%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU675^2 : 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 : n024.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 09:36:11 AM UTC 2026
% Result : Theorem 1.02s 0.95s
% Output : Refutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 93 ( 39 unt; 0 typ; 3 def)
% Number of atoms : 869 ( 172 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 1268 ( 57 ~; 63 |; 53 &;1025 @)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 26 usr; 15 con; 0-3 aty)
% ( 13 !!; 20 ??; 0 @@+; 0 @@-)
% Number of variables : 292 ( 212 ^; 63 !; 17 ?; 292 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_7,type,
subset: $i > $i > $o ).
thf(func_def_8,type,
kpair: $i > $i > $i ).
thf(func_def_9,type,
cartprod: $i > $i > $i ).
thf(func_def_10,type,
singleton: $i > $o ).
thf(func_def_11,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_12,type,
breln: $i > $i > $i > $o ).
thf(func_def_13,type,
func: $i > $i > $i > $o ).
thf(func_def_14,type,
funcSet: $i > $i > $i ).
thf(func_def_32,type,
sK5: $i > $o ).
thf(func_def_37,type,
ph8:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
sK9: $i > $i ).
thf(f110,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f70,f75,f106,f109]) ).
thf(f109,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $false = $true )
| ~ spl6_1 ),
inference(backward_demodulation,[status(thm)],[f79,f66]) ).
thf(f66,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl6_1
<=> ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f79,plain,
( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) ) )
& ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( in @ Y2
@ ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ sK1 @ sK0 ) ) )
@ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( in @ Y2
@ ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ sK1 @ sK0 ) ) )
@ sK2 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f52,f50]) ).
thf(f50,plain,
( ( in @ sK2
@ ( dsetconstr @ ( powerset @ ( cartprod @ sK1 @ sK0 ) )
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( in @ Y2
@ ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ sK1 @ sK0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( $true
= ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) )
& ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y0
@ Y1
@ Y2 ) )
@ sK1
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f32,f44]) ).
thf(f44,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) )
& ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y0
@ Y1
@ Y2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f34,f43]) ).
thf(f43,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f35,f42,f39]) ).
thf(f39,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( breln
= ( ^ [X0: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',breln) ).
thf(f42,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f40,f41]) ).
thf(f41,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) )
= singleton ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i] :
? [X2: $i] :
( ( in @ X2 @ X0 )
& ( ( setadjoin @ X2 @ emptyset )
= X0 ) ) )
= singleton ),
file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',singleton) ).
thf(f40,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',ex1) ).
thf(f35,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( breln @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( breln @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
& ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( func
= ( ^ [X0: $i,X4: $i,X6: $i] :
( ( breln @ X0 @ X4 @ X6 )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',func) ).
thf(f34,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( funcSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X1 ) )
@ ^ [X2: $i] : ( func @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( funcSet
= ( ^ [X0: $i,X4: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X4 ) )
@ ^ [X7: $i] : ( func @ X0 @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',funcSet) ).
thf(f32,plain,
( ( in @ sK2 @ ( funcSet @ sK1 @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( dsetconstrER = $true )
& ( ( in @ sK2 @ ( funcSet @ sK1 @ sK0 ) )
= $true )
& ( ( func @ sK1 @ sK0 @ sK2 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f24,f25]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true )
& ( ( func @ X1 @ X0 @ X2 )
!= $true ) )
=> ( ( ( in @ sK2 @ ( funcSet @ sK1 @ sK0 ) )
= $true )
& ( ( func @ sK1 @ sK0 @ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( dsetconstrER = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true )
& ( ( func @ X1 @ X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true )
=> ( ( func @ X1 @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
=> ( func @ X1 @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( dsetconstrER
=> ! [X4: $i,X0: $i,X7: $i] :
( ( in @ X7 @ ( funcSet @ X0 @ X4 ) )
=> ( func @ X0 @ X4 @ X7 ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( dsetconstrER
=> ! [X4: $i,X0: $i,X7: $i] :
( ( in @ X7 @ ( funcSet @ X0 @ X4 ) )
=> ( func @ X0 @ X4 @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',infuncsetfunc) ).
thf(f52,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4 @ ( dsetconstr @ X3 @ X5 ) )
!= $true )
| ( ( X5 @ X4 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X4 )
= $true )
| ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X4 )
= $true )
| ( $true != $true )
| ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f36,f33]) ).
thf(f33,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f36,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X4 )
= $true )
| ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( dsetconstrER = $true )
| ( ( $true
!= ( sK5 @ sK4 ) )
& ( $true
= ( in @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X4 )
= $true )
| ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f28,f29]) ).
thf(f29,plain,
( ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
!= $true )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
=> ( ( $true
!= ( sK5 @ sK4 ) )
& ( $true
= ( in @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
!= $true )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X4 )
= $true )
| ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
!= $true )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
=> ( ( X2 @ X1 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',dsetconstrER) ).
thf(f106,plain,
( ~ spl6_2
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
( ( $false = $true )
| ~ spl6_2
| ~ spl6_3 ),
inference(backward_demodulation,[status(thm)],[f100,f103]) ).
thf(f103,plain,
( ( $false
= ( in @ ( sK9 @ sK7 ) @ ( setadjoin @ ( sK9 @ sK7 ) @ emptyset ) ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(equality_resolution,[status(thm)],[f102]) ).
thf(f102,plain,
( ! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( setadjoin @ ( sK9 @ sK7 ) @ emptyset ) )
| ( ( in @ X1 @ ( setadjoin @ ( sK9 @ sK7 ) @ emptyset ) )
= $false ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[status(thm)],[f101,f99]) ).
