%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU681^2 : 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 : n003.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 09:36:18 AM UTC 2026
% Result : Theorem 1.59s 1.33s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 870 ( 252 equ; 0 cnn)
% Maximal formula atoms : 14 ( 12 avg)
% Number of connectives : 1022 ( 117 ~; 98 |; 68 &; 686 @)
% ( 5 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 14 con; 0-3 aty)
% Number of variables : 215 ( 15 ^; 145 !; 55 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
breln: $i > $i > $i > $o ).
thf(func_def_14,type,
sK0: $i > $i > $i > $i ).
thf(func_def_15,type,
sK1: $i > $i > $i > $i ).
thf(func_def_25,type,
sK11: $i > $o ).
thf(f86,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f85,f45]) ).
thf(f45,plain,
( $true
= ( in @ sK12 @ sK8 ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( subsetE = $true )
& ( cartprodmempair1 = $true )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK10 ) )
| ! [X5: $i] :
( ( $true
= ( sK11 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK8 ) )
| ( $true
!= ( in @ X5 @ sK9 ) ) ) )
& ( ( sK11 @ sK12 )
!= $true )
& ( $true
= ( in @ sK12 @ sK8 ) )
& ( $true
= ( breln @ sK10 @ sK9 @ sK8 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f18,f32,f31,f30]) ).
thf(f30,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X2 ) )
| ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
| ( ( in @ X5 @ X1 )
!= $true ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( $true
= ( in @ X6 @ X0 ) ) ) )
& ( $true
= ( breln @ X2 @ X1 @ X0 ) ) )
=> ( ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK10 ) )
| ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK8 ) )
| ( $true
!= ( in @ X5 @ sK9 ) ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( ( in @ X6 @ sK8 )
= $true ) ) )
& ( $true
= ( breln @ sK10 @ sK9 @ sK8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK10 ) )
| ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK8 ) )
| ( $true
!= ( in @ X5 @ sK9 ) ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( ( in @ X6 @ sK8 )
= $true ) ) )
=> ( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK10 ) )
| ! [X5: $i] :
( ( $true
= ( sK11 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK8 ) )
| ( $true
!= ( in @ X5 @ sK9 ) ) ) )
& ? [X6: $i] :
( ( ( sK11 @ X6 )
!= $true )
& ( ( in @ X6 @ sK8 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X6: $i] :
( ( ( sK11 @ X6 )
!= $true )
& ( ( in @ X6 @ sK8 )
= $true ) )
=> ( ( ( sK11 @ sK12 )
!= $true )
& ( $true
= ( in @ sK12 @ sK8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( subsetE = $true )
& ( cartprodmempair1 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X2 ) )
| ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
| ( ( in @ X5 @ X1 )
!= $true ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( $true
= ( in @ X6 @ X0 ) ) ) )
& ( $true
= ( breln @ X2 @ X1 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i > $o] :
( ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( $true
= ( in @ X6 @ X0 ) ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
| ( ( in @ X5 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X4 @ X2 ) ) ) )
& ( $true
= ( breln @ X2 @ X1 @ X0 ) ) )
& ( cartprodmempair1 = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( ( subsetE = $true )
=> ( ( cartprodmempair1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X2 @ X1 @ X0 ) )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
=> ! [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
=> ( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
=> ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) ) )
=> ! [X6: $i] :
( ( $true
= ( in @ X6 @ X0 ) )
=> ( $true
= ( X3 @ X6 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( subsetE
=> ( cartprodmempair1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X2 @ X1 @ X0 )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X0 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( X3 @ X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( subsetE
=> ( cartprodmempair1
=> ! [X6: $i,X1: $i,X0: $i] :
( ( breln @ X0 @ X1 @ X6 )
=> ! [X7: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X2 @ X4 ) @ X6 )
=> ( X7 @ ( kpair @ X2 @ X4 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X6 )
=> ( X7 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( subsetE
=> ( cartprodmempair1
=> ! [X6: $i,X1: $i,X0: $i] :
( ( breln @ X0 @ X1 @ X6 )
=> ! [X7: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X2 @ X4 ) @ X6 )
=> ( X7 @ ( kpair @ X2 @ X4 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X6 )
=> ( X7 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5ojdcbwCDM/DTF2THF_20346.p',brelnall1) ).
thf(f85,plain,
( $true
!= ( in @ sK12 @ sK8 ) ),
inference(subsumption_resolution,[status(thm)],[f84,f76]) ).
thf(f76,plain,
( ( in @ ( sK0 @ sK9 @ sK12 @ sK10 ) @ sK10 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ( in @ ( sK0 @ sK9 @ sK12 @ sK10 ) @ sK10 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f62,f68]) ).
thf(f68,plain,
( $true
= ( in @ sK12 @ ( cartprod @ sK10 @ sK9 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $true != $true )
| ( $true
= ( in @ sK12 @ ( cartprod @ sK10 @ sK9 ) ) ) ),
inference(superposition,[status(thm)],[f66,f64]) ).
thf(f64,plain,
( ( subset @ sK8 @ ( cartprod @ sK10 @ sK9 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK10
@ sK9
@ sK8 )
= $true ),
inference(definition_unfolding,[status(thm)],[f44,f43]) ).
thf(f43,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
file('/export/starexec/sandbox/tmp/tmp.5ojdcbwCDM/DTF2THF_20346.p',breln) ).
thf(f44,plain,
( $true
= ( breln @ sK10 @ sK9 @ sK8 ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f66,plain,
! [X0: $i] :
( ( ( subset @ sK8 @ X0 )
!= $true )
| ( $true
= ( in @ sK12 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( subset @ sK8 @ X0 )
!= $true )
| ( $true
= ( in @ sK12 @ X0 ) ) ),
inference(superposition,[status(thm)],[f61,f45]) ).
