%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU685^2 : 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 : n002.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 09:36:23 AM UTC 2026
% Result : Theorem 1.59s 1.36s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 538 ( 137 equ; 0 cnn)
% Maximal formula atoms : 8 ( 12 avg)
% Number of connectives : 675 ( 61 ~; 41 |; 41 &; 498 @)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 15 con; 0-4 aty)
% Number of variables : 123 ( 0 ^; 86 !; 37 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_10,type,
breln: $i > $i > $i > $o ).
thf(func_def_11,type,
func: $i > $i > $i > $o ).
thf(func_def_12,type,
funcSet: $i > $i > $i ).
thf(func_def_13,type,
ap: $i > $i > $i > $i > $i ).
thf(f68,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f67,f47]) ).
thf(f47,plain,
( ( in @ sK7 @ sK6 )
= $true ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true
= ( in @ sK4 @ ( funcSet @ sK6 @ sK5 ) ) )
& ( ( in @ sK7 @ sK6 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK7 @ ( ap @ sK6 @ sK5 @ sK4 @ sK7 ) ) @ sK4 ) )
& ( infuncsetfunc = $true )
& ( funcGraphProp1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f27,f34,f33]) ).
thf(f33,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 )
!= $true ) ) )
=> ( ( $true
= ( in @ sK4 @ ( funcSet @ sK6 @ sK5 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ sK6 )
= $true )
& ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ sK6 @ sK5 @ sK4 @ X3 ) ) @ sK4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK6 )
= $true )
& ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ sK6 @ sK5 @ sK4 @ X3 ) ) @ sK4 ) ) )
=> ( ( ( in @ sK7 @ sK6 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK7 @ ( ap @ sK6 @ sK5 @ sK4 @ sK7 ) ) @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 )
!= $true ) ) )
& ( infuncsetfunc = $true )
& ( funcGraphProp1 = $true ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 )
!= $true ) ) )
& ( funcGraphProp1 = $true )
& ( infuncsetfunc = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( ( infuncsetfunc = $true )
=> ( ( funcGraphProp1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( infuncsetfunc
=> ( funcGraphProp1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( funcSet @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( infuncsetfunc
=> ( funcGraphProp1
=> ! [X7: $i,X3: $i,X0: $i] :
( ( in @ X7 @ ( funcSet @ X0 @ X3 ) )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( kpair @ X1 @ ( ap @ X0 @ X3 @ X7 @ X1 ) ) @ X7 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( infuncsetfunc
=> ( funcGraphProp1
=> ! [X7: $i,X3: $i,X0: $i] :
( ( in @ X7 @ ( funcSet @ X0 @ X3 ) )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( kpair @ X1 @ ( ap @ X0 @ X3 @ X7 @ X1 ) ) @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oPKcaH0VDE/DTF2THF_4931.p',funcGraphProp3) ).
thf(f67,plain,
( ( in @ sK7 @ sK6 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f65,f62]) ).
thf(f62,plain,
( $true
= ( func @ sK6 @ sK5 @ sK4 ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $true
= ( func @ sK6 @ sK5 @ sK4 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f60,f48]) ).
thf(f48,plain,
( $true
= ( in @ sK4 @ ( funcSet @ sK6 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f60,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( funcSet @ X3 @ X5 ) )
!= $true )
| ( ( func @ X3 @ X5 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( func @ X3 @ X5 @ X4 )
= $true )
| ( $true != $true )
| ( ( in @ X4 @ ( funcSet @ X3 @ X5 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f49,f45]) ).
thf(f45,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f49,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( funcSet @ X3 @ X5 ) )
!= $true )
| ( ( func @ X3 @ X5 @ X4 )
= $true )
| ( infuncsetfunc != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( infuncsetfunc = $true )
| ( ( $true
= ( in @ sK9 @ ( funcSet @ sK8 @ sK10 ) ) )
& ( $true
!= ( func @ sK8 @ sK10 @ sK9 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( funcSet @ X3 @ X5 ) )
!= $true )
| ( ( func @ X3 @ X5 @ X4 )
= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f37,f38]) ).
