%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU657^2 : 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 : n024.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 09:36:00 AM UTC 2026
% Result : Theorem 0.14s 0.92s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 401 ( 114 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 612 ( 33 ~; 16 |; 36 &; 499 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 17 usr; 13 con; 0-2 aty)
% ( 0 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 99 ( 36 ^; 44 !; 19 ?; 99 :)
% 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,
iskpair: $i > $o ).
thf(func_def_6,type,
kpair: $i > $i > $i ).
thf(func_def_7,type,
kfst: $i > $i ).
thf(func_def_9,type,
ksnd: $i > $i ).
thf(f67,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f66,f60]) ).
thf(f60,plain,
( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ emptyset ) )
= sK0 ),
inference(equality_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ emptyset ) )
= sK0 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( in @ sK7 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ emptyset ) )
= sK0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) )
@ sK7 )
= $true ),
inference(sigma_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) )
& ( in @ sK6 @ ( setunion @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) )
& ( in @ Y0 @ ( setunion @ sK0 ) ) )
@ sK6 )
= $true ),
inference(sigma_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ sK0 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK0 ) ) )
& ( in @ Y0 @ ( setunion @ sK0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[status(thm)],[f30,f39]) ).
thf(f39,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= X0 )
& ( in @ X2 @ ( setunion @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= X0 )
& ( in @ X2 @ ( setunion @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Q5SuJ93TKU/DTF2THF_26097.p',iskpair) ).
thf(f30,plain,
( ( iskpair @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ksndpairEq = $true )
& ( kfstpairEq = $true )
& ( ( kpair @ ( kfst @ sK0 ) @ ( ksnd @ sK0 ) )
!= sK0 )
& ( ( iskpair @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f20]) ).
thf(f20,plain,
( ? [X0: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
!= X0 )
& ( ( iskpair @ X0 )
= $true ) )
=> ( ( ( kpair @ ( kfst @ sK0 ) @ ( ksnd @ sK0 ) )
!= sK0 )
& ( ( iskpair @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( ksndpairEq = $true )
& ( kfstpairEq = $true )
& ? [X0: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
!= X0 )
& ( ( iskpair @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
!= X0 )
& ( ( iskpair @ X0 )
= $true ) )
& ( ksndpairEq = $true )
& ( kfstpairEq = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( kfstpairEq = $true )
=> ( ( ksndpairEq = $true )
=> ! [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
=> ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( kfstpairEq
=> ( ksndpairEq
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( kfstpairEq
=> ( ksndpairEq
=> ! [X3: $i] :
( ( iskpair @ X3 )
=> ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
= X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( kfstpairEq
=> ( ksndpairEq
=> ! [X3: $i] :
( ( iskpair @ X3 )
=> ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Q5SuJ93TKU/DTF2THF_26097.p',kpairsurjEq) ).
thf(f66,plain,
( ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ emptyset ) )
!= sK0 ),
inference(backward_demodulation,[status(thm)],[f63,f65]) ).
thf(f65,plain,
( ( kfst @ sK0 )
= sK6 ),
inference(superposition,[status(thm)],[f49,f60]) ).
thf(f49,plain,
! [X0: $i,X1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= X1 ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X0: $i,X1: $i] :
( ( kfst
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ X1
@ X0 ) )
= X1 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: $i,X1: $i] :
( ( ( kfst
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ X1
@ X0 ) )
= X1 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f38,f36,f32]) ).
thf(f32,plain,
kfstpairEq = $true,
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f36,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( kpair
= ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( kpair
= ( ^ [X1: $i,X2: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Q5SuJ93TKU/DTF2THF_26097.p',kpair) ).
thf(f38,plain,
! [X0: $i,X1: $i] :
( ( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 )
| ( kfstpairEq != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 )
| ( kfstpairEq != $true ) )
& ( ( kfstpairEq = $true )
| ( sK4
!= ( kfst @ ( kpair @ sK4 @ sK3 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f27,f28]) ).
