%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU909^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 09:37:43 AM UTC 2026
% Result : Theorem 1.34s 1.38s
% Output : Refutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 22
% Syntax : Number of formulae : 118 ( 2 unt; 0 typ; 7 def)
% Number of atoms : 2140 ( 718 equ; 0 cnn)
% Maximal formula atoms : 30 ( 18 avg)
% Number of connectives : 2378 ( 427 ~; 489 |; 206 &;1153 @)
% ( 7 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 299 ( 299 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 10 con; 0-3 aty)
% Number of variables : 474 ( 97 ^; 287 !; 90 ?; 474 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cA: ( a > $o ) > $o ).
thf(func_def_9,type,
sP0: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_10,type,
sP1: ( a > $o ) > $o ).
thf(func_def_12,type,
sK3: a > $o ).
thf(func_def_13,type,
sK4: a > $o ).
thf(func_def_14,type,
sK5: a > a > $o ).
thf(func_def_15,type,
sK6: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_16,type,
sK7: ( ( a > $o ) > $o ) > a ).
thf(func_def_17,type,
sK8: ( a > $o ) > a > $o ).
thf(func_def_18,type,
sK9: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_19,type,
sK10: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_20,type,
sK11: ( a > $o ) > ( a > $o ) > a > $o ).
thf(func_def_21,type,
sK12: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_22,type,
sK13: a > $o ).
thf(func_def_24,type,
ph15:
!>[X0: $tType] : X0 ).
thf(f275,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f67,f72,f81,f82,f83,f95,f99,f274]) ).
thf(f274,plain,
( ~ spl14_3
| ~ spl14_6
| ~ spl14_9
| ~ spl14_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f273]) ).
thf(f273,plain,
( $false
| ~ spl14_3
| ~ spl14_6
| ~ spl14_9
| ~ spl14_10 ),
inference(subsumption_resolution,[status(thm)],[f272,f141]) ).
thf(f141,plain,
! [X0: a > $o] :
( $true
!= ( sP0 @ X0 @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
! [X0: a > $o] :
( ( $true
!= ( sP0 @ X0 @ X0 ) )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f137]) ).
thf(f137,plain,
! [X0: a > $o] :
( ( $true
!= ( sP0 @ X0 @ X0 ) )
| ( $true
!= ( sP0 @ X0 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f134,f102]) ).
thf(f102,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
= ( X0 @ ( sK12 @ X0 @ X1 ) ) )
| ( $true
!= ( sP0 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sP0 @ X0 @ X1 ) )
| ( $true != $true )
| ( $true
= ( X0 @ ( sK12 @ X0 @ X1 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f100]) ).
thf(f100,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
= ( X0 @ ( sK12 @ X0 @ X1 ) ) )
| ( $true
!= ( sP0 @ X0 @ X1 ) )
| ( $true != $true )
| ( $true
!= ( sP0 @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f50,f52]) ).
thf(f52,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
= ( cA @ ( sK11 @ X1 @ X0 ) ) )
| ( $true
!= ( sP0 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( $true
!= ( X0 @ X3 ) )
| ( $true
= ( sK11 @ X1 @ X0 @ X3 ) ) )
& ( $true
= ( cA @ ( sK11 @ X1 @ X0 ) ) )
& ( ( $true
!= ( cA @ ( sK11 @ X1 @ X0 ) ) )
| ( ( $true
!= ( sK11 @ X1 @ X0 @ ( sK12 @ X1 @ X0 ) ) )
& ( $true
= ( X1 @ ( sK12 @ X1 @ X0 ) ) ) ) ) )
| ( $true
!= ( sP0 @ X1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f28,f30,f29]) ).
thf(f29,plain,
! [X0: a > $o,X1: a > $o] :
( ? [X2: a > $o] :
( ! [X3: a] :
( ( $true
!= ( X0 @ X3 ) )
| ( $true
= ( X2 @ X3 ) ) )
& ( $true
= ( cA @ X2 ) )
& ( ( $true
!= ( cA @ X2 ) )
| ? [X4: a] :
( ( $true
!= ( X2 @ X4 ) )
& ( ( X1 @ X4 )
= $true ) ) ) )
=> ( ! [X3: a] :
( ( $true
!= ( X0 @ X3 ) )
| ( $true
= ( sK11 @ X1 @ X0 @ X3 ) ) )
& ( $true
= ( cA @ ( sK11 @ X1 @ X0 ) ) )
& ( ( $true
!= ( cA @ ( sK11 @ X1 @ X0 ) ) )
| ? [X4: a] :
( ( $true
!= ( sK11 @ X1 @ X0 @ X4 ) )
& ( ( X1 @ X4 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
! [X0: a > $o,X1: a > $o] :
( ? [X4: a] :
( ( $true
!= ( sK11 @ X1 @ X0 @ X4 ) )
& ( ( X1 @ X4 )
= $true ) )
=> ( ( $true
!= ( sK11 @ X1 @ X0 @ ( sK12 @ X1 @ X0 ) ) )
& ( $true
= ( X1 @ ( sK12 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
! [X0: a > $o,X1: a > $o] :
( ? [X2: a > $o] :
( ! [X3: a] :
( ( $true
!= ( X0 @ X3 ) )
| ( $true
= ( X2 @ X3 ) ) )
& ( $true
= ( cA @ X2 ) )
& ( ( $true
!= ( cA @ X2 ) )
| ? [X4: a] :
( ( $true
!= ( X2 @ X4 ) )
& ( ( X1 @ X4 )
= $true ) ) ) )
| ( $true
!= ( sP0 @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
! [X9: a > $o,X1: a > $o] :
( ? [X10: a > $o] :
( ! [X11: a] :
( ( $true
!= ( X9 @ X11 ) )
| ( $true
= ( X10 @ X11 ) ) )
& ( $true
= ( cA @ X10 ) )
& ( ( $true
!= ( cA @ X10 ) )
| ? [X12: a] :
( ( $true
!= ( X10 @ X12 ) )
& ( $true
= ( X1 @ X12 ) ) ) ) )
| ( $true
!= ( sP0 @ X1 @ X9 ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X9: a > $o,X1: a > $o] :
( ? [X10: a > $o] :
( ! [X11: a] :
( ( $true
!= ( X9 @ X11 ) )
| ( $true
= ( X10 @ X11 ) ) )
& ( $true
= ( cA @ X10 ) )
& ( ( $true
!= ( cA @ X10 ) )
| ? [X12: a] :
( ( $true
!= ( X10 @ X12 ) )
& ( $true
= ( X1 @ X12 ) ) ) ) )
| ( $true
!= ( sP0 @ X1 @ X9 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f50,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( cA @ ( sK11 @ X1 @ X0 ) ) )
| ( $true
!= ( sP0 @ X1 @ X0 ) )
| ( $true
= ( X1 @ ( sK12 @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f134,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( X1 @ ( sK12 @ X0 @ X1 ) ) )
| ( $true
!= ( sP0 @ X0 @ X1 ) ) ),
inference(subsumption_resolution,[status(thm)],[f133,f52]) ).
thf(f133,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( X1 @ ( sK12 @ X0 @ X1 ) ) )
| ( $true
!= ( sP0 @ X0 @ X1 ) )
| ( $true
!= ( cA @ ( sK11 @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( X1 @ ( sK12 @ X0 @ X1 ) ) )
| ( $true != $true )
| ( $true
!= ( sP0 @ X0 @ X1 ) )
| ( $true
!= ( cA @ ( sK11 @ X0 @ X1 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f131]) ).
thf(f131,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true != $true )
| ( $true
!= ( cA @ ( sK11 @ X0 @ X1 ) ) )
| ( $true
!= ( sP0 @ X0 @ X1 ) )
| ( $true
!= ( sP0 @ X0 @ X1 ) )
| ( $true
!= ( X1 @ ( sK12 @ X0 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f51,f53]) ).
thf(f53,plain,
! [X3: a,X0: a > $o,X1: a > $o] :
( ( $true
= ( sK11 @ X1 @ X0 @ X3 ) )
| ( $true
!= ( X0 @ X3 ) )
| ( $true
!= ( sP0 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f51,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sK11 @ X1 @ X0 @ ( sK12 @ X1 @ X0 ) ) )
| ( $true
!= ( cA @ ( sK11 @ X1 @ X0 ) ) )
| ( $true
!= ( sP0 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f272,plain,
( ( $true
= ( sP0 @ sK3 @ sK3 ) )
| ~ spl14_3
| ~ spl14_6
| ~ spl14_9
| ~ spl14_10 ),
inference(subsumption_resolution,[status(thm)],[f269,f80]) ).
thf(f80,plain,
( ( $true
= ( sP1 @ sK3 ) )
| ~ spl14_6 ),
inference(avatar_component_clause,[status(thm)],[f78]) ).
thf(f78,definition,
( spl14_6
<=> ( $true
= ( sP1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl14_6])],[avatar_definition]) ).
thf(f269,plain,
( ( $true
!= ( sP1 @ sK3 ) )
| ( $true
= ( sP0 @ sK3 @ sK3 ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(trivial_inequality_removal,[status(thm)],[f268]) ).
thf(f268,plain,
( ( $true
= ( sP0 @ sK3 @ sK3 ) )
| ( $true
!= ( sP1 @ sK3 ) )
| ( $true != $true )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(duplicate_literal_removal,[status(thm)],[f261]) ).
thf(f261,plain,
( ( $true != $true )
| ( $true
!= ( sP1 @ sK3 ) )
| ( $true
= ( sP0 @ sK3 @ sK3 ) )
| ( $true
= ( sP0 @ sK3 @ sK3 ) )
| ( $true
!= ( sP1 @ sK3 ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(superposition,[status(thm)],[f245,f201]) ).
thf(f201,plain,
( ! [X0: a > $o] :
( ( $true
= ( sK3 @ ( sK10 @ sK3 @ X0 ) ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 @ sK3 ) ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(subsumption_resolution,[status(thm)],[f200,f46]) ).
thf(f46,plain,
! [X2: a > $o,X0: a > $o] :
( ( $true
= ( X2 @ ( sK10 @ X2 @ X0 ) ) )
| ( $true
= ( sK9 @ X2
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sP0 @ X0 @ X2 ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: a > $o] :
( ( ( $true
= ( cA @ ( sK8 @ X0 ) ) )
& ! [X2: a > $o] :
( ( ! [X4: a > $o] :
( ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( sK9 @ X2
@ ^ [Y0: a] :
( ( X5 = Y0 )
| ( X4 @ Y0 ) ) ) ) )
| ( $true
!= ( sK9 @ X2 @ X4 ) ) )
& ( $true
= ( sK9 @ X2
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( sK9 @ X2 @ X2 ) ) )
| ( ( $true
= ( X2 @ ( sK10 @ X2 @ X0 ) ) )
& ( $true
!= ( sK8 @ X0 @ ( sK10 @ X2 @ X0 ) ) ) )
| ( $true
= ( sP0 @ X0 @ X2 ) ) )
& ! [X7: a] :
( ( $true
= ( sK8 @ X0 @ X7 ) )
| ( ( X0 @ X7 )
!= $true ) ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f22,f25,f24,f23]) ).
thf(f23,plain,
! [X0: a > $o] :
( ? [X1: a > $o] :
( ( $true
= ( cA @ X1 ) )
& ! [X2: a > $o] :
( ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( X3
@ ^ [Y0: a] :
( ( X5 = Y0 )
| ( X4 @ Y0 ) ) ) ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ( $true
= ( X3
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( X3 @ X2 ) ) )
| ? [X6: a] :
( ( $true
= ( X2 @ X6 ) )
& ( $true
!= ( X1 @ X6 ) ) )
| ( $true
= ( sP0 @ X0 @ X2 ) ) )
& ! [X7: a] :
( ( ( X1 @ X7 )
= $true )
| ( ( X0 @ X7 )
!= $true ) ) )
=> ( ( $true
= ( cA @ ( sK8 @ X0 ) ) )
& ! [X2: a > $o] :
( ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( X3
@ ^ [Y0: a] :
( ( X5 = Y0 )
| ( X4 @ Y0 ) ) ) ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ( $true
= ( X3
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( X3 @ X2 ) ) )
| ? [X6: a] :
( ( $true
= ( X2 @ X6 ) )
& ( $true
!= ( sK8 @ X0 @ X6 ) ) )
| ( $true
= ( sP0 @ X0 @ X2 ) ) )
& ! [X7: a] :
( ( $true
= ( sK8 @ X0 @ X7 ) )
| ( ( X0 @ X7 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
! [X2: a > $o] :
( ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( X3
@ ^ [Y0: a] :
( ( X5 = Y0 )
| ( X4 @ Y0 ) ) ) ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ( $true
= ( X3
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( X3 @ X2 ) ) )
=> ( ! [X4: a > $o] :
( ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( sK9 @ X2
@ ^ [Y0: a] :
( ( X5 = Y0 )
| ( X4 @ Y0 ) ) ) ) )
| ( $true
!= ( sK9 @ X2 @ X4 ) ) )
& ( $true
= ( sK9 @ X2
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( sK9 @ X2 @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
! [X0: a > $o,X2: a > $o] :
( ? [X6: a] :
( ( $true
= ( X2 @ X6 ) )
& ( $true
!= ( sK8 @ X0 @ X6 ) ) )
=> ( ( $true
= ( X2 @ ( sK10 @ X2 @ X0 ) ) )
& ( $true
!= ( sK8 @ X0 @ ( sK10 @ X2 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
! [X0: a > $o] :
( ? [X1: a > $o] :
( ( $true
= ( cA @ X1 ) )
& ! [X2: a > $o] :
( ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
= ( X3
@ ^ [Y0: a] :
( ( X5 = Y0 )
| ( X4 @ Y0 ) ) ) ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ( $true
= ( X3
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( X3 @ X2 ) ) )
| ? [X6: a] :
( ( $true
= ( X2 @ X6 ) )
& ( $true
!= ( X1 @ X6 ) ) )
| ( $true
= ( sP0 @ X0 @ X2 ) ) )
& ! [X7: a] :
( ( ( X1 @ X7 )
= $true )
| ( ( X0 @ X7 )
!= $true ) ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: a > $o] :
( ? [X7: a > $o] :
( ( $true
= ( cA @ X7 ) )
& ! [X9: a > $o] :
( ? [X13: ( a > $o ) > $o] :
( ! [X14: a > $o] :
( ! [X15: a] :
( ( $true
!= ( X9 @ X15 ) )
| ( $true
= ( X13
@ ^ [Y0: a] :
( ( X15 = Y0 )
| ( X14 @ Y0 ) ) ) ) )
| ( $true
!= ( X13 @ X14 ) ) )
& ( $true
= ( X13
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( X13 @ X9 ) ) )
| ? [X16: a] :
( ( $true
= ( X9 @ X16 ) )
& ( $true
!= ( X7 @ X16 ) ) )
| ( $true
= ( sP0 @ X1 @ X9 ) ) )
& ! [X8: a] :
( ( $true
= ( X7 @ X8 ) )
| ( $true
!= ( X1 @ X8 ) ) ) )
| ( $true
!= ( sP1 @ X1 ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: a > $o] :
( ? [X7: a > $o] :
( ( $true
= ( cA @ X7 ) )
& ! [X9: a > $o] :
( ? [X13: ( a > $o ) > $o] :
( ! [X14: a > $o] :
( ! [X15: a] :
( ( $true
!= ( X9 @ X15 ) )
| ( $true
= ( X13
@ ^ [Y0: a] :
( ( X15 = Y0 )
| ( X14 @ Y0 ) ) ) ) )
| ( $true
!= ( X13 @ X14 ) ) )
& ( $true
= ( X13
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( X13 @ X9 ) ) )
| ? [X16: a] :
( ( $true
= ( X9 @ X16 ) )
& ( $true
!= ( X7 @ X16 ) ) )
| ( $true
= ( sP0 @ X1 @ X9 ) ) )
& ! [X8: a] :
( ( $true
= ( X7 @ X8 ) )
| ( $true
!= ( X1 @ X8 ) ) ) )
| ( $true
!= ( sP1 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f200,plain,
( ! [X0: a > $o] :
( ( $true
!= ( sK9 @ sK3
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sK3 @ ( sK10 @ sK3 @ X0 ) ) )
| ( $true
= ( sP0 @ X0 @ sK3 ) )
| ( $true
!= ( sP1 @ X0 ) ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(subsumption_resolution,[status(thm)],[f197,f44]) ).
thf(f44,plain,
! [X2: a > $o,X0: a > $o] :
( ( $true
= ( X2 @ ( sK10 @ X2 @ X0 ) ) )
| ( $true
= ( sP0 @ X0 @ X2 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
!= ( sK9 @ X2 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f197,plain,
( ! [X0: a > $o] :
( ( $true
= ( sK3 @ ( sK10 @ sK3 @ X0 ) ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 @ sK3 ) )
| ( $true
= ( sK9 @ sK3 @ sK3 ) )
| ( $true
!= ( sK9 @ sK3
@ ^ [Y0: a] : $false ) ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(trivial_inequality_removal,[status(thm)],[f196]) ).
thf(f196,plain,
( ! [X0: a > $o] :
( ( $true
!= ( sP1 @ X0 ) )
| ( $true
!= ( sK9 @ sK3
@ ^ [Y0: a] : $false ) )
| ( $true != $true )
| ( $true
= ( sK9 @ sK3 @ sK3 ) )
| ( $true
= ( sP0 @ X0 @ sK3 ) )
| ( $true
= ( sK3 @ ( sK10 @ sK3 @ X0 ) ) ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(duplicate_literal_removal,[status(thm)],[f195]) ).
thf(f195,plain,
( ! [X0: a > $o] :
( ( $true
!= ( sP1 @ X0 ) )
| ( $true
!= ( sK9 @ sK3
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sK9 @ sK3 @ sK3 ) )
| ( $true
= ( sK3 @ ( sK10 @ sK3 @ X0 ) ) )
| ( $true != $true )
| ( $true
= ( sP0 @ X0 @ sK3 ) )
| ( $true
= ( sK9 @ sK3 @ sK3 ) ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(superposition,[status(thm)],[f188,f98]) ).
thf(f98,plain,
( ! [X5: ( a > $o ) > $o] :
( ( $true
= ( sK3 @ ( sK7 @ X5 ) ) )
| ( $true
!= ( X5
@ ^ [Y0: a] : $false ) )
| ( $true
= ( X5 @ sK3 ) ) )
| ~ spl14_10 ),
inference(avatar_component_clause,[status(thm)],[f97]) ).
thf(f97,definition,
( spl14_10
<=> ! [X5: ( a > $o ) > $o] :
( ( $true
!= ( X5
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sK3 @ ( sK7 @ X5 ) ) )
| ( $true
= ( X5 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl14_10])],[avatar_definition]) ).
thf(f188,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
= ( X0 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) ) )
| ~ spl14_3
| ~ spl14_9 ),
inference(subsumption_resolution,[status(thm)],[f187,f46]) ).
