: a] :
( ( ( X2 @ ( cP @ X4 @ X3 ) )
= $true )
& ( ( $true
!= ( X2 @ ( cP @ ( cL @ X4 ) @ ( cL @ X3 ) ) ) )
| ( ( X2 @ ( cP @ ( cR @ X4 ) @ ( cR @ X3 ) ) )
!= $true )
| ( ( cZ = X3 )
<~> ( cZ = X4 ) ) ) )
| ! [X6: a,X5: a] :
( ( ( X2 @ ( cP @ X6 @ X5 ) )
!= $true )
| ( X5 = X6 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X8: a,X7: a] :
( ( cR @ ( cP @ X8 @ X7 ) )
= X7 ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X10: a,X11: a] :
( ! [X15: a > $o] :
( ? [X17: a,X16: a] :
( ( ( $true
!= ( X15 @ ( cP @ ( cL @ X17 ) @ ( cL @ X16 ) ) ) )
| ( ( X15 @ ( cP @ ( cR @ X17 ) @ ( cR @ X16 ) ) )
!= $true )
| ( ( cZ = X16 )
& ( cZ != X17 ) ) )
& ( ( X15 @ ( cP @ X17 @ X16 ) )
= $true ) )
| ( ( X15 @ ( cP @ ( cL @ X10 ) @ ( cL @ X11 ) ) )
!= $true ) )
& ? [X12: a > $o] :
( ( $true
= ( X12 @ ( cP @ X10 @ X11 ) ) )
& ! [X14: a,X13: a] :
( ( ( X12 @ ( cP @ X14 @ X13 ) )
!= $true )
| ( ( ( X12 @ ( cP @ ( cL @ X14 ) @ ( cL @ X13 ) ) )
= $true )
& ( ( cZ != X13 )
| ( cZ = X14 ) )
& ( $true
= ( X12 @ ( cP @ ( cR @ X14 ) @ ( cR @ X13 ) ) ) ) ) ) ) )
& ! [X8: a,X7: a] :
( ( cR @ ( cP @ X8 @ X7 ) )
= X7 )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ( cZ
= ( cL @ cZ ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X9: a] :
( ( cZ != X9 )
<=> ( ( cP @ ( cL @ X9 ) @ ( cR @ X9 ) )
= X9 ) )
& ! [X2: a > $o] :
( ? [X3: a,X4: a] :
( ( ( X2 @ ( cP @ X4 @ X3 ) )
= $true )
& ( ( $true
!= ( X2 @ ( cP @ ( cL @ X4 ) @ ( cL @ X3 ) ) ) )
| ( ( X2 @ ( cP @ ( cR @ X4 ) @ ( cR @ X3 ) ) )
!= $true )
| ( ( cZ = X3 )
<~> ( cZ = X4 ) ) ) )
| ! [X6: a,X5: a] :
( ( ( X2 @ ( cP @ X6 @ X5 ) )
!= $true )
| ( X5 = X6 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X8: a,X7: a] :
( ( cR @ ( cP @ X8 @ X7 ) )
= X7 )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ( cZ
= ( cL @ cZ ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X9: a] :
( ( cZ != X9 )
<=> ( ( cP @ ( cL @ X9 ) @ ( cR @ X9 ) )
= X9 ) )
& ! [X2: a > $o] :
( ! [X4: a,X3: a] :
( ( ( X2 @ ( cP @ X4 @ X3 ) )
= $true )
=> ( ( $true
= ( X2 @ ( cP @ ( cL @ X4 ) @ ( cL @ X3 ) ) ) )
& ( ( cZ = X4 )
<=> ( cZ = X3 ) )
& ( ( X2 @ ( cP @ ( cR @ X4 ) @ ( cR @ X3 ) ) )
= $true ) ) )
=> ! [X5: a,X6: a] :
( ( ( X2 @ ( cP @ X6 @ X5 ) )
= $true )
=> ( X5 = X6 ) ) ) )
=> ! [X11: a,X10: a] :
( ? [X12: a > $o] :
( ! [X13: a,X14: a] :
( ( ( X12 @ ( cP @ X14 @ X13 ) )
= $true )
=> ( ( ( cZ = X13 )
=> ( cZ = X14 ) )
& ( $true
= ( X12 @ ( cP @ ( cR @ X14 ) @ ( cR @ X13 ) ) ) )
& ( ( X12 @ ( cP @ ( cL @ X14 ) @ ( cL @ X13 ) ) )
= $true ) ) )
& ( $true
= ( X12 @ ( cP @ X10 @ X11 ) ) ) )
=> ? [X15: a > $o] :
( ! [X16: a,X17: a] :
( ( ( X15 @ ( cP @ X17 @ X16 ) )
= $true )
=> ( ( ( cZ = X16 )
=> ( cZ = X17 ) )
& ( ( X15 @ ( cP @ ( cR @ X17 ) @ ( cR @ X16 ) ) )
= $true )
& ( $true
= ( X15 @ ( cP @ ( cL @ X17 ) @ ( cL @ X16 ) ) ) ) ) )
& ( ( X15 @ ( cP @ ( cL @ X10 ) @ ( cL @ X11 ) ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ! [X2: a > $o] :
( ! [X3: a,X4: a] :
( ( X2 @ ( cP @ X4 @ X3 ) )
=> ( ( X2 @ ( cP @ ( cR @ X4 ) @ ( cR @ X3 ) ) )
& ( ( cZ = X3 )
<=> ( cZ = X4 ) )
& ( X2 @ ( cP @ ( cL @ X4 ) @ ( cL @ X3 ) ) ) ) )
=> ! [X5: a,X6: a] :
( ( X2 @ ( cP @ X6 @ X5 ) )
=> ( X5 = X6 ) ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X7: a,X8: a] :
( ( cR @ ( cP @ X8 @ X7 ) )
= X7 )
& ( cZ
= ( cR @ cZ ) )
& ! [X9: a] :
( ( ( cP @ ( cL @ X9 ) @ ( cR @ X9 ) )
= X9 )
<=> ( cZ != X9 ) ) )
=> ! [X10: a,X11: a] :
( ? [X12: a > $o] :
( ! [X13: a,X14: a] :
( ( X12 @ ( cP @ X14 @ X13 ) )
=> ( ( X12 @ ( cP @ ( cR @ X14 ) @ ( cR @ X13 ) ) )
& ( ( cZ = X13 )
=> ( cZ = X14 ) )
& ( X12 @ ( cP @ ( cL @ X14 ) @ ( cL @ X13 ) ) ) ) )
& ( X12 @ ( cP @ X10 @ X11 ) ) )
=> ? [X15: a > $o] :
( ! [X16: a,X17: a] :
( ( X15 @ ( cP @ X17 @ X16 ) )
=> ( ( ( cZ = X16 )
=> ( cZ = X17 ) )
& ( X15 @ ( cP @ ( cR @ X17 ) @ ( cR @ X16 ) ) )
& ( X15 @ ( cP @ ( cL @ X17 ) @ ( cL @ X16 ) ) ) ) )
& ( X15 @ ( cP @ ( cL @ X10 ) @ ( cL @ X11 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ! [X3: a > $o] :
( ! [X4: a,X2: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( ( X3 @ ( cP @ ( cR @ X2 ) @ ( cR @ X4 ) ) )
& ( ( cZ = X4 )
<=> ( cZ = X2 ) )
& ( X3 @ ( cP @ ( cL @ X2 ) @ ( cL @ X4 ) ) ) ) )
=> ! [X4: a,X2: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( X2 = X4 ) ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ( cZ
= ( cR @ cZ ) )
& ! [X2: a] :
( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
<=> ( cZ != X2 ) ) )
=> ! [X0: a,X1: a] :
( ? [X3: a > $o] :
( ! [X4: a,X2: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( ( X3 @ ( cP @ ( cR @ X2 ) @ ( cR @ X4 ) ) )
& ( ( cZ = X4 )
=> ( cZ = X2 ) )
& ( X3 @ ( cP @ ( cL @ X2 ) @ ( cL @ X4 ) ) ) ) )
& ( X3 @ ( cP @ X0 @ X1 ) ) )
=> ? [X3: a > $o] :
( ! [X4: a,X2: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( ( ( cZ = X4 )
=> ( cZ = X2 ) )
& ( X3 @ ( cP @ ( cR @ X2 ) @ ( cR @ X4 ) ) )
& ( X3 @ ( cP @ ( cL @ X2 ) @ ( cL @ X4 ) ) ) ) )
& ( X3 @ ( cP @ ( cL @ X0 ) @ ( cL @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ! [X3: a > $o] :
( ! [X4: a,X2: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( ( X3 @ ( cP @ ( cR @ X2 ) @ ( cR @ X4 ) ) )
& ( ( cZ = X4 )
<=> ( cZ = X2 ) )
& ( X3 @ ( cP @ ( cL @ X2 ) @ ( cL @ X4 ) ) ) ) )
=> ! [X4: a,X2: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( X2 = X4 ) ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ( cZ
= ( cR @ cZ ) )
& ! [X2: a] :
( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
<=> ( cZ != X2 ) ) )
=> ! [X0: a,X1: a] :
( ? [X3: a > $o] :
( ! [X4: a,X2: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( ( X3 @ ( cP @ ( cR @ X2 ) @ ( cR @ X4 ) ) )
& ( ( cZ = X4 )
=> ( cZ = X2 ) )
& ( X3 @ ( cP @ ( cL @ X2 ) @ ( cL @ X4 ) ) ) ) )
& ( X3 @ ( cP @ X0 @ X1 ) ) )
=> ? [X3: a > $o] :
( ! [X4: a,X2: a] :
( ( X3 @ ( cP @ X2 @ X4 ) )
=> ( ( ( cZ = X4 )
=> ( cZ = X2 ) )
& ( X3 @ ( cP @ ( cR @ X2 ) @ ( cR @ X4 ) ) )
& ( X3 @ ( cP @ ( cL @ X2 ) @ ( cL @ X4 ) ) ) ) )
& ( X3 @ ( cP @ ( cL @ X0 ) @ ( cL @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B81vuvfMCe/DTF2THF_11165.p',cPU_LEM2B_pme) ).
