%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU782^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 09:37:09 AM UTC 2026
% Result : Theorem 1.71s 1.33s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 96 ( 31 unt; 0 typ; 2 def)
% Number of atoms : 1097 ( 298 equ; 0 cnn)
% Maximal formula atoms : 14 ( 11 avg)
% Number of connectives : 1087 ( 130 ~; 120 |; 76 &; 698 @)
% ( 10 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 19 con; 0-3 aty)
% Number of variables : 214 ( 40 ^; 132 !; 42 ?; 214 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
binunion: $i > $i > $i ).
thf(func_def_7,type,
cartprod: $i > $i > $i ).
thf(func_def_8,type,
breln: $i > $i > $i > $o ).
thf(func_def_9,type,
breln1: $i > $i > $o ).
thf(func_def_26,type,
sK10: $i > $i > $i ).
thf(f141,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f120,f130,f140]) ).
thf(f140,plain,
~ spl13_1,
inference(avatar_contradiction_clause,[status(thm)],[f139]) ).
thf(f139,plain,
( $false
| ~ spl13_1 ),
inference(subsumption_resolution,[status(thm)],[f138,f95]) ).
thf(f95,plain,
( $true
!= ( subset @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK4
@ ( binunion @ sK5 @ sK6 ) ) ),
inference(definition_unfolding,[status(thm)],[f56,f68]) ).
thf(f68,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[status(thm)],[f53,f52]) ).
thf(f52,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i,X1: $i,X4: $i] : ( subset @ X4 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',breln) ).
thf(f53,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( breln1
= ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( breln1
= ( ^ [X0: $i,X5: $i] : ( breln @ X0 @ X0 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',breln1) ).
thf(f56,plain,
( $true
!= ( breln1 @ sK4 @ ( binunion @ sK5 @ sK6 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( subsetI1 = $true )
& ( subsetE = $true )
& ( $true
= ( breln1 @ sK4 @ sK6 ) )
& ( $true
!= ( breln1 @ sK4 @ ( binunion @ sK5 @ sK6 ) ) )
& ( $true
= ( breln1 @ sK4 @ sK5 ) )
& ( binunionEcases = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f25,f33,f32]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ( $true
!= ( breln1 @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
=> ( ? [X2: $i] :
( ( $true
= ( breln1 @ sK4 @ X2 ) )
& ( $true
!= ( breln1 @ sK4 @ ( binunion @ sK5 @ X2 ) ) ) )
& ( $true
= ( breln1 @ sK4 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ? [X2: $i] :
( ( $true
= ( breln1 @ sK4 @ X2 ) )
& ( $true
!= ( breln1 @ sK4 @ ( binunion @ sK5 @ X2 ) ) ) )
=> ( ( $true
= ( breln1 @ sK4 @ sK6 ) )
& ( $true
!= ( breln1 @ sK4 @ ( binunion @ sK5 @ sK6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( subsetI1 = $true )
& ( subsetE = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ( $true
!= ( breln1 @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( binunionEcases = $true ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ( $true
!= ( breln1 @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( binunionEcases = $true )
& ( subsetE = $true )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( ( subsetI1 = $true )
=> ( ( subsetE = $true )
=> ( ( binunionEcases = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
=> ( $true
= ( breln1 @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( subsetI1
=> ( subsetE
=> ( binunionEcases
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( subsetI1
=> ( subsetE
=> ( binunionEcases
=> ! [X0: $i,X5: $i] :
( ( breln1 @ X0 @ X5 )
=> ! [X6: $i] :
( ( breln1 @ X0 @ X6 )
=> ( breln1 @ X0 @ ( binunion @ X5 @ X6 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( subsetI1
=> ( subsetE
=> ( binunionEcases
=> ! [X0: $i,X5: $i] :
( ( breln1 @ X0 @ X5 )
=> ! [X6: $i] :
( ( breln1 @ X0 @ X6 )
=> ( breln1 @ X0 @ ( binunion @ X5 @ X6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',breln1unionprop) ).
thf(f138,plain,
( ( $true
= ( subset @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) )
| ~ spl13_1 ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $true
= ( subset @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) )
| ( $true != $true )
| ~ spl13_1 ),
inference(superposition,[status(thm)],[f96,f134]) ).
thf(f134,plain,
( ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ ( cartprod @ sK4 @ sK4 ) ) )
| ~ spl13_1 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ ( cartprod @ sK4 @ sK4 ) ) )
| ( $true != $true )
| ~ spl13_1 ),
inference(superposition,[status(thm)],[f106,f115]) ).
thf(f115,plain,
( ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ sK5 ) )
| ~ spl13_1 ),
inference(avatar_component_clause,[status(thm)],[f113]) ).
thf(f113,definition,
( spl13_1
<=> ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition]) ).
thf(f106,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK5 ) )
| ( $true
= ( in @ X0 @ ( cartprod @ sK4 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( in @ X0 @ ( cartprod @ sK4 @ sK4 ) ) )
| ( $true
!= ( in @ X0 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f98,f94]) ).
thf(f94,plain,
( $true
= ( subset @ sK5 @ ( cartprod @ sK4 @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK4
@ sK5 ) ),
inference(definition_unfolding,[status(thm)],[f55,f68]) ).
thf(f55,plain,
( $true
= ( breln1 @ sK4 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f98,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( subset @ X3 @ X4 ) )
| ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5 @ X3 ) )
| ( $true
!= ( subset @ X3 @ X4 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f60,f58]) ).
thf(f58,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f60,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( subset @ X3 @ X4 ) )
| ( $true
!= ( in @ X5 @ X3 ) )
| ( $true
= ( in @ X5 @ X4 ) )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( subsetE = $true )
| ( ( $true
= ( subset @ sK7 @ sK8 ) )
& ( $true
= ( in @ sK9 @ sK7 ) )
& ( $true
!= ( in @ sK9 @ sK8 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( subset @ X3 @ X4 ) )
| ( $true
!= ( in @ X5 @ X3 ) )
| ( $true
= ( in @ X5 @ X4 ) ) )
| ( subsetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f36,f37]) ).
thf(f37,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
=> ( ( $true
= ( subset @ sK7 @ sK8 ) )
& ( $true
= ( in @ sK9 @ sK7 ) )
& ( $true
!= ( in @ sK9 @ sK8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( subset @ X3 @ X4 ) )
| ( $true
!= ( in @ X5 @ X3 ) )
| ( $true
= ( in @ X5 @ X4 ) ) )
| ( subsetE != $true ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',subsetE) ).
