%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU656^2 : 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 : n005.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 09:35:59 AM UTC 2026
% Result : Theorem 1.82s 1.58s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 90 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 722 ( 277 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 927 ( 93 ~; 73 |; 50 &; 664 @)
% ( 9 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 19 con; 0-2 aty)
% Number of variables : 237 ( 57 ^; 141 !; 39 ?; 237 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_7,type,
iskpair: $i > $o ).
thf(func_def_8,type,
kpair: $i > $i > $i ).
thf(func_def_10,type,
singleton: $i > $o ).
thf(func_def_12,type,
kfst: $i > $i ).
thf(func_def_15,type,
ksnd: $i > $i ).
thf(func_def_30,type,
sK5: $i > $o ).
thf(func_def_38,type,
sP13: $o > $o ).
thf(func_def_39,type,
sP14: $o > $o ).
thf(func_def_40,type,
sP15: $o > $o ).
thf(func_def_41,type,
sP16: $o > $o ).
thf(func_def_42,type,
sP17: $i > $o ).
thf(func_def_45,type,
ph19:
!>[X0: $tType] : X0 ).
thf(f137,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f136]) ).
thf(f136,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f106,f135]) ).
thf(f135,plain,
( $false
= ( sP17 @ sK12 ) ),
inference(backward_demodulation,[status(thm)],[f111,f132]) ).
thf(f132,plain,
! [X0: $i,X1: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) )
= X1 ),
inference(equality_resolution,[status(thm)],[f127]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair @ X2 @ X3 )
!= ( kpair @ X0 @ X1 ) )
| ( ( setunion
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) )
= X3 ) ),
inference(superposition,[status(thm)],[f113,f123]) ).
thf(f123,plain,
! [X0: $i,X1: $i] :
( ( kpair @ X0 @ X1 )
= ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) )
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
! [X0: $i,X1: $i] :
( ( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) )
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) ) )
= ( kpair @ X0 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f121]) ).
thf(f121,plain,
! [X0: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) )
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) )
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f110,f119]) ).
thf(f119,plain,
! [X0: $i,X1: $i] :
( ( in
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) )
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) )
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f108,f117]) ).
thf(f117,plain,
! [X0: $i,X1: $i] :
( ( singleton
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
! [X0: $i,X1: $i] :
( ( ( singleton
@ ( dsetconstr @ ( setunion @ ( kpair @ X0 @ X1 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ X0 @ X1 ) ) @ Y0 )
= ( kpair @ X0 @ X1 ) ) ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f107,f112]) ).
thf(f112,plain,
! [X2: $i,X3: $i] :
( ( iskpair @ ( kpair @ X3 @ X2 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X2: $i,X3: $i] :
( ( ( iskpair @ ( kpair @ X3 @ X2 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f64,f77]) ).
thf(f77,plain,
kpairp = $true,
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f60,plain,
( ( sK12
!= ( ksnd @ ( kpair @ sK11 @ sK12 ) ) )
& ( ksndsingleton = $true )
& ( dsetconstrER = $true )
& ( setukpairinjR = $true )
& ( kpairp = $true )
& ( theprop = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f34,f59]) ).
thf(f59,plain,
( ? [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
!= X1 )
=> ( sK12
!= ( ksnd @ ( kpair @ sK11 @ sK12 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
!= X1 )
& ( ksndsingleton = $true )
& ( dsetconstrER = $true )
& ( setukpairinjR = $true )
& ( kpairp = $true )
& ( theprop = $true ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
( ? [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
!= X1 )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( theprop = $true )
& ( kpairp = $true )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
~ ( ( dsetconstrER = $true )
=> ( ( kpairp = $true )
=> ( ( theprop = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f31]) ).
thf(f31,plain,
~ ( dsetconstrER
=> ( kpairp
=> ( theprop
=> ( setukpairinjR
=> ( ksndsingleton
=> ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,negated_conjecture,
~ ( dsetconstrER
=> ( kpairp
=> ( theprop
=> ( setukpairinjR
=> ( ksndsingleton
=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f10,conjecture,
( dsetconstrER
=> ( kpairp
=> ( theprop
=> ( setukpairinjR
=> ( ksndsingleton
=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',ksndpairEq) ).
thf(f64,plain,
! [X2: $i,X3: $i] :
( ( ( iskpair @ ( kpair @ X3 @ X2 ) )
= $true )
| ( kpairp != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( kpairp = $true )
| ( $true
!= ( iskpair @ ( kpair @ sK2 @ sK1 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( iskpair @ ( kpair @ X3 @ X2 ) )
= $true )
| ( kpairp != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f44,f45]) ).
thf(f45,plain,
( ? [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X1 @ X0 ) )
!= $true )
=> ( $true
!= ( iskpair @ ( kpair @ sK2 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ( ( kpairp = $true )
| ? [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X1 @ X0 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( iskpair @ ( kpair @ X3 @ X2 ) )
= $true )
| ( kpairp != $true ) ) ),
inference(rectify,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( kpairp = $true )
| ? [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X1 @ X0 ) )
!= $true ) )
& ( ! [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X1 @ X0 ) )
= $true )
| ( kpairp != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( kpairp = $true )
<=> ! [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X1 @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X1 @ X0 ) )
= kpairp ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: $i,X2: $i] :
( ( iskpair @ ( kpair @ X2 @ X3 ) )
= kpairp ),
file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',kpairp) ).
thf(f107,plain,
! [X1: $i] :
( ( ( iskpair @ X1 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X1 ) @ Y0 )
= X1 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X1: $i] :
( ( $true != $true )
| ( ( iskpair @ X1 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X1 ) @ Y0 )
= X1 ) ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f66,f80]) ).
thf(f80,plain,
ksndsingleton = $true,
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f66,plain,
! [X1: $i] :
( ( ( iskpair @ X1 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X1 ) @ Y0 )
= X1 ) ) )
= $true )
| ( ksndsingleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( ksndsingleton = $true )
| ( ( ( iskpair @ sK3 )
= $true )
& ( ( singleton
@ ( dsetconstr @ ( setunion @ sK3 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ sK3 ) @ Y0 )
= sK3 ) ) )
!= $true ) ) )
& ( ! [X1: $i] :
( ( ( iskpair @ X1 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X1 ) @ Y0 )
= X1 ) ) )
= $true ) )
| ( ksndsingleton != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f48,f49]) ).
thf(f49,plain,
( ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X0 ) @ Y0 )
= X0 ) ) )
!= $true ) )
=> ( ( ( iskpair @ sK3 )
= $true )
& ( ( singleton
@ ( dsetconstr @ ( setunion @ sK3 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ sK3 ) @ Y0 )
= sK3 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f48,plain,
( ( ( ksndsingleton = $true )
| ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X0 ) @ Y0 )
= X0 ) ) )
!= $true ) ) )
& ( ! [X1: $i] :
( ( ( iskpair @ X1 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X1 ) @ Y0 )
= X1 ) ) )
= $true ) )
| ( ksndsingleton != $true ) ) ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( ksndsingleton = $true )
| ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X0 ) @ Y0 )
= X0 ) ) )
!= $true ) ) )
& ( ! [X0: $i] :
( ( ( iskpair @ X0 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X0 ) @ Y0 )
= X0 ) ) )
= $true ) )
| ( ksndsingleton != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ksndsingleton = $true )
<=> ! [X0: $i] :
( ( ( iskpair @ X0 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X0 ) @ Y0 )
= X0 ) ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ksndsingleton = $true )
<=> ! [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
=> ( ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ X0 ) @ Y0 )
= X0 ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i] :
( ( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] :
( ( kpair @ ( kfst @ X0 ) @ X1 )
= X0 ) ) ) )
= ksndsingleton ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X6: $i] :
( ( ( iskpair @ X6 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X6 )
@ ^ [X2: $i] :
( ( kpair @ ( kfst @ X6 ) @ X2 )
= X6 ) ) ) )
= ksndsingleton ),
file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',ksndsingleton) ).
thf(f108,plain,
! [X0: $i] :
( ( ( singleton @ X0 )
!= $true )
| ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( singleton @ X0 )
!= $true )
| ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f63,f76]) ).
thf(f76,plain,
theprop = $true,
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f63,plain,
! [X0: $i] :
( ( ( singleton @ X0 )
!= $true )
| ( ( in @ ( setunion @ X0 ) @ X0 )
= $true )
| ( theprop != $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ! [X0: $i] :
( ( ( singleton @ X0 )
!= $true )
| ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) )
| ( theprop != $true ) )
& ( ( theprop = $true )
| ( ( $true
= ( singleton @ sK0 ) )
& ( $true
!= ( in @ ( setunion @ sK0 ) @ sK0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f40,f41]) ).
