%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU668^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 09:36:04 AM UTC 2026
% Result : Theorem 1.38s 1.14s
% Output : Refutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 664 ( 213 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 878 ( 66 ~; 49 |; 92 &; 610 @)
% ( 6 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 27 usr; 22 con; 0-3 aty)
% ( 0 !!; 17 ??; 0 @@+; 0 @@-)
% Number of variables : 274 ( 83 ^; 137 !; 54 ?; 274 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
cartprod: $i > $i > $i ).
thf(func_def_8,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_21,type,
sK1: $i > $i > $o ).
thf(func_def_26,type,
sK6: $i > $o ).
thf(func_def_38,type,
ph17:
!>[X0: $tType] : X0 ).
thf(f105,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f102,f40]) ).
thf(f40,plain,
( $true
!= ( sK1 @ sK3 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( setukpairinjL = $true )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ ( kpair @ sK3 @ sK4 )
@ ( dpsetconstr @ sK0 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( in @ sK4 @ sK2 ) )
& ( $true
!= ( sK1 @ sK3 @ sK4 ) )
& ( setukpairinjR = $true )
& ( dsetconstrER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f24,f23]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ? [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( in @ X4 @ X2 ) )
& ( ( X1 @ X3 @ X4 )
!= $true ) ) )
=> ( ( $true
= ( in @ sK3 @ sK0 ) )
& ? [X4: $i] :
( ( ( in @ ( kpair @ sK3 @ X4 )
@ ( dpsetconstr @ sK0 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) )
= $true )
& ( ( in @ X4 @ sK2 )
= $true )
& ( ( sK1 @ sK3 @ X4 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X4: $i] :
( ( ( in @ ( kpair @ sK3 @ X4 )
@ ( dpsetconstr @ sK0 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) )
= $true )
& ( ( in @ X4 @ sK2 )
= $true )
& ( ( sK1 @ sK3 @ X4 )
!= $true ) )
=> ( ( $true
= ( in @ ( kpair @ sK3 @ sK4 )
@ ( dpsetconstr @ sK0 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( in @ sK4 @ sK2 ) )
& ( $true
!= ( sK1 @ sK3 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( setukpairinjL = $true )
& ? [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ? [X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( in @ X4 @ X2 ) )
& ( ( X1 @ X3 @ X4 )
!= $true ) ) )
& ( setukpairinjR = $true )
& ( dsetconstrER = $true ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ? [X4: $i] :
( ( ( X1 @ X3 @ X4 )
!= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( in @ X4 @ X2 ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( setukpairinjR = $true )
& ( setukpairinjL = $true )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( ( dsetconstrER = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR = $true )
=> ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
=> ( ( X1 @ X3 @ X4 )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X2
@ ^ [X5: $i,X6: $i] : ( X1 @ X5 @ X6 ) ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [X0: $i,X1: $i > $i > $o,X6: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X6 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X0 @ X6
@ ^ [X4: $i,X5: $i] : ( X1 @ X4 @ X5 ) ) )
=> ( X1 @ X2 @ X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [X0: $i,X1: $i > $i > $o,X6: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X6 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X0 @ X6
@ ^ [X4: $i,X5: $i] : ( X1 @ X4 @ X5 ) ) )
=> ( X1 @ X2 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zSheG09iwz/DTF2THF_11678.p',dpsetconstrERa) ).
thf(f102,plain,
( $true
= ( sK1 @ sK3 @ sK4 ) ),
inference(backward_demodulation,[status(thm)],[f93,f101]) ).
thf(f101,plain,
sK19 = sK4,
inference(equality_resolution,[status(thm)],[f89]) ).
thf(f89,plain,
! [X0: $i,X1: $i] :
( ( ( kpair @ sK3 @ sK4 )
!= ( kpair @ X0 @ X1 ) )
| ( sK19 = X1 ) ),
inference(superposition,[status(thm)],[f65,f85]) ).
thf(f85,plain,
( ( kpair @ sK18 @ sK19 )
= ( kpair @ sK3 @ sK4 ) ),
inference(equality_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ( ( kpair @ sK18 @ sK19 )
= ( kpair @ sK3 @ sK4 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( sK1 @ sK18 @ sK19 )
& ( in @ sK19 @ sK2 )
& ( ( kpair @ sK18 @ sK19 )
= ( kpair @ sK3 @ sK4 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ^ [Y0: $i] :
( ( sK1 @ sK18 @ Y0 )
& ( in @ Y0 @ sK2 )
& ( ( kpair @ sK18 @ Y0 )
= ( kpair @ sK3 @ sK4 ) ) )
@ sK19 )
= $true ),
inference(sigma_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK18 @ Y0 )
& ( in @ Y0 @ sK2 )
& ( ( kpair @ sK18 @ Y0 )
= ( kpair @ sK3 @ sK4 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK18 @ Y0 )
& ( in @ Y0 @ sK2 )
& ( ( kpair @ sK18 @ Y0 )
= ( kpair @ sK3 @ sK4 ) ) ) )
& ( in @ sK18 @ sK0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y0 @ Y1 )
& ( in @ Y1 @ sK2 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK3 @ sK4 ) ) ) )
& ( in @ Y0 @ sK0 ) )
@ sK18 )
= $true ),
inference(sigma_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y0 @ Y1 )
& ( in @ Y1 @ sK2 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK3 @ sK4 ) ) ) )
& ( in @ Y0 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
& ( in @ Y2 @ sK2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK0 ) ) )
@ ( kpair @ sK3 @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
& ( in @ Y2 @ sK2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK0 ) ) )
@ ( kpair @ sK3 @ sK4 ) ) ) ),
inference(superposition,[status(thm)],[f68,f69]) ).
thf(f69,plain,
( ( in @ ( kpair @ sK3 @ sK4 )
@ ( dsetconstr @ ( cartprod @ sK0 @ sK2 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
& ( in @ Y2 @ sK2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ( in @ ( kpair @ sK3 @ sK4 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) )
@ sK0
@ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f42,f51]) ).