thf(f475,plain,
( ( ( sK4 @ ( cP @ sK0 @ sK1 ) )
!= $true )
| spl7_3 ),
inference(trivial_inequality_removal,[status(thm)],[f474]) ).
thf(f474,plain,
( ( ( sK4 @ ( cP @ sK0 @ sK1 ) )
!= $true )
| ( $true != $true )
| spl7_3 ),
inference(superposition,[status(thm)],[f103,f22]) ).
thf(f22,plain,
! [X10: a,X9: a] :
( ( ( sK4 @ ( cP @ ( cL @ X9 ) @ ( cL @ X10 ) ) )
= $true )
| ( ( sK4 @ ( cP @ X9 @ X10 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f103,plain,
( ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true )
| spl7_3 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f101,definition,
( spl7_3
<=> ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_3])],[avatar_definition]) ).
thf(f469,plain,
( ~ spl7_3
| spl7_4
| ~ spl7_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f468]) ).
thf(f468,plain,
( $false
| ~ spl7_3
| spl7_4
| ~ spl7_5 ),
inference(subsumption_resolution,[status(thm)],[f462,f107]) ).
thf(f107,plain,
( ( cZ
!= ( sK2 @ sK4 ) )
| spl7_4 ),
inference(avatar_component_clause,[status(thm)],[f105]) ).
thf(f105,definition,
( spl7_4
<=> ( cZ
= ( sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl7_4])],[avatar_definition]) ).
thf(f462,plain,
( ( cZ
= ( sK2 @ sK4 ) )
| ~ spl7_3
| ~ spl7_5 ),
inference(trivial_inequality_removal,[status(thm)],[f451]) ).
thf(f451,plain,
( ( cZ
= ( sK2 @ sK4 ) )
| ( $true != $true )
| ~ spl7_3
| ~ spl7_5 ),
inference(superposition,[status(thm)],[f32,f450]) ).
thf(f450,plain,
( ( ( sK4 @ ( cP @ ( sK2 @ sK4 ) @ cZ ) )
= $true )
| ~ spl7_3
| ~ spl7_5 ),
inference(subsumption_resolution,[status(thm)],[f448,f102]) ).
thf(f102,plain,
( ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
= $true )
| ~ spl7_3 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f448,plain,
( ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true )
| ( ( sK4 @ ( cP @ ( sK2 @ sK4 ) @ cZ ) )
= $true )
| ~ spl7_5 ),
inference(superposition,[status(thm)],[f24,f127]) ).
thf(f127,plain,
( ( cZ
= ( sK3 @ sK4 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[status(thm)],[f125]) ).
thf(f125,definition,
( spl7_5
<=> ( cZ
= ( sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition]) ).
thf(f24,plain,
! [X5: a > $o] :
( ( ( X5 @ ( cP @ ( sK2 @ X5 ) @ ( sK3 @ X5 ) ) )
= $true )
| ( ( X5 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f32,plain,
! [X9: a] :
( ( ( sK4 @ ( cP @ X9 @ cZ ) )
!= $true )
| ( cZ = X9 ) ),
inference(equality_resolution,[status(thm)],[f21]) ).
thf(f21,plain,
! [X10: a,X9: a] :
( ( ( sK4 @ ( cP @ X9 @ X10 ) )
!= $true )
| ( cZ != X10 )
| ( cZ = X9 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f445,plain,
( ~ spl7_3
| spl7_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f444]) ).
thf(f444,plain,
( $false
| ~ spl7_3
| spl7_6 ),
inference(subsumption_resolution,[status(thm)],[f443,f102]) ).
thf(f443,plain,
( ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true )
| spl7_6 ),
inference(trivial_inequality_removal,[status(thm)],[f442]) ).
thf(f442,plain,
( ( $true != $true )
| ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true )
| spl7_6 ),
inference(superposition,[status(thm)],[f311,f24]) ).
thf(f311,plain,
( ( ( sK4 @ ( cP @ ( sK2 @ sK4 ) @ ( sK3 @ sK4 ) ) )
!= $true )
| spl7_6 ),
inference(trivial_inequality_removal,[status(thm)],[f310]) ).
thf(f310,plain,
( ( ( sK4 @ ( cP @ ( sK2 @ sK4 ) @ ( sK3 @ sK4 ) ) )
!= $true )
| ( $true != $true )
| spl7_6 ),
inference(superposition,[status(thm)],[f131,f22]) ).
thf(f131,plain,
( ( ( sK4 @ ( cP @ ( cL @ ( sK2 @ sK4 ) ) @ ( cL @ ( sK3 @ sK4 ) ) ) )
!= $true )
| spl7_6 ),
inference(avatar_component_clause,[status(thm)],[f129]) ).
thf(f129,definition,
( spl7_6
<=> ( ( sK4 @ ( cP @ ( cL @ ( sK2 @ sK4 ) ) @ ( cL @ ( sK3 @ sK4 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_6])],[avatar_definition]) ).
thf(f132,plain,
( ~ spl7_3
| spl7_5
| ~ spl7_6 ),
inference(avatar_split_clause,[status(thm)],[f123,f129,f125,f101]) ).
thf(f123,plain,
( ( ( sK4 @ ( cP @ ( cL @ ( sK2 @ sK4 ) ) @ ( cL @ ( sK3 @ sK4 ) ) ) )
!= $true )
| ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true )
| ( cZ
= ( sK3 @ sK4 ) ) ),
inference(subsumption_resolution,[status(thm)],[f118,f24]) ).
thf(f118,plain,
( ( ( sK4 @ ( cP @ ( sK2 @ sK4 ) @ ( sK3 @ sK4 ) ) )
!= $true )
| ( ( sK4 @ ( cP @ ( cL @ ( sK2 @ sK4 ) ) @ ( cL @ ( sK3 @ sK4 ) ) ) )
!= $true )
| ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true )
| ( cZ
= ( sK3 @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true )
| ( ( sK4 @ ( cP @ ( cL @ ( sK2 @ sK4 ) ) @ ( cL @ ( sK3 @ sK4 ) ) ) )
!= $true )
| ( $true != $true )
| ( cZ
= ( sK3 @ sK4 ) )
| ( ( sK4 @ ( cP @ ( sK2 @ sK4 ) @ ( sK3 @ sK4 ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f26,f20]) ).
thf(f20,plain,
! [X10: a,X9: a] :
( ( ( sK4 @ ( cP @ ( cR @ X9 ) @ ( cR @ X10 ) ) )
= $true )
| ( ( sK4 @ ( cP @ X9 @ X10 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f26,plain,
! [X5: a > $o] :
( ( $true
!= ( X5 @ ( cP @ ( cR @ ( sK2 @ X5 ) ) @ ( cR @ ( sK3 @ X5 ) ) ) ) )
| ( ( X5 @ ( cP @ ( cL @ ( sK2 @ X5 ) ) @ ( cL @ ( sK3 @ X5 ) ) ) )
!= $true )
| ( ( X5 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true )
| ( cZ
= ( sK3 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f108,plain,
( ~ spl7_3
| ~ spl7_4 ),
inference(avatar_split_clause,[status(thm)],[f99,f105,f101]) ).
thf(f99,plain,
( ( cZ
!= ( sK2 @ sK4 ) )
| ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f98,f24]) ).
thf(f98,plain,
( ( cZ
!= ( sK2 @ sK4 ) )
| ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true )
| ( ( sK4 @ ( cP @ ( sK2 @ sK4 ) @ ( sK3 @ sK4 ) ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f86,f22]) ).
thf(f86,plain,
( ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true )
| ( ( sK4 @ ( cP @ ( cL @ ( sK2 @ sK4 ) ) @ ( cL @ ( sK3 @ sK4 ) ) ) )
!= $true )
| ( cZ
!= ( sK2 @ sK4 ) )
| ( ( sK4 @ ( cP @ ( sK2 @ sK4 ) @ ( sK3 @ sK4 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( sK4 @ ( cP @ ( sK2 @ sK4 ) @ ( sK3 @ sK4 ) ) )
!= $true )
| ( ( sK4 @ ( cP @ ( cL @ ( sK2 @ sK4 ) ) @ ( cL @ ( sK3 @ sK4 ) ) ) )
!= $true )
| ( $true != $true )
| ( cZ
!= ( sK2 @ sK4 ) )
| ( ( sK4 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f25,f20]) ).
thf(f25,plain,
! [X5: a > $o] :
( ( $true
!= ( X5 @ ( cP @ ( cR @ ( sK2 @ X5 ) ) @ ( cR @ ( sK3 @ X5 ) ) ) ) )
| ( ( X5 @ ( cP @ ( cL @ sK0 ) @ ( cL @ sK1 ) ) )
!= $true )
| ( ( X5 @ ( cP @ ( cL @ ( sK2 @ X5 ) ) @ ( cL @ ( sK3 @ X5 ) ) ) )
!= $true )
| ( cZ
!= ( sK2 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU975^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:37:51 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU975^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Set Theory (Relations)
% 0.20/0.46 % Problem : TPS problem from COINDUCTIVE-PU-ALG-THMS
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_1184 [Bro09]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.20/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.20/0.46 % Number of atoms : 13 ( 13 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 13 ( 13 avg)
% 0.20/0.46 % Number of connectives : 87 ( 1 ~; 0 |; 13 &; 62 @)
% 0.20/0.46 % ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 18 ( 18 avg)
% 0.20/0.46 % Number of types : 2 ( 1 usr)
% 0.20/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 18 ( 0 ^; 16 !; 2 ?; 18 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(a_type,type,
% 0.20/0.46 a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(cR,type,
% 0.20/0.46 cR: a > a ).
