%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU663^2 : 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 : n022.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 09:36:02 AM UTC 2026
% Result : Theorem 1.66s 1.49s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 182 ( 66 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 201 ( 23 ~; 8 |; 25 &; 125 @)
% ( 1 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 34 !; 24 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
kpair: $i > $i > $i ).
thf(func_def_2,type,
ksnd: $i > $i ).
thf(f47,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
sK3 != sK3,
inference(superposition,[status(thm)],[f29,f45]) ).
thf(f45,plain,
! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 ) ),
inference(definition_unfolding,[status(thm)],[f38,f28]) ).
thf(f28,plain,
ksndpairEq = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( cartprodmempaircEq = $true )
& ( ( in @ sK2 @ sK0 )
= $true )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( ( ksnd @ ( kpair @ sK2 @ sK3 ) )
!= sK3 )
& ( ksndpairEq = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f15,f17,f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( ( ksnd @ ( kpair @ X2 @ X3 ) )
!= X3 ) ) )
=> ( ( ( in @ sK2 @ sK0 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK1 )
= $true )
& ( ( ksnd @ ( kpair @ sK2 @ X3 ) )
!= X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK1 )
= $true )
& ( ( ksnd @ ( kpair @ sK2 @ X3 ) )
!= X3 ) )
=> ( ( ( in @ sK3 @ sK1 )
= $true )
& ( ( ksnd @ ( kpair @ sK2 @ sK3 ) )
!= sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ( cartprodmempaircEq = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( ( ksnd @ ( kpair @ X2 @ X3 ) )
!= X3 ) ) )
& ( ksndpairEq = $true ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
( ( cartprodmempaircEq = $true )
& ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( ( ksnd @ ( kpair @ X0 @ X3 ) )
!= X3 ) ) )
& ( ksndpairEq = $true ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( ( ksnd @ ( kpair @ X0 @ X3 ) )
!= X3 ) ) )
& ( cartprodmempaircEq = $true )
& ( ksndpairEq = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( ksndpairEq = $true )
=> ( ( cartprodmempaircEq = $true )
=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( ksnd @ ( kpair @ X0 @ X3 ) )
= X3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ksndpairEq
=> ( cartprodmempaircEq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( ksnd @ ( kpair @ X0 @ X3 ) )
= X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( ksndpairEq
=> ( cartprodmempaircEq
=> ! [X0: $i,X3: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( ksndpairEq
=> ( cartprodmempaircEq
=> ! [X0: $i,X3: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MtQBjuYWrA/DTF2THF_15776.p',cartprodsndpairEq) ).
thf(f38,plain,
! [X0: $i,X1: $i] :
( ( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
| ( ksndpairEq != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
| ( ksndpairEq != $true ) )
& ( ( ksndpairEq = $true )
| ( sK8
!= ( ksnd @ ( kpair @ sK9 @ sK8 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f25,f26]) ).
thf(f26,plain,
( ? [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X3 @ X2 ) )
!= X2 )
=> ( sK8
!= ( ksnd @ ( kpair @ sK9 @ sK8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
| ( ksndpairEq != $true ) )
& ( ( ksndpairEq = $true )
| ? [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X3 @ X2 ) )
!= X2 ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
| ( ksndpairEq != $true ) )
& ( ( ksndpairEq = $true )
| ? [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
!= X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
<=> ( ksndpairEq = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
= ksndpairEq ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
= ksndpairEq ),
file('/export/starexec/sandbox/tmp/tmp.MtQBjuYWrA/DTF2THF_15776.p',ksndpairEq) ).
thf(f29,plain,
( ( ksnd @ ( kpair @ sK2 @ sK3 ) )
!= sK3 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU663^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n022.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 12:30:06 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU663^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : Ordered Pairs - Properties of Pairs
% 0.18/0.45 % Version : Especial > Reduced > Especial.
