%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU604^2 : 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 : n015.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 09:35:33 AM UTC 2026
% Result : Theorem 1.64s 1.30s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 88 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 992 ( 295 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 896 ( 124 ~; 102 |; 71 &; 534 @)
% ( 12 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 22 con; 0-2 aty)
% Number of variables : 200 ( 0 ^; 154 !; 46 ?; 200 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_7,type,
setminus: $i > $i > $i ).
thf(func_def_21,type,
sK9: $i > $i > $i ).
thf(f160,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f159,f59]) ).
thf(f59,plain,
( emptyset
!= ( setminus @ sK3 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( subsetemptysetimpeq = $true )
& ( subsetI2 = $true )
& ( $true
= ( subset @ sK3 @ sK4 ) )
& ( emptyset
!= ( setminus @ sK3 @ sK4 ) )
& ( setminusEL = $true )
& ( subsetE = $true )
& ( setminusER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f24,f34]) ).
thf(f34,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( emptyset
!= ( setminus @ X0 @ X1 ) ) )
=> ( ( $true
= ( subset @ sK3 @ sK4 ) )
& ( emptyset
!= ( setminus @ sK3 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( subsetemptysetimpeq = $true )
& ( subsetI2 = $true )
& ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( emptyset
!= ( setminus @ X0 @ X1 ) ) )
& ( setminusEL = $true )
& ( subsetE = $true )
& ( setminusER = $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( emptyset
!= ( setminus @ X0 @ X1 ) ) )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( subsetemptysetimpeq = $true )
& ( subsetE = $true )
& ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
~ ( ( subsetI2 = $true )
=> ( ( subsetE = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( emptyset
= ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( subsetI2
=> ( subsetE
=> ( subsetemptysetimpeq
=> ( setminusEL
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( emptyset
= ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( subsetI2
=> ( subsetE
=> ( subsetemptysetimpeq
=> ( setminusEL
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( emptyset
= ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( subsetI2
=> ( subsetE
=> ( subsetemptysetimpeq
=> ( setminusEL
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( emptyset
= ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',setminusSubset2) ).
thf(f159,plain,
( emptyset
= ( setminus @ sK3 @ sK4 ) ),
inference(trivial_inequality_removal,[status(thm)],[f158]) ).
thf(f158,plain,
( ( emptyset
= ( setminus @ sK3 @ sK4 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f144,f101]) ).
thf(f101,plain,
! [X0: $i] :
( ( ( in @ ( sK9 @ emptyset @ X0 ) @ X0 )
= $true )
| ( emptyset = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
! [X0: $i] :
( ( emptyset = X0 )
| ( $true != $true )
| ( ( in @ ( sK9 @ emptyset @ X0 ) @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f99,f95]) ).
thf(f95,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( in @ ( sK9 @ X1 @ X0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK9 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( subset @ X0 @ X1 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f72,f61]) ).
thf(f61,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f72,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( in @ ( sK9 @ X1 @ X0 ) @ X0 )
= $true )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( ( in @ ( sK9 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( in @ ( sK9 @ X1 @ X0 ) @ X1 )
!= $true ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ( ( $true
!= ( subset @ sK10 @ sK11 ) )
& ! [X5: $i] :
( ( ( in @ X5 @ sK10 )
!= $true )
| ( ( in @ X5 @ sK11 )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f45,f47,f46]) ).
thf(f46,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
=> ( ( ( in @ ( sK9 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( in @ ( sK9 @ X1 @ X0 ) @ X1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f47,plain,
( ? [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( $true
= ( in @ X5 @ X4 ) ) ) )
=> ( ( $true
!= ( subset @ sK10 @ sK11 ) )
& ! [X5: $i] :
( ( ( in @ X5 @ sK10 )
!= $true )
| ( ( in @ X5 @ sK11 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( $true
= ( in @ X5 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
<=> ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( subsetI2 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetI2
= ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',subsetI2) ).
thf(f99,plain,
! [X1: $i] :
( ( $true
!= ( subset @ X1 @ emptyset ) )
| ( emptyset = X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: $i] :
( ( emptyset = X1 )
| ( $true != $true )
| ( $true
!= ( subset @ X1 @ emptyset ) ) ),
inference(definition_unfolding,[status(thm)],[f66,f62]) ).
thf(f62,plain,
subsetemptysetimpeq = $true,
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f66,plain,
! [X1: $i] :
( ( emptyset = X1 )
| ( $true
!= ( subset @ X1 @ emptyset ) )
| ( subsetemptysetimpeq != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( subsetemptysetimpeq = $true )
| ( ( emptyset != sK8 )
& ( $true
= ( subset @ sK8 @ emptyset ) ) ) )
& ( ! [X1: $i] :
( ( emptyset = X1 )
| ( $true
!= ( subset @ X1 @ emptyset ) ) )
| ( subsetemptysetimpeq != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f41,f42]) ).