thf(f28,plain,
( ? [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X3 @ X2 ) )
!= X3 )
=> ( sK4
!= ( kfst @ ( kpair @ sK4 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 )
| ( kfstpairEq != $true ) )
& ( ( kfstpairEq = $true )
| ? [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X3 @ X2 ) )
!= X3 ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 )
| ( kfstpairEq != $true ) )
& ( ( kfstpairEq = $true )
| ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
!= X1 ) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 )
<=> ( kfstpairEq = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 )
= kfstpairEq ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $i,X1: $i] :
( ( ( kfst @ ( kpair @ X1 @ X2 ) )
= X1 )
= kfstpairEq ),
file('/export/starexec/sandbox/tmp/tmp.Q5SuJ93TKU/DTF2THF_26097.p',kfstpairEq) ).
thf(f63,plain,
( ( setadjoin @ ( setadjoin @ ( kfst @ sK0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK0 ) @ ( setadjoin @ sK7 @ emptyset ) ) @ emptyset ) )
!= sK0 ),
inference(backward_demodulation,[status(thm)],[f50,f61]) ).
thf(f61,plain,
( sK7
= ( ksnd @ sK0 ) ),
inference(superposition,[status(thm)],[f47,f60]) ).
thf(f47,plain,
! [X0: $i,X1: $i] :
( ( ksnd @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= X0 ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: $i,X1: $i] :
( ( ksnd
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ X1
@ X0 ) )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( ksnd
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ X1
@ X0 ) )
= X0 ) ),
inference(definition_unfolding,[status(thm)],[f35,f36,f33]) ).
thf(f33,plain,
ksndpairEq = $true,
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f35,plain,
! [X0: $i,X1: $i] :
( ( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
| ( ksndpairEq != $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
| ( ksndpairEq != $true ) )
& ( ( ksndpairEq = $true )
| ( ( ksnd @ ( kpair @ sK2 @ sK1 ) )
!= sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f23,f24]) ).
thf(f24,plain,
( ? [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X3 @ X2 ) )
!= X2 )
=> ( ( ksnd @ ( kpair @ sK2 @ sK1 ) )
!= sK1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,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)],[f22]) ).
thf(f22,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)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
<=> ( ksndpairEq = $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( ksndpairEq
= ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ksndpairEq
= ( ! [X2: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Q5SuJ93TKU/DTF2THF_26097.p',ksndpairEq) ).
thf(f50,plain,
( ( setadjoin @ ( setadjoin @ ( kfst @ sK0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK0 ) @ ( setadjoin @ ( ksnd @ sK0 ) @ emptyset ) ) @ emptyset ) )
!= sK0 ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ ( kfst @ sK0 )
@ ( ksnd @ sK0 ) )
!= sK0 ),
inference(definition_unfolding,[status(thm)],[f31,f36]) ).
thf(f31,plain,
( ( kpair @ ( kfst @ sK0 ) @ ( ksnd @ sK0 ) )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU657^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 07:29:25 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEU657^2 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.32 % Domain : Set Theory
% 0.07/0.32 % Problem : Ordered Pairs - Properties of Pairs
% 0.07/0.32 % Version : Especial > Reduced > Especial.
% 0.07/0.32 % English : (! u:i.iskpair u -> kpair (kfst u) (ksnd u) = u)
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.07/0.32 % Source : [Bro08]
% 0.07/0.32 % Names : ZFC159l [Bro08]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.07/0.32 % Syntax : Number of formulae : 15 ( 4 unt; 10 typ; 4 def)
% 0.07/0.32 % Number of atoms : 16 ( 8 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 4 ( 3 avg)
% 0.07/0.32 % Number of connectives : 42 ( 0 ~; 0 |; 2 &; 37 @)
% 0.07/0.32 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 6 ( 2 avg)
% 0.07/0.32 % Number of types : 2 ( 0 usr)
% 0.07/0.32 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 11 ( 10 usr; 3 con; 0-2 aty)
% 0.07/0.32 % Number of variables : 10 ( 3 ^; 5 !; 2 ?; 10 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : http://mathgate.info/detsetitem.php?id=426
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(in_type,type,
% 0.07/0.32 in: $i > $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyset_type,type,
% 0.07/0.32 emptyset: $i ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoin_type,type,
% 0.07/0.32 setadjoin: $i > $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(setunion_type,type,
% 0.07/0.32 setunion: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(iskpair_type,type,
% 0.07/0.32 iskpair: $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(iskpair,definition,
% 0.07/0.32 ( iskpair
% 0.07/0.32 = ( ^ [A: $i] :
% 0.07/0.32 ? [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ ( setunion @ A ) )
% 0.07/0.32 & ? [Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ ( setunion @ A ) )
% 0.07/0.32 & ( A
% 0.07/0.32 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(kpair_type,type,
% 0.07/0.32 kpair: $i > $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(kpair,definition,
% 0.07/0.32 ( kpair
% 0.07/0.32 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(kfst_type,type,
% 0.07/0.32 kfst: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(kfstpairEq_type,type,
% 0.07/0.32 kfstpairEq: $o ).
