%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU671^2 : 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 : n031.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 09:36:06 AM UTC 2026
% Result : Theorem 1.81s 1.50s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 584 ( 195 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 791 ( 64 ~; 49 |; 78 &; 548 @)
% ( 6 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 268 ( 79 ^; 137 !; 52 ?; 268 :)
% 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_20,type,
sK0: $i > $i > $o ).
thf(func_def_27,type,
sK7: $i > $o ).
thf(func_def_38,type,
ph17:
!>[X0: $tType] : X0 ).
thf(f102,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f99,f40]) ).
thf(f40,plain,
( ( sK0 @ sK1 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( setukpairinjR = $true )
& ( ( sK0 @ sK1 @ sK2 )
!= $true )
& ( ( in @ ( kpair @ sK1 @ sK2 )
@ ( dpsetconstr @ sK4 @ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) )
= $true )
& ( dsetconstrER = $true )
& ( setukpairinjL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f19,f23]) ).
thf(f23,plain,
( ? [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X1 @ X2 )
!= $true )
& ( $true
= ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) ) )
=> ( ( ( sK0 @ sK1 @ sK2 )
!= $true )
& ( ( in @ ( kpair @ sK1 @ sK2 )
@ ( dpsetconstr @ sK4 @ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( setukpairinjR = $true )
& ? [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X1 @ X2 )
!= $true )
& ( $true
= ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) ) )
& ( dsetconstrER = $true )
& ( setukpairinjL = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X1 @ X2 )
!= $true )
& ( $true
= ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) ) )
& ( setukpairinjR = $true )
& ( setukpairinjL = $true )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( dsetconstrER = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR = $true )
=> ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
=> ( ( X0 @ X1 @ X2 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X4 @ X3
@ ^ [X5: $i,X6: $i] : ( X0 @ X5 @ X6 ) ) )
=> ( X0 @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [X1: $i > $i > $o,X2: $i,X3: $i,X6: $i,X0: $i] :
( ( 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
=> ! [X1: $i > $i > $o,X2: $i,X3: $i,X6: $i,X0: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X0 @ X6
@ ^ [X4: $i,X5: $i] : ( X1 @ X4 @ X5 ) ) )
=> ( X1 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jcFoRxn7B4/DTF2THF_21716.p',dpsetconstrER) ).
thf(f99,plain,
( ( sK0 @ sK1 @ sK2 )
= $true ),
inference(backward_demodulation,[status(thm)],[f90,f98]) ).
thf(f98,plain,
sK19 = sK2,
inference(equality_resolution,[status(thm)],[f86]) ).
thf(f86,plain,
! [X0: $i,X1: $i] :
( ( ( kpair @ sK1 @ sK2 )
!= ( kpair @ X0 @ X1 ) )
| ( sK19 = X1 ) ),
inference(superposition,[status(thm)],[f65,f82]) ).
thf(f82,plain,
( ( kpair @ sK1 @ sK2 )
= ( kpair @ sK18 @ sK19 ) ),
inference(equality_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( $true
= ( ( kpair @ sK18 @ sK19 )
= ( kpair @ sK1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ( in @ sK19 @ sK3 )
& ( sK0 @ sK18 @ sK19 )
& ( ( kpair @ sK18 @ sK19 )
= ( kpair @ sK1 @ sK2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
& ( sK0 @ sK18 @ Y0 )
& ( ( kpair @ sK18 @ Y0 )
= ( kpair @ sK1 @ sK2 ) ) )
@ sK19 )
= $true ),
inference(sigma_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
& ( sK0 @ sK18 @ Y0 )
& ( ( kpair @ sK18 @ Y0 )
= ( kpair @ sK1 @ sK2 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
& ( sK0 @ sK18 @ Y0 )
& ( ( kpair @ sK18 @ Y0 )
= ( kpair @ sK1 @ sK2 ) ) ) )
& ( in @ sK18 @ sK4 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
& ( sK0 @ Y0 @ Y1 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK1 @ sK2 ) ) ) )
& ( in @ Y0 @ sK4 ) )
@ sK18 ) ),
inference(sigma_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
& ( sK0 @ Y0 @ Y1 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK1 @ sK2 ) ) ) )
& ( in @ Y0 @ sK4 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK3 )
& ( sK0 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK4 ) ) )
@ ( kpair @ sK1 @ sK2 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK3 )
& ( sK0 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK4 ) ) )
@ ( kpair @ sK1 @ sK2 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f64,f62]) ).
thf(f62,plain,
( ( in @ ( kpair @ sK1 @ sK2 )
@ ( dsetconstr @ ( cartprod @ sK4 @ sK3 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK3 )
& ( sK0 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK4 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( ( in @ ( kpair @ sK1 @ sK2 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) )
@ sK4
@ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f39,f48]) ).
thf(f48,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,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 )
& ( X2 @ X4 @ X5 )
& ( in @ X5 @ X1 ) ) ) ) )
= 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 )
& ( X1 @ X2 @ X3 )
& ( in @ X3 @ X6 ) ) ) ) )
= dpsetconstr ),
file('/export/starexec/sandbox/tmp/tmp.jcFoRxn7B4/DTF2THF_21716.p',dpsetconstr) ).
thf(f39,plain,
( ( in @ ( kpair @ sK1 @ sK2 )
@ ( dpsetconstr @ sK4 @ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f64,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4 @ ( dsetconstr @ X3 @ X5 ) )
!= $true )
| ( ( X5 @ X4 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true )
| ( ( X5 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true != $true )
| ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true )
| ( ( X5 @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f42,f38]) ).