thf(f96,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK10 @ X1 @ X0 ) @ X0 )
!= $true )
| ( $true
= ( subset @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK10 @ X1 @ X0 ) @ X0 )
!= $true )
| ( $true != $true )
| ( $true
= ( subset @ X1 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f66,f59]) ).
thf(f59,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f66,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( ( in @ ( sK10 @ X1 @ X0 ) @ X0 )
!= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( ( $true
= ( in @ ( sK10 @ X1 @ X0 ) @ X1 ) )
& ( ( in @ ( sK10 @ X1 @ X0 ) @ X0 )
!= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ( ( $true
!= ( subset @ sK12 @ sK11 ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK12 ) )
| ( $true
= ( in @ X5 @ sK11 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f40,f42,f41]) ).
thf(f41,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
=> ( ( $true
= ( in @ ( sK10 @ X1 @ X0 ) @ X1 ) )
& ( ( in @ ( sK10 @ X1 @ X0 ) @ X0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
( ? [X3: $i,X4: $i] :
( ( $true
!= ( subset @ X4 @ X3 ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ X3 ) ) ) )
=> ( ( $true
!= ( subset @ sK12 @ sK11 ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK12 ) )
| ( $true
= ( in @ X5 @ sK11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X3: $i,X4: $i] :
( ( $true
!= ( subset @ X4 @ X3 ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
<=> ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( $true
= ( subset @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetI1
= ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',subsetI1) ).
thf(f130,plain,
~ spl13_2,
inference(avatar_contradiction_clause,[status(thm)],[f129]) ).
thf(f129,plain,
( $false
| ~ spl13_2 ),
inference(subsumption_resolution,[status(thm)],[f127,f95]) ).
thf(f127,plain,
( ( $true
= ( subset @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) )
| ~ spl13_2 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true != $true )
| ( $true
= ( subset @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) )
| ~ spl13_2 ),
inference(superposition,[status(thm)],[f96,f123]) ).
thf(f123,plain,
( ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ ( cartprod @ sK4 @ sK4 ) ) )
| ~ spl13_2 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $true != $true )
| ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ ( cartprod @ sK4 @ sK4 ) ) )
| ~ spl13_2 ),
inference(superposition,[status(thm)],[f107,f119]) ).
thf(f119,plain,
( ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ sK6 ) )
| ~ spl13_2 ),
inference(avatar_component_clause,[status(thm)],[f117]) ).
thf(f117,definition,
( spl13_2
<=> ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition]) ).
thf(f107,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK6 ) )
| ( $true
= ( in @ X0 @ ( cartprod @ sK4 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f103]) ).
thf(f103,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( in @ X0 @ ( cartprod @ sK4 @ sK4 ) ) )
| ( $true
!= ( in @ X0 @ sK6 ) ) ),
inference(superposition,[status(thm)],[f98,f97]) ).
thf(f97,plain,
( $true
= ( subset @ sK6 @ ( cartprod @ sK4 @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK4
@ sK6 )
= $true ),
inference(definition_unfolding,[status(thm)],[f57,f68]) ).
thf(f57,plain,
( $true
= ( breln1 @ sK4 @ sK6 ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f120,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[status(thm)],[f111,f117,f113]) ).
thf(f111,plain,
( ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ sK6 ) )
| ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( $true != $true )
| ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ sK6 ) )
| ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ sK5 ) ) ),
inference(superposition,[status(thm)],[f92,f101]) ).
thf(f101,plain,
( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ ( binunion @ sK5 @ sK6 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $true
= ( in @ ( sK10 @ ( binunion @ sK5 @ sK6 ) @ ( cartprod @ sK4 @ sK4 ) ) @ ( binunion @ sK5 @ sK6 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f95,f99]) ).
thf(f99,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( $true
= ( in @ ( sK10 @ X1 @ X0 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK10 @ X1 @ X0 ) @ X1 ) )
| ( $true
= ( subset @ X1 @ X0 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f67,f59]) ).
thf(f67,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( $true
= ( in @ ( sK10 @ X1 @ X0 ) @ X1 ) )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f92,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ X1 ) ) ),
inference(condensation,[status(thm)],[f91]) ).
thf(f91,plain,
! [X6: $i,X7: $i,X4: $i,X5: $o] :
( ( $true
= ( in @ X7 @ X6 ) )
| ( $true = X5 )
| ( ( in @ X7 @ X4 )
= $true )
| ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X6: $i,X7: $i,X4: $i,X5: $o] :
( ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
!= $true )
| ( $true != $true )
| ( $true = X5 )
| ( $true
= ( in @ X7 @ X6 ) )
| ( ( in @ X7 @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f47,f54]) ).
thf(f54,plain,
binunionEcases = $true,
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f47,plain,
! [X6: $i,X7: $i,X4: $i,X5: $o] :
( ( ( in @ X7 @ X4 )
= $true )
| ( $true = X5 )
| ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
!= $true )
| ( $true
= ( in @ X7 @ X6 ) )
| ( binunionEcases != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( binunionEcases = $true )
| ( ( ( $true
!= ( in @ sK3 @ sK0 ) )
| ( $true = sK1 ) )
& ( $true != sK1 )
& ( $true
= ( in @ sK3 @ ( binunion @ sK0 @ sK2 ) ) )
& ( ( $true
!= ( in @ sK3 @ sK2 ) )
| ( $true = sK1 ) ) ) )
& ( ! [X4: $i,X5: $o,X6: $i,X7: $i] :
( ( ( ( in @ X7 @ X4 )
= $true )
& ( $true != X5 ) )
| ( $true = X5 )
| ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
!= $true )
| ( ( $true
= ( in @ X7 @ X6 ) )
& ( $true != X5 ) ) )
| ( binunionEcases != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f29,f30]) ).
