%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU723^2 : 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 : n001.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 09:36:41 AM UTC 2026
% Result : Theorem 1.82s 1.53s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 674 ( 186 equ; 0 cnn)
% Maximal formula atoms : 12 ( 14 avg)
% Number of connectives : 677 ( 73 ~; 48 |; 66 &; 434 @)
% ( 6 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 132 ( 0 ^; 96 !; 36 ?; 132 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
setminus: $i > $i > $i ).
thf(f63,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f61,f34]) ).
thf(f34,plain,
( ( in @ sK3 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( setminusER = $true )
& ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $true )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( ( subset @ sK1 @ ( setminus @ sK0 @ sK2 ) )
= $true )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( ( in @ sK3 @ sK2 )
= $true )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( subsetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f17,f21,f20,f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( ( subset @ sK1 @ ( setminus @ sK0 @ X2 ) )
= $true )
& ( ( in @ X3 @ sK1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) ) )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( ( subset @ sK1 @ ( setminus @ sK0 @ X2 ) )
= $true )
& ( ( in @ X3 @ sK1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( ( subset @ sK1 @ ( setminus @ sK0 @ sK2 ) )
= $true )
& ( ( in @ X3 @ sK1 )
= $true )
& ( ( in @ X3 @ sK2 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( ( subset @ sK1 @ ( setminus @ sK0 @ sK2 ) )
= $true )
& ( ( in @ X3 @ sK1 )
= $true )
& ( ( in @ X3 @ sK2 )
= $true ) )
=> ( ( ( in @ sK3 @ sK0 )
= $true )
& ( ( subset @ sK1 @ ( setminus @ sK0 @ sK2 ) )
= $true )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( ( in @ sK3 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( setminusER = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( setminusER = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( subsetE = $true )
=> ( ( setminusER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( subsetE = $true )
=> ( ( setminusER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( subsetE
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( subsetE
=> ( setminusER
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( subset @ X3 @ ( setminus @ X0 @ X4 ) )
=> ( ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( subsetE
=> ( setminusER
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( subset @ X3 @ ( setminus @ X0 @ X4 ) )
=> ( ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tJFxPYu7Uc/DTF2THF_7010.p',contrasubsetT) ).
thf(f61,plain,
( ( in @ sK3 @ sK1 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( in @ sK3 @ sK1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f58,f33]) ).
thf(f33,plain,
( ( in @ sK3 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f58,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK2 )
!= $true )
| ( ( in @ X0 @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ X0 @ sK1 )
!= $true )
| ( ( in @ X0 @ sK2 )
!= $true ) ),
inference(superposition,[status(thm)],[f56,f35]) ).
thf(f35,plain,
( ( subset @ sK1 @ ( setminus @ sK0 @ sK2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ X3 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X3 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X3 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( subset @ X3 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f54,f53]) ).
thf(f53,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( ( subset @ X4 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( in @ X5 @ X3 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f39,f31]) ).
thf(f31,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f39,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( subset @ X4 @ X3 )
!= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( subsetE = $true )
| ( ( $true
!= ( in @ sK6 @ sK4 ) )
& ( ( in @ sK6 @ sK5 )
= $true )
& ( $true
= ( subset @ sK5 @ sK4 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f24,f25]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true ) )
=> ( ( $true
!= ( in @ sK6 @ sK4 ) )
& ( ( in @ sK6 @ sK5 )
= $true )
& ( $true
= ( subset @ sK5 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox/tmp/tmp.tJFxPYu7Uc/DTF2THF_7010.p',subsetE) ).
thf(f54,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
!= $true )
| ( ( in @ X4 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
!= $true )
| ( ( in @ X4 @ X5 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f43,f38]) ).
thf(f38,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f43,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
!= $true )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( setminusER = $true )
| ( ( ( in @ sK8 @ sK9 )
= $true )
& ( ( in @ sK8 @ ( setminus @ sK7 @ sK9 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f28,f29]) ).
thf(f29,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) )
=> ( ( ( in @ sK8 @ sK9 )
= $true )
& ( ( in @ sK8 @ ( setminus @ sK7 @ sK9 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( setminusER = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( in @ X1 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( in @ X1 @ X2 )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setminusER
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tJFxPYu7Uc/DTF2THF_7010.p',setminusER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU723^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n001.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 12:32:50 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.50 ---- Original DTF file ---
% 0.29/0.50 thf(spec,logic,$$dhol).