thf(f61,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ X3 ) )
| ( ( subset @ X4 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( $true != $true )
| ( $true
= ( in @ X5 @ X3 ) )
| ( ( subset @ X4 @ X3 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f39,f49]) ).
thf(f49,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f39,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ X3 ) )
| ( ( subset @ X4 @ X3 )
!= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( subsetE = $true )
| ( ( ( in @ sK7 @ sK6 )
= $true )
& ( $true
!= ( in @ sK7 @ sK5 ) )
& ( $true
= ( subset @ sK6 @ sK5 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ X3 ) )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f27,f28]) ).
thf(f28,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) )
=> ( ( ( in @ sK7 @ sK6 )
= $true )
& ( $true
!= ( in @ sK7 @ sK5 ) )
& ( $true
= ( subset @ sK6 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ X3 ) )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox/tmp/tmp.5ojdcbwCDM/DTF2THF_20346.p',subsetE) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f38,f48]) ).
thf(f48,plain,
cartprodmempair1 = $true,
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f38,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( cartprodmempair1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
& ( $true
= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X2 ) )
& ( ( kpair @ ( sK0 @ X2 @ X1 @ X0 ) @ ( sK1 @ X2 @ X1 @ X0 ) )
= X1 ) )
| ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) ) )
| ( cartprodmempair1 != $true ) )
& ( ( cartprodmempair1 = $true )
| ( ! [X8: $i] :
( ( ( in @ X8 @ sK2 )
!= $true )
| ! [X9: $i] :
( ( ( in @ X9 @ sK4 )
!= $true )
| ( ( kpair @ X8 @ X9 )
!= sK3 ) ) )
& ( $true
= ( in @ sK3 @ ( cartprod @ sK2 @ sK4 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f24,f23,f22]) ).
thf(f22,plain,
! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( ( kpair @ X3 @ X4 )
= X1 ) ) )
=> ( ( ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( ( kpair @ ( sK0 @ X2 @ X1 @ X0 ) @ X4 )
= X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
! [X0: $i,X1: $i,X2: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( ( kpair @ ( sK0 @ X2 @ X1 @ X0 ) @ X4 )
= X1 ) )
=> ( ( $true
= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X2 ) )
& ( ( kpair @ ( sK0 @ X2 @ X1 @ X0 ) @ ( sK1 @ X2 @ X1 @ X0 ) )
= X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X5: $i,X6: $i,X7: $i] :
( ! [X8: $i] :
( ( $true
!= ( in @ X8 @ X5 ) )
| ! [X9: $i] :
( ( $true
!= ( in @ X9 @ X7 ) )
| ( ( kpair @ X8 @ X9 )
!= X6 ) ) )
& ( ( in @ X6 @ ( cartprod @ X5 @ X7 ) )
= $true ) )
=> ( ! [X8: $i] :
( ( ( in @ X8 @ sK2 )
!= $true )
| ! [X9: $i] :
( ( ( in @ X9 @ sK4 )
!= $true )
| ( ( kpair @ X8 @ X9 )
!= sK3 ) ) )
& ( $true
= ( in @ sK3 @ ( cartprod @ sK2 @ sK4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( ( kpair @ X3 @ X4 )
= X1 ) ) )
| ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) ) )
| ( cartprodmempair1 != $true ) )
& ( ( cartprodmempair1 = $true )
| ? [X5: $i,X6: $i,X7: $i] :
( ! [X8: $i] :
( ( $true
!= ( in @ X8 @ X5 ) )
| ! [X9: $i] :
( ( $true
!= ( in @ X9 @ X7 ) )
| ( ( kpair @ X8 @ X9 )
!= X6 ) ) )
& ( ( in @ X6 @ ( cartprod @ X5 @ X7 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( ( kpair @ X3 @ X4 )
= X1 ) ) )
| ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) ) )
| ( cartprodmempair1 != $true ) )
& ( ( cartprodmempair1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X2 ) )
| ( ( kpair @ X3 @ X4 )
!= X1 ) ) )
& ( $true
= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( ( kpair @ X3 @ X4 )
= X1 ) ) )
| ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) ) )
<=> ( cartprodmempair1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( cartprodmempair1 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) )
=> ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( ( kpair @ X3 @ X4 )
= X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( cartprodmempair1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( cartprod @ X0 @ X2 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X0 )
& ? [X4: $i] :
( ( in @ X4 @ X2 )
& ( ( kpair @ X3 @ X4 )
= X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( cartprodmempair1
= ( ! [X0: $i,X3: $i,X1: $i] :
( ( in @ X3 @ ( cartprod @ X0 @ X1 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( ( kpair @ X2 @ X4 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5ojdcbwCDM/DTF2THF_20346.p',cartprodmempair1) ).
thf(f84,plain,
( ( ( in @ ( sK0 @ sK9 @ sK12 @ sK10 ) @ sK10 )
!= $true )
| ( $true
!= ( in @ sK12 @ sK8 ) ) ),
inference(subsumption_resolution,[status(thm)],[f83,f46]) ).
thf(f46,plain,
( ( sK11 @ sK12 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f83,plain,
( ( ( sK11 @ sK12 )
= $true )
| ( ( in @ ( sK0 @ sK9 @ sK12 @ sK10 ) @ sK10 )
!= $true )
| ( $true
!= ( in @ sK12 @ sK8 ) ) ),
inference(superposition,[status(thm)],[f80,f82]) ).
thf(f82,plain,
( ( kpair @ ( sK0 @ sK9 @ sK12 @ sK10 ) @ ( sK1 @ sK9 @ sK12 @ sK10 ) )
= sK12 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true != $true )
| ( ( kpair @ ( sK0 @ sK9 @ sK12 @ sK10 ) @ ( sK1 @ sK9 @ sK12 @ sK10 ) )
= sK12 ) ),
inference(superposition,[status(thm)],[f63,f68]) ).