% 0.20/0.46
% 0.20/0.46 thf(cP,type,
% 0.20/0.46 cP: a > a > a ).
% 0.20/0.46
% 0.20/0.46 thf(cL,type,
% 0.20/0.46 cL: a > a ).
% 0.20/0.46
% 0.20/0.46 thf(cZ,type,
% 0.20/0.46 cZ: a ).
% 0.20/0.46
% 0.20/0.46 thf(cPU_LEM2B_pme,conjecture,
% 0.20/0.46 ( ( ( ( cL @ cZ )
% 0.20/0.46 = cZ )
% 0.20/0.46 & ( ( cR @ cZ )
% 0.20/0.46 = cZ )
% 0.20/0.46 & ! [Xx: a,Xy: a] :
% 0.20/0.46 ( ( cL @ ( cP @ Xx @ Xy ) )
% 0.20/0.46 = Xx )
% 0.20/0.46 & ! [Xx: a,Xy: a] :
% 0.20/0.46 ( ( cR @ ( cP @ Xx @ Xy ) )
% 0.20/0.46 = Xy )
% 0.20/0.46 & ! [Xt: a] :
% 0.20/0.46 ( ( Xt != cZ )
% 0.20/0.46 <=> ( Xt
% 0.20/0.46 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
% 0.20/0.46 & ! [X: a > $o] :
% 0.20/0.46 ( ! [Xt: a,Xu: a] :
% 0.20/0.46 ( ( X @ ( cP @ Xt @ Xu ) )
% 0.20/0.46 => ( ( ( Xt = cZ )
% 0.20/0.46 <=> ( Xu = cZ ) )
% 0.20/0.46 & ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
% 0.20/0.46 & ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) )
% 0.20/0.46 => ! [Xt: a,Xu: a] :
% 0.20/0.46 ( ( X @ ( cP @ Xt @ Xu ) )
% 0.20/0.46 => ( Xt = Xu ) ) ) )
% 0.20/0.46 => ! [Xx: a,Xy: a] :
% 0.20/0.46 ( ? [X: a > $o] :
% 0.20/0.46 ( ( X @ ( cP @ Xx @ Xy ) )
% 0.20/0.46 & ! [Xt: a,Xu: a] :
% 0.20/0.46 ( ( X @ ( cP @ Xt @ Xu ) )
% 0.20/0.46 => ( ( ( Xu = cZ )
% 0.20/0.46 => ( Xt = cZ ) )
% 0.20/0.46 & ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
% 0.20/0.46 & ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
% 0.20/0.46 => ? [X: a > $o] :
% 0.20/0.46 ( ( X @ ( cP @ ( cL @ Xx ) @ ( cL @ Xy ) ) )
% 0.20/0.46 & ! [Xt: a,Xu: a] :
% 0.20/0.46 ( ( X @ ( cP @ Xt @ Xu ) )
% 0.20/0.46 => ( ( ( Xu = cZ )
% 0.20/0.46 => ( Xt = cZ ) )
% 0.20/0.46 & ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
% 0.20/0.46 & ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.50/1.26 ---- Embedded in THF ---
% 1.50/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.26 %%% Generated on Tue Feb 24 12:37:52 EST 2026
% 1.50/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.26 %%% Logic specification used:
% 1.50/1.26 %%% thf(spec, logic, $$dhol).
% 1.50/1.26
% 1.50/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.B81vuvfMCe/DTF2DTF11165.p
% See solution above
% 1.50/1.26 ------------------------
% 1.50/1.27 ---- Cleaned THF ---
% 1.50/1.27 thf(a_type,type,
% 1.50/1.27 a: $tType ).
% 1.50/1.27
% 1.50/1.27 thf(cR,type,
% 1.50/1.27 cR: a > a ).
% 1.50/1.27
% 1.50/1.27 thf(cP,type,
% 1.50/1.27 cP: a > a > a ).
% 1.50/1.27
% 1.50/1.27 thf(cL,type,
% 1.50/1.27 cL: a > a ).
% 1.50/1.27
% 1.50/1.27 thf(cZ,type,
% 1.50/1.27 cZ: a ).
% 1.50/1.27
% 1.50/1.27 thf(cPU_LEM2B_pme,conjecture,
% 1.50/1.27 ( ( ( ( cL @ cZ )
% 1.50/1.27 = cZ )
% 1.50/1.27 & ( ( cR @ cZ )
% 1.50/1.27 = cZ )
% 1.50/1.27 & ! [Xx: a,Xy: a] :
% 1.50/1.27 ( ( cL @ ( cP @ Xx @ Xy ) )
% 1.50/1.27 = Xx )
% 1.50/1.27 & ! [Xx: a,Xy: a] :
% 1.50/1.27 ( ( cR @ ( cP @ Xx @ Xy ) )
% 1.50/1.27 = Xy )
% 1.50/1.27 & ! [Xt: a] :
% 1.50/1.27 ( ( Xt != cZ )
% 1.50/1.27 <=> ( Xt
% 1.50/1.27 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
% 1.50/1.27 & ! [X: a > $o] :
% 1.50/1.27 ( ! [Xt: a,Xu: a] :
% 1.50/1.27 ( ( X @ ( cP @ Xt @ Xu ) )
% 1.50/1.27 => ( ( ( Xt = cZ )
% 1.50/1.27 <=> ( Xu = cZ ) )
% 1.50/1.27 & ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
% 1.50/1.27 & ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) )
% 1.50/1.27 => ! [Xt: a,Xu: a] :
% 1.50/1.27 ( ( X @ ( cP @ Xt @ Xu ) )
% 1.50/1.27 => ( Xt = Xu ) ) ) )
% 1.50/1.27 => ! [Xx: a,Xy: a] :
% 1.50/1.27 ( ? [X: a > $o] :
% 1.50/1.27 ( ( X @ ( cP @ Xx @ Xy ) )
% 1.50/1.27 & ! [Xt: a,Xu: a] :
% 1.50/1.27 ( ( X @ ( cP @ Xt @ Xu ) )
% 1.50/1.27 => ( ( ( Xu = cZ )
% 1.50/1.27 => ( Xt = cZ ) )
% 1.50/1.27 & ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
% 1.50/1.27 & ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
% 1.50/1.27 => ? [X: a > $o] :
% 1.50/1.27 ( ( X @ ( cP @ ( cL @ Xx ) @ ( cL @ Xy ) ) )
% 1.50/1.27 & ! [Xt: a,Xu: a] :
% 1.50/1.27 ( ( X @ ( cP @ Xt @ Xu ) )
% 1.50/1.27 => ( ( ( Xu = cZ )
% 1.50/1.27 => ( Xt = cZ ) )
% 1.50/1.27 & ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
% 1.50/1.27 & ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) ) ) ).
% 1.50/1.27 ------------------------
% 1.50/1.29 % (11356)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/2Mi)
% 1.50/1.29 % (11356)Instruction limit reached!
% 1.50/1.29 % (11356)------------------------------
% 1.50/1.29 % (11356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (11356)Termination reason: Unknown
% 1.50/1.29 % (11356)Termination phase: Preprocessing 1
% 1.50/1.29
% 1.50/1.29 % (11356)Memory used [KB]: 895
% 1.50/1.29 % (11356)Time elapsed: 0.002 s
% 1.50/1.29 % (11356)Instructions burned: 2 (million)
% 1.50/1.29 % (11356)------------------------------
% 1.50/1.29 % (11356)------------------------------
% 1.50/1.29 % (11357)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_11165 for (2999ds/2Mi)
% 1.50/1.29 % (11357)Instruction limit reached!