thf(f30,plain,
( ? [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true = X1 ) )
& ( $true != X1 )
& ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
& ( ( $true
!= ( in @ X3 @ X2 ) )
| ( $true = X1 ) ) )
=> ( ( ( $true
!= ( in @ sK3 @ sK0 ) )
| ( $true = sK1 ) )
& ( $true != sK1 )
& ( $true
= ( in @ sK3 @ ( binunion @ sK0 @ sK2 ) ) )
& ( ( $true
!= ( in @ sK3 @ sK2 ) )
| ( $true = sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ( ( binunionEcases = $true )
| ? [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true = X1 ) )
& ( $true != X1 )
& ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
& ( ( $true
!= ( in @ X3 @ X2 ) )
| ( $true = X1 ) ) ) )
& ( ! [X4: $i,X5: $o,X6: $i,X7: $i] :
( ( ( ( in @ X7 @ X4 )
= $true )
& ( $true != X5 ) )
| ( $true = X5 )
| ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
!= $true )
| ( ( $true
= ( in @ X7 @ X6 ) )
& ( $true != X5 ) ) )
| ( binunionEcases != $true ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( binunionEcases = $true )
| ? [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true = X1 ) )
& ( $true != X1 )
& ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
& ( ( $true
!= ( in @ X3 @ X2 ) )
| ( $true = X1 ) ) ) )
& ( ! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( $true
= ( in @ X3 @ X0 ) )
& ( $true != X1 ) )
| ( $true = X1 )
| ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( ( $true
= ( in @ X3 @ X2 ) )
& ( $true != X1 ) ) )
| ( binunionEcases != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( binunionEcases = $true )
<=> ! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( $true
= ( in @ X3 @ X0 ) )
& ( $true != X1 ) )
| ( $true = X1 )
| ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( ( $true
= ( in @ X3 @ X2 ) )
& ( $true != X1 ) ) ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( $true = X1 )
| ( ( $true
= ( in @ X3 @ X2 ) )
& ( $true != X1 ) )
| ( ( $true
= ( in @ X3 @ X0 ) )
& ( $true != X1 ) )
| ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) ) )
<=> ( binunionEcases = $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
=> ( ( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true = X1 ) )
=> ( ( ( $true
= ( in @ X3 @ X2 ) )
=> ( $true = X1 ) )
=> ( $true = X1 ) ) ) )
<=> ( binunionEcases = $true ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
=> ( ( ( in @ X3 @ X0 )
=> X1 )
=> ( ( ( in @ X3 @ X2 )
=> X1 )
=> X1 ) ) )
= binunionEcases ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X3: $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) )
= binunionEcases ),
file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',binunionEcases) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU782^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n025.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:33:57 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEU782^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : Binary Relations on a Set
% 0.19/0.45 % Version : Especial > Reduced > Especial.
% 0.19/0.45 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S ->
% 0.19/0.45 % breln1 A (binunion R S)))
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.45 % Source : [Bro08]
% 0.19/0.45 % Names : ZFC284l [Bro08]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.20 v5.1.0, 0.40 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.19/0.45 % Syntax : Number of formulae : 15 ( 5 unt; 9 typ; 5 def)
% 0.19/0.45 % Number of atoms : 27 ( 5 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 6 ( 4 avg)
% 0.19/0.45 % Number of connectives : 49 ( 0 ~; 0 |; 0 &; 35 @)
% 0.19/0.45 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 12 ( 3 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 10 ( 9 usr; 3 con; 0-3 aty)
% 0.19/0.45 % Number of variables : 18 ( 5 ^; 13 !; 0 ?; 18 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : http://mathgate.info/detsetitem.php?id=347
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(in_type,type,
% 0.19/0.45 in: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(subset_type,type,
% 0.19/0.45 subset: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(subsetI1_type,type,
% 0.19/0.45 subsetI1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(subsetI1,definition,
% 0.19/0.45 ( subsetI1
% 0.19/0.45 = ( ! [A: $i,B: $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ Xx @ B ) )
% 0.19/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(subsetE_type,type,
% 0.19/0.45 subsetE: $o ).
% 0.19/0.45
% 0.19/0.45 thf(subsetE,definition,
% 0.19/0.45 ( subsetE
% 0.19/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.45 ( ( subset @ A @ B )
% 0.19/0.45 => ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(binunion_type,type,
% 0.19/0.45 binunion: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(binunionEcases_type,type,
% 0.19/0.45 binunionEcases: $o ).
% 0.19/0.45
% 0.19/0.45 thf(binunionEcases,definition,
% 0.19/0.45 ( binunionEcases
% 0.19/0.45 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.19/0.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.45 => ( ( ( in @ Xx @ A )
% 0.19/0.45 => Xphi )
% 0.19/0.45 => ( ( ( in @ Xx @ B )
% 0.19/0.45 => Xphi )
% 0.19/0.45 => Xphi ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(cartprod_type,type,
% 0.19/0.45 cartprod: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(breln_type,type,
% 0.19/0.45 breln: $i > $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(breln,definition,
% 0.19/0.45 ( breln
% 0.19/0.45 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(breln1_type,type,
% 0.19/0.45 breln1: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(breln1,definition,
% 0.19/0.45 ( breln1
% 0.19/0.45 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(breln1unionprop,conjecture,
% 0.19/0.45 ( subsetI1
% 0.19/0.45 => ( subsetE
% 0.19/0.45 => ( binunionEcases
% 0.19/0.45 => ! [A: $i,R: $i] :
% 0.19/0.45 ( ( breln1 @ A @ R )
% 0.19/0.45 => ! [S: $i] :
% 0.19/0.45 ( ( breln1 @ A @ S )
% 0.19/0.45 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.54/1.28 ---- Embedded in THF ---
% 1.54/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.28 %%% Generated on Tue Feb 24 12:33:58 EST 2026
% 1.54/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.28 %%% Logic specification used:
% 1.54/1.28 %%% thf(spec, logic, $$dhol).
% 1.54/1.28
% 1.54/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2DTF1415.p
% See solution above
% 1.54/1.28 ------------------------
% 1.54/1.29 ---- Cleaned THF ---
% 1.54/1.29 thf(in_type,type,
% 1.54/1.29 in: $i > $i > $o ).
% 1.54/1.29
% 1.54/1.29 thf(subset_type,type,
% 1.54/1.29 subset: $i > $i > $o ).
% 1.54/1.29
% 1.54/1.29 thf(subsetI1_type,type,
% 1.54/1.29 subsetI1: $o ).
% 1.54/1.29
% 1.54/1.29 thf(subsetI1,definition,
% 1.54/1.29 ( subsetI1
% 1.54/1.29 = ( ! [A: $i,B: $i] :
% 1.54/1.29 ( ! [Xx: $i] :
% 1.54/1.29 ( ( in @ Xx @ A )
% 1.54/1.29 => ( in @ Xx @ B ) )
% 1.54/1.29 => ( subset @ A @ B ) ) ) ) ).
% 1.54/1.29
% 1.54/1.29 thf(subsetE_type,type,
% 1.54/1.29 subsetE: $o ).