thf(f63,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( ( kpair @ ( sK0 @ X2 @ X1 @ X0 ) @ ( sK1 @ X2 @ X1 @ X0 ) )
= X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( kpair @ ( sK0 @ X2 @ X1 @ X0 ) @ ( sK1 @ X2 @ X1 @ X0 ) )
= X1 )
| ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f36,f48]) ).
thf(f36,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( kpair @ ( sK0 @ X2 @ X1 @ X0 ) @ ( sK1 @ X2 @ X1 @ X0 ) )
= X1 )
| ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( cartprodmempair1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f80,plain,
! [X0: $i] :
( ( ( in @ ( kpair @ X0 @ ( sK1 @ sK9 @ sK12 @ sK10 ) ) @ sK8 )
!= $true )
| ( $true
= ( sK11 @ ( kpair @ X0 @ ( sK1 @ sK9 @ sK12 @ sK10 ) ) ) )
| ( $true
!= ( in @ X0 @ sK10 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
! [X0: $i] :
( ( $true
= ( sK11 @ ( kpair @ X0 @ ( sK1 @ sK9 @ sK12 @ sK10 ) ) ) )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ sK10 ) )
| ( ( in @ ( kpair @ X0 @ ( sK1 @ sK9 @ sK12 @ sK10 ) ) @ sK8 )
!= $true ) ),
inference(superposition,[status(thm)],[f47,f72]) ).
thf(f72,plain,
( $true
= ( in @ ( sK1 @ sK9 @ sK12 @ sK10 ) @ sK9 ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true
= ( in @ ( sK1 @ sK9 @ sK12 @ sK10 ) @ sK9 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f60,f68]) ).
thf(f60,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( $true
= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( $true
= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X2 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f37,f48]) ).
thf(f37,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK1 @ X2 @ X1 @ X0 ) @ X2 ) )
| ( $true
!= ( in @ X1 @ ( cartprod @ X0 @ X2 ) ) )
| ( cartprodmempair1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f47,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ sK9 ) )
| ( $true
= ( sK11 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK8 ) )
| ( $true
!= ( in @ X4 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU681^2 : 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
% 0.11/0.29 % Computer : n003.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:29:55 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU681^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.38 % Domain : Set Theory
% 0.18/0.38 % Problem : Functions - Extensionality and Beta Reduction
% 0.18/0.38 % Version : Especial > Reduced > Especial.
% 0.18/0.38 % English : (! A:i.! B:i.! R:i.breln A B R -> (! phi:i>o.(! x:i.in x A ->
% 0.18/0.38 % (! y:i.in y B -> in (kpair x y) R -> phi (kpair x y))) ->
% 0.18/0.38 % (! x:i.in x R -> phi x)))
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.38 % Source : [Bro08]
% 0.18/0.38 % Names : ZFC183l [Bro08]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.18/0.38 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.18/0.38 % Number of atoms : 21 ( 4 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 7 ( 5 avg)
% 0.18/0.38 % Number of connectives : 50 ( 0 ~; 0 |; 2 &; 37 @)
% 0.18/0.38 % ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 18 ( 5 avg)
% 0.18/0.38 % Number of types : 2 ( 0 usr)
% 0.18/0.38 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 8 ( 7 usr; 2 con; 0-3 aty)
% 0.18/0.38 % Number of variables : 18 ( 3 ^; 13 !; 2 ?; 18 :)
% 0.18/0.38 % SPC : TH0_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : http://mathgate.info/detsetitem.php?id=239
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(in_type,type,
% 0.18/0.38 in: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(subset_type,type,
% 0.18/0.38 subset: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetE_type,type,
% 0.18/0.38 subsetE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetE,definition,
% 0.18/0.38 ( subsetE
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( subset @ A @ B )
% 0.18/0.38 => ( ( in @ Xx @ A )
% 0.18/0.38 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(kpair_type,type,
% 0.18/0.38 kpair: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(cartprod_type,type,
% 0.18/0.38 cartprod: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(cartprodmempair1_type,type,
% 0.18/0.38 cartprodmempair1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(cartprodmempair1,definition,
% 0.18/0.38 ( cartprodmempair1
% 0.18/0.38 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.18/0.38 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.18/0.38 => ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 & ? [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ B )
% 0.18/0.38 & ( Xu
% 0.18/0.38 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(breln_type,type,
% 0.18/0.38 breln: $i > $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(breln,definition,
% 0.18/0.38 ( breln
% 0.18/0.38 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(brelnall1,conjecture,
% 0.18/0.38 ( subsetE
% 0.18/0.38 => ( cartprodmempair1
% 0.18/0.38 => ! [A: $i,B: $i,R: $i] :
% 0.18/0.38 ( ( breln @ A @ B @ R )
% 0.18/0.38 => ! [Xphi: $i > $o] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ! [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ B )
% 0.18/0.38 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.18/0.38 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ R )
% 0.18/0.38 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.41/1.29 ---- Embedded in THF ---
% 1.41/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.41/1.29 %%% Generated on Tue Feb 24 12:29:56 EST 2026
% 1.41/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.41/1.29 %%% Logic specification used:
% 1.41/1.29 %%% thf(spec, logic, $$dhol).
% 1.41/1.29
% 1.41/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5ojdcbwCDM/DTF2DTF20346.p
% See solution above
% 1.41/1.29 ------------------------
% 1.41/1.30 ---- Cleaned THF ---
% 1.59/1.30 thf(in_type,type,
% 1.59/1.30 in: $i > $i > $o ).
% 1.59/1.30
% 1.59/1.30 thf(subset_type,type,
% 1.59/1.30 subset: $i > $i > $o ).
