%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU756^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:57 AM UTC 2026
% Result : Theorem 1.66s 1.32s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 1104 ( 282 equ; 0 cnn)
% Maximal formula atoms : 14 ( 16 avg)
% Number of connectives : 1356 ( 124 ~; 95 |; 97 &; 976 @)
% ( 7 <=>; 57 =>; 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 : 25 ( 22 usr; 19 con; 0-2 aty)
% Number of variables : 174 ( 0 ^; 120 !; 54 ?; 174 :)
% 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,
binintersect: $i > $i > $i ).
thf(func_def_7,type,
setminus: $i > $i > $i ).
thf(f86,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f85,f79]) ).
thf(f79,plain,
( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $true != $true )
| ( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f74,f43]) ).
thf(f43,plain,
( $true
= ( in @ sK3 @ ( binintersect @ ( setminus @ sK1 @ sK0 ) @ ( setminus @ sK1 @ sK2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( binintersectER = $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
& ( ( in @ sK3 @ ( setminus @ sK1 @ ( binunion @ sK0 @ sK2 ) ) )
!= $true )
& ( $true
= ( in @ sK3 @ ( binintersect @ ( setminus @ sK1 @ sK0 ) @ ( setminus @ sK1 @ sK2 ) ) ) )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true )
& ( binintersectEL = $true )
& ( demorgan2b2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f16,f23,f22,f21]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK1 @ ( binunion @ sK0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ sK1 @ sK0 ) @ ( setminus @ sK1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ sK1 )
= $true ) ) )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK1 @ ( binunion @ sK0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ sK1 @ sK0 ) @ ( setminus @ sK1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ sK1 )
= $true ) ) )
=> ( ( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
& ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ sK1 @ ( binunion @ sK0 @ sK2 ) ) ) )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ sK1 @ sK0 ) @ ( setminus @ sK1 @ sK2 ) ) )
= $true )
& ( ( in @ X3 @ sK1 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ sK1 @ ( binunion @ sK0 @ sK2 ) ) ) )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ sK1 @ sK0 ) @ ( setminus @ sK1 @ sK2 ) ) )
= $true )
& ( ( in @ X3 @ sK1 )
= $true ) )
=> ( ( ( in @ sK3 @ ( setminus @ sK1 @ ( binunion @ sK0 @ sK2 ) ) )
!= $true )
& ( $true
= ( in @ sK3 @ ( binintersect @ ( setminus @ sK1 @ sK0 ) @ ( setminus @ sK1 @ sK2 ) ) ) )
& ( ( in @ sK3 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( binintersectER = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binintersectEL = $true )
& ( demorgan2b2 = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( demorgan2b2 = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( binintersectEL = $true )
=> ( ( binintersectER = $true )
=> ( ( demorgan2b2 = $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 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
=> ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( binintersectEL
=> ( binintersectER
=> ( demorgan2b2
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( binintersectEL
=> ( binintersectER
=> ( demorgan2b2
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) )
=> ( in @ X2 @ ( setminus @ X0 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( binintersectEL
=> ( binintersectER
=> ( demorgan2b2
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) )
=> ( in @ X2 @ ( setminus @ X0 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4eyavceOS4/DTF2THF_8679.p',demorgan2b) ).
thf(f74,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f47,f40]) ).
thf(f40,plain,
binintersectEL = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f47,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true )
| ( binintersectEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( binintersectEL = $true )
| ( ( ( in @ sK4 @ ( binintersect @ sK5 @ sK6 ) )
= $true )
& ( ( in @ sK4 @ sK5 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f26,f27]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
& ( ( in @ X0 @ X1 )
!= $true ) )
=> ( ( ( in @ sK4 @ ( binintersect @ sK5 @ sK6 ) )
= $true )
& ( ( in @ sK4 @ sK5 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
& ( ( in @ X0 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
& ( ( in @ X0 @ X1 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X1 )
= $true ) )
| ( binintersectEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( binintersectEL = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( ( in @ X0 @ X1 )
= $true ) )
<=> ( binintersectEL = $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( binintersectEL
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4eyavceOS4/DTF2THF_8679.p',binintersectEL) ).
thf(f85,plain,
( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f84,f45]) ).
thf(f45,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f84,plain,
( ( $true
!= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f83,f78]) ).
thf(f78,plain,
( ( in @ sK3 @ ( setminus @ sK1 @ sK2 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true != $true )
| ( ( in @ sK3 @ ( setminus @ sK1 @ sK2 ) )
= $true ) ),
inference(superposition,[status(thm)],[f73,f43]) ).
thf(f73,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f59,f46]) ).
thf(f46,plain,
binintersectER = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f59,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true )
| ( binintersectER != $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ( ( ( in @ sK11 @ sK12 )
!= $true )
& ( ( in @ sK11 @ ( binintersect @ sK13 @ sK12 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f36,f37]) ).