% 0.07/0.32
% 0.07/0.32 thf(kfstpairEq,definition,
% 0.07/0.32 ( kfstpairEq
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.07/0.32 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.07/0.32 = Xx ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(ksnd_type,type,
% 0.07/0.32 ksnd: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(ksndpairEq_type,type,
% 0.07/0.32 ksndpairEq: $o ).
% 0.07/0.32
% 0.07/0.32 thf(ksndpairEq,definition,
% 0.07/0.32 ( ksndpairEq
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.07/0.32 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.07/0.32 = Xy ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(kpairsurjEq,conjecture,
% 0.07/0.32 ( kfstpairEq
% 0.07/0.32 => ( ksndpairEq
% 0.07/0.32 => ! [Xu: $i] :
% 0.07/0.32 ( ( iskpair @ Xu )
% 0.07/0.32 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.07/0.32 = Xu ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.14/0.90 ---- Embedded in THF ---
% 0.14/0.90 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.14/0.90 %%% Generated on Tue Feb 24 07:29:26 EST 2026
% 0.14/0.90 %%% using '$$dhol' embedding, version 1.3.0.
% 0.14/0.90 %%% Logic specification used:
% 0.14/0.90 %%% thf(spec, logic, $$dhol).
% 0.14/0.90
% 0.14/0.90 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Q5SuJ93TKU/DTF2DTF26097.p
% See solution above
% 0.14/0.90 ------------------------
% 0.14/0.91 ---- Cleaned THF ---
% 0.14/0.91 thf(in_type,type,
% 0.14/0.91 in: $i > $i > $o ).
% 0.14/0.91
% 0.14/0.91 thf(emptyset_type,type,
% 0.14/0.91 emptyset: $i ).
% 0.14/0.91
% 0.14/0.91 thf(setadjoin_type,type,
% 0.14/0.91 setadjoin: $i > $i > $i ).
% 0.14/0.91
% 0.14/0.91 thf(setunion_type,type,
% 0.14/0.91 setunion: $i > $i ).
% 0.14/0.91
% 0.14/0.91 thf(iskpair_type,type,
% 0.14/0.91 iskpair: $i > $o ).
% 0.14/0.91
% 0.14/0.91 thf(iskpair,definition,
% 0.14/0.91 ( iskpair
% 0.14/0.91 = ( ^ [A: $i] :
% 0.14/0.91 ? [Xx: $i] :
% 0.14/0.91 ( ( in @ Xx @ ( setunion @ A ) )
% 0.14/0.91 & ? [Xy: $i] :
% 0.14/0.91 ( ( in @ Xy @ ( setunion @ A ) )
% 0.14/0.91 & ( A
% 0.14/0.91 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.14/0.91
% 0.14/0.91 thf(kpair_type,type,
% 0.14/0.91 kpair: $i > $i > $i ).
% 0.14/0.91
% 0.14/0.91 thf(kpair,definition,
% 0.14/0.91 ( kpair
% 0.14/0.91 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.14/0.91
% 0.14/0.91 thf(kfst_type,type,
% 0.14/0.91 kfst: $i > $i ).
% 0.14/0.91
% 0.14/0.91 thf(kfstpairEq_type,type,
% 0.14/0.91 kfstpairEq: $o ).
% 0.14/0.91
% 0.14/0.91 thf(kfstpairEq,definition,
% 0.14/0.91 ( kfstpairEq
% 0.14/0.91 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.91 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.14/0.91 = Xx ) ) ) ).
% 0.14/0.91
% 0.14/0.91 thf(ksnd_type,type,
% 0.14/0.91 ksnd: $i > $i ).
% 0.14/0.91
% 0.14/0.91 thf(ksndpairEq_type,type,
% 0.14/0.91 ksndpairEq: $o ).