% 1.50/1.29 % (11357)------------------------------
% 1.50/1.29 % (11357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (11357)Termination reason: Unknown
% 1.50/1.29 % (11357)Termination phase: Property scanning
% 1.50/1.29
% 1.50/1.29 % (11357)Memory used [KB]: 1023
% 1.50/1.29 % (11357)Time elapsed: 0.002 s
% 1.50/1.29 % (11357)Instructions burned: 4 (million)
% 1.50/1.29 % (11357)------------------------------
% 1.50/1.29 % (11357)------------------------------
% 1.50/1.29 % (11359)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/18Mi)
% 1.50/1.29 % (11353)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/183Mi)
% 1.50/1.30 % (11354)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_11165 for (2999ds/4Mi)
% 1.69/1.30 % (11355)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_11165 for (2999ds/27Mi)
% 1.69/1.30 % (11354)Instruction limit reached!
% 1.69/1.30 % (11354)------------------------------
% 1.69/1.30 % (11354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (11354)Termination reason: Unknown
% 1.69/1.30 % (11354)Termination phase: Saturation
% 1.69/1.30
% 1.69/1.30 % (11354)Memory used [KB]: 1023
% 1.69/1.30 % (11354)Time elapsed: 0.004 s
% 1.69/1.30 % (11354)Instructions burned: 5 (million)
% 1.69/1.30 % (11354)------------------------------
% 1.69/1.30 % (11354)------------------------------
% 1.69/1.30 % (11358)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_11165 for (2999ds/275Mi)
% 1.69/1.30 % (11360)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/3Mi)
% 1.69/1.30 % (11360)Instruction limit reached!
% 1.69/1.30 % (11360)------------------------------
% 1.69/1.30 % (11360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (11360)Termination reason: Unknown
% 1.69/1.30 % (11360)Termination phase: Property scanning
% 1.69/1.30
% 1.69/1.30 % (11360)Memory used [KB]: 1023
% 1.69/1.30 % (11360)Time elapsed: 0.002 s
% 1.69/1.30 % (11360)Instructions burned: 4 (million)
% 1.69/1.30 % (11360)------------------------------
% 1.69/1.30 % (11360)------------------------------
% 1.69/1.30 % (11361)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_11165 for (2999ds/37Mi)
% 1.69/1.30 % (11359)Instruction limit reached!
% 1.69/1.30 % (11359)------------------------------
% 1.69/1.30 % (11359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (11359)Termination reason: Unknown
% 1.69/1.30 % (11359)Termination phase: Saturation
% 1.69/1.30
% 1.69/1.30 % (11359)Memory used [KB]: 5628
% 1.69/1.30 % (11359)Time elapsed: 0.012 s
% 1.69/1.30 % (11359)Instructions burned: 19 (million)
% 1.69/1.30 % (11359)------------------------------
% 1.69/1.30 % (11359)------------------------------
% 1.69/1.31 % (11363)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_11165 for (2999ds/3Mi)
% 1.69/1.31 % (11363)Instruction limit reached!
% 1.69/1.31 % (11363)------------------------------
% 1.69/1.31 % (11363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (11363)Termination reason: Unknown
% 1.69/1.31 % (11363)Termination phase: Property scanning
% 1.69/1.31
% 1.69/1.31 % (11363)Memory used [KB]: 1023
% 1.69/1.31 % (11363)Time elapsed: 0.002 s
% 1.69/1.31 % (11363)Instructions burned: 4 (million)
% 1.69/1.31 % (11363)------------------------------
% 1.69/1.31 % (11363)------------------------------
% 1.69/1.31 % (11355)Instruction limit reached!
% 1.69/1.31 % (11355)------------------------------
% 1.69/1.31 % (11355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (11355)Termination reason: Unknown
% 1.69/1.31 % (11355)Termination phase: Saturation
% 1.69/1.31
% 1.69/1.31 % (11355)Memory used [KB]: 5628
% 1.69/1.31 % (11355)Time elapsed: 0.020 s
% 1.69/1.31 % (11355)Instructions burned: 28 (million)
% 1.69/1.31 % (11355)------------------------------
% 1.69/1.31 % (11355)------------------------------
% 1.69/1.31 % (11361)Instruction limit reached!
% 1.69/1.31 % (11361)------------------------------
% 1.69/1.31 % (11361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (11361)Termination reason: Unknown
% 1.69/1.31 % (11361)Termination phase: Saturation
% 1.69/1.31
% 1.69/1.31 % (11361)Memory used [KB]: 5628
% 1.69/1.31 % (11361)Time elapsed: 0.014 s
% 1.69/1.31 % (11361)Instructions burned: 38 (million)
% 1.69/1.31 % (11361)------------------------------
% 1.69/1.31 % (11361)------------------------------
% 1.69/1.32 % (11364)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_11165 for (2999ds/1041Mi)
% 1.69/1.32 % (11362)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_11165 for (2999ds/15Mi)
% 1.69/1.32 % (11365)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/7Mi)
% 1.69/1.32 % (11365)Instruction limit reached!
% 1.69/1.32 % (11365)------------------------------
% 1.69/1.32 % (11365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (11365)Termination reason: Unknown
% 1.69/1.32 % (11365)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (11365)Memory used [KB]: 1023
% 1.69/1.32 % (11365)Time elapsed: 0.003 s
% 1.69/1.32 % (11365)Instructions burned: 7 (million)
% 1.69/1.32 % (11365)------------------------------
% 1.69/1.32 % (11365)------------------------------
% 1.69/1.32 % (11366)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/16Mi)
% 1.69/1.33 % (11362)Instruction limit reached!
% 1.69/1.33 % (11362)------------------------------
% 1.69/1.33 % (11362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (11362)Termination reason: Unknown
% 1.69/1.33 % (11362)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (11362)Memory used [KB]: 5628
% 1.69/1.33 % (11362)Time elapsed: 0.011 s
% 1.69/1.33 % (11362)Instructions burned: 15 (million)
% 1.69/1.33 % (11362)------------------------------
% 1.69/1.33 % (11362)------------------------------
% 1.69/1.33 % (11366)Instruction limit reached!
% 1.69/1.33 % (11366)------------------------------
% 1.69/1.33 % (11366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (11366)Termination reason: Unknown
% 1.69/1.33 % (11366)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (11366)Memory used [KB]: 5628
% 1.69/1.33 % (11366)Time elapsed: 0.008 s
% 1.69/1.33 % (11366)Instructions burned: 18 (million)
% 1.69/1.33 % (11366)------------------------------
% 1.69/1.33 % (11366)------------------------------
% 1.69/1.33 % (11367)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_11165 for (2999ds/3Mi)
% 1.69/1.33 % (11368)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/3Mi)
% 1.69/1.33 % (11367)Instruction limit reached!
% 1.69/1.33 % (11367)------------------------------
% 1.69/1.33 % (11367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (11367)Termination reason: Unknown
% 1.69/1.33 % (11367)Termination phase: Property scanning
% 1.69/1.33
% 1.69/1.33 % (11367)Memory used [KB]: 1023
% 1.69/1.33 % (11367)Time elapsed: 0.004 s
% 1.69/1.33 % (11367)Instructions burned: 3 (million)
% 1.69/1.33 % (11367)------------------------------
% 1.69/1.33 % (11367)------------------------------
% 1.69/1.33 % (11368)Instruction limit reached!
% 1.69/1.33 % (11368)------------------------------
% 1.69/1.33 % (11368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (11368)Termination reason: Unknown
% 1.69/1.33 % (11368)Termination phase: Property scanning
% 1.69/1.33
% 1.69/1.33 % (11368)Memory used [KB]: 1023
% 1.69/1.33 % (11368)Time elapsed: 0.002 s
% 1.69/1.33 % (11368)Instructions burned: 4 (million)
% 1.69/1.33 % (11368)------------------------------
% 1.69/1.33 % (11368)------------------------------
% 1.69/1.34 % (11370)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/3Mi)
% 1.69/1.34 % (11370)Instruction limit reached!
% 1.69/1.34 % (11370)------------------------------
% 1.69/1.34 % (11370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (11370)Termination reason: Unknown
% 1.69/1.34 % (11370)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (11370)Memory used [KB]: 1023
% 1.69/1.34 % (11370)Time elapsed: 0.003 s
% 1.69/1.34 % (11370)Instructions burned: 4 (million)
% 1.69/1.34 % (11370)------------------------------
% 1.69/1.34 % (11370)------------------------------
% 1.69/1.34 % (11369)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/7Mi)
% 1.69/1.34 % (11372)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/18Mi)
% 1.69/1.35 % (11369)Instruction limit reached!
% 1.69/1.35 % (11369)------------------------------
% 1.69/1.35 % (11369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (11369)Termination reason: Unknown
% 1.69/1.35 % (11369)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (11369)Memory used [KB]: 5500
% 1.69/1.35 % (11369)Time elapsed: 0.006 s
% 1.69/1.35 % (11369)Instructions burned: 8 (million)
% 1.69/1.35 % (11369)------------------------------
% 1.69/1.35 % (11369)------------------------------
% 1.69/1.35 % (11372)Instruction limit reached!
% 1.69/1.35 % (11372)------------------------------
% 1.69/1.35 % (11372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (11372)Termination reason: Unknown
% 1.69/1.35 % (11372)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (11372)Memory used [KB]: 5628
% 1.69/1.35 % (11372)Time elapsed: 0.007 s
% 1.69/1.35 % (11372)Instructions burned: 19 (million)
% 1.69/1.35 % (11372)------------------------------
% 1.69/1.35 % (11372)------------------------------
% 1.69/1.35 % (11371)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/4Mi)
% 1.69/1.35 % (11371)Instruction limit reached!