thf(f99,plain,
( ( ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) )
= ( setadjoin @ ( sK9 @ sK7 ) @ emptyset ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) )
= ( setadjoin @ ( sK9 @ sK7 ) @ emptyset ) )
| ( $false = $true )
| ~ spl6_3 ),
inference(superposition,[status(thm)],[f88,f74]) ).
thf(f74,plain,
( ( ( in @ sK7 @ sK1 )
= $true )
| ~ spl6_3 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f72,definition,
( spl6_3
<=> ( ( in @ sK7 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition]) ).
thf(f88,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK1 ) )
| ( ( setadjoin @ ( sK9 @ X1 ) @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: $i] :
( ( ( ( setadjoin @ ( sK9 @ X1 ) @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
= $true )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: $i] :
( ( ( ( ( setadjoin @ ( sK9 @ X1 ) @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
& ( in @ ( sK9 @ X1 )
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) )
= $true )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) ) )
@ ( sK9 @ X1 ) )
= $true )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(sigma_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK1 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK2 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f101,plain,
( ! [X1: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) ) )
| ( ( setadjoin @ X1 @ emptyset )
!= ( setadjoin @ ( sK9 @ sK7 ) @ emptyset ) ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(backward_demodulation,[status(thm)],[f69,f99]) ).
thf(f69,plain,
( ! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) )
| ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) ) ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f68,definition,
( spl6_2
<=> ! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) )
| ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f100,plain,
( ( ( in @ ( sK9 @ sK7 ) @ ( setadjoin @ ( sK9 @ sK7 ) @ emptyset ) )
= $true )
| ~ spl6_3 ),
inference(backward_demodulation,[status(thm)],[f92,f99]) ).
thf(f92,plain,
( ( $true
= ( in @ ( sK9 @ sK7 )
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $false = $true )
| ( $true
= ( in @ ( sK9 @ sK7 )
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) ) )
| ~ spl6_3 ),
inference(superposition,[status(thm)],[f74,f86]) ).
thf(f86,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK1 ) )
| ( $true
= ( in @ ( sK9 @ X1 )
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f75,plain,
( spl6_1
| spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f58,f72,f64]) ).
thf(f58,plain,
( ( ( in @ sK7 @ sK1 )
= $true )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $false
= ( ( in @ sK7 @ sK1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK7 @ Y1 ) @ sK2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK7 @ Y1 ) @ sK2 ) ) ) ) ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) )
@ sK7 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK2 ) ) ) ) ) ) )
& ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 ) )
@ sK1
@ sK0
@ sK2 ) ),
inference(definition_unfolding,[status(thm)],[f31,f43]) ).
thf(f31,plain,
( ( func @ sK1 @ sK0 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f70,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f62,f68,f64]) ).
thf(f62,plain,
! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) )
| ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X1: $i] :
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) )
| ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) ) )
| ( $false
= ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: $i] :
( ( $false
= ( ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) )
& ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK2 ) ) ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: $i] :
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK7 @ Y1 ) @ sK2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK7 @ Y1 ) @ sK2 ) ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK7 @ Y1 ) @ sK2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK7 @ Y1 ) @ sK2 ) ) ) ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU675^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 07:30:40 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEU675^2 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.32 % Domain : Set Theory
% 0.07/0.32 % Problem : Functions - Application
% 0.07/0.32 % Version : Especial > Reduced > Especial.
% 0.07/0.32 % English : (! A:i.! B:i.! f:i.in f (funcSet A B) -> func A B f)
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.07/0.32 % Source : [Bro08]
% 0.07/0.32 % Names : ZFC177l [Bro08]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.33 v7.3.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.1.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v3.7.0
% 0.07/0.32 % Syntax : Number of formulae : 21 ( 6 unt; 14 typ; 6 def)
% 0.07/0.32 % Number of atoms : 24 ( 7 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 3 ( 3 avg)
% 0.07/0.32 % Number of connectives : 50 ( 0 ~; 0 |; 2 &; 44 @)
% 0.07/0.32 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 9 ( 2 avg)
% 0.07/0.32 % Number of types : 2 ( 0 usr)
% 0.07/0.32 % Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 15 ( 14 usr; 2 con; 0-3 aty)
% 0.07/0.32 % Number of variables : 23 ( 15 ^; 7 !; 1 ?; 23 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : http://mathgate.info/detsetitem.php?id=227
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(in_type,type,
% 0.07/0.32 in: $i > $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyset_type,type,
% 0.07/0.32 emptyset: $i ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoin_type,type,
% 0.07/0.32 setadjoin: $i > $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(powerset_type,type,
% 0.07/0.32 powerset: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstr_type,type,
% 0.07/0.32 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrER_type,type,
% 0.07/0.32 dsetconstrER: $o ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrER,definition,
% 0.07/0.32 ( dsetconstrER
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.07/0.32 => ( Xphi @ Xx ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(subset_type,type,
% 0.07/0.32 subset: $i > $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(kpair_type,type,
% 0.07/0.32 kpair: $i > $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(cartprod_type,type,
% 0.07/0.32 cartprod: $i > $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(singleton_type,type,
% 0.07/0.32 singleton: $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(singleton,definition,
% 0.07/0.32 ( singleton
% 0.07/0.32 = ( ^ [A: $i] :
% 0.07/0.32 ? [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 & ( A
% 0.07/0.32 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(ex1_type,type,
% 0.07/0.32 ex1: $i > ( $i > $o ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(ex1,definition,
% 0.07/0.32 ( ex1
% 0.07/0.32 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.07/0.32 ( singleton
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(breln_type,type,
% 0.07/0.32 breln: $i > $i > $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(breln,definition,
% 0.07/0.32 ( breln
% 0.07/0.32 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(func_type,type,
% 0.07/0.32 func: $i > $i > $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(func,definition,
% 0.07/0.32 ( func
% 0.07/0.32 = ( ^ [A: $i,B: $i,R: $i] :
% 0.07/0.32 ( ( breln @ A @ B @ R )
% 0.07/0.32 & ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( ex1 @ B
% 0.07/0.32 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(funcSet_type,type,
% 0.07/0.32 funcSet: $i > $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(funcSet,definition,
% 0.07/0.32 ( funcSet
% 0.07/0.32 = ( ^ [A: $i,B: $i] :
% 0.07/0.32 ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
% 0.07/0.32 @ ^ [Xf: $i] : ( func @ A @ B @ Xf ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(infuncsetfunc,conjecture,
% 0.07/0.32 ( dsetconstrER
% 0.07/0.32 => ! [A: $i,B: $i,Xf: $i] :
% 0.07/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.07/0.32 => ( func @ A @ B @ Xf ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 1.02/0.92 ---- Embedded in THF ---
% 1.02/0.92 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.02/0.92 %%% Generated on Tue Feb 24 07:30:41 EST 2026
% 1.02/0.92 %%% using '$$dhol' embedding, version 1.3.0.