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 % File : SEU723^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.50 % Domain : Set Theory
% 0.29/0.50 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.29/0.50 % Version : Especial > Reduced > Especial.
% 0.29/0.50 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.29/0.50 % (! x:i.in x A -> subset X (setminus A Y) -> in x Y -> ~(in x X))))
% 0.29/0.50
% 0.29/0.50 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.50 % Source : [Bro08]
% 0.29/0.50 % Names : ZFC225l [Bro08]
% 0.29/0.50
% 0.29/0.50 % Status : Theorem
% 0.29/0.50 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 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 v4.1.0, 0.00 v3.7.0
% 0.29/0.50 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.29/0.50 % Number of atoms : 17 ( 2 equ; 0 cnn)
% 0.29/0.50 % Maximal formula atoms : 8 ( 5 avg)
% 0.29/0.50 % Number of connectives : 40 ( 2 ~; 0 |; 0 &; 28 @)
% 0.29/0.50 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.29/0.50 % Maximal formula depth : 15 ( 6 avg)
% 0.29/0.50 % Number of types : 2 ( 0 usr)
% 0.29/0.50 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.29/0.50 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.29/0.50 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.29/0.50 % SPC : TH0_THM_EQU_NAR
% 0.29/0.50
% 0.29/0.50 % Comments : http://mathgate.info/detsetitem.php?id=283
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 thf(in_type,type,
% 0.29/0.50 in: $i > $i > $o ).
% 0.29/0.50
% 0.29/0.50 thf(powerset_type,type,
% 0.29/0.50 powerset: $i > $i ).
% 0.29/0.50
% 0.29/0.50 thf(subset_type,type,
% 0.29/0.50 subset: $i > $i > $o ).
% 0.29/0.50
% 0.29/0.50 thf(subsetE_type,type,
% 0.29/0.50 subsetE: $o ).
% 0.29/0.50
% 0.29/0.50 thf(subsetE,definition,
% 0.29/0.50 ( subsetE
% 0.29/0.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.50 ( ( subset @ A @ B )
% 0.29/0.50 => ( ( in @ Xx @ A )
% 0.29/0.50 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(setminus_type,type,
% 0.29/0.50 setminus: $i > $i > $i ).
% 0.29/0.50
% 0.29/0.50 thf(setminusER_type,type,
% 0.29/0.50 setminusER: $o ).
% 0.29/0.50
% 0.29/0.50 thf(setminusER,definition,
% 0.29/0.50 ( setminusER
% 0.29/0.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.50 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(contrasubsetT,conjecture,
% 0.29/0.50 ( subsetE
% 0.29/0.50 => ( setminusER
% 0.29/0.50 => ! [A: $i,X: $i] :
% 0.29/0.50 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.50 => ! [Y: $i] :
% 0.29/0.50 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.50 => ! [Xx: $i] :
% 0.29/0.50 ( ( in @ Xx @ A )
% 0.29/0.50 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.50 => ( ( in @ Xx @ Y )
% 0.29/0.50 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 ------------------------
% 1.63/1.49 ---- Embedded in THF ---
% 1.63/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.49 %%% Generated on Tue Feb 24 12:32:51 EST 2026
% 1.63/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.49 %%% Logic specification used:
% 1.63/1.49 %%% thf(spec, logic, $$dhol).
% 1.63/1.49
% 1.63/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tJFxPYu7Uc/DTF2DTF7010.p
% See solution above
% 1.63/1.49 ------------------------
% 1.82/1.50 ---- Cleaned THF ---
% 1.82/1.50 thf(in_type,type,
% 1.82/1.50 in: $i > $i > $o ).
