%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU755^2 : 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 : n019.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 09:36:56 AM UTC 2026
% Result : Theorem 1.64s 1.32s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 1269 ( 342 equ; 0 cnn)
% Maximal formula atoms : 14 ( 16 avg)
% Number of connectives : 1410 ( 159 ~; 109 |; 119 &; 940 @)
% ( 11 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 195 ( 0 ^; 137 !; 58 ?; 195 :)
% 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(f99,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f98,f47]) ).
thf(f47,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( setminusER = $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
& ( ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) )
= $true )
& ( $true
!= ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( setminusI = $true )
& ( binunionTEcontra = $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] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X0 @ X2 ) ) )
& ( $true
= ( in @ X3 @ ( setminus @ X0 @ X1 ) ) )
& ( $true
!= ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ sK0 @ X2 ) ) )
& ( ( in @ X3 @ ( setminus @ sK0 @ sK1 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ X2 ) ) )
!= $true )
& ( $true
= ( in @ X3 @ sK0 ) ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ sK0 @ X2 ) ) )
& ( ( in @ X3 @ ( setminus @ sK0 @ sK1 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ X2 ) ) )
!= $true )
& ( $true
= ( in @ X3 @ sK0 ) ) ) )
=> ( ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ sK0 @ sK2 ) ) )
& ( ( in @ X3 @ ( setminus @ sK0 @ sK1 ) )
= $true )
& ( $true
!= ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) )
& ( $true
= ( in @ X3 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ sK0 @ sK2 ) ) )
& ( ( in @ X3 @ ( setminus @ sK0 @ sK1 ) )
= $true )
& ( $true
!= ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) )
& ( $true
= ( in @ X3 @ sK0 ) ) )
=> ( ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
& ( ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) )
= $true )
& ( $true
!= ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( setminusER = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X0 @ X2 ) ) )
& ( $true
= ( in @ X3 @ ( setminus @ X0 @ X1 ) ) )
& ( $true
!= ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
& ( setminusI = $true )
& ( binunionTEcontra = $true ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( setminusER = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
& ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( setminusI = $true )
& ( binunionTEcontra = $true ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binunionTEcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( binunionTEcontra = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
=> ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( setminusI
=> ( setminusER
=> ( binunionTEcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
=> ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ( binunionTEcontra
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ X3 ) )
=> ( ( in @ X2 @ ( setminus @ X0 @ X4 ) )
=> ( in @ X2 @ ( setminus @ X0 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( setminusI
=> ( setminusER
=> ( binunionTEcontra
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ X3 ) )
=> ( ( in @ X2 @ ( setminus @ X0 @ X4 ) )
=> ( in @ X2 @ ( setminus @ X0 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.m84IBzELSV/DTF2THF_27227.p',demorgan2b2) ).
thf(f98,plain,
( $true
!= ( in @ sK3 @ sK0 ) ),
inference(subsumption_resolution,[status(thm)],[f97,f46]) ).
thf(f46,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f97,plain,
( ( $true
!= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $true
!= ( in @ sK3 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( $true
!= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ sK3 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f95,f51]) ).
thf(f51,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f95,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK3 @ X0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f94,f86]) ).
thf(f86,plain,
( $true
!= ( in @ sK3 @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK3 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f82,f50]) ).
thf(f50,plain,
( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f82,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f62,f52]) ).
thf(f52,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( $true
= ( in @ sK8 @ sK10 ) )
& ( $true
= ( in @ sK8 @ ( setminus @ sK9 @ sK10 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f37,f38]) ).
thf(f38,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) ) )
=> ( ( $true
= ( in @ sK8 @ sK10 ) )
& ( $true
= ( in @ sK8 @ ( setminus @ sK9 @ sK10 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
=> ( $true
!= ( in @ X0 @ X1 ) ) )
<=> ( setminusER = $true ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
=> ( $true
!= ( in @ X0 @ X1 ) ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
=> ~ ( in @ X0 @ X1 ) )
= setminusER ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox/tmp/tmp.m84IBzELSV/DTF2THF_27227.p',setminusER) ).
thf(f94,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ sK3 @ sK2 ) )
| ( $true
!= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK3 @ X0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f93,f87]) ).
thf(f87,plain,
( $true
!= ( in @ sK3 @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
( ( $true
!= ( in @ sK3 @ sK1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f82,f49]) ).
thf(f49,plain,
( ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f93,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK3 @ X0 ) )
| ( $true
!= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ sK3 @ sK1 ) )
| ( $true
= ( in @ sK3 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK3 @ X0 ) )
| ( $true != $true )
| ( $true
= ( in @ sK3 @ sK1 ) )
| ( $true
= ( in @ sK3 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f83,f91]) ).
thf(f91,plain,
( ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f90,f47]) ).
thf(f90,plain,
( ( $true
!= ( in @ sK3 @ sK0 ) )
| ( ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ sK3 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f48,f81]) ).
thf(f81,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ X5 )
!= $true )
| ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f63,f45]) ).
thf(f45,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f63,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
!= $true )
| ( setminusI != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( setminusI = $true )
| ( ( $true
!= ( in @ sK11 @ sK12 ) )
& ( $true
!= ( in @ sK11 @ ( setminus @ sK13 @ sK12 ) ) )
& ( $true
= ( in @ sK11 @ sK13 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( setminusI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f41,f42]) ).
thf(f42,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
& ( $true
= ( in @ X0 @ X2 ) ) )
=> ( ( $true
!= ( in @ sK11 @ sK12 ) )
& ( $true
!= ( in @ sK11 @ ( setminus @ sK13 @ sK12 ) ) )
& ( $true
= ( in @ sK11 @ sK13 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
& ( $true
= ( in @ X0 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( setminusI != $true ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( setminusI = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,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.m84IBzELSV/DTF2THF_27227.p',setminusI) ).