% 1.02/0.92 %%% Logic specification used:
% 1.02/0.92 %%% thf(spec, logic, $$dhol).
% 1.02/0.92
% 1.02/0.92 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2DTF30992.p
% See solution above
% 1.02/0.92 ------------------------
% 1.02/0.93 ---- Cleaned THF ---
% 1.02/0.93 thf(in_type,type,
% 1.02/0.93 in: $i > $i > $o ).
% 1.02/0.93
% 1.02/0.93 thf(emptyset_type,type,
% 1.02/0.93 emptyset: $i ).
% 1.02/0.93
% 1.02/0.93 thf(setadjoin_type,type,
% 1.02/0.93 setadjoin: $i > $i > $i ).
% 1.02/0.93
% 1.02/0.93 thf(powerset_type,type,
% 1.02/0.93 powerset: $i > $i ).
% 1.02/0.93
% 1.02/0.93 thf(dsetconstr_type,type,
% 1.02/0.93 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.02/0.93
% 1.02/0.93 thf(dsetconstrER_type,type,
% 1.02/0.93 dsetconstrER: $o ).
% 1.02/0.93
% 1.02/0.93 thf(dsetconstrER,definition,
% 1.02/0.93 ( dsetconstrER
% 1.02/0.93 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.02/0.93 ( ( in @ Xx
% 1.02/0.93 @ ( dsetconstr @ A
% 1.02/0.93 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.02/0.93 => ( Xphi @ Xx ) ) ) ) ).
% 1.02/0.93
% 1.02/0.93 thf(subset_type,type,
% 1.02/0.93 subset: $i > $i > $o ).
% 1.02/0.93
% 1.02/0.93 thf(kpair_type,type,
% 1.02/0.93 kpair: $i > $i > $i ).
% 1.02/0.93
% 1.02/0.93 thf(cartprod_type,type,
% 1.02/0.93 cartprod: $i > $i > $i ).
% 1.02/0.93
% 1.02/0.93 thf(singleton_type,type,
% 1.02/0.93 singleton: $i > $o ).
% 1.02/0.93
% 1.02/0.93 thf(singleton,definition,
% 1.02/0.93 ( singleton
% 1.02/0.93 = ( ^ [A: $i] :
% 1.02/0.93 ? [Xx: $i] :
% 1.02/0.93 ( ( in @ Xx @ A )
% 1.02/0.93 & ( A
% 1.02/0.93 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.02/0.93
% 1.02/0.93 thf(ex1_type,type,
% 1.02/0.93 ex1: $i > ( $i > $o ) > $o ).
% 1.02/0.93
% 1.02/0.93 thf(ex1,definition,
% 1.02/0.93 ( ex1
% 1.02/0.93 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.02/0.93 ( singleton
% 1.02/0.93 @ ( dsetconstr @ A
% 1.02/0.93 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.02/0.93
% 1.02/0.93 thf(breln_type,type,
% 1.02/0.93 breln: $i > $i > $i > $o ).
% 1.02/0.93
% 1.02/0.93 thf(breln,definition,
% 1.02/0.93 ( breln
% 1.02/0.93 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.02/0.93
% 1.02/0.93 thf(func_type,type,
% 1.02/0.93 func: $i > $i > $i > $o ).
% 1.02/0.93
% 1.02/0.93 thf(func,definition,
% 1.02/0.93 ( func
% 1.02/0.93 = ( ^ [A: $i,B: $i,R: $i] :
% 1.02/0.93 ( ( breln @ A @ B @ R )
% 1.02/0.93 & ! [Xx: $i] :
% 1.02/0.93 ( ( in @ Xx @ A )
% 1.02/0.93 => ( ex1 @ B
% 1.02/0.93 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 1.02/0.93
% 1.02/0.93 thf(funcSet_type,type,
% 1.02/0.93 funcSet: $i > $i > $i ).
% 1.02/0.93
% 1.02/0.93 thf(funcSet,definition,
% 1.02/0.93 ( funcSet
% 1.02/0.93 = ( ^ [A: $i,B: $i] :
% 1.02/0.93 ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
% 1.02/0.93 @ ^ [Xf: $i] : ( func @ A @ B @ Xf ) ) ) ) ).