thf(f41,plain,
( ? [X1: $i] :
( ( ( singleton @ X1 )
= $true )
& ( ( in @ ( setunion @ X1 ) @ X1 )
!= $true ) )
=> ( ( $true
= ( singleton @ sK0 ) )
& ( $true
!= ( in @ ( setunion @ sK0 ) @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ( ! [X0: $i] :
( ( ( singleton @ X0 )
!= $true )
| ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) )
| ( theprop != $true ) )
& ( ( theprop = $true )
| ? [X1: $i] :
( ( ( singleton @ X1 )
= $true )
& ( ( in @ ( setunion @ X1 ) @ X1 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ! [X0: $i] :
( ( ( singleton @ X0 )
!= $true )
| ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) )
| ( theprop != $true ) )
& ( ( theprop = $true )
| ? [X0: $i] :
( ( ( singleton @ X0 )
= $true )
& ( ( in @ ( setunion @ X0 ) @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ! [X0: $i] :
( ( ( singleton @ X0 )
!= $true )
| ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) )
<=> ( theprop = $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i] :
( ( ( singleton @ X0 )
= $true )
=> ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) )
<=> ( theprop = $true ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) )
= theprop ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X4: $i] :
( ( ( singleton @ X4 )
=> ( in @ ( setunion @ X4 ) @ X4 ) )
= theprop ),
file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',theprop) ).
thf(f110,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X0 @ ( dsetconstr @ X2 @ X1 ) )
!= $true )
| ( ( X1 @ X0 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f109]) ).
thf(f109,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( X1 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( ( X1 @ X0 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f72,f79]) ).
thf(f79,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f72,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( X1 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( ( sK5 @ sK4 )
!= $true )
& ( ( in @ sK4
@ ( dsetconstr @ sK6
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f52,f53]) ).
thf(f53,plain,
( ? [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X3 )
!= $true )
& ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
= $true ) )
=> ( ( ( sK5 @ sK4 )
!= $true )
& ( ( in @ sK4
@ ( dsetconstr @ sK6
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f52,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X3 )
!= $true )
& ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X0 )
!= $true )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
=> ( ( X1 @ X0 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X0 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X1: $i > $o,X0: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',dsetconstrER) ).
thf(f113,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X2 @ X1 ) )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true != $true )
| ( ( kpair @ X3 @ X0 )
!= ( kpair @ X2 @ X1 ) ) ),
inference(definition_unfolding,[status(thm)],[f75,f78]) ).
thf(f78,plain,
setukpairinjR = $true,
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f75,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X2 @ X1 ) )
| ( X0 = X1 )
| ( setukpairinjR != $true ) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X2 @ X1 ) )
| ( X0 = X1 ) )
| ( setukpairinjR != $true ) )
& ( ( setukpairinjR = $true )
| ( ( ( kpair @ sK9 @ sK8 )
= ( kpair @ sK10 @ sK7 ) )
& ( sK8 != sK7 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f56,f57]) ).
thf(f57,plain,
( ? [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( kpair @ X6 @ X5 )
= ( kpair @ X7 @ X4 ) )
& ( X4 != X5 ) )
=> ( ( ( kpair @ sK9 @ sK8 )
= ( kpair @ sK10 @ sK7 ) )
& ( sK8 != sK7 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f56,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X2 @ X1 ) )
| ( X0 = X1 ) )
| ( setukpairinjR != $true ) )
& ( ( setukpairinjR = $true )
| ? [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( kpair @ X6 @ X5 )
= ( kpair @ X7 @ X4 ) )
& ( X4 != X5 ) ) ) ),
inference(rectify,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X2 @ X1 ) )
| ( X0 = X1 ) )
| ( setukpairinjR != $true ) )
& ( ( setukpairinjR = $true )
| ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
= ( kpair @ X2 @ X1 ) )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
!= ( kpair @ X2 @ X1 ) )
| ( X0 = X1 ) )
<=> ( setukpairinjR = $true ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
= ( kpair @ X2 @ X1 ) )
=> ( X0 = X1 ) )
<=> ( setukpairinjR = $true ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( setukpairinjR
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X3 @ X0 )
= ( kpair @ X2 @ X1 ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( setukpairinjR
= ( ! [X6: $i,X3: $i,X2: $i,X5: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X5 @ X6 ) )
=> ( X3 = X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',setukpairinjR) ).
thf(f111,plain,
( ( sP17
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( kpair @ sK11 @ sK12 ) )
@ ^ [Y0: $i] :
( ( kpair @ ( kfst @ ( kpair @ sK11 @ sK12 ) ) @ Y0 )
= ( kpair @ sK11 @ sK12 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
= ( sP17
@ ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( kpair @ ( kfst @ Y0 ) @ Y1 )
= Y0 ) ) )
@ ( kpair @ sK11 @ sK12 ) ) ) ),
introduced(definition,[new_symbols(naming,[sP17])],[inequality_splitting_name_introduction]) ).
thf(f106,plain,
( ( sP17 @ sK12 )
= $true ),
inference(inequality_splitting,[status(thm)],[f96,f105]) ).
thf(f96,plain,
( sK12
!= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( kpair @ ( kfst @ Y0 ) @ Y1 )
= Y0 ) ) )
@ ( kpair @ sK11 @ sK12 ) ) ),
inference(definition_unfolding,[status(thm)],[f81,f69]) ).
thf(f69,plain,
( ksnd
= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( kpair @ ( kfst @ Y0 ) @ Y1 )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ksnd
= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( kpair @ ( kfst @ Y0 ) @ Y1 )
= Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f29]) ).
thf(f29,plain,
( ksnd
= ( ^ [X0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] :
( ( kpair @ ( kfst @ X0 ) @ X1 )
= X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
( ksnd
= ( ^ [X6: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X6 )
@ ^ [X2: $i] :
( ( kpair @ ( kfst @ X6 ) @ X2 )
= X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',ksnd) ).
thf(f81,plain,
( sK12
!= ( ksnd @ ( kpair @ sK11 @ sK12 ) ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU656^2 : 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
% 0.16/0.34 % Computer : n005.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:29:29 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEU656^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : Ordered Pairs - Properties of Pairs
% 0.28/0.47 % Version : Especial > Reduced > Especial.
% 0.28/0.47 % English : (! x:i.! y:i.ksnd (kpair x y) = y)
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.47 % Source : [Bro08]
% 0.28/0.47 % Names : ZFC158l [Bro08]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 25 ( 9 unt; 15 typ; 9 def)
% 0.28/0.47 % Number of atoms : 37 ( 16 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 6 ( 3 avg)
% 0.28/0.47 % Number of connectives : 77 ( 0 ~; 0 |; 3 &; 65 @)
% 0.28/0.47 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 8 ( 2 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 16 ( 15 usr; 6 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 24 ( 8 ^; 13 !; 3 ?; 24 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : http://mathgate.info/detsetitem.php?id=213
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(in_type,type,
% 0.28/0.47 in: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset_type,type,
% 0.28/0.47 emptyset: $i ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin_type,type,
% 0.28/0.47 setadjoin: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setunion_type,type,
% 0.28/0.47 setunion: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr_type,type,
% 0.28/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER_type,type,
% 0.28/0.47 dsetconstrER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER,definition,
% 0.28/0.47 ( dsetconstrER
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iskpair_type,type,
% 0.28/0.47 iskpair: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(iskpair,definition,
% 0.28/0.47 ( iskpair
% 0.28/0.47 = ( ^ [A: $i] :
% 0.28/0.47 ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 & ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setunion @ A ) )
% 0.28/0.47 & ( A
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpair_type,type,
% 0.28/0.47 kpair: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(kpair,definition,
% 0.28/0.47 ( kpair
% 0.28/0.47 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpairp_type,type,
% 0.28/0.47 kpairp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairp,definition,
% 0.28/0.47 ( kpairp
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singleton_type,type,
% 0.28/0.47 singleton: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(singleton,definition,
% 0.28/0.47 ( singleton
% 0.28/0.47 = ( ^ [A: $i] :
% 0.28/0.47 ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( A
% 0.28/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(theprop_type,type,
% 0.28/0.47 theprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(theprop,definition,
% 0.28/0.47 ( theprop
% 0.28/0.47 = ( ! [X: $i] :
% 0.28/0.47 ( ( singleton @ X )
% 0.28/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kfst_type,type,
% 0.28/0.47 kfst: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR_type,type,
% 0.28/0.47 setukpairinjR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR,definition,
% 0.28/0.47 ( setukpairinjR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.28/0.47 = ( kpair @ Xz @ Xu ) )
% 0.28/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ksndsingleton_type,type,
% 0.28/0.47 ksndsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ksndsingleton,definition,
% 0.28/0.47 ( ksndsingleton
% 0.28/0.47 = ( ! [Xu: $i] :
% 0.28/0.47 ( ( iskpair @ Xu )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.28/0.47 @ ^ [Xx: $i] :
% 0.28/0.47 ( Xu
% 0.28/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ksnd_type,type,
% 0.28/0.47 ksnd: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(ksnd,definition,
% 0.28/0.47 ( ksnd
% 0.28/0.47 = ( ^ [Xu: $i] :
% 0.28/0.47 ( setunion
% 0.28/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.28/0.47 @ ^ [Xx: $i] :
% 0.28/0.47 ( Xu
% 0.28/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ksndpairEq,conjecture,
% 0.28/0.47 ( dsetconstrER
% 0.28/0.47 => ( kpairp
% 0.28/0.47 => ( theprop
% 0.28/0.47 => ( setukpairinjR
% 0.28/0.47 => ( ksndsingleton
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.28/0.47 = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.62/1.39 ---- Embedded in THF ---
% 1.62/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.39 %%% Generated on Tue Feb 24 12:29:30 EST 2026
% 1.62/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.39 %%% Logic specification used:
% 1.62/1.39 %%% thf(spec, logic, $$dhol).