thf(f38,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
& ( $true
!= ( func @ X0 @ X2 @ X1 ) ) )
=> ( ( $true
= ( in @ sK9 @ ( funcSet @ sK8 @ sK10 ) ) )
& ( $true
!= ( func @ sK8 @ sK10 @ sK9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
& ( $true
!= ( func @ X0 @ X2 @ X1 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( funcSet @ X3 @ X5 ) )
!= $true )
| ( ( func @ X3 @ X5 @ X4 )
= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
& ( $true
!= ( func @ X0 @ X2 @ X1 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
| ( $true
= ( func @ X0 @ X2 @ X1 ) ) )
| ( infuncsetfunc != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( infuncsetfunc = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
| ( $true
= ( func @ X0 @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
=> ( $true
= ( func @ X0 @ X2 @ X1 ) ) )
<=> ( infuncsetfunc = $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( infuncsetfunc
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( funcSet @ X0 @ X2 ) )
=> ( func @ X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( infuncsetfunc
= ( ! [X0: $i,X7: $i,X3: $i] :
( ( in @ X7 @ ( funcSet @ X0 @ X3 ) )
=> ( func @ X0 @ X3 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oPKcaH0VDE/DTF2THF_4931.p',infuncsetfunc) ).
thf(f65,plain,
( ( $true
!= ( func @ sK6 @ sK5 @ sK4 ) )
| ( ( in @ sK7 @ sK6 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true != $true )
| ( ( in @ sK7 @ sK6 )
!= $true )
| ( $true
!= ( func @ sK6 @ sK5 @ sK4 ) ) ),
inference(superposition,[status(thm)],[f46,f59]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) )
| ( ( func @ X1 @ X0 @ X2 )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true != $true )
| ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) )
| ( ( func @ X1 @ X0 @ X2 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f43,f44]) ).
thf(f44,plain,
funcGraphProp1 = $true,
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( ( func @ X1 @ X0 @ X2 )
!= $true )
| ( funcGraphProp1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( ( func @ X1 @ X0 @ X2 )
!= $true ) )
| ( funcGraphProp1 != $true ) )
& ( ( funcGraphProp1 = $true )
| ( ( $true
!= ( in @ ( kpair @ sK3 @ ( ap @ sK1 @ sK0 @ sK2 @ sK3 ) ) @ sK2 ) )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
= ( func @ sK1 @ sK0 @ sK2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f29,f31,f30]) ).
thf(f30,plain,
( ? [X4: $i,X5: $i,X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ ( kpair @ X7 @ ( ap @ X5 @ X4 @ X6 @ X7 ) ) @ X6 ) )
& ( $true
= ( in @ X7 @ X5 ) ) )
& ( $true
= ( func @ X5 @ X4 @ X6 ) ) )
=> ( ? [X7: $i] :
( ( $true
!= ( in @ ( kpair @ X7 @ ( ap @ sK1 @ sK0 @ sK2 @ X7 ) ) @ sK2 ) )
& ( $true
= ( in @ X7 @ sK1 ) ) )
& ( $true
= ( func @ sK1 @ sK0 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ? [X7: $i] :
( ( $true
!= ( in @ ( kpair @ X7 @ ( ap @ sK1 @ sK0 @ sK2 @ X7 ) ) @ sK2 ) )
& ( $true
= ( in @ X7 @ sK1 ) ) )
=> ( ( $true
!= ( in @ ( kpair @ sK3 @ ( ap @ sK1 @ sK0 @ sK2 @ sK3 ) ) @ sK2 ) )
& ( $true
= ( in @ sK3 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( ( func @ X1 @ X0 @ X2 )
!= $true ) )
| ( funcGraphProp1 != $true ) )
& ( ( funcGraphProp1 = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ ( kpair @ X7 @ ( ap @ X5 @ X4 @ X6 @ X7 ) ) @ X6 ) )
& ( $true
= ( in @ X7 @ X5 ) ) )
& ( $true
= ( func @ X5 @ X4 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( ( func @ X1 @ X0 @ X2 )
!= $true ) )
| ( funcGraphProp1 != $true ) )
& ( ( funcGraphProp1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( ( func @ X1 @ X0 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( ( func @ X1 @ X0 @ X2 )
!= $true ) )
<=> ( funcGraphProp1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( funcGraphProp1 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( funcGraphProp1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( funcGraphProp1
= ( ! [X3: $i,X0: $i,X7: $i] :
( ( func @ X0 @ X3 @ X7 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( kpair @ X1 @ ( ap @ X0 @ X3 @ X7 @ X1 ) ) @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oPKcaH0VDE/DTF2THF_4931.p',funcGraphProp1) ).
thf(f46,plain,
( $true
!= ( in @ ( kpair @ sK7 @ ( ap @ sK6 @ sK5 @ sK4 @ sK7 ) ) @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU685^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.30 % Computer : n002.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Feb 24 12:31:03 EST 2026
% 0.10/0.30 % CPUTime :
% 0.10/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEU685^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : Functions - Extensionality and Beta Reduction
% 0.16/0.39 % Version : Especial > Reduced > Especial.