thf(f187,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sK9 @ X0
@ ^ [Y0: a] : $false ) )
| ( $true
= ( X0 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) ) )
| ~ spl14_3
| ~ spl14_9 ),
inference(trivial_inequality_removal,[status(thm)],[f186]) ).
thf(f186,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true
= ( X0 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true != $true )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
!= ( sK9 @ X0
@ ^ [Y0: a] : $false ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) ) )
| ~ spl14_3
| ~ spl14_9 ),
inference(duplicate_literal_removal,[status(thm)],[f185]) ).
thf(f185,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sP1 @ X1 ) )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
!= ( sK9 @ X0
@ ^ [Y0: a] : $false ) )
| ( $true != $true )
| ( $true
= ( X0 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) ) )
| ~ spl14_3
| ~ spl14_9 ),
inference(superposition,[status(thm)],[f144,f66]) ).
thf(f66,plain,
( ! [X5: ( a > $o ) > $o] :
( ( $true
= ( X5 @ ( sK6 @ X5 ) ) )
| ( $true
!= ( X5
@ ^ [Y0: a] : $false ) )
| ( $true
= ( X5 @ sK3 ) ) )
| ~ spl14_3 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f65,definition,
( spl14_3
<=> ! [X5: ( a > $o ) > $o] :
( ( $true
!= ( X5
@ ^ [Y0: a] : $false ) )
| ( $true
= ( X5 @ ( sK6 @ X5 ) ) )
| ( $true
= ( X5 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl14_3])],[avatar_definition]) ).
thf(f144,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sK9 @ X0 @ ( sK6 @ ( sK9 @ X0 ) ) ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true
= ( X0 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) ) )
| ~ spl14_9 ),
inference(subsumption_resolution,[status(thm)],[f143,f46]) ).
thf(f143,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true
!= ( sK9 @ X0
@ ^ [Y0: a] : $false ) )
| ( $true
!= ( sK9 @ X0 @ ( sK6 @ ( sK9 @ X0 ) ) ) )
| ( $true
= ( X0 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) ) )
| ~ spl14_9 ),
inference(trivial_inequality_removal,[status(thm)],[f142]) ).
thf(f142,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sK9 @ X0
@ ^ [Y0: a] : $false ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true != $true )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
!= ( sK9 @ X0 @ ( sK6 @ ( sK9 @ X0 ) ) ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true
= ( X0 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) ) )
| ~ spl14_9 ),
inference(superposition,[status(thm)],[f94,f48]) ).
thf(f48,plain,
! [X2: a > $o,X0: a > $o,X4: a > $o,X5: a] :
( ( $true
= ( sK9 @ X2
@ ^ [Y0: a] :
( ( X5 = Y0 )
| ( X4 @ Y0 ) ) ) )
| ( $true
= ( X2 @ ( sK10 @ X2 @ X0 ) ) )
| ( $true
!= ( X2 @ X5 ) )
| ( $true
!= ( sK9 @ X2 @ X4 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f94,plain,
( ! [X5: ( a > $o ) > $o] :
( ( $true
!= ( X5
@ ^ [Y0: a] :
( ( ( sK7 @ X5 )
= Y0 )
| ( sK6 @ X5 @ Y0 ) ) ) )
| ( $true
= ( X5 @ sK3 ) )
| ( $true
!= ( X5
@ ^ [Y0: a] : $false ) ) )
| ~ spl14_9 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f93,definition,
( spl14_9
<=> ! [X5: ( a > $o ) > $o] :
( ( $true
!= ( X5
@ ^ [Y0: a] :
( ( ( sK7 @ X5 )
= Y0 )
| ( sK6 @ X5 @ Y0 ) ) ) )
| ( $true
= ( X5 @ sK3 ) )
| ( $true
!= ( X5
@ ^ [Y0: a] : $false ) ) ) ),
introduced(definition,[new_symbols(naming,[spl14_9])],[avatar_definition]) ).
thf(f245,plain,
( ! [X0: a > $o] :
( ( $true
!= ( X0 @ ( sK10 @ sK3 @ X0 ) ) )
| ( $true
= ( sP0 @ X0 @ sK3 ) )
| ( $true
!= ( sP1 @ X0 ) ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(subsumption_resolution,[status(thm)],[f244,f130]) ).
thf(f130,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( sK9 @ X1
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sP0 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f129]) ).
thf(f129,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
= ( sK9 @ X1
@ ^ [Y0: a] : $false ) )
| ( $true
!= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true != $true )
| ( $true
= ( sP0 @ X0 @ X1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f122]) ).
thf(f122,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sP1 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 @ X1 ) )
| ( $true
= ( sK9 @ X1
@ ^ [Y0: a] : $false ) ) ),
inference(superposition,[status(thm)],[f45,f42]) ).
thf(f42,plain,
! [X0: a > $o,X7: a] :
( ( $true
= ( sK8 @ X0 @ X7 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( ( X0 @ X7 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f45,plain,
! [X2: a > $o,X0: a > $o] :
( ( $true
!= ( sK8 @ X0 @ ( sK10 @ X2 @ X0 ) ) )
| ( $true
= ( sK9 @ X2
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sP0 @ X0 @ X2 ) )
| ( $true
!= ( sP1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f244,plain,
( ! [X0: a > $o] :
( ( $true
!= ( sK9 @ sK3
@ ^ [Y0: a] : $false ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
!= ( X0 @ ( sK10 @ sK3 @ X0 ) ) )
| ( $true
= ( sP0 @ X0 @ sK3 ) ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(subsumption_resolution,[status(thm)],[f242,f107]) ).
thf(f107,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $true
!= ( sK9 @ X1 @ X1 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true != $true )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 @ X1 ) )
| ( $true
!= ( sK9 @ X1 @ X1 ) )
| ( $true
!= ( X0 @ ( sK10 @ X1 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f103]) ).
thf(f103,plain,
! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $true
!= ( sK9 @ X1 @ X1 ) )
| ( $true
= ( sP0 @ X0 @ X1 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f43,f42]) ).
thf(f43,plain,
! [X2: a > $o,X0: a > $o] :
( ( $true
!= ( sK8 @ X0 @ ( sK10 @ X2 @ X0 ) ) )
| ( $true
!= ( sK9 @ X2 @ X2 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f242,plain,
( ! [X0: a > $o] :
( ( $true
!= ( X0 @ ( sK10 @ sK3 @ X0 ) ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
!= ( sK9 @ sK3
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sK9 @ sK3 @ sK3 ) )
| ( $true
= ( sP0 @ X0 @ sK3 ) ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(trivial_inequality_removal,[status(thm)],[f241]) ).
thf(f241,plain,
( ! [X0: a > $o] :
( ( $true
!= ( X0 @ ( sK10 @ sK3 @ X0 ) ) )
| ( $true
= ( sK9 @ sK3 @ sK3 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 @ sK3 ) )
| ( $true
!= ( sK9 @ sK3
@ ^ [Y0: a] : $false ) )
| ( $true != $true ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(duplicate_literal_removal,[status(thm)],[f239]) ).
thf(f239,plain,
( ! [X0: a > $o] :
( ( $true
= ( sK9 @ sK3 @ sK3 ) )
| ( $true
!= ( X0 @ ( sK10 @ sK3 @ X0 ) ) )
| ( $true
= ( sP0 @ X0 @ sK3 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true != $true )
| ( $true
= ( sK9 @ sK3 @ sK3 ) )
| ( $true
!= ( sK9 @ sK3
@ ^ [Y0: a] : $false ) ) )
| ~ spl14_3
| ~ spl14_9
| ~ spl14_10 ),
inference(superposition,[status(thm)],[f232,f98]) ).
thf(f232,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( X1 @ ( sK7 @ ( sK9 @ X1 ) ) ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 @ X1 ) )
| ( $true
!= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $true
= ( sK9 @ X1 @ sK3 ) ) )
| ~ spl14_3
| ~ spl14_9 ),
inference(trivial_inequality_removal,[status(thm)],[f231]) ).
thf(f231,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( X1 @ ( sK7 @ ( sK9 @ X1 ) ) ) )
| ( $true
= ( sP0 @ X0 @ X1 ) )
| ( $true
!= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $true != $true )
| ( $true
= ( sK9 @ X1 @ sK3 ) )
| ( $true
!= ( sP1 @ X0 ) ) )
| ~ spl14_3
| ~ spl14_9 ),
inference(duplicate_literal_removal,[status(thm)],[f228]) ).
thf(f228,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( X1 @ ( sK7 @ ( sK9 @ X1 ) ) ) )
| ( $true
= ( sK9 @ X1 @ sK3 ) )
| ( $true
!= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $true
= ( sP0 @ X0 @ X1 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true != $true ) )
| ~ spl14_3
| ~ spl14_9 ),
inference(superposition,[status(thm)],[f192,f42]) ).
thf(f192,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sK8 @ X1 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) ) )
| ~ spl14_3
| ~ spl14_9 ),
inference(subsumption_resolution,[status(thm)],[f191,f45]) ).
thf(f191,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sK9 @ X0
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
!= ( sK8 @ X1 @ ( sK10 @ X0 @ X1 ) ) ) )
| ~ spl14_3
| ~ spl14_9 ),
inference(trivial_inequality_removal,[status(thm)],[f190]) ).
thf(f190,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) )
| ( $true
!= ( sK8 @ X1 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true
!= ( sK9 @ X0
@ ^ [Y0: a] : $false ) ) )
| ~ spl14_3
| ~ spl14_9 ),
inference(duplicate_literal_removal,[status(thm)],[f189]) ).
thf(f189,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
!= ( sK8 @ X1 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
!= ( sK9 @ X0
@ ^ [Y0: a] : $false ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true != $true ) )
| ~ spl14_3
| ~ spl14_9 ),
inference(superposition,[status(thm)],[f149,f66]) ).
thf(f149,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sK9 @ X0 @ ( sK6 @ ( sK9 @ X0 ) ) ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
!= ( sK8 @ X1 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) ) )
| ~ spl14_9 ),
inference(subsumption_resolution,[status(thm)],[f148,f45]) ).
thf(f148,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
!= ( sK9 @ X0 @ ( sK6 @ ( sK9 @ X0 ) ) ) )
| ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
!= ( sK9 @ X0
@ ^ [Y0: a] : $false ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
!= ( sK8 @ X1 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) ) )
| ~ spl14_9 ),
inference(trivial_inequality_removal,[status(thm)],[f147]) ).
thf(f147,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( $true
= ( sP0 @ X1 @ X0 ) )
| ( $true
!= ( sK8 @ X1 @ ( sK10 @ X0 @ X1 ) ) )
| ( $true
= ( sK9 @ X0 @ sK3 ) )
| ( $true != $true )
| ( $true
!= ( sK9 @ X0 @ ( sK6 @ ( sK9 @ X0 ) ) ) )
| ( $true
!= ( sP1 @ X1 ) )
| ( $true
!= ( X0 @ ( sK7 @ ( sK9 @ X0 ) ) ) )
| ( $true
!= ( sK9 @ X0
@ ^ [Y0: a] : $false ) ) )
| ~ spl14_9 ),
inference(superposition,[status(thm)],[f94,f47]) ).
thf(f47,plain,
! [X2: a > $o,X0: a > $o,X4: a > $o,X5: a] :
( ( $true
= ( sK9 @ X2
@ ^ [Y0: a] :
( ( X5 = Y0 )
| ( X4 @ Y0 ) ) ) )
| ( $true
!= ( sK9 @ X2 @ X4 ) )
| ( $true
!= ( sK8 @ X0 @ ( sK10 @ X2 @ X0 ) ) )
| ( $true
!= ( sP1 @ X0 ) )
| ( $true
= ( sP0 @ X0 @ X2 ) )
| ( $true
!= ( X2 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f99,plain,
( spl14_10
| ~ spl14_1 ),
inference(avatar_split_clause,[status(thm)],[f36,f57,f97]) ).
thf(f57,definition,
( spl14_1
<=> ( $true = sP2 ) ),
introduced(definition,[new_symbols(naming,[spl14_1])],[avatar_definition]) ).
thf(f36,plain,
! [X5: ( a > $o ) > $o] :
( ( $true != sP2 )
| ( $true
!= ( X5
@ ^ [Y0: a] : $false ) )
| ( $true
= ( X5 @ sK3 ) )
| ( $true
= ( sK3 @ ( sK7 @ X5 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( ( ! [X2: a] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
!= ( sK3 @ X2 ) ) )
& ( $true
!= ( cA @ sK4 ) )
& ( $true
= ( cA @ sK4 ) ) )
| ( $true
= ( sP1 @ sK3 ) ) )
& ! [X3: a] :
( ( $true
!= ( sK3 @ X3 ) )
| ( ( $true
= ( sK5 @ X3 @ X3 ) )
& ( $true
= ( cA @ ( sK5 @ X3 ) ) ) ) )
& ! [X5: ( a > $o ) > $o] :
( ( $true
= ( X5 @ sK3 ) )
| ( $true
!= ( X5
@ ^ [Y0: a] : $false ) )
| ( ( $true
= ( sK3 @ ( sK7 @ X5 ) ) )
& ( $true
!= ( X5
@ ^ [Y0: a] :
( ( ( sK7 @ X5 )
= Y0 )
| ( sK6 @ X5 @ Y0 ) ) ) )
& ( $true
= ( X5 @ ( sK6 @ X5 ) ) ) ) ) )
| ( $true != sP2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f14,f19,f18,f17,f16,f15]) ).
thf(f15,plain,
( ? [X0: a > $o] :
( ( ? [X1: a > $o] :
( ! [X2: a] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( X0 @ X2 ) ) )
& ( $true
!= ( cA @ X1 ) )
& ( $true
= ( cA @ X1 ) ) )
| ( $true
= ( sP1 @ X0 ) ) )
& ! [X3: a] :
( ( $true
!= ( X0 @ X3 ) )
| ? [X4: a > $o] :
( ( $true
= ( X4 @ X3 ) )
& ( $true
= ( cA @ X4 ) ) ) )
& ! [X5: ( a > $o ) > $o] :
( ( $true
= ( X5 @ X0 ) )
| ( $true
!= ( X5
@ ^ [Y0: a] : $false ) )
| ? [X6: a > $o] :
( ? [X7: a] :
( ( ( X0 @ X7 )
= $true )
& ( $true
!= ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) ) ) )
& ( $true
= ( X5 @ X6 ) ) ) ) )
=> ( ( ? [X1: a > $o] :
( ! [X2: a] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( sK3 @ X2 ) ) )
& ( $true
!= ( cA @ X1 ) )
& ( $true
= ( cA @ X1 ) ) )
| ( $true
= ( sP1 @ sK3 ) ) )
& ! [X3: a] :
( ( $true
!= ( sK3 @ X3 ) )
| ? [X4: a > $o] :
( ( $true
= ( X4 @ X3 ) )
& ( $true
= ( cA @ X4 ) ) ) )
& ! [X5: ( a > $o ) > $o] :
( ( $true
= ( X5 @ sK3 ) )
| ( $true
!= ( X5
@ ^ [Y0: a] : $false ) )
| ? [X6: a > $o] :
( ? [X7: a] :
( ( $true
= ( sK3 @ X7 ) )
& ( $true
!= ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) ) ) )
& ( $true
= ( X5 @ X6 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X1: a > $o] :
( ! [X2: a] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( sK3 @ X2 ) ) )
& ( $true
!= ( cA @ X1 ) )
& ( $true
= ( cA @ X1 ) ) )
=> ( ! [X2: a] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
!= ( sK3 @ X2 ) ) )
& ( $true
!= ( cA @ sK4 ) )
& ( $true
= ( cA @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
! [X3: a] :
( ? [X4: a > $o] :
( ( $true
= ( X4 @ X3 ) )
& ( $true
= ( cA @ X4 ) ) )
=> ( ( $true
= ( sK5 @ X3 @ X3 ) )
& ( $true
= ( cA @ ( sK5 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
! [X5: ( a > $o ) > $o] :
( ? [X6: a > $o] :
( ? [X7: a] :
( ( $true
= ( sK3 @ X7 ) )
& ( $true
!= ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) ) ) )
& ( $true
= ( X5 @ X6 ) ) )
=> ( ? [X7: a] :
( ( $true
= ( sK3 @ X7 ) )
& ( $true
!= ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( sK6 @ X5 @ Y0 ) ) ) ) )
& ( $true
= ( X5 @ ( sK6 @ X5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
! [X5: ( a > $o ) > $o] :
( ? [X7: a] :
( ( $true
= ( sK3 @ X7 ) )
& ( $true
!= ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( sK6 @ X5 @ Y0 ) ) ) ) )
=> ( ( $true
= ( sK3 @ ( sK7 @ X5 ) ) )
& ( $true
!= ( X5
@ ^ [Y0: a] :
( ( ( sK7 @ X5 )
= Y0 )
| ( sK6 @ X5 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X0: a > $o] :
( ( ? [X1: a > $o] :
( ! [X2: a] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( X0 @ X2 ) ) )
& ( $true
!= ( cA @ X1 ) )
& ( $true
= ( cA @ X1 ) ) )
| ( $true
= ( sP1 @ X0 ) ) )
& ! [X3: a] :
( ( $true
!= ( X0 @ X3 ) )
| ? [X4: a > $o] :
( ( $true
= ( X4 @ X3 ) )
& ( $true
= ( cA @ X4 ) ) ) )
& ! [X5: ( a > $o ) > $o] :
( ( $true
= ( X5 @ X0 ) )
| ( $true
!= ( X5
@ ^ [Y0: a] : $false ) )
| ? [X6: a > $o] :
( ? [X7: a] :
( ( ( X0 @ X7 )
= $true )
& ( $true
!= ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) ) ) )
& ( $true
= ( X5 @ X6 ) ) ) ) )
| ( $true != sP2 ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X1: a > $o] :
( ( ? [X17: a > $o] :
( ! [X18: a] :
( ( $true
= ( X17 @ X18 ) )
| ( $true
!= ( X1 @ X18 ) ) )
& ( $true
!= ( cA @ X17 ) )
& ( $true
= ( cA @ X17 ) ) )
| ( $true
= ( sP1 @ X1 ) ) )
& ! [X2: a] :
( ( $true
!= ( X1 @ X2 ) )
| ? [X3: a > $o] :
( ( $true
= ( X3 @ X2 ) )
& ( ( cA @ X3 )
= $true ) ) )
& ! [X4: ( a > $o ) > $o] :
( ( $true
= ( X4 @ X1 ) )
| ( $true
!= ( X4
@ ^ [Y0: a] : $false ) )
| ? [X5: a > $o] :
( ? [X6: a] :
( ( $true
= ( X1 @ X6 ) )
& ( $true
!= ( X4
@ ^ [Y0: a] :
( ( X6 = Y0 )
| ( X5 @ Y0 ) ) ) ) )
& ( $true
= ( X4 @ X5 ) ) ) ) )
| ( $true != sP2 ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ? [X1: a > $o] :
( ( ? [X17: a > $o] :
( ! [X18: a] :
( ( $true
= ( X17 @ X18 ) )
| ( $true
!= ( X1 @ X18 ) ) )
& ( $true
!= ( cA @ X17 ) )
& ( $true
= ( cA @ X17 ) ) )
| ( $true
= ( sP1 @ X1 ) ) )
& ! [X2: a] :
( ( $true
!= ( X1 @ X2 ) )
| ? [X3: a > $o] :
( ( $true
= ( X3 @ X2 ) )
& ( ( cA @ X3 )
= $true ) ) )
& ! [X4: ( a > $o ) > $o] :
( ( $true
= ( X4 @ X1 ) )
| ( $true
!= ( X4
@ ^ [Y0: a] : $false ) )
| ? [X5: a > $o] :
( ? [X6: a] :
( ( $true
= ( X1 @ X6 ) )
& ( $true
!= ( X4
@ ^ [Y0: a] :
( ( X6 = Y0 )
| ( X5 @ Y0 ) ) ) ) )
& ( $true
= ( X4 @ X5 ) ) ) ) )
| ( $true != sP2 ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f95,plain,
( spl14_9
| ~ spl14_1 ),
inference(avatar_split_clause,[status(thm)],[f35,f57,f93]) ).