% 1.82/1.50
% 1.82/1.50 thf(powerset_type,type,
% 1.82/1.50 powerset: $i > $i ).
% 1.82/1.50
% 1.82/1.50 thf(subset_type,type,
% 1.82/1.50 subset: $i > $i > $o ).
% 1.82/1.50
% 1.82/1.50 thf(subsetE_type,type,
% 1.82/1.50 subsetE: $o ).
% 1.82/1.50
% 1.82/1.50 thf(subsetE,definition,
% 1.82/1.50 ( subsetE
% 1.82/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.82/1.50 ( ( subset @ A @ B )
% 1.82/1.50 => ( ( in @ Xx @ A )
% 1.82/1.50 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.82/1.50
% 1.82/1.50 thf(setminus_type,type,
% 1.82/1.50 setminus: $i > $i > $i ).
% 1.82/1.50
% 1.82/1.50 thf(setminusER_type,type,
% 1.82/1.50 setminusER: $o ).
% 1.82/1.50
% 1.82/1.50 thf(setminusER,definition,
% 1.82/1.50 ( setminusER
% 1.82/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.82/1.50 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.82/1.50 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.82/1.50
% 1.82/1.50 thf(contrasubsetT,conjecture,
% 1.82/1.50 ( subsetE
% 1.82/1.50 => ( setminusER
% 1.82/1.50 => ! [A: $i,X: $i] :
% 1.82/1.50 ( ( in @ X @ ( powerset @ A ) )
% 1.82/1.50 => ! [Y: $i] :
% 1.82/1.50 ( ( in @ Y @ ( powerset @ A ) )
% 1.82/1.50 => ! [Xx: $i] :
% 1.82/1.50 ( ( in @ Xx @ A )
% 1.82/1.50 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 1.82/1.50 => ( ( in @ Xx @ Y )
% 1.82/1.50 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 1.82/1.50 ------------------------
% 1.82/1.52 % (7124)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_7010 for (2999ds/4Mi)
% 1.82/1.52 % (7126)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7010 for (2999ds/2Mi)
% 1.82/1.52 % (7127)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_7010 for (2999ds/2Mi)
% 1.82/1.52 % (7125)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_7010 for (2999ds/27Mi)
% 1.82/1.52 % (7128)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_7010 for (2999ds/275Mi)
% 1.82/1.52 % (7129)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7010 for (2999ds/18Mi)
% 1.82/1.52 % (7123)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7010 for (2999ds/183Mi)
% 1.82/1.52 % (7126)Instruction limit reached!
% 1.82/1.52 % (7126)------------------------------
% 1.82/1.52 % (7126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.52 % (7127)Instruction limit reached!
% 1.82/1.52 % (7127)------------------------------
% 1.82/1.52 % (7127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.52 % (7126)Termination reason: Unknown
% 1.82/1.52 % (7126)Termination phase: Saturation
% 1.82/1.52
% 1.82/1.52 % (7126)Memory used [KB]: 1023
% 1.82/1.52 % (7126)Time elapsed: 0.003 s
% 1.82/1.52 % (7126)Instructions burned: 3 (million)
% 1.82/1.52 % (7126)------------------------------
% 1.82/1.52 % (7126)------------------------------
% 1.82/1.52 % (7127)Termination reason: Unknown
% 1.82/1.52 % (7127)Termination phase: Saturation
% 1.82/1.52
% 1.82/1.52 % (7127)Memory used [KB]: 5500
% 1.82/1.52 % (7127)Time elapsed: 0.003 s
% 1.82/1.52 % (7127)Instructions burned: 3 (million)
% 1.82/1.52 % (7127)------------------------------
% 1.82/1.52 % (7127)------------------------------
% 1.82/1.52 % (7124)Instruction limit reached!