thf(f51,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ( in @ X4 @ X0 )
& ? [X5: $i] :
( ( ( kpair @ X4 @ X5 )
= X3 )
& ( in @ X5 @ X1 )
& ( X2 @ X4 @ X5 ) ) ) ) )
= dpsetconstr ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i,X6: $i,X1: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X6 )
@ ^ [X5: $i] :
? [X2: $i] :
( ( in @ X2 @ X0 )
& ? [X3: $i] :
( ( ( kpair @ X2 @ X3 )
= X5 )
& ( in @ X3 @ X6 )
& ( X1 @ X2 @ X3 ) ) ) ) )
= dpsetconstr ),
file('/export/starexec/sandbox2/tmp/tmp.zSheG09iwz/DTF2THF_11678.p',dpsetconstr) ).
thf(f42,plain,
( $true
= ( in @ ( kpair @ sK3 @ sK4 )
@ ( dpsetconstr @ sK0 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f68,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X5 @ ( dsetconstr @ X3 @ X4 ) )
!= $true )
| ( $true
= ( X4 @ X5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( X4 @ X5 ) )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) )
| ( $true
= ( X4 @ X5 ) ) ),
inference(definition_unfolding,[status(thm)],[f45,f38]) ).
thf(f38,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f45,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( X4 @ X5 ) )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( dsetconstrER = $true )
| ( ( ( sK6 @ sK7 )
!= $true )
& ( ( in @ sK7
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( sK6 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( X4 @ X5 ) )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f27,f28]) ).
thf(f28,plain,
( ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) )
=> ( ( ( sK6 @ sK7 )
!= $true )
& ( ( in @ sK7
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( sK6 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( X4 @ X5 ) )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
=> ( ( X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/tmp/tmp.zSheG09iwz/DTF2THF_11678.p',dsetconstrER) ).
thf(f65,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( kpair @ X7 @ X5 )
!= ( kpair @ X6 @ X4 ) )
| ( X4 = X5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( kpair @ X7 @ X5 )
!= ( kpair @ X6 @ X4 ) )
| ( X4 = X5 ) ),
inference(definition_unfolding,[status(thm)],[f48,f39]) ).
thf(f39,plain,
setukpairinjR = $true,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f48,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ( ( kpair @ X7 @ X5 )
!= ( kpair @ X6 @ X4 ) )
| ( setukpairinjR != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( setukpairinjR = $true )
| ( ( sK8 != sK9 )
& ( ( kpair @ sK10 @ sK8 )
= ( kpair @ sK11 @ sK9 ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( X4 = X5 )
| ( ( kpair @ X7 @ X5 )
!= ( kpair @ X6 @ X4 ) ) )
| ( setukpairinjR != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f31,f32]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X1 )
& ( ( kpair @ X3 @ X1 )
= ( kpair @ X2 @ X0 ) ) )
=> ( ( sK8 != sK9 )
& ( ( kpair @ sK10 @ sK8 )
= ( kpair @ sK11 @ sK9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ( setukpairinjR = $true )
| ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X1 )
& ( ( kpair @ X3 @ X1 )
= ( kpair @ X2 @ X0 ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( X4 = X5 )
| ( ( kpair @ X7 @ X5 )
!= ( kpair @ X6 @ X4 ) ) )
| ( setukpairinjR != $true ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( setukpairinjR = $true )
| ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X1 )
& ( ( kpair @ X3 @ X1 )
= ( kpair @ X2 @ X0 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ( ( kpair @ X3 @ X1 )
!= ( kpair @ X2 @ X0 ) ) )
| ( setukpairinjR != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( setukpairinjR = $true )
<=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ( ( kpair @ X3 @ X1 )
!= ( kpair @ X2 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( setukpairinjR = $true )
<=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X1 )
= ( kpair @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( setukpairinjR
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X1 )
= ( kpair @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( setukpairinjR
= ( ! [X5: $i,X3: $i,X4: $i,X2: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X4 @ X5 ) )
=> ( X3 = X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zSheG09iwz/DTF2THF_11678.p',setukpairinjR) ).
thf(f93,plain,
( $true
= ( sK1 @ sK3 @ sK19 ) ),
inference(backward_demodulation,[status(thm)],[f84,f91]) ).
thf(f91,plain,
sK3 = sK18,
inference(equality_resolution,[status(thm)],[f87]) ).
thf(f87,plain,
! [X0: $i,X1: $i] :
( ( ( kpair @ sK3 @ sK4 )
!= ( kpair @ X0 @ X1 ) )
| ( sK18 = X0 ) ),
inference(superposition,[status(thm)],[f66,f85]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X1 @ X2 ) )
| ( X1 = X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X1 @ X2 ) )
| ( X1 = X3 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f54,f44]) ).
thf(f44,plain,
setukpairinjL = $true,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X1 @ X2 ) )
| ( X1 = X3 )
| ( setukpairinjL != $true ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X1 @ X2 ) )
| ( X1 = X3 ) )
| ( setukpairinjL != $true ) )
& ( ( setukpairinjL = $true )
| ( ( ( kpair @ sK13 @ sK14 )
= ( kpair @ sK15 @ sK12 ) )
& ( sK15 != sK13 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f35,f36]) ).
thf(f36,plain,
( ? [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( kpair @ X7 @ X4 )
= ( kpair @ X5 @ X6 ) )
& ( X5 != X7 ) )
=> ( ( ( kpair @ sK13 @ sK14 )
= ( kpair @ sK15 @ sK12 ) )
& ( sK15 != sK13 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X1 @ X2 ) )
| ( X1 = X3 ) )
| ( setukpairinjL != $true ) )
& ( ( setukpairinjL = $true )
| ? [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( kpair @ X7 @ X4 )
= ( kpair @ X5 @ X6 ) )
& ( X5 != X7 ) ) ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X1 @ X2 ) )
| ( X1 = X3 ) )
| ( setukpairinjL != $true ) )
& ( ( setukpairinjL = $true )
| ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
= ( kpair @ X1 @ X2 ) )
& ( X1 != X3 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X1 @ X2 ) )
| ( X1 = X3 ) )
<=> ( setukpairinjL = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
= ( kpair @ X1 @ X2 ) )
=> ( X1 = X3 ) )
<=> ( setukpairinjL = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( ( kpair @ X3 @ X0 )
= ( kpair @ X1 @ X2 ) )
=> ( X1 = X3 ) )
= setukpairinjL ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X5: $i,X2: $i,X3: $i,X4: $i] :
( ( ( ( kpair @ X2 @ X3 )
= ( kpair @ X4 @ X5 ) )
=> ( X2 = X4 ) )
= setukpairinjL ),
file('/export/starexec/sandbox2/tmp/tmp.zSheG09iwz/DTF2THF_11678.p',setukpairinjL) ).
thf(f84,plain,
( $true
= ( sK1 @ sK18 @ sK19 ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ( sK1 @ sK18 @ sK19 )
& ( in @ sK19 @ sK2 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU668^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:30:11 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.41 ---- Original DTF file ---
% 0.16/0.41 thf(spec,logic,$$dhol).