% 1.54/1.29
% 1.54/1.29 thf(subsetE,definition,
% 1.54/1.29 ( subsetE
% 1.54/1.29 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.54/1.29 ( ( subset @ A @ B )
% 1.54/1.29 => ( ( in @ Xx @ A )
% 1.54/1.29 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.54/1.29
% 1.54/1.29 thf(binunion_type,type,
% 1.54/1.29 binunion: $i > $i > $i ).
% 1.54/1.29
% 1.54/1.29 thf(binunionEcases_type,type,
% 1.54/1.29 binunionEcases: $o ).
% 1.54/1.29
% 1.54/1.29 thf(binunionEcases,definition,
% 1.54/1.29 ( binunionEcases
% 1.54/1.29 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 1.54/1.29 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 1.54/1.29 => ( ( ( in @ Xx @ A )
% 1.54/1.29 => Xphi )
% 1.54/1.29 => ( ( ( in @ Xx @ B )
% 1.54/1.29 => Xphi )
% 1.54/1.29 => Xphi ) ) ) ) ) ).
% 1.54/1.29
% 1.54/1.29 thf(cartprod_type,type,
% 1.54/1.29 cartprod: $i > $i > $i ).
% 1.54/1.29
% 1.54/1.29 thf(breln_type,type,
% 1.54/1.29 breln: $i > $i > $i > $o ).
% 1.54/1.29
% 1.54/1.29 thf(breln,definition,
% 1.54/1.29 ( breln
% 1.54/1.29 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.54/1.29
% 1.54/1.29 thf(breln1_type,type,
% 1.54/1.29 breln1: $i > $i > $o ).
% 1.54/1.29
% 1.54/1.29 thf(breln1,definition,
% 1.54/1.29 ( breln1
% 1.54/1.29 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 1.54/1.29
% 1.54/1.29 thf(breln1unionprop,conjecture,
% 1.54/1.29 ( subsetI1
% 1.54/1.29 => ( subsetE
% 1.54/1.29 => ( binunionEcases
% 1.54/1.29 => ! [A: $i,R: $i] :
% 1.54/1.29 ( ( breln1 @ A @ R )
% 1.54/1.29 => ! [S: $i] :
% 1.54/1.29 ( ( breln1 @ A @ S )
% 1.54/1.29 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ) ).
% 1.54/1.29 ------------------------
% 1.71/1.31 % (1607)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_1415 for (2999ds/27Mi)
% 1.71/1.31 % (1609)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_1415 for (2999ds/2Mi)
% 1.71/1.31 % (1609)Instruction limit reached!
% 1.71/1.31 % (1609)------------------------------
% 1.71/1.31 % (1609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.31 % (1609)Termination reason: Unknown
% 1.71/1.31 % (1609)Termination phase: Property scanning
% 1.71/1.31
% 1.71/1.31 % (1609)Memory used [KB]: 1023
% 1.71/1.31 % (1609)Time elapsed: 0.002 s
% 1.71/1.31 % (1609)Instructions burned: 2 (million)
% 1.71/1.31 % (1609)------------------------------
% 1.71/1.31 % (1609)------------------------------
% 1.71/1.31 % (1605)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1415 for (2999ds/183Mi)
% 1.71/1.31 % (1606)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_1415 for (2999ds/4Mi)
% 1.71/1.31 % (1606)Instruction limit reached!
% 1.71/1.31 % (1606)------------------------------
% 1.71/1.31 % (1606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.31 % (1606)Termination reason: Unknown
% 1.71/1.31 % (1606)Termination phase: Saturation
% 1.71/1.31
% 1.71/1.31 % (1606)Memory used [KB]: 5500
% 1.71/1.31 % (1606)Time elapsed: 0.003 s
% 1.71/1.31 % (1606)Instructions burned: 4 (million)
% 1.71/1.31 % (1606)------------------------------
% 1.71/1.31 % (1606)------------------------------
% 1.71/1.31 % (1608)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1415 for (2999ds/2Mi)
% 1.71/1.31 % (1611)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1415 for (2999ds/18Mi)
% 1.71/1.32 % (1608)Instruction limit reached!
% 1.71/1.32 % (1608)------------------------------
% 1.71/1.32 % (1608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.32 % (1608)Termination reason: Unknown
% 1.71/1.32 % (1608)Termination phase: Property scanning
% 1.71/1.32
% 1.71/1.32 % (1608)Memory used [KB]: 1023
% 1.71/1.32 % (1608)Time elapsed: 0.003 s
% 1.71/1.32 % (1608)Instructions burned: 2 (million)
% 1.71/1.32 % (1608)------------------------------
% 1.71/1.32 % (1608)------------------------------
% 1.71/1.32 % (1610)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_1415 for (2999ds/275Mi)
% 1.71/1.32 % (1607)Instruction limit reached!
% 1.71/1.32 % (1607)------------------------------
% 1.71/1.32 % (1607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.32 % (1607)Termination reason: Unknown
% 1.71/1.32 % (1607)Termination phase: Saturation
% 1.71/1.32
% 1.71/1.32 % (1607)Memory used [KB]: 5628
% 1.71/1.32 % (1607)Time elapsed: 0.011 s
% 1.71/1.32 % (1607)Instructions burned: 28 (million)
% 1.71/1.32 % (1607)------------------------------
% 1.71/1.32 % (1607)------------------------------
% 1.71/1.32 % (1612)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1415 for (2999ds/3Mi)
% 1.71/1.32 % (1612)Instruction limit reached!
% 1.71/1.32 % (1612)------------------------------
% 1.71/1.32 % (1612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.32 % (1612)Termination reason: Unknown
% 1.71/1.32 % (1612)Termination phase: Saturation
% 1.71/1.32
% 1.71/1.32 % (1612)Memory used [KB]: 1023
% 1.71/1.32 % (1612)Time elapsed: 0.002 s
% 1.71/1.32 % (1612)Instructions burned: 4 (million)
% 1.71/1.32 % (1612)------------------------------
% 1.71/1.32 % (1612)------------------------------
% 1.71/1.32 % (1613)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_1415 for (2999ds/37Mi)
% 1.71/1.32 % (1611)First to succeed.
% 1.71/1.33 % (1615)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_1415 for (2999ds/3Mi)
% 1.71/1.33 % (1615)Instruction limit reached!