% 1.02/0.93
% 1.02/0.93 thf(infuncsetfunc,conjecture,
% 1.02/0.93 ( dsetconstrER
% 1.02/0.93 => ! [A: $i,B: $i,Xf: $i] :
% 1.02/0.93 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.02/0.93 => ( func @ A @ B @ Xf ) ) ) ).
% 1.02/0.93 ------------------------
% 1.02/0.95 % (31184)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_30992 for (3000ds/27Mi)
% 1.02/0.95 % (31185)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30992 for (3000ds/2Mi)
% 1.02/0.95 % (31188)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30992 for (3000ds/18Mi)
% 1.02/0.95 % (31185)Instruction limit reached!
% 1.02/0.95 % (31185)------------------------------
% 1.02/0.95 % (31185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.95 % (31185)Termination reason: Unknown
% 1.02/0.95 % (31185)Termination phase: Property scanning
% 1.02/0.95
% 1.02/0.95 % (31185)Memory used [KB]: 1023
% 1.02/0.95 % (31185)Time elapsed: 0.002 s
% 1.02/0.95 % (31185)Instructions burned: 2 (million)
% 1.02/0.95 % (31185)------------------------------
% 1.02/0.95 % (31185)------------------------------
% 1.02/0.95 % (31182)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30992 for (3000ds/183Mi)
% 1.02/0.95 % (31188)First to succeed.
% 1.02/0.95 % (31186)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_30992 for (3000ds/2Mi)
% 1.02/0.95 % (31187)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_30992 for (3000ds/275Mi)
% 1.02/0.95 % (31186)Instruction limit reached!
% 1.02/0.95 % (31186)------------------------------
% 1.02/0.95 % (31186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.95 % (31186)Termination reason: Unknown
% 1.02/0.95 % (31186)Termination phase: Property scanning
% 1.02/0.95
% 1.02/0.95 % (31186)Memory used [KB]: 1023
% 1.02/0.95 % (31186)Time elapsed: 0.003 s
% 1.02/0.95 % (31186)Instructions burned: 3 (million)
% 1.02/0.95 % (31186)------------------------------
% 1.02/0.95 % (31186)------------------------------
% 1.02/0.95 % (31187)Refutation not found, incomplete strategy
% 1.02/0.95 % (31187)------------------------------
% 1.02/0.95 % (31187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.95 % (31187)Termination reason: Refutation not found, incomplete strategy
% 1.02/0.95
% 1.02/0.95
% 1.02/0.95 % (31187)Memory used [KB]: 5500
% 1.02/0.95 % (31187)Time elapsed: 0.003 s
% 1.02/0.95 % (31187)Instructions burned: 3 (million)
% 1.02/0.95 % (31187)------------------------------
% 1.02/0.95 % (31187)------------------------------
% 1.02/0.95 % (31188)Refutation found. Thanks to Tanya!
% 1.02/0.95 % SZS status Theorem for DTF2THF_30992
% 1.02/0.95 % SZS output start Proof for DTF2THF_30992
% 1.02/0.95 thf(func_def_0, type, in: $i > $i > $o).
% 1.02/0.95 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.02/0.95 thf(func_def_3, type, powerset: $i > $i).
% 1.02/0.95 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 1.02/0.95 thf(func_def_7, type, subset: $i > $i > $o).
% 1.02/0.95 thf(func_def_8, type, kpair: $i > $i > $i).
% 1.02/0.95 thf(func_def_9, type, cartprod: $i > $i > $i).
% 1.02/0.95 thf(func_def_10, type, singleton: $i > $o).
% 1.02/0.95 thf(func_def_11, type, ex1: $i > ($i > $o) > $o).
% 1.02/0.95 thf(func_def_12, type, breln: $i > $i > $i > $o).
% 1.02/0.95 thf(func_def_13, type, func: $i > $i > $i > $o).
% 1.02/0.95 thf(func_def_14, type, funcSet: $i > $i > $i).
% 1.02/0.95 thf(func_def_32, type, sK5: $i > $o).
% 1.02/0.95 thf(func_def_37, type, ph8: !>[X0: $tType]:(X0)).
% 1.02/0.95 thf(func_def_38, type, sK9: $i > $i).
% 1.02/0.95 thf(f110,plain,(
% 1.02/0.95 $false),
% 1.02/0.95 inference(avatar_sat_refutation,[status(thm)],[f70,f75,f106,f109])).
% 1.02/0.95 thf(f109,plain,(
% 1.02/0.95 ~spl6_1),
% 1.02/0.95 inference(avatar_contradiction_clause,[status(thm)],[f108])).
% 1.02/0.95 thf(f108,plain,(
% 1.02/0.95 $false | ~spl6_1),
% 1.02/0.95 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.02/0.95 thf(f107,plain,(
% 1.02/0.95 ($false = $true) | ~spl6_1),
% 1.02/0.95 inference(backward_demodulation,[status(thm)],[f79,f66])).
% 1.02/0.95 thf(f66,plain,(
% 1.02/0.95 ($false = (subset @ sK2 @ (cartprod @ sK1 @ sK0))) | ~spl6_1),
% 1.02/0.95 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.02/0.95 thf(f64,definition,(
% 1.02/0.95 spl6_1 <=> ($false = (subset @ sK2 @ (cartprod @ sK1 @ sK0)))),
% 1.02/0.95 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.02/0.95 thf(f79,plain,(
% 1.02/0.95 ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $true)),
% 1.02/0.95 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.02/0.95 thf(f78,plain,(
% 1.02/0.95 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))))))))) & (subset @ sK2 @ (cartprod @ sK1 @ sK0))) = $true)),
% 1.02/0.95 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.02/0.95 thf(f77,plain,(
% 1.02/0.95 ($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK1) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))))))))) & (subset @ Y0 @ (cartprod @ sK1 @ sK0)))) @ sK2))),
% 1.02/0.95 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.02/0.95 thf(f76,plain,(
% 1.02/0.95 ($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK1) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))))))))) & (subset @ Y0 @ (cartprod @ sK1 @ sK0)))) @ sK2)) | ($true != $true)),
% 1.02/0.95 inference(superposition,[status(thm)],[f52,f50])).