thf(f48,plain,
( $true
!= ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ X2 ) )
| ( $true
= ( in @ X3 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
= ( in @ X3 @ X0 ) )
| ( $true != $true )
| ( $true
= ( in @ X3 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(definition_unfolding,[status(thm)],[f59,f44]) ).
thf(f44,plain,
binunionTEcontra = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ X2 ) )
| ( $true
= ( in @ X3 @ X0 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( binunionTEcontra != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ X2 ) )
| ( $true
= ( in @ X3 @ X0 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( binunionTEcontra != $true ) )
& ( ( binunionTEcontra = $true )
| ( ( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) )
& ( $true
= ( in @ sK7 @ ( binunion @ sK4 @ sK6 ) ) )
& ( $true
= ( in @ sK7 @ sK5 ) )
& ( ( in @ sK7 @ sK6 )
!= $true )
& ( ( in @ sK7 @ sK4 )
!= $true )
& ( $true
= ( in @ sK4 @ ( powerset @ sK5 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f31,f34,f33,f32]) ).
thf(f32,plain,
( ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) )
& ? [X7: $i] :
( ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
= $true )
& ( $true
= ( in @ X7 @ X5 ) )
& ( $true
!= ( in @ X7 @ X6 ) )
& ( ( in @ X7 @ X4 )
!= $true ) ) )
& ( $true
= ( in @ X4 @ ( powerset @ X5 ) ) ) )
=> ( ? [X6: $i] :
( ( $true
= ( in @ X6 @ ( powerset @ sK5 ) ) )
& ? [X7: $i] :
( ( ( in @ X7 @ ( binunion @ sK4 @ X6 ) )
= $true )
& ( $true
= ( in @ X7 @ sK5 ) )
& ( $true
!= ( in @ X7 @ X6 ) )
& ( $true
!= ( in @ X7 @ sK4 ) ) ) )
& ( $true
= ( in @ sK4 @ ( powerset @ sK5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ? [X6: $i] :
( ( $true
= ( in @ X6 @ ( powerset @ sK5 ) ) )
& ? [X7: $i] :
( ( ( in @ X7 @ ( binunion @ sK4 @ X6 ) )
= $true )
& ( $true
= ( in @ X7 @ sK5 ) )
& ( $true
!= ( in @ X7 @ X6 ) )
& ( $true
!= ( in @ X7 @ sK4 ) ) ) )
=> ( ( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ ( binunion @ sK4 @ sK6 ) ) )
& ( $true
= ( in @ X7 @ sK5 ) )
& ( $true
!= ( in @ X7 @ sK6 ) )
& ( $true
!= ( in @ X7 @ sK4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ ( binunion @ sK4 @ sK6 ) ) )
& ( $true
= ( in @ X7 @ sK5 ) )
& ( $true
!= ( in @ X7 @ sK6 ) )
& ( $true
!= ( in @ X7 @ sK4 ) ) )
=> ( ( $true
= ( in @ sK7 @ ( binunion @ sK4 @ sK6 ) ) )
& ( $true
= ( in @ sK7 @ sK5 ) )
& ( ( in @ sK7 @ sK6 )
!= $true )
& ( ( in @ sK7 @ sK4 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ X2 ) )
| ( $true
= ( in @ X3 @ X0 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( binunionTEcontra != $true ) )
& ( ( binunionTEcontra = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) )
& ? [X7: $i] :
( ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
= $true )
& ( $true
= ( in @ X7 @ X5 ) )
& ( $true
!= ( in @ X7 @ X6 ) )
& ( ( in @ X7 @ X4 )
!= $true ) ) )
& ( $true
= ( in @ X4 @ ( powerset @ X5 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ X2 ) )
| ( $true
= ( in @ X3 @ X0 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( binunionTEcontra != $true ) )
& ( ( binunionTEcontra = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
& ( $true
= ( in @ X3 @ X1 ) )
& ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ X3 @ X0 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ X2 ) )
| ( $true
= ( in @ X3 @ X0 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( binunionTEcontra = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( $true
= ( in @ X3 @ X2 ) )
| ( $true
= ( in @ X3 @ X0 ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( binunionTEcontra = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true
!= ( in @ X3 @ X0 ) )
=> ( ( $true
!= ( in @ X3 @ X2 ) )
=> ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true ) ) ) ) ) )
<=> ( binunionTEcontra = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true
!= ( in @ X3 @ X0 ) )
=> ( ( $true
!= ( in @ X3 @ X2 ) )
=> ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true ) ) ) ) ) )
<=> ( binunionTEcontra = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binunion @ X0 @ X2 ) ) ) ) ) ) )
= binunionTEcontra ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X3: $i,X0: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X3 )
=> ( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) )
= binunionTEcontra ),
file('/export/starexec/sandbox/tmp/tmp.m84IBzELSV/DTF2THF_27227.p',binunionTEcontra) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU755^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n019.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 12:33:09 EST 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SEU755^2 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.44 % Domain : Set Theory
% 0.17/0.44 % Problem : Typed Set Theory - Laws for Typed Sets - DeMorgan Laws
% 0.17/0.44 % Version : Especial > Reduced > Especial.
