%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV191^5 : 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 : n012.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 09:40:31 AM UTC 2026
% Result : Theorem 1.71s 1.41s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 85 ( 1 unt; 0 typ; 9 def)
% Number of atoms : 621 ( 362 equ; 0 cnn)
% Maximal formula atoms : 40 ( 7 avg)
% Number of connectives : 1117 ( 155 ~; 229 |; 158 &; 544 @)
% ( 9 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 21 con; 0-3 aty)
% Number of variables : 257 ( 0 ^; 123 !; 134 ?; 257 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cP: a > a > a ).
thf(func_def_2,type,
c0: a ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_7,type,
sK0: a > a > a > $o ).
thf(func_def_8,type,
sK1: a > a > a > $o ).
thf(func_def_9,type,
sK2: a ).
thf(func_def_10,type,
sK3: a ).
thf(func_def_11,type,
sK4: a ).
thf(func_def_12,type,
sK5: a ).
thf(func_def_13,type,
sK6: a ).
thf(func_def_14,type,
sK7: a ).
thf(func_def_15,type,
sK8: a ).
thf(func_def_16,type,
sK9: a ).
thf(func_def_17,type,
sK10: a ).
thf(f180,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f50,f59,f64,f69,f70,f71,f76,f81,f82,f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f179]) ).
thf(f179,plain,
( ~ spl11_9
| ~ spl11_1
| ~ spl11_6
| ~ spl11_7
| ~ spl11_8 ),
inference(avatar_split_clause,[status(thm)],[f178,f73,f66,f61,f39,f78]) ).
thf(f78,definition,
( spl11_9
<=> ( ( cP @ sK9 @ sK10 )
= sK3 ) ),
introduced(definition,[new_symbols(naming,[spl11_9])],[avatar_definition]) ).
thf(f39,definition,
( spl11_1
<=> ( ( cP @ sK6 @ sK8 )
= sK4 ) ),
introduced(definition,[new_symbols(naming,[spl11_1])],[avatar_definition]) ).
thf(f61,definition,
( spl11_6
<=> ( sK2
= ( cP @ sK7 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_6])],[avatar_definition]) ).
thf(f66,definition,
( spl11_7
<=> ( ( sK0 @ sK10 @ sK8 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_7])],[avatar_definition]) ).
thf(f73,definition,
( spl11_8
<=> ( $true
= ( sK0 @ sK9 @ sK6 @ sK7 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_8])],[avatar_definition]) ).
thf(f178,plain,
( ( ( cP @ sK9 @ sK10 )
!= sK3 )
| ~ spl11_1
| ~ spl11_6
| ~ spl11_7
| ~ spl11_8 ),
inference(trivial_inequality_removal,[status(thm)],[f177]) ).
thf(f177,plain,
( ( ( cP @ sK9 @ sK10 )
!= sK3 )
| ( sK2 != sK2 )
| ~ spl11_1
| ~ spl11_6
| ~ spl11_7
| ~ spl11_8 ),
inference(forward_demodulation,[status(thm)],[f176,f63]) ).
thf(f63,plain,
( ( sK2
= ( cP @ sK7 @ sK5 ) )
| ~ spl11_6 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f176,plain,
( ( sK2
!= ( cP @ sK7 @ sK5 ) )
| ( ( cP @ sK9 @ sK10 )
!= sK3 )
| ~ spl11_1
| ~ spl11_7
| ~ spl11_8 ),
inference(trivial_inequality_removal,[status(thm)],[f175]) ).
thf(f175,plain,
( ( sK2
!= ( cP @ sK7 @ sK5 ) )
| ( ( cP @ sK9 @ sK10 )
!= sK3 )
| ( sK4 != sK4 )
| ~ spl11_1
| ~ spl11_7
| ~ spl11_8 ),
inference(forward_demodulation,[status(thm)],[f168,f41]) ).
thf(f41,plain,
( ( ( cP @ sK6 @ sK8 )
= sK4 )
| ~ spl11_1 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f168,plain,
( ( ( cP @ sK6 @ sK8 )
!= sK4 )
| ( ( cP @ sK9 @ sK10 )
!= sK3 )
| ( sK2
!= ( cP @ sK7 @ sK5 ) )
| ~ spl11_7
| ~ spl11_8 ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
( ( ( cP @ sK9 @ sK10 )
!= sK3 )
| ( $true != $true )
| ( sK2
!= ( cP @ sK7 @ sK5 ) )
| ( ( cP @ sK6 @ sK8 )
!= sK4 )
| ~ spl11_7
| ~ spl11_8 ),
inference(superposition,[status(thm)],[f164,f103]) ).
thf(f103,plain,
( ( ( sK1 @ sK9 @ sK6 @ sK7 )
= $true )
| ~ spl11_8 ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
( ( ( sK1 @ sK9 @ sK6 @ sK7 )
= $true )
| ( $true != $true )
| ~ spl11_8 ),
inference(superposition,[status(thm)],[f37,f75]) ).
thf(f75,plain,
( ( $true
= ( sK0 @ sK9 @ sK6 @ sK7 ) )
| ~ spl11_8 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f37,plain,
! [X2: a,X3: a,X4: a] :
( ( $true
!= ( sK0 @ X2 @ X4 @ X3 ) )
| ( ( sK1 @ X2 @ X4 @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X2: a,X3: a,X4: a] :
( ( ( sK1 @ X2 @ X4 @ X3 )
= $true )
| ( $true
!= ( sK0 @ X2 @ X4 @ X3 ) ) )
& ( ( ( sK2 = sK3 )
& ( c0 = sK4 ) )
| ( ( sK2 = sK4 )
& ( c0 = sK3 ) )
| ( ( $true
= ( sK0 @ sK9 @ sK6 @ sK7 ) )
& ( ( cP @ sK9 @ sK10 )
= sK3 )
& ( ( sK0 @ sK10 @ sK8 @ sK5 )
= $true )
& ( sK2
= ( cP @ sK7 @ sK5 ) )
& ( ( cP @ sK6 @ sK8 )
= sK4 ) ) )
& ( ( sK2 != sK3 )
| ( c0 != sK4 ) )
& ( ( sK2 != sK4 )
| ( c0 != sK3 ) )
& ! [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( sK2
!= ( cP @ X14 @ X18 ) )
| ( sK4
!= ( cP @ X15 @ X19 ) )
| ( ( sK1 @ X17 @ X15 @ X14 )
!= $true )
| ( ( cP @ X17 @ X16 )
!= sK3 )
| ( $true
!= ( sK1 @ X16 @ X19 @ X18 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10])],[f9,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > a > a > $o,X1: a > a > a > $o] :
( ! [X2: a,X3: a,X4: a] :
( ( ( X1 @ X2 @ X4 @ X3 )
= $true )
| ( ( X0 @ X2 @ X4 @ X3 )
!= $true ) )
& ? [X5: a,X6: a,X7: a] :
( ( ( ( X5 = X6 )
& ( c0 = X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) )
| ? [X8: a,X9: a,X10: a,X11: a,X12: a,X13: a] :
( ( ( X0 @ X12 @ X9 @ X10 )
= $true )
& ( ( cP @ X12 @ X13 )
= X6 )
& ( ( X0 @ X13 @ X11 @ X8 )
= $true )
& ( ( cP @ X10 @ X8 )
= X5 )
& ( ( cP @ X9 @ X11 )
= X7 ) ) )
& ( ( X5 != X6 )
| ( c0 != X7 ) )
& ( ( X5 != X7 )
| ( c0 != X6 ) )
& ! [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( ( cP @ X14 @ X18 )
!= X5 )
| ( ( cP @ X15 @ X19 )
!= X7 )
| ( $true
!= ( X1 @ X17 @ X15 @ X14 ) )
| ( ( cP @ X17 @ X16 )
!= X6 )
| ( $true
!= ( X1 @ X16 @ X19 @ X18 ) ) ) ) )
=> ( ! [X4: a,X3: a,X2: a] :
( ( ( sK1 @ X2 @ X4 @ X3 )
= $true )
| ( $true
!= ( sK0 @ X2 @ X4 @ X3 ) ) )
& ? [X7: a,X6: a,X5: a] :
( ( ( ( X5 = X6 )
& ( c0 = X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) )
| ? [X13: a,X12: a,X11: a,X10: a,X9: a,X8: a] :
( ( ( sK0 @ X12 @ X9 @ X10 )
= $true )
& ( ( cP @ X12 @ X13 )
= X6 )
& ( $true
= ( sK0 @ X13 @ X11 @ X8 ) )
& ( ( cP @ X10 @ X8 )
= X5 )
& ( ( cP @ X9 @ X11 )
= X7 ) ) )
& ( ( X5 != X6 )
| ( c0 != X7 ) )
& ( ( X5 != X7 )
| ( c0 != X6 ) )
& ! [X19: a,X18: a,X17: a,X16: a,X15: a,X14: a] :
( ( ( cP @ X14 @ X18 )
!= X5 )
| ( ( cP @ X15 @ X19 )
!= X7 )