% 1.02/0.95 thf(f50,plain,(
% 1.02/0.95 ((in @ sK2 @ (dsetconstr @ (powerset @ (cartprod @ sK1 @ sK0)) @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK1) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))))))))) & (subset @ Y0 @ (cartprod @ sK1 @ sK0)))))) = $true)),
% 1.02/0.95 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.02/0.95 thf(f45,plain,(
% 1.02/0.95 ($true = (in @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))) & ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5))))))) @ Y0 @ Y1 @ Y2)))))) @ sK1 @ sK0)))),
% 1.02/0.95 inference(definition_unfolding,[status(thm)],[f32,f44])).
% 1.02/0.95 thf(f44,plain,(
% 1.02/0.95 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))) & ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5))))))) @ Y0 @ Y1 @ Y2)))))))),
% 1.02/0.95 inference(definition_unfolding,[status(thm)],[f34,f43])).
% 1.02/0.95 thf(f43,plain,(
% 1.02/0.95 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2))))))))),
% 1.02/0.95 inference(definition_unfolding,[status(thm)],[f35,f42,f39])).
% 1.02/0.95 thf(f39,plain,(
% 1.02/0.95 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.02/0.95 inference(cnf_transformation,[status(thm)],[f22])).
% 1.02/0.95 thf(f22,plain,(
% 1.02/0.95 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.02/0.95 inference(fool_elimination,[status(thm)],[f21])).
% 1.02/0.95 thf(f21,plain,(
% 1.02/0.95 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 1.02/0.95 inference(rectify,[status(thm)],[f4])).
% 1.02/0.95 thf(f4,axiom,(
% 1.02/0.95 (breln = (^[X0 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X0 @ X4))))),
% 1.02/0.95 file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',breln)).
% 1.02/0.95 thf(f42,plain,(
% 1.02/0.95 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.02/0.95 inference(definition_unfolding,[status(thm)],[f40,f41])).
% 1.02/0.95 thf(f41,plain,(
% 1.02/0.95 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.02/0.95 inference(cnf_transformation,[status(thm)],[f15])).
% 1.02/0.95 thf(f15,plain,(
% 1.02/0.95 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.02/0.95 inference(fool_elimination,[status(thm)],[f14])).
% 1.02/0.95 thf(f14,plain,(
% 1.02/0.95 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 1.02/0.95 inference(rectify,[status(thm)],[f2])).
% 1.02/0.95 thf(f2,axiom,(
% 1.02/0.95 ((^[X0 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & ((setadjoin @ X2 @ emptyset) = X0)))) = singleton)),
% 1.02/0.95 file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',singleton)).
% 1.02/0.95 thf(f40,plain,(
% 1.02/0.95 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.02/0.95 inference(cnf_transformation,[status(thm)],[f20])).
% 1.02/0.95 thf(f20,plain,(
% 1.02/0.95 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.02/0.95 inference(fool_elimination,[status(thm)],[f3])).
% 1.02/0.95 thf(f3,axiom,(
% 1.02/0.95 ((^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))) = ex1)),
% 1.02/0.95 file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',ex1)).
% 1.02/0.95 thf(f35,plain,(
% 1.02/0.95 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & (breln @ Y0 @ Y1 @ Y2))))))))),
% 1.02/0.95 inference(cnf_transformation,[status(thm)],[f17])).
% 1.02/0.95 thf(f17,plain,(
% 1.02/0.95 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & (breln @ Y0 @ Y1 @ Y2))))))))),
% 1.02/0.95 inference(fool_elimination,[status(thm)],[f16])).
% 1.02/0.95 thf(f16,plain,(
% 1.02/0.95 (func = (^[X0 : $i, X1 : $i, X2 : $i] : ((breln @ X0 @ X1 @ X2) & ! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))))))),
% 1.02/0.95 inference(rectify,[status(thm)],[f5])).
% 1.02/0.95 thf(f5,axiom,(
% 1.02/0.95 (func = (^[X0 : $i, X4 : $i, X6 : $i] : ((breln @ X0 @ X4 @ X6) & ! [X2 : $i] : ((in @ X2 @ X0) => (ex1 @ X4 @ (^[X3 : $i] : (in @ (kpair @ X2 @ X3) @ X6)))))))),
% 1.02/0.95 file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',func)).
% 1.02/0.95 thf(f34,plain,(
% 1.02/0.95 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: (func @ Y0 @ Y1 @ Y2)))))))),
% 1.02/0.95 inference(cnf_transformation,[status(thm)],[f11])).
% 1.02/0.95 thf(f11,plain,(
% 1.02/0.95 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: (func @ Y0 @ Y1 @ Y2)))))))),
% 1.02/0.95 inference(fool_elimination,[status(thm)],[f10])).
% 1.02/0.95 thf(f10,plain,(
% 1.02/0.95 (funcSet = (^[X0 : $i, X1 : $i] : (dsetconstr @ (powerset @ (cartprod @ X0 @ X1)) @ (^[X2 : $i] : (func @ X0 @ X1 @ X2)))))),
% 1.02/0.95 inference(rectify,[status(thm)],[f6])).