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 % File : SEU668^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.41 % Domain : Set Theory
% 0.16/0.41 % Problem : Ordered Pairs - Sets of Pairs
% 0.16/0.41 % Version : Especial > Reduced > Especial.
% 0.16/0.41 % English : (! A:i.! B:i.! phi:i>(i>o).! x:i.in x A -> (! y:i.in y B ->
% 0.16/0.41 % in (kpair x y) (dpsetconstr A B (^ z,u:i.phi z u)) -> phi x y))
% 0.16/0.41
% 0.16/0.41 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.41 % Source : [Bro08]
% 0.16/0.41 % Names : ZFC170l [Bro08]
% 0.16/0.41
% 0.16/0.41 % Status : Theorem
% 0.16/0.41 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 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, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0, 0.67 v3.7.0
% 0.16/0.41 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.16/0.41 % Number of atoms : 21 ( 9 equ; 0 cnn)
% 0.16/0.41 % Maximal formula atoms : 6 ( 4 avg)
% 0.16/0.41 % Number of connectives : 53 ( 0 ~; 0 |; 3 &; 41 @)
% 0.16/0.41 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.16/0.41 % Maximal formula depth : 18 ( 4 avg)
% 0.16/0.41 % Number of types : 2 ( 0 usr)
% 0.16/0.41 % Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% 0.16/0.41 % Number of symbols : 9 ( 8 usr; 3 con; 0-3 aty)
% 0.16/0.41 % Number of variables : 25 ( 7 ^; 16 !; 2 ?; 25 :)
% 0.16/0.41 % SPC : TH0_THM_EQU_NAR
% 0.16/0.41
% 0.16/0.41 % Comments : http://mathgate.info/detsetitem.php?id=234
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 thf(in_type,type,
% 0.16/0.41 in: $i > $i > $o ).
% 0.16/0.41
% 0.16/0.41 thf(dsetconstr_type,type,
% 0.16/0.41 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.41
% 0.16/0.41 thf(dsetconstrER_type,type,
% 0.16/0.41 dsetconstrER: $o ).
% 0.16/0.41
% 0.16/0.41 thf(dsetconstrER,definition,
% 0.16/0.41 ( dsetconstrER
% 0.16/0.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.41 ( ( in @ Xx
% 0.16/0.41 @ ( dsetconstr @ A
% 0.16/0.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.41 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 thf(kpair_type,type,
% 0.16/0.41 kpair: $i > $i > $i ).
% 0.16/0.41
% 0.16/0.41 thf(cartprod_type,type,
% 0.16/0.41 cartprod: $i > $i > $i ).
% 0.16/0.41
% 0.16/0.41 thf(setukpairinjL_type,type,
% 0.16/0.41 setukpairinjL: $o ).
% 0.16/0.41
% 0.16/0.41 thf(setukpairinjL,definition,
% 0.16/0.41 ( setukpairinjL
% 0.16/0.41 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.41 ( ( ( kpair @ Xx @ Xy )
% 0.16/0.41 = ( kpair @ Xz @ Xu ) )
% 0.16/0.41 => ( Xx = Xz ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 thf(setukpairinjR_type,type,
% 0.16/0.41 setukpairinjR: $o ).
% 0.16/0.41
% 0.16/0.41 thf(setukpairinjR,definition,
% 0.16/0.41 ( setukpairinjR
% 0.16/0.41 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.41 ( ( ( kpair @ Xx @ Xy )
% 0.16/0.41 = ( kpair @ Xz @ Xu ) )
% 0.16/0.41 => ( Xy = Xu ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 thf(dpsetconstr_type,type,
% 0.16/0.41 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.16/0.41
% 0.16/0.41 thf(dpsetconstr,definition,
% 0.16/0.41 ( dpsetconstr
% 0.16/0.41 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.16/0.41 ( dsetconstr @ ( cartprod @ A @ B )
% 0.16/0.41 @ ^ [Xu: $i] :
% 0.16/0.41 ? [Xx: $i] :
% 0.16/0.41 ( ( in @ Xx @ A )
% 0.16/0.41 & ? [Xy: $i] :
% 0.16/0.41 ( ( in @ Xy @ B )
% 0.16/0.41 & ( Xphi @ Xx @ Xy )
% 0.16/0.41 & ( Xu
% 0.16/0.41 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 thf(dpsetconstrERa,conjecture,
% 0.16/0.41 ( dsetconstrER
% 0.16/0.41 => ( setukpairinjL
% 0.16/0.41 => ( setukpairinjR
% 0.16/0.41 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.16/0.41 ( ( in @ Xx @ A )
% 0.16/0.41 => ! [Xy: $i] :
% 0.16/0.41 ( ( in @ Xy @ B )
% 0.16/0.41 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.16/0.41 @ ( dpsetconstr @ A @ B
% 0.16/0.41 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.16/0.41 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 ------------------------
% 1.16/1.11 ---- Embedded in THF ---
% 1.16/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.16/1.11 %%% Generated on Tue Feb 24 12:30:12 EST 2026
% 1.16/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 1.16/1.11 %%% Logic specification used:
% 1.16/1.11 %%% thf(spec, logic, $$dhol).
% 1.16/1.11
% 1.16/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.zSheG09iwz/DTF2DTF11678.p
% See solution above
% 1.16/1.11 ------------------------
% 1.16/1.12 ---- Cleaned THF ---
% 1.16/1.12 thf(in_type,type,
% 1.16/1.12 in: $i > $i > $o ).