% 0.16/0.39 % English : (! A:i.! B:i.! f:i.in f (funcSet A B) -> (! x:i.in x A ->
% 0.16/0.39 % in (kpair x (ap A B f x)) f))
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.39 % Source : [Bro08]
% 0.16/0.39 % Names : ZFC187l [Bro08]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 22 ( 6 unt; 15 typ; 6 def)
% 0.16/0.39 % Number of atoms : 30 ( 7 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 5 ( 4 avg)
% 0.16/0.39 % Number of connectives : 67 ( 0 ~; 0 |; 2 &; 57 @)
% 0.16/0.39 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 16 ( 3 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 16 ( 15 usr; 3 con; 0-4 aty)
% 0.16/0.39 % Number of variables : 24 ( 11 ^; 12 !; 1 ?; 24 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : http://mathgate.info/detsetitem.php?id=412
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(in_type,type,
% 0.16/0.39 in: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset_type,type,
% 0.16/0.39 emptyset: $i ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin_type,type,
% 0.16/0.39 setadjoin: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr_type,type,
% 0.16/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(subset_type,type,
% 0.16/0.39 subset: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(kpair_type,type,
% 0.16/0.39 kpair: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(cartprod_type,type,
% 0.16/0.39 cartprod: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(singleton_type,type,
% 0.16/0.39 singleton: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(singleton,definition,
% 0.16/0.39 ( singleton
% 0.16/0.39 = ( ^ [A: $i] :
% 0.16/0.39 ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( A
% 0.16/0.39 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ex1_type,type,
% 0.16/0.39 ex1: $i > ( $i > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(ex1,definition,
% 0.16/0.39 ( ex1
% 0.16/0.39 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( singleton
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(breln_type,type,
% 0.16/0.39 breln: $i > $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(breln,definition,
% 0.16/0.39 ( breln
% 0.16/0.39 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(func_type,type,
% 0.16/0.39 func: $i > $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(func,definition,
% 0.16/0.39 ( func
% 0.16/0.39 = ( ^ [A: $i,B: $i,R: $i] :
% 0.16/0.39 ( ( breln @ A @ B @ R )
% 0.16/0.39 & ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ex1 @ B
% 0.16/0.39 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(funcSet_type,type,
% 0.16/0.39 funcSet: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(ap_type,type,
% 0.16/0.39 ap: $i > $i > $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(infuncsetfunc_type,type,
% 0.16/0.39 infuncsetfunc: $o ).
% 0.16/0.39
% 0.16/0.39 thf(infuncsetfunc,definition,
% 0.16/0.39 ( infuncsetfunc
% 0.16/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.16/0.39 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.16/0.39 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(funcGraphProp1_type,type,
% 0.16/0.39 funcGraphProp1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(funcGraphProp1,definition,
% 0.16/0.39 ( funcGraphProp1
% 0.16/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.16/0.39 ( ( func @ A @ B @ Xf )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(funcGraphProp3,conjecture,
% 0.16/0.39 ( infuncsetfunc
% 0.16/0.39 => ( funcGraphProp1
% 0.16/0.39 => ! [A: $i,B: $i,Xf: $i] :
% 0.16/0.39 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.59/1.32 ---- Embedded in THF ---
% 1.59/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.59/1.32 %%% Generated on Tue Feb 24 12:31:04 EST 2026
% 1.59/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.59/1.32 %%% Logic specification used:
% 1.59/1.32 %%% thf(spec, logic, $$dhol).
% 1.59/1.32
% 1.59/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oPKcaH0VDE/DTF2DTF4931.p
% See solution above
% 1.59/1.32 ------------------------
% 1.59/1.33 ---- Cleaned THF ---
% 1.59/1.33 thf(in_type,type,
% 1.59/1.33 in: $i > $i > $o ).
% 1.59/1.33
% 1.59/1.33 thf(emptyset_type,type,
% 1.59/1.33 emptyset: $i ).
% 1.59/1.33
% 1.59/1.33 thf(setadjoin_type,type,
% 1.59/1.33 setadjoin: $i > $i > $i ).
% 1.59/1.33
% 1.59/1.33 thf(dsetconstr_type,type,
% 1.59/1.33 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.59/1.33
% 1.59/1.33 thf(subset_type,type,
% 1.59/1.33 subset: $i > $i > $o ).
% 1.59/1.33
% 1.59/1.33 thf(kpair_type,type,
% 1.59/1.33 kpair: $i > $i > $i ).