% 1.82/1.52 % (7124)------------------------------
% 1.82/1.52 % (7124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.52 % (7124)Termination reason: Unknown
% 1.82/1.52 % (7124)Termination phase: Saturation
% 1.82/1.52
% 1.82/1.52 % (7124)Memory used [KB]: 5500
% 1.82/1.52 % (7124)Time elapsed: 0.005 s
% 1.82/1.52 % (7124)Instructions burned: 5 (million)
% 1.82/1.52 % (7124)------------------------------
% 1.82/1.52 % (7124)------------------------------
% 1.82/1.52 % (7128)First to succeed.
% 1.82/1.53 % (7123)Also succeeded, but the first one will report.
% 1.82/1.53 % (7125)Also succeeded, but the first one will report.
% 1.82/1.53 % (7128)Refutation found. Thanks to Tanya!
% 1.82/1.53 % SZS status Theorem for DTF2THF_7010
% 1.82/1.53 % SZS output start Proof for DTF2THF_7010
% 1.82/1.53 thf(func_def_0, type, in: $i > $i > $o).
% 1.82/1.53 thf(func_def_1, type, powerset: $i > $i).
% 1.82/1.53 thf(func_def_2, type, subset: $i > $i > $o).
% 1.82/1.53 thf(func_def_5, type, setminus: $i > $i > $i).
% 1.82/1.53 thf(f63,plain,(
% 1.82/1.53 $false),
% 1.82/1.53 inference(subsumption_resolution,[status(thm)],[f61,f34])).
% 1.82/1.53 thf(f34,plain,(
% 1.82/1.53 ((in @ sK3 @ sK1) = $true)),
% 1.82/1.53 inference(cnf_transformation,[status(thm)],[f22])).
% 1.82/1.53 thf(f22,plain,(
% 1.82/1.53 (setminusER = $true) & ((((in @ sK2 @ (powerset @ sK0)) = $true) & (((in @ sK3 @ sK0) = $true) & ((subset @ sK1 @ (setminus @ sK0 @ sK2)) = $true) & ((in @ sK3 @ sK1) = $true) & ((in @ sK3 @ sK2) = $true))) & ((in @ sK1 @ (powerset @ sK0)) = $true)) & (subsetE = $true)),
% 1.82/1.53 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f17,f21,f20,f19])).
% 1.82/1.53 thf(f19,plain,(
% 1.82/1.53 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((subset @ X1 @ (setminus @ X0 @ X2)) = $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (((in @ X2 @ (powerset @ sK0)) = $true) & ? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ((subset @ sK1 @ (setminus @ sK0 @ X2)) = $true) & ((in @ X3 @ sK1) = $true) & ((in @ X3 @ X2) = $true))) & ((in @ sK1 @ (powerset @ sK0)) = $true))),
% 1.82/1.53 introduced(definition,[],[choice_axiom])).
% 1.82/1.53 thf(f20,plain,(
% 1.82/1.53 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK0)) = $true) & ? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ((subset @ sK1 @ (setminus @ sK0 @ X2)) = $true) & ((in @ X3 @ sK1) = $true) & ((in @ X3 @ X2) = $true))) => (((in @ sK2 @ (powerset @ sK0)) = $true) & ? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ((subset @ sK1 @ (setminus @ sK0 @ sK2)) = $true) & ((in @ X3 @ sK1) = $true) & ((in @ X3 @ sK2) = $true)))),
% 1.82/1.53 introduced(definition,[],[choice_axiom])).
% 1.82/1.53 thf(f21,plain,(
% 1.82/1.53 ? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ((subset @ sK1 @ (setminus @ sK0 @ sK2)) = $true) & ((in @ X3 @ sK1) = $true) & ((in @ X3 @ sK2) = $true)) => (((in @ sK3 @ sK0) = $true) & ((subset @ sK1 @ (setminus @ sK0 @ sK2)) = $true) & ((in @ sK3 @ sK1) = $true) & ((in @ sK3 @ sK2) = $true))),
% 1.82/1.53 introduced(definition,[],[choice_axiom])).
% 1.82/1.53 thf(f17,plain,(
% 1.82/1.53 (setminusER = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((subset @ X1 @ (setminus @ X0 @ X2)) = $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true)) & (subsetE = $true)),
% 1.82/1.53 inference(flattening,[status(thm)],[f16])).