% 0.14/0.91
% 0.14/0.91 thf(ksndpairEq,definition,
% 0.14/0.91 ( ksndpairEq
% 0.14/0.91 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.91 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.14/0.91 = Xy ) ) ) ).
% 0.14/0.91
% 0.14/0.91 thf(kpairsurjEq,conjecture,
% 0.14/0.91 ( kfstpairEq
% 0.14/0.91 => ( ksndpairEq
% 0.14/0.91 => ! [Xu: $i] :
% 0.14/0.91 ( ( iskpair @ Xu )
% 0.14/0.91 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.14/0.91 = Xu ) ) ) ) ).
% 0.14/0.91 ------------------------
% 0.14/0.92 % (26366)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26097 for (3000ds/183Mi)
% 0.14/0.92 % (26367)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_26097 for (3000ds/4Mi)
% 0.14/0.92 % (26371)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_26097 for (3000ds/275Mi)
% 0.14/0.92 % (26369)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26097 for (3000ds/2Mi)
% 0.14/0.92 % (26368)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_26097 for (3000ds/27Mi)
% 0.14/0.92 % (26370)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_26097 for (3000ds/2Mi)
% 0.14/0.92 % (26372)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26097 for (3000ds/18Mi)
% 0.14/0.92 % (26369)Instruction limit reached!
% 0.14/0.92 % (26369)------------------------------
% 0.14/0.92 % (26369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.14/0.92 % (26369)Termination reason: Unknown
% 0.14/0.92 % (26369)Termination phase: Property scanning
% 0.14/0.92
% 0.14/0.92 % (26369)Memory used [KB]: 1023
% 0.14/0.92 % (26369)Time elapsed: 0.002 s
% 0.14/0.92 % (26369)Instructions burned: 3 (million)
% 0.14/0.92 % (26369)------------------------------
% 0.14/0.92 % (26369)------------------------------
% 0.14/0.92 % (26370)Instruction limit reached!
% 0.14/0.92 % (26370)------------------------------
% 0.14/0.92 % (26370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.14/0.92 % (26370)Termination reason: Unknown
% 0.14/0.92 % (26370)Termination phase: Saturation
% 0.14/0.92
% 0.14/0.92 % (26370)Memory used [KB]: 1023
% 0.14/0.92 % (26370)Time elapsed: 0.002 s
% 0.14/0.92 % (26370)Instructions burned: 3 (million)
% 0.14/0.92 % (26370)------------------------------
% 0.14/0.92 % (26370)------------------------------
% 0.14/0.92 % (26371)Refutation not found, incomplete strategy
% 0.14/0.92 % (26371)------------------------------
% 0.14/0.92 % (26371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.14/0.92 % (26371)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.92
% 0.14/0.92
% 0.14/0.92 % (26371)Memory used [KB]: 5500
% 0.14/0.92 % (26371)Time elapsed: 0.002 s
% 0.14/0.92 % (26371)Instructions burned: 2 (million)
% 0.14/0.92 % (26371)------------------------------
% 0.14/0.92 % (26371)------------------------------
% 0.14/0.92 % (26367)Instruction limit reached!
% 0.14/0.92 % (26367)------------------------------
% 0.14/0.92 % (26367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.14/0.92 % (26367)Termination reason: Unknown
% 0.14/0.92 % (26367)Termination phase: Saturation
% 0.14/0.92
% 0.14/0.92 % (26367)Memory used [KB]: 5500
% 0.14/0.92 % (26367)Time elapsed: 0.003 s
% 0.14/0.92 % (26367)Instructions burned: 5 (million)
% 0.14/0.92 % (26367)------------------------------
% 0.14/0.92 % (26367)------------------------------
% 0.14/0.92 % (26372)First to succeed.
% 0.14/0.92 % (26366)Also succeeded, but the first one will report.
% 0.14/0.92 % (26372)Refutation found. Thanks to Tanya!
% 0.14/0.92 % SZS status Theorem for DTF2THF_26097
% 0.14/0.92 % SZS output start Proof for DTF2THF_26097
% 0.14/0.92 thf(func_def_0, type, in: $i > $i > $o).
% 0.14/0.92 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.14/0.92 thf(func_def_3, type, setunion: $i > $i).
% 0.14/0.92 thf(func_def_4, type, iskpair: $i > $o).