% 1.59/1.30
% 1.59/1.30 thf(subsetE_type,type,
% 1.59/1.30 subsetE: $o ).
% 1.59/1.30
% 1.59/1.30 thf(subsetE,definition,
% 1.59/1.30 ( subsetE
% 1.59/1.30 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.59/1.30 ( ( subset @ A @ B )
% 1.59/1.30 => ( ( in @ Xx @ A )
% 1.59/1.30 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.59/1.30
% 1.59/1.30 thf(kpair_type,type,
% 1.59/1.30 kpair: $i > $i > $i ).
% 1.59/1.30
% 1.59/1.30 thf(cartprod_type,type,
% 1.59/1.30 cartprod: $i > $i > $i ).
% 1.59/1.30
% 1.59/1.30 thf(cartprodmempair1_type,type,
% 1.59/1.30 cartprodmempair1: $o ).
% 1.59/1.30
% 1.59/1.30 thf(cartprodmempair1,definition,
% 1.59/1.30 ( cartprodmempair1
% 1.59/1.30 = ( ! [A: $i,B: $i,Xu: $i] :
% 1.59/1.30 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 1.59/1.30 => ? [Xx: $i] :
% 1.59/1.30 ( ( in @ Xx @ A )
% 1.59/1.30 & ? [Xy: $i] :
% 1.59/1.30 ( ( in @ Xy @ B )
% 1.59/1.30 & ( Xu
% 1.59/1.30 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 1.59/1.30
% 1.59/1.30 thf(breln_type,type,
% 1.59/1.30 breln: $i > $i > $i > $o ).
% 1.59/1.30
% 1.59/1.30 thf(breln,definition,
% 1.59/1.30 ( breln
% 1.59/1.30 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.59/1.30
% 1.59/1.30 thf(brelnall1,conjecture,
% 1.59/1.30 ( subsetE
% 1.59/1.30 => ( cartprodmempair1
% 1.59/1.30 => ! [A: $i,B: $i,R: $i] :
% 1.59/1.30 ( ( breln @ A @ B @ R )
% 1.59/1.30 => ! [Xphi: $i > $o] :
% 1.59/1.30 ( ! [Xx: $i] :
% 1.59/1.30 ( ( in @ Xx @ A )
% 1.59/1.30 => ! [Xy: $i] :
% 1.59/1.30 ( ( in @ Xy @ B )
% 1.59/1.30 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.59/1.30 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 1.59/1.30 => ! [Xx: $i] :
% 1.59/1.30 ( ( in @ Xx @ R )
% 1.59/1.30 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.59/1.30 ------------------------
% 1.59/1.32 % (20447)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20346 for (2999ds/2Mi)
% 1.59/1.32 % (20446)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_20346 for (2999ds/27Mi)
% 1.59/1.32 % (20445)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_20346 for (2999ds/4Mi)
% 1.59/1.32 % (20444)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20346 for (2999ds/183Mi)
% 1.59/1.32 % (20448)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_20346 for (2999ds/2Mi)
% 1.59/1.32 % (20450)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20346 for (2999ds/18Mi)
% 1.59/1.32 % (20449)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_20346 for (2999ds/275Mi)
% 1.59/1.32 % (20447)Instruction limit reached!
% 1.59/1.32 % (20447)------------------------------
% 1.59/1.32 % (20447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (20447)Termination reason: Unknown
% 1.59/1.32 % (20448)Instruction limit reached!
% 1.59/1.32 % (20448)------------------------------
% 1.59/1.32 % (20448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (20447)Termination phase: Function definition elimination
% 1.59/1.32
% 1.59/1.32 % (20447)Memory used [KB]: 1023
% 1.59/1.32 % (20447)Time elapsed: 0.003 s
% 1.59/1.32 % (20447)Instructions burned: 3 (million)
% 1.59/1.32 % (20447)------------------------------
% 1.59/1.32 % (20447)------------------------------
% 1.59/1.32 % (20448)Termination reason: Unknown
% 1.59/1.32 % (20448)Termination phase: Property scanning
% 1.59/1.32
% 1.59/1.32 % (20448)Memory used [KB]: 1023
% 1.59/1.32 % (20448)Time elapsed: 0.003 s
% 1.59/1.32 % (20448)Instructions burned: 3 (million)
% 1.59/1.32 % (20448)------------------------------
% 1.59/1.32 % (20448)------------------------------
% 1.59/1.32 % (20445)Instruction limit reached!
% 1.59/1.32 % (20445)------------------------------
% 1.59/1.32 % (20445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (20445)Termination reason: Unknown
% 1.59/1.32 % (20445)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (20445)Memory used [KB]: 5500
% 1.59/1.32 % (20445)Time elapsed: 0.004 s
% 1.59/1.32 % (20445)Instructions burned: 4 (million)
% 1.59/1.32 % (20445)------------------------------
% 1.59/1.32 % (20445)------------------------------
% 1.59/1.32 % (20450)First to succeed.
% 1.59/1.33 % (20450)Refutation found. Thanks to Tanya!
% 1.59/1.33 % SZS status Theorem for DTF2THF_20346
% 1.59/1.33 % SZS output start Proof for DTF2THF_20346
% 1.59/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.59/1.33 thf(func_def_1, type, subset: $i > $i > $o).
% 1.59/1.33 thf(func_def_4, type, kpair: $i > $i > $i).
% 1.59/1.33 thf(func_def_5, type, cartprod: $i > $i > $i).
% 1.59/1.33 thf(func_def_7, type, breln: $i > $i > $i > $o).
% 1.59/1.33 thf(func_def_14, type, sK0: $i > $i > $i > $i).
% 1.59/1.33 thf(func_def_15, type, sK1: $i > $i > $i > $i).
% 1.59/1.33 thf(func_def_25, type, sK11: $i > $o).