thf(f37,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
& ( ( in @ X3 @ ( binintersect @ X5 @ X4 ) )
= $true ) )
=> ( ( ( in @ sK11 @ sK12 )
!= $true )
& ( ( in @ sK11 @ ( binintersect @ sK13 @ sK12 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
& ( ( in @ X3 @ ( binintersect @ X5 @ X4 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) )
<=> ( binintersectER = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( binintersectER = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) )
= binintersectER ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) )
= binintersectER ),
file('/export/starexec/sandbox2/tmp/tmp.4eyavceOS4/DTF2THF_8679.p',binintersectER) ).
thf(f83,plain,
( ( ( in @ sK3 @ ( setminus @ sK1 @ sK2 ) )
!= $true )
| ( $true
!= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f82,f41]) ).
thf(f41,plain,
( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f82,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
!= $true )
| ( ( in @ sK3 @ ( setminus @ sK1 @ sK2 ) )
!= $true )
| ( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
!= $true )
| ( $true
!= ( in @ sK2 @ ( powerset @ sK1 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f81,f42]) ).
thf(f42,plain,
( ( in @ sK3 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f81,plain,
( ( ( in @ sK3 @ sK1 )
!= $true )
| ( ( in @ sK0 @ ( powerset @ sK1 ) )
!= $true )
| ( $true
!= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ( ( in @ sK3 @ ( setminus @ sK1 @ sK2 ) )
!= $true )
| ( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( in @ sK3 @ ( setminus @ sK1 @ sK2 ) )
!= $true )
| ( $true
!= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ( ( in @ sK3 @ sK1 )
!= $true )
| ( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
!= $true )
| ( ( in @ sK0 @ ( powerset @ sK1 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f44,f75]) ).
thf(f75,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X7 @ ( setminus @ X5 @ ( binunion @ X4 @ X6 ) ) ) )
| ( ( in @ X7 @ ( setminus @ X5 @ X6 ) )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ ( setminus @ X5 @ X4 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( $true
= ( in @ X7 @ ( setminus @ X5 @ ( binunion @ X4 @ X6 ) ) ) )
| ( ( in @ X7 @ ( setminus @ X5 @ X6 ) )
!= $true )
| ( ( in @ X7 @ ( setminus @ X5 @ X4 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f50,f39]) ).
thf(f39,plain,
demorgan2b2 = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f50,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ ( setminus @ X5 @ X4 ) )
!= $true )
| ( ( in @ X7 @ ( setminus @ X5 @ X6 ) )
!= $true )
| ( $true
= ( in @ X7 @ ( setminus @ X5 @ ( binunion @ X4 @ X6 ) ) ) )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( demorgan2b2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( demorgan2b2 = $true )
| ( ( ( in @ sK10 @ sK8 )
= $true )
& ( $true
= ( in @ sK10 @ ( setminus @ sK8 @ sK7 ) ) )
& ( ( in @ sK10 @ ( setminus @ sK8 @ sK9 ) )
= $true )
& ( $true
!= ( in @ sK10 @ ( setminus @ sK8 @ ( binunion @ sK7 @ sK9 ) ) ) )
& ( $true
= ( in @ sK9 @ ( powerset @ sK8 ) ) )
& ( ( in @ sK7 @ ( powerset @ sK8 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ ( setminus @ X5 @ X4 ) )
!= $true )
| ( ( in @ X7 @ ( setminus @ X5 @ X6 ) )
!= $true )
| ( $true
= ( in @ X7 @ ( setminus @ X5 @ ( binunion @ X4 @ X6 ) ) ) ) )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true ) )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true ) )
| ( demorgan2b2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f30,f33,f32,f31]) ).
thf(f31,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ sK8 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK8 @ sK7 ) )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK8 @ X2 ) ) )
& ( ( in @ X3 @ ( setminus @ sK8 @ ( binunion @ sK7 @ X2 ) ) )
!= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK8 ) ) ) )
& ( ( in @ sK7 @ ( powerset @ sK8 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ sK8 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK8 @ sK7 ) )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK8 @ X2 ) ) )
& ( ( in @ X3 @ ( setminus @ sK8 @ ( binunion @ sK7 @ X2 ) ) )
!= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK8 ) ) ) )
=> ( ? [X3: $i] :
( ( ( in @ X3 @ sK8 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK8 @ sK7 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ sK8 @ sK9 ) )
= $true )
& ( $true
!= ( in @ X3 @ ( setminus @ sK8 @ ( binunion @ sK7 @ sK9 ) ) ) ) )
& ( $true
= ( in @ sK9 @ ( powerset @ sK8 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK8 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK8 @ sK7 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ sK8 @ sK9 ) )
= $true )
& ( $true
!= ( in @ X3 @ ( setminus @ sK8 @ ( binunion @ sK7 @ sK9 ) ) ) ) )
=> ( ( ( in @ sK10 @ sK8 )
= $true )
& ( $true
= ( in @ sK10 @ ( setminus @ sK8 @ sK7 ) ) )
& ( ( in @ sK10 @ ( setminus @ sK8 @ sK9 ) )
= $true )
& ( $true
!= ( in @ sK10 @ ( setminus @ sK8 @ ( binunion @ sK7 @ sK9 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ( ( demorgan2b2 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ ( setminus @ X5 @ X4 ) )
!= $true )
| ( ( in @ X7 @ ( setminus @ X5 @ X6 ) )
!= $true )
| ( $true
= ( in @ X7 @ ( setminus @ X5 @ ( binunion @ X4 @ X6 ) ) ) ) )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true ) )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true ) )
| ( demorgan2b2 != $true ) ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( demorgan2b2 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( demorgan2b2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( demorgan2b2 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
| ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
<=> ( demorgan2b2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
= $true )
=> ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ) ) )
<=> ( demorgan2b2 = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [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 ) ) ) ) ) ) ) )
= demorgan2b2 ),
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 @ ( setminus @ X0 @ X3 ) )
=> ( ( in @ X2 @ ( setminus @ X0 @ X4 ) )
=> ( in @ X2 @ ( setminus @ X0 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) )
= demorgan2b2 ),
file('/export/starexec/sandbox2/tmp/tmp.4eyavceOS4/DTF2THF_8679.p',demorgan2b2) ).