% 1.02/0.95 thf(f6,axiom,(
% 1.02/0.95 (funcSet = (^[X0 : $i, X4 : $i] : (dsetconstr @ (powerset @ (cartprod @ X0 @ X4)) @ (^[X7 : $i] : (func @ X0 @ X4 @ X7)))))),
% 1.02/0.95 file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',funcSet)).
% 1.02/0.95 thf(f32,plain,(
% 1.02/0.95 ((in @ sK2 @ (funcSet @ sK1 @ sK0)) = $true)),
% 1.02/0.95 inference(cnf_transformation,[status(thm)],[f26])).
% 1.02/0.95 thf(f26,plain,(
% 1.02/0.95 (dsetconstrER = $true) & (((in @ sK2 @ (funcSet @ sK1 @ sK0)) = $true) & ((func @ sK1 @ sK0 @ sK2) != $true))),
% 1.02/0.95 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f24,f25])).
% 1.02/0.95 thf(f25,plain,(
% 1.02/0.95 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (funcSet @ X1 @ X0)) = $true) & ((func @ X1 @ X0 @ X2) != $true)) => (((in @ sK2 @ (funcSet @ sK1 @ sK0)) = $true) & ((func @ sK1 @ sK0 @ sK2) != $true))),
% 1.02/0.95 introduced(definition,[],[choice_axiom])).
% 1.02/0.95 thf(f24,plain,(
% 1.02/0.95 (dsetconstrER = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (funcSet @ X1 @ X0)) = $true) & ((func @ X1 @ X0 @ X2) != $true))),
% 1.02/0.95 inference(ennf_transformation,[status(thm)],[f13])).
% 1.02/0.95 thf(f13,plain,(
% 1.02/0.95 ~((dsetconstrER = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (funcSet @ X1 @ X0)) = $true) => ((func @ X1 @ X0 @ X2) = $true)))),
% 1.02/0.95 inference(fool_elimination,[status(thm)],[f12])).
% 1.02/0.95 thf(f12,plain,(
% 1.02/0.95 ~(dsetconstrER => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X1 @ X0)) => (func @ X1 @ X0 @ X2)))),
% 1.02/0.95 inference(rectify,[status(thm)],[f8])).
% 1.02/0.95 thf(f8,negated_conjecture,(
% 1.02/0.95 ~(dsetconstrER => ! [X4 : $i,X0 : $i,X7 : $i] : ((in @ X7 @ (funcSet @ X0 @ X4)) => (func @ X0 @ X4 @ X7)))),
% 1.02/0.95 inference(negated_conjecture,[status(cth)],[f7])).
% 1.02/0.95 thf(f7,conjecture,(
% 1.02/0.95 dsetconstrER => ! [X4 : $i,X0 : $i,X7 : $i] : ((in @ X7 @ (funcSet @ X0 @ X4)) => (func @ X0 @ X4 @ X7))),
% 1.02/0.95 file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',infuncsetfunc)).
% 1.02/0.95 thf(f52,plain,(
% 1.02/0.95 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ (dsetconstr @ X3 @ X5)) != $true) | ((X5 @ X4) = $true)) )),
% 1.02/0.95 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.02/0.95 thf(f51,plain,(
% 1.02/0.95 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((X5 @ X4) = $true) | ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true)) )),
% 1.02/0.95 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.02/0.95 thf(f49,plain,(
% 1.02/0.95 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((X5 @ X4) = $true) | ($true != $true) | ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true)) )),
% 1.02/0.95 inference(definition_unfolding,[status(thm)],[f36,f33])).
% 1.02/0.95 thf(f33,plain,(
% 1.02/0.95 (dsetconstrER = $true)),
% 1.02/0.95 inference(cnf_transformation,[status(thm)],[f26])).
% 1.02/0.95 thf(f36,plain,(
% 1.02/0.95 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((X5 @ X4) = $true) | ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true) | (dsetconstrER != $true)) )),
% 1.02/0.95 inference(cnf_transformation,[status(thm)],[f30])).
% 1.02/0.95 thf(f30,plain,(
% 1.02/0.95 ((dsetconstrER = $true) | (($true != (sK5 @ sK4)) & ($true = (in @ sK4 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (sK5 @ Y0))))))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (((X5 @ X4) = $true) | ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true)) | (dsetconstrER != $true))),
% 1.02/0.95 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f28,f29])).
% 1.02/0.95 thf(f29,plain,(
% 1.02/0.95 ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X1) != $true) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) => (($true != (sK5 @ sK4)) & ($true = (in @ sK4 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (sK5 @ Y0))))))),
% 1.02/0.95 introduced(definition,[],[choice_axiom])).
% 1.02/0.95 thf(f28,plain,(
% 1.02/0.95 ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X1) != $true) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (((X5 @ X4) = $true) | ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true)) | (dsetconstrER != $true))),
% 1.02/0.95 inference(rectify,[status(thm)],[f27])).
% 1.02/0.95 thf(f27,plain,(
% 1.02/0.95 ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X1) != $true) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))) & (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) | (dsetconstrER != $true))),
% 1.02/0.95 inference(nnf_transformation,[status(thm)],[f23])).
% 1.02/0.95 thf(f23,plain,(
% 1.02/0.95 (dsetconstrER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))),
% 1.02/0.95 inference(ennf_transformation,[status(thm)],[f19])).