| ( ( sK1 @ X17 @ X15 @ X14 )
!= $true )
| ( ( cP @ X17 @ X16 )
!= X6 )
| ( $true
!= ( sK1 @ X16 @ X19 @ X18 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X7: a,X6: a,X5: a] :
( ( ( ( X5 = X6 )
& ( c0 = X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) )
| ? [X13: a,X12: a,X11: a,X10: a,X9: a,X8: a] :
( ( ( sK0 @ X12 @ X9 @ X10 )
= $true )
& ( ( cP @ X12 @ X13 )
= X6 )
& ( $true
= ( sK0 @ X13 @ X11 @ X8 ) )
& ( ( cP @ X10 @ X8 )
= X5 )
& ( ( cP @ X9 @ X11 )
= X7 ) ) )
& ( ( X5 != X6 )
| ( c0 != X7 ) )
& ( ( X5 != X7 )
| ( c0 != X6 ) )
& ! [X19: a,X18: a,X17: a,X16: a,X15: a,X14: a] :
( ( ( cP @ X14 @ X18 )
!= X5 )
| ( ( cP @ X15 @ X19 )
!= X7 )
| ( ( sK1 @ X17 @ X15 @ X14 )
!= $true )
| ( ( cP @ X17 @ X16 )
!= X6 )
| ( $true
!= ( sK1 @ X16 @ X19 @ X18 ) ) ) )
=> ( ( ( ( sK2 = sK3 )
& ( c0 = sK4 ) )
| ( ( sK2 = sK4 )
& ( c0 = sK3 ) )
| ? [X13: a,X12: a,X11: a,X10: a,X9: a,X8: a] :
( ( ( sK0 @ X12 @ X9 @ X10 )
= $true )
& ( sK3
= ( cP @ X12 @ X13 ) )
& ( $true
= ( sK0 @ X13 @ X11 @ X8 ) )
& ( sK2
= ( cP @ X10 @ X8 ) )
& ( ( cP @ X9 @ X11 )
= sK4 ) ) )
& ( ( sK2 != sK3 )
| ( c0 != sK4 ) )
& ( ( sK2 != sK4 )
| ( c0 != sK3 ) )
& ! [X19: a,X18: a,X17: a,X16: a,X15: a,X14: a] :
( ( sK2
!= ( cP @ X14 @ X18 ) )
| ( sK4
!= ( cP @ X15 @ X19 ) )
| ( ( sK1 @ X17 @ X15 @ X14 )
!= $true )
| ( ( cP @ X17 @ X16 )
!= sK3 )
| ( $true
!= ( sK1 @ X16 @ X19 @ X18 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X13: a,X12: a,X11: a,X10: a,X9: a,X8: a] :
( ( ( sK0 @ X12 @ X9 @ X10 )
= $true )
& ( sK3
= ( cP @ X12 @ X13 ) )
& ( $true
= ( sK0 @ X13 @ X11 @ X8 ) )
& ( sK2
= ( cP @ X10 @ X8 ) )
& ( ( cP @ X9 @ X11 )
= sK4 ) )
=> ( ( $true
= ( sK0 @ sK9 @ sK6 @ sK7 ) )
& ( ( cP @ sK9 @ sK10 )
= sK3 )
& ( ( sK0 @ sK10 @ sK8 @ sK5 )
= $true )
& ( sK2
= ( cP @ sK7 @ sK5 ) )
& ( ( cP @ sK6 @ sK8 )
= sK4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > a > a > $o,X1: a > a > a > $o] :
( ! [X2: a,X3: a,X4: a] :
( ( ( X1 @ X2 @ X4 @ X3 )
= $true )
| ( ( X0 @ X2 @ X4 @ X3 )
!= $true ) )
& ? [X5: a,X6: a,X7: a] :
( ( ( ( X5 = X6 )
& ( c0 = X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) )
| ? [X8: a,X9: a,X10: a,X11: a,X12: a,X13: a] :
( ( ( X0 @ X12 @ X9 @ X10 )
= $true )
& ( ( cP @ X12 @ X13 )
= X6 )
& ( ( X0 @ X13 @ X11 @ X8 )
= $true )
& ( ( cP @ X10 @ X8 )
= X5 )
& ( ( cP @ X9 @ X11 )
= X7 ) ) )
& ( ( X5 != X6 )
| ( c0 != X7 ) )
& ( ( X5 != X7 )
| ( c0 != X6 ) )
& ! [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( ( cP @ X14 @ X18 )
!= X5 )
| ( ( cP @ X15 @ X19 )
!= X7 )
| ( $true
!= ( X1 @ X17 @ X15 @ X14 ) )
| ( ( cP @ X17 @ X16 )
!= X6 )
| ( $true
!= ( X1 @ X16 @ X19 @ X18 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X1: a > a > a > $o,X0: a > a > a > $o] :
( ! [X3: a,X4: a,X2: a] :
( ( $true
= ( X0 @ X3 @ X2 @ X4 ) )
| ( ( X1 @ X3 @ X2 @ X4 )
!= $true ) )
& ? [X5: a,X6: a,X7: a] :
( ( ( ( X5 = X6 )
& ( c0 = X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) )
| ? [X11: a,X9: a,X12: a,X13: a,X8: a,X10: a] :
( ( $true
= ( X1 @ X8 @ X9 @ X12 ) )
& ( ( cP @ X8 @ X10 )
= X6 )
& ( ( X1 @ X10 @ X13 @ X11 )
= $true )
& ( ( cP @ X12 @ X11 )
= X5 )
& ( ( cP @ X9 @ X13 )
= X7 ) ) )
& ( ( X5 != X6 )
| ( c0 != X7 ) )
& ( ( X5 != X7 )
| ( c0 != X6 ) )
& ! [X17: a,X15: a,X14: a,X16: a,X18: a,X19: a] :
( ( ( cP @ X17 @ X18 )
!= X5 )
| ( ( cP @ X15 @ X19 )
!= X7 )
| ( ( X0 @ X16 @ X15 @ X17 )
!= $true )
| ( ( cP @ X16 @ X14 )
!= X6 )
| ( $true
!= ( X0 @ X14 @ X19 @ X18 ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > a > a > $o,X1: a > a > a > $o] :
( ? [X5: a,X6: a,X7: a] :
( ( ( X5 != X6 )
| ( c0 != X7 ) )
& ! [X17: a,X15: a,X14: a,X16: a,X18: a,X19: a] :
( ( ( cP @ X17 @ X18 )
!= X5 )
| ( ( cP @ X15 @ X19 )
!= X7 )
| ( ( X0 @ X16 @ X15 @ X17 )
!= $true )
| ( ( cP @ X16 @ X14 )
!= X6 )
| ( $true
!= ( X0 @ X14 @ X19 @ X18 ) ) )
& ( ( X5 != X7 )
| ( c0 != X6 ) )
& ( ( ( X5 = X6 )
& ( c0 = X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) )
| ? [X11: a,X9: a,X12: a,X13: a,X8: a,X10: a] :
( ( $true
= ( X1 @ X8 @ X9 @ X12 ) )
& ( ( cP @ X8 @ X10 )
= X6 )
& ( ( X1 @ X10 @ X13 @ X11 )
= $true )
& ( ( cP @ X12 @ X11 )
= X5 )
& ( ( cP @ X9 @ X13 )
= X7 ) ) ) )
& ! [X3: a,X4: a,X2: a] :
( ( $true
= ( X0 @ X3 @ X2 @ X4 ) )
| ( ( X1 @ X3 @ X2 @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > a > a > $o,X1: a > a > a > $o] :
( ! [X2: a,X4: a,X3: a] :
( ( ( X1 @ X3 @ X2 @ X4 )
= $true )
=> ( $true
= ( X0 @ X3 @ X2 @ X4 ) ) )
=> ! [X5: a,X6: a,X7: a] :
( ( ( ( X5 = X6 )
& ( c0 = X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) )
| ? [X11: a,X9: a,X12: a,X13: a,X8: a,X10: a] :
( ( $true
= ( X1 @ X8 @ X9 @ X12 ) )
& ( ( cP @ X8 @ X10 )
= X6 )
& ( ( X1 @ X10 @ X13 @ X11 )
= $true )
& ( ( cP @ X12 @ X11 )
= X5 )
& ( ( cP @ X9 @ X13 )
= X7 ) ) )
=> ( ( ( X5 = X6 )
& ( c0 = X7 ) )
| ? [X14: a,X19: a,X15: a,X18: a,X17: a,X16: a] :
( ( ( cP @ X17 @ X18 )
= X5 )
& ( ( cP @ X16 @ X14 )
= X6 )
& ( $true
= ( X0 @ X14 @ X19 @ X18 ) )
& ( ( X0 @ X16 @ X15 @ X17 )
= $true )
& ( ( cP @ X15 @ X19 )
= X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) ) ) ) ),
inference(true_and_false_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a > a > a > $o,X1: a > a > a > $o] :
( ( $true
& $true
& ! [X2: a,X4: a,X3: a] :
( ( ( X1 @ X3 @ X2 @ X4 )
= $true )
=> ( $true
= ( X0 @ X3 @ X2 @ X4 ) ) ) )
=> ! [X5: a,X6: a,X7: a] :
( ( ( ( X5 = X6 )
& ( c0 = X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) )
| ? [X11: a,X9: a,X12: a,X13: a,X8: a,X10: a] :
( ( $true
= ( X1 @ X8 @ X9 @ X12 ) )
& ( ( cP @ X8 @ X10 )
= X6 )
& ( ( X1 @ X10 @ X13 @ X11 )
= $true )
& ( ( cP @ X12 @ X11 )
= X5 )
& ( ( cP @ X9 @ X13 )
= X7 ) ) )
=> ( ( ( X5 = X6 )
& ( c0 = X7 ) )
| ? [X14: a,X19: a,X15: a,X18: a,X17: a,X16: a] :
( ( ( cP @ X17 @ X18 )
= X5 )
& ( ( cP @ X16 @ X14 )
= X6 )
& ( $true
= ( X0 @ X14 @ X19 @ X18 ) )
& ( ( X0 @ X16 @ X15 @ X17 )
= $true )
& ( ( cP @ X15 @ X19 )
= X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) ) ) ) )
& ( $true
=> $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > a > a > $o,X1: a > a > a > $o] :
( ( $true
& $true
& ! [X2: a,X3: a,X4: a] :
( ( X1 @ X3 @ X2 @ X4 )
=> ( X0 @ X3 @ X2 @ X4 ) ) )