% 1.62/1.39
% 1.62/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2DTF7961.p
% See solution above
% 1.62/1.39 ------------------------
% 1.62/1.40 ---- Cleaned THF ---
% 1.62/1.40 thf(in_type,type,
% 1.62/1.40 in: $i > $i > $o ).
% 1.62/1.40
% 1.62/1.40 thf(emptyset_type,type,
% 1.62/1.40 emptyset: $i ).
% 1.62/1.40
% 1.62/1.40 thf(setadjoin_type,type,
% 1.62/1.40 setadjoin: $i > $i > $i ).
% 1.62/1.40
% 1.62/1.40 thf(setunion_type,type,
% 1.62/1.40 setunion: $i > $i ).
% 1.62/1.40
% 1.62/1.40 thf(dsetconstr_type,type,
% 1.62/1.40 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.62/1.40
% 1.62/1.40 thf(dsetconstrER_type,type,
% 1.62/1.40 dsetconstrER: $o ).
% 1.62/1.40
% 1.62/1.40 thf(dsetconstrER,definition,
% 1.62/1.40 ( dsetconstrER
% 1.62/1.40 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.62/1.40 ( ( in @ Xx
% 1.62/1.40 @ ( dsetconstr @ A
% 1.62/1.40 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.62/1.40 => ( Xphi @ Xx ) ) ) ) ).
% 1.62/1.40
% 1.62/1.40 thf(iskpair_type,type,
% 1.62/1.40 iskpair: $i > $o ).
% 1.62/1.40
% 1.62/1.40 thf(iskpair,definition,
% 1.62/1.40 ( iskpair
% 1.62/1.40 = ( ^ [A: $i] :
% 1.62/1.40 ? [Xx: $i] :
% 1.62/1.40 ( ( in @ Xx @ ( setunion @ A ) )
% 1.62/1.40 & ? [Xy: $i] :
% 1.62/1.40 ( ( in @ Xy @ ( setunion @ A ) )
% 1.62/1.40 & ( A
% 1.62/1.40 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 1.62/1.40
% 1.62/1.40 thf(kpair_type,type,
% 1.62/1.40 kpair: $i > $i > $i ).
% 1.62/1.40
% 1.62/1.40 thf(kpair,definition,
% 1.82/1.40 ( kpair
% 1.82/1.40 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 1.82/1.40
% 1.82/1.40 thf(kpairp_type,type,
% 1.82/1.40 kpairp: $o ).
% 1.82/1.40
% 1.82/1.40 thf(kpairp,definition,
% 1.82/1.40 ( kpairp
% 1.82/1.40 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 1.82/1.40
% 1.82/1.40 thf(singleton_type,type,
% 1.82/1.40 singleton: $i > $o ).
% 1.82/1.40
% 1.82/1.40 thf(singleton,definition,
% 1.82/1.40 ( singleton
% 1.82/1.40 = ( ^ [A: $i] :
% 1.82/1.40 ? [Xx: $i] :
% 1.82/1.40 ( ( in @ Xx @ A )
% 1.82/1.40 & ( A
% 1.82/1.40 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.82/1.40
% 1.82/1.40 thf(theprop_type,type,
% 1.82/1.40 theprop: $o ).
% 1.82/1.40
% 1.82/1.40 thf(theprop,definition,
% 1.82/1.40 ( theprop
% 1.82/1.40 = ( ! [X: $i] :
% 1.82/1.40 ( ( singleton @ X )
% 1.82/1.40 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 1.82/1.40
% 1.82/1.40 thf(kfst_type,type,
% 1.82/1.40 kfst: $i > $i ).
% 1.82/1.40
% 1.82/1.40 thf(setukpairinjR_type,type,
% 1.82/1.40 setukpairinjR: $o ).
% 1.82/1.40
% 1.82/1.40 thf(setukpairinjR,definition,
% 1.82/1.40 ( setukpairinjR
% 1.82/1.40 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 1.82/1.40 ( ( ( kpair @ Xx @ Xy )
% 1.82/1.40 = ( kpair @ Xz @ Xu ) )
% 1.82/1.40 => ( Xy = Xu ) ) ) ) ).
% 1.82/1.40
% 1.82/1.40 thf(ksndsingleton_type,type,
% 1.82/1.40 ksndsingleton: $o ).
% 1.82/1.40
% 1.82/1.40 thf(ksndsingleton,definition,
% 1.82/1.40 ( ksndsingleton
% 1.82/1.40 = ( ! [Xu: $i] :
% 1.82/1.40 ( ( iskpair @ Xu )
% 1.82/1.40 => ( singleton
% 1.82/1.40 @ ( dsetconstr @ ( setunion @ Xu )
% 1.82/1.40 @ ^ [Xx: $i] :
% 1.82/1.40 ( Xu
% 1.82/1.40 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 1.82/1.40
% 1.82/1.40 thf(ksnd_type,type,
% 1.82/1.40 ksnd: $i > $i ).
% 1.82/1.40
% 1.82/1.40 thf(ksnd,definition,
% 1.82/1.40 ( ksnd
% 1.82/1.40 = ( ^ [Xu: $i] :
% 1.82/1.40 ( setunion
% 1.82/1.40 @ ( dsetconstr @ ( setunion @ Xu )
% 1.82/1.40 @ ^ [Xx: $i] :
% 1.82/1.40 ( Xu
% 1.82/1.40 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ).
% 1.82/1.40
% 1.82/1.40 thf(ksndpairEq,conjecture,
% 1.82/1.40 ( dsetconstrER
% 1.82/1.40 => ( kpairp
% 1.82/1.40 => ( theprop
% 1.82/1.40 => ( setukpairinjR
% 1.82/1.40 => ( ksndsingleton
% 1.82/1.40 => ! [Xx: $i,Xy: $i] :
% 1.82/1.40 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 1.82/1.40 = Xy ) ) ) ) ) ) ).
% 1.82/1.40 ------------------------
% 1.82/1.41 % (8152)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_7961 for (2999ds/4Mi)
% 1.82/1.41 % (8151)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/183Mi)
% 1.82/1.41 % (8152)Instruction limit reached!
% 1.82/1.41 % (8152)------------------------------
% 1.82/1.41 % (8152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.41 % (8152)Termination reason: Unknown
% 1.82/1.41 % (8152)Termination phase: Saturation
% 1.82/1.41
% 1.82/1.41 % (8152)Memory used [KB]: 5500
% 1.82/1.41 % (8152)Time elapsed: 0.003 s
% 1.82/1.41 % (8152)Instructions burned: 6 (million)
% 1.82/1.41 % (8152)------------------------------
% 1.82/1.41 % (8152)------------------------------
% 1.82/1.42 % (8154)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/2Mi)
% 1.82/1.42 % (8154)Instruction limit reached!
% 1.82/1.42 % (8154)------------------------------
% 1.82/1.42 % (8154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.42 % (8154)Termination reason: Unknown
% 1.82/1.42 % (8154)Termination phase: shuffling
% 1.82/1.42
% 1.82/1.42 % (8154)Memory used [KB]: 1023
% 1.82/1.42 % (8154)Time elapsed: 0.003 s
% 1.82/1.42 % (8154)Instructions burned: 2 (million)
% 1.82/1.42 % (8154)------------------------------
% 1.82/1.42 % (8154)------------------------------
% 1.82/1.42 % (8156)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_7961 for (2999ds/275Mi)
% 1.82/1.42 % (8153)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_7961 for (2999ds/27Mi)
% 1.82/1.42 % (8155)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_7961 for (2999ds/2Mi)
% 1.82/1.42 % (8155)Instruction limit reached!
% 1.82/1.42 % (8155)------------------------------
% 1.82/1.42 % (8155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.42 % (8155)Termination reason: Unknown
% 1.82/1.42 % (8155)Termination phase: Property scanning
% 1.82/1.42
% 1.82/1.42 % (8155)Memory used [KB]: 1023
% 1.82/1.42 % (8155)Time elapsed: 0.003 s
% 1.82/1.42 % (8155)Instructions burned: 3 (million)
% 1.82/1.42 % (8155)------------------------------
% 1.82/1.42 % (8155)------------------------------
% 1.82/1.42 % (8157)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/18Mi)
% 1.82/1.42 % (8158)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/3Mi)
% 1.82/1.42 % (8156)Refutation not found, incomplete strategy
% 1.82/1.42 % (8156)------------------------------
% 1.82/1.42 % (8156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.42 % (8156)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.42
% 1.82/1.42
% 1.82/1.42 % (8156)Memory used [KB]: 5628
% 1.82/1.42 % (8156)Time elapsed: 0.006 s
% 1.82/1.42 % (8156)Instructions burned: 8 (million)
% 1.82/1.42 % (8156)------------------------------
% 1.82/1.42 % (8156)------------------------------
% 1.82/1.42 % (8158)Instruction limit reached!