thf(f42,plain,
( ? [X0: $i] :
( ( emptyset != X0 )
& ( ( subset @ X0 @ emptyset )
= $true ) )
=> ( ( emptyset != sK8 )
& ( $true
= ( subset @ sK8 @ emptyset ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ( ( subsetemptysetimpeq = $true )
| ? [X0: $i] :
( ( emptyset != X0 )
& ( ( subset @ X0 @ emptyset )
= $true ) ) )
& ( ! [X1: $i] :
( ( emptyset = X1 )
| ( $true
!= ( subset @ X1 @ emptyset ) ) )
| ( subsetemptysetimpeq != $true ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( subsetemptysetimpeq = $true )
| ? [X0: $i] :
( ( emptyset != X0 )
& ( ( subset @ X0 @ emptyset )
= $true ) ) )
& ( ! [X0: $i] :
( ( emptyset = X0 )
| ( ( subset @ X0 @ emptyset )
!= $true ) )
| ( subsetemptysetimpeq != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( subsetemptysetimpeq = $true )
<=> ! [X0: $i] :
( ( emptyset = X0 )
| ( ( subset @ X0 @ emptyset )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( subsetemptysetimpeq = $true )
<=> ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
=> ( emptyset = X0 ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
=> ( emptyset = X0 ) )
= subsetemptysetimpeq ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
=> ( emptyset = X0 ) )
= subsetemptysetimpeq ),
file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',subsetemptysetimpeq) ).
thf(f144,plain,
! [X0: $i] :
( $true
!= ( in @ ( sK9 @ emptyset @ ( setminus @ sK3 @ sK4 ) ) @ ( setminus @ X0 @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f143]) ).
thf(f143,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK9 @ emptyset @ ( setminus @ sK3 @ sK4 ) ) @ ( setminus @ X0 @ sK4 ) ) ) ),
inference(superposition,[status(thm)],[f97,f140]) ).
thf(f140,plain,
( ( in @ ( sK9 @ emptyset @ ( setminus @ sK3 @ sK4 ) ) @ sK4 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ( ( in @ ( sK9 @ emptyset @ ( setminus @ sK3 @ sK4 ) ) @ sK4 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f110,f128]) ).
thf(f128,plain,
( $true
= ( in @ ( sK9 @ emptyset @ ( setminus @ sK3 @ sK4 ) ) @ sK3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f127]) ).
thf(f127,plain,
( ( emptyset != emptyset )
| ( $true
= ( in @ ( sK9 @ emptyset @ ( setminus @ sK3 @ sK4 ) ) @ sK3 ) ) ),
inference(superposition,[status(thm)],[f59,f103]) ).
thf(f103,plain,
! [X0: $i,X1: $i] :
( ( emptyset
= ( setminus @ X0 @ X1 ) )
| ( ( in @ ( sK9 @ emptyset @ ( setminus @ X0 @ X1 ) ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
! [X0: $i,X1: $i] :
( ( emptyset
= ( setminus @ X0 @ X1 ) )
| ( ( in @ ( sK9 @ emptyset @ ( setminus @ X0 @ X1 ) ) @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f94,f101]) ).
thf(f94,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X5 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X5 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f53,f58]) ).
thf(f58,plain,
setminusEL = $true,
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f53,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( setminusEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( setminusEL = $true )
| ( ( $true
= ( in @ sK1 @ ( setminus @ sK2 @ sK0 ) ) )
& ( ( in @ sK1 @ sK2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X5 )
= $true ) )
| ( setminusEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f31,f32]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X2 )
!= $true ) )
=> ( ( $true
= ( in @ sK1 @ ( setminus @ sK2 @ sK0 ) ) )
& ( ( in @ sK1 @ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ( setminusEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X5 )
= $true ) )
| ( setminusEL != $true ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( setminusEL = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( setminusEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( setminusEL = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
=> ( ( in @ X2 @ X1 )
= $true ) )
<=> ( setminusEL = $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
=> ( in @ X2 @ X1 ) )
= setminusEL ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) )
= setminusEL ),
file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',setminusEL) ).
thf(f110,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK3 )
!= $true )
| ( $true
= ( in @ X0 @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( in @ X0 @ sK4 ) )
| ( ( in @ X0 @ sK3 )
!= $true ) ),
inference(superposition,[status(thm)],[f98,f60]) ).
thf(f60,plain,
( $true
= ( subset @ sK3 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f98,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f76,f57]) ).
thf(f57,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f76,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( ( in @ sK14 @ sK12 )
!= $true )
& ( ( subset @ sK13 @ sK12 )
= $true )
& ( $true
= ( in @ sK14 @ sK13 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f50,f51]) ).
thf(f51,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( ( subset @ X4 @ X3 )
= $true )
& ( $true
= ( in @ X5 @ X4 ) ) )
=> ( ( ( in @ sK14 @ sK12 )
!= $true )
& ( ( subset @ sK13 @ sK12 )
= $true )
& ( $true
= ( in @ sK14 @ sK13 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f50,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( ( subset @ X4 @ X3 )
= $true )
& ( $true
= ( in @ X5 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( ( subset @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X0 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) )
<=> ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( ( subset @ X2 @ X1 )
!= $true ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( in @ X0 @ X1 )
= $true ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( subsetE
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',subsetE) ).
thf(f97,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f63,f56]) ).
thf(f56,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f63,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X5 )
!= $true )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( setminusER = $true )
| ( ( ( in @ sK5 @ ( setminus @ sK6 @ sK7 ) )
= $true )
& ( $true
= ( in @ sK5 @ sK7 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f37,f38]) ).
thf(f38,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
& ( $true
= ( in @ X0 @ X2 ) ) )
=> ( ( ( in @ sK5 @ ( setminus @ sK6 @ sK7 ) )
= $true )
& ( $true
= ( in @ sK5 @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
& ( $true
= ( in @ X0 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
!= $true )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( setminusER = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( setminusER = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( setminusER = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
=> ~ ( in @ X1 @ X0 ) )
= setminusER ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',setminusER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU604^2 : 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
% 0.15/0.34 % Computer : n015.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:28:31 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEU604^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.31/0.46 % Version : Especial > Reduced > Especial.
