%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU505^2 : 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 : n001.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 09:34:58 AM UTC 2026
% Result : Theorem 1.66s 1.46s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 376 ( 120 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 385 ( 46 ~; 45 |; 24 &; 240 @)
% ( 4 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 84 ( 0 ^; 66 !; 18 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_7,type,
sK2: $i > $i > $i ).
thf(f62,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f51,f60]) ).
thf(f60,plain,
( ( in @ ( sK2 @ sK4 @ sK3 ) @ sK3 )
= $false ),
inference(subsumption_resolution,[status(thm)],[f58,f24]) ).
thf(f24,plain,
sK3 != sK4,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X2: $i] :
( ( ( in @ X2 @ sK3 )
!= $true )
| ( ( in @ X2 @ sK4 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ sK4 )
!= $true )
| ( ( in @ X3 @ sK3 )
= $true ) )
& ( sK3 != sK4 )
& ( setextAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f17,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
= $true ) )
& ( X0 != X1 ) )
=> ( ! [X2: $i] :
( ( ( in @ X2 @ sK3 )
!= $true )
| ( ( in @ X2 @ sK4 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ sK4 )
!= $true )
| ( ( in @ X3 @ sK3 )
= $true ) )
& ( sK3 != sK4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
= $true ) )
& ( X0 != X1 ) )
& ( setextAx = $true ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
( ? [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
= $true ) )
& ( X0 != X1 ) )
& ( setextAx = $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
= $true ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( setextAx = $true )
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ X3 @ X1 )
= $true ) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( setextAx
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ X3 @ X1 ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setextAx
=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setextAx
=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DfjQKKTWal/DTF2THF_7511.p',setext) ).
thf(f58,plain,
( ( ( in @ ( sK2 @ sK4 @ sK3 ) @ sK3 )
= $false )
| ( sK3 = sK4 ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $false = $true )
| ( ( in @ ( sK2 @ sK4 @ sK3 ) @ sK3 )
= $false )
| ( sK3 = sK4 ) ),
inference(superposition,[status(thm)],[f32,f53]) ).
thf(f53,plain,
( ( in @ ( sK2 @ sK4 @ sK3 ) @ sK4 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( in @ ( sK2 @ sK4 @ sK3 ) @ sK4 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f26,f51]) ).
thf(f26,plain,
! [X2: $i] :
( ( ( in @ X2 @ sK3 )
!= $true )
| ( ( in @ X2 @ sK4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f32,plain,
! [X3: $i,X4: $i] :
( ( $false
= ( in @ ( sK2 @ X4 @ X3 ) @ X4 ) )
| ( X3 = X4 )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X3: $i,X4: $i] :
( ( X3 = X4 )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= ( in @ ( sK2 @ X4 @ X3 ) @ X4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= ( in @ ( sK2 @ X4 @ X3 ) @ X4 ) )
| ( $true != $true )
| ( X3 = X4 ) ),
inference(definition_unfolding,[status(thm)],[f20,f23]) ).
thf(f23,plain,
setextAx = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f20,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= ( in @ ( sK2 @ X4 @ X3 ) @ X4 ) )
| ( X3 = X4 )
| ( setextAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( setextAx = $true )
| ( ! [X2: $i] :
( ( in @ X2 @ sK1 )
= ( in @ X2 @ sK0 ) )
& ( sK1 != sK0 ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= ( in @ ( sK2 @ X4 @ X3 ) @ X4 ) )
| ( X3 = X4 ) )
| ( setextAx != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f15,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
= ( in @ X2 @ X1 ) )
& ( X0 != X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ sK1 )
= ( in @ X2 @ sK0 ) )
& ( sK1 != sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( in @ X5 @ X4 )
!= ( in @ X5 @ X3 ) )
=> ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= ( in @ ( sK2 @ X4 @ X3 ) @ X4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( ( setextAx = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
= ( in @ X2 @ X1 ) )
& ( X0 != X1 ) ) )
& ( ! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( in @ X5 @ X4 )
!= ( in @ X5 @ X3 ) )
| ( X3 = X4 ) )
| ( setextAx != $true ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( setextAx = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
= ( in @ X2 @ X1 ) )
& ( X0 != X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
!= ( in @ X2 @ X1 ) )
| ( X0 = X1 ) )
| ( setextAx != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( setextAx = $true )
<=> ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
!= ( in @ X2 @ X1 ) )
| ( X0 = X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
= ( in @ X2 @ X1 ) )
=> ( X0 = X1 ) )
<=> ( setextAx = $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( setextAx
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
<=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setextAx
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
<=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DfjQKKTWal/DTF2THF_7511.p',setextAx) ).