% 1.82/1.42 % (8158)------------------------------
% 1.82/1.42 % (8158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.42 % (8158)Termination reason: Unknown
% 1.82/1.42 % (8158)Termination phase: Function definition elimination
% 1.82/1.42
% 1.82/1.42 % (8158)Memory used [KB]: 1023
% 1.82/1.42 % (8158)Time elapsed: 0.003 s
% 1.82/1.42 % (8158)Instructions burned: 4 (million)
% 1.82/1.42 % (8158)------------------------------
% 1.82/1.42 % (8158)------------------------------
% 1.82/1.43 % (8157)Instruction limit reached!
% 1.82/1.43 % (8157)------------------------------
% 1.82/1.43 % (8157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.43 % (8157)Termination reason: Unknown
% 1.82/1.43 % (8157)Termination phase: Saturation
% 1.82/1.43
% 1.82/1.43 % (8157)Memory used [KB]: 5628
% 1.82/1.43 % (8157)Time elapsed: 0.007 s
% 1.82/1.43 % (8157)Instructions burned: 18 (million)
% 1.82/1.43 % (8157)------------------------------
% 1.82/1.43 % (8157)------------------------------
% 1.82/1.43 % (8161)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/3Mi)
% 1.82/1.44 % (8161)Instruction limit reached!
% 1.82/1.44 % (8161)------------------------------
% 1.82/1.44 % (8161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.44 % (8161)Termination reason: Unknown
% 1.82/1.44 % (8161)Termination phase: Function definition elimination
% 1.82/1.44
% 1.82/1.44 % (8161)Memory used [KB]: 1023
% 1.82/1.44 % (8161)Time elapsed: 0.003 s
% 1.82/1.44 % (8161)Instructions burned: 4 (million)
% 1.82/1.44 % (8161)------------------------------
% 1.82/1.44 % (8161)------------------------------
% 1.82/1.44 % (8159)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/37Mi)
% 1.82/1.44 % (8160)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/15Mi)
% 1.82/1.44 % (8163)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/7Mi)
% 1.82/1.44 % (8153)Instruction limit reached!
% 1.82/1.44 % (8153)------------------------------
% 1.82/1.44 % (8153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.44 % (8153)Termination reason: Unknown
% 1.82/1.44 % (8153)Termination phase: Saturation
% 1.82/1.44
% 1.82/1.44 % (8153)Memory used [KB]: 5756
% 1.82/1.44 % (8153)Time elapsed: 0.023 s
% 1.82/1.44 % (8153)Instructions burned: 28 (million)
% 1.82/1.44 % (8153)------------------------------
% 1.82/1.44 % (8153)------------------------------
% 1.82/1.44 % (8163)Instruction limit reached!
% 1.82/1.44 % (8163)------------------------------
% 1.82/1.44 % (8163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.44 % (8163)Termination reason: Unknown
% 1.82/1.44 % (8163)Termination phase: Saturation
% 1.82/1.44
% 1.82/1.44 % (8163)Memory used [KB]: 1023
% 1.82/1.44 % (8163)Time elapsed: 0.004 s
% 1.82/1.44 % (8163)Instructions burned: 7 (million)
% 1.82/1.44 % (8163)------------------------------
% 1.82/1.44 % (8163)------------------------------
% 1.82/1.44 % (8162)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/1041Mi)
% 1.82/1.45 % (8160)Instruction limit reached!
% 1.82/1.45 % (8160)------------------------------
% 1.82/1.45 % (8160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.45 % (8160)Termination reason: Unknown
% 1.82/1.45 % (8160)Termination phase: Saturation
% 1.82/1.45
% 1.82/1.45 % (8160)Memory used [KB]: 5628
% 1.82/1.45 % (8160)Time elapsed: 0.010 s
% 1.82/1.45 % (8160)Instructions burned: 16 (million)
% 1.82/1.45 % (8160)------------------------------
% 1.82/1.45 % (8160)------------------------------
% 1.82/1.45 % (8164)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/16Mi)
% 1.82/1.45 % (8166)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/3Mi)
% 1.82/1.45 % (8164)Instruction limit reached!
% 1.82/1.45 % (8164)------------------------------
% 1.82/1.45 % (8164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.45 % (8164)Termination reason: Unknown
% 1.82/1.45 % (8164)Termination phase: Saturation
% 1.82/1.45
% 1.82/1.45 % (8164)Memory used [KB]: 5884
% 1.82/1.45 % (8164)Time elapsed: 0.008 s
% 1.82/1.45 % (8164)Instructions burned: 17 (million)
% 1.82/1.45 % (8164)------------------------------
% 1.82/1.45 % (8164)------------------------------
% 1.82/1.45 % (8166)Instruction limit reached!
% 1.82/1.45 % (8166)------------------------------
% 1.82/1.45 % (8166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.45 % (8166)Termination reason: Unknown
% 1.82/1.45 % (8166)Termination phase: Property scanning
% 1.82/1.45
% 1.82/1.45 % (8166)Memory used [KB]: 1023
% 1.82/1.45 % (8166)Time elapsed: 0.003 s
% 1.82/1.45 % (8166)Instructions burned: 4 (million)
% 1.82/1.45 % (8166)------------------------------
% 1.82/1.45 % (8166)------------------------------
% 1.82/1.46 % (8159)Instruction limit reached!
% 1.82/1.46 % (8159)------------------------------
% 1.82/1.46 % (8159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.46 % (8159)Termination reason: Unknown
% 1.82/1.46 % (8159)Termination phase: Saturation
% 1.82/1.46
% 1.82/1.46 % (8159)Memory used [KB]: 5628
% 1.82/1.46 % (8159)Time elapsed: 0.022 s
% 1.82/1.46 % (8159)Instructions burned: 37 (million)
% 1.82/1.46 % (8159)------------------------------
% 1.82/1.46 % (8159)------------------------------
% 1.82/1.46 % (8165)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/3Mi)
% 1.82/1.46 % (8165)Instruction limit reached!
% 1.82/1.46 % (8165)------------------------------
% 1.82/1.46 % (8165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.46 % (8167)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/7Mi)
% 1.82/1.46 % (8165)Termination reason: Unknown
% 1.82/1.46 % (8165)Termination phase: Property scanning
% 1.82/1.46
% 1.82/1.46 % (8165)Memory used [KB]: 1023
% 1.82/1.46 % (8165)Time elapsed: 0.005 s
% 1.82/1.46 % (8165)Instructions burned: 3 (million)
% 1.82/1.46 % (8168)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/3Mi)
% 1.82/1.46 % (8165)------------------------------
% 1.82/1.46 % (8165)------------------------------
% 1.82/1.46 % (8169)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/4Mi)
% 1.82/1.46 % (8168)Instruction limit reached!
% 1.82/1.46 % (8168)------------------------------
% 1.82/1.46 % (8168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.46 % (8168)Termination reason: Unknown
% 1.82/1.46 % (8168)Termination phase: Property scanning
% 1.82/1.46
% 1.82/1.46 % (8168)Memory used [KB]: 1023
% 1.82/1.46 % (8168)Time elapsed: 0.003 s
% 1.82/1.46 % (8168)Instructions burned: 5 (million)
% 1.82/1.46 % (8168)------------------------------
% 1.82/1.46 % (8168)------------------------------
% 1.82/1.46 % (8169)Instruction limit reached!
% 1.82/1.46 % (8169)------------------------------
% 1.82/1.46 % (8169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.46 % (8169)Termination reason: Unknown
% 1.82/1.46 % (8169)Termination phase: Function definition elimination
% 1.82/1.46
% 1.82/1.46 % (8169)Memory used [KB]: 1023
% 1.82/1.46 % (8169)Time elapsed: 0.003 s
% 1.82/1.46 % (8169)Instructions burned: 4 (million)
% 1.82/1.46 % (8169)------------------------------
% 1.82/1.46 % (8169)------------------------------
% 1.82/1.47 % (8167)Instruction limit reached!
% 1.82/1.47 % (8167)------------------------------
% 1.82/1.47 % (8167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.47 % (8167)Termination reason: Unknown
% 1.82/1.47 % (8167)Termination phase: Saturation
% 1.82/1.47
% 1.82/1.47 % (8167)Memory used [KB]: 5500
% 1.82/1.47 % (8167)Time elapsed: 0.005 s
% 1.82/1.47 % (8167)Instructions burned: 7 (million)
% 1.82/1.47 % (8167)------------------------------
% 1.82/1.47 % (8167)------------------------------
% 1.82/1.47 % (8151)Instruction limit reached!