% 1.71/1.33 % (1615)------------------------------
% 1.71/1.33 % (1615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (1615)Termination reason: Unknown
% 1.71/1.33 % (1615)Termination phase: Saturation
% 1.71/1.33
% 1.71/1.33 % (1615)Memory used [KB]: 5500
% 1.71/1.33 % (1615)Time elapsed: 0.002 s
% 1.71/1.33 % (1615)Instructions burned: 4 (million)
% 1.71/1.33 % (1615)------------------------------
% 1.71/1.33 % (1615)------------------------------
% 1.71/1.33 % (1616)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_1415 for (2999ds/1041Mi)
% 1.71/1.33 % (1611)Refutation found. Thanks to Tanya!
% 1.71/1.33 % SZS status Theorem for DTF2THF_1415
% 1.71/1.33 % SZS output start Proof for DTF2THF_1415
% 1.71/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.71/1.33 thf(func_def_1, type, subset: $i > $i > $o).
% 1.71/1.33 thf(func_def_5, type, binunion: $i > $i > $i).
% 1.71/1.33 thf(func_def_7, type, cartprod: $i > $i > $i).
% 1.71/1.33 thf(func_def_8, type, breln: $i > $i > $i > $o).
% 1.71/1.33 thf(func_def_9, type, breln1: $i > $i > $o).
% 1.71/1.33 thf(func_def_26, type, sK10: $i > $i > $i).
% 1.71/1.33 thf(f141,plain,(
% 1.71/1.33 $false),
% 1.71/1.33 inference(avatar_sat_refutation,[status(thm)],[f120,f130,f140])).
% 1.71/1.33 thf(f140,plain,(
% 1.71/1.33 ~spl13_1),
% 1.71/1.33 inference(avatar_contradiction_clause,[status(thm)],[f139])).
% 1.71/1.33 thf(f139,plain,(
% 1.71/1.33 $false | ~spl13_1),
% 1.71/1.33 inference(subsumption_resolution,[status(thm)],[f138,f95])).
% 1.71/1.33 thf(f95,plain,(
% 1.71/1.33 ($true != (subset @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)))),
% 1.71/1.33 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.71/1.33 thf(f78,plain,(
% 1.71/1.33 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK4 @ (binunion @ sK5 @ sK6)))),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f56,f68])).
% 1.71/1.33 thf(f68,plain,(
% 1.71/1.33 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f53,f52])).
% 1.71/1.33 thf(f52,plain,(
% 1.71/1.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f10])).
% 1.71/1.33 thf(f10,plain,(
% 1.71/1.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f9])).
% 1.71/1.33 thf(f9,plain,(
% 1.71/1.33 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 1.71/1.33 inference(rectify,[status(thm)],[f4])).
% 1.71/1.33 thf(f4,axiom,(
% 1.71/1.33 ((^[X0 : $i, X1 : $i, X4 : $i] : (subset @ X4 @ (cartprod @ X0 @ X1))) = breln)),
% 1.71/1.33 file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',breln)).
% 1.71/1.33 thf(f53,plain,(
% 1.71/1.33 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f20])).
% 1.71/1.33 thf(f20,plain,(
% 1.71/1.33 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f19])).
% 1.71/1.33 thf(f19,plain,(
% 1.71/1.33 (breln1 = (^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)))),
% 1.71/1.33 inference(rectify,[status(thm)],[f5])).
% 1.71/1.33 thf(f5,axiom,(
% 1.71/1.33 (breln1 = (^[X0 : $i, X5 : $i] : (breln @ X0 @ X0 @ X5)))),
% 1.71/1.33 file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',breln1)).
% 1.71/1.33 thf(f56,plain,(
% 1.71/1.33 ($true != (breln1 @ sK4 @ (binunion @ sK5 @ sK6)))),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f34])).
% 1.71/1.33 thf(f34,plain,(
% 1.71/1.33 (subsetI1 = $true) & (subsetE = $true) & ((($true = (breln1 @ sK4 @ sK6)) & ($true != (breln1 @ sK4 @ (binunion @ sK5 @ sK6)))) & ($true = (breln1 @ sK4 @ sK5))) & (binunionEcases = $true)),
% 1.71/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f25,f33,f32])).
% 1.71/1.33 thf(f32,plain,(
% 1.71/1.33 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ($true != (breln1 @ X0 @ (binunion @ X1 @ X2)))) & ($true = (breln1 @ X0 @ X1))) => (? [X2 : $i] : (($true = (breln1 @ sK4 @ X2)) & ($true != (breln1 @ sK4 @ (binunion @ sK5 @ X2)))) & ($true = (breln1 @ sK4 @ sK5)))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f33,plain,(
% 1.71/1.33 ? [X2 : $i] : (($true = (breln1 @ sK4 @ X2)) & ($true != (breln1 @ sK4 @ (binunion @ sK5 @ X2)))) => (($true = (breln1 @ sK4 @ sK6)) & ($true != (breln1 @ sK4 @ (binunion @ sK5 @ sK6))))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f25,plain,(
% 1.71/1.33 (subsetI1 = $true) & (subsetE = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ($true != (breln1 @ X0 @ (binunion @ X1 @ X2)))) & ($true = (breln1 @ X0 @ X1))) & (binunionEcases = $true)),
% 1.71/1.33 inference(flattening,[status(thm)],[f24])).
% 1.71/1.33 thf(f24,plain,(
% 1.71/1.33 ((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ($true != (breln1 @ X0 @ (binunion @ X1 @ X2)))) & ($true = (breln1 @ X0 @ X1))) & (binunionEcases = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 1.71/1.33 inference(ennf_transformation,[status(thm)],[f16])).
% 1.71/1.33 thf(f16,plain,(
% 1.71/1.33 ~((subsetI1 = $true) => ((subsetE = $true) => ((binunionEcases = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (($true = (breln1 @ X0 @ X2)) => ($true = (breln1 @ X0 @ (binunion @ X1 @ X2))))))))),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f15])).
% 1.71/1.33 thf(f15,plain,(
% 1.71/1.33 ~(subsetI1 => (subsetE => (binunionEcases => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (breln1 @ X0 @ (binunion @ X1 @ X2)))))))),
% 1.71/1.33 inference(rectify,[status(thm)],[f7])).
% 1.71/1.33 thf(f7,negated_conjecture,(
% 1.71/1.33 ~(subsetI1 => (subsetE => (binunionEcases => ! [X0 : $i,X5 : $i] : ((breln1 @ X0 @ X5) => ! [X6 : $i] : ((breln1 @ X0 @ X6) => (breln1 @ X0 @ (binunion @ X5 @ X6)))))))),
% 1.71/1.33 inference(negated_conjecture,[status(cth)],[f6])).