thf(f51,plain,
( ( in @ ( sK2 @ sK4 @ sK3 ) @ sK3 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f49,f24]) ).
thf(f49,plain,
( ( sK3 = sK4 )
| ( ( in @ ( sK2 @ sK4 @ sK3 ) @ sK3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( in @ ( sK2 @ sK4 @ sK3 ) @ sK3 )
= $true )
| ( sK3 = sK4 )
| ( $true != $true ) ),
inference(equality_factoring,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i] :
( ( ( in @ ( sK2 @ sK4 @ X0 ) @ sK3 )
= $true )
| ( sK4 = X0 )
| ( ( in @ ( sK2 @ sK4 @ X0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: $i] :
( ( $true != $true )
| ( sK4 = X0 )
| ( ( in @ ( sK2 @ sK4 @ X0 ) @ sK3 )
= $true )
| ( ( in @ ( sK2 @ sK4 @ X0 ) @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f25,f31]) ).
thf(f31,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true )
| ( X3 = X4 )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f25,plain,
! [X3: $i] :
( ( ( in @ X3 @ sK4 )
!= $true )
| ( ( in @ X3 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU505^2 : 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
% 0.18/0.34 % Computer : n001.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:25:35 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.34/0.49 ---- Original DTF file ---
% 0.34/0.49 thf(spec,logic,$$dhol).
% 0.34/0.49 %------------------------------------------------------------------------------
% 0.34/0.49 % File : SEU505^2 : TPTP v9.2.1. Released v3.7.0.
% 0.34/0.49 % Domain : Set Theory
% 0.34/0.49 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.34/0.49 % Version : Especial > Reduced > Especial.
% 0.34/0.49 % English : (! A:i.! B:i.(! x:i.in x A -> in x B) -> (! x:i.in x B -> in x A)
% 0.34/0.49 % -> A = B)
% 0.34/0.49
% 0.34/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.34/0.49 % Source : [Bro08]
% 0.34/0.49 % Names : ZFC007l [Bro08]
% 0.34/0.49
% 0.34/0.49 % Status : Theorem
% 0.34/0.49 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.34/0.49 % Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 1 def)
% 0.34/0.49 % Number of atoms : 11 ( 3 equ; 0 cnn)
% 0.34/0.49 % Maximal formula atoms : 6 ( 5 avg)
% 0.34/0.49 % Number of connectives : 19 ( 0 ~; 0 |; 0 &; 12 @)
% 0.34/0.49 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.34/0.49 % Maximal formula depth : 10 ( 6 avg)
% 0.34/0.49 % Number of types : 2 ( 0 usr)
% 0.34/0.49 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.34/0.49 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.34/0.49 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.34/0.49 % SPC : TH0_THM_EQU_NAR
% 0.34/0.49
% 0.34/0.49 % Comments : http://mathgate.info/detsetitem.php?id=78
% 0.34/0.49 %------------------------------------------------------------------------------
% 0.34/0.49 thf(in_type,type,
% 0.34/0.49 in: $i > $i > $o ).
