%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU750^2 : 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 09:36:54 AM UTC 2026
% Result : Theorem 1.59s 1.35s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 1105 ( 302 equ; 0 cnn)
% Maximal formula atoms : 12 ( 15 avg)
% Number of connectives : 1231 ( 142 ~; 95 |; 100 &; 819 @)
% ( 11 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 19 con; 0-2 aty)
% Number of variables : 194 ( 0 ^; 136 !; 58 ?; 194 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(f93,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f92,f44]) ).
thf(f44,plain,
( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( binunionTIRcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $true )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) )
!= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
= $true )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f28,f27,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ X2 ) ) )
= $true ) ) )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ X2 ) ) )
= $true ) ) )
=> ( ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ sK2 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ sK2 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
= $true ) )
=> ( ( ( in @ sK3 @ sK0 )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) )
!= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( binunionTIRcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( binunionTIRcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binunionTIRcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( binunionTIRcontra = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( setminusI
=> ( setminusER
=> ( binunionTIRcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ( binunionTIRcontra
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( binunion @ X3 @ X4 ) ) )
=> ( in @ X2 @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( setminusI
=> ( setminusER
=> ( binunionTIRcontra
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( binunion @ X3 @ X4 ) ) )
=> ( in @ X2 @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RH4uQJR8Dg/DTF2THF_29555.p',demorgan2a2) ).
thf(f92,plain,
( ( in @ sK1 @ ( powerset @ sK0 ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f91,f47]) ).
thf(f47,plain,
( ( in @ sK3 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f91,plain,
( ( ( in @ sK3 @ sK0 )
!= $true )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( ( in @ sK3 @ sK0 )
!= $true )
| ( $true != $true )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f89,f48]) ).
thf(f48,plain,
( ( in @ sK2 @ ( powerset @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f89,plain,
! [X0: $i] :
( ( ( in @ sK2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK3 @ X0 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f88,f86]) ).
thf(f86,plain,
( ( in @ sK3 @ sK2 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f85,f47]) ).
thf(f85,plain,
( ( ( in @ sK3 @ sK0 )
!= $true )
| ( ( in @ sK3 @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
( ( ( in @ sK3 @ sK0 )
!= $true )
| ( $true != $true )
| ( ( in @ sK3 @ sK2 )
= $true ) ),
inference(superposition,[status(thm)],[f46,f80]) ).
thf(f80,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f64,f49]) ).
thf(f49,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f64,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( setminusI != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ( ( ( in @ sK11 @ sK13 )
= $true )
& ( ( in @ sK11 @ sK12 )
!= $true )
& ( ( in @ sK11 @ ( setminus @ sK13 @ sK12 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f41,f42]) ).
thf(f42,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
& ( ( in @ X3 @ X4 )
!= $true )
& ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
!= $true ) )
=> ( ( ( in @ sK11 @ sK13 )
= $true )
& ( ( in @ sK11 @ sK12 )
!= $true )
& ( ( in @ sK11 @ ( setminus @ sK13 @ sK12 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
& ( ( in @ X3 @ X4 )
!= $true )
& ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true ) )
<=> ( setminusI = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X0 )
=> ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setminusI
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RH4uQJR8Dg/DTF2THF_29555.p',setminusI) ).
thf(f46,plain,
( ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f88,plain,
! [X0: $i] :
( ( ( in @ sK3 @ X0 )
!= $true )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK3 @ sK2 )
!= $true )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK3 @ sK2 )
!= $true )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK3 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f82,f79]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f57,f51]) ).
thf(f51,plain,
binunionTIRcontra = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( binunionTIRcontra != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ( ( ( in @ sK7 @ ( binunion @ sK4 @ sK6 ) )
!= $true )
& ( ( in @ sK7 @ sK6 )
= $true )
& ( ( in @ sK7 @ sK5 )
= $true )
& ( ( in @ sK6 @ ( powerset @ sK5 ) )
= $true )
& ( ( in @ sK4 @ ( powerset @ sK5 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f31,f34,f33,f32]) ).