% 1.16/1.12
% 1.16/1.12 thf(dsetconstr_type,type,
% 1.16/1.12 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.16/1.12
% 1.16/1.12 thf(dsetconstrER_type,type,
% 1.16/1.12 dsetconstrER: $o ).
% 1.16/1.12
% 1.16/1.12 thf(dsetconstrER,definition,
% 1.16/1.12 ( dsetconstrER
% 1.16/1.12 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.16/1.12 ( ( in @ Xx
% 1.16/1.12 @ ( dsetconstr @ A
% 1.16/1.12 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.16/1.12 => ( Xphi @ Xx ) ) ) ) ).
% 1.16/1.12
% 1.16/1.12 thf(kpair_type,type,
% 1.16/1.12 kpair: $i > $i > $i ).
% 1.16/1.12
% 1.16/1.12 thf(cartprod_type,type,
% 1.16/1.12 cartprod: $i > $i > $i ).
% 1.16/1.12
% 1.16/1.12 thf(setukpairinjL_type,type,
% 1.16/1.12 setukpairinjL: $o ).
% 1.16/1.12
% 1.16/1.12 thf(setukpairinjL,definition,
% 1.16/1.12 ( setukpairinjL
% 1.16/1.12 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 1.16/1.12 ( ( ( kpair @ Xx @ Xy )
% 1.16/1.12 = ( kpair @ Xz @ Xu ) )
% 1.16/1.12 => ( Xx = Xz ) ) ) ) ).
% 1.16/1.12
% 1.16/1.12 thf(setukpairinjR_type,type,
% 1.16/1.12 setukpairinjR: $o ).
% 1.16/1.12
% 1.16/1.12 thf(setukpairinjR,definition,
% 1.16/1.12 ( setukpairinjR
% 1.16/1.12 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 1.16/1.12 ( ( ( kpair @ Xx @ Xy )
% 1.16/1.12 = ( kpair @ Xz @ Xu ) )
% 1.16/1.12 => ( Xy = Xu ) ) ) ) ).
% 1.16/1.12
% 1.16/1.12 thf(dpsetconstr_type,type,
% 1.16/1.12 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.16/1.12
% 1.16/1.12 thf(dpsetconstr,definition,
% 1.16/1.12 ( dpsetconstr
% 1.16/1.12 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 1.16/1.12 ( dsetconstr @ ( cartprod @ A @ B )
% 1.16/1.12 @ ^ [Xu: $i] :
% 1.16/1.12 ? [Xx: $i] :
% 1.16/1.12 ( ( in @ Xx @ A )
% 1.16/1.12 & ? [Xy: $i] :
% 1.16/1.12 ( ( in @ Xy @ B )
% 1.16/1.12 & ( Xphi @ Xx @ Xy )
% 1.16/1.12 & ( Xu
% 1.16/1.12 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 1.16/1.12
% 1.16/1.12 thf(dpsetconstrERa,conjecture,
% 1.16/1.12 ( dsetconstrER
% 1.16/1.12 => ( setukpairinjL
% 1.16/1.12 => ( setukpairinjR
% 1.16/1.12 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 1.16/1.12 ( ( in @ Xx @ A )
% 1.16/1.12 => ! [Xy: $i] :
% 1.16/1.12 ( ( in @ Xy @ B )
% 1.16/1.12 => ( ( in @ ( kpair @ Xx @ Xy )
% 1.16/1.12 @ ( dpsetconstr @ A @ B
% 1.16/1.12 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 1.16/1.12 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ) ).
% 1.16/1.12 ------------------------
% 1.38/1.13 % (11787)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_11678 for (3000ds/2Mi)
% 1.38/1.13 % (11788)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_11678 for (3000ds/275Mi)
% 1.38/1.13 % (11789)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11678 for (3000ds/18Mi)
% 1.38/1.13 % (11785)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_11678 for (3000ds/27Mi)
% 1.38/1.13 % (11783)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11678 for (3000ds/183Mi)
% 1.38/1.13 % (11784)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_11678 for (3000ds/4Mi)
% 1.38/1.13 % (11786)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11678 for (3000ds/2Mi)
% 1.38/1.13 % (11784)Instruction limit reached!
% 1.38/1.13 % (11784)------------------------------
% 1.38/1.13 % (11784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.13 % (11784)Termination reason: Unknown
% 1.38/1.13 % (11784)Termination phase: Function definition elimination
% 1.38/1.13
% 1.38/1.13 % (11784)Memory used [KB]: 1023
% 1.38/1.13 % (11784)Time elapsed: 0.002 s
% 1.38/1.13 % (11784)Instructions burned: 4 (million)
% 1.38/1.13 % (11784)------------------------------
% 1.38/1.13 % (11784)------------------------------
% 1.38/1.13 % (11786)Instruction limit reached!
% 1.38/1.13 % (11786)------------------------------
% 1.38/1.13 % (11786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.13 % (11786)Termination reason: Unknown
% 1.38/1.13 % (11786)Termination phase: Property scanning
% 1.38/1.13
% 1.38/1.13 % (11786)Memory used [KB]: 1023
% 1.38/1.13 % (11786)Time elapsed: 0.002 s
% 1.38/1.13 % (11786)Instructions burned: 4 (million)
% 1.38/1.13 % (11786)------------------------------
% 1.38/1.13 % (11786)------------------------------
% 1.38/1.13 % (11787)Instruction limit reached!
% 1.38/1.13 % (11787)------------------------------
% 1.38/1.13 % (11787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.13 % (11787)Termination reason: Unknown
% 1.38/1.13 % (11787)Termination phase: Saturation
% 1.38/1.13
% 1.38/1.13 % (11787)Memory used [KB]: 1023
% 1.38/1.13 % (11787)Time elapsed: 0.003 s
% 1.38/1.13 % (11787)Instructions burned: 4 (million)
% 1.38/1.13 % (11787)------------------------------
% 1.38/1.13 % (11787)------------------------------
% 1.38/1.13 % (11788)Refutation not found, incomplete strategy
% 1.38/1.13 % (11788)------------------------------
% 1.38/1.13 % (11788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.13 % (11788)Termination reason: Refutation not found, incomplete strategy
% 1.38/1.13
% 1.38/1.13
% 1.38/1.13 % (11788)Memory used [KB]: 5500
% 1.38/1.13 % (11788)Time elapsed: 0.003 s
% 1.38/1.13 % (11788)Instructions burned: 4 (million)
% 1.38/1.13 % (11788)------------------------------
% 1.38/1.13 % (11788)------------------------------
% 1.38/1.13 % (11789)First to succeed.