% 0.34/0.49
% 0.34/0.49 thf(setextAx_type,type,
% 0.34/0.49 setextAx: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setextAx,definition,
% 0.34/0.49 ( setextAx
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 <=> ( in @ Xx @ B ) )
% 0.34/0.49 => ( A = B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setext,conjecture,
% 0.34/0.49 ( setextAx
% 0.34/0.49 => ! [A: $i,B: $i] :
% 0.34/0.49 ( ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( in @ Xx @ B ) )
% 0.34/0.49 => ( ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ B )
% 0.34/0.49 => ( in @ Xx @ A ) )
% 0.34/0.49 => ( A = B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 %------------------------------------------------------------------------------
% 0.34/0.49 ------------------------
% 1.66/1.42 ---- Embedded in THF ---
% 1.66/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.43 %%% Generated on Tue Feb 24 12:25:36 EST 2026
% 1.66/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.43 %%% Logic specification used:
% 1.66/1.43 %%% thf(spec, logic, $$dhol).
% 1.66/1.43
% 1.66/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.DfjQKKTWal/DTF2DTF7511.p
% See solution above
% 1.66/1.43 ------------------------
% 1.66/1.43 ---- Cleaned THF ---
% 1.66/1.43 thf(in_type,type,
% 1.66/1.43 in: $i > $i > $o ).
% 1.66/1.43
% 1.66/1.43 thf(setextAx_type,type,
% 1.66/1.43 setextAx: $o ).
% 1.66/1.43
% 1.66/1.43 thf(setextAx,definition,
% 1.66/1.43 ( setextAx
% 1.66/1.43 = ( ! [A: $i,B: $i] :
% 1.66/1.43 ( ! [Xx: $i] :
% 1.66/1.43 ( ( in @ Xx @ A )
% 1.66/1.43 <=> ( in @ Xx @ B ) )
% 1.66/1.43 => ( A = B ) ) ) ) ).
% 1.66/1.43
% 1.66/1.43 thf(setext,conjecture,
% 1.66/1.43 ( setextAx
% 1.66/1.43 => ! [A: $i,B: $i] :
% 1.66/1.43 ( ! [Xx: $i] :
% 1.66/1.43 ( ( in @ Xx @ A )
% 1.66/1.43 => ( in @ Xx @ B ) )
% 1.66/1.43 => ( ! [Xx: $i] :
% 1.66/1.43 ( ( in @ Xx @ B )
% 1.66/1.43 => ( in @ Xx @ A ) )
% 1.66/1.43 => ( A = B ) ) ) ) ).
% 1.66/1.43 ------------------------
% 1.66/1.45 % (7623)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_7511 for (2999ds/275Mi)
% 1.66/1.45 % (7618)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7511 for (2999ds/183Mi)
% 1.66/1.45 % (7620)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_7511 for (2999ds/27Mi)
% 1.66/1.45 % (7622)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_7511 for (2999ds/2Mi)
% 1.66/1.45 % (7624)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7511 for (2999ds/18Mi)
% 1.66/1.45 % (7621)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7511 for (2999ds/2Mi)
% 1.66/1.45 % (7619)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_7511 for (2999ds/4Mi)
% 1.66/1.46 % (7622)Instruction limit reached!
% 1.66/1.46 % (7622)------------------------------
% 1.66/1.46 % (7622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (7622)Termination reason: Unknown
% 1.66/1.46 % (7622)Termination phase: Property scanning
% 1.66/1.46
% 1.66/1.46 % (7622)Memory used [KB]: 895
% 1.66/1.46 % (7622)Time elapsed: 0.003 s
% 1.66/1.46 % (7622)Instructions burned: 2 (million)
% 1.66/1.46 % (7622)------------------------------
% 1.66/1.46 % (7622)------------------------------
% 1.66/1.46 % (7621)Instruction limit reached!
% 1.66/1.46 % (7621)------------------------------
% 1.66/1.46 % (7621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (7621)Termination reason: Unknown
% 1.66/1.46 % (7621)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (7621)Memory used [KB]: 5500
% 1.66/1.46 % (7621)Time elapsed: 0.004 s
% 1.66/1.46 % (7621)Instructions burned: 3 (million)
% 1.66/1.46 % (7621)------------------------------
% 1.66/1.46 % (7621)------------------------------
% 1.66/1.46 % (7619)Instruction limit reached!