thf(f32,plain,
( ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) )
& ( ( in @ X7 @ X6 )
= $true )
& ( ( in @ X7 @ X5 )
= $true ) )
& ( ( in @ X6 @ ( powerset @ X5 ) )
= $true ) )
& ( ( in @ X4 @ ( powerset @ X5 ) )
= $true ) )
=> ( ? [X6: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ ( binunion @ sK4 @ X6 ) )
!= $true )
& ( ( in @ X7 @ X6 )
= $true )
& ( ( in @ X7 @ sK5 )
= $true ) )
& ( ( in @ X6 @ ( powerset @ sK5 ) )
= $true ) )
& ( ( in @ sK4 @ ( powerset @ sK5 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ? [X6: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ ( binunion @ sK4 @ X6 ) )
!= $true )
& ( ( in @ X7 @ X6 )
= $true )
& ( ( in @ X7 @ sK5 )
= $true ) )
& ( ( in @ X6 @ ( powerset @ sK5 ) )
= $true ) )
=> ( ? [X7: $i] :
( ( ( in @ X7 @ ( binunion @ sK4 @ sK6 ) )
!= $true )
& ( ( in @ X7 @ sK6 )
= $true )
& ( ( in @ X7 @ sK5 )
= $true ) )
& ( ( in @ sK6 @ ( powerset @ sK5 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X7: $i] :
( ( ( in @ X7 @ ( binunion @ sK4 @ sK6 ) )
!= $true )
& ( ( in @ X7 @ sK6 )
= $true )
& ( ( in @ X7 @ sK5 )
= $true ) )
=> ( ( ( in @ sK7 @ ( binunion @ sK4 @ sK6 ) )
!= $true )
& ( ( in @ sK7 @ sK6 )
= $true )
& ( ( in @ sK7 @ sK5 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) )
& ( ( in @ X7 @ X6 )
= $true )
& ( ( in @ X7 @ X5 )
= $true ) )
& ( ( in @ X6 @ ( powerset @ X5 ) )
= $true ) )
& ( ( in @ X4 @ ( powerset @ X5 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
<=> ( binunionTIRcontra = $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
<=> ( binunionTIRcontra = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) )
<=> ( binunionTIRcontra = $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( binunionTIRcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( binunionTIRcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ ( binunion @ X0 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( binunionTIRcontra
= ( ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ ( binunion @ X3 @ X4 ) )
=> ~ ( in @ X2 @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RH4uQJR8Dg/DTF2THF_29555.p',binunionTIRcontra) ).
thf(f82,plain,
( ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true != $true )
| ( ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f78,f45]) ).
thf(f45,plain,
( ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f78,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f60,f50]) ).
thf(f50,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f60,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( ( in @ sK10 @ sK9 )
= $true )
& ( ( in @ sK10 @ ( setminus @ sK8 @ sK9 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f37,f38]) ).
thf(f38,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
= $true ) )
=> ( ( ( in @ sK10 @ sK9 )
= $true )
& ( ( in @ sK10 @ ( setminus @ sK8 @ sK9 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( setminusER = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
=> ( ( in @ X0 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
=> ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ X0 @ X2 ) )
= setminusER ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox/tmp/tmp.RH4uQJR8Dg/DTF2THF_29555.p',setminusER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU750^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n025.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:32:57 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.39 ---- Original DTF file ---
% 0.18/0.39 thf(spec,logic,$$dhol).
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 % File : SEU750^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.39 % Domain : Set Theory
% 0.18/0.39 % Problem : Typed Set Theory - Laws for Typed Sets - DeMorgan Laws
% 0.18/0.39 % Version : Especial > Reduced > Especial.
% 0.18/0.39 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.18/0.39 % (! x:i.in x A -> in x (setminus A (binunion X Y)) ->
% 0.18/0.39 % in x (setminus A Y))))
% 0.18/0.39
% 0.18/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.39 % Source : [Bro08]
% 0.18/0.39 % Names : ZFC252l [Bro08]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.18/0.39 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.18/0.39 % Number of atoms : 24 ( 3 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 8 ( 6 avg)
% 0.18/0.39 % Number of connectives : 64 ( 4 ~; 0 |; 0 &; 46 @)
% 0.18/0.39 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 16 ( 5 avg)
% 0.18/0.39 % Number of types : 2 ( 0 usr)
% 0.18/0.39 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.18/0.39 % Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% 0.18/0.39 % SPC : TH0_THM_EQU_NAR
% 0.18/0.39
% 0.18/0.39 % Comments : http://mathgate.info/detsetitem.php?id=311
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 thf(in_type,type,
% 0.18/0.39 in: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(powerset_type,type,
% 0.18/0.39 powerset: $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(binunion_type,type,
% 0.18/0.39 binunion: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(setminus_type,type,
% 0.18/0.39 setminus: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(setminusI_type,type,
% 0.18/0.39 setminusI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusI,definition,
% 0.18/0.39 ( setminusI
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ~ ( in @ Xx @ B )
% 0.18/0.39 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setminusER_type,type,
% 0.18/0.39 setminusER: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusER,definition,
% 0.18/0.39 ( setminusER
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.39 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binunionTIRcontra_type,type,
% 0.18/0.39 binunionTIRcontra: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binunionTIRcontra,definition,
% 0.18/0.39 ( binunionTIRcontra
% 0.18/0.39 = ( ! [A: $i,X: $i] :
% 0.18/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.18/0.39 => ! [Y: $i] :
% 0.18/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.18/0.39 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(demorgan2a2,conjecture,
% 0.18/0.39 ( setminusI
% 0.18/0.39 => ( setminusER
% 0.18/0.39 => ( binunionTIRcontra
% 0.18/0.39 => ! [A: $i,X: $i] :
% 0.18/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.18/0.39 => ! [Y: $i] :
% 0.18/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.18/0.39 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 1.59/1.31 ---- Embedded in THF ---
% 1.59/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.59/1.32 %%% Generated on Tue Feb 24 12:32:58 EST 2026
% 1.59/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.59/1.32 %%% Logic specification used:
% 1.59/1.32 %%% thf(spec, logic, $$dhol).