% 1.69/1.35 % (11371)------------------------------
% 1.69/1.35 % (11371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (11371)Termination reason: Unknown
% 1.69/1.35 % (11371)Termination phase: Property scanning
% 1.69/1.35
% 1.69/1.35 % (11371)Memory used [KB]: 1023
% 1.69/1.35 % (11371)Time elapsed: 0.004 s
% 1.69/1.35 % (11371)Instructions burned: 4 (million)
% 1.69/1.35 % (11371)------------------------------
% 1.69/1.35 % (11371)------------------------------
% 1.69/1.35 % (11373)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/710Mi)
% 1.69/1.36 % (11375)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/902Mi)
% 1.69/1.36 % (11374)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/6Mi)
% 1.69/1.37 % (11374)Instruction limit reached!
% 1.69/1.37 % (11374)------------------------------
% 1.69/1.37 % (11374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (11374)Termination reason: Unknown
% 1.69/1.37 % (11374)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (11374)Memory used [KB]: 5500
% 1.69/1.37 % (11374)Time elapsed: 0.004 s
% 1.69/1.37 % (11374)Instructions burned: 6 (million)
% 1.69/1.37 % (11374)------------------------------
% 1.69/1.37 % (11374)------------------------------
% 1.69/1.37 % (11358)First to succeed.
% 1.69/1.37 % (11353)Instruction limit reached!
% 1.69/1.37 % (11353)------------------------------
% 1.69/1.37 % (11353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (11353)Termination reason: Unknown
% 1.69/1.37 % (11353)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (11353)Memory used [KB]: 6524
% 1.69/1.37 % (11353)Time elapsed: 0.078 s
% 1.69/1.37 % (11353)Instructions burned: 183 (million)
% 1.69/1.37 % (11353)------------------------------
% 1.69/1.37 % (11353)------------------------------
% 1.69/1.37 % (11376)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_11165 for (2999ds/21Mi)
% 1.69/1.37 % (11358)Refutation found. Thanks to Tanya!
% 1.69/1.37 % SZS status Theorem for DTF2THF_11165
% 1.69/1.37 % SZS output start Proof for DTF2THF_11165
% 1.69/1.37 thf(type_def_5, type, a: $tType).
% 1.69/1.37 thf(func_def_0, type, a: $tType).
% 1.69/1.37 thf(func_def_1, type, cR: a > a).
% 1.69/1.37 thf(func_def_2, type, cP: a > a > a).
% 1.69/1.37 thf(func_def_3, type, cL: a > a).
% 1.69/1.37 thf(func_def_4, type, cZ: a).
% 1.69/1.37 thf(func_def_8, type, sK0: a).
% 1.69/1.37 thf(func_def_9, type, sK1: a).
% 1.69/1.37 thf(func_def_10, type, sK2: (a > $o) > a).
% 1.69/1.37 thf(func_def_11, type, sK3: (a > $o) > a).
% 1.69/1.37 thf(func_def_12, type, sK4: a > $o).
% 1.69/1.37 thf(func_def_13, type, sK5: (a > $o) > a).
% 1.69/1.37 thf(func_def_14, type, sK6: (a > $o) > a).
% 1.69/1.37 thf(func_def_17, type, ph8: !>[X0: $tType]:(X0)).
% 1.69/1.37 thf(f478,plain,(
% 1.69/1.37 $false),
% 1.69/1.37 inference(avatar_sat_refutation,[status(thm)],[f108,f132,f445,f469,f477])).
% 1.69/1.37 thf(f477,plain,(
% 1.69/1.37 spl7_3),
% 1.69/1.37 inference(avatar_contradiction_clause,[status(thm)],[f476])).
% 1.69/1.37 thf(f476,plain,(
% 1.69/1.37 $false | spl7_3),
% 1.69/1.37 inference(subsumption_resolution,[status(thm)],[f475,f23])).
% 1.69/1.37 thf(f23,plain,(
% 1.69/1.37 ((sK4 @ (cP @ sK0 @ sK1)) = $true)),
% 1.69/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.37 thf(f14,plain,(
% 1.69/1.37 ! [X0 : a] : (((cZ != X0) | ((cP @ (cL @ X0) @ (cR @ X0)) != X0)) & (((cP @ (cL @ X0) @ (cR @ X0)) = X0) | (cZ = X0))) & (cZ = (cL @ cZ)) & ! [X1 : a,X2 : a] : ((cL @ (cP @ X1 @ X2)) = X1) & (! [X5 : a > $o] : (((((X5 @ (cP @ (cL @ (sK2 @ X5)) @ (cL @ (sK3 @ X5)))) != $true) | ($true != (X5 @ (cP @ (cR @ (sK2 @ X5)) @ (cR @ (sK3 @ X5))))) | ((cZ = (sK3 @ X5)) & (cZ != (sK2 @ X5)))) & ((X5 @ (cP @ (sK2 @ X5) @ (sK3 @ X5))) = $true)) | ((X5 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true)) & (((sK4 @ (cP @ sK0 @ sK1)) = $true) & ! [X9 : a,X10 : a] : (((sK4 @ (cP @ X9 @ X10)) != $true) | (((sK4 @ (cP @ (cL @ X9) @ (cL @ X10))) = $true) & ((cZ != X10) | (cZ = X9)) & ((sK4 @ (cP @ (cR @ X9) @ (cR @ X10))) = $true))))) & ! [X11 : a > $o] : ((((X11 @ (cP @ (sK6 @ X11) @ (sK5 @ X11))) = $true) & (((X11 @ (cP @ (cL @ (sK6 @ X11)) @ (cL @ (sK5 @ X11)))) != $true) | ((X11 @ (cP @ (cR @ (sK6 @ X11)) @ (cR @ (sK5 @ X11)))) != $true) | (((cZ != (sK6 @ X11)) | (cZ != (sK5 @ X11))) & ((cZ = (sK6 @ X11)) | (cZ = (sK5 @ X11)))))) | ! [X14 : a,X15 : a] : (((X11 @ (cP @ X14 @ X15)) != $true) | (X14 = X15))) & (cZ = (cR @ cZ)) & ! [X16 : a,X17 : a] : ((cR @ (cP @ X16 @ X17)) = X17)),
% 1.69/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f9,f13,f12,f11,f10])).
% 1.69/1.37 thf(f10,plain,(
% 1.69/1.37 ? [X3 : a,X4 : a] : (! [X5 : a > $o] : (? [X6 : a,X7 : a] : ((((X5 @ (cP @ (cL @ X6) @ (cL @ X7))) != $true) | ((X5 @ (cP @ (cR @ X6) @ (cR @ X7))) != $true) | ((cZ = X7) & (cZ != X6))) & ((X5 @ (cP @ X6 @ X7)) = $true)) | ((X5 @ (cP @ (cL @ X3) @ (cL @ X4))) != $true)) & ? [X8 : a > $o] : (((X8 @ (cP @ X3 @ X4)) = $true) & ! [X9 : a,X10 : a] : (((X8 @ (cP @ X9 @ X10)) != $true) | (((X8 @ (cP @ (cL @ X9) @ (cL @ X10))) = $true) & ((cZ != X10) | (cZ = X9)) & ((X8 @ (cP @ (cR @ X9) @ (cR @ X10))) = $true))))) => (! [X5 : a > $o] : (? [X6 : a,X7 : a] : ((((X5 @ (cP @ (cL @ X6) @ (cL @ X7))) != $true) | ((X5 @ (cP @ (cR @ X6) @ (cR @ X7))) != $true) | ((cZ = X7) & (cZ != X6))) & ((X5 @ (cP @ X6 @ X7)) = $true)) | ((X5 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true)) & ? [X8 : a > $o] : (($true = (X8 @ (cP @ sK0 @ sK1))) & ! [X9 : a,X10 : a] : (((X8 @ (cP @ X9 @ X10)) != $true) | (((X8 @ (cP @ (cL @ X9) @ (cL @ X10))) = $true) & ((cZ != X10) | (cZ = X9)) & ((X8 @ (cP @ (cR @ X9) @ (cR @ X10))) = $true)))))),
% 1.69/1.37 introduced(definition,[],[choice_axiom])).
% 1.69/1.37 thf(f11,plain,(
% 1.69/1.37 ! [X5 : a > $o] : (? [X6 : a,X7 : a] : ((((X5 @ (cP @ (cL @ X6) @ (cL @ X7))) != $true) | ((X5 @ (cP @ (cR @ X6) @ (cR @ X7))) != $true) | ((cZ = X7) & (cZ != X6))) & ((X5 @ (cP @ X6 @ X7)) = $true)) => ((((X5 @ (cP @ (cL @ (sK2 @ X5)) @ (cL @ (sK3 @ X5)))) != $true) | ($true != (X5 @ (cP @ (cR @ (sK2 @ X5)) @ (cR @ (sK3 @ X5))))) | ((cZ = (sK3 @ X5)) & (cZ != (sK2 @ X5)))) & ((X5 @ (cP @ (sK2 @ X5) @ (sK3 @ X5))) = $true)))),
% 1.69/1.37 introduced(definition,[],[choice_axiom])).