% 1.66/1.46 % (7619)------------------------------
% 1.66/1.46 % (7619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (7619)Termination reason: Unknown
% 1.66/1.46 % (7619)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (7619)Memory used [KB]: 5500
% 1.66/1.46 % (7619)Time elapsed: 0.004 s
% 1.66/1.46 % (7619)Instructions burned: 4 (million)
% 1.66/1.46 % (7619)------------------------------
% 1.66/1.46 % (7619)------------------------------
% 1.66/1.46 % (7624)First to succeed.
% 1.66/1.46 % (7623)Also succeeded, but the first one will report.
% 1.66/1.46 % (7618)Also succeeded, but the first one will report.
% 1.66/1.46 % (7624)Refutation found. Thanks to Tanya!
% 1.66/1.46 % SZS status Theorem for DTF2THF_7511
% 1.66/1.46 % SZS output start Proof for DTF2THF_7511
% 1.66/1.46 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.46 thf(func_def_7, type, sK2: $i > $i > $i).
% 1.66/1.46 thf(f62,plain,(
% 1.66/1.46 $false),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.66/1.46 thf(f61,plain,(
% 1.66/1.46 ($false = $true)),
% 1.66/1.46 inference(backward_demodulation,[status(thm)],[f51,f60])).
% 1.66/1.46 thf(f60,plain,(
% 1.66/1.46 ((in @ (sK2 @ sK4 @ sK3) @ sK3) = $false)),
% 1.66/1.46 inference(subsumption_resolution,[status(thm)],[f58,f24])).
% 1.66/1.46 thf(f24,plain,(
% 1.66/1.46 (sK3 != sK4)),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.66/1.46 thf(f19,plain,(
% 1.66/1.46 (! [X2 : $i] : (((in @ X2 @ sK3) != $true) | ((in @ X2 @ sK4) = $true)) & ! [X3 : $i] : (((in @ X3 @ sK4) != $true) | ((in @ X3 @ sK3) = $true)) & (sK3 != sK4)) & (setextAx = $true)),
% 1.66/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f17,f18])).
% 1.66/1.46 thf(f18,plain,(
% 1.66/1.46 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X0) = $true)) & (X0 != X1)) => (! [X2 : $i] : (((in @ X2 @ sK3) != $true) | ((in @ X2 @ sK4) = $true)) & ! [X3 : $i] : (((in @ X3 @ sK4) != $true) | ((in @ X3 @ sK3) = $true)) & (sK3 != sK4))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f17,plain,(
% 1.66/1.46 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X0) = $true)) & (X0 != X1)) & (setextAx = $true)),
% 1.66/1.46 inference(rectify,[status(thm)],[f11])).
% 1.66/1.46 thf(f11,plain,(
% 1.66/1.46 ? [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) = $true)) & (X0 != X1)) & (setextAx = $true)),
% 1.66/1.46 inference(flattening,[status(thm)],[f10])).
% 1.66/1.46 thf(f10,plain,(
% 1.66/1.46 ? [X0 : $i,X1 : $i] : (((X0 != X1) & ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) = $true))) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))) & (setextAx = $true)),
% 1.66/1.46 inference(ennf_transformation,[status(thm)],[f8])).
% 1.66/1.46 thf(f8,plain,(
% 1.66/1.46 ~((setextAx = $true) => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => (! [X3 : $i] : (((in @ X3 @ X0) = $true) => ((in @ X3 @ X1) = $true)) => (X0 = X1))))),
% 1.66/1.46 inference(fool_elimination,[status(thm)],[f7])).
% 1.66/1.46 thf(f7,plain,(
% 1.66/1.46 ~(setextAx => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))))),
% 1.66/1.46 inference(rectify,[status(thm)],[f3])).