% 0.17/0.44 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.17/0.44 % (! x:i.in x A -> in x (setminus A X) -> in x (setminus A Y) ->
% 0.17/0.44 % in x (setminus A (binunion X Y)))))
% 0.17/0.44
% 0.17/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.44 % Source : [Bro08]
% 0.17/0.44 % Names : ZFC257l [Bro08]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 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, 0.33 v3.7.0
% 0.17/0.44 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.17/0.44 % Number of atoms : 26 ( 3 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 9 ( 6 avg)
% 0.17/0.44 % Number of connectives : 73 ( 5 ~; 0 |; 0 &; 52 @)
% 0.17/0.44 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 17 ( 5 avg)
% 0.17/0.44 % Number of types : 2 ( 0 usr)
% 0.17/0.44 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.17/0.44 % Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% 0.17/0.44 % SPC : TH0_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : http://mathgate.info/detsetitem.php?id=316
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf(in_type,type,
% 0.17/0.44 in: $i > $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(powerset_type,type,
% 0.17/0.44 powerset: $i > $i ).
% 0.17/0.44
% 0.17/0.44 thf(binunion_type,type,
% 0.17/0.44 binunion: $i > $i > $i ).
% 0.17/0.44
% 0.17/0.44 thf(setminus_type,type,
% 0.17/0.44 setminus: $i > $i > $i ).
% 0.17/0.44
% 0.17/0.44 thf(setminusI_type,type,
% 0.17/0.44 setminusI: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setminusI,definition,
% 0.17/0.44 ( setminusI
% 0.17/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( ~ ( in @ Xx @ B )
% 0.17/0.44 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setminusER_type,type,
% 0.17/0.44 setminusER: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setminusER,definition,
% 0.17/0.44 ( setminusER
% 0.17/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.44 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(binunionTEcontra_type,type,
% 0.17/0.44 binunionTEcontra: $o ).
% 0.17/0.44
% 0.17/0.44 thf(binunionTEcontra,definition,
% 0.17/0.44 ( binunionTEcontra
% 0.17/0.44 = ( ! [A: $i,X: $i] :
% 0.17/0.44 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.44 => ! [Y: $i] :
% 0.17/0.44 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.44 => ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( ~ ( in @ Xx @ X )
% 0.17/0.44 => ( ~ ( in @ Xx @ Y )
% 0.17/0.44 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(demorgan2b2,conjecture,
% 0.17/0.44 ( setminusI
% 0.17/0.44 => ( setminusER
% 0.17/0.44 => ( binunionTEcontra
% 0.17/0.44 => ! [A: $i,X: $i] :
% 0.17/0.44 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.44 => ! [Y: $i] :
% 0.17/0.44 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.44 => ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.17/0.44 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.17/0.44 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 1.49/1.27 ---- Embedded in THF ---
% 1.49/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.27 %%% Generated on Tue Feb 24 12:33:10 EST 2026
% 1.49/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.27 %%% Logic specification used:
% 1.49/1.27 %%% thf(spec, logic, $$dhol).
% 1.49/1.27
% 1.49/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.m84IBzELSV/DTF2DTF27227.p
% See solution above
% 1.49/1.27 ------------------------
% 1.49/1.28 ---- Cleaned THF ---
% 1.49/1.28 thf(in_type,type,
% 1.49/1.28 in: $i > $i > $o ).
% 1.49/1.28
% 1.49/1.28 thf(powerset_type,type,
% 1.49/1.28 powerset: $i > $i ).
% 1.49/1.28
% 1.49/1.28 thf(binunion_type,type,
% 1.49/1.28 binunion: $i > $i > $i ).
% 1.49/1.28
% 1.49/1.28 thf(setminus_type,type,
% 1.49/1.28 setminus: $i > $i > $i ).
% 1.49/1.28
% 1.49/1.28 thf(setminusI_type,type,
% 1.49/1.28 setminusI: $o ).
% 1.49/1.28
% 1.49/1.28 thf(setminusI,definition,
% 1.49/1.28 ( setminusI
% 1.49/1.28 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.49/1.28 ( ( in @ Xx @ A )
% 1.49/1.28 => ( ~ ( in @ Xx @ B )
% 1.49/1.28 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 1.49/1.28
% 1.49/1.28 thf(setminusER_type,type,
% 1.49/1.28 setminusER: $o ).
% 1.49/1.28
% 1.49/1.28 thf(setminusER,definition,
% 1.49/1.28 ( setminusER
% 1.49/1.28 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.49/1.28 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.49/1.28 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.49/1.28
% 1.49/1.28 thf(binunionTEcontra_type,type,
% 1.49/1.28 binunionTEcontra: $o ).
% 1.49/1.28
% 1.49/1.28 thf(binunionTEcontra,definition,
% 1.49/1.28 ( binunionTEcontra
% 1.49/1.28 = ( ! [A: $i,X: $i] :
% 1.49/1.28 ( ( in @ X @ ( powerset @ A ) )
% 1.49/1.28 => ! [Y: $i] :
% 1.49/1.28 ( ( in @ Y @ ( powerset @ A ) )
% 1.49/1.28 => ! [Xx: $i] :
% 1.49/1.28 ( ( in @ Xx @ A )
% 1.49/1.28 => ( ~ ( in @ Xx @ X )
% 1.49/1.28 => ( ~ ( in @ Xx @ Y )
% 1.49/1.28 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 1.49/1.28
% 1.49/1.28 thf(demorgan2b2,conjecture,
% 1.49/1.28 ( setminusI
% 1.49/1.28 => ( setminusER
% 1.49/1.28 => ( binunionTEcontra
% 1.49/1.28 => ! [A: $i,X: $i] :
% 1.49/1.28 ( ( in @ X @ ( powerset @ A ) )
% 1.49/1.28 => ! [Y: $i] :
% 1.49/1.28 ( ( in @ Y @ ( powerset @ A ) )
% 1.49/1.28 => ! [Xx: $i] :
% 1.49/1.28 ( ( in @ Xx @ A )
% 1.49/1.28 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 1.49/1.28 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 1.49/1.28 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ).