% 1.59/1.32
% 1.59/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RH4uQJR8Dg/DTF2DTF29555.p
% See solution above
% 1.59/1.32 ------------------------
% 1.59/1.32 ---- Cleaned THF ---
% 1.59/1.33 thf(in_type,type,
% 1.59/1.33 in: $i > $i > $o ).
% 1.59/1.33
% 1.59/1.33 thf(powerset_type,type,
% 1.59/1.33 powerset: $i > $i ).
% 1.59/1.33
% 1.59/1.33 thf(binunion_type,type,
% 1.59/1.33 binunion: $i > $i > $i ).
% 1.59/1.33
% 1.59/1.33 thf(setminus_type,type,
% 1.59/1.33 setminus: $i > $i > $i ).
% 1.59/1.33
% 1.59/1.33 thf(setminusI_type,type,
% 1.59/1.33 setminusI: $o ).
% 1.59/1.33
% 1.59/1.33 thf(setminusI,definition,
% 1.59/1.33 ( setminusI
% 1.59/1.33 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.59/1.33 ( ( in @ Xx @ A )
% 1.59/1.33 => ( ~ ( in @ Xx @ B )
% 1.59/1.33 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 1.59/1.33
% 1.59/1.33 thf(setminusER_type,type,
% 1.59/1.33 setminusER: $o ).
% 1.59/1.33
% 1.59/1.33 thf(setminusER,definition,
% 1.59/1.33 ( setminusER
% 1.59/1.33 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.59/1.33 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.59/1.33 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.59/1.33
% 1.59/1.33 thf(binunionTIRcontra_type,type,
% 1.59/1.33 binunionTIRcontra: $o ).
% 1.59/1.33
% 1.59/1.33 thf(binunionTIRcontra,definition,
% 1.59/1.33 ( binunionTIRcontra
% 1.59/1.33 = ( ! [A: $i,X: $i] :
% 1.59/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.59/1.33 => ! [Y: $i] :
% 1.59/1.33 ( ( in @ Y @ ( powerset @ A ) )
% 1.59/1.33 => ! [Xx: $i] :
% 1.59/1.33 ( ( in @ Xx @ A )
% 1.59/1.33 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 1.59/1.33 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 1.59/1.33
% 1.59/1.33 thf(demorgan2a2,conjecture,
% 1.59/1.33 ( setminusI
% 1.59/1.33 => ( setminusER
% 1.59/1.33 => ( binunionTIRcontra
% 1.59/1.33 => ! [A: $i,X: $i] :
% 1.59/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.59/1.33 => ! [Y: $i] :
% 1.59/1.33 ( ( in @ Y @ ( powerset @ A ) )
% 1.59/1.33 => ! [Xx: $i] :
% 1.59/1.33 ( ( in @ Xx @ A )
% 1.59/1.33 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 1.59/1.33 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 1.59/1.33 ------------------------
% 1.59/1.35 % (29654)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_29555 for (2999ds/4Mi)
% 1.59/1.35 % (29653)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29555 for (2999ds/183Mi)
% 1.59/1.35 % (29658)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_29555 for (2999ds/275Mi)
% 1.59/1.35 % (29655)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_29555 for (2999ds/27Mi)
% 1.59/1.35 % (29657)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_29555 for (2999ds/2Mi)
% 1.59/1.35 % (29656)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29555 for (2999ds/2Mi)
% 1.59/1.35 % (29660)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29555 for (2999ds/18Mi)
% 1.59/1.35 % (29656)Instruction limit reached!
% 1.59/1.35 % (29656)------------------------------
% 1.59/1.35 % (29656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (29656)Termination reason: Unknown
% 1.59/1.35 % (29656)Termination phase: Property scanning
% 1.59/1.35
% 1.59/1.35 % (29656)Memory used [KB]: 1023
% 1.59/1.35 % (29656)Time elapsed: 0.003 s
% 1.59/1.35 % (29656)Instructions burned: 3 (million)
% 1.59/1.35 % (29656)------------------------------
% 1.59/1.35 % (29656)------------------------------
% 1.59/1.35 % (29657)Instruction limit reached!
% 1.59/1.35 % (29657)------------------------------
% 1.59/1.35 % (29657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (29657)Termination reason: Unknown
% 1.59/1.35 % (29657)Termination phase: Function definition elimination
% 1.59/1.35
% 1.59/1.35 % (29657)Memory used [KB]: 1023
% 1.59/1.35 % (29657)Time elapsed: 0.003 s
% 1.59/1.35 % (29657)Instructions burned: 3 (million)
% 1.59/1.35 % (29657)------------------------------
% 1.59/1.35 % (29657)------------------------------
% 1.59/1.35 % (29654)Instruction limit reached!