% 1.82/1.53 thf(f16,plain,(
% 1.82/1.53 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) = $true)) & ((subset @ X1 @ (setminus @ X0 @ X2)) = $true)) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (setminusER = $true)) & (subsetE = $true)),
% 1.82/1.53 inference(ennf_transformation,[status(thm)],[f12])).
% 1.82/1.53 thf(f12,plain,(
% 1.82/1.53 ~((subsetE = $true) => ((setminusER = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((subset @ X1 @ (setminus @ X0 @ X2)) = $true) => (((in @ X3 @ X2) = $true) => ((in @ X3 @ X1) != $true))))))))),
% 1.82/1.53 inference(flattening,[status(thm)],[f11])).
% 1.82/1.53 thf(f11,plain,(
% 1.82/1.53 ~((subsetE = $true) => ((setminusER = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((subset @ X1 @ (setminus @ X0 @ X2)) = $true) => (((in @ X3 @ X2) = $true) => ~((in @ X3 @ X1) = $true))))))))),
% 1.82/1.53 inference(fool_elimination,[status(thm)],[f10])).
% 1.82/1.53 thf(f10,plain,(
% 1.82/1.53 ~(subsetE => (setminusER => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((subset @ X1 @ (setminus @ X0 @ X2)) => ((in @ X3 @ X2) => ~(in @ X3 @ X1))))))))),
% 1.82/1.53 inference(rectify,[status(thm)],[f4])).
% 1.82/1.53 thf(f4,negated_conjecture,(
% 1.82/1.53 ~(subsetE => (setminusER => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((subset @ X3 @ (setminus @ X0 @ X4)) => ((in @ X2 @ X4) => ~(in @ X2 @ X3))))))))),
% 1.82/1.53 inference(negated_conjecture,[status(cth)],[f3])).
% 1.82/1.53 thf(f3,conjecture,(
% 1.82/1.53 subsetE => (setminusER => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((subset @ X3 @ (setminus @ X0 @ X4)) => ((in @ X2 @ X4) => ~(in @ X2 @ X3)))))))),
% 1.82/1.53 file('/export/starexec/sandbox/tmp/tmp.tJFxPYu7Uc/DTF2THF_7010.p',contrasubsetT)).
% 1.82/1.53 thf(f61,plain,(
% 1.82/1.53 ((in @ sK3 @ sK1) != $true)),
% 1.82/1.53 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.82/1.53 thf(f60,plain,(
% 1.82/1.53 ((in @ sK3 @ sK1) != $true) | ($true != $true)),
% 1.82/1.53 inference(superposition,[status(thm)],[f58,f33])).
% 1.82/1.53 thf(f33,plain,(
% 1.82/1.53 ((in @ sK3 @ sK2) = $true)),
% 1.82/1.53 inference(cnf_transformation,[status(thm)],[f22])).
% 1.82/1.53 thf(f58,plain,(
% 1.82/1.53 ( ! [X0 : $i] : (((in @ X0 @ sK2) != $true) | ((in @ X0 @ sK1) != $true)) )),
% 1.82/1.53 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.82/1.53 thf(f57,plain,(
% 1.82/1.53 ( ! [X0 : $i] : (($true != $true) | ((in @ X0 @ sK1) != $true) | ((in @ X0 @ sK2) != $true)) )),
% 1.82/1.53 inference(superposition,[status(thm)],[f56,f35])).
% 1.82/1.53 thf(f35,plain,(
% 1.82/1.53 ((subset @ sK1 @ (setminus @ sK0 @ sK2)) = $true)),
% 1.82/1.53 inference(cnf_transformation,[status(thm)],[f22])).
% 1.82/1.53 thf(f56,plain,(
% 1.82/1.53 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((subset @ X3 @ (setminus @ X1 @ X2)) != $true) | ((in @ X0 @ X3) != $true) | ((in @ X0 @ X2) != $true)) )),
% 1.82/1.53 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.82/1.53 thf(f55,plain,(
% 1.82/1.53 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X3) != $true) | ((in @ X0 @ X2) != $true) | ((subset @ X3 @ (setminus @ X1 @ X2)) != $true) | ($true != $true)) )),
% 1.82/1.53 inference(superposition,[status(thm)],[f54,f53])).