thf(f38,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f42,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true )
| ( ( X5 @ X4 )
= $true )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( dsetconstrER = $true )
| ( ( $true
= ( in @ sK6
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( sK7 @ Y0 ) ) ) )
& ( $true
!= ( sK7 @ sK6 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true )
| ( ( X5 @ X4 )
= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f26,f27]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
& ( ( X2 @ X1 )
!= $true ) )
=> ( ( $true
= ( in @ sK6
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( sK7 @ Y0 ) ) ) )
& ( $true
!= ( sK7 @ sK6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
& ( ( X2 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true )
| ( ( X5 @ X4 )
= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
& ( ( X2 @ X1 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X1 )
= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
=> ( ( X2 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jcFoRxn7B4/DTF2THF_21716.p',dsetconstrER) ).
thf(f65,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair @ X2 @ X3 )
!= ( kpair @ X1 @ X0 ) )
| ( X0 = X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( X0 = X3 )
| ( ( kpair @ X2 @ X3 )
!= ( kpair @ X1 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f47,f41]) ).
thf(f41,plain,
setukpairinjR = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 = X3 )
| ( ( kpair @ X2 @ X3 )
!= ( kpair @ X1 @ X0 ) )
| ( setukpairinjR != $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( ( kpair @ X2 @ X3 )
!= ( kpair @ X1 @ X0 ) ) )
| ( setukpairinjR != $true ) )
& ( ( setukpairinjR = $true )
| ( ( sK8 != sK11 )
& ( ( kpair @ sK10 @ sK11 )
= ( kpair @ sK9 @ sK8 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f30,f31]) ).
thf(f31,plain,
( ? [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( X4 != X7 )
& ( ( kpair @ X6 @ X7 )
= ( kpair @ X5 @ X4 ) ) )
=> ( ( sK8 != sK11 )
& ( ( kpair @ sK10 @ sK11 )
= ( kpair @ sK9 @ sK8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( ( kpair @ X2 @ X3 )
!= ( kpair @ X1 @ X0 ) ) )
| ( setukpairinjR != $true ) )
& ( ( setukpairinjR = $true )
| ? [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( X4 != X7 )
& ( ( kpair @ X6 @ X7 )
= ( kpair @ X5 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( ( kpair @ X2 @ X3 )
!= ( kpair @ X1 @ X0 ) ) )
| ( setukpairinjR != $true ) )
& ( ( setukpairinjR = $true )
| ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X3 )
& ( ( kpair @ X2 @ X3 )
= ( kpair @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( ( kpair @ X2 @ X3 )
!= ( kpair @ X1 @ X0 ) ) )
<=> ( setukpairinjR = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X1 @ X0 ) )
=> ( X0 = X3 ) )
<=> ( setukpairinjR = $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( setukpairinjR
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X1 @ X0 ) )
=> ( X0 = X3 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( setukpairinjR
= ( ! [X3: $i,X2: $i,X4: $i,X5: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X4 @ X5 ) )
=> ( X3 = X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jcFoRxn7B4/DTF2THF_21716.p',setukpairinjR) ).
thf(f90,plain,
( ( sK0 @ sK1 @ sK19 )
= $true ),
inference(backward_demodulation,[status(thm)],[f80,f88]) ).
thf(f88,plain,
sK1 = sK18,
inference(equality_resolution,[status(thm)],[f83]) ).
thf(f83,plain,
! [X0: $i,X1: $i] :
( ( ( kpair @ sK1 @ sK2 )
!= ( kpair @ X0 @ X1 ) )
| ( sK18 = X0 ) ),
inference(superposition,[status(thm)],[f66,f82]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair @ X0 @ X1 )
!= ( kpair @ X3 @ X2 ) )
| ( X0 = X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( X0 = X3 )
| ( ( kpair @ X0 @ X1 )
!= ( kpair @ X3 @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f51,f37]) ).
thf(f37,plain,
setukpairinjL = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 = X3 )
| ( ( kpair @ X0 @ X1 )
!= ( kpair @ X3 @ X2 ) )
| ( setukpairinjL != $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( ( kpair @ X0 @ X1 )
!= ( kpair @ X3 @ X2 ) ) )
| ( setukpairinjL != $true ) )
& ( ( setukpairinjL = $true )
| ( ( sK12 != sK15 )
& ( ( kpair @ sK12 @ sK13 )
= ( kpair @ sK15 @ sK14 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f34,f35]) ).
thf(f35,plain,
( ? [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( X4 != X7 )
& ( ( kpair @ X4 @ X5 )
= ( kpair @ X7 @ X6 ) ) )
=> ( ( sK12 != sK15 )
& ( ( kpair @ sK12 @ sK13 )
= ( kpair @ sK15 @ sK14 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( ( kpair @ X0 @ X1 )
!= ( kpair @ X3 @ X2 ) ) )
| ( setukpairinjL != $true ) )
& ( ( setukpairinjL = $true )
| ? [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( X4 != X7 )
& ( ( kpair @ X4 @ X5 )
= ( kpair @ X7 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( ( kpair @ X0 @ X1 )
!= ( kpair @ X3 @ X2 ) ) )
| ( setukpairinjL != $true ) )
& ( ( setukpairinjL = $true )
| ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X3 )
& ( ( kpair @ X0 @ X1 )
= ( kpair @ X3 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( ( kpair @ X0 @ X1 )
!= ( kpair @ X3 @ X2 ) ) )
<=> ( setukpairinjL = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( setukpairinjL = $true )
<=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X3 @ X2 ) )
=> ( X0 = X3 ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( setukpairinjL
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X3 @ X2 ) )
=> ( X0 = X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setukpairinjL
= ( ! [X2: $i,X3: $i,X5: $i,X4: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X4 @ X5 ) )
=> ( X2 = X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jcFoRxn7B4/DTF2THF_21716.p',setukpairinjL) ).
thf(f80,plain,
( ( sK0 @ sK18 @ sK19 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( in @ sK19 @ sK3 )
& ( sK0 @ sK18 @ sK19 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU671^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n031.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 12:31:33 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.49 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SEU671^2 : TPTP v9.2.1. Released v3.7.0.