% 1.59/1.35 % (29654)------------------------------
% 1.59/1.35 % (29654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (29654)Termination reason: Unknown
% 1.59/1.35 % (29654)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (29654)Memory used [KB]: 5500
% 1.59/1.35 % (29654)Time elapsed: 0.004 s
% 1.59/1.35 % (29654)Instructions burned: 4 (million)
% 1.59/1.35 % (29654)------------------------------
% 1.59/1.35 % (29654)------------------------------
% 1.59/1.35 % (29658)First to succeed.
% 1.59/1.35 % (29658)Refutation found. Thanks to Tanya!
% 1.59/1.35 % SZS status Theorem for DTF2THF_29555
% 1.59/1.35 % SZS output start Proof for DTF2THF_29555
% 1.59/1.35 thf(func_def_0, type, in: $i > $i > $o).
% 1.59/1.35 thf(func_def_1, type, powerset: $i > $i).
% 1.59/1.35 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.59/1.35 thf(func_def_3, type, setminus: $i > $i > $i).
% 1.59/1.35 thf(f93,plain,(
% 1.59/1.35 $false),
% 1.59/1.35 inference(subsumption_resolution,[status(thm)],[f92,f44])).
% 1.59/1.35 thf(f44,plain,(
% 1.59/1.35 ((in @ sK1 @ (powerset @ sK0)) = $true)),
% 1.59/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.59/1.35 thf(f29,plain,(
% 1.59/1.35 (binunionTIRcontra = $true) & (setminusER = $true) & (setminusI = $true) & ((((in @ sK2 @ (powerset @ sK0)) = $true) & (((in @ sK3 @ sK0) = $true) & ((in @ sK3 @ (setminus @ sK0 @ sK2)) != $true) & ((in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))) = $true))) & ((in @ sK1 @ (powerset @ sK0)) = $true))),
% 1.59/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f28,f27,f26])).
% 1.59/1.35 thf(f26,plain,(
% 1.59/1.35 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ (setminus @ X0 @ X2)) != $true) & ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (((in @ X2 @ (powerset @ sK0)) = $true) & ? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ((in @ X3 @ (setminus @ sK0 @ X2)) != $true) & ((in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ X2))) = $true))) & ((in @ sK1 @ (powerset @ sK0)) = $true))),
% 1.59/1.35 introduced(definition,[],[choice_axiom])).
% 1.59/1.35 thf(f27,plain,(
% 1.59/1.35 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK0)) = $true) & ? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ((in @ X3 @ (setminus @ sK0 @ X2)) != $true) & ((in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ X2))) = $true))) => (((in @ sK2 @ (powerset @ sK0)) = $true) & ? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ((in @ X3 @ (setminus @ sK0 @ sK2)) != $true) & ((in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))) = $true)))),
% 1.59/1.35 introduced(definition,[],[choice_axiom])).
% 1.59/1.35 thf(f28,plain,(
% 1.59/1.35 ? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ((in @ X3 @ (setminus @ sK0 @ sK2)) != $true) & ((in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))) = $true)) => (((in @ sK3 @ sK0) = $true) & ((in @ sK3 @ (setminus @ sK0 @ sK2)) != $true) & ((in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))) = $true))),
% 1.59/1.35 introduced(definition,[],[choice_axiom])).
% 1.59/1.35 thf(f25,plain,(
% 1.59/1.35 (binunionTIRcontra = $true) & (setminusER = $true) & (setminusI = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ (setminus @ X0 @ X2)) != $true) & ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true))),
% 1.59/1.35 inference(rectify,[status(thm)],[f21])).
% 1.59/1.35 thf(f21,plain,(
% 1.59/1.35 (binunionTIRcontra = $true) & (setminusER = $true) & (setminusI = $true) & ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ (setminus @ X1 @ X2)) != $true) & ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) = $true))) & ((in @ X0 @ (powerset @ X1)) = $true))),
% 1.59/1.35 inference(flattening,[status(thm)],[f20])).
% 1.59/1.35 thf(f20,plain,(
% 1.59/1.35 ((? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ (setminus @ X1 @ X2)) != $true) & ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) = $true)) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (binunionTIRcontra = $true)) & (setminusER = $true)) & (setminusI = $true)),
% 1.59/1.35 inference(ennf_transformation,[status(thm)],[f14])).
% 1.59/1.35 thf(f14,plain,(
% 1.59/1.35 ~((setminusI = $true) => ((setminusER = $true) => ((binunionTIRcontra = $true) => ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) = $true) => ((in @ X3 @ (setminus @ X1 @ X2)) = $true))))))))),
% 1.59/1.35 inference(fool_elimination,[status(thm)],[f13])).