% 0.18/0.45 % English : (! A:i.! B:i.! x:i.in x A -> (! y:i.in y B ->
% 0.18/0.45 % ksnd (kpair x y) = y))
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.45 % Source : [Bro08]
% 0.18/0.45 % Names : ZFC165l [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.18/0.45 % Number of atoms : 13 ( 5 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 5 ( 4 avg)
% 0.18/0.45 % Number of connectives : 24 ( 0 ~; 0 |; 0 &; 18 @)
% 0.18/0.45 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 11 ( 4 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=217
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(in_type,type,
% 0.18/0.45 in: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(kpair_type,type,
% 0.18/0.45 kpair: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(ksnd_type,type,
% 0.18/0.45 ksnd: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(ksndpairEq_type,type,
% 0.18/0.45 ksndpairEq: $o ).
% 0.18/0.45
% 0.18/0.45 thf(ksndpairEq,definition,
% 0.18/0.45 ( ksndpairEq
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.18/0.45 = Xy ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(cartprodmempaircEq_type,type,
% 0.18/0.45 cartprodmempaircEq: $o ).
% 0.18/0.45
% 0.18/0.45 thf(cartprodmempaircEq,definition,
% 0.18/0.45 ( cartprodmempaircEq
% 0.18/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ! [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ B )
% 0.18/0.45 => ( ( kpair @ Xx @ Xy )
% 0.18/0.45 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(cartprodsndpairEq,conjecture,
% 0.18/0.45 ( ksndpairEq
% 0.18/0.45 => ( cartprodmempaircEq
% 0.18/0.45 => ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ! [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ B )
% 0.18/0.45 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.18/0.45 = Xy ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.66/1.46 ---- Embedded in THF ---
% 1.66/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.47 %%% Generated on Tue Feb 24 12:30:07 EST 2026
% 1.66/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.47 %%% Logic specification used:
% 1.66/1.47 %%% thf(spec, logic, $$dhol).
% 1.66/1.47
% 1.66/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.MtQBjuYWrA/DTF2DTF15776.p
% See solution above
% 1.66/1.47 ------------------------
% 1.66/1.47 ---- Cleaned THF ---
% 1.66/1.48 thf(in_type,type,
% 1.66/1.48 in: $i > $i > $o ).
% 1.66/1.48
% 1.66/1.48 thf(kpair_type,type,
% 1.66/1.48 kpair: $i > $i > $i ).
% 1.66/1.48
% 1.66/1.48 thf(ksnd_type,type,
% 1.66/1.48 ksnd: $i > $i ).
% 1.66/1.48
% 1.66/1.48 thf(ksndpairEq_type,type,
% 1.66/1.48 ksndpairEq: $o ).
% 1.66/1.48
% 1.66/1.48 thf(ksndpairEq,definition,
% 1.66/1.48 ( ksndpairEq
% 1.66/1.48 = ( ! [Xx: $i,Xy: $i] :
% 1.66/1.48 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 1.66/1.48 = Xy ) ) ) ).
% 1.66/1.48
% 1.66/1.48 thf(cartprodmempaircEq_type,type,
% 1.66/1.48 cartprodmempaircEq: $o ).
% 1.66/1.48
% 1.66/1.48 thf(cartprodmempaircEq,definition,
% 1.66/1.48 ( cartprodmempaircEq
% 1.66/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.66/1.48 ( ( in @ Xx @ A )
% 1.66/1.48 => ! [Xy: $i] :
% 1.66/1.48 ( ( in @ Xy @ B )
% 1.66/1.48 => ( ( kpair @ Xx @ Xy )
% 1.66/1.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 1.66/1.48
% 1.66/1.48 thf(cartprodsndpairEq,conjecture,
% 1.66/1.48 ( ksndpairEq
% 1.66/1.48 => ( cartprodmempaircEq
% 1.66/1.48 => ! [A: $i,B: $i,Xx: $i] :
% 1.66/1.48 ( ( in @ Xx @ A )
% 1.66/1.48 => ! [Xy: $i] :
% 1.66/1.48 ( ( in @ Xy @ B )
% 1.66/1.48 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 1.66/1.48 = Xy ) ) ) ) ) ).
% 1.66/1.48 ------------------------
% 1.66/1.49 % (15970)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15776 for (2999ds/18Mi)
% 1.66/1.49 % (15970)First to succeed.
% 1.66/1.49 % (15970)Refutation found. Thanks to Tanya!