% 0.14/0.92 thf(func_def_6, type, kpair: $i > $i > $i).
% 0.14/0.92 thf(func_def_7, type, kfst: $i > $i).
% 0.14/0.92 thf(func_def_9, type, ksnd: $i > $i).
% 0.14/0.92 thf(f67,plain,(
% 0.14/0.92 $false),
% 0.14/0.92 inference(subsumption_resolution,[status(thm)],[f66,f60])).
% 0.14/0.92 thf(f60,plain,(
% 0.14/0.92 ((setadjoin @ (setadjoin @ sK6 @ emptyset) @ (setadjoin @ (setadjoin @ sK6 @ (setadjoin @ sK7 @ emptyset)) @ emptyset)) = sK0)),
% 0.14/0.92 inference(equality_proxy_clausification,[status(thm)],[f58])).
% 0.14/0.92 thf(f58,plain,(
% 0.14/0.92 (((setadjoin @ (setadjoin @ sK6 @ emptyset) @ (setadjoin @ (setadjoin @ sK6 @ (setadjoin @ sK7 @ emptyset)) @ emptyset)) = sK0) = $true)),
% 0.14/0.92 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 0.14/0.92 thf(f57,plain,(
% 0.14/0.92 (((in @ sK7 @ (setunion @ sK0)) & ((setadjoin @ (setadjoin @ sK6 @ emptyset) @ (setadjoin @ (setadjoin @ sK6 @ (setadjoin @ sK7 @ emptyset)) @ emptyset)) = sK0)) = $true)),
% 0.14/0.92 inference(beta_eta_normalization,[status(thm)],[f56])).
% 0.14/0.92 thf(f56,plain,(
% 0.14/0.92 (((^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK0)) & ((setadjoin @ (setadjoin @ sK6 @ emptyset) @ (setadjoin @ (setadjoin @ sK6 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK0))) @ sK7) = $true)),
% 0.14/0.92 inference(sigma_clausification,[status(thm)],[f55])).
% 0.14/0.92 thf(f55,plain,(
% 0.14/0.92 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK0)) & ((setadjoin @ (setadjoin @ sK6 @ emptyset) @ (setadjoin @ (setadjoin @ sK6 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK0)))) = $true)),
% 0.14/0.92 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 0.14/0.92 thf(f53,plain,(
% 0.14/0.92 (((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK0)) & ((setadjoin @ (setadjoin @ sK6 @ emptyset) @ (setadjoin @ (setadjoin @ sK6 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK0)))) & (in @ sK6 @ (setunion @ sK0))) = $true)),
% 0.14/0.92 inference(beta_eta_normalization,[status(thm)],[f52])).
% 0.14/0.92 thf(f52,plain,(
% 0.14/0.92 (((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ sK0)) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK0)))) & (in @ Y0 @ (setunion @ sK0)))) @ sK6) = $true)),
% 0.14/0.92 inference(sigma_clausification,[status(thm)],[f51])).
% 0.14/0.92 thf(f51,plain,(
% 0.14/0.92 ((?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ sK0)) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK0)))) & (in @ Y0 @ (setunion @ sK0))))) = $true)),
% 0.14/0.92 inference(beta_eta_normalization,[status(thm)],[f41])).
% 0.14/0.92 thf(f41,plain,(
% 0.14/0.92 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0)))))) @ sK0) = $true)),
% 0.14/0.92 inference(definition_unfolding,[status(thm)],[f30,f39])).
% 0.14/0.92 thf(f39,plain,(
% 0.14/0.92 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0)))))))),
% 0.14/0.92 inference(cnf_transformation,[status(thm)],[f15])).
% 0.14/0.92 thf(f15,plain,(
% 0.14/0.92 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0)))))))),
% 0.14/0.92 inference(fool_elimination,[status(thm)],[f14])).
% 0.14/0.92 thf(f14,plain,(
% 0.14/0.92 (iskpair = (^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ (setunion @ X0)) & ? [X2 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0) & (in @ X2 @ (setunion @ X0)))))))),
% 0.14/0.92 inference(rectify,[status(thm)],[f1])).
% 0.14/0.92 thf(f1,axiom,(
% 0.14/0.92 (iskpair = (^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ (setunion @ X0)) & ? [X2 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0) & (in @ X2 @ (setunion @ X0)))))))),
% 0.14/0.92 file('/export/starexec/sandbox/tmp/tmp.Q5SuJ93TKU/DTF2THF_26097.p',iskpair)).