% 1.59/1.35 thf(f13,plain,(
% 1.59/1.35 ~(setminusI => (setminusER => (binunionTIRcontra => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) => (in @ X3 @ (setminus @ X1 @ X2)))))))))),
% 1.59/1.35 inference(rectify,[status(thm)],[f5])).
% 1.59/1.35 thf(f5,negated_conjecture,(
% 1.59/1.35 ~(setminusI => (setminusER => (binunionTIRcontra => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4))) => (in @ X2 @ (setminus @ X0 @ X4)))))))))),
% 1.59/1.35 inference(negated_conjecture,[status(cth)],[f4])).
% 1.59/1.35 thf(f4,conjecture,(
% 1.59/1.35 setminusI => (setminusER => (binunionTIRcontra => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4))) => (in @ X2 @ (setminus @ X0 @ X4))))))))),
% 1.59/1.35 file('/export/starexec/sandbox/tmp/tmp.RH4uQJR8Dg/DTF2THF_29555.p',demorgan2a2)).
% 1.59/1.35 thf(f92,plain,(
% 1.59/1.35 ((in @ sK1 @ (powerset @ sK0)) != $true)),
% 1.59/1.35 inference(subsumption_resolution,[status(thm)],[f91,f47])).
% 1.59/1.35 thf(f47,plain,(
% 1.59/1.35 ((in @ sK3 @ sK0) = $true)),
% 1.59/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.59/1.35 thf(f91,plain,(
% 1.59/1.35 ((in @ sK3 @ sK0) != $true) | ((in @ sK1 @ (powerset @ sK0)) != $true)),
% 1.59/1.35 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.59/1.35 thf(f90,plain,(
% 1.59/1.35 ((in @ sK3 @ sK0) != $true) | ($true != $true) | ((in @ sK1 @ (powerset @ sK0)) != $true)),
% 1.59/1.35 inference(superposition,[status(thm)],[f89,f48])).
% 1.59/1.35 thf(f48,plain,(
% 1.59/1.35 ((in @ sK2 @ (powerset @ sK0)) = $true)),
% 1.59/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.59/1.35 thf(f89,plain,(
% 1.59/1.35 ( ! [X0 : $i] : (((in @ sK2 @ (powerset @ X0)) != $true) | ((in @ sK1 @ (powerset @ X0)) != $true) | ((in @ sK3 @ X0) != $true)) )),
% 1.59/1.35 inference(subsumption_resolution,[status(thm)],[f88,f86])).
% 1.59/1.35 thf(f86,plain,(
% 1.59/1.35 ((in @ sK3 @ sK2) = $true)),
% 1.59/1.35 inference(subsumption_resolution,[status(thm)],[f85,f47])).
% 1.59/1.35 thf(f85,plain,(
% 1.59/1.35 ((in @ sK3 @ sK0) != $true) | ((in @ sK3 @ sK2) = $true)),
% 1.59/1.35 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.59/1.35 thf(f84,plain,(
% 1.59/1.35 ((in @ sK3 @ sK0) != $true) | ($true != $true) | ((in @ sK3 @ sK2) = $true)),
% 1.59/1.35 inference(superposition,[status(thm)],[f46,f80])).
% 1.59/1.35 thf(f80,plain,(
% 1.59/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (setminus @ X2 @ X1)) = $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) != $true)) )),
% 1.59/1.35 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.59/1.35 thf(f74,plain,(
% 1.59/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X0 @ (setminus @ X2 @ X1)) = $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true)) )),
% 1.59/1.35 inference(definition_unfolding,[status(thm)],[f64,f49])).
% 1.59/1.35 thf(f49,plain,(
% 1.59/1.35 (setminusI = $true)),
% 1.59/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.59/1.35 thf(f64,plain,(
% 1.59/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ (setminus @ X2 @ X1)) = $true) | (setminusI != $true)) )),
% 1.59/1.35 inference(cnf_transformation,[status(thm)],[f43])).
% 1.59/1.35 thf(f43,plain,(
% 1.59/1.35 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ (setminus @ X2 @ X1)) = $true)) | (setminusI != $true)) & ((setminusI = $true) | (((in @ sK11 @ sK13) = $true) & ((in @ sK11 @ sK12) != $true) & ((in @ sK11 @ (setminus @ sK13 @ sK12)) != $true)))),
% 1.59/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f41,f42])).
% 1.59/1.35 thf(f42,plain,(
% 1.59/1.35 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) = $true) & ((in @ X3 @ X4) != $true) & ((in @ X3 @ (setminus @ X5 @ X4)) != $true)) => (((in @ sK11 @ sK13) = $true) & ((in @ sK11 @ sK12) != $true) & ((in @ sK11 @ (setminus @ sK13 @ sK12)) != $true))),
% 1.59/1.35 introduced(definition,[],[choice_axiom])).