thf(f44,plain,
( ( in @ sK3 @ ( setminus @ sK1 @ ( binunion @ sK0 @ sK2 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU756^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:33:12 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU756^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Typed Set Theory - Laws for Typed Sets - DeMorgan Laws
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.30/0.46 % (! x:i.in x A -> in x (binintersect (setminus A X) (setminus A Y))
% 0.30/0.46 % -> in x (setminus A (binunion X Y)))))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC258l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 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 v4.0.0, 0.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 12 ( 3 unt; 8 typ; 3 def)
% 0.30/0.46 % Number of atoms : 24 ( 3 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 8 ( 6 avg)
% 0.30/0.46 % Number of connectives : 70 ( 0 ~; 0 |; 0 &; 56 @)
% 0.30/0.46 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 17 ( 5 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 9 ( 8 usr; 3 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=317
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(powerset_type,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binunion_type,type,
% 0.30/0.46 binunion: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binintersect_type,type,
% 0.30/0.46 binintersect: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectEL_type,type,
% 0.30/0.46 binintersectEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectEL,definition,
% 0.30/0.46 ( binintersectEL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectER_type,type,
% 0.30/0.46 binintersectER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectER,definition,
% 0.30/0.46 ( binintersectER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminus_type,type,
% 0.30/0.46 setminus: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(demorgan2b2_type,type,
% 0.30/0.46 demorgan2b2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(demorgan2b2,definition,
% 0.30/0.46 ( demorgan2b2
% 0.30/0.46 = ( ! [A: $i,X: $i] :
% 0.30/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.46 => ! [Y: $i] :
% 0.30/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.30/0.46 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.30/0.46 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(demorgan2b,conjecture,
% 0.30/0.46 ( binintersectEL
% 0.30/0.46 => ( binintersectER
% 0.30/0.46 => ( demorgan2b2
% 0.30/0.46 => ! [A: $i,X: $i] :
% 0.30/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.46 => ! [Y: $i] :
% 0.30/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.30/0.46 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.49/1.29 ---- Embedded in THF ---
% 1.49/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.29 %%% Generated on Tue Feb 24 12:33:13 EST 2026
% 1.49/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.29 %%% Logic specification used:
% 1.49/1.29 %%% thf(spec, logic, $$dhol).
% 1.49/1.29
% 1.49/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.4eyavceOS4/DTF2DTF8679.p
% See solution above
% 1.49/1.29 ------------------------
% 1.66/1.30 ---- Cleaned THF ---
% 1.66/1.30 thf(in_type,type,
% 1.66/1.30 in: $i > $i > $o ).
% 1.66/1.30
% 1.66/1.30 thf(powerset_type,type,
% 1.66/1.30 powerset: $i > $i ).
% 1.66/1.30
% 1.66/1.30 thf(binunion_type,type,
% 1.66/1.30 binunion: $i > $i > $i ).
% 1.66/1.30
% 1.66/1.30 thf(binintersect_type,type,
% 1.66/1.30 binintersect: $i > $i > $i ).
% 1.66/1.30
% 1.66/1.30 thf(binintersectEL_type,type,
% 1.66/1.30 binintersectEL: $o ).
% 1.66/1.30
% 1.66/1.30 thf(binintersectEL,definition,
% 1.66/1.30 ( binintersectEL
% 1.66/1.30 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.66/1.30 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.66/1.30 => ( in @ Xx @ A ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(binintersectER_type,type,
% 1.66/1.30 binintersectER: $o ).
% 1.66/1.30
% 1.66/1.30 thf(binintersectER,definition,
% 1.66/1.30 ( binintersectER
% 1.66/1.30 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.66/1.30 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.66/1.30 => ( in @ Xx @ B ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(setminus_type,type,
% 1.66/1.30 setminus: $i > $i > $i ).
% 1.66/1.30
% 1.66/1.30 thf(demorgan2b2_type,type,
% 1.66/1.30 demorgan2b2: $o ).