% 0.31/0.46 % English : (! A:i.! B:i.subset A B -> setminus A B = emptyset)
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.46 % Source : [Bro08]
% 0.31/0.46 % Names : ZFC106l [Bro08]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.31/0.46 % Syntax : Number of formulae : 15 ( 5 unt; 9 typ; 5 def)
% 0.31/0.46 % Number of atoms : 29 ( 7 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 7 ( 4 avg)
% 0.31/0.46 % Number of connectives : 44 ( 1 ~; 0 |; 0 &; 30 @)
% 0.31/0.46 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 11 ( 3 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 10 ( 9 usr; 6 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : http://mathgate.info/detsetitem.php?id=481
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(in_type,type,
% 0.31/0.46 in: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(emptyset_type,type,
% 0.31/0.46 emptyset: $i ).
% 0.31/0.46
% 0.31/0.46 thf(subset_type,type,
% 0.31/0.46 subset: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(subsetI2_type,type,
% 0.31/0.46 subsetI2: $o ).
% 0.31/0.46
% 0.31/0.46 thf(subsetI2,definition,
% 0.31/0.46 ( subsetI2
% 0.31/0.46 = ( ! [A: $i,B: $i] :
% 0.31/0.46 ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 => ( in @ Xx @ B ) )
% 0.31/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(subsetE_type,type,
% 0.31/0.46 subsetE: $o ).
% 0.31/0.46
% 0.31/0.46 thf(subsetE,definition,
% 0.31/0.46 ( subsetE
% 0.31/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.46 ( ( subset @ A @ B )
% 0.31/0.46 => ( ( in @ Xx @ A )
% 0.31/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(subsetemptysetimpeq_type,type,
% 0.31/0.46 subsetemptysetimpeq: $o ).
% 0.31/0.46
% 0.31/0.46 thf(subsetemptysetimpeq,definition,
% 0.31/0.46 ( subsetemptysetimpeq
% 0.31/0.46 = ( ! [A: $i] :
% 0.31/0.46 ( ( subset @ A @ emptyset )
% 0.31/0.46 => ( A = emptyset ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(setminus_type,type,
% 0.31/0.46 setminus: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(setminusEL_type,type,
% 0.31/0.46 setminusEL: $o ).
% 0.31/0.46
% 0.31/0.46 thf(setminusEL,definition,
% 0.31/0.46 ( setminusEL
% 0.31/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.31/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(setminusER_type,type,
% 0.31/0.46 setminusER: $o ).
% 0.31/0.46
% 0.31/0.46 thf(setminusER,definition,
% 0.31/0.46 ( setminusER
% 0.31/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.31/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(setminusSubset2,conjecture,
% 0.31/0.46 ( subsetI2
% 0.31/0.46 => ( subsetE
% 0.31/0.46 => ( subsetemptysetimpeq
% 0.31/0.46 => ( setminusEL
% 0.31/0.46 => ( setminusER
% 0.31/0.46 => ! [A: $i,B: $i] :
% 0.31/0.46 ( ( subset @ A @ B )
% 0.31/0.46 => ( ( setminus @ A @ B )
% 0.31/0.46 = emptyset ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.51/1.27 ---- Embedded in THF ---
% 1.51/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.27 %%% Generated on Tue Feb 24 12:28:32 EST 2026
% 1.51/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.27 %%% Logic specification used:
% 1.51/1.27 %%% thf(spec, logic, $$dhol).
% 1.51/1.27
% 1.51/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2DTF29852.p
% See solution above
% 1.51/1.27 ------------------------
% 1.51/1.28 ---- Cleaned THF ---
% 1.51/1.28 thf(in_type,type,
% 1.51/1.28 in: $i > $i > $o ).
% 1.51/1.28
% 1.51/1.28 thf(emptyset_type,type,
% 1.51/1.28 emptyset: $i ).
% 1.51/1.28
% 1.51/1.28 thf(subset_type,type,
% 1.51/1.28 subset: $i > $i > $o ).
% 1.51/1.28
% 1.51/1.28 thf(subsetI2_type,type,
% 1.51/1.28 subsetI2: $o ).
% 1.51/1.28
% 1.51/1.28 thf(subsetI2,definition,
% 1.51/1.28 ( subsetI2
% 1.51/1.28 = ( ! [A: $i,B: $i] :
% 1.51/1.28 ( ! [Xx: $i] :
% 1.51/1.28 ( ( in @ Xx @ A )
% 1.51/1.28 => ( in @ Xx @ B ) )
% 1.51/1.28 => ( subset @ A @ B ) ) ) ) ).
% 1.51/1.28
% 1.51/1.28 thf(subsetE_type,type,
% 1.51/1.28 subsetE: $o ).