% 1.38/1.13 % (11783)Also succeeded, but the first one will report.
% 1.38/1.14 % (11789)Refutation found. Thanks to Tanya!
% 1.38/1.14 % SZS status Theorem for DTF2THF_11678
% 1.38/1.14 % SZS output start Proof for DTF2THF_11678
% 1.38/1.14 thf(func_def_0, type, in: $i > $i > $o).
% 1.38/1.14 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.38/1.14 thf(func_def_4, type, kpair: $i > $i > $i).
% 1.38/1.14 thf(func_def_5, type, cartprod: $i > $i > $i).
% 1.38/1.14 thf(func_def_8, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.38/1.14 thf(func_def_21, type, sK1: $i > $i > $o).
% 1.38/1.14 thf(func_def_26, type, sK6: $i > $o).
% 1.38/1.14 thf(func_def_38, type, ph17: !>[X0: $tType]:(X0)).
% 1.38/1.14 thf(f105,plain,(
% 1.38/1.14 $false),
% 1.38/1.14 inference(subsumption_resolution,[status(thm)],[f102,f40])).
% 1.38/1.14 thf(f40,plain,(
% 1.38/1.14 ($true != (sK1 @ sK3 @ sK4))),
% 1.38/1.14 inference(cnf_transformation,[status(thm)],[f25])).
% 1.38/1.14 thf(f25,plain,(
% 1.38/1.14 (setukpairinjL = $true) & (($true = (in @ sK3 @ sK0)) & (($true = (in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1))))))) & ($true = (in @ sK4 @ sK2)) & ($true != (sK1 @ sK3 @ sK4)))) & (setukpairinjR = $true) & (dsetconstrER = $true)),
% 1.38/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f24,f23])).
% 1.38/1.14 thf(f23,plain,(
% 1.38/1.14 ? [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : (((in @ X3 @ X0) = $true) & ? [X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))) & ($true = (in @ X4 @ X2)) & ((X1 @ X3 @ X4) != $true))) => (($true = (in @ sK3 @ sK0)) & ? [X4 : $i] : (((in @ (kpair @ sK3 @ X4) @ (dpsetconstr @ sK0 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))) = $true) & ((in @ X4 @ sK2) = $true) & ((sK1 @ sK3 @ X4) != $true)))),
% 1.38/1.14 introduced(definition,[],[choice_axiom])).
% 1.38/1.14 thf(f24,plain,(
% 1.38/1.14 ? [X4 : $i] : (((in @ (kpair @ sK3 @ X4) @ (dpsetconstr @ sK0 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))) = $true) & ((in @ X4 @ sK2) = $true) & ((sK1 @ sK3 @ X4) != $true)) => (($true = (in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1))))))) & ($true = (in @ sK4 @ sK2)) & ($true != (sK1 @ sK3 @ sK4)))),
% 1.38/1.14 introduced(definition,[],[choice_axiom])).
% 1.38/1.14 thf(f21,plain,(
% 1.38/1.14 (setukpairinjL = $true) & ? [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : (((in @ X3 @ X0) = $true) & ? [X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))) & ($true = (in @ X4 @ X2)) & ((X1 @ X3 @ X4) != $true))) & (setukpairinjR = $true) & (dsetconstrER = $true)),
% 1.38/1.14 inference(flattening,[status(thm)],[f20])).
% 1.38/1.14 thf(f20,plain,(
% 1.38/1.14 ((? [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : (? [X4 : $i] : ((((X1 @ X3 @ X4) != $true) & ($true = (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))))) & ($true = (in @ X4 @ X2))) & ((in @ X3 @ X0) = $true)) & (setukpairinjR = $true)) & (setukpairinjL = $true)) & (dsetconstrER = $true)),
% 1.38/1.14 inference(ennf_transformation,[status(thm)],[f17])).
% 1.38/1.14 thf(f17,plain,(
% 1.38/1.14 ~((dsetconstrER = $true) => ((setukpairinjL = $true) => ((setukpairinjR = $true) => ! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : (((in @ X3 @ X0) = $true) => ! [X4 : $i] : (($true = (in @ X4 @ X2)) => (($true = (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))) => ((X1 @ X3 @ X4) = $true)))))))),
% 1.38/1.14 inference(fool_elimination,[status(thm)],[f16])).
% 1.38/1.14 thf(f16,plain,(
% 1.38/1.14 ~(dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X2) => ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X2 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6)))) => (X1 @ X3 @ X4)))))))),
% 1.38/1.14 inference(rectify,[status(thm)],[f6])).
% 1.38/1.14 thf(f6,negated_conjecture,(
% 1.38/1.14 ~(dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X0 : $i,X1 : $i > $i > $o,X6 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X6) => ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X6 @ (^[X4 : $i, X5 : $i] : (X1 @ X4 @ X5)))) => (X1 @ X2 @ X3)))))))),
% 1.38/1.14 inference(negated_conjecture,[status(cth)],[f5])).
% 1.38/1.14 thf(f5,conjecture,(
% 1.38/1.14 dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X0 : $i,X1 : $i > $i > $o,X6 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X6) => ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X6 @ (^[X4 : $i, X5 : $i] : (X1 @ X4 @ X5)))) => (X1 @ X2 @ X3))))))),
% 1.38/1.14 file('/export/starexec/sandbox2/tmp/tmp.zSheG09iwz/DTF2THF_11678.p',dpsetconstrERa)).
% 1.38/1.14 thf(f102,plain,(
% 1.38/1.14 ($true = (sK1 @ sK3 @ sK4))),
% 1.38/1.14 inference(backward_demodulation,[status(thm)],[f93,f101])).