% 1.59/1.33
% 1.59/1.33 thf(cartprod_type,type,
% 1.59/1.33 cartprod: $i > $i > $i ).
% 1.59/1.33
% 1.59/1.33 thf(singleton_type,type,
% 1.59/1.33 singleton: $i > $o ).
% 1.59/1.33
% 1.59/1.33 thf(singleton,definition,
% 1.59/1.33 ( singleton
% 1.59/1.33 = ( ^ [A: $i] :
% 1.59/1.33 ? [Xx: $i] :
% 1.59/1.33 ( ( in @ Xx @ A )
% 1.59/1.33 & ( A
% 1.59/1.33 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.59/1.33
% 1.59/1.33 thf(ex1_type,type,
% 1.59/1.33 ex1: $i > ( $i > $o ) > $o ).
% 1.59/1.33
% 1.59/1.33 thf(ex1,definition,
% 1.59/1.33 ( ex1
% 1.59/1.33 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.59/1.33 ( singleton
% 1.59/1.33 @ ( dsetconstr @ A
% 1.59/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.59/1.33
% 1.59/1.33 thf(breln_type,type,
% 1.59/1.33 breln: $i > $i > $i > $o ).
% 1.59/1.33
% 1.59/1.33 thf(breln,definition,
% 1.59/1.33 ( breln
% 1.59/1.33 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.59/1.33
% 1.59/1.33 thf(func_type,type,
% 1.59/1.33 func: $i > $i > $i > $o ).
% 1.59/1.33
% 1.59/1.33 thf(func,definition,
% 1.59/1.33 ( func
% 1.59/1.33 = ( ^ [A: $i,B: $i,R: $i] :
% 1.59/1.33 ( ( breln @ A @ B @ R )
% 1.59/1.33 & ! [Xx: $i] :
% 1.59/1.33 ( ( in @ Xx @ A )
% 1.59/1.33 => ( ex1 @ B
% 1.59/1.33 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 1.59/1.33
% 1.59/1.33 thf(funcSet_type,type,
% 1.59/1.33 funcSet: $i > $i > $i ).
% 1.59/1.33
% 1.59/1.33 thf(ap_type,type,
% 1.59/1.33 ap: $i > $i > $i > $i > $i ).
% 1.59/1.33
% 1.59/1.33 thf(infuncsetfunc_type,type,
% 1.59/1.33 infuncsetfunc: $o ).
% 1.59/1.33
% 1.59/1.33 thf(infuncsetfunc,definition,
% 1.59/1.33 ( infuncsetfunc
% 1.59/1.33 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.59/1.33 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.59/1.33 => ( func @ A @ B @ Xf ) ) ) ) ).
% 1.59/1.33
% 1.59/1.33 thf(funcGraphProp1_type,type,
% 1.59/1.33 funcGraphProp1: $o ).
% 1.59/1.33
% 1.59/1.33 thf(funcGraphProp1,definition,
% 1.59/1.33 ( funcGraphProp1
% 1.59/1.33 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.59/1.33 ( ( func @ A @ B @ Xf )
% 1.59/1.33 => ! [Xx: $i] :
% 1.59/1.33 ( ( in @ Xx @ A )
% 1.59/1.33 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 1.59/1.33
% 1.59/1.33 thf(funcGraphProp3,conjecture,
% 1.59/1.33 ( infuncsetfunc
% 1.59/1.33 => ( funcGraphProp1
% 1.59/1.33 => ! [A: $i,B: $i,Xf: $i] :
% 1.59/1.33 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.59/1.33 => ! [Xx: $i] :
% 1.59/1.33 ( ( in @ Xx @ A )
% 1.59/1.33 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 1.59/1.33 ------------------------
% 1.59/1.35 % (5034)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_4931 for (2999ds/275Mi)
% 1.59/1.35 % (5030)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_4931 for (2999ds/4Mi)
% 1.59/1.35 % (5035)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4931 for (2999ds/18Mi)
% 1.59/1.35 % (5029)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4931 for (2999ds/183Mi)
% 1.59/1.35 % (5031)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_4931 for (2999ds/27Mi)
% 1.59/1.35 % (5033)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_4931 for (2999ds/2Mi)
% 1.59/1.35 % (5032)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4931 for (2999ds/2Mi)
% 1.59/1.35 % (5032)Instruction limit reached!