% 1.59/1.33 thf(f86,plain,(
% 1.59/1.33 $false),
% 1.59/1.33 inference(subsumption_resolution,[status(thm)],[f85,f45])).
% 1.59/1.33 thf(f45,plain,(
% 1.59/1.33 ($true = (in @ sK12 @ sK8))),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.59/1.33 thf(f33,plain,(
% 1.59/1.33 (subsetE = $true) & (cartprodmempair1 = $true) & ((! [X4 : $i] : (($true != (in @ X4 @ sK10)) | ! [X5 : $i] : (($true = (sK11 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ sK8)) | ($true != (in @ X5 @ sK9)))) & (((sK11 @ sK12) != $true) & ($true = (in @ sK12 @ sK8)))) & ($true = (breln @ sK10 @ sK9 @ sK8)))),
% 1.59/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f18,f32,f31,f30])).
% 1.59/1.33 thf(f30,plain,(
% 1.59/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ X2)) | ! [X5 : $i] : (($true = (X3 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ X0)) | ((in @ X5 @ X1) != $true))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ($true = (in @ X6 @ X0)))) & ($true = (breln @ X2 @ X1 @ X0))) => (? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ sK10)) | ! [X5 : $i] : (($true = (X3 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ sK8)) | ($true != (in @ X5 @ sK9)))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ((in @ X6 @ sK8) = $true))) & ($true = (breln @ sK10 @ sK9 @ sK8)))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f31,plain,(
% 1.59/1.33 ? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ sK10)) | ! [X5 : $i] : (($true = (X3 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ sK8)) | ($true != (in @ X5 @ sK9)))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ((in @ X6 @ sK8) = $true))) => (! [X4 : $i] : (($true != (in @ X4 @ sK10)) | ! [X5 : $i] : (($true = (sK11 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ sK8)) | ($true != (in @ X5 @ sK9)))) & ? [X6 : $i] : (((sK11 @ X6) != $true) & ((in @ X6 @ sK8) = $true)))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f32,plain,(
% 1.59/1.33 ? [X6 : $i] : (((sK11 @ X6) != $true) & ((in @ X6 @ sK8) = $true)) => (((sK11 @ sK12) != $true) & ($true = (in @ sK12 @ sK8)))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f18,plain,(
% 1.59/1.33 (subsetE = $true) & (cartprodmempair1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ X2)) | ! [X5 : $i] : (($true = (X3 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ X0)) | ((in @ X5 @ X1) != $true))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ($true = (in @ X6 @ X0)))) & ($true = (breln @ X2 @ X1 @ X0)))),
% 1.59/1.33 inference(flattening,[status(thm)],[f17])).
% 1.59/1.33 thf(f17,plain,(
% 1.59/1.33 (? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i > $o] : (? [X6 : $i] : (($true != (X3 @ X6)) & ($true = (in @ X6 @ X0))) & ! [X4 : $i] : (! [X5 : $i] : ((($true = (X3 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ X0))) | ((in @ X5 @ X1) != $true)) | ($true != (in @ X4 @ X2)))) & ($true = (breln @ X2 @ X1 @ X0))) & (cartprodmempair1 = $true)) & (subsetE = $true)),
% 1.59/1.33 inference(ennf_transformation,[status(thm)],[f14])).
% 1.59/1.33 thf(f14,plain,(
% 1.59/1.33 ~((subsetE = $true) => ((cartprodmempair1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X2 @ X1 @ X0)) => ! [X3 : $i > $o] : (! [X4 : $i] : (($true = (in @ X4 @ X2)) => ! [X5 : $i] : (((in @ X5 @ X1) = $true) => (($true = (in @ (kpair @ X4 @ X5) @ X0)) => ($true = (X3 @ (kpair @ X4 @ X5)))))) => ! [X6 : $i] : (($true = (in @ X6 @ X0)) => ($true = (X3 @ X6)))))))),
% 1.59/1.33 inference(fool_elimination,[status(thm)],[f13])).
% 1.59/1.33 thf(f13,plain,(
% 1.59/1.33 ~(subsetE => (cartprodmempair1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X2 @ X1 @ X0) => ! [X3 : $i > $o] : (! [X4 : $i] : ((in @ X4 @ X2) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X0) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X0) => (X3 @ X6))))))),
% 1.59/1.33 inference(rectify,[status(thm)],[f5])).
% 1.59/1.33 thf(f5,negated_conjecture,(
% 1.59/1.33 ~(subsetE => (cartprodmempair1 => ! [X6 : $i,X1 : $i,X0 : $i] : ((breln @ X0 @ X1 @ X6) => ! [X7 : $i > $o] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X2 @ X4) @ X6) => (X7 @ (kpair @ X2 @ X4))))) => ! [X2 : $i] : ((in @ X2 @ X6) => (X7 @ X2))))))),
% 1.59/1.33 inference(negated_conjecture,[status(cth)],[f4])).
% 1.59/1.33 thf(f4,conjecture,(
% 1.59/1.33 subsetE => (cartprodmempair1 => ! [X6 : $i,X1 : $i,X0 : $i] : ((breln @ X0 @ X1 @ X6) => ! [X7 : $i > $o] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X2 @ X4) @ X6) => (X7 @ (kpair @ X2 @ X4))))) => ! [X2 : $i] : ((in @ X2 @ X6) => (X7 @ X2)))))),
% 1.59/1.33 file('/export/starexec/sandbox/tmp/tmp.5ojdcbwCDM/DTF2THF_20346.p',brelnall1)).
% 1.59/1.33 thf(f85,plain,(
% 1.59/1.33 ($true != (in @ sK12 @ sK8))),
% 1.59/1.33 inference(subsumption_resolution,[status(thm)],[f84,f76])).