thf(f35,plain,
! [X5: ( a > $o ) > $o] :
( ( $true
!= ( X5
@ ^ [Y0: a] :
( ( ( sK7 @ X5 )
= Y0 )
| ( sK6 @ X5 @ Y0 ) ) ) )
| ( $true
!= ( X5
@ ^ [Y0: a] : $false ) )
| ( $true
= ( X5 @ sK3 ) )
| ( $true != sP2 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f83,plain,
( ~ spl14_5
| ~ spl14_1
| spl14_6 ),
inference(avatar_split_clause,[status(thm)],[f40,f78,f57,f74]) ).
thf(f74,definition,
( spl14_5
<=> ( $true
= ( cA @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl14_5])],[avatar_definition]) ).
thf(f40,plain,
( ( $true
= ( sP1 @ sK3 ) )
| ( $true != sP2 )
| ( $true
!= ( cA @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f82,plain,
( spl14_1
| spl14_4 ),
inference(avatar_split_clause,[status(thm)],[f54,f69,f57]) ).
thf(f69,definition,
( spl14_4
<=> ( $true
= ( cA @ sK13 ) ) ),
introduced(definition,[new_symbols(naming,[spl14_4])],[avatar_definition]) ).
thf(f54,plain,
( ( $true = sP2 )
| ( $true
= ( cA @ sK13 ) ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $true = sP2 )
| ( ( $true
!= ( cA @ sK13 ) )
& ( $true
= ( cA @ sK13 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f12,f32]) ).
thf(f32,plain,
( ? [X0: a > $o] :
( ( ( cA @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true ) )
=> ( ( $true
!= ( cA @ sK13 ) )
& ( $true
= ( cA @ sK13 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ( $true = sP2 )
| ? [X0: a > $o] :
( ( ( cA @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true ) ) ),
inference(definition_folding,[status(thm)],[f8,f11,f10,f9]) ).
thf(f8,plain,
( ? [X1: a > $o] :
( ( ? [X17: a > $o] :
( ! [X18: a] :
( ( $true
= ( X17 @ X18 ) )
| ( $true
!= ( X1 @ X18 ) ) )
& ( $true
!= ( cA @ X17 ) )
& ( $true
= ( cA @ X17 ) ) )
| ? [X7: a > $o] :
( ( $true
= ( cA @ X7 ) )
& ! [X9: a > $o] :
( ? [X13: ( a > $o ) > $o] :
( ! [X14: a > $o] :
( ! [X15: a] :
( ( $true
!= ( X9 @ X15 ) )
| ( $true
= ( X13
@ ^ [Y0: a] :
( ( X15 = Y0 )
| ( X14 @ Y0 ) ) ) ) )
| ( $true
!= ( X13 @ X14 ) ) )
& ( $true
= ( X13
@ ^ [Y0: a] : $false ) )
& ( $true
!= ( X13 @ X9 ) ) )
| ? [X16: a] :
( ( $true
= ( X9 @ X16 ) )
& ( $true
!= ( X7 @ X16 ) ) )
| ? [X10: a > $o] :
( ! [X11: a] :
( ( $true
!= ( X9 @ X11 ) )
| ( $true
= ( X10 @ X11 ) ) )
& ( $true
= ( cA @ X10 ) )
& ( ( $true
!= ( cA @ X10 ) )
| ? [X12: a] :
( ( $true
!= ( X10 @ X12 ) )
& ( $true
= ( X1 @ X12 ) ) ) ) ) )
& ! [X8: a] :
( ( $true
= ( X7 @ X8 ) )
| ( $true
!= ( X1 @ X8 ) ) ) ) )
& ! [X2: a] :
( ( $true
!= ( X1 @ X2 ) )
| ? [X3: a > $o] :
( ( $true
= ( X3 @ X2 ) )
& ( ( cA @ X3 )
= $true ) ) )
& ! [X4: ( a > $o ) > $o] :
( ( $true
= ( X4 @ X1 ) )
| ( $true
!= ( X4
@ ^ [Y0: a] : $false ) )
| ? [X5: a > $o] :
( ? [X6: a] :
( ( $true
= ( X1 @ X6 ) )
& ( $true
!= ( X4
@ ^ [Y0: a] :
( ( X6 = Y0 )
| ( X5 @ Y0 ) ) ) ) )
& ( $true
= ( X4 @ X5 ) ) ) ) )
| ? [X0: a > $o] :
( ( ( cA @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X0: a > $o] :
( ( ( cA @ X0 )
!= $true )
& ( ( cA @ X0 )
= $true ) )
| ? [X1: a > $o] :
( ( ? [X7: a > $o] :
( ! [X9: a > $o] :
( ? [X10: a > $o] :
( ( ( $true
!= ( cA @ X10 ) )
| ? [X12: a] :
( ( $true
!= ( X10 @ X12 ) )
& ( $true
= ( X1 @ X12 ) ) ) )
& ! [X11: a] :
( ( $true
!= ( X9 @ X11 ) )
| ( $true
= ( X10 @ X11 ) ) )
& ( $true
= ( cA @ X10 ) ) )
| ? [X16: a] :
( ( $true
= ( X9 @ X16 ) )
& ( $true
!= ( X7 @ X16 ) ) )
| ? [X13: ( a > $o ) > $o] :
( ( $true
!= ( X13 @ X9 ) )
& ( $true
= ( X13
@ ^ [Y0: a] : $false ) )
& ! [X14: a > $o] :
( ! [X15: a] :
( ( $true
!= ( X9 @ X15 ) )
| ( $true
= ( X13
@ ^ [Y0: a] :
( ( X15 = Y0 )
| ( X14 @ Y0 ) ) ) ) )
| ( $true
!= ( X13 @ X14 ) ) ) ) )
& ! [X8: a] :
( ( $true
= ( X7 @ X8 ) )
| ( $true
!= ( X1 @ X8 ) ) )
& ( $true
= ( cA @ X7 ) ) )
| ? [X17: a > $o] :
( ( $true
!= ( cA @ X17 ) )
& ( $true
= ( cA @ X17 ) )
& ! [X18: a] :
( ( $true
= ( X17 @ X18 ) )
| ( $true
!= ( X1 @ X18 ) ) ) ) )
& ! [X4: ( a > $o ) > $o] :
( ( $true
= ( X4 @ X1 ) )
| ( $true
!= ( X4
@ ^ [Y0: a] : $false ) )
| ? [X5: a > $o] :
( ? [X6: a] :
( ( $true
= ( X1 @ X6 ) )
& ( $true
!= ( X4
@ ^ [Y0: a] :
( ( X6 = Y0 )
| ( X5 @ Y0 ) ) ) ) )
& ( $true
= ( X4 @ X5 ) ) ) )
& ! [X2: a] :
( ( $true
!= ( X1 @ X2 ) )
| ? [X3: a > $o] :
( ( $true
= ( X3 @ X2 ) )
& ( ( cA @ X3 )
= $true ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: a > $o] :
( ( ( cA @ X0 )
= $true )
=> ( ( cA @ X0 )
= $true ) )
& ! [X1: a > $o] :
( ( ! [X4: ( a > $o ) > $o] :
( ( ( $true
= ( X4
@ ^ [Y0: a] : $false ) )
& ! [X5: a > $o] :
( ( $true
= ( X4 @ X5 ) )
=> ! [X6: a] :
( ( $true
= ( X1 @ X6 ) )
=> ( $true
= ( X4
@ ^ [Y0: a] :
( ( X6 = Y0 )
| ( X5 @ Y0 ) ) ) ) ) ) )
=> ( $true
= ( X4 @ X1 ) ) )
& ! [X2: a] :
( ( $true
= ( X1 @ X2 ) )
=> ? [X3: a > $o] :
( ( $true
= ( X3 @ X2 ) )
& ( ( cA @ X3 )
= $true ) ) ) )
=> ( ! [X7: a > $o] :
( ( ! [X8: a] :
( ( $true
= ( X1 @ X8 ) )
=> ( $true
= ( X7 @ X8 ) ) )
& ( $true
= ( cA @ X7 ) ) )
=> ? [X9: a > $o] :
( ! [X10: a > $o] :
( ( ! [X11: a] :
( ( $true
= ( X9 @ X11 ) )
=> ( $true
= ( X10 @ X11 ) ) )
& ( $true
= ( cA @ X10 ) ) )
=> ( ! [X12: a] :
( ( $true
= ( X1 @ X12 ) )
=> ( $true
= ( X10 @ X12 ) ) )
& ( $true
= ( cA @ X10 ) ) ) )
& ! [X16: a] :
( ( $true
= ( X9 @ X16 ) )
=> ( $true
= ( X7 @ X16 ) ) )
& ! [X13: ( a > $o ) > $o] :
( ( ( $true
= ( X13
@ ^ [Y0: a] : $false ) )
& ! [X14: a > $o] :
( ( $true
= ( X13 @ X14 ) )
=> ! [X15: a] :
( ( $true
= ( X9 @ X15 ) )
=> ( $true
= ( X13
@ ^ [Y0: a] :
( ( X15 = Y0 )
| ( X14 @ Y0 ) ) ) ) ) ) )
=> ( $true
= ( X13 @ X9 ) ) ) ) )
& ! [X17: a > $o] :
( ( ( $true
= ( cA @ X17 ) )
& ! [X18: a] :
( ( $true
= ( X1 @ X18 ) )
=> ( $true
= ( X17 @ X18 ) ) ) )
=> ( $true
= ( cA @ X17 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a > $o] :
( ( ( cA @ X0 )
= $true )
=> ( ( cA @ X0 )
= $true ) )
& ! [X1: a > $o] :
( ( ! [X4: ( a > $o ) > $o] :
( ( ( $true
= ( X4
@ ^ [Y0: a] : $false ) )
& ! [X5: a > $o] :
( ( $true
= ( X4 @ X5 ) )
=> ! [X6: a] :
( ( $true
= ( X1 @ X6 ) )
=> ( $true
= ( X4
@ ^ [Y0: a] :
( ( X6 = Y0 )
| ( X5 @ Y0 ) ) ) ) ) ) )
=> ( $true
= ( X4 @ X1 ) ) )
& ! [X2: a] :
( ( $true
= ( X1 @ X2 ) )
=> ? [X3: a > $o] :
( ( $true
= ( X3 @ X2 ) )
& ( ( cA @ X3 )
= $true ) ) ) )
=> ( ! [X9: a > $o] :
( ( ( $true
= ( cA @ X9 ) )
& ! [X10: a] :
( ( $true
= ( X1 @ X10 ) )
=> ( $true
= ( X9 @ X10 ) ) ) )
=> ? [X11: a > $o] :
( ! [X12: a > $o] :
( ( ( $true
= ( cA @ X12 ) )
& ! [X13: a] :
( ( $true
= ( X11 @ X13 ) )
=> ( $true
= ( X12 @ X13 ) ) ) )
=> ( ( $true
= ( cA @ X12 ) )
& ! [X14: a] :
( ( $true
= ( X1 @ X14 ) )
=> ( $true
= ( X12 @ X14 ) ) ) ) )
& ! [X15: ( a > $o ) > $o] :
( ( ! [X16: a > $o] :
( ( $true
= ( X15 @ X16 ) )
=> ! [X17: a] :
( ( $true
= ( X11 @ X17 ) )
=> ( ( X15
@ ^ [Y0: a] :
( ( X17 = Y0 )
| ( X16 @ Y0 ) ) )
= $true ) ) )
& ( $true
= ( X15
@ ^ [Y0: a] : $false ) ) )
=> ( $true
= ( X15 @ X11 ) ) )
& ! [X20: a] :
( ( $true
= ( X11 @ X20 ) )
=> ( $true
= ( X9 @ X20 ) ) ) ) )
& ! [X21: a > $o] :
( ( ( $true
= ( cA @ X21 ) )
& ! [X22: a] :
( ( $true
= ( X1 @ X22 ) )
=> ( $true
= ( X21 @ X22 ) ) ) )
=> ( $true
= ( cA @ X21 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > $o] :
( ( cA @ X0 )
=> ( cA @ X0 ) )
& ! [X1: a > $o] :
( ( ! [X2: a] :
( ( X1 @ X2 )
=> ? [X3: a > $o] :
( ( cA @ X3 )
& ( X3 @ X2 ) ) )
& ! [X4: ( a > $o ) > $o] :
( ( ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ( X5 @ X7 )
| ( X6 = X7 ) ) ) ) )
& ( X4
@ ^ [X8: a] : $false ) )
=> ( X4 @ X1 ) ) )
=> ( ! [X9: a > $o] :
( ( ( cA @ X9 )
& ! [X10: a] :
( ( X1 @ X10 )
=> ( X9 @ X10 ) ) )
=> ? [X11: a > $o] :
( ! [X12: a > $o] :
( ( ( cA @ X12 )
& ! [X13: a] :
( ( X11 @ X13 )
=> ( X12 @ X13 ) ) )
=> ( ( cA @ X12 )
& ! [X14: a] :
( ( X1 @ X14 )
=> ( X12 @ X14 ) ) ) )
& ! [X15: ( a > $o ) > $o] :
( ( ! [X16: a > $o] :
( ( X15 @ X16 )
=> ! [X17: a] :
( ( X11 @ X17 )
=> ( X15
@ ^ [X18: a] :
( ( X16 @ X18 )
| ( X17 = X18 ) ) ) ) )
& ( X15
@ ^ [X19: a] : $false ) )
=> ( X15 @ X11 ) )
& ! [X20: a] :
( ( X11 @ X20 )
=> ( X9 @ X20 ) ) ) )
& ! [X21: a > $o] :
( ( ( cA @ X21 )
& ! [X22: a] :
( ( X1 @ X22 )
=> ( X21 @ X22 ) ) )
=> ( cA @ X21 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a > $o] :
( ( cA @ X0 )
=> ( cA @ X0 ) )
& ! [X1: a > $o] :
( ( ! [X0: a] :
( ( X1 @ X0 )
=> ? [X6: a > $o] :
( ( cA @ X6 )
& ( X6 @ X0 ) ) )
& ! [X2: ( a > $o ) > $o] :
( ( ! [X0: a > $o] :
( ( X2 @ X0 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X0 @ X5 )
| ( X4 = X5 ) ) ) ) )
& ( X2
@ ^ [X3: a] : $false ) )
=> ( X2 @ X1 ) ) )
=> ( ! [X0: a > $o] :
( ( ( cA @ X0 )
& ! [X7: a] :
( ( X1 @ X7 )
=> ( X0 @ X7 ) ) )
=> ? [X8: a > $o] :
( ! [X3: a > $o] :
( ( ( cA @ X3 )
& ! [X7: a] :
( ( X8 @ X7 )
=> ( X3 @ X7 ) ) )
=> ( ( cA @ X3 )
& ! [X7: a] :
( ( X1 @ X7 )
=> ( X3 @ X7 ) ) ) )
& ! [X2: ( a > $o ) > $o] :
( ( ! [X7: a > $o] :
( ( X2 @ X7 )
=> ! [X4: a] :
( ( X8 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X7 @ X5 )
| ( X4 = X5 ) ) ) ) )
& ( X2
@ ^ [X3: a] : $false ) )
=> ( X2 @ X8 ) )
& ! [X7: a] :
( ( X8 @ X7 )
=> ( X0 @ X7 ) ) ) )
& ! [X0: a > $o] :
( ( ( cA @ X0 )
& ! [X7: a] :
( ( X1 @ X7 )
=> ( X0 @ X7 ) ) )
=> ( cA @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a > $o] :
( ( cA @ X0 )
=> ( cA @ X0 ) )
& ! [X1: a > $o] :
( ( ! [X0: a] :
( ( X1 @ X0 )
=> ? [X6: a > $o] :
( ( cA @ X6 )
& ( X6 @ X0 ) ) )
& ! [X2: ( a > $o ) > $o] :
( ( ! [X0: a > $o] :
( ( X2 @ X0 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X0 @ X5 )
| ( X4 = X5 ) ) ) ) )
& ( X2
@ ^ [X3: a] : $false ) )
=> ( X2 @ X1 ) ) )
=> ( ! [X0: a > $o] :
( ( ( cA @ X0 )
& ! [X7: a] :
( ( X1 @ X7 )
=> ( X0 @ X7 ) ) )
=> ? [X8: a > $o] :
( ! [X3: a > $o] :
( ( ( cA @ X3 )
& ! [X7: a] :
( ( X8 @ X7 )
=> ( X3 @ X7 ) ) )
=> ( ( cA @ X3 )
& ! [X7: a] :
( ( X1 @ X7 )
=> ( X3 @ X7 ) ) ) )
& ! [X2: ( a > $o ) > $o] :
( ( ! [X7: a > $o] :
( ( X2 @ X7 )
=> ! [X4: a] :
( ( X8 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X7 @ X5 )
| ( X4 = X5 ) ) ) ) )
& ( X2
@ ^ [X3: a] : $false ) )
=> ( X2 @ X8 ) )
& ! [X7: a] :
( ( X8 @ X7 )
=> ( X0 @ X7 ) ) ) )
& ! [X0: a > $o] :
( ( ( cA @ X0 )
& ! [X7: a] :
( ( X1 @ X7 )
=> ( X0 @ X7 ) ) )
=> ( cA @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SRfGWKMZ63/DTF2THF_22685.p',cDOMTHM8_pme) ).
thf(f81,plain,
( ~ spl14_1
| spl14_5
| spl14_6 ),
inference(avatar_split_clause,[status(thm)],[f39,f78,f74,f57]) ).
thf(f39,plain,
( ( $true
= ( cA @ sK4 ) )
| ( $true
= ( sP1 @ sK3 ) )
| ( $true != sP2 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f72,plain,
( ~ spl14_4
| spl14_1 ),
inference(avatar_split_clause,[status(thm)],[f55,f57,f69]) ).
thf(f55,plain,
( ( $true
!= ( cA @ sK13 ) )
| ( $true = sP2 ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f67,plain,
( ~ spl14_1
| spl14_3 ),
inference(avatar_split_clause,[status(thm)],[f34,f65,f57]) ).
thf(f34,plain,
! [X5: ( a > $o ) > $o] :
( ( $true != sP2 )
| ( $true
!= ( X5
@ ^ [Y0: a] : $false ) )
| ( $true
= ( X5 @ sK3 ) )
| ( $true
= ( X5 @ ( sK6 @ X5 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU909^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:36:57 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.42 ---- Original DTF file ---
% 0.17/0.43 thf(spec,logic,$$dhol).