% 0.33/0.49 % Domain : Set Theory
% 0.33/0.49 % Problem : Ordered Pairs - Sets of Pairs
% 0.33/0.49 % Version : Especial > Reduced > Especial.
% 0.33/0.49 % English : (! A:i.! B:i.! phi:i>(i>o).! x:i.! y:i.in (kpair x y)
% 0.33/0.49 % (dpsetconstr A B (^ z,u:i.phi z u)) -> phi x y)
% 0.33/0.49
% 0.33/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.33/0.49 % Source : [Bro08]
% 0.33/0.49 % Names : ZFC173l [Bro08]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.46 v8.1.0, 0.55 v7.5.0, 0.43 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v4.0.0, 0.67 v3.7.0
% 0.33/0.49 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.33/0.49 % Number of atoms : 19 ( 9 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 4 ( 3 avg)
% 0.33/0.49 % Number of connectives : 47 ( 0 ~; 0 |; 3 &; 37 @)
% 0.33/0.49 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 16 ( 4 avg)
% 0.33/0.49 % Number of types : 2 ( 0 usr)
% 0.33/0.49 % Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 9 ( 8 usr; 3 con; 0-3 aty)
% 0.33/0.49 % Number of variables : 25 ( 7 ^; 16 !; 2 ?; 25 :)
% 0.33/0.49 % SPC : TH0_THM_EQU_NAR
% 0.33/0.49
% 0.33/0.49 % Comments : http://mathgate.info/detsetitem.php?id=341
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(in_type,type,
% 0.33/0.49 in: $i > $i > $o ).
% 0.33/0.49
% 0.33/0.49 thf(dsetconstr_type,type,
% 0.33/0.49 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.33/0.49
% 0.33/0.49 thf(dsetconstrER_type,type,
% 0.33/0.49 dsetconstrER: $o ).
% 0.33/0.49
% 0.33/0.49 thf(dsetconstrER,definition,
% 0.33/0.49 ( dsetconstrER
% 0.33/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/0.49 ( ( in @ Xx
% 0.33/0.49 @ ( dsetconstr @ A
% 0.33/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.33/0.49 => ( Xphi @ Xx ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(kpair_type,type,
% 0.33/0.49 kpair: $i > $i > $i ).
% 0.33/0.49
% 0.33/0.49 thf(cartprod_type,type,
% 0.33/0.49 cartprod: $i > $i > $i ).
% 0.33/0.49
% 0.33/0.49 thf(setukpairinjL_type,type,
% 0.33/0.49 setukpairinjL: $o ).
% 0.33/0.49
% 0.33/0.49 thf(setukpairinjL,definition,
% 0.33/0.49 ( setukpairinjL
% 0.33/0.49 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/0.49 ( ( ( kpair @ Xx @ Xy )
% 0.33/0.49 = ( kpair @ Xz @ Xu ) )
% 0.33/0.49 => ( Xx = Xz ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(setukpairinjR_type,type,
% 0.33/0.49 setukpairinjR: $o ).
% 0.33/0.49
% 0.33/0.49 thf(setukpairinjR,definition,
% 0.33/0.49 ( setukpairinjR
% 0.33/0.49 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/0.49 ( ( ( kpair @ Xx @ Xy )
% 0.33/0.49 = ( kpair @ Xz @ Xu ) )
% 0.33/0.49 => ( Xy = Xu ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(dpsetconstr_type,type,
% 0.33/0.49 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.33/0.49
% 0.33/0.49 thf(dpsetconstr,definition,
% 0.33/0.49 ( dpsetconstr
% 0.33/0.49 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.33/0.49 ( dsetconstr @ ( cartprod @ A @ B )
% 0.33/0.49 @ ^ [Xu: $i] :
% 0.33/0.49 ? [Xx: $i] :
% 0.33/0.49 ( ( in @ Xx @ A )
% 0.33/0.49 & ? [Xy: $i] :
% 0.33/0.49 ( ( in @ Xy @ B )
% 0.33/0.49 & ( Xphi @ Xx @ Xy )
% 0.33/0.49 & ( Xu
% 0.33/0.49 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(dpsetconstrER,conjecture,
% 0.33/0.49 ( dsetconstrER
% 0.33/0.49 => ( setukpairinjL
% 0.33/0.49 => ( setukpairinjR
% 0.33/0.49 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.33/0.49 ( ( in @ ( kpair @ Xx @ Xy )
% 0.33/0.49 @ ( dpsetconstr @ A @ B
% 0.33/0.49 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.33/0.49 => ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.69/1.46 ---- Embedded in THF ---
% 1.69/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.69/1.46 %%% Generated on Tue Feb 24 12:31:34 EST 2026
% 1.69/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.69/1.46 %%% Logic specification used:
% 1.69/1.46 %%% thf(spec, logic, $$dhol).