% 0.14/0.92 thf(f30,plain,(
% 0.14/0.92 ((iskpair @ sK0) = $true)),
% 0.14/0.92 inference(cnf_transformation,[status(thm)],[f21])).
% 0.14/0.92 thf(f21,plain,(
% 0.14/0.92 (ksndpairEq = $true) & (kfstpairEq = $true) & (((kpair @ (kfst @ sK0) @ (ksnd @ sK0)) != sK0) & ((iskpair @ sK0) = $true))),
% 0.14/0.92 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f20])).
% 0.14/0.92 thf(f20,plain,(
% 0.14/0.92 ? [X0 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) != X0) & ((iskpair @ X0) = $true)) => (((kpair @ (kfst @ sK0) @ (ksnd @ sK0)) != sK0) & ((iskpair @ sK0) = $true))),
% 0.14/0.92 introduced(definition,[],[choice_axiom])).
% 0.14/0.92 thf(f19,plain,(
% 0.14/0.92 (ksndpairEq = $true) & (kfstpairEq = $true) & ? [X0 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) != X0) & ((iskpair @ X0) = $true))),
% 0.14/0.92 inference(flattening,[status(thm)],[f18])).
% 0.14/0.92 thf(f18,plain,(
% 0.14/0.92 (? [X0 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) != X0) & ((iskpair @ X0) = $true)) & (ksndpairEq = $true)) & (kfstpairEq = $true)),
% 0.14/0.92 inference(ennf_transformation,[status(thm)],[f9])).
% 0.14/0.92 thf(f9,plain,(
% 0.14/0.92 ~((kfstpairEq = $true) => ((ksndpairEq = $true) => ! [X0 : $i] : (((iskpair @ X0) = $true) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0))))),
% 0.14/0.92 inference(fool_elimination,[status(thm)],[f8])).
% 0.14/0.92 thf(f8,plain,(
% 0.14/0.92 ~(kfstpairEq => (ksndpairEq => ! [X0 : $i] : ((iskpair @ X0) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0))))),
% 0.14/0.92 inference(rectify,[status(thm)],[f6])).
% 0.14/0.92 thf(f6,negated_conjecture,(
% 0.14/0.92 ~(kfstpairEq => (ksndpairEq => ! [X3 : $i] : ((iskpair @ X3) => ((kpair @ (kfst @ X3) @ (ksnd @ X3)) = X3))))),
% 0.14/0.92 inference(negated_conjecture,[status(cth)],[f5])).
% 0.14/0.92 thf(f5,conjecture,(
% 0.14/0.92 kfstpairEq => (ksndpairEq => ! [X3 : $i] : ((iskpair @ X3) => ((kpair @ (kfst @ X3) @ (ksnd @ X3)) = X3)))),
% 0.14/0.92 file('/export/starexec/sandbox/tmp/tmp.Q5SuJ93TKU/DTF2THF_26097.p',kpairsurjEq)).
% 0.14/0.92 thf(f66,plain,(
% 0.14/0.92 ((setadjoin @ (setadjoin @ sK6 @ emptyset) @ (setadjoin @ (setadjoin @ sK6 @ (setadjoin @ sK7 @ emptyset)) @ emptyset)) != sK0)),
% 0.14/0.92 inference(backward_demodulation,[status(thm)],[f63,f65])).
% 0.14/0.92 thf(f65,plain,(
% 0.14/0.92 ((kfst @ sK0) = sK6)),
% 0.14/0.92 inference(superposition,[status(thm)],[f49,f60])).
% 0.14/0.92 thf(f49,plain,(
% 0.14/0.92 ( ! [X0 : $i,X1 : $i] : (((kfst @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) = X1)) )),
% 0.14/0.92 inference(beta_eta_normalization,[status(thm)],[f48])).
% 0.14/0.92 thf(f48,plain,(
% 0.14/0.92 ( ! [X0 : $i,X1 : $i] : (((kfst @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ X1 @ X0)) = X1)) )),
% 0.14/0.92 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 0.14/0.92 thf(f44,plain,(
% 0.14/0.92 ( ! [X0 : $i,X1 : $i] : (((kfst @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ X1 @ X0)) = X1) | ($true != $true)) )),
% 0.14/0.92 inference(definition_unfolding,[status(thm)],[f38,f36,f32])).