% 1.49/1.28 ------------------------
% 1.64/1.30 % (27519)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27227 for (2999ds/18Mi)
% 1.64/1.30 % (27516)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27227 for (2999ds/2Mi)
% 1.64/1.30 % (27516)Instruction limit reached!
% 1.64/1.30 % (27516)------------------------------
% 1.64/1.30 % (27516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (27516)Termination reason: Unknown
% 1.64/1.30 % (27516)Termination phase: Property scanning
% 1.64/1.30
% 1.64/1.30 % (27516)Memory used [KB]: 1023
% 1.64/1.30 % (27516)Time elapsed: 0.002 s
% 1.64/1.30 % (27516)Instructions burned: 3 (million)
% 1.64/1.30 % (27516)------------------------------
% 1.64/1.30 % (27516)------------------------------
% 1.64/1.30 % (27513)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27227 for (2999ds/183Mi)
% 1.64/1.30 % (27519)Instruction limit reached!
% 1.64/1.30 % (27519)------------------------------
% 1.64/1.30 % (27519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (27519)Termination reason: Unknown
% 1.64/1.30 % (27519)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (27519)Memory used [KB]: 5628
% 1.64/1.30 % (27519)Time elapsed: 0.008 s
% 1.64/1.30 % (27519)Instructions burned: 20 (million)
% 1.64/1.30 % (27519)------------------------------
% 1.64/1.30 % (27519)------------------------------
% 1.64/1.30 % (27514)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_27227 for (2999ds/4Mi)
% 1.64/1.30 % (27515)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_27227 for (2999ds/27Mi)
% 1.64/1.30 % (27517)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_27227 for (2999ds/2Mi)
% 1.64/1.30 % (27518)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_27227 for (2999ds/275Mi)
% 1.64/1.31 % (27517)Instruction limit reached!
% 1.64/1.31 % (27517)------------------------------
% 1.64/1.31 % (27517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (27517)Termination reason: Unknown
% 1.64/1.31 % (27517)Termination phase: shuffling
% 1.64/1.31
% 1.64/1.31 % (27517)Memory used [KB]: 895
% 1.64/1.31 % (27517)Time elapsed: 0.003 s
% 1.64/1.31 % (27517)Instructions burned: 2 (million)
% 1.64/1.31 % (27517)------------------------------
% 1.64/1.31 % (27517)------------------------------
% 1.64/1.31 % (27514)Instruction limit reached!
% 1.64/1.31 % (27514)------------------------------
% 1.64/1.31 % (27514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (27514)Termination reason: Unknown
% 1.64/1.31 % (27514)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (27514)Memory used [KB]: 5500
% 1.64/1.31 % (27514)Time elapsed: 0.005 s
% 1.64/1.31 % (27514)Instructions burned: 5 (million)
% 1.64/1.31 % (27514)------------------------------
% 1.64/1.31 % (27514)------------------------------
% 1.64/1.31 % (27520)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27227 for (2999ds/3Mi)
% 1.64/1.31 % (27520)Instruction limit reached!
% 1.64/1.31 % (27520)------------------------------
% 1.64/1.31 % (27520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (27520)Termination reason: Unknown
% 1.64/1.31 % (27520)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (27520)Memory used [KB]: 5500
% 1.64/1.31 % (27520)Time elapsed: 0.003 s
% 1.64/1.31 % (27520)Instructions burned: 4 (million)
% 1.64/1.31 % (27520)------------------------------
% 1.64/1.31 % (27520)------------------------------
% 1.64/1.31 % (27518)First to succeed.
% 1.64/1.31 % (27521)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_27227 for (2999ds/37Mi)
% 1.64/1.31 % (27513)Also succeeded, but the first one will report.
% 1.64/1.32 % (27518)Refutation found. Thanks to Tanya!
% 1.64/1.32 % SZS status Theorem for DTF2THF_27227
% 1.64/1.32 % SZS output start Proof for DTF2THF_27227
% 1.64/1.32 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.32 thf(func_def_1, type, powerset: $i > $i).
% 1.64/1.32 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.64/1.32 thf(func_def_3, type, setminus: $i > $i > $i).
% 1.64/1.32 thf(f99,plain,(
% 1.64/1.32 $false),
% 1.64/1.32 inference(subsumption_resolution,[status(thm)],[f98,f47])).
% 1.64/1.32 thf(f47,plain,(
% 1.64/1.32 ($true = (in @ sK3 @ sK0))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f29,plain,(
% 1.64/1.32 (setminusER = $true) & ((($true = (in @ sK2 @ (powerset @ sK0))) & (($true = (in @ sK3 @ (setminus @ sK0 @ sK2))) & ((in @ sK3 @ (setminus @ sK0 @ sK1)) = $true) & ($true != (in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)))) & ($true = (in @ sK3 @ sK0)))) & ($true = (in @ sK1 @ (powerset @ sK0)))) & (setminusI = $true) & (binunionTEcontra = $true)),
% 1.64/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f28,f27,f26])).