% 1.59/1.33 thf(f76,plain,(
% 1.59/1.33 ((in @ (sK0 @ sK9 @ sK12 @ sK10) @ sK10) = $true)),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.59/1.33 thf(f75,plain,(
% 1.59/1.33 ((in @ (sK0 @ sK9 @ sK12 @ sK10) @ sK10) = $true) | ($true != $true)),
% 1.59/1.33 inference(superposition,[status(thm)],[f62,f68])).
% 1.59/1.33 thf(f68,plain,(
% 1.59/1.33 ($true = (in @ sK12 @ (cartprod @ sK10 @ sK9)))),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.59/1.33 thf(f67,plain,(
% 1.59/1.33 ($true != $true) | ($true = (in @ sK12 @ (cartprod @ sK10 @ sK9)))),
% 1.59/1.33 inference(superposition,[status(thm)],[f66,f64])).
% 1.59/1.33 thf(f64,plain,(
% 1.59/1.33 ((subset @ sK8 @ (cartprod @ sK10 @ sK9)) = $true)),
% 1.59/1.33 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.59/1.33 thf(f59,plain,(
% 1.59/1.33 (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ sK10 @ sK9 @ sK8) = $true)),
% 1.59/1.33 inference(definition_unfolding,[status(thm)],[f44,f43])).
% 1.59/1.33 thf(f43,plain,(
% 1.59/1.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f10])).
% 1.59/1.33 thf(f10,plain,(
% 1.59/1.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.59/1.33 inference(fool_elimination,[status(thm)],[f9])).
% 1.59/1.33 thf(f9,plain,(
% 1.59/1.33 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 1.59/1.33 inference(rectify,[status(thm)],[f3])).
% 1.59/1.33 thf(f3,axiom,(
% 1.59/1.33 ((^[X0 : $i, X1 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X0 @ X1))) = breln)),
% 1.59/1.33 file('/export/starexec/sandbox/tmp/tmp.5ojdcbwCDM/DTF2THF_20346.p',breln)).
% 1.59/1.33 thf(f44,plain,(
% 1.59/1.33 ($true = (breln @ sK10 @ sK9 @ sK8))),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.59/1.33 thf(f66,plain,(
% 1.59/1.33 ( ! [X0 : $i] : (((subset @ sK8 @ X0) != $true) | ($true = (in @ sK12 @ X0))) )),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.59/1.33 thf(f65,plain,(
% 1.59/1.33 ( ! [X0 : $i] : (($true != $true) | ((subset @ sK8 @ X0) != $true) | ($true = (in @ sK12 @ X0))) )),
% 1.59/1.33 inference(superposition,[status(thm)],[f61,f45])).
% 1.59/1.33 thf(f61,plain,(
% 1.59/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X4)) | ($true = (in @ X5 @ X3)) | ((subset @ X4 @ X3) != $true)) )),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.59/1.33 thf(f58,plain,(
% 1.59/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X4)) | ($true != $true) | ($true = (in @ X5 @ X3)) | ((subset @ X4 @ X3) != $true)) )),
% 1.59/1.33 inference(definition_unfolding,[status(thm)],[f39,f49])).
% 1.59/1.33 thf(f49,plain,(
% 1.59/1.33 (subsetE = $true)),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.59/1.33 thf(f39,plain,(
% 1.59/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X4)) | ($true = (in @ X5 @ X3)) | ((subset @ X4 @ X3) != $true) | (subsetE != $true)) )),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f29])).
% 1.59/1.33 thf(f29,plain,(
% 1.59/1.33 ((subsetE = $true) | (((in @ sK7 @ sK6) = $true) & ($true != (in @ sK7 @ sK5)) & ($true = (subset @ sK6 @ sK5)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X4)) | ($true = (in @ X5 @ X3)) | ((subset @ X4 @ X3) != $true)) | (subsetE != $true))),
% 1.59/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f27,f28])).
% 1.59/1.33 thf(f28,plain,(
% 1.59/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true) & ($true = (subset @ X1 @ X0))) => (((in @ sK7 @ sK6) = $true) & ($true != (in @ sK7 @ sK5)) & ($true = (subset @ sK6 @ sK5)))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f27,plain,(
% 1.59/1.33 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true) & ($true = (subset @ X1 @ X0)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X4)) | ($true = (in @ X5 @ X3)) | ((subset @ X4 @ X3) != $true)) | (subsetE != $true))),
% 1.59/1.33 inference(rectify,[status(thm)],[f26])).
% 1.59/1.33 thf(f26,plain,(
% 1.59/1.33 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true) & ($true = (subset @ X1 @ X0)))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true) | ($true != (subset @ X1 @ X0))) | (subsetE != $true))),
% 1.59/1.33 inference(nnf_transformation,[status(thm)],[f16])).
% 1.59/1.33 thf(f16,plain,(
% 1.59/1.33 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true) | ($true != (subset @ X1 @ X0)))),
% 1.59/1.33 inference(flattening,[status(thm)],[f15])).
% 1.59/1.33 thf(f15,plain,(
% 1.59/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) | ($true != (subset @ X1 @ X0))) <=> (subsetE = $true)),
% 1.59/1.33 inference(ennf_transformation,[status(thm)],[f12])).
% 1.59/1.33 thf(f12,plain,(
% 1.59/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X1 @ X0)) => (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true))) <=> (subsetE = $true)),
% 1.59/1.33 inference(fool_elimination,[status(thm)],[f11])).
% 1.59/1.33 thf(f11,plain,(
% 1.59/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = subsetE)),
% 1.59/1.33 inference(rectify,[status(thm)],[f1])).
% 1.59/1.33 thf(f1,axiom,(
% 1.59/1.33 (! [X1 : $i,X0 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.59/1.33 file('/export/starexec/sandbox/tmp/tmp.5ojdcbwCDM/DTF2THF_20346.p',subsetE)).