% 1.69/1.46
% 1.69/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jcFoRxn7B4/DTF2DTF21716.p
% See solution above
% 1.69/1.46 ------------------------
% 1.69/1.47 ---- Cleaned THF ---
% 1.69/1.47 thf(in_type,type,
% 1.69/1.47 in: $i > $i > $o ).
% 1.69/1.47
% 1.69/1.47 thf(dsetconstr_type,type,
% 1.69/1.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.69/1.47
% 1.69/1.47 thf(dsetconstrER_type,type,
% 1.69/1.47 dsetconstrER: $o ).
% 1.69/1.47
% 1.69/1.47 thf(dsetconstrER,definition,
% 1.69/1.47 ( dsetconstrER
% 1.69/1.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.69/1.47 ( ( in @ Xx
% 1.69/1.47 @ ( dsetconstr @ A
% 1.69/1.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.69/1.47 => ( Xphi @ Xx ) ) ) ) ).
% 1.69/1.47
% 1.69/1.47 thf(kpair_type,type,
% 1.69/1.47 kpair: $i > $i > $i ).
% 1.69/1.47
% 1.69/1.47 thf(cartprod_type,type,
% 1.69/1.47 cartprod: $i > $i > $i ).
% 1.69/1.47
% 1.69/1.47 thf(setukpairinjL_type,type,
% 1.69/1.47 setukpairinjL: $o ).
% 1.69/1.47
% 1.69/1.47 thf(setukpairinjL,definition,
% 1.69/1.47 ( setukpairinjL
% 1.69/1.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 1.69/1.47 ( ( ( kpair @ Xx @ Xy )
% 1.69/1.47 = ( kpair @ Xz @ Xu ) )
% 1.69/1.47 => ( Xx = Xz ) ) ) ) ).
% 1.69/1.47
% 1.69/1.47 thf(setukpairinjR_type,type,
% 1.69/1.47 setukpairinjR: $o ).
% 1.69/1.47
% 1.69/1.47 thf(setukpairinjR,definition,
% 1.69/1.47 ( setukpairinjR
% 1.69/1.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 1.69/1.47 ( ( ( kpair @ Xx @ Xy )
% 1.69/1.47 = ( kpair @ Xz @ Xu ) )
% 1.69/1.47 => ( Xy = Xu ) ) ) ) ).
% 1.69/1.47
% 1.69/1.47 thf(dpsetconstr_type,type,
% 1.69/1.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.69/1.47
% 1.69/1.47 thf(dpsetconstr,definition,
% 1.69/1.47 ( dpsetconstr
% 1.69/1.47 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 1.69/1.47 ( dsetconstr @ ( cartprod @ A @ B )
% 1.69/1.47 @ ^ [Xu: $i] :
% 1.69/1.47 ? [Xx: $i] :
% 1.69/1.47 ( ( in @ Xx @ A )
% 1.69/1.47 & ? [Xy: $i] :
% 1.69/1.47 ( ( in @ Xy @ B )
% 1.69/1.47 & ( Xphi @ Xx @ Xy )
% 1.69/1.47 & ( Xu
% 1.69/1.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 1.69/1.47
% 1.69/1.47 thf(dpsetconstrER,conjecture,
% 1.69/1.47 ( dsetconstrER
% 1.69/1.47 => ( setukpairinjL
% 1.69/1.47 => ( setukpairinjR
% 1.69/1.47 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 1.69/1.47 ( ( in @ ( kpair @ Xx @ Xy )
% 1.69/1.47 @ ( dpsetconstr @ A @ B
% 1.69/1.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 1.69/1.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 1.69/1.47 ------------------------
% 1.69/1.49 % (21813)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21716 for (2999ds/183Mi)
% 1.69/1.49 % (21818)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_21716 for (2999ds/275Mi)
% 1.69/1.49 % (21816)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21716 for (2999ds/2Mi)
% 1.69/1.49 % (21815)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_21716 for (2999ds/27Mi)
% 1.69/1.49 % (21817)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_21716 for (2999ds/2Mi)
% 1.69/1.49 % (21819)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21716 for (2999ds/18Mi)
% 1.69/1.49 % (21814)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_21716 for (2999ds/4Mi)
% 1.69/1.49 % (21816)Instruction limit reached!
% 1.69/1.49 % (21816)------------------------------
% 1.69/1.49 % (21816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.49 % (21816)Termination reason: Unknown
% 1.69/1.49 % (21817)Instruction limit reached!
% 1.69/1.49 % (21817)------------------------------
% 1.69/1.49 % (21817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.49 % (21816)Termination phase: Clausification
% 1.69/1.49
% 1.69/1.49 % (21816)Memory used [KB]: 1023
% 1.69/1.49 % (21816)Time elapsed: 0.003 s
% 1.69/1.49 % (21816)Instructions burned: 3 (million)
% 1.69/1.49 % (21816)------------------------------
% 1.69/1.49 % (21816)------------------------------
% 1.69/1.49 % (21817)Termination reason: Unknown
% 1.69/1.49 % (21817)Termination phase: Property scanning
% 1.69/1.49
% 1.69/1.49 % (21817)Memory used [KB]: 1023
% 1.69/1.49 % (21817)Time elapsed: 0.003 s
% 1.69/1.49 % (21817)Instructions burned: 3 (million)
% 1.69/1.49 % (21817)------------------------------
% 1.69/1.49 % (21817)------------------------------
% 1.69/1.49 % (21814)Instruction limit reached!