=> ! [X5: a,X6: a,X7: a] :
( ( ( ( c0 = X7 )
& ( X5 = X6 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) )
| ? [X8: a,X9: a,X10: a,X11: a,X12: a,X13: a] :
( ( X1 @ X8 @ X9 @ X12 )
& ( ( cP @ X12 @ X11 )
= X5 )
& ( ( cP @ X9 @ X13 )
= X7 )
& ( X1 @ X10 @ X13 @ X11 )
& ( ( cP @ X8 @ X10 )
= X6 ) ) )
=> ( ? [X14: a,X15: a,X16: a,X17: a,X18: a,X19: a] :
( ( ( cP @ X17 @ X18 )
= X5 )
& ( ( cP @ X16 @ X14 )
= X6 )
& ( X0 @ X14 @ X19 @ X18 )
& ( ( cP @ X15 @ X19 )
= X7 )
& ( X0 @ X16 @ X15 @ X17 ) )
| ( ( X5 = X6 )
& ( c0 = X7 ) )
| ( ( X5 = X7 )
& ( c0 = X6 ) ) ) ) )
& ( $true
=> $true ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: a > a > a > $o,X0: a > a > a > $o] :
( ( $true
& $true
& ! [X3: a,X2: a,X4: a] :
( ( X0 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ! [X4: a,X2: a,X3: a] :
( ( ( ( c0 = X3 )
& ( X2 = X4 ) )
| ( ( X3 = X4 )
& ( c0 = X2 ) )
| ? [X5: a,X7: a,X6: a,X10: a,X9: a,X8: a] :
( ( X0 @ X5 @ X7 @ X9 )
& ( ( cP @ X9 @ X10 )
= X4 )
& ( ( cP @ X7 @ X8 )
= X3 )
& ( X0 @ X6 @ X8 @ X10 )
& ( ( cP @ X5 @ X6 )
= X2 ) ) )
=> ( ? [X6: a,X7: a,X5: a,X9: a,X10: a,X8: a] :
( ( ( cP @ X9 @ X10 )
= X4 )
& ( ( cP @ X5 @ X6 )
= X2 )
& ( X1 @ X6 @ X8 @ X10 )
& ( ( cP @ X7 @ X8 )
= X3 )
& ( X1 @ X5 @ X7 @ X9 ) )
| ( ( X2 = X4 )
& ( c0 = X3 ) )
| ( ( X3 = X4 )
& ( c0 = X2 ) ) ) ) )
& ! [X0: a > a > a > $o] :
( $true
=> $true ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: a > a > a > $o,X0: a > a > a > $o] :
( ( $true
& $true
& ! [X3: a,X2: a,X4: a] :
( ( X0 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ! [X4: a,X2: a,X3: a] :
( ( ( ( c0 = X3 )
& ( X2 = X4 ) )
| ( ( X3 = X4 )
& ( c0 = X2 ) )
| ? [X5: a,X7: a,X6: a,X10: a,X9: a,X8: a] :
( ( X0 @ X5 @ X7 @ X9 )
& ( ( cP @ X9 @ X10 )
= X4 )
& ( ( cP @ X7 @ X8 )
= X3 )
& ( X0 @ X6 @ X8 @ X10 )
& ( ( cP @ X5 @ X6 )
= X2 ) ) )
=> ( ? [X6: a,X7: a,X5: a,X9: a,X10: a,X8: a] :
( ( ( cP @ X9 @ X10 )
= X4 )
& ( ( cP @ X5 @ X6 )
= X2 )
& ( X1 @ X6 @ X8 @ X10 )
& ( ( cP @ X7 @ X8 )
= X3 )
& ( X1 @ X5 @ X7 @ X9 ) )
| ( ( X2 = X4 )
& ( c0 = X3 ) )
| ( ( X3 = X4 )
& ( c0 = X2 ) ) ) ) )
& ! [X0: a > a > a > $o] :
( $true
=> $true ) ),
file('/export/starexec/sandbox/tmp/tmp.5bBMCy7dxu/DTF2THF_17541.p',cS_JOINFN_MONOTONE_pme) ).
thf(f164,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true
!= ( sK1 @ X0 @ X1 @ X2 ) )
| ( ( cP @ X0 @ sK10 )
!= sK3 )
| ( sK4
!= ( cP @ X1 @ sK8 ) )
| ( sK2
!= ( cP @ X2 @ sK5 ) ) )
| ~ spl11_7 ),
inference(trivial_inequality_removal,[status(thm)],[f163]) ).
thf(f163,plain,
( ! [X2: a,X0: a,X1: a] :
( ( sK2
!= ( cP @ X2 @ sK5 ) )
| ( ( cP @ X0 @ sK10 )
!= sK3 )
| ( sK4
!= ( cP @ X1 @ sK8 ) )
| ( $true
!= ( sK1 @ X0 @ X1 @ X2 ) )
| ( $true != $true ) )
| ~ spl11_7 ),
inference(superposition,[status(thm)],[f14,f104]) ).
thf(f104,plain,
( ( $true
= ( sK1 @ sK10 @ sK8 @ sK5 ) )
| ~ spl11_7 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $true
= ( sK1 @ sK10 @ sK8 @ sK5 ) )
| ( $true != $true )
| ~ spl11_7 ),
inference(superposition,[status(thm)],[f37,f68]) ).
thf(f68,plain,
( ( ( sK0 @ sK10 @ sK8 @ sK5 )
= $true )
| ~ spl11_7 ),
inference(avatar_component_clause,[status(thm)],[f66]) ).
thf(f14,plain,
! [X18: a,X19: a,X16: a,X14: a,X17: a,X15: a] :
( ( $true
!= ( sK1 @ X16 @ X19 @ X18 ) )
| ( ( sK1 @ X17 @ X15 @ X14 )
!= $true )
| ( sK4
!= ( cP @ X15 @ X19 ) )
| ( sK2
!= ( cP @ X14 @ X18 ) )
| ( ( cP @ X17 @ X16 )
!= sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f95,plain,
( spl11_1
| spl11_4
| spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f27,f43,f52,f39]) ).
thf(f52,definition,
( spl11_4
<=> ( sK2 = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl11_4])],[avatar_definition]) ).
thf(f43,definition,
( spl11_2
<=> ( c0 = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition]) ).
thf(f27,plain,
( ( ( cP @ sK6 @ sK8 )
= sK4 )
| ( c0 = sK3 )
| ( sK2 = sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f94,plain,
( spl11_3
| spl11_6
| spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f18,f43,f61,f47]) ).
thf(f47,definition,
( spl11_3
<=> ( c0 = sK4 ) ),
introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition]) ).
thf(f18,plain,
( ( c0 = sK4 )
| ( sK2
= ( cP @ sK7 @ sK5 ) )
| ( c0 = sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f93,plain,
( spl11_5
| spl11_3
| spl11_9 ),
inference(avatar_split_clause,[status(thm)],[f25,f78,f47,f56]) ).
thf(f56,definition,
( spl11_5
<=> ( sK2 = sK4 ) ),
introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition]) ).
thf(f25,plain,
( ( sK2 = sK4 )
| ( ( cP @ sK9 @ sK10 )
= sK3 )
| ( c0 = sK4 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f92,plain,
( spl11_7
| spl11_2
| spl11_4 ),
inference(avatar_split_clause,[status(thm)],[f29,f52,f43,f66]) ).
thf(f29,plain,
( ( sK2 = sK3 )
| ( c0 = sK3 )
| ( ( sK0 @ sK10 @ sK8 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f91,plain,
( spl11_4
| spl11_8
| spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f31,f43,f73,f52]) ).
thf(f31,plain,
( ( sK2 = sK3 )
| ( c0 = sK3 )
| ( $true
= ( sK0 @ sK9 @ sK6 @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f90,plain,
( spl11_7
| spl11_4
| spl11_5 ),
inference(avatar_split_clause,[status(thm)],[f34,f56,f52,f66]) ).
thf(f34,plain,
( ( sK2 = sK4 )
| ( sK2 = sK3 )
| ( ( sK0 @ sK10 @ sK8 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f89,plain,
( spl11_9
| spl11_2
| spl11_3 ),
inference(avatar_split_clause,[status(thm)],[f20,f47,f43,f78]) ).
thf(f20,plain,
( ( c0 = sK3 )
| ( ( cP @ sK9 @ sK10 )
= sK3 )
| ( c0 = sK4 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f88,plain,
( spl11_5
| spl11_1
| spl11_3 ),
inference(avatar_split_clause,[status(thm)],[f22,f47,f39,f56]) ).
thf(f22,plain,
( ( sK2 = sK4 )
| ( ( cP @ sK6 @ sK8 )
= sK4 )
| ( c0 = sK4 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f87,plain,
( spl11_8
| spl11_3
| spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f43,f47,f73]) ).
thf(f21,plain,
( ( $true
= ( sK0 @ sK9 @ sK6 @ sK7 ) )
| ( c0 = sK4 )
| ( c0 = sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f86,plain,
( spl11_2
| spl11_9
| spl11_4 ),
inference(avatar_split_clause,[status(thm)],[f30,f52,f78,f43]) ).