% 1.66/1.30
% 1.66/1.30 thf(demorgan2b2,definition,
% 1.66/1.30 ( demorgan2b2
% 1.66/1.30 = ( ! [A: $i,X: $i] :
% 1.66/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.66/1.30 => ! [Y: $i] :
% 1.66/1.30 ( ( in @ Y @ ( powerset @ A ) )
% 1.66/1.30 => ! [Xx: $i] :
% 1.66/1.30 ( ( in @ Xx @ A )
% 1.66/1.30 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 1.66/1.30 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 1.66/1.30 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(demorgan2b,conjecture,
% 1.66/1.30 ( binintersectEL
% 1.66/1.30 => ( binintersectER
% 1.66/1.30 => ( demorgan2b2
% 1.66/1.30 => ! [A: $i,X: $i] :
% 1.66/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.66/1.30 => ! [Y: $i] :
% 1.66/1.30 ( ( in @ Y @ ( powerset @ A ) )
% 1.66/1.30 => ! [Xx: $i] :
% 1.66/1.30 ( ( in @ Xx @ A )
% 1.66/1.30 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 1.66/1.30 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 1.66/1.30 ------------------------
% 1.66/1.31 % (8895)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_8679 for (2999ds/4Mi)
% 1.66/1.31 % (8899)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_8679 for (2999ds/275Mi)
% 1.66/1.32 % (8895)Instruction limit reached!
% 1.66/1.32 % (8895)------------------------------
% 1.66/1.32 % (8895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (8895)Termination reason: Unknown
% 1.66/1.32 % (8895)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (8895)Memory used [KB]: 5500
% 1.66/1.32 % (8895)Time elapsed: 0.003 s
% 1.66/1.32 % (8895)Instructions burned: 6 (million)
% 1.66/1.32 % (8895)------------------------------
% 1.66/1.32 % (8895)------------------------------
% 1.66/1.32 % (8899)First to succeed.
% 1.66/1.32 % (8899)Refutation found. Thanks to Tanya!
% 1.66/1.32 % SZS status Theorem for DTF2THF_8679
% 1.66/1.32 % SZS output start Proof for DTF2THF_8679
% 1.66/1.32 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.32 thf(func_def_1, type, powerset: $i > $i).
% 1.66/1.32 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.66/1.32 thf(func_def_3, type, binintersect: $i > $i > $i).
% 1.66/1.32 thf(func_def_7, type, setminus: $i > $i > $i).
% 1.66/1.32 thf(f86,plain,(
% 1.66/1.32 $false),
% 1.66/1.32 inference(subsumption_resolution,[status(thm)],[f85,f79])).
% 1.66/1.32 thf(f79,plain,(
% 1.66/1.32 ((in @ sK3 @ (setminus @ sK1 @ sK0)) = $true)),
% 1.66/1.32 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.66/1.32 thf(f76,plain,(
% 1.66/1.32 ($true != $true) | ((in @ sK3 @ (setminus @ sK1 @ sK0)) = $true)),
% 1.66/1.32 inference(superposition,[status(thm)],[f74,f43])).
% 1.66/1.32 thf(f43,plain,(
% 1.66/1.32 ($true = (in @ sK3 @ (binintersect @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2))))),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.32 thf(f24,plain,(
% 1.66/1.32 (binintersectER = $true) & ((($true = (in @ sK2 @ (powerset @ sK1))) & (((in @ sK3 @ (setminus @ sK1 @ (binunion @ sK0 @ sK2))) != $true) & ($true = (in @ sK3 @ (binintersect @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2)))) & ((in @ sK3 @ sK1) = $true))) & ((in @ sK0 @ (powerset @ sK1)) = $true)) & (binintersectEL = $true) & (demorgan2b2 = $true)),
% 1.66/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f16,f23,f22,f21])).
% 1.66/1.32 thf(f21,plain,(
% 1.66/1.32 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (($true != (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ((in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) & ((in @ X3 @ X1) = $true))) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK1))) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK1 @ (binunion @ sK0 @ X2))) != $true) & ((in @ X3 @ (binintersect @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ X2))) = $true) & ((in @ X3 @ sK1) = $true))) & ((in @ sK0 @ (powerset @ sK1)) = $true))),
% 1.66/1.32 introduced(definition,[],[choice_axiom])).
% 1.66/1.32 thf(f22,plain,(
% 1.66/1.32 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK1))) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK1 @ (binunion @ sK0 @ X2))) != $true) & ((in @ X3 @ (binintersect @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ X2))) = $true) & ((in @ X3 @ sK1) = $true))) => (($true = (in @ sK2 @ (powerset @ sK1))) & ? [X3 : $i] : (($true != (in @ X3 @ (setminus @ sK1 @ (binunion @ sK0 @ sK2)))) & ((in @ X3 @ (binintersect @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2))) = $true) & ((in @ X3 @ sK1) = $true)))),
% 1.66/1.32 introduced(definition,[],[choice_axiom])).
% 1.66/1.32 thf(f23,plain,(
% 1.66/1.32 ? [X3 : $i] : (($true != (in @ X3 @ (setminus @ sK1 @ (binunion @ sK0 @ sK2)))) & ((in @ X3 @ (binintersect @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2))) = $true) & ((in @ X3 @ sK1) = $true)) => (((in @ sK3 @ (setminus @ sK1 @ (binunion @ sK0 @ sK2))) != $true) & ($true = (in @ sK3 @ (binintersect @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2)))) & ((in @ sK3 @ sK1) = $true))),
% 1.66/1.32 introduced(definition,[],[choice_axiom])).