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 % File : SEU909^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.43 % Domain : Set Theory
% 0.17/0.43 % Problem : TPS problem from SET-TOP-CATEGORY-THMS
% 0.17/0.43 % Version : Especial.
% 0.17/0.43 % English :
% 0.17/0.43
% 0.17/0.43 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.43 % Source : [Bro09]
% 0.17/0.43 % Names : tps_1161 [Bro09]
% 0.17/0.43
% 0.17/0.43 % Status : Theorem
% 0.17/0.43 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.57 v7.4.0, 0.22 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.17/0.43 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.17/0.43 % Number of atoms : 12 ( 2 equ; 0 cnn)
% 0.17/0.43 % Maximal formula atoms : 12 ( 12 avg)
% 0.17/0.43 % Number of connectives : 63 ( 0 ~; 2 |; 12 &; 32 @)
% 0.17/0.43 % ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% 0.17/0.43 % Maximal formula depth : 20 ( 20 avg)
% 0.17/0.43 % Number of types : 2 ( 1 usr)
% 0.17/0.43 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.17/0.43 % Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% 0.17/0.43 % Number of variables : 23 ( 4 ^; 17 !; 2 ?; 23 :)
% 0.17/0.43 % SPC : TH0_THM_EQU_NAR
% 0.17/0.43
% 0.17/0.43 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.43 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.43 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.43 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 thf(a_type,type,
% 0.17/0.43 a: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(cA,type,
% 0.17/0.43 cA: ( a > $o ) > $o ).
% 0.17/0.43
% 0.17/0.43 thf(cDOMTHM8_pme,conjecture,
% 0.17/0.43 ( ! [Xx: a > $o] :
% 0.17/0.43 ( ( cA @ Xx )
% 0.17/0.43 => ( cA @ Xx ) )
% 0.17/0.43 & ! [Xe: a > $o] :
% 0.17/0.43 ( ( ! [X: ( a > $o ) > $o] :
% 0.17/0.43 ( ( ( X
% 0.17/0.43 @ ^ [Xy: a] : $false )
% 0.17/0.43 & ! [Xx: a > $o] :
% 0.17/0.43 ( ( X @ Xx )
% 0.17/0.43 => ! [Xt: a] :
% 0.17/0.43 ( ( Xe @ Xt )
% 0.17/0.43 => ( X
% 0.17/0.43 @ ^ [Xz: a] :
% 0.17/0.43 ( ( Xx @ Xz )
% 0.17/0.43 | ( Xt = Xz ) ) ) ) ) )
% 0.17/0.43 => ( X @ Xe ) )
% 0.17/0.43 & ! [Xx: a] :
% 0.17/0.43 ( ( Xe @ Xx )
% 0.17/0.43 => ? [S: a > $o] :
% 0.17/0.43 ( ( cA @ S )
% 0.17/0.43 & ( S @ Xx ) ) ) )
% 0.17/0.43 => ( ! [Xx: a > $o] :
% 0.17/0.43 ( ( ( cA @ Xx )
% 0.17/0.43 & ! [Xx0: a] :
% 0.17/0.43 ( ( Xe @ Xx0 )
% 0.17/0.43 => ( Xx @ Xx0 ) ) )
% 0.17/0.43 => ( cA @ Xx ) )
% 0.17/0.43 & ! [Xx: a > $o] :
% 0.17/0.43 ( ( ( cA @ Xx )
% 0.17/0.43 & ! [Xx0: a] :
% 0.17/0.43 ( ( Xe @ Xx0 )
% 0.17/0.43 => ( Xx @ Xx0 ) ) )
% 0.17/0.43 => ? [Xe_0: a > $o] :
% 0.17/0.43 ( ! [X: ( a > $o ) > $o] :
% 0.17/0.43 ( ( ( X
% 0.17/0.43 @ ^ [Xy: a] : $false )
% 0.17/0.43 & ! [Xx0: a > $o] :
% 0.17/0.43 ( ( X @ Xx0 )
% 0.17/0.43 => ! [Xt: a] :
% 0.17/0.43 ( ( Xe_0 @ Xt )
% 0.17/0.43 => ( X
% 0.17/0.43 @ ^ [Xz: a] :
% 0.17/0.43 ( ( Xx0 @ Xz )
% 0.17/0.43 | ( Xt = Xz ) ) ) ) ) )
% 0.17/0.43 => ( X @ Xe_0 ) )
% 0.17/0.43 & ! [Xx0: a] :
% 0.17/0.43 ( ( Xe_0 @ Xx0 )
% 0.17/0.43 => ( Xx @ Xx0 ) )
% 0.17/0.43 & ! [Xy: a > $o] :
% 0.17/0.43 ( ( ( cA @ Xy )
% 0.17/0.43 & ! [Xx0: a] :
% 0.17/0.43 ( ( Xe_0 @ Xx0 )
% 0.17/0.43 => ( Xy @ Xx0 ) ) )
% 0.17/0.43 => ( ( cA @ Xy )
% 0.17/0.43 & ! [Xx0: a] :
% 0.17/0.43 ( ( Xe @ Xx0 )
% 0.17/0.43 => ( Xy @ Xx0 ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 ------------------------
% 1.30/1.15 ---- Embedded in THF ---
% 1.30/1.15 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.30/1.15 %%% Generated on Tue Feb 24 12:36:58 EST 2026
% 1.30/1.15 %%% using '$$dhol' embedding, version 1.3.0.
% 1.30/1.15 %%% Logic specification used:
% 1.30/1.15 %%% thf(spec, logic, $$dhol).
% 1.30/1.15
% 1.30/1.15 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.SRfGWKMZ63/DTF2DTF22685.p
% See solution above
% 1.30/1.15 ------------------------
% 1.30/1.15 ---- Cleaned THF ---
% 1.30/1.15 thf(a_type,type,
% 1.30/1.15 a: $tType ).
% 1.30/1.15
% 1.30/1.15 thf(cA,type,
% 1.30/1.15 cA: ( a > $o ) > $o ).
% 1.30/1.15
% 1.30/1.15 thf(cDOMTHM8_pme,conjecture,
% 1.30/1.15 ( ! [Xx: a > $o] :
% 1.30/1.15 ( ( cA @ Xx )
% 1.30/1.15 => ( cA @ Xx ) )
% 1.30/1.15 & ! [Xe: a > $o] :
% 1.30/1.15 ( ( ! [X: ( a > $o ) > $o] :
% 1.30/1.15 ( ( ( X
% 1.30/1.15 @ ^ [Xy: a] : $false )
% 1.30/1.15 & ! [Xx: a > $o] :
% 1.30/1.15 ( ( X @ Xx )
% 1.30/1.15 => ! [Xt: a] :
% 1.30/1.15 ( ( Xe @ Xt )
% 1.30/1.15 => ( X
% 1.30/1.15 @ ^ [Xz: a] :
% 1.30/1.15 ( ( Xx @ Xz )
% 1.30/1.15 | ( Xt = Xz ) ) ) ) ) )
% 1.30/1.15 => ( X @ Xe ) )
% 1.30/1.15 & ! [Xx: a] :
% 1.30/1.15 ( ( Xe @ Xx )
% 1.30/1.15 => ? [S: a > $o] :
% 1.30/1.15 ( ( cA @ S )
% 1.30/1.15 & ( S @ Xx ) ) ) )
% 1.30/1.15 => ( ! [Xx: a > $o] :
% 1.30/1.15 ( ( ( cA @ Xx )
% 1.30/1.15 & ! [Xx0: a] :
% 1.30/1.15 ( ( Xe @ Xx0 )
% 1.30/1.15 => ( Xx @ Xx0 ) ) )
% 1.30/1.15 => ( cA @ Xx ) )
% 1.30/1.15 & ! [Xx: a > $o] :
% 1.30/1.15 ( ( ( cA @ Xx )
% 1.30/1.15 & ! [Xx0: a] :
% 1.30/1.15 ( ( Xe @ Xx0 )
% 1.30/1.15 => ( Xx @ Xx0 ) ) )
% 1.30/1.15 => ? [Xe_0: a > $o] :
% 1.30/1.15 ( ! [X: ( a > $o ) > $o] :
% 1.30/1.15 ( ( ( X
% 1.30/1.15 @ ^ [Xy: a] : $false )
% 1.30/1.15 & ! [Xx0: a > $o] :
% 1.30/1.15 ( ( X @ Xx0 )
% 1.30/1.15 => ! [Xt: a] :
% 1.30/1.15 ( ( Xe_0 @ Xt )
% 1.30/1.15 => ( X
% 1.30/1.15 @ ^ [Xz: a] :
% 1.30/1.15 ( ( Xx0 @ Xz )
% 1.30/1.15 | ( Xt = Xz ) ) ) ) ) )
% 1.30/1.15 => ( X @ Xe_0 ) )
% 1.30/1.15 & ! [Xx0: a] :
% 1.30/1.15 ( ( Xe_0 @ Xx0 )
% 1.30/1.15 => ( Xx @ Xx0 ) )
% 1.30/1.15 & ! [Xy: a > $o] :
% 1.30/1.15 ( ( ( cA @ Xy )
% 1.30/1.15 & ! [Xx0: a] :
% 1.30/1.15 ( ( Xe_0 @ Xx0 )
% 1.30/1.15 => ( Xy @ Xx0 ) ) )
% 1.30/1.15 => ( ( cA @ Xy )
% 1.30/1.15 & ! [Xx0: a] :
% 1.30/1.15 ( ( Xe @ Xx0 )
% 1.30/1.15 => ( Xy @ Xx0 ) ) ) ) ) ) ) ) ) ).
% 1.30/1.15 ------------------------
% 1.30/1.17 % (22782)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22685 for (3000ds/183Mi)
% 1.30/1.17 % (22785)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22685 for (3000ds/2Mi)
% 1.30/1.17 % (22783)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_22685 for (3000ds/4Mi)
% 1.30/1.17 % (22784)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_22685 for (3000ds/27Mi)
% 1.30/1.17 % (22786)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_22685 for (3000ds/2Mi)
% 1.30/1.17 % (22787)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_22685 for (3000ds/275Mi)
% 1.30/1.17 % (22788)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22685 for (3000ds/18Mi)
% 1.30/1.17 % (22785)Instruction limit reached!
% 1.30/1.17 % (22785)------------------------------
% 1.30/1.17 % (22785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.17 % (22786)Instruction limit reached!
% 1.30/1.17 % (22786)------------------------------
% 1.30/1.17 % (22786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.17 % (22785)Termination reason: Unknown
% 1.30/1.17 % (22785)Termination phase: Preprocessing 3
% 1.30/1.17
% 1.30/1.17 % (22785)Memory used [KB]: 1023
% 1.30/1.17 % (22785)Time elapsed: 0.003 s
% 1.30/1.17 % (22785)Instructions burned: 3 (million)
% 1.30/1.17 % (22785)------------------------------
% 1.30/1.17 % (22785)------------------------------
% 1.30/1.17 % (22786)Termination reason: Unknown
% 1.30/1.17 % (22786)Termination phase: Property scanning
% 1.30/1.17
% 1.30/1.17 % (22786)Memory used [KB]: 1023
% 1.30/1.17 % (22786)Time elapsed: 0.003 s
% 1.30/1.17 % (22786)Instructions burned: 3 (million)
% 1.30/1.17 % (22786)------------------------------
% 1.30/1.17 % (22786)------------------------------
% 1.30/1.17 % (22783)Instruction limit reached!
% 1.30/1.17 % (22783)------------------------------
% 1.30/1.17 % (22783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.17 % (22783)Termination reason: Unknown
% 1.30/1.17 % (22783)Termination phase: Saturation
% 1.30/1.17
% 1.30/1.17 % (22783)Memory used [KB]: 5500
% 1.30/1.17 % (22783)Time elapsed: 0.004 s
% 1.30/1.17 % (22783)Instructions burned: 5 (million)
% 1.30/1.17 % (22783)------------------------------
% 1.30/1.17 % (22783)------------------------------
% 1.30/1.18 % (22787)Refutation not found, incomplete strategy
% 1.30/1.18 % (22787)------------------------------
% 1.30/1.18 % (22787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.18 % (22787)Termination reason: Refutation not found, incomplete strategy
% 1.30/1.18
% 1.30/1.18
% 1.30/1.18 % (22787)Memory used [KB]: 5628
% 1.30/1.18 % (22787)Time elapsed: 0.005 s
% 1.30/1.18 % (22787)Instructions burned: 5 (million)
% 1.30/1.18 % (22787)------------------------------
% 1.30/1.18 % (22787)------------------------------
% 1.30/1.18 % (22788)Instruction limit reached!
% 1.30/1.18 % (22788)------------------------------
% 1.30/1.18 % (22788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.18 % (22788)Termination reason: Unknown
% 1.30/1.18 % (22788)Termination phase: Saturation
% 1.30/1.18
% 1.30/1.18 % (22788)Memory used [KB]: 5756
% 1.30/1.18 % (22788)Time elapsed: 0.011 s
% 1.30/1.18 % (22788)Instructions burned: 18 (million)
% 1.30/1.18 % (22788)------------------------------
% 1.30/1.18 % (22788)------------------------------
% 1.30/1.19 % (22784)Instruction limit reached!
% 1.30/1.19 % (22784)------------------------------
% 1.30/1.19 % (22784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.19 % (22784)Termination reason: Unknown
% 1.30/1.19 % (22784)Termination phase: Saturation
% 1.30/1.19
% 1.30/1.19 % (22784)Memory used [KB]: 5756
% 1.30/1.19 % (22784)Time elapsed: 0.017 s
% 1.30/1.19 % (22784)Instructions burned: 28 (million)
% 1.30/1.19 % (22784)------------------------------
% 1.30/1.19 % (22784)------------------------------
% 1.30/1.19 % (22790)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_22685 for (2999ds/37Mi)
% 1.30/1.19 % (22789)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/3Mi)
% 1.30/1.19 % (22789)Instruction limit reached!
% 1.30/1.19 % (22789)------------------------------
% 1.30/1.19 % (22789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.19 % (22789)Termination reason: Unknown
% 1.30/1.19 % (22789)Termination phase: Preprocessing 3
% 1.30/1.19
% 1.30/1.19 % (22789)Memory used [KB]: 1023
% 1.30/1.19 % (22789)Time elapsed: 0.003 s
% 1.30/1.19 % (22789)Instructions burned: 3 (million)
% 1.30/1.19 % (22789)------------------------------
% 1.30/1.19 % (22789)------------------------------
% 1.30/1.19 % (22792)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_22685 for (2999ds/3Mi)
% 1.30/1.19 % (22792)Instruction limit reached!
% 1.30/1.19 % (22792)------------------------------
% 1.30/1.19 % (22792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.19 % (22792)Termination reason: Unknown
% 1.30/1.19 % (22792)Termination phase: Property scanning
% 1.30/1.19
% 1.30/1.19 % (22792)Memory used [KB]: 1023
% 1.30/1.19 % (22792)Time elapsed: 0.003 s
% 1.30/1.19 % (22792)Instructions burned: 4 (million)
% 1.30/1.19 % (22792)------------------------------
% 1.30/1.19 % (22792)------------------------------
% 1.34/1.20 % (22793)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_22685 for (2999ds/1041Mi)
% 1.34/1.20 % (22791)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_22685 for (2999ds/15Mi)
% 1.34/1.20 % (22794)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/7Mi)
% 1.34/1.21 % (22790)Instruction limit reached!
% 1.34/1.21 % (22790)------------------------------
% 1.34/1.21 % (22790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.21 % (22790)Termination reason: Unknown
% 1.34/1.21 % (22790)Termination phase: Saturation
% 1.34/1.21
% 1.34/1.21 % (22790)Memory used [KB]: 5628
% 1.34/1.21 % (22790)Time elapsed: 0.019 s
% 1.34/1.21 % (22790)Instructions burned: 37 (million)
% 1.34/1.21 % (22790)------------------------------
% 1.34/1.21 % (22790)------------------------------
% 1.34/1.21 % (22795)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/16Mi)
% 1.34/1.21 % (22791)Instruction limit reached!
% 1.34/1.21 % (22791)------------------------------
% 1.34/1.21 % (22791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.21 % (22791)Termination reason: Unknown
% 1.34/1.21 % (22791)Termination phase: Saturation
% 1.34/1.21
% 1.34/1.21 % (22791)Memory used [KB]: 5756
% 1.34/1.21 % (22791)Time elapsed: 0.011 s
% 1.34/1.21 % (22791)Instructions burned: 15 (million)
% 1.34/1.21 % (22791)------------------------------
% 1.34/1.21 % (22791)------------------------------
% 1.34/1.21 % (22794)Instruction limit reached!
% 1.34/1.21 % (22794)------------------------------
% 1.34/1.21 % (22794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.21 % (22794)Termination reason: Unknown
% 1.34/1.21 % (22794)Termination phase: Saturation
% 1.34/1.21
% 1.34/1.21 % (22794)Memory used [KB]: 1151
% 1.34/1.21 % (22794)Time elapsed: 0.006 s
% 1.34/1.21 % (22794)Instructions burned: 8 (million)
% 1.34/1.21 % (22794)------------------------------
% 1.34/1.21 % (22794)------------------------------
% 1.34/1.21 % (22796)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_22685 for (2999ds/3Mi)
% 1.34/1.21 % (22796)Instruction limit reached!
% 1.34/1.21 % (22796)------------------------------
% 1.34/1.21 % (22796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.21 % (22796)Termination reason: Unknown
% 1.34/1.21 % (22796)Termination phase: Preprocessing 3
% 1.34/1.21
% 1.34/1.21 % (22796)Memory used [KB]: 1023
% 1.34/1.21 % (22796)Time elapsed: 0.003 s
% 1.34/1.21 % (22796)Instructions burned: 3 (million)
% 1.34/1.21 % (22796)------------------------------
% 1.34/1.21 % (22796)------------------------------
% 1.34/1.22 % (22795)Instruction limit reached!