% 1.66/1.49 % SZS status Theorem for DTF2THF_15776
% 1.66/1.49 % SZS output start Proof for DTF2THF_15776
% 1.66/1.49 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.49 thf(func_def_1, type, kpair: $i > $i > $i).
% 1.66/1.49 thf(func_def_2, type, ksnd: $i > $i).
% 1.66/1.49 thf(f47,plain,(
% 1.66/1.49 $false),
% 1.66/1.49 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.66/1.49 thf(f46,plain,(
% 1.66/1.49 (sK3 != sK3)),
% 1.66/1.49 inference(superposition,[status(thm)],[f29,f45])).
% 1.66/1.49 thf(f45,plain,(
% 1.66/1.49 ( ! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X1 @ X0)) = X0)) )),
% 1.66/1.49 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.66/1.49 thf(f43,plain,(
% 1.66/1.49 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((ksnd @ (kpair @ X1 @ X0)) = X0)) )),
% 1.66/1.49 inference(definition_unfolding,[status(thm)],[f38,f28])).
% 1.66/1.49 thf(f28,plain,(
% 1.66/1.49 (ksndpairEq = $true)),
% 1.66/1.49 inference(cnf_transformation,[status(thm)],[f18])).
% 1.66/1.49 thf(f18,plain,(
% 1.66/1.49 (cartprodmempaircEq = $true) & (((in @ sK2 @ sK0) = $true) & (((in @ sK3 @ sK1) = $true) & ((ksnd @ (kpair @ sK2 @ sK3)) != sK3))) & (ksndpairEq = $true)),
% 1.66/1.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f15,f17,f16])).
% 1.66/1.49 thf(f16,plain,(
% 1.66/1.49 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X0)) & ? [X3 : $i] : (($true = (in @ X3 @ X1)) & ((ksnd @ (kpair @ X2 @ X3)) != X3))) => (((in @ sK2 @ sK0) = $true) & ? [X3 : $i] : (((in @ X3 @ sK1) = $true) & ((ksnd @ (kpair @ sK2 @ X3)) != X3)))),
% 1.66/1.49 introduced(definition,[],[choice_axiom])).
% 1.66/1.49 thf(f17,plain,(
% 1.66/1.49 ? [X3 : $i] : (((in @ X3 @ sK1) = $true) & ((ksnd @ (kpair @ sK2 @ X3)) != X3)) => (((in @ sK3 @ sK1) = $true) & ((ksnd @ (kpair @ sK2 @ sK3)) != sK3))),
% 1.66/1.49 introduced(definition,[],[choice_axiom])).
% 1.66/1.49 thf(f15,plain,(
% 1.66/1.49 (cartprodmempaircEq = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X0)) & ? [X3 : $i] : (($true = (in @ X3 @ X1)) & ((ksnd @ (kpair @ X2 @ X3)) != X3))) & (ksndpairEq = $true)),
% 1.66/1.49 inference(rectify,[status(thm)],[f14])).
% 1.66/1.49 thf(f14,plain,(
% 1.66/1.49 (cartprodmempaircEq = $true) & ? [X2 : $i,X1 : $i,X0 : $i] : (((in @ X0 @ X2) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ X1)) & ((ksnd @ (kpair @ X0 @ X3)) != X3))) & (ksndpairEq = $true)),
% 1.66/1.49 inference(flattening,[status(thm)],[f13])).
% 1.66/1.49 thf(f13,plain,(
% 1.66/1.49 (? [X2 : $i,X1 : $i,X0 : $i] : (((in @ X0 @ X2) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ X1)) & ((ksnd @ (kpair @ X0 @ X3)) != X3))) & (cartprodmempaircEq = $true)) & (ksndpairEq = $true)),
% 1.66/1.49 inference(ennf_transformation,[status(thm)],[f11])).
% 1.66/1.49 thf(f11,plain,(
% 1.66/1.49 ~((ksndpairEq = $true) => ((cartprodmempaircEq = $true) => ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => ((ksnd @ (kpair @ X0 @ X3)) = X3)))))),
% 1.66/1.49 inference(fool_elimination,[status(thm)],[f10])).