% 1.59/1.35 % (5032)------------------------------
% 1.59/1.35 % (5032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (5032)Termination reason: Unknown
% 1.59/1.35 % (5032)Termination phase: Unused predicate definition removal
% 1.59/1.35
% 1.59/1.35 % (5032)Memory used [KB]: 1023
% 1.59/1.35 % (5032)Time elapsed: 0.003 s
% 1.59/1.35 % (5032)Instructions burned: 3 (million)
% 1.59/1.35 % (5032)------------------------------
% 1.59/1.35 % (5032)------------------------------
% 1.59/1.35 % (5033)Instruction limit reached!
% 1.59/1.35 % (5033)------------------------------
% 1.59/1.35 % (5033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (5033)Termination reason: Unknown
% 1.59/1.35 % (5033)Termination phase: Property scanning
% 1.59/1.35
% 1.59/1.35 % (5033)Memory used [KB]: 1023
% 1.59/1.35 % (5033)Time elapsed: 0.003 s
% 1.59/1.35 % (5033)Instructions burned: 3 (million)
% 1.59/1.35 % (5033)------------------------------
% 1.59/1.35 % (5033)------------------------------
% 1.59/1.35 % (5030)Instruction limit reached!
% 1.59/1.35 % (5030)------------------------------
% 1.59/1.35 % (5030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (5030)Termination reason: Unknown
% 1.59/1.35 % (5030)Termination phase: Property scanning
% 1.59/1.35
% 1.59/1.35 % (5030)Memory used [KB]: 1023
% 1.59/1.35 % (5030)Time elapsed: 0.004 s
% 1.59/1.35 % (5030)Instructions burned: 4 (million)
% 1.59/1.35 % (5030)------------------------------
% 1.59/1.35 % (5030)------------------------------
% 1.59/1.35 % (5034)First to succeed.
% 1.59/1.36 % (5034)Refutation found. Thanks to Tanya!
% 1.59/1.36 % SZS status Theorem for DTF2THF_4931
% 1.59/1.36 % SZS output start Proof for DTF2THF_4931
% 1.59/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 1.59/1.36 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.59/1.36 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.59/1.36 thf(func_def_4, type, subset: $i > $i > $o).
% 1.59/1.36 thf(func_def_5, type, kpair: $i > $i > $i).
% 1.59/1.36 thf(func_def_6, type, cartprod: $i > $i > $i).
% 1.59/1.36 thf(func_def_7, type, singleton: $i > $o).
% 1.59/1.36 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 1.59/1.36 thf(func_def_10, type, breln: $i > $i > $i > $o).
% 1.59/1.36 thf(func_def_11, type, func: $i > $i > $i > $o).
% 1.59/1.36 thf(func_def_12, type, funcSet: $i > $i > $i).
% 1.59/1.36 thf(func_def_13, type, ap: $i > $i > $i > $i > $i).
% 1.59/1.36 thf(f68,plain,(
% 1.59/1.36 $false),
% 1.59/1.36 inference(subsumption_resolution,[status(thm)],[f67,f47])).
% 1.59/1.36 thf(f47,plain,(
% 1.59/1.36 ((in @ sK7 @ sK6) = $true)),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f35])).
% 1.59/1.36 thf(f35,plain,(
% 1.59/1.36 (($true = (in @ sK4 @ (funcSet @ sK6 @ sK5))) & (((in @ sK7 @ sK6) = $true) & ($true != (in @ (kpair @ sK7 @ (ap @ sK6 @ sK5 @ sK4 @ sK7)) @ sK4)))) & (infuncsetfunc = $true) & (funcGraphProp1 = $true)),
% 1.59/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f27,f34,f33])).
% 1.59/1.36 thf(f33,plain,(
% 1.59/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (funcSet @ X2 @ X1))) & ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0) != $true))) => (($true = (in @ sK4 @ (funcSet @ sK6 @ sK5))) & ? [X3 : $i] : (((in @ X3 @ sK6) = $true) & ($true != (in @ (kpair @ X3 @ (ap @ sK6 @ sK5 @ sK4 @ X3)) @ sK4))))),
% 1.59/1.36 introduced(definition,[],[choice_axiom])).
% 1.59/1.36 thf(f34,plain,(
% 1.59/1.36 ? [X3 : $i] : (((in @ X3 @ sK6) = $true) & ($true != (in @ (kpair @ X3 @ (ap @ sK6 @ sK5 @ sK4 @ X3)) @ sK4))) => (((in @ sK7 @ sK6) = $true) & ($true != (in @ (kpair @ sK7 @ (ap @ sK6 @ sK5 @ sK4 @ sK7)) @ sK4)))),
% 1.59/1.36 introduced(definition,[],[choice_axiom])).