% 1.69/1.37 thf(f12,plain,(
% 1.69/1.37 ? [X8 : a > $o] : (($true = (X8 @ (cP @ sK0 @ sK1))) & ! [X9 : a,X10 : a] : (((X8 @ (cP @ X9 @ X10)) != $true) | (((X8 @ (cP @ (cL @ X9) @ (cL @ X10))) = $true) & ((cZ != X10) | (cZ = X9)) & ((X8 @ (cP @ (cR @ X9) @ (cR @ X10))) = $true)))) => (((sK4 @ (cP @ sK0 @ sK1)) = $true) & ! [X10 : a,X9 : a] : (((sK4 @ (cP @ X9 @ X10)) != $true) | (((sK4 @ (cP @ (cL @ X9) @ (cL @ X10))) = $true) & ((cZ != X10) | (cZ = X9)) & ((sK4 @ (cP @ (cR @ X9) @ (cR @ X10))) = $true))))),
% 1.69/1.37 introduced(definition,[],[choice_axiom])).
% 1.69/1.37 thf(f13,plain,(
% 1.69/1.37 ! [X11 : a > $o] : (? [X12 : a,X13 : a] : (((X11 @ (cP @ X13 @ X12)) = $true) & (((X11 @ (cP @ (cL @ X13) @ (cL @ X12))) != $true) | ((X11 @ (cP @ (cR @ X13) @ (cR @ X12))) != $true) | (((cZ != X13) | (cZ != X12)) & ((cZ = X13) | (cZ = X12))))) => (((X11 @ (cP @ (sK6 @ X11) @ (sK5 @ X11))) = $true) & (((X11 @ (cP @ (cL @ (sK6 @ X11)) @ (cL @ (sK5 @ X11)))) != $true) | ((X11 @ (cP @ (cR @ (sK6 @ X11)) @ (cR @ (sK5 @ X11)))) != $true) | (((cZ != (sK6 @ X11)) | (cZ != (sK5 @ X11))) & ((cZ = (sK6 @ X11)) | (cZ = (sK5 @ X11)))))))),
% 1.69/1.37 introduced(definition,[],[choice_axiom])).
% 1.69/1.37 thf(f9,plain,(
% 1.69/1.37 ! [X0 : a] : (((cZ != X0) | ((cP @ (cL @ X0) @ (cR @ X0)) != X0)) & (((cP @ (cL @ X0) @ (cR @ X0)) = X0) | (cZ = X0))) & (cZ = (cL @ cZ)) & ! [X1 : a,X2 : a] : ((cL @ (cP @ X1 @ X2)) = X1) & ? [X3 : a,X4 : a] : (! [X5 : a > $o] : (? [X6 : a,X7 : a] : ((((X5 @ (cP @ (cL @ X6) @ (cL @ X7))) != $true) | ((X5 @ (cP @ (cR @ X6) @ (cR @ X7))) != $true) | ((cZ = X7) & (cZ != X6))) & ((X5 @ (cP @ X6 @ X7)) = $true)) | ((X5 @ (cP @ (cL @ X3) @ (cL @ X4))) != $true)) & ? [X8 : a > $o] : (((X8 @ (cP @ X3 @ X4)) = $true) & ! [X9 : a,X10 : a] : (((X8 @ (cP @ X9 @ X10)) != $true) | (((X8 @ (cP @ (cL @ X9) @ (cL @ X10))) = $true) & ((cZ != X10) | (cZ = X9)) & ((X8 @ (cP @ (cR @ X9) @ (cR @ X10))) = $true))))) & ! [X11 : a > $o] : (? [X12 : a,X13 : a] : (((X11 @ (cP @ X13 @ X12)) = $true) & (((X11 @ (cP @ (cL @ X13) @ (cL @ X12))) != $true) | ((X11 @ (cP @ (cR @ X13) @ (cR @ X12))) != $true) | (((cZ != X13) | (cZ != X12)) & ((cZ = X13) | (cZ = X12))))) | ! [X14 : a,X15 : a] : (((X11 @ (cP @ X14 @ X15)) != $true) | (X14 = X15))) & (cZ = (cR @ cZ)) & ! [X16 : a,X17 : a] : ((cR @ (cP @ X16 @ X17)) = X17)),
% 1.69/1.37 inference(rectify,[status(thm)],[f8])).
% 1.69/1.37 thf(f8,plain,(
% 1.69/1.37 ! [X9 : a] : (((cZ != X9) | ((cP @ (cL @ X9) @ (cR @ X9)) != X9)) & (((cP @ (cL @ X9) @ (cR @ X9)) = X9) | (cZ = X9))) & (cZ = (cL @ cZ)) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & ? [X10 : a,X11 : a] : (! [X15 : a > $o] : (? [X17 : a,X16 : a] : ((($true != (X15 @ (cP @ (cL @ X17) @ (cL @ X16)))) | ((X15 @ (cP @ (cR @ X17) @ (cR @ X16))) != $true) | ((cZ = X16) & (cZ != X17))) & ((X15 @ (cP @ X17 @ X16)) = $true)) | ((X15 @ (cP @ (cL @ X10) @ (cL @ X11))) != $true)) & ? [X12 : a > $o] : (($true = (X12 @ (cP @ X10 @ X11))) & ! [X14 : a,X13 : a] : (((X12 @ (cP @ X14 @ X13)) != $true) | (((X12 @ (cP @ (cL @ X14) @ (cL @ X13))) = $true) & ((cZ != X13) | (cZ = X14)) & ($true = (X12 @ (cP @ (cR @ X14) @ (cR @ X13)))))))) & ! [X2 : a > $o] : (? [X3 : a,X4 : a] : (((X2 @ (cP @ X4 @ X3)) = $true) & (($true != (X2 @ (cP @ (cL @ X4) @ (cL @ X3)))) | ((X2 @ (cP @ (cR @ X4) @ (cR @ X3))) != $true) | (((cZ != X4) | (cZ != X3)) & ((cZ = X4) | (cZ = X3))))) | ! [X6 : a,X5 : a] : (((X2 @ (cP @ X6 @ X5)) != $true) | (X5 = X6))) & (cZ = (cR @ cZ)) & ! [X8 : a,X7 : a] : ((cR @ (cP @ X8 @ X7)) = X7)),
% 1.69/1.37 inference(nnf_transformation,[status(thm)],[f7])).
% 1.69/1.37 thf(f7,plain,(
% 1.69/1.37 ! [X9 : a] : ((cZ != X9) <=> ((cP @ (cL @ X9) @ (cR @ X9)) = X9)) & (cZ = (cL @ cZ)) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & ? [X10 : a,X11 : a] : (! [X15 : a > $o] : (? [X17 : a,X16 : a] : ((($true != (X15 @ (cP @ (cL @ X17) @ (cL @ X16)))) | ((X15 @ (cP @ (cR @ X17) @ (cR @ X16))) != $true) | ((cZ = X16) & (cZ != X17))) & ((X15 @ (cP @ X17 @ X16)) = $true)) | ((X15 @ (cP @ (cL @ X10) @ (cL @ X11))) != $true)) & ? [X12 : a > $o] : (($true = (X12 @ (cP @ X10 @ X11))) & ! [X14 : a,X13 : a] : (((X12 @ (cP @ X14 @ X13)) != $true) | (((X12 @ (cP @ (cL @ X14) @ (cL @ X13))) = $true) & ((cZ != X13) | (cZ = X14)) & ($true = (X12 @ (cP @ (cR @ X14) @ (cR @ X13)))))))) & ! [X2 : a > $o] : (? [X3 : a,X4 : a] : (((X2 @ (cP @ X4 @ X3)) = $true) & (($true != (X2 @ (cP @ (cL @ X4) @ (cL @ X3)))) | ((X2 @ (cP @ (cR @ X4) @ (cR @ X3))) != $true) | ((cZ = X3) <~> (cZ = X4)))) | ! [X6 : a,X5 : a] : (((X2 @ (cP @ X6 @ X5)) != $true) | (X5 = X6))) & (cZ = (cR @ cZ)) & ! [X8 : a,X7 : a] : ((cR @ (cP @ X8 @ X7)) = X7)),
% 1.69/1.37 inference(flattening,[status(thm)],[f6])).
% 1.69/1.37 thf(f6,plain,(
% 1.69/1.37 ? [X10 : a,X11 : a] : (! [X15 : a > $o] : (? [X17 : a,X16 : a] : ((($true != (X15 @ (cP @ (cL @ X17) @ (cL @ X16)))) | ((X15 @ (cP @ (cR @ X17) @ (cR @ X16))) != $true) | ((cZ = X16) & (cZ != X17))) & ((X15 @ (cP @ X17 @ X16)) = $true)) | ((X15 @ (cP @ (cL @ X10) @ (cL @ X11))) != $true)) & ? [X12 : a > $o] : (($true = (X12 @ (cP @ X10 @ X11))) & ! [X14 : a,X13 : a] : (((X12 @ (cP @ X14 @ X13)) != $true) | (((X12 @ (cP @ (cL @ X14) @ (cL @ X13))) = $true) & ((cZ != X13) | (cZ = X14)) & ($true = (X12 @ (cP @ (cR @ X14) @ (cR @ X13)))))))) & (! [X8 : a,X7 : a] : ((cR @ (cP @ X8 @ X7)) = X7) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & (cZ = (cL @ cZ)) & (cZ = (cR @ cZ)) & ! [X9 : a] : ((cZ != X9) <=> ((cP @ (cL @ X9) @ (cR @ X9)) = X9)) & ! [X2 : a > $o] : (? [X3 : a,X4 : a] : (((X2 @ (cP @ X4 @ X3)) = $true) & (($true != (X2 @ (cP @ (cL @ X4) @ (cL @ X3)))) | ((X2 @ (cP @ (cR @ X4) @ (cR @ X3))) != $true) | ((cZ = X3) <~> (cZ = X4)))) | ! [X6 : a,X5 : a] : (((X2 @ (cP @ X6 @ X5)) != $true) | (X5 = X6))))),
% 1.69/1.37 inference(ennf_transformation,[status(thm)],[f5])).