% 1.69/1.49 % (21814)------------------------------
% 1.69/1.49 % (21814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.49 % (21814)Termination reason: Unknown
% 1.69/1.49 % (21814)Termination phase: Saturation
% 1.69/1.49
% 1.69/1.49 % (21814)Memory used [KB]: 5500
% 1.69/1.49 % (21814)Time elapsed: 0.004 s
% 1.69/1.49 % (21814)Instructions burned: 4 (million)
% 1.69/1.49 % (21814)------------------------------
% 1.69/1.49 % (21814)------------------------------
% 1.69/1.49 % (21818)Refutation not found, incomplete strategy
% 1.69/1.49 % (21818)------------------------------
% 1.69/1.49 % (21818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.49 % (21818)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.49
% 1.69/1.49
% 1.69/1.49 % (21818)Memory used [KB]: 5500
% 1.69/1.49 % (21818)Time elapsed: 0.004 s
% 1.69/1.49 % (21818)Instructions burned: 4 (million)
% 1.69/1.49 % (21818)------------------------------
% 1.69/1.49 % (21818)------------------------------
% 1.81/1.50 % (21819)First to succeed.
% 1.81/1.50 % (21813)Also succeeded, but the first one will report.
% 1.81/1.50 % (21819)Refutation found. Thanks to Tanya!
% 1.81/1.50 % SZS status Theorem for DTF2THF_21716
% 1.81/1.50 % SZS output start Proof for DTF2THF_21716
% 1.81/1.50 thf(func_def_0, type, in: $i > $i > $o).
% 1.81/1.50 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.81/1.50 thf(func_def_4, type, kpair: $i > $i > $i).
% 1.81/1.50 thf(func_def_5, type, cartprod: $i > $i > $i).
% 1.81/1.50 thf(func_def_8, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.81/1.50 thf(func_def_20, type, sK0: $i > $i > $o).
% 1.81/1.50 thf(func_def_27, type, sK7: $i > $o).
% 1.81/1.50 thf(func_def_38, type, ph17: !>[X0: $tType]:(X0)).
% 1.81/1.50 thf(f102,plain,(
% 1.81/1.50 $false),
% 1.81/1.50 inference(subsumption_resolution,[status(thm)],[f99,f40])).
% 1.81/1.50 thf(f40,plain,(
% 1.81/1.50 ((sK0 @ sK1 @ sK2) != $true)),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f24])).
% 1.81/1.50 thf(f24,plain,(
% 1.81/1.50 (setukpairinjR = $true) & (((sK0 @ sK1 @ sK2) != $true) & ((in @ (kpair @ sK1 @ sK2) @ (dpsetconstr @ sK4 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) = $true)) & (dsetconstrER = $true) & (setukpairinjL = $true)),
% 1.81/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f19,f23])).
% 1.81/1.50 thf(f23,plain,(
% 1.81/1.50 ? [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : (((X0 @ X1 @ X2) != $true) & ($true = (in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))))) => (((sK0 @ sK1 @ sK2) != $true) & ((in @ (kpair @ sK1 @ sK2) @ (dpsetconstr @ sK4 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) = $true))),
% 1.81/1.50 introduced(definition,[],[choice_axiom])).
% 1.81/1.50 thf(f19,plain,(
% 1.81/1.50 (setukpairinjR = $true) & ? [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : (((X0 @ X1 @ X2) != $true) & ($true = (in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))))) & (dsetconstrER = $true) & (setukpairinjL = $true)),
% 1.81/1.50 inference(flattening,[status(thm)],[f18])).
% 1.81/1.50 thf(f18,plain,(
% 1.81/1.50 ((? [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : (((X0 @ X1 @ X2) != $true) & ($true = (in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))))) & (setukpairinjR = $true)) & (setukpairinjL = $true)) & (dsetconstrER = $true)),
% 1.81/1.50 inference(ennf_transformation,[status(thm)],[f9])).
% 1.81/1.50 thf(f9,plain,(
% 1.81/1.50 ~((dsetconstrER = $true) => ((setukpairinjL = $true) => ((setukpairinjR = $true) => ! [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : (($true = (in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) => ((X0 @ X1 @ X2) = $true)))))),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f8])).
% 1.81/1.50 thf(f8,plain,(
% 1.81/1.50 ~(dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i,X4 : $i] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6)))) => (X0 @ X1 @ X2)))))),
% 1.81/1.50 inference(rectify,[status(thm)],[f6])).
% 1.81/1.50 thf(f6,negated_conjecture,(
% 1.81/1.50 ~(dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X1 : $i > $i > $o,X2 : $i,X3 : $i,X6 : $i,X0 : $i] : ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X6 @ (^[X4 : $i, X5 : $i] : (X1 @ X4 @ X5)))) => (X1 @ X2 @ X3)))))),
% 1.81/1.50 inference(negated_conjecture,[status(cth)],[f5])).
% 1.81/1.50 thf(f5,conjecture,(
% 1.81/1.50 dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X1 : $i > $i > $o,X2 : $i,X3 : $i,X6 : $i,X0 : $i] : ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X6 @ (^[X4 : $i, X5 : $i] : (X1 @ X4 @ X5)))) => (X1 @ X2 @ X3))))),
% 1.81/1.50 file('/export/starexec/sandbox/tmp/tmp.jcFoRxn7B4/DTF2THF_21716.p',dpsetconstrER)).
% 1.81/1.50 thf(f99,plain,(
% 1.81/1.50 ((sK0 @ sK1 @ sK2) = $true)),
% 1.81/1.50 inference(backward_demodulation,[status(thm)],[f90,f98])).