% 1.82/1.53 thf(f53,plain,(
% 1.82/1.53 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) | ((subset @ X4 @ X3) != $true) | ((in @ X5 @ X4) != $true)) )),
% 1.82/1.53 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.82/1.53 thf(f49,plain,(
% 1.82/1.53 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X3) != $true) | ((in @ X5 @ X4) != $true) | ((in @ X5 @ X3) = $true) | ($true != $true)) )),
% 1.82/1.53 inference(definition_unfolding,[status(thm)],[f39,f31])).
% 1.82/1.53 thf(f31,plain,(
% 1.82/1.53 (subsetE = $true)),
% 1.82/1.53 inference(cnf_transformation,[status(thm)],[f22])).
% 1.82/1.53 thf(f39,plain,(
% 1.82/1.53 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ X4) != $true) | ((subset @ X4 @ X3) != $true) | (subsetE != $true)) )),
% 1.82/1.53 inference(cnf_transformation,[status(thm)],[f26])).
% 1.82/1.53 thf(f26,plain,(
% 1.82/1.53 ((subsetE = $true) | (($true != (in @ sK6 @ sK4)) & ((in @ sK6 @ sK5) = $true) & ($true = (subset @ sK5 @ sK4)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ X4) != $true) | ((subset @ X4 @ X3) != $true)) | (subsetE != $true))),
% 1.82/1.53 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f24,f25])).
% 1.82/1.53 thf(f25,plain,(
% 1.82/1.53 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true) & ((subset @ X1 @ X0) = $true)) => (($true != (in @ sK6 @ sK4)) & ((in @ sK6 @ sK5) = $true) & ($true = (subset @ sK5 @ sK4)))),
% 1.82/1.53 introduced(definition,[],[choice_axiom])).
% 1.82/1.53 thf(f24,plain,(
% 1.82/1.53 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true) & ((subset @ X1 @ X0) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ X4) != $true) | ((subset @ X4 @ X3) != $true)) | (subsetE != $true))),
% 1.82/1.53 inference(rectify,[status(thm)],[f23])).
% 1.82/1.53 thf(f23,plain,(
% 1.82/1.53 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true) & ((subset @ X1 @ X0) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true) | ((subset @ X1 @ X0) != $true)) | (subsetE != $true))),
% 1.82/1.53 inference(nnf_transformation,[status(thm)],[f15])).
% 1.82/1.53 thf(f15,plain,(
% 1.82/1.53 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true) | ((subset @ X1 @ X0) != $true))),
% 1.82/1.53 inference(flattening,[status(thm)],[f14])).
% 1.82/1.53 thf(f14,plain,(
% 1.82/1.53 ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) | ((subset @ X1 @ X0) != $true)) <=> (subsetE = $true)),
% 1.82/1.53 inference(ennf_transformation,[status(thm)],[f7])).
% 1.82/1.53 thf(f7,plain,(
% 1.82/1.53 ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true))) <=> (subsetE = $true)),
% 1.82/1.53 inference(fool_elimination,[status(thm)],[f6])).
% 1.82/1.53 thf(f6,plain,(
% 1.82/1.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = subsetE)),
% 1.82/1.53 inference(rectify,[status(thm)],[f1])).
% 1.82/1.53 thf(f1,axiom,(
% 1.82/1.53 (! [X1 : $i,X0 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.82/1.53 file('/export/starexec/sandbox/tmp/tmp.tJFxPYu7Uc/DTF2THF_7010.p',subsetE)).
% 1.82/1.53 thf(f54,plain,(
% 1.82/1.53 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X3 @ X5)) != $true) | ((in @ X4 @ X5) != $true)) )),
% 1.82/1.53 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.82/1.53 thf(f52,plain,(
% 1.82/1.53 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X3 @ X5)) != $true) | ((in @ X4 @ X5) != $true) | ($true != $true)) )),
% 1.82/1.53 inference(definition_unfolding,[status(thm)],[f43,f38])).