% 1.82/1.47 % (8151)------------------------------
% 1.82/1.47 % (8151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.47 % (8151)Termination reason: Unknown
% 1.82/1.47 % (8151)Termination phase: Saturation
% 1.82/1.47
% 1.82/1.47 % (8151)Memory used [KB]: 6396
% 1.82/1.47 % (8151)Time elapsed: 0.059 s
% 1.82/1.47 % (8151)Instructions burned: 185 (million)
% 1.82/1.47 % (8151)------------------------------
% 1.82/1.47 % (8151)------------------------------
% 1.82/1.47 % (8170)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/18Mi)
% 1.82/1.47 % (8172)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/6Mi)
% 1.82/1.47 % (8173)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/902Mi)
% 1.82/1.48 % (8172)Instruction limit reached!
% 1.82/1.48 % (8172)------------------------------
% 1.82/1.48 % (8172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.48 % (8172)Termination reason: Unknown
% 1.82/1.48 % (8172)Termination phase: Saturation
% 1.82/1.48
% 1.82/1.48 % (8172)Memory used [KB]: 5500
% 1.82/1.48 % (8172)Time elapsed: 0.004 s
% 1.82/1.48 % (8172)Instructions burned: 7 (million)
% 1.82/1.48 % (8172)------------------------------
% 1.82/1.48 % (8172)------------------------------
% 1.82/1.48 % (8173)Refutation not found, incomplete strategy
% 1.82/1.48 % (8173)------------------------------
% 1.82/1.48 % (8173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.48 % (8173)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.48
% 1.82/1.48
% 1.82/1.48 % (8173)Memory used [KB]: 5500
% 1.82/1.48 % (8173)Time elapsed: 0.026 s
% 1.82/1.48 % (8173)Instructions burned: 4 (million)
% 1.82/1.48 % (8173)------------------------------
% 1.82/1.48 % (8173)------------------------------
% 1.82/1.48 % (8175)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/5Mi)
% 1.82/1.48 % (8170)Instruction limit reached!
% 1.82/1.48 % (8170)------------------------------
% 1.82/1.48 % (8170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.48 % (8170)Termination reason: Unknown
% 1.82/1.48 % (8170)Termination phase: Saturation
% 1.82/1.48
% 1.82/1.48 % (8170)Memory used [KB]: 5628
% 1.82/1.48 % (8170)Time elapsed: 0.009 s
% 1.82/1.48 % (8170)Instructions burned: 18 (million)
% 1.82/1.48 % (8170)------------------------------
% 1.82/1.48 % (8170)------------------------------
% 1.82/1.48 % (8174)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/21Mi)
% 1.82/1.48 % (8175)Instruction limit reached!
% 1.82/1.48 % (8175)------------------------------
% 1.82/1.48 % (8175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.48 % (8175)Termination reason: Unknown
% 1.82/1.48 % (8175)Termination phase: Saturation
% 1.82/1.48
% 1.82/1.48 % (8175)Memory used [KB]: 5500
% 1.82/1.48 % (8175)Time elapsed: 0.003 s
% 1.82/1.48 % (8175)Instructions burned: 6 (million)
% 1.82/1.48 % (8175)------------------------------
% 1.82/1.48 % (8175)------------------------------
% 1.82/1.49 % (8176)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/6Mi)
% 1.82/1.49 % (8177)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/377Mi)
% 1.82/1.49 % (8171)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/710Mi)
% 1.82/1.49 % (8176)Instruction limit reached!
% 1.82/1.49 % (8176)------------------------------
% 1.82/1.49 % (8176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.49 % (8176)Termination reason: Unknown
% 1.82/1.49 % (8176)Termination phase: Saturation
% 1.82/1.49
% 1.82/1.49 % (8176)Memory used [KB]: 5500
% 1.82/1.49 % (8176)Time elapsed: 0.004 s
% 1.82/1.49 % (8176)Instructions burned: 7 (million)
% 1.82/1.49 % (8176)------------------------------
% 1.82/1.49 % (8176)------------------------------
% 1.82/1.49 % (8174)Instruction limit reached!
% 1.82/1.49 % (8174)------------------------------
% 1.82/1.49 % (8174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.49 % (8174)Termination reason: Unknown
% 1.82/1.49 % (8174)Termination phase: Saturation
% 1.82/1.49
% 1.82/1.49 % (8174)Memory used [KB]: 5628
% 1.82/1.49 % (8174)Time elapsed: 0.009 s
% 1.82/1.49 % (8174)Instructions burned: 24 (million)
% 1.82/1.49 % (8174)------------------------------
% 1.82/1.49 % (8174)------------------------------
% 1.82/1.49 % (8179)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/19Mi)
% 1.82/1.49 % (8178)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/779Mi)
% 1.82/1.50 % (8179)Refutation not found, incomplete strategy
% 1.82/1.50 % (8179)------------------------------
% 1.82/1.50 % (8179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.50 % (8179)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.50
% 1.82/1.50
% 1.82/1.50 % (8179)Memory used [KB]: 5628
% 1.82/1.50 % (8179)Time elapsed: 0.006 s
% 1.82/1.50 % (8179)Instructions burned: 12 (million)
% 1.82/1.50 % (8179)------------------------------
% 1.82/1.50 % (8179)------------------------------
% 1.82/1.50 % (8181)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/17Mi)
% 1.82/1.50 % (8180)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/879Mi)
% 1.82/1.50 % (8181)Instruction limit reached!
% 1.82/1.50 % (8181)------------------------------
% 1.82/1.50 % (8181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.50 % (8181)Termination reason: Unknown
% 1.82/1.50 % (8181)Termination phase: Saturation
% 1.82/1.50
% 1.82/1.50 % (8181)Memory used [KB]: 5756
% 1.82/1.50 % (8181)Time elapsed: 0.006 s
% 1.82/1.50 % (8181)Instructions burned: 17 (million)
% 1.82/1.50 % (8181)------------------------------
% 1.82/1.50 % (8181)------------------------------
% 1.82/1.51 % (8182)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7961 for (2999ds/3Mi)
% 1.82/1.51 % (8182)Instruction limit reached!
% 1.82/1.51 % (8182)------------------------------
% 1.82/1.51 % (8182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.51 % (8182)Termination reason: Unknown
% 1.82/1.51 % (8182)Termination phase: Function definition elimination
% 1.82/1.51
% 1.82/1.51 % (8182)Memory used [KB]: 1023
% 1.82/1.51 % (8182)Time elapsed: 0.003 s
% 1.82/1.51 % (8182)Instructions burned: 4 (million)
% 1.82/1.51 % (8182)------------------------------
% 1.82/1.51 % (8182)------------------------------
% 1.82/1.51 % (8183)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7961 for (2998ds/30Mi)
% 1.82/1.52 % (8183)Refutation not found, incomplete strategy
% 1.82/1.52 % (8183)------------------------------
% 1.82/1.52 % (8183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.52 % (8183)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.52
% 1.82/1.52
% 1.82/1.52 % (8183)Memory used [KB]: 5500
% 1.82/1.52 % (8183)Time elapsed: 0.006 s
% 1.82/1.52 % (8183)Instructions burned: 18 (million)
% 1.82/1.52 % (8183)------------------------------
% 1.82/1.52 % (8183)------------------------------
% 1.82/1.52 % (8184)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7961 for (2998ds/127Mi)
% 1.82/1.53 % (8185)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7961 for (2998ds/100Mi)
% 1.82/1.56 % (8184)Instruction limit reached!
% 1.82/1.56 % (8184)------------------------------
% 1.82/1.56 % (8184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.56 % (8184)Termination reason: Unknown
% 1.82/1.56 % (8184)Termination phase: Saturation
% 1.82/1.56
% 1.82/1.56 % (8184)Memory used [KB]: 5884
% 1.82/1.56 % (8184)Time elapsed: 0.043 s
% 1.82/1.56 % (8184)Instructions burned: 128 (million)
% 1.82/1.56 % (8184)------------------------------
% 1.82/1.56 % (8184)------------------------------
% 1.82/1.57 % (8185)Instruction limit reached!
% 1.82/1.57 % (8185)------------------------------
% 1.82/1.57 % (8185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.57 % (8185)Termination reason: Unknown
% 1.82/1.57 % (8185)Termination phase: Saturation
% 1.82/1.57
% 1.82/1.57 % (8185)Memory used [KB]: 6012
% 1.82/1.57 % (8185)Time elapsed: 0.037 s
% 1.82/1.57 % (8185)Instructions burned: 101 (million)
% 1.82/1.57 % (8185)------------------------------
% 1.82/1.57 % (8185)------------------------------
% 1.82/1.57 % (8186)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_7961 for (2998ds/3Mi)
% 1.82/1.57 % (8186)Instruction limit reached!
% 1.82/1.57 % (8186)------------------------------
% 1.82/1.57 % (8186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.57 % (8186)Termination reason: Unknown
% 1.82/1.57 % (8186)Termination phase: Property scanning
% 1.82/1.57
% 1.82/1.57 % (8186)Memory used [KB]: 1023
% 1.82/1.57 % (8186)Time elapsed: 0.002 s
% 1.82/1.57 % (8186)Instructions burned: 3 (million)
% 1.82/1.57 % (8186)------------------------------
% 1.82/1.57 % (8186)------------------------------
% 1.82/1.58 % (8187)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_7961 for (2998ds/20Mi)
% 1.82/1.58 % (8187)First to succeed.