% 1.81/1.50 thf(f98,plain,(
% 1.81/1.50 (sK19 = sK2)),
% 1.81/1.50 inference(equality_resolution,[status(thm)],[f86])).
% 1.81/1.50 thf(f86,plain,(
% 1.81/1.50 ( ! [X0 : $i,X1 : $i] : (((kpair @ sK1 @ sK2) != (kpair @ X0 @ X1)) | (sK19 = X1)) )),
% 1.81/1.50 inference(superposition,[status(thm)],[f65,f82])).
% 1.81/1.50 thf(f82,plain,(
% 1.81/1.50 ((kpair @ sK1 @ sK2) = (kpair @ sK18 @ sK19))),
% 1.81/1.50 inference(equality_proxy_clausification,[status(thm)],[f78])).
% 1.81/1.50 thf(f78,plain,(
% 1.81/1.50 ($true = ((kpair @ sK18 @ sK19) = (kpair @ sK1 @ sK2)))),
% 1.81/1.50 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.81/1.50 thf(f77,plain,(
% 1.81/1.50 ((((in @ sK19 @ sK3) & (sK0 @ sK18 @ sK19)) & ((kpair @ sK18 @ sK19) = (kpair @ sK1 @ sK2))) = $true)),
% 1.81/1.50 inference(beta_eta_normalization,[status(thm)],[f76])).
% 1.81/1.50 thf(f76,plain,(
% 1.81/1.50 (((^[Y0 : $i]: (((in @ Y0 @ sK3) & (sK0 @ sK18 @ Y0)) & ((kpair @ sK18 @ Y0) = (kpair @ sK1 @ sK2)))) @ sK19) = $true)),
% 1.81/1.50 inference(sigma_clausification,[status(thm)],[f75])).
% 1.81/1.50 thf(f75,plain,(
% 1.81/1.50 ((?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ sK3) & (sK0 @ sK18 @ Y0)) & ((kpair @ sK18 @ Y0) = (kpair @ sK1 @ sK2))))) = $true)),
% 1.81/1.50 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.81/1.50 thf(f73,plain,(
% 1.81/1.50 (((?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ sK3) & (sK0 @ sK18 @ Y0)) & ((kpair @ sK18 @ Y0) = (kpair @ sK1 @ sK2))))) & (in @ sK18 @ sK4)) = $true)),
% 1.81/1.50 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.81/1.50 thf(f72,plain,(
% 1.81/1.50 ($true = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((in @ Y1 @ sK3) & (sK0 @ Y0 @ Y1)) & ((kpair @ Y0 @ Y1) = (kpair @ sK1 @ sK2))))) & (in @ Y0 @ sK4))) @ sK18))),
% 1.81/1.50 inference(sigma_clausification,[status(thm)],[f71])).
% 1.81/1.50 thf(f71,plain,(
% 1.81/1.50 ((?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((in @ Y1 @ sK3) & (sK0 @ Y0 @ Y1)) & ((kpair @ Y0 @ Y1) = (kpair @ sK1 @ sK2))))) & (in @ Y0 @ sK4)))) = $true)),
% 1.81/1.50 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.81/1.50 thf(f70,plain,(
% 1.81/1.50 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK3) & (sK0 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK4))))) @ (kpair @ sK1 @ sK2)) = $true)),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.81/1.50 thf(f69,plain,(
% 1.81/1.50 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK3) & (sK0 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK4))))) @ (kpair @ sK1 @ sK2)) = $true) | ($true != $true)),
% 1.81/1.50 inference(superposition,[status(thm)],[f64,f62])).
% 1.81/1.50 thf(f62,plain,(
% 1.81/1.50 ((in @ (kpair @ sK1 @ sK2) @ (dsetconstr @ (cartprod @ sK4 @ sK3) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK3) & (sK0 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK4))))))) = $true)),
% 1.81/1.50 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.81/1.50 thf(f52,plain,(
% 1.81/1.50 ((in @ (kpair @ sK1 @ sK2) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))) @ sK4 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) = $true)),
% 1.81/1.50 inference(definition_unfolding,[status(thm)],[f39,f48])).
% 1.81/1.50 thf(f48,plain,(
% 1.81/1.50 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))))),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f17])).
% 1.81/1.50 thf(f17,plain,(
% 1.81/1.50 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))))),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f16])).
% 1.81/1.50 thf(f16,plain,(
% 1.81/1.50 ((^[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) & (X2 @ X4 @ X5) & (in @ X5 @ X1))))))) = dpsetconstr)),
% 1.81/1.50 inference(rectify,[status(thm)],[f4])).
% 1.81/1.50 thf(f4,axiom,(
% 1.81/1.50 ((^[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) & (X1 @ X2 @ X3) & (in @ X3 @ X6))))))) = dpsetconstr)),
% 1.81/1.50 file('/export/starexec/sandbox/tmp/tmp.jcFoRxn7B4/DTF2THF_21716.p',dpsetconstr)).
% 1.81/1.50 thf(f39,plain,(
% 1.81/1.50 ((in @ (kpair @ sK1 @ sK2) @ (dpsetconstr @ sK4 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) = $true)),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f24])).
% 1.81/1.50 thf(f64,plain,(
% 1.81/1.50 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ (dsetconstr @ X3 @ X5)) != $true) | ((X5 @ X4) = $true)) )),
% 1.81/1.50 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.81/1.50 thf(f63,plain,(
% 1.81/1.50 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true) | ((X5 @ X4) = $true)) )),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.81/1.50 thf(f55,plain,(
% 1.81/1.50 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != $true) | ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true) | ((X5 @ X4) = $true)) )),
% 1.81/1.50 inference(definition_unfolding,[status(thm)],[f42,f38])).