% 1.59/1.33 thf(f62,plain,(
% 1.59/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (cartprod @ X0 @ X2))) | ((in @ (sK0 @ X2 @ X1 @ X0) @ X0) = $true)) )),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.59/1.33 thf(f50,plain,(
% 1.59/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK0 @ X2 @ X1 @ X0) @ X0) = $true) | ($true != $true) | ($true != (in @ X1 @ (cartprod @ X0 @ X2)))) )),
% 1.59/1.33 inference(definition_unfolding,[status(thm)],[f38,f48])).
% 1.59/1.33 thf(f48,plain,(
% 1.59/1.33 (cartprodmempair1 = $true)),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.59/1.33 thf(f38,plain,(
% 1.59/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK0 @ X2 @ X1 @ X0) @ X0) = $true) | ($true != (in @ X1 @ (cartprod @ X0 @ X2))) | (cartprodmempair1 != $true)) )),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f25])).
% 1.59/1.33 thf(f25,plain,(
% 1.59/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ (sK0 @ X2 @ X1 @ X0) @ X0) = $true) & (($true = (in @ (sK1 @ X2 @ X1 @ X0) @ X2)) & ((kpair @ (sK0 @ X2 @ X1 @ X0) @ (sK1 @ X2 @ X1 @ X0)) = X1))) | ($true != (in @ X1 @ (cartprod @ X0 @ X2)))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | (! [X8 : $i] : (((in @ X8 @ sK2) != $true) | ! [X9 : $i] : (((in @ X9 @ sK4) != $true) | ((kpair @ X8 @ X9) != sK3))) & ($true = (in @ sK3 @ (cartprod @ sK2 @ sK4)))))),
% 1.59/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f24,f23,f22])).
% 1.59/1.33 thf(f22,plain,(
% 1.59/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ? [X4 : $i] : (($true = (in @ X4 @ X2)) & ((kpair @ X3 @ X4) = X1))) => (((in @ (sK0 @ X2 @ X1 @ X0) @ X0) = $true) & ? [X4 : $i] : (($true = (in @ X4 @ X2)) & ((kpair @ (sK0 @ X2 @ X1 @ X0) @ X4) = X1))))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f23,plain,(
% 1.59/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X2)) & ((kpair @ (sK0 @ X2 @ X1 @ X0) @ X4) = X1)) => (($true = (in @ (sK1 @ X2 @ X1 @ X0) @ X2)) & ((kpair @ (sK0 @ X2 @ X1 @ X0) @ (sK1 @ X2 @ X1 @ X0)) = X1)))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f24,plain,(
% 1.59/1.33 ? [X5 : $i,X6 : $i,X7 : $i] : (! [X8 : $i] : (($true != (in @ X8 @ X5)) | ! [X9 : $i] : (($true != (in @ X9 @ X7)) | ((kpair @ X8 @ X9) != X6))) & ((in @ X6 @ (cartprod @ X5 @ X7)) = $true)) => (! [X8 : $i] : (((in @ X8 @ sK2) != $true) | ! [X9 : $i] : (((in @ X9 @ sK4) != $true) | ((kpair @ X8 @ X9) != sK3))) & ($true = (in @ sK3 @ (cartprod @ sK2 @ sK4))))),
% 1.59/1.33 introduced(definition,[],[choice_axiom])).
% 1.59/1.33 thf(f21,plain,(
% 1.59/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ? [X4 : $i] : (($true = (in @ X4 @ X2)) & ((kpair @ X3 @ X4) = X1))) | ($true != (in @ X1 @ (cartprod @ X0 @ X2)))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | ? [X5 : $i,X6 : $i,X7 : $i] : (! [X8 : $i] : (($true != (in @ X8 @ X5)) | ! [X9 : $i] : (($true != (in @ X9 @ X7)) | ((kpair @ X8 @ X9) != X6))) & ((in @ X6 @ (cartprod @ X5 @ X7)) = $true)))),
% 1.59/1.33 inference(rectify,[status(thm)],[f20])).
% 1.59/1.33 thf(f20,plain,(
% 1.59/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ? [X4 : $i] : (($true = (in @ X4 @ X2)) & ((kpair @ X3 @ X4) = X1))) | ($true != (in @ X1 @ (cartprod @ X0 @ X2)))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ! [X4 : $i] : (($true != (in @ X4 @ X2)) | ((kpair @ X3 @ X4) != X1))) & ($true = (in @ X1 @ (cartprod @ X0 @ X2)))))),
% 1.59/1.33 inference(nnf_transformation,[status(thm)],[f19])).
% 1.59/1.33 thf(f19,plain,(
% 1.59/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ? [X4 : $i] : (($true = (in @ X4 @ X2)) & ((kpair @ X3 @ X4) = X1))) | ($true != (in @ X1 @ (cartprod @ X0 @ X2)))) <=> (cartprodmempair1 = $true)),
% 1.59/1.33 inference(ennf_transformation,[status(thm)],[f8])).
% 1.59/1.33 thf(f8,plain,(
% 1.59/1.33 (cartprodmempair1 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (cartprod @ X0 @ X2))) => ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ? [X4 : $i] : (($true = (in @ X4 @ X2)) & ((kpair @ X3 @ X4) = X1))))),
% 1.59/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 1.59/1.33 thf(f7,plain,(
% 1.59/1.33 (cartprodmempair1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X0 @ X2)) => ? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((in @ X4 @ X2) & ((kpair @ X3 @ X4) = X1)))))),
% 1.59/1.33 inference(rectify,[status(thm)],[f2])).