% 1.69/1.37 thf(f5,plain,(
% 1.69/1.37 ~((! [X8 : a,X7 : a] : ((cR @ (cP @ X8 @ X7)) = X7) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & (cZ = (cL @ cZ)) & (cZ = (cR @ cZ)) & ! [X9 : a] : ((cZ != X9) <=> ((cP @ (cL @ X9) @ (cR @ X9)) = X9)) & ! [X2 : a > $o] : (! [X4 : a,X3 : a] : (((X2 @ (cP @ X4 @ X3)) = $true) => (($true = (X2 @ (cP @ (cL @ X4) @ (cL @ X3)))) & ((cZ = X4) <=> (cZ = X3)) & ((X2 @ (cP @ (cR @ X4) @ (cR @ X3))) = $true))) => ! [X5 : a,X6 : a] : (((X2 @ (cP @ X6 @ X5)) = $true) => (X5 = X6)))) => ! [X11 : a,X10 : a] : (? [X12 : a > $o] : (! [X13 : a,X14 : a] : (((X12 @ (cP @ X14 @ X13)) = $true) => (((cZ = X13) => (cZ = X14)) & ($true = (X12 @ (cP @ (cR @ X14) @ (cR @ X13)))) & ((X12 @ (cP @ (cL @ X14) @ (cL @ X13))) = $true))) & ($true = (X12 @ (cP @ X10 @ X11)))) => ? [X15 : a > $o] : (! [X16 : a,X17 : a] : (((X15 @ (cP @ X17 @ X16)) = $true) => (((cZ = X16) => (cZ = X17)) & ((X15 @ (cP @ (cR @ X17) @ (cR @ X16))) = $true) & ($true = (X15 @ (cP @ (cL @ X17) @ (cL @ X16)))))) & ((X15 @ (cP @ (cL @ X10) @ (cL @ X11))) = $true))))),
% 1.69/1.37 inference(fool_elimination,[status(thm)],[f4])).
% 1.69/1.37 thf(f4,plain,(
% 1.69/1.37 ~((! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & ! [X2 : a > $o] : (! [X3 : a,X4 : a] : ((X2 @ (cP @ X4 @ X3)) => ((X2 @ (cP @ (cR @ X4) @ (cR @ X3))) & ((cZ = X3) <=> (cZ = X4)) & (X2 @ (cP @ (cL @ X4) @ (cL @ X3))))) => ! [X5 : a,X6 : a] : ((X2 @ (cP @ X6 @ X5)) => (X5 = X6))) & (cZ = (cL @ cZ)) & ! [X7 : a,X8 : a] : ((cR @ (cP @ X8 @ X7)) = X7) & (cZ = (cR @ cZ)) & ! [X9 : a] : (((cP @ (cL @ X9) @ (cR @ X9)) = X9) <=> (cZ != X9))) => ! [X10 : a,X11 : a] : (? [X12 : a > $o] : (! [X13 : a,X14 : a] : ((X12 @ (cP @ X14 @ X13)) => ((X12 @ (cP @ (cR @ X14) @ (cR @ X13))) & ((cZ = X13) => (cZ = X14)) & (X12 @ (cP @ (cL @ X14) @ (cL @ X13))))) & (X12 @ (cP @ X10 @ X11))) => ? [X15 : a > $o] : (! [X16 : a,X17 : a] : ((X15 @ (cP @ X17 @ X16)) => (((cZ = X16) => (cZ = X17)) & (X15 @ (cP @ (cR @ X17) @ (cR @ X16))) & (X15 @ (cP @ (cL @ X17) @ (cL @ X16))))) & (X15 @ (cP @ (cL @ X10) @ (cL @ X11))))))),
% 1.69/1.37 inference(rectify,[status(thm)],[f2])).
% 1.69/1.37 thf(f2,negated_conjecture,(
% 1.69/1.37 ~((! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & ! [X3 : a > $o] : (! [X4 : a,X2 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & ((cZ = X4) <=> (cZ = X2)) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))))) => ! [X4 : a,X2 : a] : ((X3 @ (cP @ X2 @ X4)) => (X2 = X4))) & (cZ = (cL @ cZ)) & ! [X1 : a,X0 : a] : ((cR @ (cP @ X0 @ X1)) = X1) & (cZ = (cR @ cZ)) & ! [X2 : a] : (((cP @ (cL @ X2) @ (cR @ X2)) = X2) <=> (cZ != X2))) => ! [X0 : a,X1 : a] : (? [X3 : a > $o] : (! [X4 : a,X2 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & ((cZ = X4) => (cZ = X2)) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))))) & (X3 @ (cP @ X0 @ X1))) => ? [X3 : a > $o] : (! [X4 : a,X2 : a] : ((X3 @ (cP @ X2 @ X4)) => (((cZ = X4) => (cZ = X2)) & (X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))))) & (X3 @ (cP @ (cL @ X0) @ (cL @ X1))))))),
% 1.69/1.37 inference(negated_conjecture,[status(cth)],[f1])).
% 1.69/1.37 thf(f1,conjecture,(
% 1.69/1.37 (! [X0 : a,X1 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & ! [X3 : a > $o] : (! [X4 : a,X2 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & ((cZ = X4) <=> (cZ = X2)) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))))) => ! [X4 : a,X2 : a] : ((X3 @ (cP @ X2 @ X4)) => (X2 = X4))) & (cZ = (cL @ cZ)) & ! [X1 : a,X0 : a] : ((cR @ (cP @ X0 @ X1)) = X1) & (cZ = (cR @ cZ)) & ! [X2 : a] : (((cP @ (cL @ X2) @ (cR @ X2)) = X2) <=> (cZ != X2))) => ! [X0 : a,X1 : a] : (? [X3 : a > $o] : (! [X4 : a,X2 : a] : ((X3 @ (cP @ X2 @ X4)) => ((X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & ((cZ = X4) => (cZ = X2)) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))))) & (X3 @ (cP @ X0 @ X1))) => ? [X3 : a > $o] : (! [X4 : a,X2 : a] : ((X3 @ (cP @ X2 @ X4)) => (((cZ = X4) => (cZ = X2)) & (X3 @ (cP @ (cR @ X2) @ (cR @ X4))) & (X3 @ (cP @ (cL @ X2) @ (cL @ X4))))) & (X3 @ (cP @ (cL @ X0) @ (cL @ X1)))))),
% 1.69/1.37 file('/export/starexec/sandbox/tmp/tmp.B81vuvfMCe/DTF2THF_11165.p',cPU_LEM2B_pme)).
% 1.69/1.37 thf(f475,plain,(
% 1.69/1.37 ((sK4 @ (cP @ sK0 @ sK1)) != $true) | spl7_3),
% 1.69/1.37 inference(trivial_inequality_removal,[status(thm)],[f474])).
% 1.69/1.37 thf(f474,plain,(
% 1.69/1.37 ((sK4 @ (cP @ sK0 @ sK1)) != $true) | ($true != $true) | spl7_3),
% 1.69/1.37 inference(superposition,[status(thm)],[f103,f22])).
% 1.69/1.37 thf(f22,plain,(
% 1.69/1.37 ( ! [X10 : a,X9 : a] : (((sK4 @ (cP @ (cL @ X9) @ (cL @ X10))) = $true) | ((sK4 @ (cP @ X9 @ X10)) != $true)) )),
% 1.69/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.37 thf(f103,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true) | spl7_3),
% 1.69/1.37 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.69/1.37 thf(f101,definition,(
% 1.69/1.37 spl7_3 <=> ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) = $true)),
% 1.69/1.37 introduced(definition,[new_symbols(naming,[spl7_3])],[avatar_definition])).
% 1.69/1.37 thf(f469,plain,(
% 1.69/1.37 ~spl7_3 | spl7_4 | ~spl7_5),
% 1.69/1.37 inference(avatar_contradiction_clause,[status(thm)],[f468])).
% 1.69/1.37 thf(f468,plain,(
% 1.69/1.37 $false | (~spl7_3 | spl7_4 | ~spl7_5)),
% 1.69/1.37 inference(subsumption_resolution,[status(thm)],[f462,f107])).
% 1.69/1.37 thf(f107,plain,(
% 1.69/1.37 (cZ != (sK2 @ sK4)) | spl7_4),
% 1.69/1.37 inference(avatar_component_clause,[status(thm)],[f105])).