% 1.81/1.50 thf(f38,plain,(
% 1.81/1.50 (dsetconstrER = $true)),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f24])).
% 1.81/1.50 thf(f42,plain,(
% 1.81/1.50 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true) | ((X5 @ X4) = $true) | (dsetconstrER != $true)) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f28])).
% 1.81/1.50 thf(f28,plain,(
% 1.81/1.50 ((dsetconstrER = $true) | (($true = (in @ sK6 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (sK7 @ Y0))))) & ($true != (sK7 @ sK6)))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true) | ((X5 @ X4) = $true)) | (dsetconstrER != $true))),
% 1.81/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f26,f27])).
% 1.81/1.50 thf(f27,plain,(
% 1.81/1.50 ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) & ((X2 @ X1) != $true)) => (($true = (in @ sK6 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (sK7 @ Y0))))) & ($true != (sK7 @ sK6)))),
% 1.81/1.50 introduced(definition,[],[choice_axiom])).
% 1.81/1.50 thf(f26,plain,(
% 1.81/1.50 ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) & ((X2 @ X1) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true) | ((X5 @ X4) = $true)) | (dsetconstrER != $true))),
% 1.81/1.50 inference(rectify,[status(thm)],[f25])).
% 1.81/1.50 thf(f25,plain,(
% 1.81/1.50 ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) & ((X2 @ X1) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) | ((X2 @ X1) = $true)) | (dsetconstrER != $true))),
% 1.81/1.50 inference(nnf_transformation,[status(thm)],[f20])).
% 1.81/1.50 thf(f20,plain,(
% 1.81/1.50 (dsetconstrER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) | ((X2 @ X1) = $true))),
% 1.81/1.50 inference(ennf_transformation,[status(thm)],[f11])).
% 1.81/1.50 thf(f11,plain,(
% 1.81/1.50 (dsetconstrER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) => ((X2 @ X1) = $true))),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f10])).
% 1.81/1.50 thf(f10,plain,(
% 1.81/1.50 (dsetconstrER = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X1)))),
% 1.81/1.50 inference(rectify,[status(thm)],[f1])).
% 1.81/1.50 thf(f1,axiom,(
% 1.81/1.50 (dsetconstrER = ! [X0 : $i,X2 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)))),
% 1.81/1.50 file('/export/starexec/sandbox/tmp/tmp.jcFoRxn7B4/DTF2THF_21716.p',dsetconstrER)).
% 1.81/1.50 thf(f65,plain,(
% 1.81/1.50 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X2 @ X3) != (kpair @ X1 @ X0)) | (X0 = X3)) )),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.81/1.50 thf(f56,plain,(
% 1.81/1.50 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | (X0 = X3) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0))) )),
% 1.81/1.50 inference(definition_unfolding,[status(thm)],[f47,f41])).
% 1.81/1.50 thf(f41,plain,(
% 1.81/1.50 (setukpairinjR = $true)),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f24])).
% 1.81/1.50 thf(f47,plain,(
% 1.81/1.50 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X0 = X3) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0)) | (setukpairinjR != $true)) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f32])).
% 1.81/1.50 thf(f32,plain,(
% 1.81/1.50 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0))) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | ((sK8 != sK11) & ((kpair @ sK10 @ sK11) = (kpair @ sK9 @ sK8))))),
% 1.81/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f30,f31])).
% 1.81/1.50 thf(f31,plain,(
% 1.81/1.50 ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : ((X4 != X7) & ((kpair @ X6 @ X7) = (kpair @ X5 @ X4))) => ((sK8 != sK11) & ((kpair @ sK10 @ sK11) = (kpair @ sK9 @ sK8)))),
% 1.81/1.50 introduced(definition,[],[choice_axiom])).
% 1.81/1.50 thf(f30,plain,(
% 1.81/1.50 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0))) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : ((X4 != X7) & ((kpair @ X6 @ X7) = (kpair @ X5 @ X4))))),
% 1.81/1.50 inference(rectify,[status(thm)],[f29])).
% 1.81/1.50 thf(f29,plain,(
% 1.81/1.50 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0))) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 != X3) & ((kpair @ X2 @ X3) = (kpair @ X1 @ X0))))),
% 1.81/1.50 inference(nnf_transformation,[status(thm)],[f21])).
% 1.81/1.50 thf(f21,plain,(
% 1.81/1.50 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0))) <=> (setukpairinjR = $true)),
% 1.81/1.50 inference(ennf_transformation,[status(thm)],[f15])).
% 1.81/1.50 thf(f15,plain,(
% 1.81/1.50 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X2 @ X3) = (kpair @ X1 @ X0)) => (X0 = X3)) <=> (setukpairinjR = $true)),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f14])).
% 1.81/1.50 thf(f14,plain,(
% 1.81/1.50 (setukpairinjR = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X2 @ X3) = (kpair @ X1 @ X0)) => (X0 = X3)))),
% 1.81/1.50 inference(rectify,[status(thm)],[f3])).
% 1.81/1.50 thf(f3,axiom,(
% 1.81/1.50 (setukpairinjR = ! [X3 : $i,X2 : $i,X4 : $i,X5 : $i] : (((kpair @ X2 @ X3) = (kpair @ X4 @ X5)) => (X3 = X5)))),
% 1.81/1.50 file('/export/starexec/sandbox/tmp/tmp.jcFoRxn7B4/DTF2THF_21716.p',setukpairinjR)).