% 1.82/1.58 % (8193)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_7961 for (2998ds/86Mi)
% 1.82/1.58 % (8187)Refutation found. Thanks to Tanya!
% 1.82/1.58 % SZS status Theorem for DTF2THF_7961
% 1.82/1.58 % SZS output start Proof for DTF2THF_7961
% 1.82/1.58 thf(func_def_0, type, in: $i > $i > $o).
% 1.82/1.58 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.82/1.58 thf(func_def_3, type, setunion: $i > $i).
% 1.82/1.58 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 1.82/1.58 thf(func_def_7, type, iskpair: $i > $o).
% 1.82/1.58 thf(func_def_8, type, kpair: $i > $i > $i).
% 1.82/1.58 thf(func_def_10, type, singleton: $i > $o).
% 1.82/1.58 thf(func_def_12, type, kfst: $i > $i).
% 1.82/1.58 thf(func_def_15, type, ksnd: $i > $i).
% 1.82/1.58 thf(func_def_30, type, sK5: $i > $o).
% 1.82/1.58 thf(func_def_38, type, sP13: $o > $o).
% 1.82/1.58 thf(func_def_39, type, sP14: $o > $o).
% 1.82/1.58 thf(func_def_40, type, sP15: $o > $o).
% 1.82/1.58 thf(func_def_41, type, sP16: $o > $o).
% 1.82/1.58 thf(func_def_42, type, sP17: $i > $o).
% 1.82/1.58 thf(func_def_45, type, ph19: !>[X0: $tType]:(X0)).
% 1.82/1.58 thf(f137,plain,(
% 1.82/1.58 $false),
% 1.82/1.58 inference(trivial_inequality_removal,[status(thm)],[f136])).
% 1.82/1.58 thf(f136,plain,(
% 1.82/1.58 ($false = $true)),
% 1.82/1.58 inference(backward_demodulation,[status(thm)],[f106,f135])).
% 1.82/1.58 thf(f135,plain,(
% 1.82/1.58 ($false = (sP17 @ sK12))),
% 1.82/1.58 inference(backward_demodulation,[status(thm)],[f111,f132])).
% 1.82/1.58 thf(f132,plain,(
% 1.82/1.58 ( ! [X0 : $i,X1 : $i] : (((setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = X1)) )),
% 1.82/1.58 inference(equality_resolution,[status(thm)],[f127])).
% 1.82/1.58 thf(f127,plain,(
% 1.82/1.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X2 @ X3) != (kpair @ X0 @ X1)) | ((setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = X3)) )),
% 1.82/1.58 inference(superposition,[status(thm)],[f113,f123])).
% 1.82/1.58 thf(f123,plain,(
% 1.82/1.58 ( ! [X0 : $i,X1 : $i] : (((kpair @ X0 @ X1) = (kpair @ (kfst @ (kpair @ X0 @ X1)) @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1)))))))) )),
% 1.82/1.58 inference(equality_proxy_clausification,[status(thm)],[f122])).
% 1.82/1.58 thf(f122,plain,(
% 1.82/1.58 ( ! [X0 : $i,X1 : $i] : ((((kpair @ (kfst @ (kpair @ X0 @ X1)) @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1)))))) = (kpair @ X0 @ X1)) = $true)) )),
% 1.82/1.58 inference(beta_eta_normalization,[status(thm)],[f121])).
% 1.82/1.58 thf(f121,plain,(
% 1.82/1.58 ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))) @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1)))))) = $true)) )),
% 1.82/1.58 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.82/1.58 thf(f120,plain,(
% 1.82/1.58 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))) @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1)))))) = $true)) )),
% 1.82/1.58 inference(superposition,[status(thm)],[f110,f119])).
% 1.82/1.58 thf(f119,plain,(
% 1.82/1.58 ( ! [X0 : $i,X1 : $i] : (((in @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = $true)) )),
% 1.82/1.58 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.82/1.58 thf(f118,plain,(
% 1.82/1.58 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = $true)) )),
% 1.82/1.58 inference(superposition,[status(thm)],[f108,f117])).
% 1.82/1.58 thf(f117,plain,(
% 1.82/1.58 ( ! [X0 : $i,X1 : $i] : (((singleton @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = $true)) )),
% 1.82/1.58 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.82/1.58 thf(f116,plain,(
% 1.82/1.58 ( ! [X0 : $i,X1 : $i] : (((singleton @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = $true) | ($true != $true)) )),
% 1.82/1.58 inference(superposition,[status(thm)],[f107,f112])).
% 1.82/1.58 thf(f112,plain,(
% 1.82/1.58 ( ! [X2 : $i,X3 : $i] : (((iskpair @ (kpair @ X3 @ X2)) = $true)) )),
% 1.82/1.58 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.82/1.58 thf(f86,plain,(
% 1.82/1.58 ( ! [X2 : $i,X3 : $i] : (((iskpair @ (kpair @ X3 @ X2)) = $true) | ($true != $true)) )),
% 1.82/1.58 inference(definition_unfolding,[status(thm)],[f64,f77])).
% 1.82/1.58 thf(f77,plain,(
% 1.82/1.58 (kpairp = $true)),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f60])).
% 1.82/1.58 thf(f60,plain,(
% 1.82/1.58 (sK12 != (ksnd @ (kpair @ sK11 @ sK12))) & (ksndsingleton = $true) & (dsetconstrER = $true) & (setukpairinjR = $true) & (kpairp = $true) & (theprop = $true)),
% 1.82/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f34,f59])).
% 1.82/1.58 thf(f59,plain,(
% 1.82/1.58 ? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) != X1) => (sK12 != (ksnd @ (kpair @ sK11 @ sK12)))),
% 1.82/1.58 introduced(definition,[],[choice_axiom])).
% 1.82/1.58 thf(f34,plain,(
% 1.82/1.58 ? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) != X1) & (ksndsingleton = $true) & (dsetconstrER = $true) & (setukpairinjR = $true) & (kpairp = $true) & (theprop = $true)),
% 1.82/1.58 inference(flattening,[status(thm)],[f33])).
% 1.82/1.58 thf(f33,plain,(
% 1.82/1.58 ((((? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) != X1) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (theprop = $true)) & (kpairp = $true)) & (dsetconstrER = $true)),
% 1.82/1.58 inference(ennf_transformation,[status(thm)],[f32])).
% 1.82/1.58 thf(f32,plain,(
% 1.82/1.58 ~((dsetconstrER = $true) => ((kpairp = $true) => ((theprop = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1))))))),
% 1.82/1.58 inference(fool_elimination,[status(thm)],[f31])).
% 1.82/1.58 thf(f31,plain,(
% 1.82/1.58 ~(dsetconstrER => (kpairp => (theprop => (setukpairinjR => (ksndsingleton => ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1))))))),
% 1.82/1.58 inference(rectify,[status(thm)],[f11])).
% 1.82/1.58 thf(f11,negated_conjecture,(
% 1.82/1.58 ~(dsetconstrER => (kpairp => (theprop => (setukpairinjR => (ksndsingleton => ! [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X2 @ X3)) = X3))))))),
% 1.82/1.58 inference(negated_conjecture,[status(cth)],[f10])).
% 1.82/1.58 thf(f10,conjecture,(
% 1.82/1.58 dsetconstrER => (kpairp => (theprop => (setukpairinjR => (ksndsingleton => ! [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X2 @ X3)) = X3)))))),
% 1.82/1.58 file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',ksndpairEq)).
% 1.82/1.58 thf(f64,plain,(
% 1.82/1.58 ( ! [X2 : $i,X3 : $i] : (((iskpair @ (kpair @ X3 @ X2)) = $true) | (kpairp != $true)) )),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f46])).
% 1.82/1.58 thf(f46,plain,(
% 1.82/1.58 ((kpairp = $true) | ($true != (iskpair @ (kpair @ sK2 @ sK1)))) & (! [X2 : $i,X3 : $i] : ((iskpair @ (kpair @ X3 @ X2)) = $true) | (kpairp != $true))),
% 1.82/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f44,f45])).
% 1.82/1.58 thf(f45,plain,(
% 1.82/1.58 ? [X0 : $i,X1 : $i] : ((iskpair @ (kpair @ X1 @ X0)) != $true) => ($true != (iskpair @ (kpair @ sK2 @ sK1)))),
% 1.82/1.58 introduced(definition,[],[choice_axiom])).
% 1.82/1.58 thf(f44,plain,(
% 1.82/1.58 ((kpairp = $true) | ? [X0 : $i,X1 : $i] : ((iskpair @ (kpair @ X1 @ X0)) != $true)) & (! [X2 : $i,X3 : $i] : ((iskpair @ (kpair @ X3 @ X2)) = $true) | (kpairp != $true))),
% 1.82/1.58 inference(rectify,[status(thm)],[f43])).
% 1.82/1.58 thf(f43,plain,(
% 1.82/1.58 ((kpairp = $true) | ? [X0 : $i,X1 : $i] : ((iskpair @ (kpair @ X1 @ X0)) != $true)) & (! [X0 : $i,X1 : $i] : ((iskpair @ (kpair @ X1 @ X0)) = $true) | (kpairp != $true))),
% 1.82/1.58 inference(nnf_transformation,[status(thm)],[f18])).