% 1.66/1.46 thf(f3,negated_conjecture,(
% 1.66/1.46 ~(setextAx => ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))))),
% 1.66/1.46 inference(negated_conjecture,[status(cth)],[f2])).
% 1.66/1.46 thf(f2,conjecture,(
% 1.66/1.46 setextAx => ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1)))),
% 1.66/1.46 file('/export/starexec/sandbox/tmp/tmp.DfjQKKTWal/DTF2THF_7511.p',setext)).
% 1.66/1.46 thf(f58,plain,(
% 1.66/1.46 ((in @ (sK2 @ sK4 @ sK3) @ sK3) = $false) | (sK3 = sK4)),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.66/1.46 thf(f55,plain,(
% 1.66/1.46 ($false = $true) | ((in @ (sK2 @ sK4 @ sK3) @ sK3) = $false) | (sK3 = sK4)),
% 1.66/1.46 inference(superposition,[status(thm)],[f32,f53])).
% 1.66/1.46 thf(f53,plain,(
% 1.66/1.46 ((in @ (sK2 @ sK4 @ sK3) @ sK4) = $true)),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.66/1.46 thf(f52,plain,(
% 1.66/1.46 ((in @ (sK2 @ sK4 @ sK3) @ sK4) = $true) | ($true != $true)),
% 1.66/1.46 inference(superposition,[status(thm)],[f26,f51])).
% 1.66/1.46 thf(f26,plain,(
% 1.66/1.46 ( ! [X2 : $i] : (((in @ X2 @ sK3) != $true) | ((in @ X2 @ sK4) = $true)) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.66/1.46 thf(f32,plain,(
% 1.66/1.46 ( ! [X3 : $i,X4 : $i] : (($false = (in @ (sK2 @ X4 @ X3) @ X4)) | (X3 = X4) | ((in @ (sK2 @ X4 @ X3) @ X3) = $false)) )),
% 1.66/1.46 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.66/1.46 thf(f30,plain,(
% 1.66/1.46 ( ! [X3 : $i,X4 : $i] : ((X3 = X4) | ((in @ (sK2 @ X4 @ X3) @ X3) != (in @ (sK2 @ X4 @ X3) @ X4))) )),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.66/1.46 thf(f29,plain,(
% 1.66/1.46 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X3) != (in @ (sK2 @ X4 @ X3) @ X4)) | ($true != $true) | (X3 = X4)) )),
% 1.66/1.46 inference(definition_unfolding,[status(thm)],[f20,f23])).
% 1.66/1.46 thf(f23,plain,(
% 1.66/1.46 (setextAx = $true)),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.66/1.46 thf(f20,plain,(
% 1.66/1.46 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X3) != (in @ (sK2 @ X4 @ X3) @ X4)) | (X3 = X4) | (setextAx != $true)) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f16])).
% 1.66/1.46 thf(f16,plain,(
% 1.66/1.46 ((setextAx = $true) | (! [X2 : $i] : ((in @ X2 @ sK1) = (in @ X2 @ sK0)) & (sK1 != sK0))) & (! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X3) != (in @ (sK2 @ X4 @ X3) @ X4)) | (X3 = X4)) | (setextAx != $true))),
% 1.66/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f15,f14])).
% 1.66/1.46 thf(f14,plain,(
% 1.66/1.46 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) = (in @ X2 @ X1)) & (X0 != X1)) => (! [X2 : $i] : ((in @ X2 @ sK1) = (in @ X2 @ sK0)) & (sK1 != sK0))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f15,plain,(
% 1.66/1.46 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : ((in @ X5 @ X4) != (in @ X5 @ X3)) => ((in @ (sK2 @ X4 @ X3) @ X3) != (in @ (sK2 @ X4 @ X3) @ X4)))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f13,plain,(
% 1.66/1.46 ((setextAx = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) = (in @ X2 @ X1)) & (X0 != X1))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : ((in @ X5 @ X4) != (in @ X5 @ X3)) | (X3 = X4)) | (setextAx != $true))),
% 1.66/1.46 inference(rectify,[status(thm)],[f12])).