% 1.64/1.32 thf(f26,plain,(
% 1.64/1.32 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ X0 @ X2))) & ($true = (in @ X3 @ (setminus @ X0 @ X1))) & ($true != (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) & ($true = (in @ X3 @ X0)))) & ($true = (in @ X1 @ (powerset @ X0)))) => (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK0))) & ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ sK0 @ X2))) & ((in @ X3 @ (setminus @ sK0 @ sK1)) = $true) & ((in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ X2))) != $true) & ($true = (in @ X3 @ sK0)))) & ($true = (in @ sK1 @ (powerset @ sK0))))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f27,plain,(
% 1.64/1.32 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK0))) & ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ sK0 @ X2))) & ((in @ X3 @ (setminus @ sK0 @ sK1)) = $true) & ((in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ X2))) != $true) & ($true = (in @ X3 @ sK0)))) => (($true = (in @ sK2 @ (powerset @ sK0))) & ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ sK0 @ sK2))) & ((in @ X3 @ (setminus @ sK0 @ sK1)) = $true) & ($true != (in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)))) & ($true = (in @ X3 @ sK0))))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f28,plain,(
% 1.64/1.32 ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ sK0 @ sK2))) & ((in @ X3 @ (setminus @ sK0 @ sK1)) = $true) & ($true != (in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)))) & ($true = (in @ X3 @ sK0))) => (($true = (in @ sK3 @ (setminus @ sK0 @ sK2))) & ((in @ sK3 @ (setminus @ sK0 @ sK1)) = $true) & ($true != (in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)))) & ($true = (in @ sK3 @ sK0)))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f25,plain,(
% 1.64/1.32 (setminusER = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ X0 @ X2))) & ($true = (in @ X3 @ (setminus @ X0 @ X1))) & ($true != (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) & ($true = (in @ X3 @ X0)))) & ($true = (in @ X1 @ (powerset @ X0)))) & (setminusI = $true) & (binunionTEcontra = $true)),
% 1.64/1.32 inference(rectify,[status(thm)],[f21])).
% 1.64/1.32 thf(f21,plain,(
% 1.64/1.32 (setminusER = $true) & ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ X1 @ X2))) & ($true = (in @ X3 @ (setminus @ X1 @ X0))) & ($true != (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ($true = (in @ X3 @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) & (setminusI = $true) & (binunionTEcontra = $true)),
% 1.64/1.32 inference(flattening,[status(thm)],[f20])).
% 1.64/1.32 thf(f20,plain,(
% 1.64/1.32 ((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((($true != (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ($true = (in @ X3 @ (setminus @ X1 @ X2)))) & ($true = (in @ X3 @ (setminus @ X1 @ X0)))) & ($true = (in @ X3 @ X1))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ($true = (in @ X0 @ (powerset @ X1)))) & (binunionTEcontra = $true)) & (setminusER = $true)) & (setminusI = $true)),
% 1.64/1.32 inference(ennf_transformation,[status(thm)],[f12])).
% 1.64/1.32 thf(f12,plain,(
% 1.64/1.32 ~((setminusI = $true) => ((setminusER = $true) => ((binunionTEcontra = $true) => ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => (($true = (in @ X3 @ (setminus @ X1 @ X0))) => (($true = (in @ X3 @ (setminus @ X1 @ X2))) => ($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))))))))))))),
% 1.64/1.32 inference(fool_elimination,[status(thm)],[f11])).
% 1.64/1.32 thf(f11,plain,(
% 1.64/1.32 ~(setminusI => (setminusER => (binunionTEcontra => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ X0)) => ((in @ X3 @ (setminus @ X1 @ X2)) => (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))))))))))),
% 1.64/1.32 inference(rectify,[status(thm)],[f5])).
% 1.64/1.32 thf(f5,negated_conjecture,(
% 1.64/1.32 ~(setminusI => (setminusER => (binunionTEcontra => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ X3)) => ((in @ X2 @ (setminus @ X0 @ X4)) => (in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4)))))))))))),
% 1.64/1.32 inference(negated_conjecture,[status(cth)],[f4])).
% 1.64/1.32 thf(f4,conjecture,(
% 1.64/1.32 setminusI => (setminusER => (binunionTEcontra => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ X3)) => ((in @ X2 @ (setminus @ X0 @ X4)) => (in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4))))))))))),
% 1.64/1.32 file('/export/starexec/sandbox/tmp/tmp.m84IBzELSV/DTF2THF_27227.p',demorgan2b2)).
% 1.64/1.32 thf(f98,plain,(
% 1.64/1.32 ($true != (in @ sK3 @ sK0))),
% 1.64/1.32 inference(subsumption_resolution,[status(thm)],[f97,f46])).
% 1.64/1.32 thf(f46,plain,(
% 1.64/1.32 ($true = (in @ sK1 @ (powerset @ sK0)))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f97,plain,(
% 1.64/1.32 ($true != (in @ sK1 @ (powerset @ sK0))) | ($true != (in @ sK3 @ sK0))),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.64/1.32 thf(f96,plain,(
% 1.64/1.32 ($true != (in @ sK1 @ (powerset @ sK0))) | ($true != $true) | ($true != (in @ sK3 @ sK0))),
% 1.64/1.32 inference(superposition,[status(thm)],[f95,f51])).
% 1.64/1.32 thf(f51,plain,(
% 1.64/1.32 ($true = (in @ sK2 @ (powerset @ sK0)))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f95,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (($true != (in @ sK2 @ (powerset @ X0))) | ($true != (in @ sK1 @ (powerset @ X0))) | ($true != (in @ sK3 @ X0))) )),
% 1.64/1.32 inference(subsumption_resolution,[status(thm)],[f94,f86])).
% 1.64/1.32 thf(f86,plain,(
% 1.64/1.32 ($true != (in @ sK3 @ sK2))),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.64/1.32 thf(f85,plain,(
% 1.64/1.32 ($true != $true) | ($true != (in @ sK3 @ sK2))),
% 1.64/1.32 inference(superposition,[status(thm)],[f82,f50])).
% 1.64/1.32 thf(f50,plain,(
% 1.64/1.32 ($true = (in @ sK3 @ (setminus @ sK0 @ sK2)))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f82,plain,(
% 1.64/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) | ($true != (in @ X0 @ X2))) )),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.64/1.32 thf(f74,plain,(
% 1.64/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) | ($true != (in @ X0 @ X2)) | ($true != $true)) )),
% 1.64/1.32 inference(definition_unfolding,[status(thm)],[f62,f52])).