thf(f30,plain,
( ( c0 = sK3 )
| ( sK2 = sK3 )
| ( ( cP @ sK9 @ sK10 )
= sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f85,plain,
( spl11_5
| spl11_7
| spl11_3 ),
inference(avatar_split_clause,[status(thm)],[f24,f47,f66,f56]) ).
thf(f24,plain,
( ( sK2 = sK4 )
| ( c0 = sK4 )
| ( ( sK0 @ sK10 @ sK8 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f84,plain,
( ~ spl11_5
| ~ spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f43,f56]) ).
thf(f15,plain,
( ( sK2 != sK4 )
| ( c0 != sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f83,plain,
( spl11_8
| spl11_3
| spl11_5 ),
inference(avatar_split_clause,[status(thm)],[f26,f56,f47,f73]) ).
thf(f26,plain,
( ( sK2 = sK4 )
| ( c0 = sK4 )
| ( $true
= ( sK0 @ sK9 @ sK6 @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f82,plain,
( ~ spl11_4
| ~ spl11_3 ),
inference(avatar_split_clause,[status(thm)],[f16,f47,f52]) ).
thf(f16,plain,
( ( sK2 != sK3 )
| ( c0 != sK4 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f81,plain,
( spl11_9
| spl11_5
| spl11_4 ),
inference(avatar_split_clause,[status(thm)],[f35,f52,f56,f78]) ).
thf(f35,plain,
( ( sK2 = sK3 )
| ( ( cP @ sK9 @ sK10 )
= sK3 )
| ( sK2 = sK4 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f76,plain,
( spl11_5
| spl11_8
| spl11_4 ),
inference(avatar_split_clause,[status(thm)],[f36,f52,f73,f56]) ).
thf(f36,plain,
( ( sK2 = sK4 )
| ( $true
= ( sK0 @ sK9 @ sK6 @ sK7 ) )
| ( sK2 = sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f71,plain,
( spl11_6
| spl11_5
| spl11_3 ),
inference(avatar_split_clause,[status(thm)],[f23,f47,f56,f61]) ).
thf(f23,plain,
( ( sK2
= ( cP @ sK7 @ sK5 ) )
| ( c0 = sK4 )
| ( sK2 = sK4 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f70,plain,
( spl11_4
| spl11_5
| spl11_6 ),
inference(avatar_split_clause,[status(thm)],[f33,f61,f56,f52]) ).
thf(f33,plain,
( ( sK2 = sK4 )
| ( sK2 = sK3 )
| ( sK2
= ( cP @ sK7 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f69,plain,
( spl11_7
| spl11_3
| spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f43,f47,f66]) ).
thf(f19,plain,
( ( c0 = sK3 )
| ( c0 = sK4 )
| ( ( sK0 @ sK10 @ sK8 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f64,plain,
( spl11_6
| spl11_2
| spl11_4 ),
inference(avatar_split_clause,[status(thm)],[f28,f52,f43,f61]) ).
thf(f28,plain,
( ( c0 = sK3 )
| ( sK2 = sK3 )
| ( sK2
= ( cP @ sK7 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f59,plain,
( spl11_1
| spl11_4
| spl11_5 ),
inference(avatar_split_clause,[status(thm)],[f32,f56,f52,f39]) ).
thf(f32,plain,
( ( ( cP @ sK6 @ sK8 )
= sK4 )
| ( sK2 = sK3 )
| ( sK2 = sK4 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f50,plain,
( spl11_1
| spl11_2
| spl11_3 ),
inference(avatar_split_clause,[status(thm)],[f17,f47,f43,f39]) ).
thf(f17,plain,
( ( c0 = sK3 )
| ( c0 = sK4 )
| ( ( cP @ sK6 @ sK8 )
= sK4 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV191^5 : 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
% 0.14/0.30 % Computer : n012.cluster.edu
% 0.14/0.30 % Model : x86_64 x86_64
% 0.14/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.30 % Memory : 8042.1875MB
% 0.14/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.30 % CPULimit : 300
% 0.14/0.30 % WCLimit : 300
% 0.14/0.30 % DateTime : Tue Feb 24 12:41:30 EST 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : SEV191^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.40 % Domain : Set Theory (Sets of sets)
% 0.17/0.40 % Problem : TPS problem S-JOINFN-MONOTONE
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English : The function used to define JOIN as a LFP is monotone.
% 0.17/0.40
% 0.17/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.40 % Source : [Bro09]
% 0.17/0.40 % Names : tps_0503 [Bro09]
% 0.17/0.40 % : S-JOINFN-MONOTONE [TPS]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.17/0.40 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.17/0.40 % Number of atoms : 18 ( 14 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 18 ( 18 avg)
% 0.17/0.40 % Number of connectives : 53 ( 0 ~; 4 |; 15 &; 30 @)
% 0.17/0.40 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 24 ( 24 avg)
% 0.17/0.40 % Number of types : 2 ( 1 usr)
% 0.17/0.40 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 4 ( 2 usr; 2 con; 0-2 aty)
% 0.17/0.40 % Number of variables : 21 ( 0 ^; 9 !; 12 ?; 21 :)
% 0.17/0.40 % SPC : TH0_THM_EQU_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.40 % : Polymorphic definitions expanded.
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(a_type,type,
% 0.17/0.40 a: $tType ).
% 0.17/0.40
% 0.17/0.40 thf(cP,type,
% 0.17/0.40 cP: a > a > a ).
% 0.17/0.40
% 0.17/0.40 thf(c0,type,
% 0.17/0.40 c0: a ).
% 0.17/0.40
% 0.17/0.40 thf(cS_JOINFN_MONOTONE_pme,conjecture,
% 0.17/0.40 ( ! [R: a > a > a > $o] :
% 0.17/0.40 ( $true
% 0.17/0.40 => $true )
% 0.17/0.40 & ! [R: a > a > a > $o,S: a > a > a > $o] :
% 0.17/0.40 ( ( $true
% 0.17/0.40 & $true
% 0.17/0.40 & ! [Xa: a,Xb: a,Xc: a] :
% 0.17/0.40 ( ( R @ Xa @ Xb @ Xc )
% 0.17/0.40 => ( S @ Xa @ Xb @ Xc ) ) )
% 0.17/0.40 => ! [Xa: a,Xb: a,Xc: a] :
% 0.17/0.40 ( ( ( ( Xa = c0 )
% 0.17/0.40 & ( Xb = Xc ) )
% 0.17/0.40 | ( ( Xb = c0 )
% 0.17/0.40 & ( Xa = Xc ) )
% 0.17/0.40 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 0.17/0.40 ( ( Xa
% 0.17/0.40 = ( cP @ Xx1 @ Xx2 ) )
% 0.17/0.40 & ( Xb
% 0.17/0.40 = ( cP @ Xy1 @ Xy2 ) )
% 0.17/0.40 & ( Xc
% 0.17/0.40 = ( cP @ Xz1 @ Xz2 ) )
% 0.17/0.40 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.17/0.40 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.17/0.40 => ( ( ( Xa = c0 )
% 0.17/0.40 & ( Xb = Xc ) )
% 0.17/0.40 | ( ( Xb = c0 )
% 0.17/0.40 & ( Xa = Xc ) )
% 0.17/0.40 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 0.17/0.40 ( ( Xa
% 0.17/0.40 = ( cP @ Xx1 @ Xx2 ) )
% 0.17/0.40 & ( Xb
% 0.17/0.40 = ( cP @ Xy1 @ Xy2 ) )
% 0.17/0.40 & ( Xc
% 0.17/0.40 = ( cP @ Xz1 @ Xz2 ) )
% 0.17/0.40 & ( S @ Xx1 @ Xy1 @ Xz1 )
% 0.17/0.40 & ( S @ Xx2 @ Xy2 @ Xz2 ) ) ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.55/1.37 ---- Embedded in THF ---
% 1.55/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.37 %%% Generated on Tue Feb 24 12:41:31 EST 2026
% 1.55/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.37 %%% Logic specification used:
% 1.55/1.37 %%% thf(spec, logic, $$dhol).
% 1.55/1.37
% 1.55/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5bBMCy7dxu/DTF2DTF17541.p
% See solution above
% 1.55/1.37 ------------------------
% 1.55/1.38 ---- Cleaned THF ---
% 1.55/1.38 thf(a_type,type,
% 1.55/1.38 a: $tType ).
% 1.55/1.38
% 1.55/1.38 thf(cP,type,
% 1.55/1.38 cP: a > a > a ).
% 1.55/1.38
% 1.55/1.38 thf(c0,type,
% 1.55/1.38 c0: a ).