% 1.66/1.46 thf(f12,plain,(
% 1.66/1.46 ((setextAx = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) = (in @ X2 @ X1)) & (X0 != X1))) & (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) != (in @ X2 @ X1)) | (X0 = X1)) | (setextAx != $true))),
% 1.66/1.46 inference(nnf_transformation,[status(thm)],[f9])).
% 1.66/1.46 thf(f9,plain,(
% 1.66/1.46 (setextAx = $true) <=> ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) != (in @ X2 @ X1)) | (X0 = X1))),
% 1.66/1.46 inference(ennf_transformation,[status(thm)],[f6])).
% 1.66/1.46 thf(f6,plain,(
% 1.66/1.46 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) = (in @ X2 @ X1)) => (X0 = X1)) <=> (setextAx = $true)),
% 1.66/1.46 inference(fool_elimination,[status(thm)],[f5])).
% 1.66/1.46 thf(f5,plain,(
% 1.66/1.46 (setextAx = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) <=> (in @ X2 @ X0)) => (X0 = X1)))),
% 1.66/1.46 inference(rectify,[status(thm)],[f1])).
% 1.66/1.46 thf(f1,axiom,(
% 1.66/1.46 (setextAx = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) <=> (in @ X2 @ X0)) => (X0 = X1)))),
% 1.66/1.46 file('/export/starexec/sandbox/tmp/tmp.DfjQKKTWal/DTF2THF_7511.p',setextAx)).
% 1.66/1.46 thf(f51,plain,(
% 1.66/1.46 ((in @ (sK2 @ sK4 @ sK3) @ sK3) = $true)),
% 1.66/1.46 inference(subsumption_resolution,[status(thm)],[f49,f24])).
% 1.66/1.46 thf(f49,plain,(
% 1.66/1.46 (sK3 = sK4) | ((in @ (sK2 @ sK4 @ sK3) @ sK3) = $true)),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.66/1.46 thf(f48,plain,(
% 1.66/1.46 ((in @ (sK2 @ sK4 @ sK3) @ sK3) = $true) | (sK3 = sK4) | ($true != $true)),
% 1.66/1.46 inference(equality_factoring,[status(thm)],[f36])).
% 1.66/1.46 thf(f36,plain,(
% 1.66/1.46 ( ! [X0 : $i] : (((in @ (sK2 @ sK4 @ X0) @ sK3) = $true) | (sK4 = X0) | ((in @ (sK2 @ sK4 @ X0) @ X0) = $true)) )),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.66/1.46 thf(f33,plain,(
% 1.66/1.46 ( ! [X0 : $i] : (($true != $true) | (sK4 = X0) | ((in @ (sK2 @ sK4 @ X0) @ sK3) = $true) | ((in @ (sK2 @ sK4 @ X0) @ X0) = $true)) )),
% 1.66/1.46 inference(superposition,[status(thm)],[f25,f31])).
% 1.66/1.46 thf(f31,plain,(
% 1.66/1.46 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X4) = $true) | (X3 = X4) | ((in @ (sK2 @ X4 @ X3) @ X3) = $true)) )),
% 1.66/1.46 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.66/1.46 thf(f25,plain,(
% 1.66/1.46 ( ! [X3 : $i] : (((in @ X3 @ sK4) != $true) | ((in @ X3 @ sK3) = $true)) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.66/1.46 % SZS output end Proof for DTF2THF_7511
% 1.66/1.46 % (7624)------------------------------
% 1.66/1.46 % (7624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (7624)Termination reason: Refutation
% 1.66/1.46
% 1.66/1.46 % (7624)Memory used [KB]: 5500
% 1.66/1.46 % (7624)Time elapsed: 0.007 s
% 1.66/1.46 % (7624)Instructions burned: 6 (million)
% 1.66/1.46 % (7624)------------------------------
% 1.66/1.46 % (7624)------------------------------
% 1.66/1.46 % (7617)Success in time 0.022 s
%------------------------------------------------------------------------------