% 1.59/1.36 thf(f27,plain,(
% 1.59/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (funcSet @ X2 @ X1))) & ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0) != $true))) & (infuncsetfunc = $true) & (funcGraphProp1 = $true)),
% 1.59/1.36 inference(flattening,[status(thm)],[f26])).
% 1.59/1.36 thf(f26,plain,(
% 1.59/1.36 (? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (funcSet @ X2 @ X1))) & ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0) != $true))) & (funcGraphProp1 = $true)) & (infuncsetfunc = $true)),
% 1.59/1.36 inference(ennf_transformation,[status(thm)],[f15])).
% 1.59/1.36 thf(f15,plain,(
% 1.59/1.36 ~((infuncsetfunc = $true) => ((funcGraphProp1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (funcSet @ X2 @ X1))) => ! [X3 : $i] : (($true = (in @ X3 @ X2)) => ((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0) = $true)))))),
% 1.59/1.36 inference(fool_elimination,[status(thm)],[f14])).
% 1.59/1.36 thf(f14,plain,(
% 1.59/1.36 ~(infuncsetfunc => (funcGraphProp1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (funcSet @ X2 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0)))))),
% 1.59/1.36 inference(rectify,[status(thm)],[f8])).
% 1.59/1.36 thf(f8,negated_conjecture,(
% 1.59/1.36 ~(infuncsetfunc => (funcGraphProp1 => ! [X7 : $i,X3 : $i,X0 : $i] : ((in @ X7 @ (funcSet @ X0 @ X3)) => ! [X1 : $i] : ((in @ X1 @ X0) => (in @ (kpair @ X1 @ (ap @ X0 @ X3 @ X7 @ X1)) @ X7)))))),
% 1.59/1.36 inference(negated_conjecture,[status(cth)],[f7])).
% 1.59/1.36 thf(f7,conjecture,(
% 1.59/1.36 infuncsetfunc => (funcGraphProp1 => ! [X7 : $i,X3 : $i,X0 : $i] : ((in @ X7 @ (funcSet @ X0 @ X3)) => ! [X1 : $i] : ((in @ X1 @ X0) => (in @ (kpair @ X1 @ (ap @ X0 @ X3 @ X7 @ X1)) @ X7))))),
% 1.59/1.36 file('/export/starexec/sandbox/tmp/tmp.oPKcaH0VDE/DTF2THF_4931.p',funcGraphProp3)).
% 1.59/1.36 thf(f67,plain,(
% 1.59/1.36 ((in @ sK7 @ sK6) != $true)),
% 1.59/1.36 inference(subsumption_resolution,[status(thm)],[f65,f62])).
% 1.59/1.36 thf(f62,plain,(
% 1.59/1.36 ($true = (func @ sK6 @ sK5 @ sK4))),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.59/1.36 thf(f61,plain,(
% 1.59/1.36 ($true = (func @ sK6 @ sK5 @ sK4)) | ($true != $true)),
% 1.59/1.36 inference(superposition,[status(thm)],[f60,f48])).
% 1.59/1.36 thf(f48,plain,(
% 1.59/1.36 ($true = (in @ sK4 @ (funcSet @ sK6 @ sK5)))),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f35])).
% 1.59/1.36 thf(f60,plain,(
% 1.59/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (funcSet @ X3 @ X5)) != $true) | ((func @ X3 @ X5 @ X4) = $true)) )),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.59/1.36 thf(f58,plain,(
% 1.59/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((func @ X3 @ X5 @ X4) = $true) | ($true != $true) | ((in @ X4 @ (funcSet @ X3 @ X5)) != $true)) )),
% 1.59/1.36 inference(definition_unfolding,[status(thm)],[f49,f45])).
% 1.59/1.36 thf(f45,plain,(
% 1.59/1.36 (infuncsetfunc = $true)),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f35])).
% 1.59/1.36 thf(f49,plain,(
% 1.59/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (funcSet @ X3 @ X5)) != $true) | ((func @ X3 @ X5 @ X4) = $true) | (infuncsetfunc != $true)) )),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f39])).
% 1.59/1.36 thf(f39,plain,(
% 1.59/1.36 ((infuncsetfunc = $true) | (($true = (in @ sK9 @ (funcSet @ sK8 @ sK10))) & ($true != (func @ sK8 @ sK10 @ sK9)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (funcSet @ X3 @ X5)) != $true) | ((func @ X3 @ X5 @ X4) = $true)) | (infuncsetfunc != $true))),
% 1.59/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f37,f38])).