% 1.34/1.22 % (22795)------------------------------
% 1.34/1.22 % (22795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.22 % (22795)Termination reason: Unknown
% 1.34/1.22 % (22795)Termination phase: Saturation
% 1.34/1.22
% 1.34/1.22 % (22795)Memory used [KB]: 5756
% 1.34/1.22 % (22795)Time elapsed: 0.010 s
% 1.34/1.22 % (22795)Instructions burned: 16 (million)
% 1.34/1.22 % (22795)------------------------------
% 1.34/1.22 % (22795)------------------------------
% 1.34/1.22 % (22800)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/4Mi)
% 1.34/1.22 % (22797)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_22685 for (2999ds/3Mi)
% 1.34/1.22 % (22800)Instruction limit reached!
% 1.34/1.22 % (22800)------------------------------
% 1.34/1.22 % (22800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.22 % (22798)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/7Mi)
% 1.34/1.22 % (22800)Termination reason: Unknown
% 1.34/1.22 % (22800)Termination phase: Saturation
% 1.34/1.22
% 1.34/1.22 % (22800)Memory used [KB]: 5500
% 1.34/1.22 % (22800)Time elapsed: 0.003 s
% 1.34/1.22 % (22800)Instructions burned: 5 (million)
% 1.34/1.22 % (22800)------------------------------
% 1.34/1.22 % (22800)------------------------------
% 1.34/1.22 % (22799)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/3Mi)
% 1.34/1.22 % (22797)Instruction limit reached!
% 1.34/1.22 % (22797)------------------------------
% 1.34/1.22 % (22797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.22 % (22797)Termination reason: Unknown
% 1.34/1.22 % (22797)Termination phase: Preprocessing 3
% 1.34/1.22
% 1.34/1.22 % (22797)Memory used [KB]: 1023
% 1.34/1.22 % (22797)Time elapsed: 0.003 s
% 1.34/1.22 % (22797)Instructions burned: 3 (million)
% 1.34/1.22 % (22797)------------------------------
% 1.34/1.22 % (22797)------------------------------
% 1.34/1.23 % (22799)Instruction limit reached!
% 1.34/1.23 % (22799)------------------------------
% 1.34/1.23 % (22799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.23 % (22799)Termination reason: Unknown
% 1.34/1.23 % (22799)Termination phase: Property scanning
% 1.34/1.23
% 1.34/1.23 % (22799)Memory used [KB]: 1023
% 1.34/1.23 % (22799)Time elapsed: 0.003 s
% 1.34/1.23 % (22799)Instructions burned: 3 (million)
% 1.34/1.23 % (22799)------------------------------
% 1.34/1.23 % (22799)------------------------------
% 1.34/1.23 % (22798)Instruction limit reached!
% 1.34/1.23 % (22798)------------------------------
% 1.34/1.23 % (22798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.23 % (22798)Termination reason: Unknown
% 1.34/1.23 % (22798)Termination phase: Saturation
% 1.34/1.23
% 1.34/1.23 % (22798)Memory used [KB]: 5500
% 1.34/1.23 % (22798)Time elapsed: 0.005 s
% 1.34/1.23 % (22798)Instructions burned: 7 (million)
% 1.34/1.23 % (22798)------------------------------
% 1.34/1.23 % (22798)------------------------------
% 1.34/1.23 % (22801)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/18Mi)
% 1.34/1.23 % (22802)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/710Mi)
% 1.34/1.24 % (22803)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/6Mi)
% 1.34/1.24 % (22782)Instruction limit reached!
% 1.34/1.24 % (22782)------------------------------
% 1.34/1.24 % (22782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.24 % (22782)Termination reason: Unknown
% 1.34/1.24 % (22782)Termination phase: Saturation
% 1.34/1.24
% 1.34/1.24 % (22782)Memory used [KB]: 6780
% 1.34/1.24 % (22782)Time elapsed: 0.076 s
% 1.34/1.24 % (22782)Instructions burned: 184 (million)
% 1.34/1.24 % (22782)------------------------------
% 1.34/1.24 % (22782)------------------------------
% 1.34/1.24 % (22801)Instruction limit reached!
% 1.34/1.24 % (22801)------------------------------
% 1.34/1.24 % (22801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.24 % (22801)Termination reason: Unknown
% 1.34/1.24 % (22801)Termination phase: Saturation
% 1.34/1.24
% 1.34/1.24 % (22801)Memory used [KB]: 5628
% 1.34/1.24 % (22801)Time elapsed: 0.011 s
% 1.34/1.24 % (22801)Instructions burned: 18 (million)
% 1.34/1.24 % (22801)------------------------------
% 1.34/1.24 % (22801)------------------------------
% 1.34/1.24 % (22804)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_22685 for (2999ds/902Mi)
% 1.34/1.24 % (22805)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_22685 for (2999ds/21Mi)
% 1.34/1.24 % (22803)Instruction limit reached!
% 1.34/1.24 % (22803)------------------------------
% 1.34/1.24 % (22803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.24 % (22803)Termination reason: Unknown
% 1.34/1.24 % (22803)Termination phase: Saturation
% 1.34/1.24
% 1.34/1.24 % (22803)Memory used [KB]: 5628
% 1.34/1.24 % (22803)Time elapsed: 0.005 s
% 1.34/1.24 % (22803)Instructions burned: 7 (million)
% 1.34/1.24 % (22803)------------------------------
% 1.34/1.24 % (22803)------------------------------
% 1.34/1.24 % (22804)Refutation not found, incomplete strategy
% 1.34/1.24 % (22804)------------------------------
% 1.34/1.24 % (22804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.24 % (22804)Termination reason: Refutation not found, incomplete strategy
% 1.34/1.24
% 1.34/1.24
% 1.34/1.24 % (22804)Memory used [KB]: 5500
% 1.34/1.24 % (22804)Time elapsed: 0.004 s
% 1.34/1.24 % (22804)Instructions burned: 4 (million)
% 1.34/1.24 % (22804)------------------------------
% 1.34/1.24 % (22804)------------------------------
% 1.34/1.26 % (22805)Instruction limit reached!
% 1.34/1.26 % (22805)------------------------------
% 1.34/1.26 % (22805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.26 % (22805)Termination reason: Unknown
% 1.34/1.26 % (22805)Termination phase: Saturation
% 1.34/1.26
% 1.34/1.26 % (22805)Memory used [KB]: 5756
% 1.34/1.26 % (22805)Time elapsed: 0.014 s
% 1.34/1.26 % (22805)Instructions burned: 21 (million)
% 1.34/1.26 % (22805)------------------------------
% 1.34/1.26 % (22805)------------------------------
% 1.34/1.26 % (22806)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/5Mi)
% 1.34/1.26 % (22807)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/6Mi)
% 1.34/1.26 % (22806)Instruction limit reached!
% 1.34/1.26 % (22806)------------------------------
% 1.34/1.26 % (22806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.26 % (22806)Termination reason: Unknown
% 1.34/1.26 % (22806)Termination phase: Saturation
% 1.34/1.26
% 1.34/1.26 % (22806)Memory used [KB]: 5500
% 1.34/1.26 % (22806)Time elapsed: 0.004 s
% 1.34/1.26 % (22806)Instructions burned: 5 (million)
% 1.34/1.26 % (22806)------------------------------
% 1.34/1.26 % (22806)------------------------------
% 1.34/1.26 % (22807)Instruction limit reached!
% 1.34/1.26 % (22807)------------------------------
% 1.34/1.26 % (22807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.26 % (22807)Termination reason: Unknown
% 1.34/1.26 % (22807)Termination phase: Saturation
% 1.34/1.26
% 1.34/1.26 % (22807)Memory used [KB]: 5500
% 1.34/1.26 % (22807)Time elapsed: 0.004 s
% 1.34/1.26 % (22807)Instructions burned: 6 (million)
% 1.34/1.26 % (22807)------------------------------
% 1.34/1.26 % (22807)------------------------------
% 1.34/1.26 % (22808)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/377Mi)
% 1.34/1.26 % (22809)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/779Mi)
% 1.34/1.27 % (22811)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/19Mi)
% 1.34/1.27 % (22812)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/879Mi)
% 1.34/1.28 % (22813)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22685 for (2999ds/17Mi)
% 1.34/1.28 % (22811)Instruction limit reached!
% 1.34/1.28 % (22811)------------------------------
% 1.34/1.28 % (22811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.28 % (22811)Termination reason: Unknown
% 1.34/1.28 % (22811)Termination phase: Saturation
% 1.34/1.28
% 1.34/1.28 % (22811)Memory used [KB]: 5500
% 1.34/1.28 % (22811)Time elapsed: 0.011 s
% 1.34/1.28 % (22811)Instructions burned: 20 (million)
% 1.34/1.28 % (22811)------------------------------
% 1.34/1.28 % (22811)------------------------------
% 1.34/1.28 % (22813)Instruction limit reached!
% 1.34/1.28 % (22813)------------------------------
% 1.34/1.28 % (22813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.29 % (22813)Termination reason: Unknown
% 1.34/1.29 % (22813)Termination phase: Saturation
% 1.34/1.29
% 1.34/1.29 % (22813)Memory used [KB]: 5756
% 1.34/1.29 % (22813)Time elapsed: 0.032 s
% 1.34/1.29 % (22813)Instructions burned: 18 (million)
% 1.34/1.29 % (22813)------------------------------
% 1.34/1.29 % (22813)------------------------------
% 1.34/1.30 % (22814)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22685 for (2998ds/3Mi)
% 1.34/1.30 % (22814)Instruction limit reached!
% 1.34/1.30 % (22814)------------------------------
% 1.34/1.30 % (22814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.30 % (22814)Termination reason: Unknown
% 1.34/1.30 % (22814)Termination phase: Preprocessing 3
% 1.34/1.30
% 1.34/1.30 % (22814)Memory used [KB]: 1023
% 1.34/1.30 % (22814)Time elapsed: 0.003 s
% 1.34/1.30 % (22814)Instructions burned: 3 (million)
% 1.34/1.30 % (22814)------------------------------
% 1.34/1.30 % (22814)------------------------------
% 1.34/1.30 % (22815)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22685 for (2998ds/30Mi)
% 1.34/1.32 % (22816)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22685 for (2998ds/127Mi)
% 1.34/1.32 % (22815)Instruction limit reached!
% 1.34/1.32 % (22815)------------------------------
% 1.34/1.32 % (22815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.32 % (22815)Termination reason: Unknown
% 1.34/1.32 % (22815)Termination phase: Saturation
% 1.34/1.32
% 1.34/1.32 % (22815)Memory used [KB]: 5756
% 1.34/1.32 % (22815)Time elapsed: 0.039 s
% 1.34/1.32 % (22815)Instructions burned: 31 (million)
% 1.34/1.32 % (22815)------------------------------
% 1.34/1.32 % (22815)------------------------------
% 1.34/1.33 % (22817)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22685 for (2998ds/100Mi)
% 1.34/1.37 % (22817)First to succeed.
% 1.34/1.38 % (22817)Refutation found. Thanks to Tanya!
% 1.34/1.38 % SZS status Theorem for DTF2THF_22685
% 1.34/1.38 % SZS output start Proof for DTF2THF_22685
% 1.34/1.38 thf(type_def_5, type, a: $tType).
% 1.34/1.38 thf(func_def_0, type, a: $tType).
% 1.34/1.38 thf(func_def_1, type, cA: (a > $o) > $o).
% 1.34/1.38 thf(func_def_9, type, sP0: (a > $o) > (a > $o) > $o).
% 1.34/1.38 thf(func_def_10, type, sP1: (a > $o) > $o).
% 1.34/1.38 thf(func_def_12, type, sK3: a > $o).
% 1.34/1.38 thf(func_def_13, type, sK4: a > $o).
% 1.34/1.38 thf(func_def_14, type, sK5: a > a > $o).
% 1.34/1.38 thf(func_def_15, type, sK6: ((a > $o) > $o) > a > $o).
% 1.34/1.38 thf(func_def_16, type, sK7: ((a > $o) > $o) > a).
% 1.34/1.38 thf(func_def_17, type, sK8: (a > $o) > a > $o).
% 1.34/1.38 thf(func_def_18, type, sK9: (a > $o) > (a > $o) > $o).
% 1.34/1.38 thf(func_def_19, type, sK10: (a > $o) > (a > $o) > a).
% 1.34/1.38 thf(func_def_20, type, sK11: (a > $o) > (a > $o) > a > $o).
% 1.34/1.38 thf(func_def_21, type, sK12: (a > $o) > (a > $o) > a).
% 1.34/1.38 thf(func_def_22, type, sK13: a > $o).
% 1.34/1.38 thf(func_def_24, type, ph15: !>[X0: $tType]:(X0)).
% 1.34/1.38 thf(f275,plain,(
% 1.34/1.38 $false),
% 1.34/1.38 inference(avatar_sat_refutation,[status(thm)],[f67,f72,f81,f82,f83,f95,f99,f274])).
% 1.34/1.38 thf(f274,plain,(
% 1.34/1.38 ~spl14_3 | ~spl14_6 | ~spl14_9 | ~spl14_10),
% 1.34/1.38 inference(avatar_contradiction_clause,[status(thm)],[f273])).
% 1.34/1.38 thf(f273,plain,(
% 1.34/1.38 $false | (~spl14_3 | ~spl14_6 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(subsumption_resolution,[status(thm)],[f272,f141])).
% 1.34/1.38 thf(f141,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true != (sP0 @ X0 @ X0))) )),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.34/1.38 thf(f140,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true != (sP0 @ X0 @ X0)) | ($true != $true)) )),
% 1.34/1.38 inference(duplicate_literal_removal,[status(thm)],[f137])).
% 1.34/1.38 thf(f137,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true != (sP0 @ X0 @ X0)) | ($true != (sP0 @ X0 @ X0)) | ($true != $true)) )),
% 1.34/1.38 inference(superposition,[status(thm)],[f134,f102])).
% 1.34/1.38 thf(f102,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true = (X0 @ (sK12 @ X0 @ X1))) | ($true != (sP0 @ X0 @ X1))) )),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.34/1.38 thf(f101,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sP0 @ X0 @ X1)) | ($true != $true) | ($true = (X0 @ (sK12 @ X0 @ X1)))) )),
% 1.34/1.38 inference(duplicate_literal_removal,[status(thm)],[f100])).
% 1.34/1.38 thf(f100,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true = (X0 @ (sK12 @ X0 @ X1))) | ($true != (sP0 @ X0 @ X1)) | ($true != $true) | ($true != (sP0 @ X0 @ X1))) )),
% 1.34/1.38 inference(superposition,[status(thm)],[f50,f52])).
% 1.34/1.38 thf(f52,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true = (cA @ (sK11 @ X1 @ X0))) | ($true != (sP0 @ X1 @ X0))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f31])).
% 1.34/1.38 thf(f31,plain,(
% 1.34/1.38 ! [X0 : a > $o,X1 : a > $o] : ((! [X3 : a] : (($true != (X0 @ X3)) | ($true = (sK11 @ X1 @ X0 @ X3))) & ($true = (cA @ (sK11 @ X1 @ X0))) & (($true != (cA @ (sK11 @ X1 @ X0))) | (($true != (sK11 @ X1 @ X0 @ (sK12 @ X1 @ X0))) & ($true = (X1 @ (sK12 @ X1 @ X0)))))) | ($true != (sP0 @ X1 @ X0)))),
% 1.34/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f28,f30,f29])).
% 1.34/1.38 thf(f29,plain,(
% 1.34/1.38 ! [X0 : a > $o,X1 : a > $o] : (? [X2 : a > $o] : (! [X3 : a] : (($true != (X0 @ X3)) | ($true = (X2 @ X3))) & ($true = (cA @ X2)) & (($true != (cA @ X2)) | ? [X4 : a] : (($true != (X2 @ X4)) & ((X1 @ X4) = $true)))) => (! [X3 : a] : (($true != (X0 @ X3)) | ($true = (sK11 @ X1 @ X0 @ X3))) & ($true = (cA @ (sK11 @ X1 @ X0))) & (($true != (cA @ (sK11 @ X1 @ X0))) | ? [X4 : a] : (($true != (sK11 @ X1 @ X0 @ X4)) & ((X1 @ X4) = $true)))))),
% 1.34/1.38 introduced(definition,[],[choice_axiom])).
% 1.34/1.38 thf(f30,plain,(
% 1.34/1.38 ! [X0 : a > $o,X1 : a > $o] : (? [X4 : a] : (($true != (sK11 @ X1 @ X0 @ X4)) & ((X1 @ X4) = $true)) => (($true != (sK11 @ X1 @ X0 @ (sK12 @ X1 @ X0))) & ($true = (X1 @ (sK12 @ X1 @ X0)))))),
% 1.34/1.38 introduced(definition,[],[choice_axiom])).
% 1.34/1.38 thf(f28,plain,(
% 1.34/1.38 ! [X0 : a > $o,X1 : a > $o] : (? [X2 : a > $o] : (! [X3 : a] : (($true != (X0 @ X3)) | ($true = (X2 @ X3))) & ($true = (cA @ X2)) & (($true != (cA @ X2)) | ? [X4 : a] : (($true != (X2 @ X4)) & ((X1 @ X4) = $true)))) | ($true != (sP0 @ X1 @ X0)))),
% 1.34/1.38 inference(rectify,[status(thm)],[f27])).
% 1.34/1.38 thf(f27,plain,(
% 1.34/1.38 ! [X9 : a > $o,X1 : a > $o] : (? [X10 : a > $o] : (! [X11 : a] : (($true != (X9 @ X11)) | ($true = (X10 @ X11))) & ($true = (cA @ X10)) & (($true != (cA @ X10)) | ? [X12 : a] : (($true != (X10 @ X12)) & ($true = (X1 @ X12))))) | ($true != (sP0 @ X1 @ X9)))),
% 1.34/1.38 inference(nnf_transformation,[status(thm)],[f9])).
% 1.34/1.38 thf(f9,plain,(
% 1.34/1.38 ! [X9 : a > $o,X1 : a > $o] : (? [X10 : a > $o] : (! [X11 : a] : (($true != (X9 @ X11)) | ($true = (X10 @ X11))) & ($true = (cA @ X10)) & (($true != (cA @ X10)) | ? [X12 : a] : (($true != (X10 @ X12)) & ($true = (X1 @ X12))))) | ~($true = (sP0 @ X1 @ X9)))),
% 1.34/1.38 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.34/1.38 thf(f50,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (cA @ (sK11 @ X1 @ X0))) | ($true != (sP0 @ X1 @ X0)) | ($true = (X1 @ (sK12 @ X1 @ X0)))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f31])).
% 1.34/1.38 thf(f134,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (X1 @ (sK12 @ X0 @ X1))) | ($true != (sP0 @ X0 @ X1))) )),
% 1.34/1.38 inference(subsumption_resolution,[status(thm)],[f133,f52])).
% 1.34/1.38 thf(f133,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (X1 @ (sK12 @ X0 @ X1))) | ($true != (sP0 @ X0 @ X1)) | ($true != (cA @ (sK11 @ X0 @ X1)))) )),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.34/1.38 thf(f132,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (X1 @ (sK12 @ X0 @ X1))) | ($true != $true) | ($true != (sP0 @ X0 @ X1)) | ($true != (cA @ (sK11 @ X0 @ X1)))) )),
% 1.34/1.38 inference(duplicate_literal_removal,[status(thm)],[f131])).