% 1.59/1.35 thf(f41,plain,(
% 1.59/1.35 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ (setminus @ X2 @ X1)) = $true)) | (setminusI != $true)) & ((setminusI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) = $true) & ((in @ X3 @ X4) != $true) & ((in @ X3 @ (setminus @ X5 @ X4)) != $true)))),
% 1.59/1.35 inference(rectify,[status(thm)],[f40])).
% 1.59/1.35 thf(f40,plain,(
% 1.59/1.35 (! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true) | ((in @ X2 @ (setminus @ X1 @ X0)) = $true)) | (setminusI != $true)) & ((setminusI = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true) & ((in @ X2 @ (setminus @ X1 @ X0)) != $true)))),
% 1.59/1.35 inference(nnf_transformation,[status(thm)],[f19])).
% 1.59/1.35 thf(f19,plain,(
% 1.59/1.35 ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true) | ((in @ X2 @ (setminus @ X1 @ X0)) = $true)) <=> (setminusI = $true)),
% 1.59/1.35 inference(flattening,[status(thm)],[f18])).
% 1.59/1.35 thf(f18,plain,(
% 1.59/1.35 (setminusI = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X2 @ (setminus @ X1 @ X0)) = $true) | ((in @ X2 @ X0) = $true)) | ((in @ X2 @ X1) != $true))),
% 1.59/1.35 inference(ennf_transformation,[status(thm)],[f16])).
% 1.59/1.35 thf(f16,plain,(
% 1.59/1.35 (setminusI = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ X1) = $true) => (((in @ X2 @ X0) != $true) => ((in @ X2 @ (setminus @ X1 @ X0)) = $true)))),
% 1.59/1.35 inference(flattening,[status(thm)],[f8])).
% 1.59/1.35 thf(f8,plain,(
% 1.59/1.35 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) => (~((in @ X2 @ X0) = $true) => ((in @ X2 @ (setminus @ X1 @ X0)) = $true)))),
% 1.59/1.35 inference(fool_elimination,[status(thm)],[f7])).
% 1.59/1.35 thf(f7,plain,(
% 1.59/1.35 (setminusI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (~(in @ X2 @ X0) => (in @ X2 @ (setminus @ X1 @ X0)))))),
% 1.59/1.35 inference(rectify,[status(thm)],[f1])).
% 1.59/1.35 thf(f1,axiom,(
% 1.59/1.35 (setminusI = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))),
% 1.59/1.35 file('/export/starexec/sandbox/tmp/tmp.RH4uQJR8Dg/DTF2THF_29555.p',setminusI)).
% 1.59/1.35 thf(f46,plain,(
% 1.59/1.35 ((in @ sK3 @ (setminus @ sK0 @ sK2)) != $true)),
% 1.59/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.59/1.35 thf(f88,plain,(
% 1.59/1.35 ( ! [X0 : $i] : (((in @ sK3 @ X0) != $true) | ((in @ sK2 @ (powerset @ X0)) != $true) | ((in @ sK3 @ sK2) != $true) | ((in @ sK1 @ (powerset @ X0)) != $true)) )),
% 1.59/1.35 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.59/1.35 thf(f87,plain,(
% 1.59/1.35 ( ! [X0 : $i] : (($true != $true) | ((in @ sK2 @ (powerset @ X0)) != $true) | ((in @ sK3 @ sK2) != $true) | ((in @ sK1 @ (powerset @ X0)) != $true) | ((in @ sK3 @ X0) != $true)) )),
% 1.59/1.35 inference(superposition,[status(thm)],[f82,f79])).
% 1.59/1.35 thf(f79,plain,(
% 1.59/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X3 @ X2) != $true)) )),
% 1.59/1.35 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.59/1.35 thf(f65,plain,(
% 1.59/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ X2) != $true) | ($true != $true) | ((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X3 @ (binunion @ X0 @ X2)) = $true) | ((in @ X3 @ X1) != $true) | ((in @ X2 @ (powerset @ X1)) != $true)) )),
% 1.59/1.35 inference(definition_unfolding,[status(thm)],[f57,f51])).
% 1.59/1.35 thf(f51,plain,(
% 1.59/1.35 (binunionTIRcontra = $true)),
% 1.59/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.59/1.35 thf(f57,plain,(
% 1.59/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) | ((in @ X3 @ X2) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ((in @ X0 @ (powerset @ X1)) != $true) | (binunionTIRcontra != $true)) )),
% 1.59/1.35 inference(cnf_transformation,[status(thm)],[f35])).
% 1.59/1.35 thf(f35,plain,(
% 1.59/1.35 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) | ((in @ X3 @ X2) != $true) | ((in @ X3 @ X1) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) | (binunionTIRcontra != $true)) & ((binunionTIRcontra = $true) | (((((in @ sK7 @ (binunion @ sK4 @ sK6)) != $true) & ((in @ sK7 @ sK6) = $true) & ((in @ sK7 @ sK5) = $true)) & ((in @ sK6 @ (powerset @ sK5)) = $true)) & ((in @ sK4 @ (powerset @ sK5)) = $true)))),
% 1.59/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f31,f34,f33,f32])).