% 1.71/1.33 thf(f6,conjecture,(
% 1.71/1.33 subsetI1 => (subsetE => (binunionEcases => ! [X0 : $i,X5 : $i] : ((breln1 @ X0 @ X5) => ! [X6 : $i] : ((breln1 @ X0 @ X6) => (breln1 @ X0 @ (binunion @ X5 @ X6))))))),
% 1.71/1.33 file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',breln1unionprop)).
% 1.71/1.33 thf(f138,plain,(
% 1.71/1.33 ($true = (subset @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4))) | ~spl13_1),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.71/1.33 thf(f135,plain,(
% 1.71/1.33 ($true = (subset @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4))) | ($true != $true) | ~spl13_1),
% 1.71/1.33 inference(superposition,[status(thm)],[f96,f134])).
% 1.71/1.33 thf(f134,plain,(
% 1.71/1.33 ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ (cartprod @ sK4 @ sK4))) | ~spl13_1),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.71/1.33 thf(f131,plain,(
% 1.71/1.33 ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ (cartprod @ sK4 @ sK4))) | ($true != $true) | ~spl13_1),
% 1.71/1.33 inference(superposition,[status(thm)],[f106,f115])).
% 1.71/1.33 thf(f115,plain,(
% 1.71/1.33 ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ sK5)) | ~spl13_1),
% 1.71/1.33 inference(avatar_component_clause,[status(thm)],[f113])).
% 1.71/1.33 thf(f113,definition,(
% 1.71/1.33 spl13_1 <=> ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ sK5))),
% 1.71/1.33 introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition])).
% 1.71/1.33 thf(f106,plain,(
% 1.71/1.33 ( ! [X0 : $i] : (($true != (in @ X0 @ sK5)) | ($true = (in @ X0 @ (cartprod @ sK4 @ sK4)))) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.71/1.33 thf(f102,plain,(
% 1.71/1.33 ( ! [X0 : $i] : (($true != $true) | ($true = (in @ X0 @ (cartprod @ sK4 @ sK4))) | ($true != (in @ X0 @ sK5))) )),
% 1.71/1.33 inference(superposition,[status(thm)],[f98,f94])).
% 1.71/1.33 thf(f94,plain,(
% 1.71/1.33 ($true = (subset @ sK5 @ (cartprod @ sK4 @ sK4)))),
% 1.71/1.33 inference(beta_eta_normalization,[status(thm)],[f79])).
% 1.71/1.33 thf(f79,plain,(
% 1.71/1.33 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK4 @ sK5))),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f55,f68])).
% 1.71/1.33 thf(f55,plain,(
% 1.71/1.33 ($true = (breln1 @ sK4 @ sK5))),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f34])).
% 1.71/1.33 thf(f98,plain,(
% 1.71/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (subset @ X3 @ X4)) | ($true = (in @ X5 @ X4)) | ($true != (in @ X5 @ X3))) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.71/1.33 thf(f83,plain,(
% 1.71/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ X4)) | ($true != (in @ X5 @ X3)) | ($true != (subset @ X3 @ X4)) | ($true != $true)) )),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f60,f58])).
% 1.71/1.33 thf(f58,plain,(
% 1.71/1.33 (subsetE = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f34])).
% 1.71/1.33 thf(f60,plain,(
% 1.71/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (subset @ X3 @ X4)) | ($true != (in @ X5 @ X3)) | ($true = (in @ X5 @ X4)) | (subsetE != $true)) )),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f38])).
% 1.71/1.33 thf(f38,plain,(
% 1.71/1.33 ((subsetE = $true) | (($true = (subset @ sK7 @ sK8)) & ($true = (in @ sK9 @ sK7)) & ($true != (in @ sK9 @ sK8)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (subset @ X3 @ X4)) | ($true != (in @ X5 @ X3)) | ($true = (in @ X5 @ X4))) | (subsetE != $true))),
% 1.71/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f36,f37])).
% 1.71/1.33 thf(f37,plain,(
% 1.71/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X1) = $true) & ((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) => (($true = (subset @ sK7 @ sK8)) & ($true = (in @ sK9 @ sK7)) & ($true != (in @ sK9 @ sK8)))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f36,plain,(
% 1.71/1.33 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X1) = $true) & ((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (subset @ X3 @ X4)) | ($true != (in @ X5 @ X3)) | ($true = (in @ X5 @ X4))) | (subsetE != $true))),
% 1.71/1.33 inference(rectify,[status(thm)],[f35])).
% 1.71/1.33 thf(f35,plain,(
% 1.71/1.33 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X1) = $true) & ((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X1) != $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)) | (subsetE != $true))),
% 1.71/1.33 inference(nnf_transformation,[status(thm)],[f22])).
% 1.71/1.33 thf(f22,plain,(
% 1.71/1.33 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X1) != $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true))),
% 1.71/1.33 inference(flattening,[status(thm)],[f21])).
% 1.71/1.33 thf(f21,plain,(
% 1.71/1.33 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) | ((subset @ X0 @ X1) != $true))),
% 1.71/1.33 inference(ennf_transformation,[status(thm)],[f12])).
% 1.71/1.33 thf(f12,plain,(
% 1.71/1.33 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X1) = $true) => (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)))),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f11])).
% 1.71/1.33 thf(f11,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.71/1.33 inference(rectify,[status(thm)],[f2])).
% 1.71/1.33 thf(f2,axiom,(
% 1.71/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.71/1.33 file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',subsetE)).
% 1.71/1.33 thf(f96,plain,(
% 1.71/1.33 ( ! [X0 : $i,X1 : $i] : (((in @ (sK10 @ X1 @ X0) @ X0) != $true) | ($true = (subset @ X1 @ X0))) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.71/1.33 thf(f85,plain,(
% 1.71/1.33 ( ! [X0 : $i,X1 : $i] : (((in @ (sK10 @ X1 @ X0) @ X0) != $true) | ($true != $true) | ($true = (subset @ X1 @ X0))) )),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f66,f59])).
% 1.71/1.33 thf(f59,plain,(
% 1.71/1.33 (subsetI1 = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f34])).
% 1.71/1.33 thf(f66,plain,(
% 1.71/1.33 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ((in @ (sK10 @ X1 @ X0) @ X0) != $true) | (subsetI1 != $true)) )),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f43])).