% 1.66/1.32 thf(f16,plain,(
% 1.66/1.32 (binintersectER = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (($true != (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ((in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) & ((in @ X3 @ X1) = $true))) & ((in @ X0 @ (powerset @ X1)) = $true)) & (binintersectEL = $true) & (demorgan2b2 = $true)),
% 1.66/1.32 inference(flattening,[status(thm)],[f15])).
% 1.66/1.32 thf(f15,plain,(
% 1.66/1.32 ((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((($true != (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ((in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true)) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (demorgan2b2 = $true)) & (binintersectER = $true)) & (binintersectEL = $true)),
% 1.66/1.32 inference(ennf_transformation,[status(thm)],[f10])).
% 1.66/1.32 thf(f10,plain,(
% 1.66/1.32 ~((binintersectEL = $true) => ((binintersectER = $true) => ((demorgan2b2 = $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 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) => ($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))))))))))),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f9])).
% 1.66/1.32 thf(f9,plain,(
% 1.66/1.32 ~(binintersectEL => (binintersectER => (demorgan2b2 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) => (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))))))))))),
% 1.66/1.32 inference(rectify,[status(thm)],[f5])).
% 1.66/1.32 thf(f5,negated_conjecture,(
% 1.66/1.32 ~(binintersectEL => (binintersectER => (demorgan2b2 => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4))) => (in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4))))))))))),
% 1.66/1.32 inference(negated_conjecture,[status(cth)],[f4])).
% 1.66/1.32 thf(f4,conjecture,(
% 1.66/1.32 binintersectEL => (binintersectER => (demorgan2b2 => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4))) => (in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4)))))))))),
% 1.66/1.32 file('/export/starexec/sandbox2/tmp/tmp.4eyavceOS4/DTF2THF_8679.p',demorgan2b)).
% 1.66/1.32 thf(f74,plain,(
% 1.66/1.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binintersect @ X4 @ X5)) != $true) | ((in @ X3 @ X4) = $true)) )),
% 1.66/1.32 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.66/1.32 thf(f62,plain,(
% 1.66/1.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ((in @ X3 @ (binintersect @ X4 @ X5)) != $true) | ($true != $true)) )),
% 1.66/1.32 inference(definition_unfolding,[status(thm)],[f47,f40])).
% 1.66/1.32 thf(f40,plain,(
% 1.66/1.32 (binintersectEL = $true)),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.32 thf(f47,plain,(
% 1.66/1.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binintersect @ X4 @ X5)) != $true) | ((in @ X3 @ X4) = $true) | (binintersectEL != $true)) )),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f28])).
% 1.66/1.32 thf(f28,plain,(
% 1.66/1.32 ((binintersectEL = $true) | (((in @ sK4 @ (binintersect @ sK5 @ sK6)) = $true) & ((in @ sK4 @ sK5) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binintersect @ X4 @ X5)) != $true) | ((in @ X3 @ X4) = $true)) | (binintersectEL != $true))),
% 1.66/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f26,f27])).
% 1.66/1.32 thf(f27,plain,(
% 1.66/1.32 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binintersect @ X1 @ X2))) & ((in @ X0 @ X1) != $true)) => (((in @ sK4 @ (binintersect @ sK5 @ sK6)) = $true) & ((in @ sK4 @ sK5) != $true))),
% 1.66/1.32 introduced(definition,[],[choice_axiom])).
% 1.66/1.32 thf(f26,plain,(
% 1.66/1.32 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binintersect @ X1 @ X2))) & ((in @ X0 @ X1) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binintersect @ X4 @ X5)) != $true) | ((in @ X3 @ X4) = $true)) | (binintersectEL != $true))),
% 1.66/1.32 inference(rectify,[status(thm)],[f25])).
% 1.66/1.32 thf(f25,plain,(
% 1.66/1.32 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binintersect @ X1 @ X2))) & ((in @ X0 @ X1) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (binintersect @ X1 @ X2))) | ((in @ X0 @ X1) = $true)) | (binintersectEL != $true))),
% 1.66/1.32 inference(nnf_transformation,[status(thm)],[f18])).
% 1.66/1.32 thf(f18,plain,(
% 1.66/1.32 (binintersectEL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (binintersect @ X1 @ X2))) | ((in @ X0 @ X1) = $true))),
% 1.66/1.32 inference(ennf_transformation,[status(thm)],[f12])).
% 1.66/1.32 thf(f12,plain,(
% 1.66/1.32 ! [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X0 @ (binintersect @ X1 @ X2))) => ((in @ X0 @ X1) = $true)) <=> (binintersectEL = $true)),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f11])).
% 1.66/1.32 thf(f11,plain,(
% 1.66/1.32 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X1 @ X2)) => (in @ X0 @ X1)))),
% 1.66/1.32 inference(rectify,[status(thm)],[f1])).