% 1.82/1.58 thf(f18,plain,(
% 1.82/1.58 (kpairp = $true) <=> ! [X0 : $i,X1 : $i] : ((iskpair @ (kpair @ X1 @ X0)) = $true)),
% 1.82/1.58 inference(fool_elimination,[status(thm)],[f17])).
% 1.82/1.58 thf(f17,plain,(
% 1.82/1.58 (! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X1 @ X0)) = kpairp)),
% 1.82/1.58 inference(rectify,[status(thm)],[f4])).
% 1.82/1.58 thf(f4,axiom,(
% 1.82/1.58 (! [X3 : $i,X2 : $i] : (iskpair @ (kpair @ X2 @ X3)) = kpairp)),
% 1.82/1.58 file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',kpairp)).
% 1.82/1.58 thf(f107,plain,(
% 1.82/1.58 ( ! [X1 : $i] : (((iskpair @ X1) != $true) | ((singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: ((kpair @ (kfst @ X1) @ Y0) = X1)))) = $true)) )),
% 1.82/1.58 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.82/1.58 thf(f89,plain,(
% 1.82/1.58 ( ! [X1 : $i] : (($true != $true) | ((iskpair @ X1) != $true) | ((singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: ((kpair @ (kfst @ X1) @ Y0) = X1)))) = $true)) )),
% 1.82/1.58 inference(definition_unfolding,[status(thm)],[f66,f80])).
% 1.82/1.58 thf(f80,plain,(
% 1.82/1.58 (ksndsingleton = $true)),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f60])).
% 1.82/1.58 thf(f66,plain,(
% 1.82/1.58 ( ! [X1 : $i] : (((iskpair @ X1) != $true) | ((singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: ((kpair @ (kfst @ X1) @ Y0) = X1)))) = $true) | (ksndsingleton != $true)) )),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f50])).
% 1.82/1.58 thf(f50,plain,(
% 1.82/1.58 ((ksndsingleton = $true) | (((iskpair @ sK3) = $true) & ((singleton @ (dsetconstr @ (setunion @ sK3) @ (^[Y0 : $i]: ((kpair @ (kfst @ sK3) @ Y0) = sK3)))) != $true))) & (! [X1 : $i] : (((iskpair @ X1) != $true) | ((singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: ((kpair @ (kfst @ X1) @ Y0) = X1)))) = $true)) | (ksndsingleton != $true))),
% 1.82/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f48,f49])).
% 1.82/1.58 thf(f49,plain,(
% 1.82/1.58 ? [X0 : $i] : (((iskpair @ X0) = $true) & ((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) != $true)) => (((iskpair @ sK3) = $true) & ((singleton @ (dsetconstr @ (setunion @ sK3) @ (^[Y0 : $i]: ((kpair @ (kfst @ sK3) @ Y0) = sK3)))) != $true))),
% 1.82/1.58 introduced(definition,[],[choice_axiom])).
% 1.82/1.58 thf(f48,plain,(
% 1.82/1.58 ((ksndsingleton = $true) | ? [X0 : $i] : (((iskpair @ X0) = $true) & ((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) != $true))) & (! [X1 : $i] : (((iskpair @ X1) != $true) | ((singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: ((kpair @ (kfst @ X1) @ Y0) = X1)))) = $true)) | (ksndsingleton != $true))),
% 1.82/1.58 inference(rectify,[status(thm)],[f47])).
% 1.82/1.58 thf(f47,plain,(
% 1.82/1.58 ((ksndsingleton = $true) | ? [X0 : $i] : (((iskpair @ X0) = $true) & ((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) != $true))) & (! [X0 : $i] : (((iskpair @ X0) != $true) | ((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) = $true)) | (ksndsingleton != $true))),
% 1.82/1.58 inference(nnf_transformation,[status(thm)],[f35])).
% 1.82/1.58 thf(f35,plain,(
% 1.82/1.58 (ksndsingleton = $true) <=> ! [X0 : $i] : (((iskpair @ X0) != $true) | ((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) = $true))),
% 1.82/1.58 inference(ennf_transformation,[status(thm)],[f20])).
% 1.82/1.58 thf(f20,plain,(
% 1.82/1.58 (ksndsingleton = $true) <=> ! [X0 : $i] : (((iskpair @ X0) = $true) => ((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) = $true))),
% 1.82/1.58 inference(fool_elimination,[status(thm)],[f19])).
% 1.82/1.58 thf(f19,plain,(
% 1.82/1.58 (! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (((kpair @ (kfst @ X0) @ X1) = X0)))))) = ksndsingleton)),
% 1.82/1.58 inference(rectify,[status(thm)],[f8])).
% 1.82/1.58 thf(f8,axiom,(
% 1.82/1.58 (! [X6 : $i] : ((iskpair @ X6) => (singleton @ (dsetconstr @ (setunion @ X6) @ (^[X2 : $i] : (((kpair @ (kfst @ X6) @ X2) = X6)))))) = ksndsingleton)),
% 1.82/1.58 file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',ksndsingleton)).
% 1.82/1.58 thf(f108,plain,(
% 1.82/1.58 ( ! [X0 : $i] : (((singleton @ X0) != $true) | ((in @ (setunion @ X0) @ X0) = $true)) )),
% 1.82/1.58 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.82/1.58 thf(f82,plain,(
% 1.82/1.58 ( ! [X0 : $i] : (($true != $true) | ((singleton @ X0) != $true) | ((in @ (setunion @ X0) @ X0) = $true)) )),
% 1.82/1.58 inference(definition_unfolding,[status(thm)],[f63,f76])).
% 1.82/1.58 thf(f76,plain,(
% 1.82/1.58 (theprop = $true)),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f60])).
% 1.82/1.58 thf(f63,plain,(
% 1.82/1.58 ( ! [X0 : $i] : (((singleton @ X0) != $true) | ((in @ (setunion @ X0) @ X0) = $true) | (theprop != $true)) )),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f42])).
% 1.82/1.58 thf(f42,plain,(
% 1.82/1.58 (! [X0 : $i] : (((singleton @ X0) != $true) | ((in @ (setunion @ X0) @ X0) = $true)) | (theprop != $true)) & ((theprop = $true) | (($true = (singleton @ sK0)) & ($true != (in @ (setunion @ sK0) @ sK0))))),
% 1.82/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f40,f41])).
% 1.82/1.58 thf(f41,plain,(
% 1.82/1.58 ? [X1 : $i] : (((singleton @ X1) = $true) & ((in @ (setunion @ X1) @ X1) != $true)) => (($true = (singleton @ sK0)) & ($true != (in @ (setunion @ sK0) @ sK0)))),
% 1.82/1.58 introduced(definition,[],[choice_axiom])).
% 1.82/1.58 thf(f40,plain,(
% 1.82/1.58 (! [X0 : $i] : (((singleton @ X0) != $true) | ((in @ (setunion @ X0) @ X0) = $true)) | (theprop != $true)) & ((theprop = $true) | ? [X1 : $i] : (((singleton @ X1) = $true) & ((in @ (setunion @ X1) @ X1) != $true)))),
% 1.82/1.58 inference(rectify,[status(thm)],[f39])).
% 1.82/1.58 thf(f39,plain,(
% 1.82/1.58 (! [X0 : $i] : (((singleton @ X0) != $true) | ((in @ (setunion @ X0) @ X0) = $true)) | (theprop != $true)) & ((theprop = $true) | ? [X0 : $i] : (((singleton @ X0) = $true) & ((in @ (setunion @ X0) @ X0) != $true)))),
% 1.82/1.58 inference(nnf_transformation,[status(thm)],[f36])).
% 1.82/1.58 thf(f36,plain,(
% 1.82/1.58 ! [X0 : $i] : (((singleton @ X0) != $true) | ((in @ (setunion @ X0) @ X0) = $true)) <=> (theprop = $true)),
% 1.82/1.58 inference(ennf_transformation,[status(thm)],[f16])).
% 1.82/1.58 thf(f16,plain,(
% 1.82/1.58 ! [X0 : $i] : (((singleton @ X0) = $true) => ((in @ (setunion @ X0) @ X0) = $true)) <=> (theprop = $true)),
% 1.82/1.58 inference(fool_elimination,[status(thm)],[f15])).
% 1.82/1.58 thf(f15,plain,(
% 1.82/1.58 (! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)),
% 1.82/1.58 inference(rectify,[status(thm)],[f6])).
% 1.82/1.58 thf(f6,axiom,(
% 1.82/1.58 (! [X4 : $i] : ((singleton @ X4) => (in @ (setunion @ X4) @ X4)) = theprop)),
% 1.82/1.58 file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',theprop)).
% 1.82/1.58 thf(f110,plain,(
% 1.82/1.58 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X0 @ (dsetconstr @ X2 @ X1)) != $true) | ((X1 @ X0) = $true)) )),
% 1.82/1.58 inference(beta_eta_normalization,[status(thm)],[f109])).