% 1.34/1.38 thf(f131,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != $true) | ($true != (cA @ (sK11 @ X0 @ X1))) | ($true != (sP0 @ X0 @ X1)) | ($true != (sP0 @ X0 @ X1)) | ($true != (X1 @ (sK12 @ X0 @ X1)))) )),
% 1.34/1.38 inference(superposition,[status(thm)],[f51,f53])).
% 1.34/1.38 thf(f53,plain,(
% 1.34/1.38 ( ! [X3 : a,X0 : a > $o,X1 : a > $o] : (($true = (sK11 @ X1 @ X0 @ X3)) | ($true != (X0 @ X3)) | ($true != (sP0 @ X1 @ X0))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f31])).
% 1.34/1.38 thf(f51,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sK11 @ X1 @ X0 @ (sK12 @ X1 @ X0))) | ($true != (cA @ (sK11 @ X1 @ X0))) | ($true != (sP0 @ X1 @ X0))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f31])).
% 1.34/1.38 thf(f272,plain,(
% 1.34/1.38 ($true = (sP0 @ sK3 @ sK3)) | (~spl14_3 | ~spl14_6 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(subsumption_resolution,[status(thm)],[f269,f80])).
% 1.34/1.38 thf(f80,plain,(
% 1.34/1.38 ($true = (sP1 @ sK3)) | ~spl14_6),
% 1.34/1.38 inference(avatar_component_clause,[status(thm)],[f78])).
% 1.34/1.38 thf(f78,definition,(
% 1.34/1.38 spl14_6 <=> ($true = (sP1 @ sK3))),
% 1.34/1.38 introduced(definition,[new_symbols(naming,[spl14_6])],[avatar_definition])).
% 1.34/1.38 thf(f269,plain,(
% 1.34/1.38 ($true != (sP1 @ sK3)) | ($true = (sP0 @ sK3 @ sK3)) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f268])).
% 1.34/1.38 thf(f268,plain,(
% 1.34/1.38 ($true = (sP0 @ sK3 @ sK3)) | ($true != (sP1 @ sK3)) | ($true != $true) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(duplicate_literal_removal,[status(thm)],[f261])).
% 1.34/1.38 thf(f261,plain,(
% 1.34/1.38 ($true != $true) | ($true != (sP1 @ sK3)) | ($true = (sP0 @ sK3 @ sK3)) | ($true = (sP0 @ sK3 @ sK3)) | ($true != (sP1 @ sK3)) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(superposition,[status(thm)],[f245,f201])).
% 1.34/1.38 thf(f201,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true = (sK3 @ (sK10 @ sK3 @ X0))) | ($true != (sP1 @ X0)) | ($true = (sP0 @ X0 @ sK3))) ) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(subsumption_resolution,[status(thm)],[f200,f46])).
% 1.34/1.38 thf(f46,plain,(
% 1.34/1.38 ( ! [X2 : a > $o,X0 : a > $o] : (($true = (X2 @ (sK10 @ X2 @ X0))) | ($true = (sK9 @ X2 @ (^[Y0 : a]: ($false)))) | ($true = (sP0 @ X0 @ X2)) | ($true != (sP1 @ X0))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f26])).
% 1.34/1.38 thf(f26,plain,(
% 1.34/1.38 ! [X0 : a > $o] : ((($true = (cA @ (sK8 @ X0))) & ! [X2 : a > $o] : ((! [X4 : a > $o] : (! [X5 : a] : (($true != (X2 @ X5)) | ($true = (sK9 @ X2 @ (^[Y0 : a]: ((X5 = Y0) | (X4 @ Y0)))))) | ($true != (sK9 @ X2 @ X4))) & ($true = (sK9 @ X2 @ (^[Y0 : a]: ($false)))) & ($true != (sK9 @ X2 @ X2))) | (($true = (X2 @ (sK10 @ X2 @ X0))) & ($true != (sK8 @ X0 @ (sK10 @ X2 @ X0)))) | ($true = (sP0 @ X0 @ X2))) & ! [X7 : a] : (($true = (sK8 @ X0 @ X7)) | ((X0 @ X7) != $true))) | ($true != (sP1 @ X0)))),
% 1.34/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f22,f25,f24,f23])).
% 1.34/1.38 thf(f23,plain,(
% 1.34/1.38 ! [X0 : a > $o] : (? [X1 : a > $o] : (($true = (cA @ X1)) & ! [X2 : a > $o] : (? [X3 : (a > $o) > $o] : (! [X4 : a > $o] : (! [X5 : a] : (($true != (X2 @ X5)) | ($true = (X3 @ (^[Y0 : a]: ((X5 = Y0) | (X4 @ Y0)))))) | ($true != (X3 @ X4))) & ($true = (X3 @ (^[Y0 : a]: ($false)))) & ($true != (X3 @ X2))) | ? [X6 : a] : (($true = (X2 @ X6)) & ($true != (X1 @ X6))) | ($true = (sP0 @ X0 @ X2))) & ! [X7 : a] : (((X1 @ X7) = $true) | ((X0 @ X7) != $true))) => (($true = (cA @ (sK8 @ X0))) & ! [X2 : a > $o] : (? [X3 : (a > $o) > $o] : (! [X4 : a > $o] : (! [X5 : a] : (($true != (X2 @ X5)) | ($true = (X3 @ (^[Y0 : a]: ((X5 = Y0) | (X4 @ Y0)))))) | ($true != (X3 @ X4))) & ($true = (X3 @ (^[Y0 : a]: ($false)))) & ($true != (X3 @ X2))) | ? [X6 : a] : (($true = (X2 @ X6)) & ($true != (sK8 @ X0 @ X6))) | ($true = (sP0 @ X0 @ X2))) & ! [X7 : a] : (($true = (sK8 @ X0 @ X7)) | ((X0 @ X7) != $true))))),
% 1.34/1.38 introduced(definition,[],[choice_axiom])).
% 1.34/1.38 thf(f24,plain,(
% 1.34/1.38 ! [X2 : a > $o] : (? [X3 : (a > $o) > $o] : (! [X4 : a > $o] : (! [X5 : a] : (($true != (X2 @ X5)) | ($true = (X3 @ (^[Y0 : a]: ((X5 = Y0) | (X4 @ Y0)))))) | ($true != (X3 @ X4))) & ($true = (X3 @ (^[Y0 : a]: ($false)))) & ($true != (X3 @ X2))) => (! [X4 : a > $o] : (! [X5 : a] : (($true != (X2 @ X5)) | ($true = (sK9 @ X2 @ (^[Y0 : a]: ((X5 = Y0) | (X4 @ Y0)))))) | ($true != (sK9 @ X2 @ X4))) & ($true = (sK9 @ X2 @ (^[Y0 : a]: ($false)))) & ($true != (sK9 @ X2 @ X2))))),
% 1.34/1.38 introduced(definition,[],[choice_axiom])).
% 1.34/1.38 thf(f25,plain,(
% 1.34/1.38 ! [X0 : a > $o,X2 : a > $o] : (? [X6 : a] : (($true = (X2 @ X6)) & ($true != (sK8 @ X0 @ X6))) => (($true = (X2 @ (sK10 @ X2 @ X0))) & ($true != (sK8 @ X0 @ (sK10 @ X2 @ X0)))))),
% 1.34/1.38 introduced(definition,[],[choice_axiom])).
% 1.34/1.38 thf(f22,plain,(
% 1.34/1.38 ! [X0 : a > $o] : (? [X1 : a > $o] : (($true = (cA @ X1)) & ! [X2 : a > $o] : (? [X3 : (a > $o) > $o] : (! [X4 : a > $o] : (! [X5 : a] : (($true != (X2 @ X5)) | ($true = (X3 @ (^[Y0 : a]: ((X5 = Y0) | (X4 @ Y0)))))) | ($true != (X3 @ X4))) & ($true = (X3 @ (^[Y0 : a]: ($false)))) & ($true != (X3 @ X2))) | ? [X6 : a] : (($true = (X2 @ X6)) & ($true != (X1 @ X6))) | ($true = (sP0 @ X0 @ X2))) & ! [X7 : a] : (((X1 @ X7) = $true) | ((X0 @ X7) != $true))) | ($true != (sP1 @ X0)))),
% 1.34/1.38 inference(rectify,[status(thm)],[f21])).
% 1.34/1.38 thf(f21,plain,(
% 1.34/1.38 ! [X1 : a > $o] : (? [X7 : a > $o] : (($true = (cA @ X7)) & ! [X9 : a > $o] : (? [X13 : (a > $o) > $o] : (! [X14 : a > $o] : (! [X15 : a] : (($true != (X9 @ X15)) | ($true = (X13 @ (^[Y0 : a]: ((X15 = Y0) | (X14 @ Y0)))))) | ($true != (X13 @ X14))) & ($true = (X13 @ (^[Y0 : a]: ($false)))) & ($true != (X13 @ X9))) | ? [X16 : a] : (($true = (X9 @ X16)) & ($true != (X7 @ X16))) | ($true = (sP0 @ X1 @ X9))) & ! [X8 : a] : (($true = (X7 @ X8)) | ($true != (X1 @ X8)))) | ($true != (sP1 @ X1)))),
% 1.34/1.38 inference(nnf_transformation,[status(thm)],[f10])).
% 1.34/1.38 thf(f10,plain,(
% 1.34/1.38 ! [X1 : a > $o] : (? [X7 : a > $o] : (($true = (cA @ X7)) & ! [X9 : a > $o] : (? [X13 : (a > $o) > $o] : (! [X14 : a > $o] : (! [X15 : a] : (($true != (X9 @ X15)) | ($true = (X13 @ (^[Y0 : a]: ((X15 = Y0) | (X14 @ Y0)))))) | ($true != (X13 @ X14))) & ($true = (X13 @ (^[Y0 : a]: ($false)))) & ($true != (X13 @ X9))) | ? [X16 : a] : (($true = (X9 @ X16)) & ($true != (X7 @ X16))) | ($true = (sP0 @ X1 @ X9))) & ! [X8 : a] : (($true = (X7 @ X8)) | ($true != (X1 @ X8)))) | ~($true = (sP1 @ X1)))),
% 1.34/1.38 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.34/1.38 thf(f200,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true != (sK9 @ sK3 @ (^[Y0 : a]: ($false)))) | ($true = (sK3 @ (sK10 @ sK3 @ X0))) | ($true = (sP0 @ X0 @ sK3)) | ($true != (sP1 @ X0))) ) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(subsumption_resolution,[status(thm)],[f197,f44])).
% 1.34/1.38 thf(f44,plain,(
% 1.34/1.38 ( ! [X2 : a > $o,X0 : a > $o] : (($true = (X2 @ (sK10 @ X2 @ X0))) | ($true = (sP0 @ X0 @ X2)) | ($true != (sP1 @ X0)) | ($true != (sK9 @ X2 @ X2))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f26])).
% 1.34/1.38 thf(f197,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true = (sK3 @ (sK10 @ sK3 @ X0))) | ($true != (sP1 @ X0)) | ($true = (sP0 @ X0 @ sK3)) | ($true = (sK9 @ sK3 @ sK3)) | ($true != (sK9 @ sK3 @ (^[Y0 : a]: ($false))))) ) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f196])).
% 1.34/1.38 thf(f196,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true != (sP1 @ X0)) | ($true != (sK9 @ sK3 @ (^[Y0 : a]: ($false)))) | ($true != $true) | ($true = (sK9 @ sK3 @ sK3)) | ($true = (sP0 @ X0 @ sK3)) | ($true = (sK3 @ (sK10 @ sK3 @ X0)))) ) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(duplicate_literal_removal,[status(thm)],[f195])).
% 1.34/1.38 thf(f195,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true != (sP1 @ X0)) | ($true != (sK9 @ sK3 @ (^[Y0 : a]: ($false)))) | ($true = (sK9 @ sK3 @ sK3)) | ($true = (sK3 @ (sK10 @ sK3 @ X0))) | ($true != $true) | ($true = (sP0 @ X0 @ sK3)) | ($true = (sK9 @ sK3 @ sK3))) ) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(superposition,[status(thm)],[f188,f98])).
% 1.34/1.38 thf(f98,plain,(
% 1.34/1.38 ( ! [X5 : (a > $o) > $o] : (($true = (sK3 @ (sK7 @ X5))) | ($true != (X5 @ (^[Y0 : a]: ($false)))) | ($true = (X5 @ sK3))) ) | ~spl14_10),
% 1.34/1.38 inference(avatar_component_clause,[status(thm)],[f97])).
% 1.34/1.38 thf(f97,definition,(
% 1.34/1.38 spl14_10 <=> ! [X5 : (a > $o) > $o] : (($true != (X5 @ (^[Y0 : a]: ($false)))) | ($true = (sK3 @ (sK7 @ X5))) | ($true = (X5 @ sK3)))),
% 1.34/1.38 introduced(definition,[new_symbols(naming,[spl14_10])],[avatar_definition])).
% 1.34/1.38 thf(f188,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (X0 @ (sK7 @ (sK9 @ X0)))) | ($true != (sP1 @ X1)) | ($true = (X0 @ (sK10 @ X0 @ X1))) | ($true = (sP0 @ X1 @ X0)) | ($true = (sK9 @ X0 @ sK3))) ) | (~spl14_3 | ~spl14_9)),
% 1.34/1.38 inference(subsumption_resolution,[status(thm)],[f187,f46])).
% 1.34/1.38 thf(f187,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sK9 @ X0 @ (^[Y0 : a]: ($false)))) | ($true = (X0 @ (sK10 @ X0 @ X1))) | ($true != (X0 @ (sK7 @ (sK9 @ X0)))) | ($true = (sP0 @ X1 @ X0)) | ($true != (sP1 @ X1)) | ($true = (sK9 @ X0 @ sK3))) ) | (~spl14_3 | ~spl14_9)),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f186])).
% 1.34/1.38 thf(f186,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true = (sK9 @ X0 @ sK3)) | ($true = (X0 @ (sK10 @ X0 @ X1))) | ($true != $true) | ($true = (sP0 @ X1 @ X0)) | ($true != (sP1 @ X1)) | ($true != (sK9 @ X0 @ (^[Y0 : a]: ($false)))) | ($true != (X0 @ (sK7 @ (sK9 @ X0))))) ) | (~spl14_3 | ~spl14_9)),
% 1.34/1.38 inference(duplicate_literal_removal,[status(thm)],[f185])).
% 1.34/1.38 thf(f185,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sP1 @ X1)) | ($true = (sP0 @ X1 @ X0)) | ($true != (sK9 @ X0 @ (^[Y0 : a]: ($false)))) | ($true != $true) | ($true = (X0 @ (sK10 @ X0 @ X1))) | ($true != (X0 @ (sK7 @ (sK9 @ X0)))) | ($true = (sK9 @ X0 @ sK3)) | ($true = (sK9 @ X0 @ sK3))) ) | (~spl14_3 | ~spl14_9)),
% 1.34/1.38 inference(superposition,[status(thm)],[f144,f66])).
% 1.34/1.38 thf(f66,plain,(
% 1.34/1.38 ( ! [X5 : (a > $o) > $o] : (($true = (X5 @ (sK6 @ X5))) | ($true != (X5 @ (^[Y0 : a]: ($false)))) | ($true = (X5 @ sK3))) ) | ~spl14_3),
% 1.34/1.38 inference(avatar_component_clause,[status(thm)],[f65])).
% 1.34/1.38 thf(f65,definition,(
% 1.34/1.38 spl14_3 <=> ! [X5 : (a > $o) > $o] : (($true != (X5 @ (^[Y0 : a]: ($false)))) | ($true = (X5 @ (sK6 @ X5))) | ($true = (X5 @ sK3)))),
% 1.34/1.38 introduced(definition,[new_symbols(naming,[spl14_3])],[avatar_definition])).
% 1.34/1.38 thf(f144,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sK9 @ X0 @ (sK6 @ (sK9 @ X0)))) | ($true = (sK9 @ X0 @ sK3)) | ($true = (X0 @ (sK10 @ X0 @ X1))) | ($true != (sP1 @ X1)) | ($true = (sP0 @ X1 @ X0)) | ($true != (X0 @ (sK7 @ (sK9 @ X0))))) ) | ~spl14_9),
% 1.34/1.38 inference(subsumption_resolution,[status(thm)],[f143,f46])).
% 1.34/1.38 thf(f143,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true = (sP0 @ X1 @ X0)) | ($true = (sK9 @ X0 @ sK3)) | ($true != (sK9 @ X0 @ (^[Y0 : a]: ($false)))) | ($true != (sK9 @ X0 @ (sK6 @ (sK9 @ X0)))) | ($true = (X0 @ (sK10 @ X0 @ X1))) | ($true != (sP1 @ X1)) | ($true != (X0 @ (sK7 @ (sK9 @ X0))))) ) | ~spl14_9),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f142])).
% 1.34/1.38 thf(f142,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sK9 @ X0 @ (^[Y0 : a]: ($false)))) | ($true != (sP1 @ X1)) | ($true != $true) | ($true = (sP0 @ X1 @ X0)) | ($true != (sK9 @ X0 @ (sK6 @ (sK9 @ X0)))) | ($true = (sK9 @ X0 @ sK3)) | ($true = (X0 @ (sK10 @ X0 @ X1))) | ($true != (X0 @ (sK7 @ (sK9 @ X0))))) ) | ~spl14_9),
% 1.34/1.38 inference(superposition,[status(thm)],[f94,f48])).
% 1.34/1.38 thf(f48,plain,(
% 1.34/1.38 ( ! [X2 : a > $o,X0 : a > $o,X4 : a > $o,X5 : a] : (($true = (sK9 @ X2 @ (^[Y0 : a]: ((X5 = Y0) | (X4 @ Y0))))) | ($true = (X2 @ (sK10 @ X2 @ X0))) | ($true != (X2 @ X5)) | ($true != (sK9 @ X2 @ X4)) | ($true != (sP1 @ X0)) | ($true = (sP0 @ X0 @ X2))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f26])).
% 1.34/1.38 thf(f94,plain,(
% 1.34/1.38 ( ! [X5 : (a > $o) > $o] : (($true != (X5 @ (^[Y0 : a]: (((sK7 @ X5) = Y0) | (sK6 @ X5 @ Y0))))) | ($true = (X5 @ sK3)) | ($true != (X5 @ (^[Y0 : a]: ($false))))) ) | ~spl14_9),
% 1.34/1.38 inference(avatar_component_clause,[status(thm)],[f93])).