% 1.59/1.33 thf(f2,axiom,(
% 1.59/1.33 (cartprodmempair1 = ! [X0 : $i,X3 : $i,X1 : $i] : ((in @ X3 @ (cartprod @ X0 @ X1)) => ? [X2 : $i] : ((in @ X2 @ X0) & ? [X4 : $i] : ((in @ X4 @ X1) & ((kpair @ X2 @ X4) = X3)))))),
% 1.59/1.33 file('/export/starexec/sandbox/tmp/tmp.5ojdcbwCDM/DTF2THF_20346.p',cartprodmempair1)).
% 1.59/1.33 thf(f84,plain,(
% 1.59/1.33 ((in @ (sK0 @ sK9 @ sK12 @ sK10) @ sK10) != $true) | ($true != (in @ sK12 @ sK8))),
% 1.59/1.33 inference(subsumption_resolution,[status(thm)],[f83,f46])).
% 1.59/1.33 thf(f46,plain,(
% 1.59/1.33 ((sK11 @ sK12) != $true)),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.59/1.33 thf(f83,plain,(
% 1.59/1.33 ((sK11 @ sK12) = $true) | ((in @ (sK0 @ sK9 @ sK12 @ sK10) @ sK10) != $true) | ($true != (in @ sK12 @ sK8))),
% 1.59/1.33 inference(superposition,[status(thm)],[f80,f82])).
% 1.59/1.33 thf(f82,plain,(
% 1.59/1.33 ((kpair @ (sK0 @ sK9 @ sK12 @ sK10) @ (sK1 @ sK9 @ sK12 @ sK10)) = sK12)),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.59/1.33 thf(f81,plain,(
% 1.59/1.33 ($true != $true) | ((kpair @ (sK0 @ sK9 @ sK12 @ sK10) @ (sK1 @ sK9 @ sK12 @ sK10)) = sK12)),
% 1.59/1.33 inference(superposition,[status(thm)],[f63,f68])).
% 1.59/1.33 thf(f63,plain,(
% 1.59/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (cartprod @ X0 @ X2))) | ((kpair @ (sK0 @ X2 @ X1 @ X0) @ (sK1 @ X2 @ X1 @ X0)) = X1)) )),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.59/1.33 thf(f52,plain,(
% 1.59/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((kpair @ (sK0 @ X2 @ X1 @ X0) @ (sK1 @ X2 @ X1 @ X0)) = X1) | ($true != (in @ X1 @ (cartprod @ X0 @ X2))) | ($true != $true)) )),
% 1.59/1.33 inference(definition_unfolding,[status(thm)],[f36,f48])).
% 1.59/1.33 thf(f36,plain,(
% 1.59/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((kpair @ (sK0 @ X2 @ X1 @ X0) @ (sK1 @ X2 @ X1 @ X0)) = X1) | ($true != (in @ X1 @ (cartprod @ X0 @ X2))) | (cartprodmempair1 != $true)) )),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f25])).
% 1.59/1.33 thf(f80,plain,(
% 1.59/1.33 ( ! [X0 : $i] : (((in @ (kpair @ X0 @ (sK1 @ sK9 @ sK12 @ sK10)) @ sK8) != $true) | ($true = (sK11 @ (kpair @ X0 @ (sK1 @ sK9 @ sK12 @ sK10)))) | ($true != (in @ X0 @ sK10))) )),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.59/1.33 thf(f79,plain,(
% 1.59/1.33 ( ! [X0 : $i] : (($true = (sK11 @ (kpair @ X0 @ (sK1 @ sK9 @ sK12 @ sK10)))) | ($true != $true) | ($true != (in @ X0 @ sK10)) | ((in @ (kpair @ X0 @ (sK1 @ sK9 @ sK12 @ sK10)) @ sK8) != $true)) )),
% 1.59/1.33 inference(superposition,[status(thm)],[f47,f72])).
% 1.59/1.33 thf(f72,plain,(
% 1.59/1.33 ($true = (in @ (sK1 @ sK9 @ sK12 @ sK10) @ sK9))),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.59/1.33 thf(f71,plain,(
% 1.59/1.33 ($true = (in @ (sK1 @ sK9 @ sK12 @ sK10) @ sK9)) | ($true != $true)),
% 1.59/1.33 inference(superposition,[status(thm)],[f60,f68])).
% 1.59/1.33 thf(f60,plain,(
% 1.59/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (cartprod @ X0 @ X2))) | ($true = (in @ (sK1 @ X2 @ X1 @ X0) @ X2))) )),
% 1.59/1.33 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.59/1.33 thf(f51,plain,(
% 1.59/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (cartprod @ X0 @ X2))) | ($true = (in @ (sK1 @ X2 @ X1 @ X0) @ X2)) | ($true != $true)) )),
% 1.59/1.33 inference(definition_unfolding,[status(thm)],[f37,f48])).
% 1.59/1.33 thf(f37,plain,(
% 1.59/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK1 @ X2 @ X1 @ X0) @ X2)) | ($true != (in @ X1 @ (cartprod @ X0 @ X2))) | (cartprodmempair1 != $true)) )),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f25])).
% 1.59/1.33 thf(f47,plain,(
% 1.59/1.33 ( ! [X4 : $i,X5 : $i] : (($true != (in @ X5 @ sK9)) | ($true = (sK11 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ sK8)) | ($true != (in @ X4 @ sK10))) )),
% 1.59/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.59/1.33 % SZS output end Proof for DTF2THF_20346
% 1.59/1.33 % (20450)------------------------------
% 1.59/1.33 % (20450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (20450)Termination reason: Refutation
% 1.59/1.33
% 1.59/1.33 % (20450)Memory used [KB]: 5628
% 1.59/1.33 % (20450)Time elapsed: 0.010 s
% 1.59/1.33 % (20450)Instructions burned: 9 (million)
% 1.59/1.33 % (20450)------------------------------
% 1.59/1.33 % (20450)------------------------------
% 1.59/1.33 % (20443)Success in time 0.015 s
%------------------------------------------------------------------------------