% 1.82/1.58 thf(f109,plain,(
% 1.82/1.58 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((X1 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) )),
% 1.82/1.58 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.82/1.58 thf(f90,plain,(
% 1.82/1.58 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((X1 @ X0) = $true) | ($true != $true)) )),
% 1.82/1.58 inference(definition_unfolding,[status(thm)],[f72,f79])).
% 1.82/1.58 thf(f79,plain,(
% 1.82/1.58 (dsetconstrER = $true)),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f60])).
% 1.82/1.58 thf(f72,plain,(
% 1.82/1.58 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((X1 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | (dsetconstrER != $true)) )),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f54])).
% 1.82/1.58 thf(f54,plain,(
% 1.82/1.58 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (((sK5 @ sK4) != $true) & ((in @ sK4 @ (dsetconstr @ sK6 @ (^[Y0 : $i]: (sK5 @ Y0)))) = $true)))),
% 1.82/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f52,f53])).
% 1.82/1.58 thf(f53,plain,(
% 1.82/1.58 ? [X3 : $i,X4 : $i > $o,X5 : $i] : (((X4 @ X3) != $true) & ((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) = $true)) => (((sK5 @ sK4) != $true) & ((in @ sK4 @ (dsetconstr @ sK6 @ (^[Y0 : $i]: (sK5 @ Y0)))) = $true))),
% 1.82/1.58 introduced(definition,[],[choice_axiom])).
% 1.82/1.58 thf(f52,plain,(
% 1.82/1.58 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3 : $i,X4 : $i > $o,X5 : $i] : (((X4 @ X3) != $true) & ((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) = $true)))),
% 1.82/1.58 inference(rectify,[status(thm)],[f51])).
% 1.82/1.58 thf(f51,plain,(
% 1.82/1.58 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X0) != $true) & ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true)))),
% 1.82/1.58 inference(nnf_transformation,[status(thm)],[f38])).
% 1.82/1.58 thf(f38,plain,(
% 1.82/1.58 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) <=> (dsetconstrER = $true)),
% 1.82/1.58 inference(ennf_transformation,[status(thm)],[f26])).
% 1.82/1.58 thf(f26,plain,(
% 1.82/1.58 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) => ((X1 @ X0) = $true)) <=> (dsetconstrER = $true)),
% 1.82/1.58 inference(fool_elimination,[status(thm)],[f25])).
% 1.82/1.58 thf(f25,plain,(
% 1.82/1.58 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X0)) = dsetconstrER)),
% 1.82/1.58 inference(rectify,[status(thm)],[f1])).
% 1.82/1.58 thf(f1,axiom,(
% 1.82/1.58 (! [X2 : $i,X1 : $i > $o,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.82/1.58 file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',dsetconstrER)).
% 1.82/1.58 thf(f113,plain,(
% 1.82/1.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X3 @ X0) != (kpair @ X2 @ X1)) | (X0 = X1)) )),
% 1.82/1.58 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.82/1.58 thf(f93,plain,(
% 1.82/1.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X0 = X1) | ($true != $true) | ((kpair @ X3 @ X0) != (kpair @ X2 @ X1))) )),
% 1.82/1.58 inference(definition_unfolding,[status(thm)],[f75,f78])).
% 1.82/1.58 thf(f78,plain,(
% 1.82/1.58 (setukpairinjR = $true)),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f60])).
% 1.82/1.58 thf(f75,plain,(
% 1.82/1.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X3 @ X0) != (kpair @ X2 @ X1)) | (X0 = X1) | (setukpairinjR != $true)) )),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f58])).
% 1.82/1.58 thf(f58,plain,(
% 1.82/1.58 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) != (kpair @ X2 @ X1)) | (X0 = X1)) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | (((kpair @ sK9 @ sK8) = (kpair @ sK10 @ sK7)) & (sK8 != sK7)))),
% 1.82/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f56,f57])).
% 1.82/1.58 thf(f57,plain,(
% 1.82/1.58 ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((kpair @ X6 @ X5) = (kpair @ X7 @ X4)) & (X4 != X5)) => (((kpair @ sK9 @ sK8) = (kpair @ sK10 @ sK7)) & (sK8 != sK7))),
% 1.82/1.58 introduced(definition,[],[choice_axiom])).
% 1.82/1.58 thf(f56,plain,(
% 1.82/1.58 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) != (kpair @ X2 @ X1)) | (X0 = X1)) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((kpair @ X6 @ X5) = (kpair @ X7 @ X4)) & (X4 != X5)))),
% 1.82/1.58 inference(rectify,[status(thm)],[f55])).
% 1.82/1.58 thf(f55,plain,(
% 1.82/1.58 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) != (kpair @ X2 @ X1)) | (X0 = X1)) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) = (kpair @ X2 @ X1)) & (X0 != X1)))),
% 1.82/1.58 inference(nnf_transformation,[status(thm)],[f37])).
% 1.82/1.58 thf(f37,plain,(
% 1.82/1.58 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) != (kpair @ X2 @ X1)) | (X0 = X1)) <=> (setukpairinjR = $true)),
% 1.82/1.58 inference(ennf_transformation,[status(thm)],[f24])).
% 1.82/1.58 thf(f24,plain,(
% 1.82/1.58 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) = (kpair @ X2 @ X1)) => (X0 = X1)) <=> (setukpairinjR = $true)),
% 1.82/1.58 inference(fool_elimination,[status(thm)],[f23])).
% 1.82/1.58 thf(f23,plain,(
% 1.82/1.58 (setukpairinjR = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X3 @ X0) = (kpair @ X2 @ X1)) => (X0 = X1)))),
% 1.82/1.58 inference(rectify,[status(thm)],[f7])).
% 1.82/1.58 thf(f7,axiom,(
% 1.82/1.58 (setukpairinjR = ! [X6 : $i,X3 : $i,X2 : $i,X5 : $i] : (((kpair @ X2 @ X3) = (kpair @ X5 @ X6)) => (X3 = X6)))),
% 1.82/1.58 file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',setukpairinjR)).
% 1.82/1.58 thf(f111,plain,(
% 1.82/1.58 ((sP17 @ (setunion @ (dsetconstr @ (setunion @ (kpair @ sK11 @ sK12)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ sK11 @ sK12)) @ Y0) = (kpair @ sK11 @ sK12)))))) = $false)),
% 1.82/1.58 inference(beta_eta_normalization,[status(thm)],[f105])).
% 1.82/1.58 thf(f105,plain,(
% 1.82/1.58 ($false = (sP17 @ ((^[Y0 : $i]: (setunion @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))) @ (kpair @ sK11 @ sK12))))),
% 1.82/1.58 introduced(definition,[new_symbols(naming,[sP17])],[inequality_splitting_name_introduction])).
% 1.82/1.58 thf(f106,plain,(
% 1.82/1.58 ((sP17 @ sK12) = $true)),
% 1.82/1.58 inference(inequality_splitting,[status(thm)],[f96,f105])).
% 1.82/1.58 thf(f96,plain,(
% 1.82/1.58 (sK12 != ((^[Y0 : $i]: (setunion @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))) @ (kpair @ sK11 @ sK12)))),
% 1.82/1.58 inference(definition_unfolding,[status(thm)],[f81,f69])).
% 1.82/1.58 thf(f69,plain,(
% 1.82/1.58 (ksnd = (^[Y0 : $i]: (setunion @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f30])).
% 1.82/1.58 thf(f30,plain,(
% 1.82/1.58 (ksnd = (^[Y0 : $i]: (setunion @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))),
% 1.82/1.58 inference(fool_elimination,[status(thm)],[f29])).
% 1.82/1.58 thf(f29,plain,(
% 1.82/1.58 (ksnd = (^[X0 : $i] : (setunion @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (((kpair @ (kfst @ X0) @ X1) = X0)))))))),
% 1.82/1.58 inference(rectify,[status(thm)],[f9])).
% 1.82/1.58 thf(f9,axiom,(
% 1.82/1.58 (ksnd = (^[X6 : $i] : (setunion @ (dsetconstr @ (setunion @ X6) @ (^[X2 : $i] : (((kpair @ (kfst @ X6) @ X2) = X6)))))))),
% 1.82/1.58 file('/export/starexec/sandbox/tmp/tmp.O8Of9Xs71f/DTF2THF_7961.p',ksnd)).
% 1.82/1.58 thf(f81,plain,(
% 1.82/1.58 (sK12 != (ksnd @ (kpair @ sK11 @ sK12)))),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f60])).
% 1.82/1.58 % SZS output end Proof for DTF2THF_7961
% 1.82/1.58 % (8187)------------------------------
% 1.82/1.58 % (8187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.58 % (8187)Termination reason: Refutation
% 1.82/1.58
% 1.82/1.58 % (8187)Memory used [KB]: 5628
% 1.82/1.58 % (8187)Time elapsed: 0.009 s
% 1.82/1.58 % (8187)Instructions burned: 17 (million)
% 1.82/1.58 % (8187)------------------------------
% 1.82/1.58 % (8187)------------------------------
% 1.82/1.58 % (8150)Success in time 0.18 s
%------------------------------------------------------------------------------