% 1.51/1.28
% 1.51/1.28 thf(subsetE,definition,
% 1.51/1.28 ( subsetE
% 1.51/1.28 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.51/1.28 ( ( subset @ A @ B )
% 1.51/1.28 => ( ( in @ Xx @ A )
% 1.51/1.28 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.51/1.28
% 1.51/1.28 thf(subsetemptysetimpeq_type,type,
% 1.51/1.28 subsetemptysetimpeq: $o ).
% 1.51/1.28
% 1.51/1.28 thf(subsetemptysetimpeq,definition,
% 1.51/1.28 ( subsetemptysetimpeq
% 1.51/1.28 = ( ! [A: $i] :
% 1.51/1.28 ( ( subset @ A @ emptyset )
% 1.51/1.28 => ( A = emptyset ) ) ) ) ).
% 1.51/1.28
% 1.51/1.28 thf(setminus_type,type,
% 1.51/1.28 setminus: $i > $i > $i ).
% 1.51/1.28
% 1.51/1.28 thf(setminusEL_type,type,
% 1.51/1.28 setminusEL: $o ).
% 1.51/1.28
% 1.51/1.28 thf(setminusEL,definition,
% 1.51/1.28 ( setminusEL
% 1.51/1.28 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.51/1.28 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.51/1.28 => ( in @ Xx @ A ) ) ) ) ).
% 1.51/1.28
% 1.51/1.28 thf(setminusER_type,type,
% 1.51/1.28 setminusER: $o ).
% 1.51/1.28
% 1.51/1.28 thf(setminusER,definition,
% 1.51/1.28 ( setminusER
% 1.51/1.28 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.51/1.28 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.51/1.28 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.51/1.28
% 1.51/1.28 thf(setminusSubset2,conjecture,
% 1.51/1.28 ( subsetI2
% 1.51/1.28 => ( subsetE
% 1.51/1.28 => ( subsetemptysetimpeq
% 1.51/1.28 => ( setminusEL
% 1.51/1.28 => ( setminusER
% 1.51/1.28 => ! [A: $i,B: $i] :
% 1.51/1.28 ( ( subset @ A @ B )
% 1.51/1.28 => ( ( setminus @ A @ B )
% 1.51/1.28 = emptyset ) ) ) ) ) ) ) ).
% 1.51/1.28 ------------------------
% 1.51/1.30 % (30138)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29852 for (2999ds/18Mi)
% 1.51/1.30 % (30133)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_29852 for (2999ds/4Mi)
% 1.64/1.30 % (30133)Instruction limit reached!
% 1.64/1.30 % (30133)------------------------------
% 1.64/1.30 % (30133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (30133)Termination reason: Unknown
% 1.64/1.30 % (30133)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (30133)Memory used [KB]: 5500
% 1.64/1.30 % (30133)Time elapsed: 0.003 s
% 1.64/1.30 % (30133)Instructions burned: 5 (million)
% 1.64/1.30 % (30133)------------------------------
% 1.64/1.30 % (30133)------------------------------
% 1.64/1.30 % (30138)First to succeed.
% 1.64/1.30 % (30132)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29852 for (2999ds/183Mi)
% 1.64/1.30 % (30134)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_29852 for (2999ds/27Mi)
% 1.64/1.30 % (30135)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29852 for (2999ds/2Mi)
% 1.64/1.30 % (30136)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_29852 for (2999ds/2Mi)
% 1.64/1.30 % (30137)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_29852 for (2999ds/275Mi)
% 1.64/1.30 % (30138)Refutation found. Thanks to Tanya!
% 1.64/1.30 % SZS status Theorem for DTF2THF_29852
% 1.64/1.30 % SZS output start Proof for DTF2THF_29852
% 1.64/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.30 thf(func_def_2, type, subset: $i > $i > $o).
% 1.64/1.30 thf(func_def_7, type, setminus: $i > $i > $i).
% 1.64/1.30 thf(func_def_21, type, sK9: $i > $i > $i).
% 1.64/1.30 thf(f160,plain,(
% 1.64/1.30 $false),
% 1.64/1.30 inference(subsumption_resolution,[status(thm)],[f159,f59])).
% 1.64/1.30 thf(f59,plain,(
% 1.64/1.30 (emptyset != (setminus @ sK3 @ sK4))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f35])).
% 1.64/1.30 thf(f35,plain,(
% 1.64/1.30 (subsetemptysetimpeq = $true) & (subsetI2 = $true) & (($true = (subset @ sK3 @ sK4)) & (emptyset != (setminus @ sK3 @ sK4))) & (setminusEL = $true) & (subsetE = $true) & (setminusER = $true)),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f24,f34])).
% 1.64/1.30 thf(f34,plain,(
% 1.64/1.30 ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & (emptyset != (setminus @ X0 @ X1))) => (($true = (subset @ sK3 @ sK4)) & (emptyset != (setminus @ sK3 @ sK4)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f24,plain,(
% 1.64/1.30 (subsetemptysetimpeq = $true) & (subsetI2 = $true) & ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & (emptyset != (setminus @ X0 @ X1))) & (setminusEL = $true) & (subsetE = $true) & (setminusER = $true)),
% 1.64/1.30 inference(flattening,[status(thm)],[f23])).