% 1.02/0.95 thf(f19,plain,(
% 1.02/0.95 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) => ((X2 @ X1) = $true)) <=> (dsetconstrER = $true)),
% 1.02/0.95 inference(fool_elimination,[status(thm)],[f18])).
% 1.02/0.95 thf(f18,plain,(
% 1.02/0.95 (dsetconstrER = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X1)))),
% 1.02/0.95 inference(rectify,[status(thm)],[f1])).
% 1.02/0.95 thf(f1,axiom,(
% 1.02/0.95 (dsetconstrER = ! [X0 : $i,X2 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)))),
% 1.02/0.95 file('/export/starexec/sandbox/tmp/tmp.6e1z9DOh1l/DTF2THF_30992.p',dsetconstrER)).
% 1.02/0.95 thf(f106,plain,(
% 1.02/0.95 ~spl6_2 | ~spl6_3),
% 1.02/0.95 inference(avatar_contradiction_clause,[status(thm)],[f105])).
% 1.02/0.95 thf(f105,plain,(
% 1.02/0.95 $false | (~spl6_2 | ~spl6_3)),
% 1.02/0.95 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.02/0.95 thf(f104,plain,(
% 1.02/0.95 ($false = $true) | (~spl6_2 | ~spl6_3)),
% 1.02/0.95 inference(backward_demodulation,[status(thm)],[f100,f103])).
% 1.02/0.95 thf(f103,plain,(
% 1.02/0.95 ($false = (in @ (sK9 @ sK7) @ (setadjoin @ (sK9 @ sK7) @ emptyset))) | (~spl6_2 | ~spl6_3)),
% 1.02/0.95 inference(equality_resolution,[status(thm)],[f102])).
% 1.02/0.95 thf(f102,plain,(
% 1.02/0.95 ( ! [X1 : $i] : (((setadjoin @ X1 @ emptyset) != (setadjoin @ (sK9 @ sK7) @ emptyset)) | ((in @ X1 @ (setadjoin @ (sK9 @ sK7) @ emptyset)) = $false)) ) | (~spl6_2 | ~spl6_3)),
% 1.02/0.95 inference(forward_demodulation,[status(thm)],[f101,f99])).
% 1.02/0.95 thf(f99,plain,(
% 1.02/0.95 ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2))) = (setadjoin @ (sK9 @ sK7) @ emptyset)) | ~spl6_3),
% 1.02/0.95 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.02/0.95 thf(f96,plain,(
% 1.02/0.95 ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2))) = (setadjoin @ (sK9 @ sK7) @ emptyset)) | ($false = $true) | ~spl6_3),
% 1.02/0.95 inference(superposition,[status(thm)],[f88,f74])).
% 1.02/0.95 thf(f74,plain,(
% 1.02/0.95 ((in @ sK7 @ sK1) = $true) | ~spl6_3),
% 1.02/0.95 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.02/0.95 thf(f72,definition,(
% 1.02/0.95 spl6_3 <=> ((in @ sK7 @ sK1) = $true)),
% 1.02/0.95 introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition])).
% 1.02/0.95 thf(f88,plain,(
% 1.02/0.95 ( ! [X1 : $i] : (($false = (in @ X1 @ sK1)) | ((setadjoin @ (sK9 @ X1) @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK2))))) )),
% 1.02/0.95 inference(equality_proxy_clausification,[status(thm)],[f87])).
% 1.02/0.95 thf(f87,plain,(
% 1.02/0.95 ( ! [X1 : $i] : ((((setadjoin @ (sK9 @ X1) @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK2)))) = $true) | ($false = (in @ X1 @ sK1))) )),
% 1.02/0.95 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.02/0.95 thf(f85,plain,(
% 1.02/0.95 ( ! [X1 : $i] : (((((setadjoin @ (sK9 @ X1) @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK2)))) & (in @ (sK9 @ X1) @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK2))))) = $true) | ($false = (in @ X1 @ sK1))) )),
% 1.02/0.95 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.02/0.95 thf(f84,plain,(
% 1.02/0.95 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK2)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK2)))))) @ (sK9 @ X1)) = $true) | ($false = (in @ X1 @ sK1))) )),
% 1.02/0.95 inference(sigma_clausification,[status(thm)],[f83])).
% 1.02/0.95 thf(f83,plain,(
% 1.02/0.95 ( ! [X1 : $i] : (($false = (in @ X1 @ sK1)) | ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK2)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK2))))))) = $true)) )),
% 1.02/0.95 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.02/0.95 thf(f82,plain,(
% 1.02/0.95 ( ! [X1 : $i] : ((((in @ X1 @ sK1) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK2)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK2)))))))) = $true)) )),
% 1.02/0.95 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.02/0.95 thf(f81,plain,(
% 1.02/0.95 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2))))))))) @ X1) = $true)) )),
% 1.02/0.95 inference(pi_clausification,[status(thm)],[f80])).
% 1.02/0.95 thf(f80,plain,(
% 1.02/0.95 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))))))))) = $true)),
% 1.02/0.95 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.02/0.95 thf(f101,plain,(
% 1.02/0.95 ( ! [X1 : $i] : (($false = (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2))))) | ((setadjoin @ X1 @ emptyset) != (setadjoin @ (sK9 @ sK7) @ emptyset))) ) | (~spl6_2 | ~spl6_3)),
% 1.02/0.95 inference(backward_demodulation,[status(thm)],[f69,f99])).