% 1.38/1.14 thf(f101,plain,(
% 1.38/1.14 (sK19 = sK4)),
% 1.38/1.14 inference(equality_resolution,[status(thm)],[f89])).
% 1.38/1.14 thf(f89,plain,(
% 1.38/1.14 ( ! [X0 : $i,X1 : $i] : (((kpair @ sK3 @ sK4) != (kpair @ X0 @ X1)) | (sK19 = X1)) )),
% 1.38/1.14 inference(superposition,[status(thm)],[f65,f85])).
% 1.38/1.14 thf(f85,plain,(
% 1.38/1.14 ((kpair @ sK18 @ sK19) = (kpair @ sK3 @ sK4))),
% 1.38/1.14 inference(equality_proxy_clausification,[status(thm)],[f81])).
% 1.38/1.14 thf(f81,plain,(
% 1.38/1.14 (((kpair @ sK18 @ sK19) = (kpair @ sK3 @ sK4)) = $true)),
% 1.38/1.14 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.38/1.14 thf(f80,plain,(
% 1.38/1.14 ((((sK1 @ sK18 @ sK19) & (in @ sK19 @ sK2)) & ((kpair @ sK18 @ sK19) = (kpair @ sK3 @ sK4))) = $true)),
% 1.38/1.14 inference(beta_eta_normalization,[status(thm)],[f79])).
% 1.38/1.14 thf(f79,plain,(
% 1.38/1.14 (((^[Y0 : $i]: (((sK1 @ sK18 @ Y0) & (in @ Y0 @ sK2)) & ((kpair @ sK18 @ Y0) = (kpair @ sK3 @ sK4)))) @ sK19) = $true)),
% 1.38/1.14 inference(sigma_clausification,[status(thm)],[f78])).
% 1.38/1.14 thf(f78,plain,(
% 1.38/1.14 ((?? @ $i @ (^[Y0 : $i]: (((sK1 @ sK18 @ Y0) & (in @ Y0 @ sK2)) & ((kpair @ sK18 @ Y0) = (kpair @ sK3 @ sK4))))) = $true)),
% 1.38/1.14 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.38/1.14 thf(f76,plain,(
% 1.38/1.14 (((?? @ $i @ (^[Y0 : $i]: (((sK1 @ sK18 @ Y0) & (in @ Y0 @ sK2)) & ((kpair @ sK18 @ Y0) = (kpair @ sK3 @ sK4))))) & (in @ sK18 @ sK0)) = $true)),
% 1.38/1.14 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.38/1.14 thf(f75,plain,(
% 1.38/1.14 (((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((sK1 @ Y0 @ Y1) & (in @ Y1 @ sK2)) & ((kpair @ Y0 @ Y1) = (kpair @ sK3 @ sK4))))) & (in @ Y0 @ sK0))) @ sK18) = $true)),
% 1.38/1.14 inference(sigma_clausification,[status(thm)],[f74])).
% 1.38/1.14 thf(f74,plain,(
% 1.38/1.14 ((?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((sK1 @ Y0 @ Y1) & (in @ Y1 @ sK2)) & ((kpair @ Y0 @ Y1) = (kpair @ sK3 @ sK4))))) & (in @ Y0 @ sK0)))) = $true)),
% 1.38/1.14 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.38/1.14 thf(f73,plain,(
% 1.38/1.14 ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((sK1 @ Y1 @ Y2) & (in @ Y2 @ sK2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK0))))) @ (kpair @ sK3 @ sK4)))),
% 1.38/1.14 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.38/1.14 thf(f72,plain,(
% 1.38/1.14 ($true != $true) | ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((sK1 @ Y1 @ Y2) & (in @ Y2 @ sK2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK0))))) @ (kpair @ sK3 @ sK4)))),
% 1.38/1.14 inference(superposition,[status(thm)],[f68,f69])).
% 1.38/1.14 thf(f69,plain,(
% 1.38/1.14 ((in @ (kpair @ sK3 @ sK4) @ (dsetconstr @ (cartprod @ sK0 @ sK2) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((sK1 @ Y1 @ Y2) & (in @ Y2 @ sK2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK0))))))) = $true)),
% 1.38/1.14 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.38/1.14 thf(f55,plain,(
% 1.38/1.14 ((in @ (kpair @ sK3 @ sK4) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))) @ sK0 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))) = $true)),
% 1.38/1.14 inference(definition_unfolding,[status(thm)],[f42,f51])).
% 1.38/1.14 thf(f51,plain,(
% 1.38/1.14 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))))),
% 1.38/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.38/1.14 thf(f15,plain,(
% 1.38/1.14 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))))),
% 1.38/1.14 inference(fool_elimination,[status(thm)],[f14])).
% 1.38/1.14 thf(f14,plain,(
% 1.38/1.14 ((^[X0 : $i, X1 : $i, X2 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : ((in @ X4 @ X0) & ? [X5 : $i] : (((kpair @ X4 @ X5) = X3) & (in @ X5 @ X1) & (X2 @ X4 @ X5))))))) = dpsetconstr)),
% 1.38/1.14 inference(rectify,[status(thm)],[f4])).
% 1.38/1.14 thf(f4,axiom,(
% 1.38/1.14 ((^[X0 : $i, X6 : $i, X1 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X6) @ (^[X5 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & ? [X3 : $i] : (((kpair @ X2 @ X3) = X5) & (in @ X3 @ X6) & (X1 @ X2 @ X3))))))) = dpsetconstr)),
% 1.38/1.14 file('/export/starexec/sandbox2/tmp/tmp.zSheG09iwz/DTF2THF_11678.p',dpsetconstr)).
% 1.38/1.14 thf(f42,plain,(
% 1.38/1.14 ($true = (in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))))),
% 1.38/1.14 inference(cnf_transformation,[status(thm)],[f25])).
% 1.38/1.14 thf(f68,plain,(
% 1.38/1.14 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ (dsetconstr @ X3 @ X4)) != $true) | ($true = (X4 @ X5))) )),
% 1.38/1.14 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.38/1.14 thf(f67,plain,(
% 1.38/1.14 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (($true = (X4 @ X5)) | ($true != (in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))))) )),
% 1.38/1.14 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.38/1.14 thf(f58,plain,(
% 1.38/1.14 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (($true != $true) | ($true != (in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0))))) | ($true = (X4 @ X5))) )),
% 1.38/1.14 inference(definition_unfolding,[status(thm)],[f45,f38])).