% 1.64/1.30 thf(f23,plain,(
% 1.64/1.30 ((((? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & (emptyset != (setminus @ X0 @ X1))) & (setminusER = $true)) & (setminusEL = $true)) & (subsetemptysetimpeq = $true)) & (subsetE = $true)) & (subsetI2 = $true)),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f20])).
% 1.64/1.30 thf(f20,plain,(
% 1.64/1.30 ~((subsetI2 = $true) => ((subsetE = $true) => ((subsetemptysetimpeq = $true) => ((setminusEL = $true) => ((setminusER = $true) => ! [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) = $true) => (emptyset = (setminus @ X0 @ X1))))))))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f19])).
% 1.64/1.30 thf(f19,plain,(
% 1.64/1.30 ~(subsetI2 => (subsetE => (subsetemptysetimpeq => (setminusEL => (setminusER => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (emptyset = (setminus @ X0 @ X1))))))))),
% 1.64/1.30 inference(rectify,[status(thm)],[f7])).
% 1.64/1.30 thf(f7,negated_conjecture,(
% 1.64/1.30 ~(subsetI2 => (subsetE => (subsetemptysetimpeq => (setminusEL => (setminusER => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (emptyset = (setminus @ X0 @ X1))))))))),
% 1.64/1.30 inference(negated_conjecture,[status(cth)],[f6])).
% 1.64/1.30 thf(f6,conjecture,(
% 1.64/1.30 subsetI2 => (subsetE => (subsetemptysetimpeq => (setminusEL => (setminusER => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (emptyset = (setminus @ X0 @ X1)))))))),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',setminusSubset2)).
% 1.64/1.30 thf(f159,plain,(
% 1.64/1.30 (emptyset = (setminus @ sK3 @ sK4))),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f158])).
% 1.64/1.30 thf(f158,plain,(
% 1.64/1.30 (emptyset = (setminus @ sK3 @ sK4)) | ($true != $true)),
% 1.64/1.30 inference(superposition,[status(thm)],[f144,f101])).
% 1.64/1.30 thf(f101,plain,(
% 1.64/1.30 ( ! [X0 : $i] : (((in @ (sK9 @ emptyset @ X0) @ X0) = $true) | (emptyset = X0)) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.64/1.30 thf(f100,plain,(
% 1.64/1.30 ( ! [X0 : $i] : ((emptyset = X0) | ($true != $true) | ((in @ (sK9 @ emptyset @ X0) @ X0) = $true)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f99,f95])).
% 1.64/1.30 thf(f95,plain,(
% 1.64/1.30 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK9 @ X1 @ X0) @ X0) = $true)) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.64/1.30 thf(f86,plain,(
% 1.64/1.30 ( ! [X0 : $i,X1 : $i] : (((in @ (sK9 @ X1 @ X0) @ X0) = $true) | ((subset @ X0 @ X1) = $true) | ($true != $true)) )),
% 1.64/1.30 inference(definition_unfolding,[status(thm)],[f72,f61])).
% 1.64/1.30 thf(f61,plain,(
% 1.64/1.30 (subsetI2 = $true)),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f35])).
% 1.64/1.30 thf(f72,plain,(
% 1.64/1.30 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK9 @ X1 @ X0) @ X0) = $true) | (subsetI2 != $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f48])).
% 1.64/1.30 thf(f48,plain,(
% 1.64/1.30 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (((in @ (sK9 @ X1 @ X0) @ X0) = $true) & ((in @ (sK9 @ X1 @ X0) @ X1) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | (($true != (subset @ sK10 @ sK11)) & ! [X5 : $i] : (((in @ X5 @ sK10) != $true) | ((in @ X5 @ sK11) = $true))))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f45,f47,f46])).
% 1.64/1.30 thf(f46,plain,(
% 1.64/1.30 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) => (((in @ (sK9 @ X1 @ X0) @ X0) = $true) & ((in @ (sK9 @ X1 @ X0) @ X1) != $true)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f47,plain,(
% 1.64/1.30 ? [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) != $true) & ! [X5 : $i] : (((in @ X5 @ X3) != $true) | ($true = (in @ X5 @ X4)))) => (($true != (subset @ sK10 @ sK11)) & ! [X5 : $i] : (((in @ X5 @ sK10) != $true) | ((in @ X5 @ sK11) = $true)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f45,plain,(
% 1.64/1.30 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) != $true) & ! [X5 : $i] : (((in @ X5 @ X3) != $true) | ($true = (in @ X5 @ X4)))))),
% 1.64/1.30 inference(rectify,[status(thm)],[f44])).
% 1.64/1.30 thf(f44,plain,(
% 1.64/1.30 (! [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))))),
% 1.64/1.30 inference(nnf_transformation,[status(thm)],[f22])).
% 1.64/1.30 thf(f22,plain,(
% 1.64/1.30 ! [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) <=> (subsetI2 = $true)),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f10])).
% 1.64/1.30 thf(f10,plain,(
% 1.64/1.30 (subsetI2 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ((subset @ X1 @ X0) = $true))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f9])).
% 1.64/1.30 thf(f9,plain,(
% 1.64/1.30 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 1.64/1.30 inference(rectify,[status(thm)],[f1])).
% 1.64/1.30 thf(f1,axiom,(
% 1.64/1.30 (subsetI2 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',subsetI2)).