% 1.64/1.32 thf(f52,plain,(
% 1.64/1.32 (setminusER = $true)),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f62,plain,(
% 1.64/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X2)) | ((in @ X0 @ (setminus @ X1 @ X2)) != $true) | (setminusER != $true)) )),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f39])).
% 1.64/1.32 thf(f39,plain,(
% 1.64/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) | ((in @ X0 @ (setminus @ X1 @ X2)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | (($true = (in @ sK8 @ sK10)) & ($true = (in @ sK8 @ (setminus @ sK9 @ sK10)))))),
% 1.64/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f37,f38])).
% 1.64/1.32 thf(f38,plain,(
% 1.64/1.32 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) = $true) & ($true = (in @ X3 @ (setminus @ X4 @ X5)))) => (($true = (in @ sK8 @ sK10)) & ($true = (in @ sK8 @ (setminus @ sK9 @ sK10))))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f37,plain,(
% 1.64/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) | ((in @ X0 @ (setminus @ X1 @ X2)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) = $true) & ($true = (in @ X3 @ (setminus @ X4 @ X5)))))),
% 1.64/1.32 inference(rectify,[status(thm)],[f36])).
% 1.64/1.32 thf(f36,plain,(
% 1.64/1.32 (! [X0 : $i,X2 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ($true != (in @ X0 @ (setminus @ X2 @ X1)))) | (setminusER != $true)) & ((setminusER = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X0 @ X1)) & ($true = (in @ X0 @ (setminus @ X2 @ X1)))))),
% 1.64/1.32 inference(nnf_transformation,[status(thm)],[f22])).
% 1.64/1.32 thf(f22,plain,(
% 1.64/1.32 ! [X0 : $i,X2 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ($true != (in @ X0 @ (setminus @ X2 @ X1)))) <=> (setminusER = $true)),
% 1.64/1.32 inference(ennf_transformation,[status(thm)],[f17])).
% 1.64/1.32 thf(f17,plain,(
% 1.64/1.32 ! [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X0 @ (setminus @ X2 @ X1))) => ($true != (in @ X0 @ X1))) <=> (setminusER = $true)),
% 1.64/1.32 inference(flattening,[status(thm)],[f8])).
% 1.64/1.32 thf(f8,plain,(
% 1.64/1.32 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setminus @ X2 @ X1))) => ~($true = (in @ X0 @ X1))) <=> (setminusER = $true)),
% 1.64/1.32 inference(fool_elimination,[status(thm)],[f7])).
% 1.64/1.32 thf(f7,plain,(
% 1.64/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X2 @ X1)) => ~(in @ X0 @ X1)) = setminusER)),
% 1.64/1.32 inference(rectify,[status(thm)],[f2])).
% 1.64/1.32 thf(f2,axiom,(
% 1.64/1.32 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 1.64/1.32 file('/export/starexec/sandbox/tmp/tmp.m84IBzELSV/DTF2THF_27227.p',setminusER)).
% 1.64/1.32 thf(f94,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (($true != (in @ sK1 @ (powerset @ X0))) | ($true = (in @ sK3 @ sK2)) | ($true != (in @ sK2 @ (powerset @ X0))) | ($true != (in @ sK3 @ X0))) )),
% 1.64/1.32 inference(subsumption_resolution,[status(thm)],[f93,f87])).
% 1.64/1.32 thf(f87,plain,(
% 1.64/1.32 ($true != (in @ sK3 @ sK1))),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.64/1.32 thf(f84,plain,(
% 1.64/1.32 ($true != (in @ sK3 @ sK1)) | ($true != $true)),
% 1.64/1.32 inference(superposition,[status(thm)],[f82,f49])).
% 1.64/1.32 thf(f49,plain,(
% 1.64/1.32 ((in @ sK3 @ (setminus @ sK0 @ sK1)) = $true)),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f93,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (($true != (in @ sK1 @ (powerset @ X0))) | ($true != (in @ sK3 @ X0)) | ($true != (in @ sK2 @ (powerset @ X0))) | ($true = (in @ sK3 @ sK1)) | ($true = (in @ sK3 @ sK2))) )),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.64/1.32 thf(f92,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (($true != (in @ sK2 @ (powerset @ X0))) | ($true != (in @ sK1 @ (powerset @ X0))) | ($true != (in @ sK3 @ X0)) | ($true != $true) | ($true = (in @ sK3 @ sK1)) | ($true = (in @ sK3 @ sK2))) )),
% 1.64/1.32 inference(superposition,[status(thm)],[f83,f91])).
% 1.64/1.32 thf(f91,plain,(
% 1.64/1.32 ((in @ sK3 @ (binunion @ sK1 @ sK2)) = $true)),
% 1.64/1.32 inference(subsumption_resolution,[status(thm)],[f90,f47])).
% 1.64/1.32 thf(f90,plain,(
% 1.64/1.32 ($true != (in @ sK3 @ sK0)) | ((in @ sK3 @ (binunion @ sK1 @ sK2)) = $true)),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.64/1.32 thf(f89,plain,(
% 1.64/1.32 ((in @ sK3 @ (binunion @ sK1 @ sK2)) = $true) | ($true != $true) | ($true != (in @ sK3 @ sK0))),
% 1.64/1.32 inference(superposition,[status(thm)],[f48,f81])).
% 1.64/1.32 thf(f81,plain,(
% 1.64/1.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ (setminus @ X5 @ X4))) | ((in @ X3 @ X5) != $true) | ((in @ X3 @ X4) = $true)) )),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.64/1.32 thf(f80,plain,(
% 1.64/1.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ((in @ X3 @ X5) != $true) | ($true = (in @ X3 @ (setminus @ X5 @ X4))) | ($true != $true)) )),
% 1.64/1.32 inference(definition_unfolding,[status(thm)],[f63,f45])).