% 1.55/1.38
% 1.55/1.38 thf(cS_JOINFN_MONOTONE_pme,conjecture,
% 1.55/1.38 ( ! [R: a > a > a > $o] :
% 1.55/1.38 ( $true
% 1.55/1.38 => $true )
% 1.55/1.38 & ! [R: a > a > a > $o,S: a > a > a > $o] :
% 1.55/1.38 ( ( $true
% 1.55/1.38 & $true
% 1.55/1.38 & ! [Xa: a,Xb: a,Xc: a] :
% 1.55/1.38 ( ( R @ Xa @ Xb @ Xc )
% 1.55/1.38 => ( S @ Xa @ Xb @ Xc ) ) )
% 1.55/1.38 => ! [Xa: a,Xb: a,Xc: a] :
% 1.55/1.38 ( ( ( ( Xa = c0 )
% 1.55/1.38 & ( Xb = Xc ) )
% 1.55/1.38 | ( ( Xb = c0 )
% 1.55/1.38 & ( Xa = Xc ) )
% 1.55/1.38 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 1.55/1.38 ( ( Xa
% 1.55/1.38 = ( cP @ Xx1 @ Xx2 ) )
% 1.55/1.38 & ( Xb
% 1.55/1.38 = ( cP @ Xy1 @ Xy2 ) )
% 1.55/1.38 & ( Xc
% 1.55/1.38 = ( cP @ Xz1 @ Xz2 ) )
% 1.55/1.38 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 1.55/1.38 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 1.55/1.38 => ( ( ( Xa = c0 )
% 1.55/1.38 & ( Xb = Xc ) )
% 1.55/1.38 | ( ( Xb = c0 )
% 1.55/1.38 & ( Xa = Xc ) )
% 1.55/1.38 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 1.55/1.38 ( ( Xa
% 1.55/1.38 = ( cP @ Xx1 @ Xx2 ) )
% 1.55/1.38 & ( Xb
% 1.55/1.38 = ( cP @ Xy1 @ Xy2 ) )
% 1.55/1.38 & ( Xc
% 1.55/1.38 = ( cP @ Xz1 @ Xz2 ) )
% 1.55/1.38 & ( S @ Xx1 @ Xy1 @ Xz1 )
% 1.55/1.38 & ( S @ Xx2 @ Xy2 @ Xz2 ) ) ) ) ) ) ).
% 1.55/1.38 ------------------------
% 1.71/1.40 % (17638)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17541 for (2999ds/183Mi)
% 1.71/1.40 % (17642)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_17541 for (2999ds/2Mi)
% 1.71/1.40 % (17640)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_17541 for (2999ds/27Mi)
% 1.71/1.40 % (17639)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_17541 for (2999ds/4Mi)
% 1.71/1.40 % (17643)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_17541 for (2999ds/275Mi)
% 1.71/1.40 % (17644)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17541 for (2999ds/18Mi)
% 1.71/1.40 % (17641)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17541 for (2999ds/2Mi)
% 1.71/1.40 % (17642)Instruction limit reached!
% 1.71/1.40 % (17642)------------------------------
% 1.71/1.40 % (17642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.40 % (17642)Termination reason: Unknown
% 1.71/1.40 % (17642)Termination phase: Property scanning
% 1.71/1.40
% 1.71/1.40 % (17642)Memory used [KB]: 1023
% 1.71/1.40 % (17642)Time elapsed: 0.003 s
% 1.71/1.40 % (17642)Instructions burned: 3 (million)
% 1.71/1.40 % (17642)------------------------------
% 1.71/1.40 % (17642)------------------------------
% 1.71/1.41 % (17639)Instruction limit reached!
% 1.71/1.41 % (17639)------------------------------
% 1.71/1.41 % (17639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.41 % (17639)Termination reason: Unknown
% 1.71/1.41 % (17639)Termination phase: Saturation
% 1.71/1.41
% 1.71/1.41 % (17639)Memory used [KB]: 5500
% 1.71/1.41 % (17639)Time elapsed: 0.004 s
% 1.71/1.41 % (17639)Instructions burned: 4 (million)
% 1.71/1.41 % (17639)------------------------------
% 1.71/1.41 % (17639)------------------------------
% 1.71/1.41 % (17641)Instruction limit reached!
% 1.71/1.41 % (17641)------------------------------
% 1.71/1.41 % (17641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.41 % (17641)Termination reason: Unknown
% 1.71/1.41 % (17641)Termination phase: Property scanning
% 1.71/1.41
% 1.71/1.41 % (17641)Memory used [KB]: 1023
% 1.71/1.41 % (17641)Time elapsed: 0.003 s
% 1.71/1.41 % (17641)Instructions burned: 3 (million)
% 1.71/1.41 % (17641)------------------------------
% 1.71/1.41 % (17641)------------------------------
% 1.71/1.41 % (17640)First to succeed.
% 1.71/1.41 % (17644)Also succeeded, but the first one will report.
% 1.71/1.41 % (17640)Refutation found. Thanks to Tanya!
% 1.71/1.41 % SZS status Theorem for DTF2THF_17541
% 1.71/1.41 % SZS output start Proof for DTF2THF_17541
% 1.71/1.41 thf(type_def_5, type, a: $tType).
% 1.71/1.41 thf(func_def_0, type, a: $tType).
% 1.71/1.41 thf(func_def_1, type, cP: a > a > a).
% 1.71/1.41 thf(func_def_2, type, c0: a).
% 1.71/1.41 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.71/1.41 thf(func_def_7, type, sK0: a > a > a > $o).
% 1.71/1.41 thf(func_def_8, type, sK1: a > a > a > $o).
% 1.71/1.41 thf(func_def_9, type, sK2: a).
% 1.71/1.41 thf(func_def_10, type, sK3: a).
% 1.71/1.41 thf(func_def_11, type, sK4: a).
% 1.71/1.41 thf(func_def_12, type, sK5: a).
% 1.71/1.41 thf(func_def_13, type, sK6: a).
% 1.71/1.41 thf(func_def_14, type, sK7: a).
% 1.71/1.41 thf(func_def_15, type, sK8: a).
% 1.71/1.41 thf(func_def_16, type, sK9: a).
% 1.71/1.41 thf(func_def_17, type, sK10: a).
% 1.71/1.41 thf(f180,plain,(
% 1.71/1.41 $false),
% 1.71/1.41 inference(avatar_sat_refutation,[status(thm)],[f50,f59,f64,f69,f70,f71,f76,f81,f82,f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f179])).
% 1.71/1.41 thf(f179,plain,(
% 1.71/1.41 ~spl11_9 | ~spl11_1 | ~spl11_6 | ~spl11_7 | ~spl11_8),
% 1.71/1.41 inference(avatar_split_clause,[status(thm)],[f178,f73,f66,f61,f39,f78])).
% 1.71/1.41 thf(f78,definition,(
% 1.71/1.41 spl11_9 <=> ((cP @ sK9 @ sK10) = sK3)),
% 1.71/1.41 introduced(definition,[new_symbols(naming,[spl11_9])],[avatar_definition])).
% 1.71/1.41 thf(f39,definition,(
% 1.71/1.41 spl11_1 <=> ((cP @ sK6 @ sK8) = sK4)),
% 1.71/1.41 introduced(definition,[new_symbols(naming,[spl11_1])],[avatar_definition])).
% 1.71/1.41 thf(f61,definition,(
% 1.71/1.41 spl11_6 <=> (sK2 = (cP @ sK7 @ sK5))),
% 1.71/1.41 introduced(definition,[new_symbols(naming,[spl11_6])],[avatar_definition])).
% 1.71/1.41 thf(f66,definition,(
% 1.71/1.41 spl11_7 <=> ((sK0 @ sK10 @ sK8 @ sK5) = $true)),
% 1.71/1.41 introduced(definition,[new_symbols(naming,[spl11_7])],[avatar_definition])).
% 1.71/1.41 thf(f73,definition,(
% 1.71/1.41 spl11_8 <=> ($true = (sK0 @ sK9 @ sK6 @ sK7))),
% 1.71/1.41 introduced(definition,[new_symbols(naming,[spl11_8])],[avatar_definition])).
% 1.71/1.41 thf(f178,plain,(
% 1.71/1.41 ((cP @ sK9 @ sK10) != sK3) | (~spl11_1 | ~spl11_6 | ~spl11_7 | ~spl11_8)),
% 1.71/1.41 inference(trivial_inequality_removal,[status(thm)],[f177])).
% 1.71/1.41 thf(f177,plain,(
% 1.71/1.41 ((cP @ sK9 @ sK10) != sK3) | (sK2 != sK2) | (~spl11_1 | ~spl11_6 | ~spl11_7 | ~spl11_8)),
% 1.71/1.41 inference(forward_demodulation,[status(thm)],[f176,f63])).
% 1.71/1.41 thf(f63,plain,(
% 1.71/1.41 (sK2 = (cP @ sK7 @ sK5)) | ~spl11_6),
% 1.71/1.41 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.71/1.41 thf(f176,plain,(
% 1.71/1.41 (sK2 != (cP @ sK7 @ sK5)) | ((cP @ sK9 @ sK10) != sK3) | (~spl11_1 | ~spl11_7 | ~spl11_8)),
% 1.71/1.41 inference(trivial_inequality_removal,[status(thm)],[f175])).
% 1.71/1.41 thf(f175,plain,(
% 1.71/1.41 (sK2 != (cP @ sK7 @ sK5)) | ((cP @ sK9 @ sK10) != sK3) | (sK4 != sK4) | (~spl11_1 | ~spl11_7 | ~spl11_8)),
% 1.71/1.41 inference(forward_demodulation,[status(thm)],[f168,f41])).
% 1.71/1.41 thf(f41,plain,(
% 1.71/1.41 ((cP @ sK6 @ sK8) = sK4) | ~spl11_1),
% 1.71/1.41 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.71/1.41 thf(f168,plain,(
% 1.71/1.41 ((cP @ sK6 @ sK8) != sK4) | ((cP @ sK9 @ sK10) != sK3) | (sK2 != (cP @ sK7 @ sK5)) | (~spl11_7 | ~spl11_8)),
% 1.71/1.41 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 1.71/1.41 thf(f166,plain,(
% 1.71/1.41 ((cP @ sK9 @ sK10) != sK3) | ($true != $true) | (sK2 != (cP @ sK7 @ sK5)) | ((cP @ sK6 @ sK8) != sK4) | (~spl11_7 | ~spl11_8)),
% 1.71/1.41 inference(superposition,[status(thm)],[f164,f103])).