% 1.59/1.36 thf(f38,plain,(
% 1.59/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X0 @ X2))) & ($true != (func @ X0 @ X2 @ X1))) => (($true = (in @ sK9 @ (funcSet @ sK8 @ sK10))) & ($true != (func @ sK8 @ sK10 @ sK9)))),
% 1.59/1.36 introduced(definition,[],[choice_axiom])).
% 1.59/1.36 thf(f37,plain,(
% 1.59/1.36 ((infuncsetfunc = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X0 @ X2))) & ($true != (func @ X0 @ X2 @ X1)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (funcSet @ X3 @ X5)) != $true) | ((func @ X3 @ X5 @ X4) = $true)) | (infuncsetfunc != $true))),
% 1.59/1.36 inference(rectify,[status(thm)],[f36])).
% 1.59/1.36 thf(f36,plain,(
% 1.59/1.36 ((infuncsetfunc = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X0 @ X2))) & ($true != (func @ X0 @ X2 @ X1)))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (funcSet @ X0 @ X2))) | ($true = (func @ X0 @ X2 @ X1))) | (infuncsetfunc != $true))),
% 1.59/1.36 inference(nnf_transformation,[status(thm)],[f24])).
% 1.59/1.36 thf(f24,plain,(
% 1.59/1.36 (infuncsetfunc = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (funcSet @ X0 @ X2))) | ($true = (func @ X0 @ X2 @ X1)))),
% 1.59/1.36 inference(ennf_transformation,[status(thm)],[f17])).
% 1.59/1.36 thf(f17,plain,(
% 1.59/1.36 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X0 @ X2))) => ($true = (func @ X0 @ X2 @ X1))) <=> (infuncsetfunc = $true)),
% 1.59/1.36 inference(fool_elimination,[status(thm)],[f16])).
% 1.59/1.36 thf(f16,plain,(
% 1.59/1.36 (infuncsetfunc = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X0 @ X2)) => (func @ X0 @ X2 @ X1)))),
% 1.59/1.36 inference(rectify,[status(thm)],[f5])).
% 1.59/1.36 thf(f5,axiom,(
% 1.59/1.36 (infuncsetfunc = ! [X0 : $i,X7 : $i,X3 : $i] : ((in @ X7 @ (funcSet @ X0 @ X3)) => (func @ X0 @ X3 @ X7)))),
% 1.59/1.36 file('/export/starexec/sandbox/tmp/tmp.oPKcaH0VDE/DTF2THF_4931.p',infuncsetfunc)).
% 1.59/1.36 thf(f65,plain,(
% 1.59/1.36 ($true != (func @ sK6 @ sK5 @ sK4)) | ((in @ sK7 @ sK6) != $true)),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.59/1.36 thf(f63,plain,(
% 1.59/1.36 ($true != $true) | ((in @ sK7 @ sK6) != $true) | ($true != (func @ sK6 @ sK5 @ sK4))),
% 1.59/1.36 inference(superposition,[status(thm)],[f46,f59])).
% 1.59/1.36 thf(f59,plain,(
% 1.59/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2)) | ((func @ X1 @ X0 @ X2) != $true) | ($true != (in @ X3 @ X1))) )),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.59/1.36 thf(f52,plain,(
% 1.59/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X3 @ X1)) | ($true != $true) | ($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2)) | ((func @ X1 @ X0 @ X2) != $true)) )),
% 1.59/1.36 inference(definition_unfolding,[status(thm)],[f43,f44])).
% 1.59/1.36 thf(f44,plain,(
% 1.59/1.36 (funcGraphProp1 = $true)),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f35])).
% 1.59/1.36 thf(f43,plain,(
% 1.59/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2)) | ($true != (in @ X3 @ X1)) | ((func @ X1 @ X0 @ X2) != $true) | (funcGraphProp1 != $true)) )),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f32])).
% 1.59/1.36 thf(f32,plain,(
% 1.59/1.36 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2)) | ($true != (in @ X3 @ X1))) | ((func @ X1 @ X0 @ X2) != $true)) | (funcGraphProp1 != $true)) & ((funcGraphProp1 = $true) | ((($true != (in @ (kpair @ sK3 @ (ap @ sK1 @ sK0 @ sK2 @ sK3)) @ sK2)) & ($true = (in @ sK3 @ sK1))) & ($true = (func @ sK1 @ sK0 @ sK2))))),
% 1.59/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f29,f31,f30])).