% 1.71/1.33 thf(f43,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | (($true = (in @ (sK10 @ X1 @ X0) @ X1)) & ((in @ (sK10 @ X1 @ X0) @ X0) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | (($true != (subset @ sK12 @ sK11)) & ! [X5 : $i] : (($true != (in @ X5 @ sK12)) | ($true = (in @ X5 @ sK11)))))),
% 1.71/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f40,f42,f41])).
% 1.71/1.33 thf(f41,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) => (($true = (in @ (sK10 @ X1 @ X0) @ X1)) & ((in @ (sK10 @ X1 @ X0) @ X0) != $true)))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f42,plain,(
% 1.71/1.33 ? [X3 : $i,X4 : $i] : (($true != (subset @ X4 @ X3)) & ! [X5 : $i] : (($true != (in @ X5 @ X4)) | ($true = (in @ X5 @ X3)))) => (($true != (subset @ sK12 @ sK11)) & ! [X5 : $i] : (($true != (in @ X5 @ sK12)) | ($true = (in @ X5 @ sK11))))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f40,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (($true != (subset @ X4 @ X3)) & ! [X5 : $i] : (($true != (in @ X5 @ X4)) | ($true = (in @ X5 @ X3)))))),
% 1.71/1.33 inference(rectify,[status(thm)],[f39])).
% 1.71/1.33 thf(f39,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))))),
% 1.71/1.33 inference(nnf_transformation,[status(thm)],[f23])).
% 1.71/1.33 thf(f23,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) <=> (subsetI1 = $true)),
% 1.71/1.33 inference(ennf_transformation,[status(thm)],[f14])).
% 1.71/1.33 thf(f14,plain,(
% 1.71/1.33 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ($true = (subset @ X1 @ X0)))),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f13])).
% 1.71/1.33 thf(f13,plain,(
% 1.71/1.33 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 1.71/1.33 inference(rectify,[status(thm)],[f1])).
% 1.71/1.33 thf(f1,axiom,(
% 1.71/1.33 (subsetI1 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.71/1.33 file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',subsetI1)).
% 1.71/1.33 thf(f130,plain,(
% 1.71/1.33 ~spl13_2),
% 1.71/1.33 inference(avatar_contradiction_clause,[status(thm)],[f129])).
% 1.71/1.33 thf(f129,plain,(
% 1.71/1.33 $false | ~spl13_2),
% 1.71/1.33 inference(subsumption_resolution,[status(thm)],[f127,f95])).
% 1.71/1.33 thf(f127,plain,(
% 1.71/1.33 ($true = (subset @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4))) | ~spl13_2),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.71/1.33 thf(f125,plain,(
% 1.71/1.33 ($true != $true) | ($true = (subset @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4))) | ~spl13_2),
% 1.71/1.33 inference(superposition,[status(thm)],[f96,f123])).
% 1.71/1.33 thf(f123,plain,(
% 1.71/1.33 ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ (cartprod @ sK4 @ sK4))) | ~spl13_2),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.71/1.33 thf(f121,plain,(
% 1.71/1.33 ($true != $true) | ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ (cartprod @ sK4 @ sK4))) | ~spl13_2),
% 1.71/1.33 inference(superposition,[status(thm)],[f107,f119])).
% 1.71/1.33 thf(f119,plain,(
% 1.71/1.33 ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ sK6)) | ~spl13_2),
% 1.71/1.33 inference(avatar_component_clause,[status(thm)],[f117])).
% 1.71/1.33 thf(f117,definition,(
% 1.71/1.33 spl13_2 <=> ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ sK6))),
% 1.71/1.33 introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition])).
% 1.71/1.33 thf(f107,plain,(
% 1.71/1.33 ( ! [X0 : $i] : (($true != (in @ X0 @ sK6)) | ($true = (in @ X0 @ (cartprod @ sK4 @ sK4)))) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f103])).
% 1.71/1.33 thf(f103,plain,(
% 1.71/1.33 ( ! [X0 : $i] : (($true != $true) | ($true = (in @ X0 @ (cartprod @ sK4 @ sK4))) | ($true != (in @ X0 @ sK6))) )),
% 1.71/1.33 inference(superposition,[status(thm)],[f98,f97])).
% 1.71/1.33 thf(f97,plain,(
% 1.71/1.33 ($true = (subset @ sK6 @ (cartprod @ sK4 @ sK4)))),
% 1.71/1.33 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.71/1.33 thf(f77,plain,(
% 1.71/1.33 (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK4 @ sK6) = $true)),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f57,f68])).
% 1.71/1.33 thf(f57,plain,(
% 1.71/1.33 ($true = (breln1 @ sK4 @ sK6))),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f34])).
% 1.71/1.33 thf(f120,plain,(
% 1.71/1.33 spl13_1 | spl13_2),
% 1.71/1.33 inference(avatar_split_clause,[status(thm)],[f111,f117,f113])).
% 1.71/1.33 thf(f111,plain,(
% 1.71/1.33 ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ sK6)) | ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ sK5))),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.71/1.33 thf(f108,plain,(
% 1.71/1.33 ($true != $true) | ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ sK6)) | ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ sK5))),
% 1.71/1.33 inference(superposition,[status(thm)],[f92,f101])).
% 1.71/1.33 thf(f101,plain,(
% 1.71/1.33 ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ (binunion @ sK5 @ sK6)))),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.71/1.33 thf(f100,plain,(
% 1.71/1.33 ($true = (in @ (sK10 @ (binunion @ sK5 @ sK6) @ (cartprod @ sK4 @ sK4)) @ (binunion @ sK5 @ sK6))) | ($true != $true)),
% 1.71/1.33 inference(superposition,[status(thm)],[f95,f99])).
% 1.71/1.33 thf(f99,plain,(
% 1.71/1.33 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ($true = (in @ (sK10 @ X1 @ X0) @ X1))) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.71/1.33 thf(f84,plain,(
% 1.71/1.33 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK10 @ X1 @ X0) @ X1)) | ($true = (subset @ X1 @ X0)) | ($true != $true)) )),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f67,f59])).
% 1.71/1.33 thf(f67,plain,(
% 1.71/1.33 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ($true = (in @ (sK10 @ X1 @ X0) @ X1)) | (subsetI1 != $true)) )),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f43])).
% 1.71/1.33 thf(f92,plain,(
% 1.71/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (binunion @ X2 @ X1))) | ($true = (in @ X0 @ X2)) | ($true = (in @ X0 @ X1))) )),
% 1.71/1.33 inference(condensation,[status(thm)],[f91])).