% 1.66/1.32 thf(f1,axiom,(
% 1.66/1.32 (binintersectEL = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 1.66/1.32 file('/export/starexec/sandbox2/tmp/tmp.4eyavceOS4/DTF2THF_8679.p',binintersectEL)).
% 1.66/1.32 thf(f85,plain,(
% 1.66/1.32 ((in @ sK3 @ (setminus @ sK1 @ sK0)) != $true)),
% 1.66/1.32 inference(subsumption_resolution,[status(thm)],[f84,f45])).
% 1.66/1.32 thf(f45,plain,(
% 1.66/1.32 ($true = (in @ sK2 @ (powerset @ sK1)))),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.32 thf(f84,plain,(
% 1.66/1.32 ($true != (in @ sK2 @ (powerset @ sK1))) | ((in @ sK3 @ (setminus @ sK1 @ sK0)) != $true)),
% 1.66/1.32 inference(subsumption_resolution,[status(thm)],[f83,f78])).
% 1.66/1.32 thf(f78,plain,(
% 1.66/1.32 ((in @ sK3 @ (setminus @ sK1 @ sK2)) = $true)),
% 1.66/1.32 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.66/1.32 thf(f77,plain,(
% 1.66/1.32 ($true != $true) | ((in @ sK3 @ (setminus @ sK1 @ sK2)) = $true)),
% 1.66/1.32 inference(superposition,[status(thm)],[f73,f43])).
% 1.66/1.32 thf(f73,plain,(
% 1.66/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) != $true) | ((in @ X0 @ X1) = $true)) )),
% 1.66/1.32 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.66/1.32 thf(f70,plain,(
% 1.66/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) != $true) | ($true != $true) | ((in @ X0 @ X1) = $true)) )),
% 1.66/1.32 inference(definition_unfolding,[status(thm)],[f59,f46])).
% 1.66/1.32 thf(f46,plain,(
% 1.66/1.32 (binintersectER = $true)),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.32 thf(f59,plain,(
% 1.66/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ (binintersect @ X2 @ X1)) != $true) | (binintersectER != $true)) )),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f38])).
% 1.66/1.32 thf(f38,plain,(
% 1.66/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ (binintersect @ X2 @ X1)) != $true)) | (binintersectER != $true)) & ((binintersectER = $true) | (((in @ sK11 @ sK12) != $true) & ((in @ sK11 @ (binintersect @ sK13 @ sK12)) = $true)))),
% 1.66/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f36,f37])).
% 1.66/1.32 thf(f37,plain,(
% 1.66/1.32 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) & ((in @ X3 @ (binintersect @ X5 @ X4)) = $true)) => (((in @ sK11 @ sK12) != $true) & ((in @ sK11 @ (binintersect @ sK13 @ sK12)) = $true))),
% 1.66/1.32 introduced(definition,[],[choice_axiom])).
% 1.66/1.32 thf(f36,plain,(
% 1.66/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ (binintersect @ X2 @ X1)) != $true)) | (binintersectER != $true)) & ((binintersectER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) & ((in @ X3 @ (binintersect @ X5 @ X4)) = $true)))),
% 1.66/1.32 inference(rectify,[status(thm)],[f35])).
% 1.66/1.32 thf(f35,plain,(
% 1.66/1.32 (! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) | (binintersectER != $true)) & ((binintersectER = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ (binintersect @ X0 @ X1)) = $true)))),
% 1.66/1.32 inference(nnf_transformation,[status(thm)],[f17])).
% 1.66/1.32 thf(f17,plain,(
% 1.66/1.32 ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) <=> (binintersectER = $true)),
% 1.66/1.32 inference(ennf_transformation,[status(thm)],[f14])).
% 1.66/1.32 thf(f14,plain,(
% 1.66/1.32 (binintersectER = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) => ((in @ X2 @ X1) = $true))),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f13])).
% 1.66/1.32 thf(f13,plain,(
% 1.66/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)) = binintersectER)),
% 1.66/1.32 inference(rectify,[status(thm)],[f2])).
% 1.66/1.32 thf(f2,axiom,(
% 1.66/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)) = binintersectER)),
% 1.66/1.32 file('/export/starexec/sandbox2/tmp/tmp.4eyavceOS4/DTF2THF_8679.p',binintersectER)).
% 1.66/1.32 thf(f83,plain,(
% 1.66/1.32 ((in @ sK3 @ (setminus @ sK1 @ sK2)) != $true) | ($true != (in @ sK2 @ (powerset @ sK1))) | ((in @ sK3 @ (setminus @ sK1 @ sK0)) != $true)),
% 1.66/1.32 inference(subsumption_resolution,[status(thm)],[f82,f41])).
% 1.66/1.32 thf(f41,plain,(
% 1.66/1.32 ((in @ sK0 @ (powerset @ sK1)) = $true)),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.32 thf(f82,plain,(
% 1.66/1.32 ((in @ sK0 @ (powerset @ sK1)) != $true) | ((in @ sK3 @ (setminus @ sK1 @ sK2)) != $true) | ((in @ sK3 @ (setminus @ sK1 @ sK0)) != $true) | ($true != (in @ sK2 @ (powerset @ sK1)))),
% 1.66/1.32 inference(subsumption_resolution,[status(thm)],[f81,f42])).