% 1.64/1.32 thf(f45,plain,(
% 1.64/1.32 (setminusI = $true)),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f63,plain,(
% 1.64/1.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ($true = (in @ X3 @ (setminus @ X5 @ X4))) | ((in @ X3 @ X5) != $true) | (setminusI != $true)) )),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f43])).
% 1.64/1.32 thf(f43,plain,(
% 1.64/1.32 ((setminusI = $true) | (($true != (in @ sK11 @ sK12)) & ($true != (in @ sK11 @ (setminus @ sK13 @ sK12))) & ($true = (in @ sK11 @ sK13)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ($true = (in @ X3 @ (setminus @ X5 @ X4))) | ((in @ X3 @ X5) != $true)) | (setminusI != $true))),
% 1.64/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f41,f42])).
% 1.64/1.32 thf(f42,plain,(
% 1.64/1.32 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) & ($true != (in @ X0 @ (setminus @ X2 @ X1))) & ($true = (in @ X0 @ X2))) => (($true != (in @ sK11 @ sK12)) & ($true != (in @ sK11 @ (setminus @ sK13 @ sK12))) & ($true = (in @ sK11 @ sK13)))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f41,plain,(
% 1.64/1.32 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) & ($true != (in @ X0 @ (setminus @ X2 @ X1))) & ($true = (in @ X0 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ($true = (in @ X3 @ (setminus @ X5 @ X4))) | ((in @ X3 @ X5) != $true)) | (setminusI != $true))),
% 1.64/1.32 inference(rectify,[status(thm)],[f40])).
% 1.64/1.32 thf(f40,plain,(
% 1.64/1.32 ((setminusI = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) != $true) & ($true != (in @ X2 @ (setminus @ X1 @ X0))) & ((in @ X2 @ X1) = $true))) & (! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ($true = (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X1) != $true)) | (setminusI != $true))),
% 1.64/1.32 inference(nnf_transformation,[status(thm)],[f24])).
% 1.64/1.32 thf(f24,plain,(
% 1.64/1.32 (setminusI = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ($true = (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X1) != $true))),
% 1.64/1.32 inference(flattening,[status(thm)],[f23])).
% 1.64/1.32 thf(f23,plain,(
% 1.64/1.32 (setminusI = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((($true = (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X0) = $true)) | ((in @ X2 @ X1) != $true))),
% 1.64/1.32 inference(ennf_transformation,[status(thm)],[f16])).
% 1.64/1.32 thf(f16,plain,(
% 1.64/1.32 (setminusI = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X2 @ X1) = $true) => (((in @ X2 @ X0) != $true) => ($true = (in @ X2 @ (setminus @ X1 @ X0)))))),
% 1.64/1.32 inference(flattening,[status(thm)],[f10])).
% 1.64/1.32 thf(f10,plain,(
% 1.64/1.32 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) => (~((in @ X2 @ X0) = $true) => ($true = (in @ X2 @ (setminus @ X1 @ X0)))))),
% 1.64/1.32 inference(fool_elimination,[status(thm)],[f9])).
% 1.64/1.32 thf(f9,plain,(
% 1.64/1.32 (setminusI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (~(in @ X2 @ X0) => (in @ X2 @ (setminus @ X1 @ X0)))))),
% 1.64/1.32 inference(rectify,[status(thm)],[f1])).
% 1.64/1.32 thf(f1,axiom,(
% 1.64/1.32 (setminusI = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))),
% 1.64/1.32 file('/export/starexec/sandbox/tmp/tmp.m84IBzELSV/DTF2THF_27227.p',setminusI)).
% 1.64/1.32 thf(f48,plain,(
% 1.64/1.32 ($true != (in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f83,plain,(
% 1.64/1.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ X2)) | ($true = (in @ X3 @ X0))) )),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.64/1.32 thf(f67,plain,(
% 1.64/1.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true = (in @ X3 @ X0)) | ($true != $true) | ($true = (in @ X3 @ X2)) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != (in @ X3 @ X1))) )),
% 1.64/1.32 inference(definition_unfolding,[status(thm)],[f59,f44])).
% 1.64/1.32 thf(f44,plain,(
% 1.64/1.32 (binunionTEcontra = $true)),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f59,plain,(
% 1.64/1.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ X2)) | ($true = (in @ X3 @ X0)) | ($true != (in @ X0 @ (powerset @ X1))) | (binunionTEcontra != $true)) )),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f35])).
% 1.64/1.32 thf(f35,plain,(
% 1.64/1.32 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ! [X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ X2)) | ($true = (in @ X3 @ X0)))) | ($true != (in @ X0 @ (powerset @ X1)))) | (binunionTEcontra != $true)) & ((binunionTEcontra = $true) | ((($true = (in @ sK6 @ (powerset @ sK5))) & (($true = (in @ sK7 @ (binunion @ sK4 @ sK6))) & ($true = (in @ sK7 @ sK5)) & ((in @ sK7 @ sK6) != $true) & ((in @ sK7 @ sK4) != $true))) & ($true = (in @ sK4 @ (powerset @ sK5)))))),
% 1.64/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f31,f34,f33,f32])).