% 1.81/1.50 thf(f90,plain,(
% 1.81/1.50 ((sK0 @ sK1 @ sK19) = $true)),
% 1.81/1.50 inference(backward_demodulation,[status(thm)],[f80,f88])).
% 1.81/1.50 thf(f88,plain,(
% 1.81/1.50 (sK1 = sK18)),
% 1.81/1.50 inference(equality_resolution,[status(thm)],[f83])).
% 1.81/1.50 thf(f83,plain,(
% 1.81/1.50 ( ! [X0 : $i,X1 : $i] : (((kpair @ sK1 @ sK2) != (kpair @ X0 @ X1)) | (sK18 = X0)) )),
% 1.81/1.50 inference(superposition,[status(thm)],[f66,f82])).
% 1.81/1.50 thf(f66,plain,(
% 1.81/1.50 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X0 @ X1) != (kpair @ X3 @ X2)) | (X0 = X3)) )),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.81/1.50 thf(f59,plain,(
% 1.81/1.50 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | (X0 = X3) | ((kpair @ X0 @ X1) != (kpair @ X3 @ X2))) )),
% 1.81/1.50 inference(definition_unfolding,[status(thm)],[f51,f37])).
% 1.81/1.50 thf(f37,plain,(
% 1.81/1.50 (setukpairinjL = $true)),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f24])).
% 1.81/1.50 thf(f51,plain,(
% 1.81/1.50 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X0 = X3) | ((kpair @ X0 @ X1) != (kpair @ X3 @ X2)) | (setukpairinjL != $true)) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f36])).
% 1.81/1.50 thf(f36,plain,(
% 1.81/1.50 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) | ((kpair @ X0 @ X1) != (kpair @ X3 @ X2))) | (setukpairinjL != $true)) & ((setukpairinjL = $true) | ((sK12 != sK15) & ((kpair @ sK12 @ sK13) = (kpair @ sK15 @ sK14))))),
% 1.81/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f34,f35])).
% 1.81/1.50 thf(f35,plain,(
% 1.81/1.50 ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : ((X4 != X7) & ((kpair @ X4 @ X5) = (kpair @ X7 @ X6))) => ((sK12 != sK15) & ((kpair @ sK12 @ sK13) = (kpair @ sK15 @ sK14)))),
% 1.81/1.50 introduced(definition,[],[choice_axiom])).
% 1.81/1.50 thf(f34,plain,(
% 1.81/1.50 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) | ((kpair @ X0 @ X1) != (kpair @ X3 @ X2))) | (setukpairinjL != $true)) & ((setukpairinjL = $true) | ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : ((X4 != X7) & ((kpair @ X4 @ X5) = (kpair @ X7 @ X6))))),
% 1.81/1.50 inference(rectify,[status(thm)],[f33])).
% 1.81/1.50 thf(f33,plain,(
% 1.81/1.50 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) | ((kpair @ X0 @ X1) != (kpair @ X3 @ X2))) | (setukpairinjL != $true)) & ((setukpairinjL = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 != X3) & ((kpair @ X0 @ X1) = (kpair @ X3 @ X2))))),
% 1.81/1.50 inference(nnf_transformation,[status(thm)],[f22])).
% 1.81/1.50 thf(f22,plain,(
% 1.81/1.50 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 = X3) | ((kpair @ X0 @ X1) != (kpair @ X3 @ X2))) <=> (setukpairinjL = $true)),
% 1.81/1.50 inference(ennf_transformation,[status(thm)],[f13])).
% 1.81/1.50 thf(f13,plain,(
% 1.81/1.50 (setukpairinjL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X0 @ X1) = (kpair @ X3 @ X2)) => (X0 = X3))),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f12])).
% 1.81/1.50 thf(f12,plain,(
% 1.81/1.50 (setukpairinjL = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X0 @ X1) = (kpair @ X3 @ X2)) => (X0 = X3)))),
% 1.81/1.50 inference(rectify,[status(thm)],[f2])).
% 1.81/1.50 thf(f2,axiom,(
% 1.81/1.50 (setukpairinjL = ! [X2 : $i,X3 : $i,X5 : $i,X4 : $i] : (((kpair @ X2 @ X3) = (kpair @ X4 @ X5)) => (X2 = X4)))),
% 1.81/1.50 file('/export/starexec/sandbox/tmp/tmp.jcFoRxn7B4/DTF2THF_21716.p',setukpairinjL)).
% 1.81/1.50 thf(f80,plain,(
% 1.81/1.50 ((sK0 @ sK18 @ sK19) = $true)),
% 1.81/1.50 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.81/1.50 thf(f79,plain,(
% 1.81/1.50 (((in @ sK19 @ sK3) & (sK0 @ sK18 @ sK19)) = $true)),
% 1.81/1.50 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.81/1.50 % SZS output end Proof for DTF2THF_21716
% 1.81/1.50 % (21819)------------------------------
% 1.81/1.50 % (21819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.50 % (21819)Termination reason: Refutation
% 1.81/1.50
% 1.81/1.50 % (21819)Memory used [KB]: 5628
% 1.81/1.50 % (21819)Time elapsed: 0.010 s
% 1.81/1.50 % (21819)Instructions burned: 10 (million)
% 1.81/1.50 % (21819)------------------------------
% 1.81/1.50 % (21819)------------------------------
% 1.81/1.50 % (21812)Success in time 0.022 s
%------------------------------------------------------------------------------