% 1.64/1.30 thf(f99,plain,(
% 1.64/1.30 ( ! [X1 : $i] : (($true != (subset @ X1 @ emptyset)) | (emptyset = X1)) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.64/1.30 thf(f85,plain,(
% 1.64/1.30 ( ! [X1 : $i] : ((emptyset = X1) | ($true != $true) | ($true != (subset @ X1 @ emptyset))) )),
% 1.64/1.30 inference(definition_unfolding,[status(thm)],[f66,f62])).
% 1.64/1.30 thf(f62,plain,(
% 1.64/1.30 (subsetemptysetimpeq = $true)),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f35])).
% 1.64/1.30 thf(f66,plain,(
% 1.64/1.30 ( ! [X1 : $i] : ((emptyset = X1) | ($true != (subset @ X1 @ emptyset)) | (subsetemptysetimpeq != $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f43])).
% 1.64/1.30 thf(f43,plain,(
% 1.64/1.30 ((subsetemptysetimpeq = $true) | ((emptyset != sK8) & ($true = (subset @ sK8 @ emptyset)))) & (! [X1 : $i] : ((emptyset = X1) | ($true != (subset @ X1 @ emptyset))) | (subsetemptysetimpeq != $true))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f41,f42])).
% 1.64/1.30 thf(f42,plain,(
% 1.64/1.30 ? [X0 : $i] : ((emptyset != X0) & ((subset @ X0 @ emptyset) = $true)) => ((emptyset != sK8) & ($true = (subset @ sK8 @ emptyset)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f41,plain,(
% 1.64/1.30 ((subsetemptysetimpeq = $true) | ? [X0 : $i] : ((emptyset != X0) & ((subset @ X0 @ emptyset) = $true))) & (! [X1 : $i] : ((emptyset = X1) | ($true != (subset @ X1 @ emptyset))) | (subsetemptysetimpeq != $true))),
% 1.64/1.30 inference(rectify,[status(thm)],[f40])).
% 1.64/1.30 thf(f40,plain,(
% 1.64/1.30 ((subsetemptysetimpeq = $true) | ? [X0 : $i] : ((emptyset != X0) & ((subset @ X0 @ emptyset) = $true))) & (! [X0 : $i] : ((emptyset = X0) | ((subset @ X0 @ emptyset) != $true)) | (subsetemptysetimpeq != $true))),
% 1.64/1.30 inference(nnf_transformation,[status(thm)],[f26])).
% 1.64/1.30 thf(f26,plain,(
% 1.64/1.30 (subsetemptysetimpeq = $true) <=> ! [X0 : $i] : ((emptyset = X0) | ((subset @ X0 @ emptyset) != $true))),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f16])).
% 1.64/1.30 thf(f16,plain,(
% 1.64/1.30 (subsetemptysetimpeq = $true) <=> ! [X0 : $i] : (((subset @ X0 @ emptyset) = $true) => (emptyset = X0))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f15])).
% 1.64/1.30 thf(f15,plain,(
% 1.64/1.30 (! [X0 : $i] : ((subset @ X0 @ emptyset) => (emptyset = X0)) = subsetemptysetimpeq)),
% 1.64/1.30 inference(rectify,[status(thm)],[f3])).
% 1.64/1.30 thf(f3,axiom,(
% 1.64/1.30 (! [X0 : $i] : ((subset @ X0 @ emptyset) => (emptyset = X0)) = subsetemptysetimpeq)),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',subsetemptysetimpeq)).
% 1.64/1.30 thf(f144,plain,(
% 1.64/1.30 ( ! [X0 : $i] : (($true != (in @ (sK9 @ emptyset @ (setminus @ sK3 @ sK4)) @ (setminus @ X0 @ sK4)))) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f143])).
% 1.64/1.30 thf(f143,plain,(
% 1.64/1.30 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ (sK9 @ emptyset @ (setminus @ sK3 @ sK4)) @ (setminus @ X0 @ sK4)))) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f97,f140])).
% 1.64/1.30 thf(f140,plain,(
% 1.64/1.30 ((in @ (sK9 @ emptyset @ (setminus @ sK3 @ sK4)) @ sK4) = $true)),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.64/1.30 thf(f138,plain,(
% 1.64/1.30 ((in @ (sK9 @ emptyset @ (setminus @ sK3 @ sK4)) @ sK4) = $true) | ($true != $true)),
% 1.64/1.30 inference(superposition,[status(thm)],[f110,f128])).
% 1.64/1.30 thf(f128,plain,(
% 1.64/1.30 ($true = (in @ (sK9 @ emptyset @ (setminus @ sK3 @ sK4)) @ sK3))),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f127])).
% 1.64/1.30 thf(f127,plain,(
% 1.64/1.30 (emptyset != emptyset) | ($true = (in @ (sK9 @ emptyset @ (setminus @ sK3 @ sK4)) @ sK3))),
% 1.64/1.30 inference(superposition,[status(thm)],[f59,f103])).
% 1.64/1.30 thf(f103,plain,(
% 1.64/1.30 ( ! [X0 : $i,X1 : $i] : ((emptyset = (setminus @ X0 @ X1)) | ((in @ (sK9 @ emptyset @ (setminus @ X0 @ X1)) @ X0) = $true)) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.64/1.30 thf(f102,plain,(
% 1.64/1.30 ( ! [X0 : $i,X1 : $i] : ((emptyset = (setminus @ X0 @ X1)) | ((in @ (sK9 @ emptyset @ (setminus @ X0 @ X1)) @ X0) = $true) | ($true != $true)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f94,f101])).