% 1.34/1.38 thf(f93,definition,(
% 1.34/1.38 spl14_9 <=> ! [X5 : (a > $o) > $o] : (($true != (X5 @ (^[Y0 : a]: (((sK7 @ X5) = Y0) | (sK6 @ X5 @ Y0))))) | ($true = (X5 @ sK3)) | ($true != (X5 @ (^[Y0 : a]: ($false)))))),
% 1.34/1.38 introduced(definition,[new_symbols(naming,[spl14_9])],[avatar_definition])).
% 1.34/1.38 thf(f245,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true != (X0 @ (sK10 @ sK3 @ X0))) | ($true = (sP0 @ X0 @ sK3)) | ($true != (sP1 @ X0))) ) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(subsumption_resolution,[status(thm)],[f244,f130])).
% 1.34/1.38 thf(f130,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (X0 @ (sK10 @ X1 @ X0))) | ($true != (sP1 @ X0)) | ($true = (sK9 @ X1 @ (^[Y0 : a]: ($false)))) | ($true = (sP0 @ X0 @ X1))) )),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f129])).
% 1.34/1.38 thf(f129,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true = (sK9 @ X1 @ (^[Y0 : a]: ($false)))) | ($true != (X0 @ (sK10 @ X1 @ X0))) | ($true != (sP1 @ X0)) | ($true != $true) | ($true = (sP0 @ X0 @ X1))) )),
% 1.34/1.38 inference(duplicate_literal_removal,[status(thm)],[f122])).
% 1.34/1.38 thf(f122,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sP1 @ X0)) | ($true != $true) | ($true != (X0 @ (sK10 @ X1 @ X0))) | ($true != (sP1 @ X0)) | ($true = (sP0 @ X0 @ X1)) | ($true = (sK9 @ X1 @ (^[Y0 : a]: ($false))))) )),
% 1.34/1.38 inference(superposition,[status(thm)],[f45,f42])).
% 1.34/1.38 thf(f42,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X7 : a] : (($true = (sK8 @ X0 @ X7)) | ($true != (sP1 @ X0)) | ((X0 @ X7) != $true)) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f26])).
% 1.34/1.38 thf(f45,plain,(
% 1.34/1.38 ( ! [X2 : a > $o,X0 : a > $o] : (($true != (sK8 @ X0 @ (sK10 @ X2 @ X0))) | ($true = (sK9 @ X2 @ (^[Y0 : a]: ($false)))) | ($true = (sP0 @ X0 @ X2)) | ($true != (sP1 @ X0))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f26])).
% 1.34/1.38 thf(f244,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true != (sK9 @ sK3 @ (^[Y0 : a]: ($false)))) | ($true != (sP1 @ X0)) | ($true != (X0 @ (sK10 @ sK3 @ X0))) | ($true = (sP0 @ X0 @ sK3))) ) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(subsumption_resolution,[status(thm)],[f242,f107])).
% 1.34/1.38 thf(f107,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (X0 @ (sK10 @ X1 @ X0))) | ($true != (sK9 @ X1 @ X1)) | ($true != (sP1 @ X0)) | ($true = (sP0 @ X0 @ X1))) )),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.34/1.38 thf(f106,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != $true) | ($true != (sP1 @ X0)) | ($true = (sP0 @ X0 @ X1)) | ($true != (sK9 @ X1 @ X1)) | ($true != (X0 @ (sK10 @ X1 @ X0)))) )),
% 1.34/1.38 inference(duplicate_literal_removal,[status(thm)],[f103])).
% 1.34/1.38 thf(f103,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (X0 @ (sK10 @ X1 @ X0))) | ($true != (sK9 @ X1 @ X1)) | ($true = (sP0 @ X0 @ X1)) | ($true != (sP1 @ X0)) | ($true != (sP1 @ X0)) | ($true != $true)) )),
% 1.34/1.38 inference(superposition,[status(thm)],[f43,f42])).
% 1.34/1.38 thf(f43,plain,(
% 1.34/1.38 ( ! [X2 : a > $o,X0 : a > $o] : (($true != (sK8 @ X0 @ (sK10 @ X2 @ X0))) | ($true != (sK9 @ X2 @ X2)) | ($true != (sP1 @ X0)) | ($true = (sP0 @ X0 @ X2))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f26])).
% 1.34/1.38 thf(f242,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true != (X0 @ (sK10 @ sK3 @ X0))) | ($true != (sP1 @ X0)) | ($true != (sK9 @ sK3 @ (^[Y0 : a]: ($false)))) | ($true = (sK9 @ sK3 @ sK3)) | ($true = (sP0 @ X0 @ sK3))) ) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f241])).
% 1.34/1.38 thf(f241,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true != (X0 @ (sK10 @ sK3 @ X0))) | ($true = (sK9 @ sK3 @ sK3)) | ($true != (sP1 @ X0)) | ($true = (sP0 @ X0 @ sK3)) | ($true != (sK9 @ sK3 @ (^[Y0 : a]: ($false)))) | ($true != $true)) ) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(duplicate_literal_removal,[status(thm)],[f239])).
% 1.34/1.38 thf(f239,plain,(
% 1.34/1.38 ( ! [X0 : a > $o] : (($true = (sK9 @ sK3 @ sK3)) | ($true != (X0 @ (sK10 @ sK3 @ X0))) | ($true = (sP0 @ X0 @ sK3)) | ($true != (sP1 @ X0)) | ($true != $true) | ($true = (sK9 @ sK3 @ sK3)) | ($true != (sK9 @ sK3 @ (^[Y0 : a]: ($false))))) ) | (~spl14_3 | ~spl14_9 | ~spl14_10)),
% 1.34/1.38 inference(superposition,[status(thm)],[f232,f98])).
% 1.34/1.38 thf(f232,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (X1 @ (sK7 @ (sK9 @ X1)))) | ($true != (sP1 @ X0)) | ($true = (sP0 @ X0 @ X1)) | ($true != (X0 @ (sK10 @ X1 @ X0))) | ($true = (sK9 @ X1 @ sK3))) ) | (~spl14_3 | ~spl14_9)),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f231])).
% 1.34/1.38 thf(f231,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (X1 @ (sK7 @ (sK9 @ X1)))) | ($true = (sP0 @ X0 @ X1)) | ($true != (X0 @ (sK10 @ X1 @ X0))) | ($true != $true) | ($true = (sK9 @ X1 @ sK3)) | ($true != (sP1 @ X0))) ) | (~spl14_3 | ~spl14_9)),
% 1.34/1.38 inference(duplicate_literal_removal,[status(thm)],[f228])).
% 1.34/1.38 thf(f228,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (X1 @ (sK7 @ (sK9 @ X1)))) | ($true = (sK9 @ X1 @ sK3)) | ($true != (X0 @ (sK10 @ X1 @ X0))) | ($true = (sP0 @ X0 @ X1)) | ($true != (sP1 @ X0)) | ($true != (sP1 @ X0)) | ($true != $true)) ) | (~spl14_3 | ~spl14_9)),
% 1.34/1.38 inference(superposition,[status(thm)],[f192,f42])).
% 1.34/1.38 thf(f192,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sK8 @ X1 @ (sK10 @ X0 @ X1))) | ($true = (sP0 @ X1 @ X0)) | ($true != (X0 @ (sK7 @ (sK9 @ X0)))) | ($true != (sP1 @ X1)) | ($true = (sK9 @ X0 @ sK3))) ) | (~spl14_3 | ~spl14_9)),
% 1.34/1.38 inference(subsumption_resolution,[status(thm)],[f191,f45])).
% 1.34/1.38 thf(f191,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sK9 @ X0 @ (^[Y0 : a]: ($false)))) | ($true = (sP0 @ X1 @ X0)) | ($true != (X0 @ (sK7 @ (sK9 @ X0)))) | ($true = (sK9 @ X0 @ sK3)) | ($true != (sP1 @ X1)) | ($true != (sK8 @ X1 @ (sK10 @ X0 @ X1)))) ) | (~spl14_3 | ~spl14_9)),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f190])).
% 1.34/1.38 thf(f190,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (X0 @ (sK7 @ (sK9 @ X0)))) | ($true != (sK8 @ X1 @ (sK10 @ X0 @ X1))) | ($true = (sP0 @ X1 @ X0)) | ($true != $true) | ($true != (sP1 @ X1)) | ($true = (sK9 @ X0 @ sK3)) | ($true != (sK9 @ X0 @ (^[Y0 : a]: ($false))))) ) | (~spl14_3 | ~spl14_9)),
% 1.34/1.38 inference(duplicate_literal_removal,[status(thm)],[f189])).
% 1.34/1.38 thf(f189,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true = (sK9 @ X0 @ sK3)) | ($true != (X0 @ (sK7 @ (sK9 @ X0)))) | ($true != (sP1 @ X1)) | ($true != (sK8 @ X1 @ (sK10 @ X0 @ X1))) | ($true != (sK9 @ X0 @ (^[Y0 : a]: ($false)))) | ($true = (sK9 @ X0 @ sK3)) | ($true = (sP0 @ X1 @ X0)) | ($true != $true)) ) | (~spl14_3 | ~spl14_9)),
% 1.34/1.38 inference(superposition,[status(thm)],[f149,f66])).
% 1.34/1.38 thf(f149,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sK9 @ X0 @ (sK6 @ (sK9 @ X0)))) | ($true = (sK9 @ X0 @ sK3)) | ($true != (sP1 @ X1)) | ($true = (sP0 @ X1 @ X0)) | ($true != (sK8 @ X1 @ (sK10 @ X0 @ X1))) | ($true != (X0 @ (sK7 @ (sK9 @ X0))))) ) | ~spl14_9),
% 1.34/1.38 inference(subsumption_resolution,[status(thm)],[f148,f45])).
% 1.34/1.38 thf(f148,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true != (sK9 @ X0 @ (sK6 @ (sK9 @ X0)))) | ($true = (sP0 @ X1 @ X0)) | ($true != (sK9 @ X0 @ (^[Y0 : a]: ($false)))) | ($true != (sP1 @ X1)) | ($true != (sK8 @ X1 @ (sK10 @ X0 @ X1))) | ($true = (sK9 @ X0 @ sK3)) | ($true != (X0 @ (sK7 @ (sK9 @ X0))))) ) | ~spl14_9),
% 1.34/1.38 inference(trivial_inequality_removal,[status(thm)],[f147])).
% 1.34/1.38 thf(f147,plain,(
% 1.34/1.38 ( ! [X0 : a > $o,X1 : a > $o] : (($true = (sP0 @ X1 @ X0)) | ($true != (sK8 @ X1 @ (sK10 @ X0 @ X1))) | ($true = (sK9 @ X0 @ sK3)) | ($true != $true) | ($true != (sK9 @ X0 @ (sK6 @ (sK9 @ X0)))) | ($true != (sP1 @ X1)) | ($true != (X0 @ (sK7 @ (sK9 @ X0)))) | ($true != (sK9 @ X0 @ (^[Y0 : a]: ($false))))) ) | ~spl14_9),
% 1.34/1.38 inference(superposition,[status(thm)],[f94,f47])).
% 1.34/1.38 thf(f47,plain,(
% 1.34/1.38 ( ! [X2 : a > $o,X0 : a > $o,X4 : a > $o,X5 : a] : (($true = (sK9 @ X2 @ (^[Y0 : a]: ((X5 = Y0) | (X4 @ Y0))))) | ($true != (sK9 @ X2 @ X4)) | ($true != (sK8 @ X0 @ (sK10 @ X2 @ X0))) | ($true != (sP1 @ X0)) | ($true = (sP0 @ X0 @ X2)) | ($true != (X2 @ X5))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f26])).
% 1.34/1.38 thf(f99,plain,(
% 1.34/1.38 spl14_10 | ~spl14_1),
% 1.34/1.38 inference(avatar_split_clause,[status(thm)],[f36,f57,f97])).
% 1.34/1.38 thf(f57,definition,(
% 1.34/1.38 spl14_1 <=> ($true = sP2)),
% 1.34/1.38 introduced(definition,[new_symbols(naming,[spl14_1])],[avatar_definition])).
% 1.34/1.38 thf(f36,plain,(
% 1.34/1.38 ( ! [X5 : (a > $o) > $o] : (($true != sP2) | ($true != (X5 @ (^[Y0 : a]: ($false)))) | ($true = (X5 @ sK3)) | ($true = (sK3 @ (sK7 @ X5)))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f20])).
% 1.34/1.38 thf(f20,plain,(
% 1.34/1.38 (((! [X2 : a] : (($true = (sK4 @ X2)) | ($true != (sK3 @ X2))) & ($true != (cA @ sK4)) & ($true = (cA @ sK4))) | ($true = (sP1 @ sK3))) & ! [X3 : a] : (($true != (sK3 @ X3)) | (($true = (sK5 @ X3 @ X3)) & ($true = (cA @ (sK5 @ X3))))) & ! [X5 : (a > $o) > $o] : (($true = (X5 @ sK3)) | ($true != (X5 @ (^[Y0 : a]: ($false)))) | ((($true = (sK3 @ (sK7 @ X5))) & ($true != (X5 @ (^[Y0 : a]: (((sK7 @ X5) = Y0) | (sK6 @ X5 @ Y0)))))) & ($true = (X5 @ (sK6 @ X5)))))) | ($true != sP2)),
% 1.34/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f14,f19,f18,f17,f16,f15])).
% 1.34/1.38 thf(f15,plain,(
% 1.34/1.38 ? [X0 : a > $o] : ((? [X1 : a > $o] : (! [X2 : a] : (($true = (X1 @ X2)) | ($true != (X0 @ X2))) & ($true != (cA @ X1)) & ($true = (cA @ X1))) | ($true = (sP1 @ X0))) & ! [X3 : a] : (($true != (X0 @ X3)) | ? [X4 : a > $o] : (($true = (X4 @ X3)) & ($true = (cA @ X4)))) & ! [X5 : (a > $o) > $o] : (($true = (X5 @ X0)) | ($true != (X5 @ (^[Y0 : a]: ($false)))) | ? [X6 : a > $o] : (? [X7 : a] : (((X0 @ X7) = $true) & ($true != (X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))))) & ($true = (X5 @ X6))))) => ((? [X1 : a > $o] : (! [X2 : a] : (($true = (X1 @ X2)) | ($true != (sK3 @ X2))) & ($true != (cA @ X1)) & ($true = (cA @ X1))) | ($true = (sP1 @ sK3))) & ! [X3 : a] : (($true != (sK3 @ X3)) | ? [X4 : a > $o] : (($true = (X4 @ X3)) & ($true = (cA @ X4)))) & ! [X5 : (a > $o) > $o] : (($true = (X5 @ sK3)) | ($true != (X5 @ (^[Y0 : a]: ($false)))) | ? [X6 : a > $o] : (? [X7 : a] : (($true = (sK3 @ X7)) & ($true != (X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))))) & ($true = (X5 @ X6)))))),
% 1.34/1.38 introduced(definition,[],[choice_axiom])).
% 1.34/1.38 thf(f16,plain,(
% 1.34/1.38 ? [X1 : a > $o] : (! [X2 : a] : (($true = (X1 @ X2)) | ($true != (sK3 @ X2))) & ($true != (cA @ X1)) & ($true = (cA @ X1))) => (! [X2 : a] : (($true = (sK4 @ X2)) | ($true != (sK3 @ X2))) & ($true != (cA @ sK4)) & ($true = (cA @ sK4)))),
% 1.34/1.38 introduced(definition,[],[choice_axiom])).
% 1.34/1.38 thf(f17,plain,(
% 1.34/1.38 ! [X3 : a] : (? [X4 : a > $o] : (($true = (X4 @ X3)) & ($true = (cA @ X4))) => (($true = (sK5 @ X3 @ X3)) & ($true = (cA @ (sK5 @ X3)))))),
% 1.34/1.38 introduced(definition,[],[choice_axiom])).
% 1.34/1.38 thf(f18,plain,(
% 1.34/1.38 ! [X5 : (a > $o) > $o] : (? [X6 : a > $o] : (? [X7 : a] : (($true = (sK3 @ X7)) & ($true != (X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))))) & ($true = (X5 @ X6))) => (? [X7 : a] : (($true = (sK3 @ X7)) & ($true != (X5 @ (^[Y0 : a]: ((X7 = Y0) | (sK6 @ X5 @ Y0)))))) & ($true = (X5 @ (sK6 @ X5)))))),
% 1.34/1.38 introduced(definition,[],[choice_axiom])).
% 1.34/1.38 thf(f19,plain,(
% 1.34/1.38 ! [X5 : (a > $o) > $o] : (? [X7 : a] : (($true = (sK3 @ X7)) & ($true != (X5 @ (^[Y0 : a]: ((X7 = Y0) | (sK6 @ X5 @ Y0)))))) => (($true = (sK3 @ (sK7 @ X5))) & ($true != (X5 @ (^[Y0 : a]: (((sK7 @ X5) = Y0) | (sK6 @ X5 @ Y0)))))))),
% 1.34/1.38 introduced(definition,[],[choice_axiom])).
% 1.34/1.38 thf(f14,plain,(
% 1.34/1.38 ? [X0 : a > $o] : ((? [X1 : a > $o] : (! [X2 : a] : (($true = (X1 @ X2)) | ($true != (X0 @ X2))) & ($true != (cA @ X1)) & ($true = (cA @ X1))) | ($true = (sP1 @ X0))) & ! [X3 : a] : (($true != (X0 @ X3)) | ? [X4 : a > $o] : (($true = (X4 @ X3)) & ($true = (cA @ X4)))) & ! [X5 : (a > $o) > $o] : (($true = (X5 @ X0)) | ($true != (X5 @ (^[Y0 : a]: ($false)))) | ? [X6 : a > $o] : (? [X7 : a] : (((X0 @ X7) = $true) & ($true != (X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))))) & ($true = (X5 @ X6))))) | ($true != sP2)),
% 1.34/1.38 inference(rectify,[status(thm)],[f13])).
% 1.34/1.38 thf(f13,plain,(
% 1.34/1.38 ? [X1 : a > $o] : ((? [X17 : a > $o] : (! [X18 : a] : (($true = (X17 @ X18)) | ($true != (X1 @ X18))) & ($true != (cA @ X17)) & ($true = (cA @ X17))) | ($true = (sP1 @ X1))) & ! [X2 : a] : (($true != (X1 @ X2)) | ? [X3 : a > $o] : (($true = (X3 @ X2)) & ((cA @ X3) = $true))) & ! [X4 : (a > $o) > $o] : (($true = (X4 @ X1)) | ($true != (X4 @ (^[Y0 : a]: ($false)))) | ? [X5 : a > $o] : (? [X6 : a] : (($true = (X1 @ X6)) & ($true != (X4 @ (^[Y0 : a]: ((X6 = Y0) | (X5 @ Y0)))))) & ($true = (X4 @ X5))))) | ($true != sP2)),
% 1.34/1.38 inference(nnf_transformation,[status(thm)],[f11])).