% 1.02/0.95 thf(f69,plain,(
% 1.02/0.95 ( ! [X1 : $i] : (((setadjoin @ X1 @ emptyset) != (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2)))) | ($false = (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2)))))) ) | ~spl6_2),
% 1.02/0.95 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.02/0.95 thf(f68,definition,(
% 1.02/0.95 spl6_2 <=> ! [X1 : $i] : (((setadjoin @ X1 @ emptyset) != (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2)))) | ($false = (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2))))))),
% 1.02/0.95 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.02/0.95 thf(f100,plain,(
% 1.02/0.95 ((in @ (sK9 @ sK7) @ (setadjoin @ (sK9 @ sK7) @ emptyset)) = $true) | ~spl6_3),
% 1.02/0.95 inference(backward_demodulation,[status(thm)],[f92,f99])).
% 1.02/0.95 thf(f92,plain,(
% 1.02/0.95 ($true = (in @ (sK9 @ sK7) @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2))))) | ~spl6_3),
% 1.02/0.95 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.02/0.95 thf(f90,plain,(
% 1.02/0.95 ($false = $true) | ($true = (in @ (sK9 @ sK7) @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2))))) | ~spl6_3),
% 1.02/0.95 inference(superposition,[status(thm)],[f74,f86])).
% 1.02/0.95 thf(f86,plain,(
% 1.02/0.95 ( ! [X1 : $i] : (($false = (in @ X1 @ sK1)) | ($true = (in @ (sK9 @ X1) @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK2)))))) )),
% 1.02/0.95 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.02/0.95 thf(f75,plain,(
% 1.02/0.95 spl6_1 | spl6_3),
% 1.02/0.95 inference(avatar_split_clause,[status(thm)],[f58,f72,f64])).
% 1.02/0.95 thf(f58,plain,(
% 1.02/0.95 ((in @ sK7 @ sK1) = $true) | ($false = (subset @ sK2 @ (cartprod @ sK1 @ sK0)))),
% 1.02/0.95 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.02/0.95 thf(f56,plain,(
% 1.02/0.95 ($false = ((in @ sK7 @ sK1) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK2)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK2))))))))) | ($false = (subset @ sK2 @ (cartprod @ sK1 @ sK0)))),
% 1.02/0.95 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.02/0.95 thf(f55,plain,(
% 1.02/0.95 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2))))))))) @ sK7)) | ($false = (subset @ sK2 @ (cartprod @ sK1 @ sK0)))),
% 1.02/0.95 inference(sigma_clausification,[status(thm)],[f54])).
% 1.02/0.95 thf(f54,plain,(
% 1.02/0.95 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2))))))))))) | ($false = (subset @ sK2 @ (cartprod @ sK1 @ sK0)))),
% 1.02/0.95 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.02/0.95 thf(f53,plain,(
% 1.02/0.95 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))))))))) & (subset @ sK2 @ (cartprod @ sK1 @ sK0))) != $true)),
% 1.02/0.95 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.02/0.95 thf(f46,plain,(
% 1.02/0.95 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2))))))) @ sK1 @ sK0 @ sK2))),
% 1.02/0.95 inference(definition_unfolding,[status(thm)],[f31,f43])).
% 1.02/0.95 thf(f31,plain,(
% 1.02/0.95 ((func @ sK1 @ sK0 @ sK2) != $true)),
% 1.02/0.95 inference(cnf_transformation,[status(thm)],[f26])).
% 1.02/0.95 thf(f70,plain,(
% 1.02/0.95 spl6_1 | spl6_2),
% 1.02/0.95 inference(avatar_split_clause,[status(thm)],[f62,f68,f64])).
% 1.02/0.95 thf(f62,plain,(
% 1.02/0.95 ( ! [X1 : $i] : (((setadjoin @ X1 @ emptyset) != (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2)))) | ($false = (subset @ sK2 @ (cartprod @ sK1 @ sK0))) | ($false = (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2)))))) )),
% 1.02/0.95 inference(equality_proxy_clausification,[status(thm)],[f61])).
% 1.02/0.95 thf(f61,plain,(
% 1.02/0.95 ( ! [X1 : $i] : (($false = (subset @ sK2 @ (cartprod @ sK1 @ sK0))) | ($false = (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2))))) | ($false = ((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2)))))) )),
% 1.02/0.95 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.02/0.95 thf(f60,plain,(
% 1.02/0.95 ( ! [X1 : $i] : (($false = (((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2)))) & (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK2)))))) | ($false = (subset @ sK2 @ (cartprod @ sK1 @ sK0)))) )),
% 1.02/0.95 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.02/0.95 thf(f59,plain,(
% 1.02/0.95 ( ! [X1 : $i] : (($false = (subset @ sK2 @ (cartprod @ sK1 @ sK0))) | ($false = ((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK2)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK2)))))) @ X1))) )),
% 1.02/0.95 inference(pi_clausification,[status(thm)],[f57])).
% 1.02/0.95 thf(f57,plain,(
% 1.02/0.95 ($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK2)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK7 @ Y1) @ sK2)))))))) | ($false = (subset @ sK2 @ (cartprod @ sK1 @ sK0)))),
% 1.02/0.95 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.02/0.95 % SZS output end Proof for DTF2THF_30992
% 1.02/0.95 % (31188)------------------------------
% 1.02/0.95 % (31188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.95 % (31188)Termination reason: Refutation
% 1.02/0.95
% 1.02/0.95 % (31188)Memory used [KB]: 5628
% 1.02/0.95 % (31188)Time elapsed: 0.008 s
% 1.02/0.95 % (31188)Instructions burned: 12 (million)
% 1.02/0.95 % (31188)------------------------------
% 1.02/0.95 % (31188)------------------------------
% 1.02/0.95 % (31181)Success in time 0.005 s
%------------------------------------------------------------------------------