% 1.71/1.41 thf(f103,plain,(
% 1.71/1.41 ((sK1 @ sK9 @ sK6 @ sK7) = $true) | ~spl11_8),
% 1.71/1.41 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.71/1.41 thf(f102,plain,(
% 1.71/1.41 ((sK1 @ sK9 @ sK6 @ sK7) = $true) | ($true != $true) | ~spl11_8),
% 1.71/1.41 inference(superposition,[status(thm)],[f37,f75])).
% 1.71/1.41 thf(f75,plain,(
% 1.71/1.41 ($true = (sK0 @ sK9 @ sK6 @ sK7)) | ~spl11_8),
% 1.71/1.41 inference(avatar_component_clause,[status(thm)],[f73])).
% 1.71/1.41 thf(f37,plain,(
% 1.71/1.41 ( ! [X2 : a,X3 : a,X4 : a] : (($true != (sK0 @ X2 @ X4 @ X3)) | ((sK1 @ X2 @ X4 @ X3) = $true)) )),
% 1.71/1.41 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.41 thf(f13,plain,(
% 1.71/1.41 ! [X2 : a,X3 : a,X4 : a] : (((sK1 @ X2 @ X4 @ X3) = $true) | ($true != (sK0 @ X2 @ X4 @ X3))) & ((((sK2 = sK3) & (c0 = sK4)) | ((sK2 = sK4) & (c0 = sK3)) | (($true = (sK0 @ sK9 @ sK6 @ sK7)) & ((cP @ sK9 @ sK10) = sK3) & ((sK0 @ sK10 @ sK8 @ sK5) = $true) & (sK2 = (cP @ sK7 @ sK5)) & ((cP @ sK6 @ sK8) = sK4))) & ((sK2 != sK3) | (c0 != sK4)) & ((sK2 != sK4) | (c0 != sK3)) & ! [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((sK2 != (cP @ X14 @ X18)) | (sK4 != (cP @ X15 @ X19)) | ((sK1 @ X17 @ X15 @ X14) != $true) | ((cP @ X17 @ X16) != sK3) | ($true != (sK1 @ X16 @ X19 @ X18))))),
% 1.71/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10])],[f9,f12,f11,f10])).
% 1.71/1.41 thf(f10,plain,(
% 1.71/1.41 ? [X0 : a > a > a > $o,X1 : a > a > a > $o] : (! [X2 : a,X3 : a,X4 : a] : (((X1 @ X2 @ X4 @ X3) = $true) | ((X0 @ X2 @ X4 @ X3) != $true)) & ? [X5 : a,X6 : a,X7 : a] : ((((X5 = X6) & (c0 = X7)) | ((X5 = X7) & (c0 = X6)) | ? [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : (((X0 @ X12 @ X9 @ X10) = $true) & ((cP @ X12 @ X13) = X6) & ((X0 @ X13 @ X11 @ X8) = $true) & ((cP @ X10 @ X8) = X5) & ((cP @ X9 @ X11) = X7))) & ((X5 != X6) | (c0 != X7)) & ((X5 != X7) | (c0 != X6)) & ! [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : (((cP @ X14 @ X18) != X5) | ((cP @ X15 @ X19) != X7) | ($true != (X1 @ X17 @ X15 @ X14)) | ((cP @ X17 @ X16) != X6) | ($true != (X1 @ X16 @ X19 @ X18))))) => (! [X4 : a,X3 : a,X2 : a] : (((sK1 @ X2 @ X4 @ X3) = $true) | ($true != (sK0 @ X2 @ X4 @ X3))) & ? [X7 : a,X6 : a,X5 : a] : ((((X5 = X6) & (c0 = X7)) | ((X5 = X7) & (c0 = X6)) | ? [X13 : a,X12 : a,X11 : a,X10 : a,X9 : a,X8 : a] : (((sK0 @ X12 @ X9 @ X10) = $true) & ((cP @ X12 @ X13) = X6) & ($true = (sK0 @ X13 @ X11 @ X8)) & ((cP @ X10 @ X8) = X5) & ((cP @ X9 @ X11) = X7))) & ((X5 != X6) | (c0 != X7)) & ((X5 != X7) | (c0 != X6)) & ! [X19 : a,X18 : a,X17 : a,X16 : a,X15 : a,X14 : a] : (((cP @ X14 @ X18) != X5) | ((cP @ X15 @ X19) != X7) | ((sK1 @ X17 @ X15 @ X14) != $true) | ((cP @ X17 @ X16) != X6) | ($true != (sK1 @ X16 @ X19 @ X18)))))),
% 1.71/1.41 introduced(definition,[],[choice_axiom])).
% 1.71/1.41 thf(f11,plain,(
% 1.71/1.41 ? [X7 : a,X6 : a,X5 : a] : ((((X5 = X6) & (c0 = X7)) | ((X5 = X7) & (c0 = X6)) | ? [X13 : a,X12 : a,X11 : a,X10 : a,X9 : a,X8 : a] : (((sK0 @ X12 @ X9 @ X10) = $true) & ((cP @ X12 @ X13) = X6) & ($true = (sK0 @ X13 @ X11 @ X8)) & ((cP @ X10 @ X8) = X5) & ((cP @ X9 @ X11) = X7))) & ((X5 != X6) | (c0 != X7)) & ((X5 != X7) | (c0 != X6)) & ! [X19 : a,X18 : a,X17 : a,X16 : a,X15 : a,X14 : a] : (((cP @ X14 @ X18) != X5) | ((cP @ X15 @ X19) != X7) | ((sK1 @ X17 @ X15 @ X14) != $true) | ((cP @ X17 @ X16) != X6) | ($true != (sK1 @ X16 @ X19 @ X18)))) => ((((sK2 = sK3) & (c0 = sK4)) | ((sK2 = sK4) & (c0 = sK3)) | ? [X13 : a,X12 : a,X11 : a,X10 : a,X9 : a,X8 : a] : (((sK0 @ X12 @ X9 @ X10) = $true) & (sK3 = (cP @ X12 @ X13)) & ($true = (sK0 @ X13 @ X11 @ X8)) & (sK2 = (cP @ X10 @ X8)) & ((cP @ X9 @ X11) = sK4))) & ((sK2 != sK3) | (c0 != sK4)) & ((sK2 != sK4) | (c0 != sK3)) & ! [X19 : a,X18 : a,X17 : a,X16 : a,X15 : a,X14 : a] : ((sK2 != (cP @ X14 @ X18)) | (sK4 != (cP @ X15 @ X19)) | ((sK1 @ X17 @ X15 @ X14) != $true) | ((cP @ X17 @ X16) != sK3) | ($true != (sK1 @ X16 @ X19 @ X18))))),
% 1.71/1.41 introduced(definition,[],[choice_axiom])).
% 1.71/1.41 thf(f12,plain,(
% 1.71/1.41 ? [X13 : a,X12 : a,X11 : a,X10 : a,X9 : a,X8 : a] : (((sK0 @ X12 @ X9 @ X10) = $true) & (sK3 = (cP @ X12 @ X13)) & ($true = (sK0 @ X13 @ X11 @ X8)) & (sK2 = (cP @ X10 @ X8)) & ((cP @ X9 @ X11) = sK4)) => (($true = (sK0 @ sK9 @ sK6 @ sK7)) & ((cP @ sK9 @ sK10) = sK3) & ((sK0 @ sK10 @ sK8 @ sK5) = $true) & (sK2 = (cP @ sK7 @ sK5)) & ((cP @ sK6 @ sK8) = sK4))),
% 1.71/1.41 introduced(definition,[],[choice_axiom])).
% 1.71/1.41 thf(f9,plain,(
% 1.71/1.41 ? [X0 : a > a > a > $o,X1 : a > a > a > $o] : (! [X2 : a,X3 : a,X4 : a] : (((X1 @ X2 @ X4 @ X3) = $true) | ((X0 @ X2 @ X4 @ X3) != $true)) & ? [X5 : a,X6 : a,X7 : a] : ((((X5 = X6) & (c0 = X7)) | ((X5 = X7) & (c0 = X6)) | ? [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : (((X0 @ X12 @ X9 @ X10) = $true) & ((cP @ X12 @ X13) = X6) & ((X0 @ X13 @ X11 @ X8) = $true) & ((cP @ X10 @ X8) = X5) & ((cP @ X9 @ X11) = X7))) & ((X5 != X6) | (c0 != X7)) & ((X5 != X7) | (c0 != X6)) & ! [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : (((cP @ X14 @ X18) != X5) | ((cP @ X15 @ X19) != X7) | ($true != (X1 @ X17 @ X15 @ X14)) | ((cP @ X17 @ X16) != X6) | ($true != (X1 @ X16 @ X19 @ X18)))))),
% 1.71/1.41 inference(rectify,[status(thm)],[f8])).
% 1.71/1.41 thf(f8,plain,(
% 1.71/1.41 ? [X1 : a > a > a > $o,X0 : a > a > a > $o] : (! [X3 : a,X4 : a,X2 : a] : (($true = (X0 @ X3 @ X2 @ X4)) | ((X1 @ X3 @ X2 @ X4) != $true)) & ? [X5 : a,X6 : a,X7 : a] : ((((X5 = X6) & (c0 = X7)) | ((X5 = X7) & (c0 = X6)) | ? [X11 : a,X9 : a,X12 : a,X13 : a,X8 : a,X10 : a] : (($true = (X1 @ X8 @ X9 @ X12)) & ((cP @ X8 @ X10) = X6) & ((X1 @ X10 @ X13 @ X11) = $true) & ((cP @ X12 @ X11) = X5) & ((cP @ X9 @ X13) = X7))) & ((X5 != X6) | (c0 != X7)) & ((X5 != X7) | (c0 != X6)) & ! [X17 : a,X15 : a,X14 : a,X16 : a,X18 : a,X19 : a] : (((cP @ X17 @ X18) != X5) | ((cP @ X15 @ X19) != X7) | ((X0 @ X16 @ X15 @ X17) != $true) | ((cP @ X16 @ X14) != X6) | ($true != (X0 @ X14 @ X19 @ X18)))))),
% 1.71/1.41 inference(flattening,[status(thm)],[f7])).