% 1.59/1.36 thf(f30,plain,(
% 1.59/1.36 ? [X4 : $i,X5 : $i,X6 : $i] : (? [X7 : $i] : (($true != (in @ (kpair @ X7 @ (ap @ X5 @ X4 @ X6 @ X7)) @ X6)) & ($true = (in @ X7 @ X5))) & ($true = (func @ X5 @ X4 @ X6))) => (? [X7 : $i] : (($true != (in @ (kpair @ X7 @ (ap @ sK1 @ sK0 @ sK2 @ X7)) @ sK2)) & ($true = (in @ X7 @ sK1))) & ($true = (func @ sK1 @ sK0 @ sK2)))),
% 1.59/1.36 introduced(definition,[],[choice_axiom])).
% 1.59/1.36 thf(f31,plain,(
% 1.59/1.36 ? [X7 : $i] : (($true != (in @ (kpair @ X7 @ (ap @ sK1 @ sK0 @ sK2 @ X7)) @ sK2)) & ($true = (in @ X7 @ sK1))) => (($true != (in @ (kpair @ sK3 @ (ap @ sK1 @ sK0 @ sK2 @ sK3)) @ sK2)) & ($true = (in @ sK3 @ sK1)))),
% 1.59/1.36 introduced(definition,[],[choice_axiom])).
% 1.59/1.36 thf(f29,plain,(
% 1.59/1.36 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2)) | ($true != (in @ X3 @ X1))) | ((func @ X1 @ X0 @ X2) != $true)) | (funcGraphProp1 != $true)) & ((funcGraphProp1 = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : (? [X7 : $i] : (($true != (in @ (kpair @ X7 @ (ap @ X5 @ X4 @ X6 @ X7)) @ X6)) & ($true = (in @ X7 @ X5))) & ($true = (func @ X5 @ X4 @ X6))))),
% 1.59/1.36 inference(rectify,[status(thm)],[f28])).
% 1.59/1.36 thf(f28,plain,(
% 1.59/1.36 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2)) | ($true != (in @ X3 @ X1))) | ((func @ X1 @ X0 @ X2) != $true)) | (funcGraphProp1 != $true)) & ((funcGraphProp1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2)) & ($true = (in @ X3 @ X1))) & ((func @ X1 @ X0 @ X2) = $true)))),
% 1.59/1.36 inference(nnf_transformation,[status(thm)],[f25])).
% 1.59/1.36 thf(f25,plain,(
% 1.59/1.36 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2)) | ($true != (in @ X3 @ X1))) | ((func @ X1 @ X0 @ X2) != $true)) <=> (funcGraphProp1 = $true)),
% 1.59/1.36 inference(ennf_transformation,[status(thm)],[f13])).
% 1.59/1.36 thf(f13,plain,(
% 1.59/1.36 (funcGraphProp1 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((func @ X1 @ X0 @ X2) = $true) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => ($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2))))),
% 1.59/1.36 inference(fool_elimination,[status(thm)],[f12])).
% 1.59/1.36 thf(f12,plain,(
% 1.59/1.36 (funcGraphProp1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2))))),
% 1.59/1.36 inference(rectify,[status(thm)],[f6])).
% 1.59/1.36 thf(f6,axiom,(
% 1.59/1.36 (funcGraphProp1 = ! [X3 : $i,X0 : $i,X7 : $i] : ((func @ X0 @ X3 @ X7) => ! [X1 : $i] : ((in @ X1 @ X0) => (in @ (kpair @ X1 @ (ap @ X0 @ X3 @ X7 @ X1)) @ X7))))),
% 1.59/1.36 file('/export/starexec/sandbox/tmp/tmp.oPKcaH0VDE/DTF2THF_4931.p',funcGraphProp1)).
% 1.59/1.36 thf(f46,plain,(
% 1.59/1.36 ($true != (in @ (kpair @ sK7 @ (ap @ sK6 @ sK5 @ sK4 @ sK7)) @ sK4))),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f35])).
% 1.59/1.36 % SZS output end Proof for DTF2THF_4931
% 1.59/1.36 % (5034)------------------------------
% 1.59/1.36 % (5034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (5034)Termination reason: Refutation
% 1.59/1.36
% 1.59/1.36 % (5034)Memory used [KB]: 5500
% 1.59/1.36 % (5034)Time elapsed: 0.007 s
% 1.59/1.36 % (5034)Instructions burned: 6 (million)
% 1.59/1.36 % (5034)------------------------------
% 1.59/1.36 % (5034)------------------------------
% 1.59/1.36 % (5028)Success in time 0.022 s
%------------------------------------------------------------------------------