% 1.69/1.37 thf(f105,definition,(
% 1.69/1.37 spl7_4 <=> (cZ = (sK2 @ sK4))),
% 1.69/1.37 introduced(definition,[new_symbols(naming,[spl7_4])],[avatar_definition])).
% 1.69/1.37 thf(f462,plain,(
% 1.69/1.37 (cZ = (sK2 @ sK4)) | (~spl7_3 | ~spl7_5)),
% 1.69/1.37 inference(trivial_inequality_removal,[status(thm)],[f451])).
% 1.69/1.37 thf(f451,plain,(
% 1.69/1.37 (cZ = (sK2 @ sK4)) | ($true != $true) | (~spl7_3 | ~spl7_5)),
% 1.69/1.37 inference(superposition,[status(thm)],[f32,f450])).
% 1.69/1.37 thf(f450,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (sK2 @ sK4) @ cZ)) = $true) | (~spl7_3 | ~spl7_5)),
% 1.69/1.37 inference(subsumption_resolution,[status(thm)],[f448,f102])).
% 1.69/1.37 thf(f102,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) = $true) | ~spl7_3),
% 1.69/1.37 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.69/1.37 thf(f448,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true) | ((sK4 @ (cP @ (sK2 @ sK4) @ cZ)) = $true) | ~spl7_5),
% 1.69/1.37 inference(superposition,[status(thm)],[f24,f127])).
% 1.69/1.37 thf(f127,plain,(
% 1.69/1.37 (cZ = (sK3 @ sK4)) | ~spl7_5),
% 1.69/1.37 inference(avatar_component_clause,[status(thm)],[f125])).
% 1.69/1.37 thf(f125,definition,(
% 1.69/1.37 spl7_5 <=> (cZ = (sK3 @ sK4))),
% 1.69/1.37 introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition])).
% 1.69/1.37 thf(f24,plain,(
% 1.69/1.37 ( ! [X5 : a > $o] : (((X5 @ (cP @ (sK2 @ X5) @ (sK3 @ X5))) = $true) | ((X5 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true)) )),
% 1.69/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.37 thf(f32,plain,(
% 1.69/1.37 ( ! [X9 : a] : (((sK4 @ (cP @ X9 @ cZ)) != $true) | (cZ = X9)) )),
% 1.69/1.37 inference(equality_resolution,[status(thm)],[f21])).
% 1.69/1.37 thf(f21,plain,(
% 1.69/1.37 ( ! [X10 : a,X9 : a] : (((sK4 @ (cP @ X9 @ X10)) != $true) | (cZ != X10) | (cZ = X9)) )),
% 1.69/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.37 thf(f445,plain,(
% 1.69/1.37 ~spl7_3 | spl7_6),
% 1.69/1.37 inference(avatar_contradiction_clause,[status(thm)],[f444])).
% 1.69/1.37 thf(f444,plain,(
% 1.69/1.37 $false | (~spl7_3 | spl7_6)),
% 1.69/1.37 inference(subsumption_resolution,[status(thm)],[f443,f102])).
% 1.69/1.37 thf(f443,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true) | spl7_6),
% 1.69/1.37 inference(trivial_inequality_removal,[status(thm)],[f442])).
% 1.69/1.37 thf(f442,plain,(
% 1.69/1.37 ($true != $true) | ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true) | spl7_6),
% 1.69/1.37 inference(superposition,[status(thm)],[f311,f24])).
% 1.69/1.37 thf(f311,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (sK2 @ sK4) @ (sK3 @ sK4))) != $true) | spl7_6),
% 1.69/1.37 inference(trivial_inequality_removal,[status(thm)],[f310])).
% 1.69/1.37 thf(f310,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (sK2 @ sK4) @ (sK3 @ sK4))) != $true) | ($true != $true) | spl7_6),
% 1.69/1.37 inference(superposition,[status(thm)],[f131,f22])).
% 1.69/1.37 thf(f131,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (cL @ (sK2 @ sK4)) @ (cL @ (sK3 @ sK4)))) != $true) | spl7_6),
% 1.69/1.37 inference(avatar_component_clause,[status(thm)],[f129])).
% 1.69/1.37 thf(f129,definition,(
% 1.69/1.37 spl7_6 <=> ((sK4 @ (cP @ (cL @ (sK2 @ sK4)) @ (cL @ (sK3 @ sK4)))) = $true)),
% 1.69/1.37 introduced(definition,[new_symbols(naming,[spl7_6])],[avatar_definition])).
% 1.69/1.37 thf(f132,plain,(
% 1.69/1.37 ~spl7_3 | spl7_5 | ~spl7_6),
% 1.69/1.37 inference(avatar_split_clause,[status(thm)],[f123,f129,f125,f101])).
% 1.69/1.37 thf(f123,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (cL @ (sK2 @ sK4)) @ (cL @ (sK3 @ sK4)))) != $true) | ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true) | (cZ = (sK3 @ sK4))),
% 1.69/1.37 inference(subsumption_resolution,[status(thm)],[f118,f24])).
% 1.69/1.37 thf(f118,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (sK2 @ sK4) @ (sK3 @ sK4))) != $true) | ((sK4 @ (cP @ (cL @ (sK2 @ sK4)) @ (cL @ (sK3 @ sK4)))) != $true) | ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true) | (cZ = (sK3 @ sK4))),
% 1.69/1.37 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.69/1.37 thf(f112,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true) | ((sK4 @ (cP @ (cL @ (sK2 @ sK4)) @ (cL @ (sK3 @ sK4)))) != $true) | ($true != $true) | (cZ = (sK3 @ sK4)) | ((sK4 @ (cP @ (sK2 @ sK4) @ (sK3 @ sK4))) != $true)),
% 1.69/1.37 inference(superposition,[status(thm)],[f26,f20])).
% 1.69/1.37 thf(f20,plain,(
% 1.69/1.37 ( ! [X10 : a,X9 : a] : (((sK4 @ (cP @ (cR @ X9) @ (cR @ X10))) = $true) | ((sK4 @ (cP @ X9 @ X10)) != $true)) )),
% 1.69/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.37 thf(f26,plain,(
% 1.69/1.37 ( ! [X5 : a > $o] : (($true != (X5 @ (cP @ (cR @ (sK2 @ X5)) @ (cR @ (sK3 @ X5))))) | ((X5 @ (cP @ (cL @ (sK2 @ X5)) @ (cL @ (sK3 @ X5)))) != $true) | ((X5 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true) | (cZ = (sK3 @ X5))) )),
% 1.69/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.37 thf(f108,plain,(
% 1.69/1.37 ~spl7_3 | ~spl7_4),
% 1.69/1.37 inference(avatar_split_clause,[status(thm)],[f99,f105,f101])).
% 1.69/1.37 thf(f99,plain,(
% 1.69/1.37 (cZ != (sK2 @ sK4)) | ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true)),
% 1.69/1.37 inference(subsumption_resolution,[status(thm)],[f98,f24])).
% 1.69/1.37 thf(f98,plain,(
% 1.69/1.37 (cZ != (sK2 @ sK4)) | ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true) | ((sK4 @ (cP @ (sK2 @ sK4) @ (sK3 @ sK4))) != $true)),
% 1.69/1.37 inference(subsumption_resolution,[status(thm)],[f86,f22])).
% 1.69/1.37 thf(f86,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true) | ((sK4 @ (cP @ (cL @ (sK2 @ sK4)) @ (cL @ (sK3 @ sK4)))) != $true) | (cZ != (sK2 @ sK4)) | ((sK4 @ (cP @ (sK2 @ sK4) @ (sK3 @ sK4))) != $true)),
% 1.69/1.37 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.69/1.37 thf(f78,plain,(
% 1.69/1.37 ((sK4 @ (cP @ (sK2 @ sK4) @ (sK3 @ sK4))) != $true) | ((sK4 @ (cP @ (cL @ (sK2 @ sK4)) @ (cL @ (sK3 @ sK4)))) != $true) | ($true != $true) | (cZ != (sK2 @ sK4)) | ((sK4 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true)),
% 1.69/1.37 inference(superposition,[status(thm)],[f25,f20])).
% 1.69/1.37 thf(f25,plain,(
% 1.69/1.37 ( ! [X5 : a > $o] : (($true != (X5 @ (cP @ (cR @ (sK2 @ X5)) @ (cR @ (sK3 @ X5))))) | ((X5 @ (cP @ (cL @ sK0) @ (cL @ sK1))) != $true) | ((X5 @ (cP @ (cL @ (sK2 @ X5)) @ (cL @ (sK3 @ X5)))) != $true) | (cZ != (sK2 @ X5))) )),
% 1.69/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.37 % SZS output end Proof for DTF2THF_11165
% 1.69/1.37 % (11358)------------------------------
% 1.69/1.37 % (11358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (11358)Termination reason: Refutation
% 1.69/1.37
% 1.69/1.37 % (11358)Memory used [KB]: 5884
% 1.69/1.37 % (11358)Time elapsed: 0.075 s
% 1.69/1.37 % (11358)Instructions burned: 79 (million)
% 1.69/1.37 % (11358)------------------------------
% 1.69/1.37 % (11358)------------------------------
% 1.69/1.37 % (11352)Success in time 0.093 s
%------------------------------------------------------------------------------