% 1.64/1.30 thf(f94,plain,(
% 1.64/1.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X5 @ X3)) != $true) | ((in @ X4 @ X5) = $true)) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.64/1.30 thf(f79,plain,(
% 1.64/1.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X4 @ (setminus @ X5 @ X3)) != $true) | ((in @ X4 @ X5) = $true)) )),
% 1.64/1.30 inference(definition_unfolding,[status(thm)],[f53,f58])).
% 1.64/1.30 thf(f58,plain,(
% 1.64/1.30 (setminusEL = $true)),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f35])).
% 1.64/1.30 thf(f53,plain,(
% 1.64/1.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X5 @ X3)) != $true) | ((in @ X4 @ X5) = $true) | (setminusEL != $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f33])).
% 1.64/1.30 thf(f33,plain,(
% 1.64/1.30 ((setminusEL = $true) | (($true = (in @ sK1 @ (setminus @ sK2 @ sK0))) & ((in @ sK1 @ sK2) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X5 @ X3)) != $true) | ((in @ X4 @ X5) = $true)) | (setminusEL != $true))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f31,f32])).
% 1.64/1.30 thf(f32,plain,(
% 1.64/1.30 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) = $true) & ((in @ X1 @ X2) != $true)) => (($true = (in @ sK1 @ (setminus @ sK2 @ sK0))) & ((in @ sK1 @ sK2) != $true))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f31,plain,(
% 1.64/1.30 ((setminusEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) = $true) & ((in @ X1 @ X2) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X5 @ X3)) != $true) | ((in @ X4 @ X5) = $true)) | (setminusEL != $true))),
% 1.64/1.30 inference(rectify,[status(thm)],[f30])).
% 1.64/1.30 thf(f30,plain,(
% 1.64/1.30 ((setminusEL = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) & ((in @ X2 @ X1) != $true))) & (! [X0 : $i,X2 : $i,X1 : $i] : (($true != (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X1) = $true)) | (setminusEL != $true))),
% 1.64/1.30 inference(nnf_transformation,[status(thm)],[f25])).
% 1.64/1.30 thf(f25,plain,(
% 1.64/1.30 (setminusEL = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true != (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X1) = $true))),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f12])).
% 1.64/1.30 thf(f12,plain,(
% 1.64/1.30 ! [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) => ((in @ X2 @ X1) = $true)) <=> (setminusEL = $true)),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f11])).
% 1.64/1.30 thf(f11,plain,(
% 1.64/1.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X1 @ X0)) => (in @ X2 @ X1)) = setminusEL)),
% 1.64/1.30 inference(rectify,[status(thm)],[f4])).
% 1.64/1.30 thf(f4,axiom,(
% 1.64/1.30 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X0)) = setminusEL)),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',setminusEL)).
% 1.64/1.30 thf(f110,plain,(
% 1.64/1.30 ( ! [X0 : $i] : (((in @ X0 @ sK3) != $true) | ($true = (in @ X0 @ sK4))) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.64/1.30 thf(f107,plain,(
% 1.64/1.30 ( ! [X0 : $i] : (($true != $true) | ($true = (in @ X0 @ sK4)) | ((in @ X0 @ sK3) != $true)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f98,f60])).
% 1.64/1.30 thf(f60,plain,(
% 1.64/1.30 ($true = (subset @ sK3 @ sK4))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f35])).
% 1.64/1.30 thf(f98,plain,(
% 1.64/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.64/1.30 thf(f90,plain,(
% 1.64/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true) | ((subset @ X1 @ X0) != $true)) )),
% 1.64/1.30 inference(definition_unfolding,[status(thm)],[f76,f57])).
% 1.64/1.30 thf(f57,plain,(
% 1.64/1.30 (subsetE = $true)),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f35])).
% 1.64/1.30 thf(f76,plain,(
% 1.64/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ((subset @ X1 @ X0) != $true) | ((in @ X2 @ X1) != $true) | (subsetE != $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f52])).
% 1.64/1.30 thf(f52,plain,(
% 1.64/1.30 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ((subset @ X1 @ X0) != $true) | ((in @ X2 @ X1) != $true)) | (subsetE != $true)) & ((subsetE = $true) | (((in @ sK14 @ sK12) != $true) & ((subset @ sK13 @ sK12) = $true) & ($true = (in @ sK14 @ sK13))))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f50,f51])).
% 1.64/1.30 thf(f51,plain,(
% 1.64/1.30 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) & ((subset @ X4 @ X3) = $true) & ($true = (in @ X5 @ X4))) => (((in @ sK14 @ sK12) != $true) & ((subset @ sK13 @ sK12) = $true) & ($true = (in @ sK14 @ sK13)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f50,plain,(
% 1.64/1.30 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ((subset @ X1 @ X0) != $true) | ((in @ X2 @ X1) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) & ((subset @ X4 @ X3) = $true) & ($true = (in @ X5 @ X4))))),
% 1.64/1.30 inference(rectify,[status(thm)],[f49])).