% 1.59/1.35 thf(f32,plain,(
% 1.59/1.35 ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (? [X7 : $i] : (($true != (in @ X7 @ (binunion @ X4 @ X6))) & ((in @ X7 @ X6) = $true) & ((in @ X7 @ X5) = $true)) & ((in @ X6 @ (powerset @ X5)) = $true)) & ((in @ X4 @ (powerset @ X5)) = $true)) => (? [X6 : $i] : (? [X7 : $i] : (((in @ X7 @ (binunion @ sK4 @ X6)) != $true) & ((in @ X7 @ X6) = $true) & ((in @ X7 @ sK5) = $true)) & ((in @ X6 @ (powerset @ sK5)) = $true)) & ((in @ sK4 @ (powerset @ sK5)) = $true))),
% 1.59/1.35 introduced(definition,[],[choice_axiom])).
% 1.59/1.35 thf(f33,plain,(
% 1.59/1.35 ? [X6 : $i] : (? [X7 : $i] : (((in @ X7 @ (binunion @ sK4 @ X6)) != $true) & ((in @ X7 @ X6) = $true) & ((in @ X7 @ sK5) = $true)) & ((in @ X6 @ (powerset @ sK5)) = $true)) => (? [X7 : $i] : (((in @ X7 @ (binunion @ sK4 @ sK6)) != $true) & ((in @ X7 @ sK6) = $true) & ((in @ X7 @ sK5) = $true)) & ((in @ sK6 @ (powerset @ sK5)) = $true))),
% 1.59/1.35 introduced(definition,[],[choice_axiom])).
% 1.59/1.35 thf(f34,plain,(
% 1.59/1.35 ? [X7 : $i] : (((in @ X7 @ (binunion @ sK4 @ sK6)) != $true) & ((in @ X7 @ sK6) = $true) & ((in @ X7 @ sK5) = $true)) => (((in @ sK7 @ (binunion @ sK4 @ sK6)) != $true) & ((in @ sK7 @ sK6) = $true) & ((in @ sK7 @ sK5) = $true))),
% 1.59/1.35 introduced(definition,[],[choice_axiom])).
% 1.59/1.35 thf(f31,plain,(
% 1.59/1.35 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) | ((in @ X3 @ X2) != $true) | ((in @ X3 @ X1) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) | (binunionTIRcontra != $true)) & ((binunionTIRcontra = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (? [X7 : $i] : (($true != (in @ X7 @ (binunion @ X4 @ X6))) & ((in @ X7 @ X6) = $true) & ((in @ X7 @ X5) = $true)) & ((in @ X6 @ (powerset @ X5)) = $true)) & ((in @ X4 @ (powerset @ X5)) = $true)))),
% 1.59/1.35 inference(rectify,[status(thm)],[f30])).
% 1.59/1.35 thf(f30,plain,(
% 1.59/1.35 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) | ((in @ X3 @ X2) != $true) | ((in @ X3 @ X1) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) | (binunionTIRcontra != $true)) & ((binunionTIRcontra = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) != $true) & ((in @ X3 @ X2) = $true) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)))),
% 1.59/1.35 inference(nnf_transformation,[status(thm)],[f24])).
% 1.59/1.35 thf(f24,plain,(
% 1.59/1.35 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) | ((in @ X3 @ X2) != $true) | ((in @ X3 @ X1) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) <=> (binunionTIRcontra = $true)),
% 1.59/1.35 inference(flattening,[status(thm)],[f23])).
% 1.59/1.35 thf(f23,plain,(
% 1.59/1.35 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2) != $true) | ((in @ X3 @ (binunion @ X0 @ X2)) = $true)) | ((in @ X3 @ X1) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) <=> (binunionTIRcontra = $true)),
% 1.59/1.35 inference(ennf_transformation,[status(thm)],[f15])).
% 1.59/1.35 thf(f15,plain,(
% 1.59/1.35 ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ (binunion @ X0 @ X2)) != $true) => ((in @ X3 @ X2) != $true))))) <=> (binunionTIRcontra = $true)),
% 1.59/1.35 inference(flattening,[status(thm)],[f10])).
% 1.59/1.35 thf(f10,plain,(
% 1.59/1.35 (binunionTIRcontra = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (~((in @ X3 @ (binunion @ X0 @ X2)) = $true) => ~((in @ X3 @ X2) = $true)))))),
% 1.59/1.35 inference(fool_elimination,[status(thm)],[f9])).
% 1.59/1.35 thf(f9,plain,(
% 1.59/1.35 (binunionTIRcontra = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => (~(in @ X3 @ (binunion @ X0 @ X2)) => ~(in @ X3 @ X2))))))),
% 1.59/1.35 inference(rectify,[status(thm)],[f3])).