% 1.34/1.38 thf(f11,plain,(
% 1.34/1.38 ? [X1 : a > $o] : ((? [X17 : a > $o] : (! [X18 : a] : (($true = (X17 @ X18)) | ($true != (X1 @ X18))) & ($true != (cA @ X17)) & ($true = (cA @ X17))) | ($true = (sP1 @ X1))) & ! [X2 : a] : (($true != (X1 @ X2)) | ? [X3 : a > $o] : (($true = (X3 @ X2)) & ((cA @ X3) = $true))) & ! [X4 : (a > $o) > $o] : (($true = (X4 @ X1)) | ($true != (X4 @ (^[Y0 : a]: ($false)))) | ? [X5 : a > $o] : (? [X6 : a] : (($true = (X1 @ X6)) & ($true != (X4 @ (^[Y0 : a]: ((X6 = Y0) | (X5 @ Y0)))))) & ($true = (X4 @ X5))))) | ~($true = sP2)),
% 1.34/1.38 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.34/1.38 thf(f95,plain,(
% 1.34/1.38 spl14_9 | ~spl14_1),
% 1.34/1.38 inference(avatar_split_clause,[status(thm)],[f35,f57,f93])).
% 1.34/1.38 thf(f35,plain,(
% 1.34/1.38 ( ! [X5 : (a > $o) > $o] : (($true != (X5 @ (^[Y0 : a]: (((sK7 @ X5) = Y0) | (sK6 @ X5 @ Y0))))) | ($true != (X5 @ (^[Y0 : a]: ($false)))) | ($true = (X5 @ sK3)) | ($true != sP2)) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f20])).
% 1.34/1.38 thf(f83,plain,(
% 1.34/1.38 ~spl14_5 | ~spl14_1 | spl14_6),
% 1.34/1.38 inference(avatar_split_clause,[status(thm)],[f40,f78,f57,f74])).
% 1.34/1.38 thf(f74,definition,(
% 1.34/1.38 spl14_5 <=> ($true = (cA @ sK4))),
% 1.34/1.38 introduced(definition,[new_symbols(naming,[spl14_5])],[avatar_definition])).
% 1.34/1.38 thf(f40,plain,(
% 1.34/1.38 ($true = (sP1 @ sK3)) | ($true != sP2) | ($true != (cA @ sK4))),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f20])).
% 1.34/1.38 thf(f82,plain,(
% 1.34/1.38 spl14_1 | spl14_4),
% 1.34/1.38 inference(avatar_split_clause,[status(thm)],[f54,f69,f57])).
% 1.34/1.38 thf(f69,definition,(
% 1.34/1.38 spl14_4 <=> ($true = (cA @ sK13))),
% 1.34/1.38 introduced(definition,[new_symbols(naming,[spl14_4])],[avatar_definition])).
% 1.34/1.38 thf(f54,plain,(
% 1.34/1.38 ($true = sP2) | ($true = (cA @ sK13))),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f33])).
% 1.34/1.38 thf(f33,plain,(
% 1.34/1.38 ($true = sP2) | (($true != (cA @ sK13)) & ($true = (cA @ sK13)))),
% 1.34/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f12,f32])).
% 1.34/1.38 thf(f32,plain,(
% 1.34/1.38 ? [X0 : a > $o] : (((cA @ X0) != $true) & ((cA @ X0) = $true)) => (($true != (cA @ sK13)) & ($true = (cA @ sK13)))),
% 1.34/1.38 introduced(definition,[],[choice_axiom])).
% 1.34/1.38 thf(f12,plain,(
% 1.34/1.38 ($true = sP2) | ? [X0 : a > $o] : (((cA @ X0) != $true) & ((cA @ X0) = $true))),
% 1.34/1.38 inference(definition_folding,[status(thm)],[f8,f11,f10,f9])).
% 1.34/1.38 thf(f8,plain,(
% 1.34/1.38 ? [X1 : a > $o] : ((? [X17 : a > $o] : (! [X18 : a] : (($true = (X17 @ X18)) | ($true != (X1 @ X18))) & ($true != (cA @ X17)) & ($true = (cA @ X17))) | ? [X7 : a > $o] : (($true = (cA @ X7)) & ! [X9 : a > $o] : (? [X13 : (a > $o) > $o] : (! [X14 : a > $o] : (! [X15 : a] : (($true != (X9 @ X15)) | ($true = (X13 @ (^[Y0 : a]: ((X15 = Y0) | (X14 @ Y0)))))) | ($true != (X13 @ X14))) & ($true = (X13 @ (^[Y0 : a]: ($false)))) & ($true != (X13 @ X9))) | ? [X16 : a] : (($true = (X9 @ X16)) & ($true != (X7 @ X16))) | ? [X10 : a > $o] : (! [X11 : a] : (($true != (X9 @ X11)) | ($true = (X10 @ X11))) & ($true = (cA @ X10)) & (($true != (cA @ X10)) | ? [X12 : a] : (($true != (X10 @ X12)) & ($true = (X1 @ X12)))))) & ! [X8 : a] : (($true = (X7 @ X8)) | ($true != (X1 @ X8))))) & ! [X2 : a] : (($true != (X1 @ X2)) | ? [X3 : a > $o] : (($true = (X3 @ X2)) & ((cA @ X3) = $true))) & ! [X4 : (a > $o) > $o] : (($true = (X4 @ X1)) | ($true != (X4 @ (^[Y0 : a]: ($false)))) | ? [X5 : a > $o] : (? [X6 : a] : (($true = (X1 @ X6)) & ($true != (X4 @ (^[Y0 : a]: ((X6 = Y0) | (X5 @ Y0)))))) & ($true = (X4 @ X5))))) | ? [X0 : a > $o] : (((cA @ X0) != $true) & ((cA @ X0) = $true))),
% 1.34/1.38 inference(flattening,[status(thm)],[f7])).
% 1.34/1.38 thf(f7,plain,(
% 1.34/1.38 ? [X0 : a > $o] : (((cA @ X0) != $true) & ((cA @ X0) = $true)) | ? [X1 : a > $o] : ((? [X7 : a > $o] : (! [X9 : a > $o] : (? [X10 : a > $o] : ((($true != (cA @ X10)) | ? [X12 : a] : (($true != (X10 @ X12)) & ($true = (X1 @ X12)))) & (! [X11 : a] : (($true != (X9 @ X11)) | ($true = (X10 @ X11))) & ($true = (cA @ X10)))) | ? [X16 : a] : (($true = (X9 @ X16)) & ($true != (X7 @ X16))) | ? [X13 : (a > $o) > $o] : (($true != (X13 @ X9)) & (($true = (X13 @ (^[Y0 : a]: ($false)))) & ! [X14 : a > $o] : (! [X15 : a] : (($true != (X9 @ X15)) | ($true = (X13 @ (^[Y0 : a]: ((X15 = Y0) | (X14 @ Y0)))))) | ($true != (X13 @ X14)))))) & (! [X8 : a] : (($true = (X7 @ X8)) | ($true != (X1 @ X8))) & ($true = (cA @ X7)))) | ? [X17 : a > $o] : (($true != (cA @ X17)) & (($true = (cA @ X17)) & ! [X18 : a] : (($true = (X17 @ X18)) | ($true != (X1 @ X18)))))) & (! [X4 : (a > $o) > $o] : (($true = (X4 @ X1)) | (($true != (X4 @ (^[Y0 : a]: ($false)))) | ? [X5 : a > $o] : (? [X6 : a] : (($true = (X1 @ X6)) & ($true != (X4 @ (^[Y0 : a]: ((X6 = Y0) | (X5 @ Y0)))))) & ($true = (X4 @ X5))))) & ! [X2 : a] : (($true != (X1 @ X2)) | ? [X3 : a > $o] : (($true = (X3 @ X2)) & ((cA @ X3) = $true)))))),
% 1.34/1.38 inference(ennf_transformation,[status(thm)],[f6])).
% 1.34/1.38 thf(f6,plain,(
% 1.34/1.38 ~(! [X0 : a > $o] : (((cA @ X0) = $true) => ((cA @ X0) = $true)) & ! [X1 : a > $o] : ((! [X4 : (a > $o) > $o] : ((($true = (X4 @ (^[Y0 : a]: ($false)))) & ! [X5 : a > $o] : (($true = (X4 @ X5)) => ! [X6 : a] : (($true = (X1 @ X6)) => ($true = (X4 @ (^[Y0 : a]: ((X6 = Y0) | (X5 @ Y0)))))))) => ($true = (X4 @ X1))) & ! [X2 : a] : (($true = (X1 @ X2)) => ? [X3 : a > $o] : (($true = (X3 @ X2)) & ((cA @ X3) = $true)))) => (! [X7 : a > $o] : ((! [X8 : a] : (($true = (X1 @ X8)) => ($true = (X7 @ X8))) & ($true = (cA @ X7))) => ? [X9 : a > $o] : (! [X10 : a > $o] : ((! [X11 : a] : (($true = (X9 @ X11)) => ($true = (X10 @ X11))) & ($true = (cA @ X10))) => (! [X12 : a] : (($true = (X1 @ X12)) => ($true = (X10 @ X12))) & ($true = (cA @ X10)))) & ! [X16 : a] : (($true = (X9 @ X16)) => ($true = (X7 @ X16))) & ! [X13 : (a > $o) > $o] : ((($true = (X13 @ (^[Y0 : a]: ($false)))) & ! [X14 : a > $o] : (($true = (X13 @ X14)) => ! [X15 : a] : (($true = (X9 @ X15)) => ($true = (X13 @ (^[Y0 : a]: ((X15 = Y0) | (X14 @ Y0)))))))) => ($true = (X13 @ X9))))) & ! [X17 : a > $o] : ((($true = (cA @ X17)) & ! [X18 : a] : (($true = (X1 @ X18)) => ($true = (X17 @ X18)))) => ($true = (cA @ X17))))))),
% 1.34/1.38 inference(rectify,[status(thm)],[f5])).
% 1.34/1.38 thf(f5,plain,(
% 1.34/1.38 ~(! [X0 : a > $o] : (((cA @ X0) = $true) => ((cA @ X0) = $true)) & ! [X1 : a > $o] : ((! [X4 : (a > $o) > $o] : ((($true = (X4 @ (^[Y0 : a]: ($false)))) & ! [X5 : a > $o] : (($true = (X4 @ X5)) => ! [X6 : a] : (($true = (X1 @ X6)) => ($true = (X4 @ (^[Y0 : a]: ((X6 = Y0) | (X5 @ Y0)))))))) => ($true = (X4 @ X1))) & ! [X2 : a] : (($true = (X1 @ X2)) => ? [X3 : a > $o] : (($true = (X3 @ X2)) & ((cA @ X3) = $true)))) => (! [X9 : a > $o] : ((($true = (cA @ X9)) & ! [X10 : a] : (($true = (X1 @ X10)) => ($true = (X9 @ X10)))) => ? [X11 : a > $o] : (! [X12 : a > $o] : ((($true = (cA @ X12)) & ! [X13 : a] : (($true = (X11 @ X13)) => ($true = (X12 @ X13)))) => (($true = (cA @ X12)) & ! [X14 : a] : (($true = (X1 @ X14)) => ($true = (X12 @ X14))))) & ! [X15 : (a > $o) > $o] : ((! [X16 : a > $o] : (($true = (X15 @ X16)) => ! [X17 : a] : (($true = (X11 @ X17)) => ((X15 @ (^[Y0 : a]: ((X17 = Y0) | (X16 @ Y0)))) = $true))) & ($true = (X15 @ (^[Y0 : a]: ($false))))) => ($true = (X15 @ X11))) & ! [X20 : a] : (($true = (X11 @ X20)) => ($true = (X9 @ X20))))) & ! [X21 : a > $o] : ((($true = (cA @ X21)) & ! [X22 : a] : (($true = (X1 @ X22)) => ($true = (X21 @ X22)))) => ($true = (cA @ X21))))))),
% 1.34/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.34/1.38 thf(f4,plain,(
% 1.34/1.38 ~(! [X0 : a > $o] : ((cA @ X0) => (cA @ X0)) & ! [X1 : a > $o] : ((! [X2 : a] : ((X1 @ X2) => ? [X3 : a > $o] : ((cA @ X3) & (X3 @ X2))) & ! [X4 : (a > $o) > $o] : ((! [X5 : a > $o] : ((X4 @ X5) => ! [X6 : a] : ((X1 @ X6) => (X4 @ (^[X7 : a] : ((X5 @ X7) | (X6 = X7)))))) & (X4 @ (^[X8 : a] : ($false)))) => (X4 @ X1))) => (! [X9 : a > $o] : (((cA @ X9) & ! [X10 : a] : ((X1 @ X10) => (X9 @ X10))) => ? [X11 : a > $o] : (! [X12 : a > $o] : (((cA @ X12) & ! [X13 : a] : ((X11 @ X13) => (X12 @ X13))) => ((cA @ X12) & ! [X14 : a] : ((X1 @ X14) => (X12 @ X14)))) & ! [X15 : (a > $o) > $o] : ((! [X16 : a > $o] : ((X15 @ X16) => ! [X17 : a] : ((X11 @ X17) => (X15 @ (^[X18 : a] : ((X16 @ X18) | (X17 = X18)))))) & (X15 @ (^[X19 : a] : ($false)))) => (X15 @ X11)) & ! [X20 : a] : ((X11 @ X20) => (X9 @ X20)))) & ! [X21 : a > $o] : (((cA @ X21) & ! [X22 : a] : ((X1 @ X22) => (X21 @ X22))) => (cA @ X21)))))),
% 1.34/1.38 inference(rectify,[status(thm)],[f2])).
% 1.34/1.38 thf(f2,negated_conjecture,(
% 1.34/1.38 ~(! [X0 : a > $o] : ((cA @ X0) => (cA @ X0)) & ! [X1 : a > $o] : ((! [X0 : a] : ((X1 @ X0) => ? [X6 : a > $o] : ((cA @ X6) & (X6 @ X0))) & ! [X2 : (a > $o) > $o] : ((! [X0 : a > $o] : ((X2 @ X0) => ! [X4 : a] : ((X1 @ X4) => (X2 @ (^[X5 : a] : ((X0 @ X5) | (X4 = X5)))))) & (X2 @ (^[X3 : a] : ($false)))) => (X2 @ X1))) => (! [X0 : a > $o] : (((cA @ X0) & ! [X7 : a] : ((X1 @ X7) => (X0 @ X7))) => ? [X8 : a > $o] : (! [X3 : a > $o] : (((cA @ X3) & ! [X7 : a] : ((X8 @ X7) => (X3 @ X7))) => ((cA @ X3) & ! [X7 : a] : ((X1 @ X7) => (X3 @ X7)))) & ! [X2 : (a > $o) > $o] : ((! [X7 : a > $o] : ((X2 @ X7) => ! [X4 : a] : ((X8 @ X4) => (X2 @ (^[X5 : a] : ((X7 @ X5) | (X4 = X5)))))) & (X2 @ (^[X3 : a] : ($false)))) => (X2 @ X8)) & ! [X7 : a] : ((X8 @ X7) => (X0 @ X7)))) & ! [X0 : a > $o] : (((cA @ X0) & ! [X7 : a] : ((X1 @ X7) => (X0 @ X7))) => (cA @ X0)))))),
% 1.34/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.34/1.38 thf(f1,conjecture,(
% 1.34/1.38 ! [X0 : a > $o] : ((cA @ X0) => (cA @ X0)) & ! [X1 : a > $o] : ((! [X0 : a] : ((X1 @ X0) => ? [X6 : a > $o] : ((cA @ X6) & (X6 @ X0))) & ! [X2 : (a > $o) > $o] : ((! [X0 : a > $o] : ((X2 @ X0) => ! [X4 : a] : ((X1 @ X4) => (X2 @ (^[X5 : a] : ((X0 @ X5) | (X4 = X5)))))) & (X2 @ (^[X3 : a] : ($false)))) => (X2 @ X1))) => (! [X0 : a > $o] : (((cA @ X0) & ! [X7 : a] : ((X1 @ X7) => (X0 @ X7))) => ? [X8 : a > $o] : (! [X3 : a > $o] : (((cA @ X3) & ! [X7 : a] : ((X8 @ X7) => (X3 @ X7))) => ((cA @ X3) & ! [X7 : a] : ((X1 @ X7) => (X3 @ X7)))) & ! [X2 : (a > $o) > $o] : ((! [X7 : a > $o] : ((X2 @ X7) => ! [X4 : a] : ((X8 @ X4) => (X2 @ (^[X5 : a] : ((X7 @ X5) | (X4 = X5)))))) & (X2 @ (^[X3 : a] : ($false)))) => (X2 @ X8)) & ! [X7 : a] : ((X8 @ X7) => (X0 @ X7)))) & ! [X0 : a > $o] : (((cA @ X0) & ! [X7 : a] : ((X1 @ X7) => (X0 @ X7))) => (cA @ X0))))),
% 1.34/1.38 file('/export/starexec/sandbox2/tmp/tmp.SRfGWKMZ63/DTF2THF_22685.p',cDOMTHM8_pme)).
% 1.34/1.38 thf(f81,plain,(
% 1.34/1.38 ~spl14_1 | spl14_5 | spl14_6),
% 1.34/1.38 inference(avatar_split_clause,[status(thm)],[f39,f78,f74,f57])).
% 1.34/1.38 thf(f39,plain,(
% 1.34/1.38 ($true = (cA @ sK4)) | ($true = (sP1 @ sK3)) | ($true != sP2)),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f20])).
% 1.34/1.38 thf(f72,plain,(
% 1.34/1.38 ~spl14_4 | spl14_1),
% 1.34/1.38 inference(avatar_split_clause,[status(thm)],[f55,f57,f69])).
% 1.34/1.38 thf(f55,plain,(
% 1.34/1.38 ($true != (cA @ sK13)) | ($true = sP2)),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f33])).
% 1.34/1.38 thf(f67,plain,(
% 1.34/1.38 ~spl14_1 | spl14_3),
% 1.34/1.38 inference(avatar_split_clause,[status(thm)],[f34,f65,f57])).
% 1.34/1.38 thf(f34,plain,(
% 1.34/1.38 ( ! [X5 : (a > $o) > $o] : (($true != sP2) | ($true != (X5 @ (^[Y0 : a]: ($false)))) | ($true = (X5 @ sK3)) | ($true = (X5 @ (sK6 @ X5)))) )),
% 1.34/1.38 inference(cnf_transformation,[status(thm)],[f20])).
% 1.34/1.38 % SZS output end Proof for DTF2THF_22685
% 1.34/1.38 % (22817)------------------------------
% 1.34/1.38 % (22817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.38 % (22817)Termination reason: Refutation
% 1.34/1.38
% 1.34/1.38 % (22817)Memory used [KB]: 5884
% 1.34/1.38 % (22817)Time elapsed: 0.042 s
% 1.34/1.38 % (22817)Instructions burned: 67 (million)
% 1.34/1.38 % (22817)------------------------------
% 1.34/1.38 % (22817)------------------------------
% 1.34/1.38 % (22781)Success in time 0.225 s
%------------------------------------------------------------------------------