% 0.14/0.92 thf(f32,plain,(
% 0.14/0.92 (kfstpairEq = $true)),
% 0.14/0.92 inference(cnf_transformation,[status(thm)],[f21])).
% 0.14/0.92 thf(f36,plain,(
% 0.14/0.92 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.14/0.92 inference(cnf_transformation,[status(thm)],[f13])).
% 0.14/0.92 thf(f13,plain,(
% 0.14/0.92 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.14/0.92 inference(fool_elimination,[status(thm)],[f12])).
% 0.14/0.92 thf(f12,plain,(
% 0.14/0.92 (kpair = (^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))),
% 0.14/0.92 inference(rectify,[status(thm)],[f2])).
% 0.14/0.92 thf(f2,axiom,(
% 0.14/0.92 (kpair = (^[X1 : $i, X2 : $i] : (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))),
% 0.14/0.92 file('/export/starexec/sandbox/tmp/tmp.Q5SuJ93TKU/DTF2THF_26097.p',kpair)).
% 0.14/0.92 thf(f38,plain,(
% 0.14/0.92 ( ! [X0 : $i,X1 : $i] : (((kfst @ (kpair @ X1 @ X0)) = X1) | (kfstpairEq != $true)) )),
% 0.14/0.92 inference(cnf_transformation,[status(thm)],[f29])).
% 0.14/0.92 thf(f29,plain,(
% 0.14/0.92 (! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X0)) = X1) | (kfstpairEq != $true)) & ((kfstpairEq = $true) | (sK4 != (kfst @ (kpair @ sK4 @ sK3))))),
% 0.14/0.92 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f27,f28])).
% 0.14/0.92 thf(f28,plain,(
% 0.14/0.92 ? [X2 : $i,X3 : $i] : ((kfst @ (kpair @ X3 @ X2)) != X3) => (sK4 != (kfst @ (kpair @ sK4 @ sK3)))),
% 0.14/0.92 introduced(definition,[],[choice_axiom])).
% 0.14/0.92 thf(f27,plain,(
% 0.14/0.92 (! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X0)) = X1) | (kfstpairEq != $true)) & ((kfstpairEq = $true) | ? [X2 : $i,X3 : $i] : ((kfst @ (kpair @ X3 @ X2)) != X3))),
% 0.14/0.92 inference(rectify,[status(thm)],[f26])).
% 0.14/0.92 thf(f26,plain,(
% 0.14/0.92 (! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X0)) = X1) | (kfstpairEq != $true)) & ((kfstpairEq = $true) | ? [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X0)) != X1))),
% 0.14/0.92 inference(nnf_transformation,[status(thm)],[f11])).
% 0.14/0.92 thf(f11,plain,(
% 0.14/0.92 ! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X0)) = X1) <=> (kfstpairEq = $true)),
% 0.14/0.92 inference(fool_elimination,[status(thm)],[f10])).
% 0.14/0.92 thf(f10,plain,(
% 0.14/0.92 (! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X0)) = X1) = kfstpairEq)),
% 0.14/0.92 inference(rectify,[status(thm)],[f3])).
% 0.14/0.92 thf(f3,axiom,(
% 0.14/0.92 (! [X2 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X2)) = X1) = kfstpairEq)),
% 0.14/0.92 file('/export/starexec/sandbox/tmp/tmp.Q5SuJ93TKU/DTF2THF_26097.p',kfstpairEq)).
% 0.14/0.92 thf(f63,plain,(
% 0.14/0.92 ((setadjoin @ (setadjoin @ (kfst @ sK0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK0) @ (setadjoin @ sK7 @ emptyset)) @ emptyset)) != sK0)),
% 0.14/0.92 inference(backward_demodulation,[status(thm)],[f50,f61])).
% 0.14/0.92 thf(f61,plain,(
% 0.14/0.92 (sK7 = (ksnd @ sK0))),
% 0.14/0.92 inference(superposition,[status(thm)],[f47,f60])).
% 0.14/0.92 thf(f47,plain,(
% 0.14/0.92 ( ! [X0 : $i,X1 : $i] : (((ksnd @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) = X0)) )),
% 0.14/0.92 inference(beta_eta_normalization,[status(thm)],[f46])).