% 1.38/1.14 thf(f38,plain,(
% 1.38/1.14 (dsetconstrER = $true)),
% 1.38/1.14 inference(cnf_transformation,[status(thm)],[f25])).
% 1.38/1.14 thf(f45,plain,(
% 1.38/1.14 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (($true = (X4 @ X5)) | ($true != (in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0))))) | (dsetconstrER != $true)) )),
% 1.38/1.14 inference(cnf_transformation,[status(thm)],[f29])).
% 1.38/1.14 thf(f29,plain,(
% 1.38/1.14 ((dsetconstrER = $true) | (((sK6 @ sK7) != $true) & ((in @ sK7 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (sK6 @ Y0)))) = $true))) & (! [X3 : $i,X4 : $i > $o,X5 : $i] : (($true = (X4 @ X5)) | ($true != (in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))))) | (dsetconstrER != $true))),
% 1.38/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f27,f28])).
% 1.38/1.14 thf(f28,plain,(
% 1.38/1.14 ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X2) != $true) & ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true)) => (((sK6 @ sK7) != $true) & ((in @ sK7 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (sK6 @ Y0)))) = $true))),
% 1.38/1.14 introduced(definition,[],[choice_axiom])).
% 1.38/1.14 thf(f27,plain,(
% 1.38/1.14 ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X2) != $true) & ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true))) & (! [X3 : $i,X4 : $i > $o,X5 : $i] : (($true = (X4 @ X5)) | ($true != (in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))))) | (dsetconstrER != $true))),
% 1.38/1.14 inference(rectify,[status(thm)],[f26])).
% 1.38/1.14 thf(f26,plain,(
% 1.38/1.14 ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X2) != $true) & ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true))) & (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) | (dsetconstrER != $true))),
% 1.38/1.14 inference(nnf_transformation,[status(thm)],[f19])).
% 1.38/1.14 thf(f19,plain,(
% 1.38/1.14 (dsetconstrER = $true) <=> ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true))),
% 1.38/1.14 inference(ennf_transformation,[status(thm)],[f13])).
% 1.38/1.14 thf(f13,plain,(
% 1.38/1.14 (dsetconstrER = $true) <=> ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) => ((X1 @ X2) = $true))),
% 1.38/1.14 inference(fool_elimination,[status(thm)],[f12])).
% 1.38/1.14 thf(f12,plain,(
% 1.38/1.14 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.38/1.14 inference(rectify,[status(thm)],[f1])).
% 1.38/1.14 thf(f1,axiom,(
% 1.38/1.14 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.38/1.14 file('/export/starexec/sandbox2/tmp/tmp.zSheG09iwz/DTF2THF_11678.p',dsetconstrER)).
% 1.38/1.14 thf(f65,plain,(
% 1.38/1.14 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((kpair @ X7 @ X5) != (kpair @ X6 @ X4)) | (X4 = X5)) )),
% 1.38/1.14 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.38/1.14 thf(f61,plain,(
% 1.38/1.14 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((kpair @ X7 @ X5) != (kpair @ X6 @ X4)) | (X4 = X5)) )),
% 1.38/1.14 inference(definition_unfolding,[status(thm)],[f48,f39])).
% 1.38/1.14 thf(f39,plain,(
% 1.38/1.14 (setukpairinjR = $true)),
% 1.38/1.14 inference(cnf_transformation,[status(thm)],[f25])).
% 1.38/1.14 thf(f48,plain,(
% 1.38/1.14 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((X4 = X5) | ((kpair @ X7 @ X5) != (kpair @ X6 @ X4)) | (setukpairinjR != $true)) )),
% 1.38/1.14 inference(cnf_transformation,[status(thm)],[f33])).
% 1.38/1.14 thf(f33,plain,(
% 1.38/1.14 ((setukpairinjR = $true) | ((sK8 != sK9) & ((kpair @ sK10 @ sK8) = (kpair @ sK11 @ sK9)))) & (! [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : ((X4 = X5) | ((kpair @ X7 @ X5) != (kpair @ X6 @ X4))) | (setukpairinjR != $true))),
% 1.38/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f31,f32])).
% 1.38/1.14 thf(f32,plain,(
% 1.38/1.14 ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 != X1) & ((kpair @ X3 @ X1) = (kpair @ X2 @ X0))) => ((sK8 != sK9) & ((kpair @ sK10 @ sK8) = (kpair @ sK11 @ sK9)))),
% 1.38/1.14 introduced(definition,[],[choice_axiom])).
% 1.38/1.14 thf(f31,plain,(
% 1.38/1.14 ((setukpairinjR = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 != X1) & ((kpair @ X3 @ X1) = (kpair @ X2 @ X0)))) & (! [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : ((X4 = X5) | ((kpair @ X7 @ X5) != (kpair @ X6 @ X4))) | (setukpairinjR != $true))),
% 1.38/1.14 inference(rectify,[status(thm)],[f30])).
% 1.38/1.14 thf(f30,plain,(
% 1.38/1.14 ((setukpairinjR = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 != X1) & ((kpair @ X3 @ X1) = (kpair @ X2 @ X0)))) & (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X1) | ((kpair @ X3 @ X1) != (kpair @ X2 @ X0))) | (setukpairinjR != $true))),
% 1.38/1.14 inference(nnf_transformation,[status(thm)],[f22])).
% 1.38/1.14 thf(f22,plain,(
% 1.38/1.14 (setukpairinjR = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X1) | ((kpair @ X3 @ X1) != (kpair @ X2 @ X0)))),
% 1.38/1.14 inference(ennf_transformation,[status(thm)],[f11])).
% 1.38/1.14 thf(f11,plain,(
% 1.38/1.14 (setukpairinjR = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X1) = (kpair @ X2 @ X0)) => (X0 = X1))),
% 1.38/1.14 inference(fool_elimination,[status(thm)],[f10])).