% 1.66/1.32 thf(f42,plain,(
% 1.66/1.32 ((in @ sK3 @ sK1) = $true)),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.32 thf(f81,plain,(
% 1.66/1.32 ((in @ sK3 @ sK1) != $true) | ((in @ sK0 @ (powerset @ sK1)) != $true) | ($true != (in @ sK2 @ (powerset @ sK1))) | ((in @ sK3 @ (setminus @ sK1 @ sK2)) != $true) | ((in @ sK3 @ (setminus @ sK1 @ sK0)) != $true)),
% 1.66/1.32 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.66/1.32 thf(f80,plain,(
% 1.66/1.32 ((in @ sK3 @ (setminus @ sK1 @ sK2)) != $true) | ($true != (in @ sK2 @ (powerset @ sK1))) | ((in @ sK3 @ sK1) != $true) | ((in @ sK3 @ (setminus @ sK1 @ sK0)) != $true) | ((in @ sK0 @ (powerset @ sK1)) != $true) | ($true != $true)),
% 1.66/1.32 inference(superposition,[status(thm)],[f44,f75])).
% 1.66/1.32 thf(f75,plain,(
% 1.66/1.32 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (in @ X7 @ (setminus @ X5 @ (binunion @ X4 @ X6)))) | ((in @ X7 @ (setminus @ X5 @ X6)) != $true) | ((in @ X4 @ (powerset @ X5)) != $true) | ((in @ X6 @ (powerset @ X5)) != $true) | ((in @ X7 @ X5) != $true) | ((in @ X7 @ (setminus @ X5 @ X4)) != $true)) )),
% 1.66/1.32 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.66/1.32 thf(f69,plain,(
% 1.66/1.32 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X7 @ X5) != $true) | ((in @ X4 @ (powerset @ X5)) != $true) | ((in @ X6 @ (powerset @ X5)) != $true) | ($true = (in @ X7 @ (setminus @ X5 @ (binunion @ X4 @ X6)))) | ((in @ X7 @ (setminus @ X5 @ X6)) != $true) | ((in @ X7 @ (setminus @ X5 @ X4)) != $true)) )),
% 1.66/1.32 inference(definition_unfolding,[status(thm)],[f50,f39])).
% 1.66/1.32 thf(f39,plain,(
% 1.66/1.32 (demorgan2b2 = $true)),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.32 thf(f50,plain,(
% 1.66/1.32 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ X5) != $true) | ((in @ X7 @ (setminus @ X5 @ X4)) != $true) | ((in @ X7 @ (setminus @ X5 @ X6)) != $true) | ($true = (in @ X7 @ (setminus @ X5 @ (binunion @ X4 @ X6)))) | ((in @ X6 @ (powerset @ X5)) != $true) | ((in @ X4 @ (powerset @ X5)) != $true) | (demorgan2b2 != $true)) )),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f34])).
% 1.66/1.32 thf(f34,plain,(
% 1.66/1.32 ((demorgan2b2 = $true) | (((((in @ sK10 @ sK8) = $true) & ($true = (in @ sK10 @ (setminus @ sK8 @ sK7))) & ((in @ sK10 @ (setminus @ sK8 @ sK9)) = $true) & ($true != (in @ sK10 @ (setminus @ sK8 @ (binunion @ sK7 @ sK9))))) & ($true = (in @ sK9 @ (powerset @ sK8)))) & ((in @ sK7 @ (powerset @ sK8)) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (! [X7 : $i] : (((in @ X7 @ X5) != $true) | ((in @ X7 @ (setminus @ X5 @ X4)) != $true) | ((in @ X7 @ (setminus @ X5 @ X6)) != $true) | ($true = (in @ X7 @ (setminus @ X5 @ (binunion @ X4 @ X6))))) | ((in @ X6 @ (powerset @ X5)) != $true)) | ((in @ X4 @ (powerset @ X5)) != $true)) | (demorgan2b2 != $true))),
% 1.66/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f30,f33,f32,f31])).
% 1.66/1.32 thf(f31,plain,(
% 1.66/1.32 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ (setminus @ X1 @ X0)) = $true) & ((in @ X3 @ (setminus @ X1 @ X2)) = $true) & ($true != (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ sK8) = $true) & ((in @ X3 @ (setminus @ sK8 @ sK7)) = $true) & ($true = (in @ X3 @ (setminus @ sK8 @ X2))) & ((in @ X3 @ (setminus @ sK8 @ (binunion @ sK7 @ X2))) != $true)) & ($true = (in @ X2 @ (powerset @ sK8)))) & ((in @ sK7 @ (powerset @ sK8)) = $true))),
% 1.66/1.32 introduced(definition,[],[choice_axiom])).