% 1.71/1.41 thf(f7,plain,(
% 1.71/1.41 ? [X0 : a > a > a > $o,X1 : a > a > a > $o] : (? [X5 : a,X6 : a,X7 : a] : ((((X5 != X6) | (c0 != X7)) & ! [X17 : a,X15 : a,X14 : a,X16 : a,X18 : a,X19 : a] : (((cP @ X17 @ X18) != X5) | ((cP @ X15 @ X19) != X7) | ((X0 @ X16 @ X15 @ X17) != $true) | ((cP @ X16 @ X14) != X6) | ($true != (X0 @ X14 @ X19 @ X18))) & ((X5 != X7) | (c0 != X6))) & (((X5 = X6) & (c0 = X7)) | ((X5 = X7) & (c0 = X6)) | ? [X11 : a,X9 : a,X12 : a,X13 : a,X8 : a,X10 : a] : (($true = (X1 @ X8 @ X9 @ X12)) & ((cP @ X8 @ X10) = X6) & ((X1 @ X10 @ X13 @ X11) = $true) & ((cP @ X12 @ X11) = X5) & ((cP @ X9 @ X13) = X7)))) & ! [X3 : a,X4 : a,X2 : a] : (($true = (X0 @ X3 @ X2 @ X4)) | ((X1 @ X3 @ X2 @ X4) != $true)))),
% 1.71/1.41 inference(ennf_transformation,[status(thm)],[f6])).
% 1.71/1.41 thf(f6,plain,(
% 1.71/1.41 ~! [X0 : a > a > a > $o,X1 : a > a > a > $o] : (! [X2 : a,X4 : a,X3 : a] : (((X1 @ X3 @ X2 @ X4) = $true) => ($true = (X0 @ X3 @ X2 @ X4))) => ! [X5 : a,X6 : a,X7 : a] : ((((X5 = X6) & (c0 = X7)) | ((X5 = X7) & (c0 = X6)) | ? [X11 : a,X9 : a,X12 : a,X13 : a,X8 : a,X10 : a] : (($true = (X1 @ X8 @ X9 @ X12)) & ((cP @ X8 @ X10) = X6) & ((X1 @ X10 @ X13 @ X11) = $true) & ((cP @ X12 @ X11) = X5) & ((cP @ X9 @ X13) = X7))) => (((X5 = X6) & (c0 = X7)) | ? [X14 : a,X19 : a,X15 : a,X18 : a,X17 : a,X16 : a] : (((cP @ X17 @ X18) = X5) & ((cP @ X16 @ X14) = X6) & ($true = (X0 @ X14 @ X19 @ X18)) & ((X0 @ X16 @ X15 @ X17) = $true) & ((cP @ X15 @ X19) = X7)) | ((X5 = X7) & (c0 = X6)))))),
% 1.71/1.41 inference(true_and_false_elimination,[status(thm)],[f5])).
% 1.71/1.41 thf(f5,plain,(
% 1.71/1.41 ~(! [X0 : a > a > a > $o,X1 : a > a > a > $o] : (($true & $true & ! [X2 : a,X4 : a,X3 : a] : (((X1 @ X3 @ X2 @ X4) = $true) => ($true = (X0 @ X3 @ X2 @ X4)))) => ! [X5 : a,X6 : a,X7 : a] : ((((X5 = X6) & (c0 = X7)) | ((X5 = X7) & (c0 = X6)) | ? [X11 : a,X9 : a,X12 : a,X13 : a,X8 : a,X10 : a] : (($true = (X1 @ X8 @ X9 @ X12)) & ((cP @ X8 @ X10) = X6) & ((X1 @ X10 @ X13 @ X11) = $true) & ((cP @ X12 @ X11) = X5) & ((cP @ X9 @ X13) = X7))) => (((X5 = X6) & (c0 = X7)) | ? [X14 : a,X19 : a,X15 : a,X18 : a,X17 : a,X16 : a] : (((cP @ X17 @ X18) = X5) & ((cP @ X16 @ X14) = X6) & ($true = (X0 @ X14 @ X19 @ X18)) & ((X0 @ X16 @ X15 @ X17) = $true) & ((cP @ X15 @ X19) = X7)) | ((X5 = X7) & (c0 = X6))))) & ($true => $true))),
% 1.71/1.41 inference(fool_elimination,[status(thm)],[f4])).
% 1.71/1.41 thf(f4,plain,(
% 1.71/1.41 ~(! [X0 : a > a > a > $o,X1 : a > a > a > $o] : (($true & $true & ! [X2 : a,X3 : a,X4 : a] : ((X1 @ X3 @ X2 @ X4) => (X0 @ X3 @ X2 @ X4))) => ! [X5 : a,X6 : a,X7 : a] : ((((c0 = X7) & (X5 = X6)) | ((X5 = X7) & (c0 = X6)) | ? [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : ((X1 @ X8 @ X9 @ X12) & ((cP @ X12 @ X11) = X5) & ((cP @ X9 @ X13) = X7) & (X1 @ X10 @ X13 @ X11) & ((cP @ X8 @ X10) = X6))) => (? [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : (((cP @ X17 @ X18) = X5) & ((cP @ X16 @ X14) = X6) & (X0 @ X14 @ X19 @ X18) & ((cP @ X15 @ X19) = X7) & (X0 @ X16 @ X15 @ X17)) | ((X5 = X6) & (c0 = X7)) | ((X5 = X7) & (c0 = X6))))) & ($true => $true))),
% 1.71/1.41 inference(rectify,[status(thm)],[f2])).
% 1.71/1.41 thf(f2,negated_conjecture,(
% 1.71/1.41 ~(! [X1 : a > a > a > $o,X0 : a > a > a > $o] : (($true & $true & ! [X3 : a,X2 : a,X4 : a] : ((X0 @ X2 @ X3 @ X4) => (X1 @ X2 @ X3 @ X4))) => ! [X4 : a,X2 : a,X3 : a] : ((((c0 = X3) & (X2 = X4)) | ((X3 = X4) & (c0 = X2)) | ? [X5 : a,X7 : a,X6 : a,X10 : a,X9 : a,X8 : a] : ((X0 @ X5 @ X7 @ X9) & ((cP @ X9 @ X10) = X4) & ((cP @ X7 @ X8) = X3) & (X0 @ X6 @ X8 @ X10) & ((cP @ X5 @ X6) = X2))) => (? [X6 : a,X7 : a,X5 : a,X9 : a,X10 : a,X8 : a] : (((cP @ X9 @ X10) = X4) & ((cP @ X5 @ X6) = X2) & (X1 @ X6 @ X8 @ X10) & ((cP @ X7 @ X8) = X3) & (X1 @ X5 @ X7 @ X9)) | ((X2 = X4) & (c0 = X3)) | ((X3 = X4) & (c0 = X2))))) & ! [X0 : a > a > a > $o] : ($true => $true))),
% 1.71/1.41 inference(negated_conjecture,[status(cth)],[f1])).
% 1.71/1.41 thf(f1,conjecture,(
% 1.71/1.41 ! [X1 : a > a > a > $o,X0 : a > a > a > $o] : (($true & $true & ! [X3 : a,X2 : a,X4 : a] : ((X0 @ X2 @ X3 @ X4) => (X1 @ X2 @ X3 @ X4))) => ! [X4 : a,X2 : a,X3 : a] : ((((c0 = X3) & (X2 = X4)) | ((X3 = X4) & (c0 = X2)) | ? [X5 : a,X7 : a,X6 : a,X10 : a,X9 : a,X8 : a] : ((X0 @ X5 @ X7 @ X9) & ((cP @ X9 @ X10) = X4) & ((cP @ X7 @ X8) = X3) & (X0 @ X6 @ X8 @ X10) & ((cP @ X5 @ X6) = X2))) => (? [X6 : a,X7 : a,X5 : a,X9 : a,X10 : a,X8 : a] : (((cP @ X9 @ X10) = X4) & ((cP @ X5 @ X6) = X2) & (X1 @ X6 @ X8 @ X10) & ((cP @ X7 @ X8) = X3) & (X1 @ X5 @ X7 @ X9)) | ((X2 = X4) & (c0 = X3)) | ((X3 = X4) & (c0 = X2))))) & ! [X0 : a > a > a > $o] : ($true => $true)),
% 1.71/1.41 file('/export/starexec/sandbox/tmp/tmp.5bBMCy7dxu/DTF2THF_17541.p',cS_JOINFN_MONOTONE_pme)).
% 1.71/1.42 thf(f164,plain,(
% 1.71/1.42 ( ! [X2 : a,X0 : a,X1 : a] : (($true != (sK1 @ X0 @ X1 @ X2)) | ((cP @ X0 @ sK10) != sK3) | (sK4 != (cP @ X1 @ sK8)) | (sK2 != (cP @ X2 @ sK5))) ) | ~spl11_7),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f163])).