% 1.64/1.32 thf(f32,plain,(
% 1.64/1.32 ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (($true = (in @ X6 @ (powerset @ X5))) & ? [X7 : $i] : (((in @ X7 @ (binunion @ X4 @ X6)) = $true) & ($true = (in @ X7 @ X5)) & ($true != (in @ X7 @ X6)) & ((in @ X7 @ X4) != $true))) & ($true = (in @ X4 @ (powerset @ X5)))) => (? [X6 : $i] : (($true = (in @ X6 @ (powerset @ sK5))) & ? [X7 : $i] : (((in @ X7 @ (binunion @ sK4 @ X6)) = $true) & ($true = (in @ X7 @ sK5)) & ($true != (in @ X7 @ X6)) & ($true != (in @ X7 @ sK4)))) & ($true = (in @ sK4 @ (powerset @ sK5))))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f33,plain,(
% 1.64/1.32 ? [X6 : $i] : (($true = (in @ X6 @ (powerset @ sK5))) & ? [X7 : $i] : (((in @ X7 @ (binunion @ sK4 @ X6)) = $true) & ($true = (in @ X7 @ sK5)) & ($true != (in @ X7 @ X6)) & ($true != (in @ X7 @ sK4)))) => (($true = (in @ sK6 @ (powerset @ sK5))) & ? [X7 : $i] : (($true = (in @ X7 @ (binunion @ sK4 @ sK6))) & ($true = (in @ X7 @ sK5)) & ($true != (in @ X7 @ sK6)) & ($true != (in @ X7 @ sK4))))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f34,plain,(
% 1.64/1.32 ? [X7 : $i] : (($true = (in @ X7 @ (binunion @ sK4 @ sK6))) & ($true = (in @ X7 @ sK5)) & ($true != (in @ X7 @ sK6)) & ($true != (in @ X7 @ sK4))) => (($true = (in @ sK7 @ (binunion @ sK4 @ sK6))) & ($true = (in @ sK7 @ sK5)) & ((in @ sK7 @ sK6) != $true) & ((in @ sK7 @ sK4) != $true))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f31,plain,(
% 1.64/1.32 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ! [X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ X2)) | ($true = (in @ X3 @ X0)))) | ($true != (in @ X0 @ (powerset @ X1)))) | (binunionTEcontra != $true)) & ((binunionTEcontra = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (($true = (in @ X6 @ (powerset @ X5))) & ? [X7 : $i] : (((in @ X7 @ (binunion @ X4 @ X6)) = $true) & ($true = (in @ X7 @ X5)) & ($true != (in @ X7 @ X6)) & ((in @ X7 @ X4) != $true))) & ($true = (in @ X4 @ (powerset @ X5)))))),
% 1.64/1.32 inference(rectify,[status(thm)],[f30])).
% 1.64/1.32 thf(f30,plain,(
% 1.64/1.32 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ! [X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ X2)) | ($true = (in @ X3 @ X0)))) | ($true != (in @ X0 @ (powerset @ X1)))) | (binunionTEcontra != $true)) & ((binunionTEcontra = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) & ($true = (in @ X3 @ X1)) & ($true != (in @ X3 @ X2)) & ($true != (in @ X3 @ X0)))) & ($true = (in @ X0 @ (powerset @ X1)))))),
% 1.64/1.32 inference(nnf_transformation,[status(thm)],[f19])).
% 1.64/1.32 thf(f19,plain,(
% 1.64/1.32 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ! [X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ X2)) | ($true = (in @ X3 @ X0)))) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (binunionTEcontra = $true)),
% 1.64/1.32 inference(flattening,[status(thm)],[f18])).
% 1.64/1.32 thf(f18,plain,(
% 1.64/1.32 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ($true = (in @ X3 @ X2))) | ($true = (in @ X3 @ X0))) | ($true != (in @ X3 @ X1))) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (binunionTEcontra = $true)),
% 1.64/1.32 inference(ennf_transformation,[status(thm)],[f15])).
% 1.64/1.32 thf(f15,plain,(
% 1.64/1.32 ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => (($true != (in @ X3 @ X0)) => (($true != (in @ X3 @ X2)) => ((in @ X3 @ (binunion @ X0 @ X2)) != $true)))))) <=> (binunionTEcontra = $true)),
% 1.64/1.32 inference(flattening,[status(thm)],[f14])).
% 1.64/1.32 thf(f14,plain,(
% 1.64/1.32 ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => (~($true = (in @ X3 @ X0)) => (~($true = (in @ X3 @ X2)) => ~((in @ X3 @ (binunion @ X0 @ X2)) = $true)))))) <=> (binunionTEcontra = $true)),
% 1.64/1.32 inference(fool_elimination,[status(thm)],[f13])).
% 1.64/1.32 thf(f13,plain,(
% 1.64/1.32 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => (~(in @ X3 @ X0) => (~(in @ X3 @ X2) => ~(in @ X3 @ (binunion @ X0 @ X2))))))) = binunionTEcontra)),
% 1.64/1.32 inference(rectify,[status(thm)],[f3])).
% 1.64/1.32 thf(f3,axiom,(
% 1.64/1.32 (! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X3) => (~(in @ X2 @ X4) => ~(in @ X2 @ (binunion @ X3 @ X4))))))) = binunionTEcontra)),
% 1.64/1.32 file('/export/starexec/sandbox/tmp/tmp.m84IBzELSV/DTF2THF_27227.p',binunionTEcontra)).
% 1.64/1.32 % SZS output end Proof for DTF2THF_27227
% 1.64/1.32 % (27518)------------------------------
% 1.64/1.32 % (27518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (27518)Termination reason: Refutation
% 1.64/1.32
% 1.64/1.32 % (27518)Memory used [KB]: 5628
% 1.64/1.32 % (27518)Time elapsed: 0.011 s
% 1.64/1.32 % (27518)Instructions burned: 9 (million)
% 1.64/1.32 % (27518)------------------------------
% 1.64/1.32 % (27518)------------------------------
% 1.64/1.32 % (27512)Success in time 0.026 s
%------------------------------------------------------------------------------