% 1.66/1.32 thf(f32,plain,(
% 1.66/1.32 ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ sK8) = $true) & ((in @ X3 @ (setminus @ sK8 @ sK7)) = $true) & ($true = (in @ X3 @ (setminus @ sK8 @ X2))) & ((in @ X3 @ (setminus @ sK8 @ (binunion @ sK7 @ X2))) != $true)) & ($true = (in @ X2 @ (powerset @ sK8)))) => (? [X3 : $i] : (((in @ X3 @ sK8) = $true) & ((in @ X3 @ (setminus @ sK8 @ sK7)) = $true) & ((in @ X3 @ (setminus @ sK8 @ sK9)) = $true) & ($true != (in @ X3 @ (setminus @ sK8 @ (binunion @ sK7 @ sK9))))) & ($true = (in @ sK9 @ (powerset @ sK8))))),
% 1.66/1.32 introduced(definition,[],[choice_axiom])).
% 1.66/1.32 thf(f33,plain,(
% 1.66/1.32 ? [X3 : $i] : (((in @ X3 @ sK8) = $true) & ((in @ X3 @ (setminus @ sK8 @ sK7)) = $true) & ((in @ X3 @ (setminus @ sK8 @ sK9)) = $true) & ($true != (in @ X3 @ (setminus @ sK8 @ (binunion @ sK7 @ sK9))))) => (((in @ sK10 @ sK8) = $true) & ($true = (in @ sK10 @ (setminus @ sK8 @ sK7))) & ((in @ sK10 @ (setminus @ sK8 @ sK9)) = $true) & ($true != (in @ sK10 @ (setminus @ sK8 @ (binunion @ sK7 @ sK9)))))),
% 1.66/1.32 introduced(definition,[],[choice_axiom])).
% 1.66/1.32 thf(f30,plain,(
% 1.66/1.32 ((demorgan2b2 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ (setminus @ X1 @ X0)) = $true) & ((in @ X3 @ (setminus @ X1 @ X2)) = $true) & ($true != (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (! [X7 : $i] : (((in @ X7 @ X5) != $true) | ((in @ X7 @ (setminus @ X5 @ X4)) != $true) | ((in @ X7 @ (setminus @ X5 @ X6)) != $true) | ($true = (in @ X7 @ (setminus @ X5 @ (binunion @ X4 @ X6))))) | ((in @ X6 @ (powerset @ X5)) != $true)) | ((in @ X4 @ (powerset @ X5)) != $true)) | (demorgan2b2 != $true))),
% 1.66/1.32 inference(rectify,[status(thm)],[f29])).
% 1.66/1.32 thf(f29,plain,(
% 1.66/1.32 ((demorgan2b2 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ (setminus @ X1 @ X0)) = $true) & ((in @ X3 @ (setminus @ X1 @ X2)) = $true) & ($true != (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true))) & (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ (setminus @ X1 @ X0)) != $true) | ((in @ X3 @ (setminus @ X1 @ X2)) != $true) | ($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))))) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) | (demorgan2b2 != $true))),
% 1.66/1.32 inference(nnf_transformation,[status(thm)],[f20])).
% 1.66/1.32 thf(f20,plain,(
% 1.66/1.32 (demorgan2b2 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ (setminus @ X1 @ X0)) != $true) | ((in @ X3 @ (setminus @ X1 @ X2)) != $true) | ($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))))) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 1.66/1.32 inference(flattening,[status(thm)],[f19])).
% 1.66/1.32 thf(f19,plain,(
% 1.66/1.32 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) | ((in @ X3 @ (setminus @ X1 @ X2)) != $true)) | ((in @ X3 @ (setminus @ X1 @ X0)) != $true)) | ((in @ X3 @ X1) != $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) <=> (demorgan2b2 = $true)),
% 1.66/1.32 inference(ennf_transformation,[status(thm)],[f8])).
% 1.66/1.32 thf(f8,plain,(
% 1.66/1.32 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ (setminus @ X1 @ X0)) = $true) => (((in @ X3 @ (setminus @ X1 @ X2)) = $true) => ($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))))))))) <=> (demorgan2b2 = $true)),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f7])).
% 1.66/1.32 thf(f7,plain,(
% 1.66/1.32 (! [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)))))))) = demorgan2b2)),
% 1.66/1.32 inference(rectify,[status(thm)],[f3])).
% 1.66/1.32 thf(f3,axiom,(
% 1.66/1.32 (! [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)))))))) = demorgan2b2)),
% 1.66/1.32 file('/export/starexec/sandbox2/tmp/tmp.4eyavceOS4/DTF2THF_8679.p',demorgan2b2)).
% 1.66/1.32 thf(f44,plain,(
% 1.66/1.32 ((in @ sK3 @ (setminus @ sK1 @ (binunion @ sK0 @ sK2))) != $true)),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.32 % SZS output end Proof for DTF2THF_8679
% 1.66/1.32 % (8899)------------------------------
% 1.66/1.32 % (8899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (8899)Termination reason: Refutation
% 1.66/1.32
% 1.66/1.32 % (8899)Memory used [KB]: 5628
% 1.66/1.32 % (8899)Time elapsed: 0.005 s
% 1.66/1.32 % (8899)Instructions burned: 6 (million)
% 1.66/1.32 % (8899)------------------------------
% 1.66/1.32 % (8899)------------------------------
% 1.66/1.32 % (8893)Success in time 0.016 s
%------------------------------------------------------------------------------