% 1.71/1.42 thf(f163,plain,(
% 1.71/1.42 ( ! [X2 : a,X0 : a,X1 : a] : ((sK2 != (cP @ X2 @ sK5)) | ((cP @ X0 @ sK10) != sK3) | (sK4 != (cP @ X1 @ sK8)) | ($true != (sK1 @ X0 @ X1 @ X2)) | ($true != $true)) ) | ~spl11_7),
% 1.71/1.42 inference(superposition,[status(thm)],[f14,f104])).
% 1.71/1.42 thf(f104,plain,(
% 1.71/1.42 ($true = (sK1 @ sK10 @ sK8 @ sK5)) | ~spl11_7),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.71/1.42 thf(f101,plain,(
% 1.71/1.42 ($true = (sK1 @ sK10 @ sK8 @ sK5)) | ($true != $true) | ~spl11_7),
% 1.71/1.42 inference(superposition,[status(thm)],[f37,f68])).
% 1.71/1.42 thf(f68,plain,(
% 1.71/1.42 ((sK0 @ sK10 @ sK8 @ sK5) = $true) | ~spl11_7),
% 1.71/1.42 inference(avatar_component_clause,[status(thm)],[f66])).
% 1.71/1.42 thf(f14,plain,(
% 1.71/1.42 ( ! [X18 : a,X19 : a,X16 : a,X14 : a,X17 : a,X15 : a] : (($true != (sK1 @ X16 @ X19 @ X18)) | ((sK1 @ X17 @ X15 @ X14) != $true) | (sK4 != (cP @ X15 @ X19)) | (sK2 != (cP @ X14 @ X18)) | ((cP @ X17 @ X16) != sK3)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f95,plain,(
% 1.71/1.42 spl11_1 | spl11_4 | spl11_2),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f27,f43,f52,f39])).
% 1.71/1.42 thf(f52,definition,(
% 1.71/1.42 spl11_4 <=> (sK2 = sK3)),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl11_4])],[avatar_definition])).
% 1.71/1.42 thf(f43,definition,(
% 1.71/1.42 spl11_2 <=> (c0 = sK3)),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition])).
% 1.71/1.42 thf(f27,plain,(
% 1.71/1.42 ((cP @ sK6 @ sK8) = sK4) | (c0 = sK3) | (sK2 = sK3)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f94,plain,(
% 1.71/1.42 spl11_3 | spl11_6 | spl11_2),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f18,f43,f61,f47])).
% 1.71/1.42 thf(f47,definition,(
% 1.71/1.42 spl11_3 <=> (c0 = sK4)),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition])).
% 1.71/1.42 thf(f18,plain,(
% 1.71/1.42 (c0 = sK4) | (sK2 = (cP @ sK7 @ sK5)) | (c0 = sK3)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f93,plain,(
% 1.71/1.42 spl11_5 | spl11_3 | spl11_9),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f25,f78,f47,f56])).
% 1.71/1.42 thf(f56,definition,(
% 1.71/1.42 spl11_5 <=> (sK2 = sK4)),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition])).
% 1.71/1.42 thf(f25,plain,(
% 1.71/1.42 (sK2 = sK4) | ((cP @ sK9 @ sK10) = sK3) | (c0 = sK4)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f92,plain,(
% 1.71/1.42 spl11_7 | spl11_2 | spl11_4),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f29,f52,f43,f66])).
% 1.71/1.42 thf(f29,plain,(
% 1.71/1.42 (sK2 = sK3) | (c0 = sK3) | ((sK0 @ sK10 @ sK8 @ sK5) = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f91,plain,(
% 1.71/1.42 spl11_4 | spl11_8 | spl11_2),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f31,f43,f73,f52])).
% 1.71/1.42 thf(f31,plain,(
% 1.71/1.42 (sK2 = sK3) | (c0 = sK3) | ($true = (sK0 @ sK9 @ sK6 @ sK7))),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f90,plain,(
% 1.71/1.42 spl11_7 | spl11_4 | spl11_5),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f34,f56,f52,f66])).
% 1.71/1.42 thf(f34,plain,(
% 1.71/1.42 (sK2 = sK4) | (sK2 = sK3) | ((sK0 @ sK10 @ sK8 @ sK5) = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f89,plain,(
% 1.71/1.42 spl11_9 | spl11_2 | spl11_3),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f20,f47,f43,f78])).
% 1.71/1.42 thf(f20,plain,(
% 1.71/1.42 (c0 = sK3) | ((cP @ sK9 @ sK10) = sK3) | (c0 = sK4)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f88,plain,(
% 1.71/1.42 spl11_5 | spl11_1 | spl11_3),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f22,f47,f39,f56])).
% 1.71/1.42 thf(f22,plain,(
% 1.71/1.42 (sK2 = sK4) | ((cP @ sK6 @ sK8) = sK4) | (c0 = sK4)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f87,plain,(
% 1.71/1.42 spl11_8 | spl11_3 | spl11_2),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f21,f43,f47,f73])).
% 1.71/1.42 thf(f21,plain,(
% 1.71/1.42 ($true = (sK0 @ sK9 @ sK6 @ sK7)) | (c0 = sK4) | (c0 = sK3)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f86,plain,(
% 1.71/1.42 spl11_2 | spl11_9 | spl11_4),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f30,f52,f78,f43])).
% 1.71/1.42 thf(f30,plain,(
% 1.71/1.42 (c0 = sK3) | (sK2 = sK3) | ((cP @ sK9 @ sK10) = sK3)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f85,plain,(
% 1.71/1.42 spl11_5 | spl11_7 | spl11_3),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f24,f47,f66,f56])).
% 1.71/1.42 thf(f24,plain,(
% 1.71/1.42 (sK2 = sK4) | (c0 = sK4) | ((sK0 @ sK10 @ sK8 @ sK5) = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f84,plain,(
% 1.71/1.42 ~spl11_5 | ~spl11_2),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f15,f43,f56])).
% 1.71/1.42 thf(f15,plain,(
% 1.71/1.42 (sK2 != sK4) | (c0 != sK3)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f83,plain,(
% 1.71/1.42 spl11_8 | spl11_3 | spl11_5),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f26,f56,f47,f73])).
% 1.71/1.42 thf(f26,plain,(
% 1.71/1.42 (sK2 = sK4) | (c0 = sK4) | ($true = (sK0 @ sK9 @ sK6 @ sK7))),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f82,plain,(
% 1.71/1.42 ~spl11_4 | ~spl11_3),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f16,f47,f52])).
% 1.71/1.42 thf(f16,plain,(
% 1.71/1.42 (sK2 != sK3) | (c0 != sK4)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f81,plain,(
% 1.71/1.42 spl11_9 | spl11_5 | spl11_4),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f35,f52,f56,f78])).
% 1.71/1.42 thf(f35,plain,(
% 1.71/1.42 (sK2 = sK3) | ((cP @ sK9 @ sK10) = sK3) | (sK2 = sK4)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f76,plain,(
% 1.71/1.42 spl11_5 | spl11_8 | spl11_4),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f36,f52,f73,f56])).
% 1.71/1.42 thf(f36,plain,(
% 1.71/1.42 (sK2 = sK4) | ($true = (sK0 @ sK9 @ sK6 @ sK7)) | (sK2 = sK3)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f71,plain,(
% 1.71/1.42 spl11_6 | spl11_5 | spl11_3),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f23,f47,f56,f61])).
% 1.71/1.42 thf(f23,plain,(
% 1.71/1.42 (sK2 = (cP @ sK7 @ sK5)) | (c0 = sK4) | (sK2 = sK4)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f70,plain,(
% 1.71/1.42 spl11_4 | spl11_5 | spl11_6),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f33,f61,f56,f52])).
% 1.71/1.42 thf(f33,plain,(
% 1.71/1.42 (sK2 = sK4) | (sK2 = sK3) | (sK2 = (cP @ sK7 @ sK5))),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f69,plain,(
% 1.71/1.42 spl11_7 | spl11_3 | spl11_2),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f19,f43,f47,f66])).
% 1.71/1.42 thf(f19,plain,(
% 1.71/1.42 (c0 = sK3) | (c0 = sK4) | ((sK0 @ sK10 @ sK8 @ sK5) = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f64,plain,(
% 1.71/1.42 spl11_6 | spl11_2 | spl11_4),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f28,f52,f43,f61])).
% 1.71/1.42 thf(f28,plain,(
% 1.71/1.42 (c0 = sK3) | (sK2 = sK3) | (sK2 = (cP @ sK7 @ sK5))),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f59,plain,(
% 1.71/1.42 spl11_1 | spl11_4 | spl11_5),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f32,f56,f52,f39])).
% 1.71/1.42 thf(f32,plain,(
% 1.71/1.42 ((cP @ sK6 @ sK8) = sK4) | (sK2 = sK3) | (sK2 = sK4)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 thf(f50,plain,(
% 1.71/1.42 spl11_1 | spl11_2 | spl11_3),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f17,f47,f43,f39])).
% 1.71/1.42 thf(f17,plain,(
% 1.71/1.42 (c0 = sK3) | (c0 = sK4) | ((cP @ sK6 @ sK8) = sK4)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.42 % SZS output end Proof for DTF2THF_17541
% 1.71/1.42 % (17640)------------------------------
% 1.71/1.42 % (17640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.42 % (17640)Termination reason: Refutation
% 1.71/1.42
% 1.71/1.42 % (17640)Memory used [KB]: 5628
% 1.71/1.42 % (17640)Time elapsed: 0.012 s
% 1.71/1.42 % (17640)Instructions burned: 13 (million)
% 1.71/1.42 % (17640)------------------------------
% 1.71/1.42 % (17640)------------------------------
% 1.71/1.42 % (17637)Success in time 0.025 s
%------------------------------------------------------------------------------