% 1.64/1.30 thf(f49,plain,(
% 1.64/1.30 (! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true) | ($true != (in @ X0 @ X2))) | (subsetE != $true)) & ((subsetE = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X1) != $true) & ((subset @ X2 @ X1) = $true) & ($true = (in @ X0 @ X2))))),
% 1.64/1.30 inference(nnf_transformation,[status(thm)],[f29])).
% 1.64/1.30 thf(f29,plain,(
% 1.64/1.30 ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true) | ($true != (in @ X0 @ X2))) <=> (subsetE = $true)),
% 1.64/1.30 inference(flattening,[status(thm)],[f28])).
% 1.64/1.30 thf(f28,plain,(
% 1.64/1.30 ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X0 @ X1) = $true) | ($true != (in @ X0 @ X2))) | ((subset @ X2 @ X1) != $true)) <=> (subsetE = $true)),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f14])).
% 1.64/1.30 thf(f14,plain,(
% 1.64/1.30 ! [X1 : $i,X0 : $i,X2 : $i] : (((subset @ X2 @ X1) = $true) => (($true = (in @ X0 @ X2)) => ((in @ X0 @ X1) = $true))) <=> (subsetE = $true)),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f13])).
% 1.64/1.30 thf(f13,plain,(
% 1.64/1.30 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ X1))))),
% 1.64/1.30 inference(rectify,[status(thm)],[f2])).
% 1.64/1.30 thf(f2,axiom,(
% 1.64/1.30 (subsetE = ! [X2 : $i,X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',subsetE)).
% 1.64/1.30 thf(f97,plain,(
% 1.64/1.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) != $true) | ((in @ X3 @ (setminus @ X4 @ X5)) != $true)) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.64/1.30 thf(f82,plain,(
% 1.64/1.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) != $true) | ((in @ X3 @ (setminus @ X4 @ X5)) != $true) | ($true != $true)) )),
% 1.64/1.30 inference(definition_unfolding,[status(thm)],[f63,f56])).
% 1.64/1.30 thf(f56,plain,(
% 1.64/1.30 (setminusER = $true)),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f35])).
% 1.64/1.30 thf(f63,plain,(
% 1.64/1.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setminus @ X4 @ X5)) != $true) | ((in @ X3 @ X5) != $true) | (setminusER != $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f39])).
% 1.64/1.30 thf(f39,plain,(
% 1.64/1.30 ((setminusER = $true) | (((in @ sK5 @ (setminus @ sK6 @ sK7)) = $true) & ($true = (in @ sK5 @ sK7)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setminus @ X4 @ X5)) != $true) | ((in @ X3 @ X5) != $true)) | (setminusER != $true))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f37,f38])).
% 1.64/1.30 thf(f38,plain,(
% 1.64/1.30 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setminus @ X1 @ X2))) & ($true = (in @ X0 @ X2))) => (((in @ sK5 @ (setminus @ sK6 @ sK7)) = $true) & ($true = (in @ sK5 @ sK7)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f37,plain,(
% 1.64/1.30 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setminus @ X1 @ X2))) & ($true = (in @ X0 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setminus @ X4 @ X5)) != $true) | ((in @ X3 @ X5) != $true)) | (setminusER != $true))),
% 1.64/1.30 inference(rectify,[status(thm)],[f36])).
% 1.64/1.30 thf(f36,plain,(
% 1.64/1.30 ((setminusER = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) = $true) & ((in @ X1 @ X0) = $true))) & (! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) != $true) | ((in @ X1 @ X0) != $true)) | (setminusER != $true))),
% 1.64/1.30 inference(nnf_transformation,[status(thm)],[f27])).
% 1.64/1.30 thf(f27,plain,(
% 1.64/1.30 (setminusER = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) != $true) | ((in @ X1 @ X0) != $true))),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f21])).
% 1.64/1.30 thf(f21,plain,(
% 1.64/1.30 (setminusER = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) = $true) => ((in @ X1 @ X0) != $true))),
% 1.64/1.30 inference(flattening,[status(thm)],[f18])).
% 1.64/1.30 thf(f18,plain,(
% 1.64/1.30 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) = $true) => ~((in @ X1 @ X0) = $true)) <=> (setminusER = $true)),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f17])).
% 1.64/1.30 thf(f17,plain,(
% 1.64/1.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setminus @ X2 @ X0)) => ~(in @ X1 @ X0)) = setminusER)),
% 1.64/1.30 inference(rectify,[status(thm)],[f5])).
% 1.64/1.30 thf(f5,axiom,(
% 1.64/1.30 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.8HYPFkHrJi/DTF2THF_29852.p',setminusER)).
% 1.64/1.30 % SZS output end Proof for DTF2THF_29852
% 1.64/1.30 % (30138)------------------------------
% 1.64/1.30 % (30138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (30138)Termination reason: Refutation
% 1.64/1.30
% 1.64/1.30 % (30138)Memory used [KB]: 5628
% 1.64/1.30 % (30138)Time elapsed: 0.008 s
% 1.64/1.30 % (30138)Instructions burned: 14 (million)
% 1.64/1.30 % (30138)------------------------------
% 1.64/1.30 % (30138)------------------------------
% 1.64/1.30 % (30131)Success in time 0.018 s
%------------------------------------------------------------------------------