% 0.14/0.92 thf(f46,plain,(
% 0.14/0.92 ( ! [X0 : $i,X1 : $i] : (((ksnd @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ X1 @ X0)) = X0)) )),
% 0.14/0.92 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 0.14/0.92 thf(f42,plain,(
% 0.14/0.92 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((ksnd @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ X1 @ X0)) = X0)) )),
% 0.14/0.92 inference(definition_unfolding,[status(thm)],[f35,f36,f33])).
% 0.14/0.92 thf(f33,plain,(
% 0.14/0.92 (ksndpairEq = $true)),
% 0.14/0.92 inference(cnf_transformation,[status(thm)],[f21])).
% 0.14/0.92 thf(f35,plain,(
% 0.14/0.92 ( ! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X1 @ X0)) = X0) | (ksndpairEq != $true)) )),
% 0.14/0.92 inference(cnf_transformation,[status(thm)],[f25])).
% 0.14/0.92 thf(f25,plain,(
% 0.14/0.92 (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) = X0) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | ((ksnd @ (kpair @ sK2 @ sK1)) != sK1))),
% 0.14/0.92 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f23,f24])).
% 0.14/0.92 thf(f24,plain,(
% 0.14/0.92 ? [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X3 @ X2)) != X2) => ((ksnd @ (kpair @ sK2 @ sK1)) != sK1)),
% 0.14/0.92 introduced(definition,[],[choice_axiom])).
% 0.14/0.92 thf(f23,plain,(
% 0.14/0.92 (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) = X0) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | ? [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X3 @ X2)) != X2))),
% 0.14/0.92 inference(rectify,[status(thm)],[f22])).
% 0.14/0.92 thf(f22,plain,(
% 0.14/0.92 (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) = X0) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | ? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) != X0))),
% 0.14/0.92 inference(nnf_transformation,[status(thm)],[f17])).
% 0.14/0.92 thf(f17,plain,(
% 0.14/0.92 ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) = X0) <=> (ksndpairEq = $true)),
% 0.14/0.92 inference(fool_elimination,[status(thm)],[f16])).
% 0.14/0.92 thf(f16,plain,(
% 0.14/0.92 (ksndpairEq = ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X0)) = X0))),
% 0.14/0.92 inference(rectify,[status(thm)],[f4])).
% 0.14/0.92 thf(f4,axiom,(
% 0.14/0.92 (ksndpairEq = ! [X2 : $i,X1 : $i] : ((ksnd @ (kpair @ X1 @ X2)) = X2))),
% 0.14/0.92 file('/export/starexec/sandbox/tmp/tmp.Q5SuJ93TKU/DTF2THF_26097.p',ksndpairEq)).
% 0.14/0.92 thf(f50,plain,(
% 0.14/0.92 ((setadjoin @ (setadjoin @ (kfst @ sK0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK0) @ (setadjoin @ (ksnd @ sK0) @ emptyset)) @ emptyset)) != sK0)),
% 0.14/0.92 inference(beta_eta_normalization,[status(thm)],[f40])).
% 0.14/0.92 thf(f40,plain,(
% 0.14/0.92 (((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ (kfst @ sK0) @ (ksnd @ sK0)) != sK0)),
% 0.14/0.92 inference(definition_unfolding,[status(thm)],[f31,f36])).
% 0.14/0.92 thf(f31,plain,(
% 0.14/0.92 ((kpair @ (kfst @ sK0) @ (ksnd @ sK0)) != sK0)),
% 0.14/0.92 inference(cnf_transformation,[status(thm)],[f21])).
% 0.14/0.92 % SZS output end Proof for DTF2THF_26097
% 0.14/0.92 % (26372)------------------------------
% 0.14/0.92 % (26372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.14/0.92 % (26372)Termination reason: Refutation
% 0.14/0.92
% 0.14/0.92 % (26372)Memory used [KB]: 5500
% 0.14/0.92 % (26372)Time elapsed: 0.004 s
% 0.14/0.92 % (26372)Instructions burned: 6 (million)
% 0.14/0.92 % (26372)------------------------------
% 0.14/0.92 % (26372)------------------------------
% 0.14/0.92 % (26365)Success in time 0.012 s
%------------------------------------------------------------------------------