% 1.71/1.33 thf(f91,plain,(
% 1.71/1.33 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $o] : (($true = (in @ X7 @ X6)) | ($true = X5) | ((in @ X7 @ X4) = $true) | ((in @ X7 @ (binunion @ X4 @ X6)) != $true)) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.71/1.33 thf(f73,plain,(
% 1.71/1.33 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $o] : (((in @ X7 @ (binunion @ X4 @ X6)) != $true) | ($true != $true) | ($true = X5) | ($true = (in @ X7 @ X6)) | ((in @ X7 @ X4) = $true)) )),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f47,f54])).
% 1.71/1.33 thf(f54,plain,(
% 1.71/1.33 (binunionEcases = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f34])).
% 1.71/1.33 thf(f47,plain,(
% 1.71/1.33 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $o] : (((in @ X7 @ X4) = $true) | ($true = X5) | ((in @ X7 @ (binunion @ X4 @ X6)) != $true) | ($true = (in @ X7 @ X6)) | (binunionEcases != $true)) )),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f31])).
% 1.71/1.33 thf(f31,plain,(
% 1.71/1.33 ((binunionEcases = $true) | ((($true != (in @ sK3 @ sK0)) | ($true = sK1)) & ($true != sK1) & ($true = (in @ sK3 @ (binunion @ sK0 @ sK2))) & (($true != (in @ sK3 @ sK2)) | ($true = sK1)))) & (! [X4 : $i,X5 : $o,X6 : $i,X7 : $i] : ((((in @ X7 @ X4) = $true) & ($true != X5)) | ($true = X5) | ((in @ X7 @ (binunion @ X4 @ X6)) != $true) | (($true = (in @ X7 @ X6)) & ($true != X5))) | (binunionEcases != $true))),
% 1.71/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f29,f30])).
% 1.71/1.33 thf(f30,plain,(
% 1.71/1.33 ? [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((($true != (in @ X3 @ X0)) | ($true = X1)) & ($true != X1) & ($true = (in @ X3 @ (binunion @ X0 @ X2))) & (($true != (in @ X3 @ X2)) | ($true = X1))) => ((($true != (in @ sK3 @ sK0)) | ($true = sK1)) & ($true != sK1) & ($true = (in @ sK3 @ (binunion @ sK0 @ sK2))) & (($true != (in @ sK3 @ sK2)) | ($true = sK1)))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f29,plain,(
% 1.71/1.33 ((binunionEcases = $true) | ? [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((($true != (in @ X3 @ X0)) | ($true = X1)) & ($true != X1) & ($true = (in @ X3 @ (binunion @ X0 @ X2))) & (($true != (in @ X3 @ X2)) | ($true = X1)))) & (! [X4 : $i,X5 : $o,X6 : $i,X7 : $i] : ((((in @ X7 @ X4) = $true) & ($true != X5)) | ($true = X5) | ((in @ X7 @ (binunion @ X4 @ X6)) != $true) | (($true = (in @ X7 @ X6)) & ($true != X5))) | (binunionEcases != $true))),
% 1.71/1.33 inference(rectify,[status(thm)],[f28])).
% 1.71/1.33 thf(f28,plain,(
% 1.71/1.33 ((binunionEcases = $true) | ? [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((($true != (in @ X3 @ X0)) | ($true = X1)) & ($true != X1) & ($true = (in @ X3 @ (binunion @ X0 @ X2))) & (($true != (in @ X3 @ X2)) | ($true = X1)))) & (! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((($true = (in @ X3 @ X0)) & ($true != X1)) | ($true = X1) | ($true != (in @ X3 @ (binunion @ X0 @ X2))) | (($true = (in @ X3 @ X2)) & ($true != X1))) | (binunionEcases != $true))),
% 1.71/1.33 inference(nnf_transformation,[status(thm)],[f27])).
% 1.71/1.33 thf(f27,plain,(
% 1.71/1.33 (binunionEcases = $true) <=> ! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((($true = (in @ X3 @ X0)) & ($true != X1)) | ($true = X1) | ($true != (in @ X3 @ (binunion @ X0 @ X2))) | (($true = (in @ X3 @ X2)) & ($true != X1)))),
% 1.71/1.33 inference(flattening,[status(thm)],[f26])).
% 1.71/1.33 thf(f26,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : (((($true = X1) | (($true = (in @ X3 @ X2)) & ($true != X1))) | (($true = (in @ X3 @ X0)) & ($true != X1))) | ($true != (in @ X3 @ (binunion @ X0 @ X2)))) <=> (binunionEcases = $true)),
% 1.71/1.33 inference(ennf_transformation,[status(thm)],[f18])).
% 1.71/1.33 thf(f18,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : (($true = (in @ X3 @ (binunion @ X0 @ X2))) => ((($true = (in @ X3 @ X0)) => ($true = X1)) => ((($true = (in @ X3 @ X2)) => ($true = X1)) => ($true = X1)))) <=> (binunionEcases = $true)),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f17])).
% 1.71/1.33 thf(f17,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((in @ X3 @ (binunion @ X0 @ X2)) => (((in @ X3 @ X0) => X1) => (((in @ X3 @ X2) => X1) => X1))) = binunionEcases)),
% 1.71/1.33 inference(rectify,[status(thm)],[f3])).
% 1.71/1.33 thf(f3,axiom,(
% 1.71/1.33 (! [X0 : $i,X3 : $o,X1 : $i,X2 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => (((in @ X2 @ X0) => X3) => (((in @ X2 @ X1) => X3) => X3))) = binunionEcases)),
% 1.71/1.33 file('/export/starexec/sandbox/tmp/tmp.GJtuJkm9AT/DTF2THF_1415.p',binunionEcases)).
% 1.71/1.33 % SZS output end Proof for DTF2THF_1415
% 1.71/1.33 % (1611)------------------------------
% 1.71/1.33 % (1611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (1611)Termination reason: Refutation
% 1.71/1.33
% 1.71/1.33 % (1611)Memory used [KB]: 5628
% 1.71/1.33 % (1611)Time elapsed: 0.015 s
% 1.71/1.33 % (1611)Instructions burned: 14 (million)
% 1.71/1.33 % (1611)------------------------------
% 1.71/1.33 % (1611)------------------------------
% 1.71/1.33 % (1604)Success in time 0.024 s
%------------------------------------------------------------------------------