% 1.38/1.14 thf(f10,plain,(
% 1.38/1.14 (setukpairinjR = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X1) = (kpair @ X2 @ X0)) => (X0 = X1)))),
% 1.38/1.14 inference(rectify,[status(thm)],[f3])).
% 1.38/1.14 thf(f3,axiom,(
% 1.38/1.14 (setukpairinjR = ! [X5 : $i,X3 : $i,X4 : $i,X2 : $i] : (((kpair @ X2 @ X3) = (kpair @ X4 @ X5)) => (X3 = X5)))),
% 1.38/1.14 file('/export/starexec/sandbox2/tmp/tmp.zSheG09iwz/DTF2THF_11678.p',setukpairinjR)).
% 1.38/1.14 thf(f93,plain,(
% 1.38/1.14 ($true = (sK1 @ sK3 @ sK19))),
% 1.38/1.14 inference(backward_demodulation,[status(thm)],[f84,f91])).
% 1.38/1.14 thf(f91,plain,(
% 1.38/1.14 (sK3 = sK18)),
% 1.38/1.14 inference(equality_resolution,[status(thm)],[f87])).
% 1.38/1.14 thf(f87,plain,(
% 1.38/1.14 ( ! [X0 : $i,X1 : $i] : (((kpair @ sK3 @ sK4) != (kpair @ X0 @ X1)) | (sK18 = X0)) )),
% 1.38/1.14 inference(superposition,[status(thm)],[f66,f85])).
% 1.38/1.14 thf(f66,plain,(
% 1.38/1.14 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X3 @ X0) != (kpair @ X1 @ X2)) | (X1 = X3)) )),
% 1.38/1.14 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.38/1.14 thf(f62,plain,(
% 1.38/1.14 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X3 @ X0) != (kpair @ X1 @ X2)) | (X1 = X3) | ($true != $true)) )),
% 1.38/1.14 inference(definition_unfolding,[status(thm)],[f54,f44])).
% 1.38/1.14 thf(f44,plain,(
% 1.38/1.14 (setukpairinjL = $true)),
% 1.38/1.14 inference(cnf_transformation,[status(thm)],[f25])).
% 1.38/1.14 thf(f54,plain,(
% 1.38/1.14 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X3 @ X0) != (kpair @ X1 @ X2)) | (X1 = X3) | (setukpairinjL != $true)) )),
% 1.38/1.14 inference(cnf_transformation,[status(thm)],[f37])).
% 1.38/1.14 thf(f37,plain,(
% 1.38/1.14 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) != (kpair @ X1 @ X2)) | (X1 = X3)) | (setukpairinjL != $true)) & ((setukpairinjL = $true) | (((kpair @ sK13 @ sK14) = (kpair @ sK15 @ sK12)) & (sK15 != sK13)))),
% 1.38/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f35,f36])).
% 1.38/1.14 thf(f36,plain,(
% 1.38/1.14 ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((kpair @ X7 @ X4) = (kpair @ X5 @ X6)) & (X5 != X7)) => (((kpair @ sK13 @ sK14) = (kpair @ sK15 @ sK12)) & (sK15 != sK13))),
% 1.38/1.14 introduced(definition,[],[choice_axiom])).
% 1.38/1.14 thf(f35,plain,(
% 1.38/1.14 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) != (kpair @ X1 @ X2)) | (X1 = X3)) | (setukpairinjL != $true)) & ((setukpairinjL = $true) | ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((kpair @ X7 @ X4) = (kpair @ X5 @ X6)) & (X5 != X7)))),
% 1.38/1.14 inference(rectify,[status(thm)],[f34])).
% 1.38/1.14 thf(f34,plain,(
% 1.38/1.14 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) != (kpair @ X1 @ X2)) | (X1 = X3)) | (setukpairinjL != $true)) & ((setukpairinjL = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) = (kpair @ X1 @ X2)) & (X1 != X3)))),
% 1.38/1.14 inference(nnf_transformation,[status(thm)],[f18])).
% 1.38/1.14 thf(f18,plain,(
% 1.38/1.14 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) != (kpair @ X1 @ X2)) | (X1 = X3)) <=> (setukpairinjL = $true)),
% 1.38/1.14 inference(ennf_transformation,[status(thm)],[f9])).
% 1.38/1.14 thf(f9,plain,(
% 1.38/1.14 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) = (kpair @ X1 @ X2)) => (X1 = X3)) <=> (setukpairinjL = $true)),
% 1.38/1.14 inference(fool_elimination,[status(thm)],[f8])).
% 1.38/1.14 thf(f8,plain,(
% 1.38/1.14 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) = (kpair @ X1 @ X2)) => (X1 = X3)) = setukpairinjL)),
% 1.38/1.14 inference(rectify,[status(thm)],[f2])).
% 1.38/1.14 thf(f2,axiom,(
% 1.38/1.14 (! [X5 : $i,X2 : $i,X3 : $i,X4 : $i] : (((kpair @ X2 @ X3) = (kpair @ X4 @ X5)) => (X2 = X4)) = setukpairinjL)),
% 1.38/1.14 file('/export/starexec/sandbox2/tmp/tmp.zSheG09iwz/DTF2THF_11678.p',setukpairinjL)).
% 1.38/1.14 thf(f84,plain,(
% 1.38/1.14 ($true = (sK1 @ sK18 @ sK19))),
% 1.38/1.14 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.38/1.14 thf(f82,plain,(
% 1.38/1.14 (((sK1 @ sK18 @ sK19) & (in @ sK19 @ sK2)) = $true)),
% 1.38/1.14 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.38/1.14 % SZS output end Proof for DTF2THF_11678
% 1.38/1.14 % (11789)------------------------------
% 1.38/1.14 % (11789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.14 % (11789)Termination reason: Refutation
% 1.38/1.14
% 1.38/1.14 % (11789)Memory used [KB]: 5628
% 1.38/1.14 % (11789)Time elapsed: 0.007 s
% 1.38/1.14 % (11789)Instructions burned: 9 (million)
% 1.38/1.14 % (11789)------------------------------
% 1.38/1.14 % (11789)------------------------------
% 1.38/1.14 % (11782)Success in time 0.015 s
%------------------------------------------------------------------------------