% 1.82/1.53 thf(f38,plain,(
% 1.82/1.53 (setminusER = $true)),
% 1.82/1.53 inference(cnf_transformation,[status(thm)],[f22])).
% 1.82/1.53 thf(f43,plain,(
% 1.82/1.53 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) != $true) | ((in @ X4 @ (setminus @ X3 @ X5)) != $true) | (setminusER != $true)) )),
% 1.82/1.53 inference(cnf_transformation,[status(thm)],[f30])).
% 1.82/1.53 thf(f30,plain,(
% 1.82/1.53 ((setminusER = $true) | (((in @ sK8 @ sK9) = $true) & ((in @ sK8 @ (setminus @ sK7 @ sK9)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) != $true) | ((in @ X4 @ (setminus @ X3 @ X5)) != $true)) | (setminusER != $true))),
% 1.82/1.53 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f28,f29])).
% 1.82/1.53 thf(f29,plain,(
% 1.82/1.53 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X1 @ (setminus @ X0 @ X2)) = $true)) => (((in @ sK8 @ sK9) = $true) & ((in @ sK8 @ (setminus @ sK7 @ sK9)) = $true))),
% 1.82/1.53 introduced(definition,[],[choice_axiom])).
% 1.82/1.53 thf(f28,plain,(
% 1.82/1.53 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X1 @ (setminus @ X0 @ X2)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) != $true) | ((in @ X4 @ (setminus @ X3 @ X5)) != $true)) | (setminusER != $true))),
% 1.82/1.53 inference(rectify,[status(thm)],[f27])).
% 1.82/1.53 thf(f27,plain,(
% 1.82/1.53 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X1 @ (setminus @ X0 @ X2)) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X1 @ (setminus @ X0 @ X2)) != $true)) | (setminusER != $true))),
% 1.82/1.53 inference(nnf_transformation,[status(thm)],[f18])).
% 1.82/1.53 thf(f18,plain,(
% 1.82/1.53 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X1 @ (setminus @ X0 @ X2)) != $true))),
% 1.82/1.53 inference(ennf_transformation,[status(thm)],[f13])).
% 1.82/1.53 thf(f13,plain,(
% 1.82/1.53 (setminusER = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X1 @ (setminus @ X0 @ X2)) = $true) => ((in @ X1 @ X2) != $true))),
% 1.82/1.53 inference(flattening,[status(thm)],[f9])).
% 1.82/1.53 thf(f9,plain,(
% 1.82/1.53 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X0 @ X2)) = $true) => ~((in @ X1 @ X2) = $true))),
% 1.82/1.53 inference(fool_elimination,[status(thm)],[f8])).
% 1.82/1.53 thf(f8,plain,(
% 1.82/1.53 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setminus @ X0 @ X2)) => ~(in @ X1 @ X2)))),
% 1.82/1.53 inference(rectify,[status(thm)],[f2])).
% 1.82/1.53 thf(f2,axiom,(
% 1.82/1.53 (setminusER = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 1.82/1.53 file('/export/starexec/sandbox/tmp/tmp.tJFxPYu7Uc/DTF2THF_7010.p',setminusER)).
% 1.82/1.53 % SZS output end Proof for DTF2THF_7010
% 1.82/1.53 % (7128)------------------------------
% 1.82/1.53 % (7128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.53 % (7128)Termination reason: Refutation
% 1.82/1.53
% 1.82/1.53 % (7128)Memory used [KB]: 5500
% 1.82/1.53 % (7128)Time elapsed: 0.007 s
% 1.82/1.53 % (7128)Instructions burned: 6 (million)
% 1.82/1.53 % (7128)------------------------------
% 1.82/1.53 % (7128)------------------------------
% 1.82/1.53 % (7122)Success in time 0.022 s
%------------------------------------------------------------------------------