% 1.66/1.49 thf(f10,plain,(
% 1.66/1.49 ~(ksndpairEq => (cartprodmempaircEq => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => ((ksnd @ (kpair @ X0 @ X3)) = X3)))))),
% 1.66/1.49 inference(rectify,[status(thm)],[f4])).
% 1.66/1.49 thf(f4,negated_conjecture,(
% 1.66/1.49 ~(ksndpairEq => (cartprodmempaircEq => ! [X0 : $i,X3 : $i,X2 : $i] : ((in @ X0 @ X2) => ! [X1 : $i] : ((in @ X1 @ X3) => ((ksnd @ (kpair @ X0 @ X1)) = X1)))))),
% 1.66/1.49 inference(negated_conjecture,[status(cth)],[f3])).
% 1.66/1.49 thf(f3,conjecture,(
% 1.66/1.49 ksndpairEq => (cartprodmempaircEq => ! [X0 : $i,X3 : $i,X2 : $i] : ((in @ X0 @ X2) => ! [X1 : $i] : ((in @ X1 @ X3) => ((ksnd @ (kpair @ X0 @ X1)) = X1))))),
% 1.66/1.49 file('/export/starexec/sandbox/tmp/tmp.MtQBjuYWrA/DTF2THF_15776.p',cartprodsndpairEq)).
% 1.66/1.49 thf(f38,plain,(
% 1.66/1.49 ( ! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X1 @ X0)) = X0) | (ksndpairEq != $true)) )),
% 1.66/1.49 inference(cnf_transformation,[status(thm)],[f27])).
% 1.66/1.49 thf(f27,plain,(
% 1.66/1.49 (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) = X0) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | (sK8 != (ksnd @ (kpair @ sK9 @ sK8))))),
% 1.66/1.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f25,f26])).
% 1.66/1.49 thf(f26,plain,(
% 1.66/1.49 ? [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X3 @ X2)) != X2) => (sK8 != (ksnd @ (kpair @ sK9 @ sK8)))),
% 1.66/1.49 introduced(definition,[],[choice_axiom])).
% 1.66/1.49 thf(f25,plain,(
% 1.66/1.49 (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) = X0) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | ? [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X3 @ X2)) != X2))),
% 1.66/1.49 inference(rectify,[status(thm)],[f24])).
% 1.66/1.49 thf(f24,plain,(
% 1.66/1.49 (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) = X0) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | ? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) != X0))),
% 1.66/1.49 inference(nnf_transformation,[status(thm)],[f9])).
% 1.66/1.49 thf(f9,plain,(
% 1.66/1.49 ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) = X0) <=> (ksndpairEq = $true)),
% 1.66/1.49 inference(fool_elimination,[status(thm)],[f8])).
% 1.66/1.49 thf(f8,plain,(
% 1.66/1.49 (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) = X0) = ksndpairEq)),
% 1.66/1.49 inference(rectify,[status(thm)],[f1])).
% 1.66/1.49 thf(f1,axiom,(
% 1.66/1.49 (! [X1 : $i,X0 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1) = ksndpairEq)),
% 1.66/1.49 file('/export/starexec/sandbox/tmp/tmp.MtQBjuYWrA/DTF2THF_15776.p',ksndpairEq)).
% 1.66/1.49 thf(f29,plain,(
% 1.66/1.49 ((ksnd @ (kpair @ sK2 @ sK3)) != sK3)),
% 1.66/1.49 inference(cnf_transformation,[status(thm)],[f18])).
% 1.66/1.49 % SZS output end Proof for DTF2THF_15776
% 1.66/1.49 % (15970)------------------------------
% 1.66/1.49 % (15970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.49 % (15970)Termination reason: Refutation
% 1.66/1.49
% 1.66/1.49 % (15970)Memory used [KB]: 5500
% 1.66/1.49 % (15970)Time elapsed: 0.003 s
% 1.66/1.49 % (15970)Instructions burned: 2 (million)
% 1.66/1.49 % (15970)------------------------------
% 1.66/1.49 % (15970)------------------------------
% 1.66/1.49 % (15963)Success in time 0.005 s
%------------------------------------------------------------------------------