% 1.59/1.35 thf(f3,axiom,(
% 1.59/1.35 (binunionTIRcontra = ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (binunion @ X3 @ X4)) => ~(in @ X2 @ X4))))))),
% 1.59/1.35 file('/export/starexec/sandbox/tmp/tmp.RH4uQJR8Dg/DTF2THF_29555.p',binunionTIRcontra)).
% 1.59/1.35 thf(f82,plain,(
% 1.59/1.35 ((in @ sK3 @ (binunion @ sK1 @ sK2)) != $true)),
% 1.59/1.35 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.59/1.35 thf(f81,plain,(
% 1.59/1.35 ($true != $true) | ((in @ sK3 @ (binunion @ sK1 @ sK2)) != $true)),
% 1.59/1.35 inference(superposition,[status(thm)],[f78,f45])).
% 1.59/1.35 thf(f45,plain,(
% 1.59/1.35 ((in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))) = $true)),
% 1.59/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.59/1.35 thf(f78,plain,(
% 1.59/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (setminus @ X0 @ X1)) != $true) | ((in @ X2 @ X1) != $true)) )),
% 1.59/1.35 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.59/1.35 thf(f71,plain,(
% 1.59/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X2 @ (setminus @ X0 @ X1)) != $true) | ((in @ X2 @ X1) != $true)) )),
% 1.59/1.35 inference(definition_unfolding,[status(thm)],[f60,f50])).
% 1.59/1.35 thf(f50,plain,(
% 1.59/1.35 (setminusER = $true)),
% 1.59/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.59/1.35 thf(f60,plain,(
% 1.59/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ (setminus @ X0 @ X1)) != $true) | (setminusER != $true)) )),
% 1.59/1.35 inference(cnf_transformation,[status(thm)],[f39])).
% 1.59/1.35 thf(f39,plain,(
% 1.59/1.35 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ (setminus @ X0 @ X1)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | (((in @ sK10 @ sK9) = $true) & ((in @ sK10 @ (setminus @ sK8 @ sK9)) = $true)))),
% 1.59/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f37,f38])).
% 1.59/1.35 thf(f38,plain,(
% 1.59/1.35 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ (setminus @ X3 @ X4)) = $true)) => (((in @ sK10 @ sK9) = $true) & ((in @ sK10 @ (setminus @ sK8 @ sK9)) = $true))),
% 1.59/1.35 introduced(definition,[],[choice_axiom])).
% 1.59/1.35 thf(f37,plain,(
% 1.59/1.35 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ (setminus @ X0 @ X1)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ (setminus @ X3 @ X4)) = $true)))),
% 1.59/1.35 inference(rectify,[status(thm)],[f36])).
% 1.59/1.35 thf(f36,plain,(
% 1.59/1.35 (! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ (setminus @ X1 @ X2)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X2) = $true) & ((in @ X0 @ (setminus @ X1 @ X2)) = $true)))),
% 1.59/1.35 inference(nnf_transformation,[status(thm)],[f22])).
% 1.59/1.35 thf(f22,plain,(
% 1.59/1.35 ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ (setminus @ X1 @ X2)) != $true)) <=> (setminusER = $true)),
% 1.59/1.35 inference(ennf_transformation,[status(thm)],[f17])).
% 1.59/1.35 thf(f17,plain,(
% 1.59/1.35 (setminusER = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) = $true) => ((in @ X0 @ X2) != $true))),
% 1.59/1.35 inference(flattening,[status(thm)],[f12])).
% 1.59/1.35 thf(f12,plain,(
% 1.59/1.35 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) = $true) => ~((in @ X0 @ X2) = $true)) <=> (setminusER = $true)),
% 1.59/1.35 inference(fool_elimination,[status(thm)],[f11])).
% 1.59/1.35 thf(f11,plain,(
% 1.59/1.35 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X1 @ X2)) => ~(in @ X0 @ X2)) = setminusER)),
% 1.59/1.35 inference(rectify,[status(thm)],[f2])).
% 1.59/1.35 thf(f2,axiom,(
% 1.59/1.35 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 1.59/1.35 file('/export/starexec/sandbox/tmp/tmp.RH4uQJR8Dg/DTF2THF_29555.p',setminusER)).
% 1.59/1.35 % SZS output end Proof for DTF2THF_29555
% 1.59/1.35 % (29658)------------------------------
% 1.59/1.35 % (29658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (29658)Termination reason: Refutation
% 1.59/1.35
% 1.59/1.35 % (29658)Memory used [KB]: 5628
% 1.59/1.35 % (29658)Time elapsed: 0.010 s
% 1.59/1.35 % (29658)Instructions burned: 6 (million)
% 1.59/1.35 % (29658)------------------------------
% 1.59/1.35 % (29658)------------------------------
% 1.59/1.35 % (29652)Success in time 0.023 s
%------------------------------------------------------------------------------