%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU722^2 : 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 : n020.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 09:36:40 AM UTC 2026
% Result : Theorem 1.66s 1.33s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 309 ( 73 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 406 ( 24 ~; 2 |; 33 &; 293 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 8 con; 0-2 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 77 ( 18 ^; 41 !; 18 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binintersect: $i > $i > $i ).
thf(f35,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f34,f21]) ).
thf(f21,plain,
( $true
!= ( in @ sK3 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
!= ( in @ sK3 @ sK2 ) )
& ( $true
= ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( binintersectER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f14,f13,f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ ( binintersect @ sK1 @ X2 ) ) )
& ( $true
= ( in @ X3 @ sK0 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ ( binintersect @ sK1 @ X2 ) ) )
& ( $true
= ( in @ X3 @ sK0 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) ) )
=> ( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ sK2 ) )
& ( $true
= ( in @ X3 @ ( binintersect @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ X3 @ sK0 ) ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ sK2 ) )
& ( $true
= ( in @ X3 @ ( binintersect @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ X3 @ sK0 ) ) )
=> ( ( $true
!= ( in @ sK3 @ sK2 ) )
& ( $true
= ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
& ( binintersectER = $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) )
& ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
& ( binintersectER = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( binintersectER = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( ( $true
!= ( in @ X3 @ X2 ) )
=> ( $true
!= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( binintersectER = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( ( $true
!= ( in @ X3 @ X2 ) )
=> ( $true
!= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( binintersectER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( binintersectER
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( binintersectER
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5r2ewAf1sC/DTF2THF_7967.p',binintersectTERcontra) ).
thf(f34,plain,
( $true
= ( in @ sK3 @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $true
= ( in @ sK3 @ sK2 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f30,f20]) ).
thf(f20,plain,
( $true
= ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( binintersect @ X3 @ X2 ) )
= $false )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( binintersect @ X3 @ X2 ) )
=> ( in @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ X2 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f16]) ).
thf(f16,plain,
binintersectER = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f22,plain,
( binintersectER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( binintersectER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) )
= binintersectER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) )
= binintersectER ),
file('/export/starexec/sandbox/tmp/tmp.5r2ewAf1sC/DTF2THF_7967.p',binintersectER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU722^2 : 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 : n020.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 12:32:12 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 ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU722^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.28/0.46 % Version : Especial > Reduced > Especial.
% 0.28/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.28/0.46 % (! x:i.in x A -> ~(in x Y) -> ~(in x (binintersect X Y)))))
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.46 % Source : [Bro08]
% 0.28/0.46 % Names : ZFC224l [Bro08]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % 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 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.28/0.46 % Number of atoms : 10 ( 1 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 6 ( 5 avg)
% 0.28/0.46 % Number of connectives : 28 ( 2 ~; 0 |; 0 &; 20 @)
% 0.28/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 14 ( 8 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : http://mathgate.info/detsetitem.php?id=282
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(in_type,type,
% 0.28/0.46 in: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(powerset_type,type,
% 0.28/0.46 powerset: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(binintersect_type,type,
% 0.28/0.46 binintersect: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectER_type,type,
% 0.28/0.46 binintersectER: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectER,definition,
% 0.28/0.46 ( binintersectER
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectTERcontra,conjecture,
% 0.28/0.46 ( binintersectER
% 0.28/0.46 => ! [A: $i,X: $i] :
% 0.28/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.46 => ! [Y: $i] :
% 0.28/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ~ ( in @ Xx @ Y )
% 0.28/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.47/1.29 ---- Embedded in THF ---
% 1.47/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.29 %%% Generated on Tue Feb 24 12:32:13 EST 2026
% 1.47/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.29 %%% Logic specification used:
% 1.47/1.29 %%% thf(spec, logic, $$dhol).
% 1.47/1.29
% 1.47/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5r2ewAf1sC/DTF2DTF7967.p
% See solution above
% 1.47/1.29 ------------------------
% 1.66/1.30 ---- Cleaned THF ---
% 1.66/1.30 thf(in_type,type,
% 1.66/1.30 in: $i > $i > $o ).
% 1.66/1.30
% 1.66/1.30 thf(powerset_type,type,
% 1.66/1.30 powerset: $i > $i ).
% 1.66/1.30
% 1.66/1.30 thf(binintersect_type,type,
% 1.66/1.30 binintersect: $i > $i > $i ).
% 1.66/1.30
% 1.66/1.30 thf(binintersectER_type,type,
% 1.66/1.30 binintersectER: $o ).
% 1.66/1.30
% 1.66/1.30 thf(binintersectER,definition,
% 1.66/1.30 ( binintersectER
% 1.66/1.30 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.66/1.30 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.66/1.30 => ( in @ Xx @ B ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(binintersectTERcontra,conjecture,
% 1.66/1.30 ( binintersectER
% 1.66/1.30 => ! [A: $i,X: $i] :
% 1.66/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.66/1.30 => ! [Y: $i] :
% 1.66/1.30 ( ( in @ Y @ ( powerset @ A ) )
% 1.66/1.30 => ! [Xx: $i] :
% 1.66/1.30 ( ( in @ Xx @ A )
% 1.66/1.30 => ( ~ ( in @ Xx @ Y )
% 1.66/1.30 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 1.66/1.30 ------------------------
% 1.66/1.32 % (8269)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7967 for (2999ds/2Mi)
% 1.66/1.32 % (8269)Instruction limit reached!
% 1.66/1.32 % (8269)------------------------------
% 1.66/1.32 % (8269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (8269)Termination reason: Unknown
% 1.66/1.32 % (8269)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (8269)Memory used [KB]: 5500
% 1.66/1.32 % (8269)Time elapsed: 0.002 s
% 1.66/1.32 % (8269)Instructions burned: 2 (million)
% 1.66/1.32 % (8269)------------------------------
% 1.66/1.32 % (8269)------------------------------
% 1.66/1.32 % (8266)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7967 for (2999ds/183Mi)
% 1.66/1.32 % (8267)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_7967 for (2999ds/4Mi)
% 1.66/1.32 % (8268)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_7967 for (2999ds/27Mi)
% 1.66/1.32 % (8270)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_7967 for (2999ds/2Mi)
% 1.66/1.32 % (8271)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_7967 for (2999ds/275Mi)
% 1.66/1.32 % (8272)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7967 for (2999ds/18Mi)
% 1.66/1.32 % (8270)Instruction limit reached!
% 1.66/1.32 % (8270)------------------------------
% 1.66/1.32 % (8270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (8270)Termination reason: Unknown
% 1.66/1.32 % (8270)Termination phase: Property scanning
% 1.66/1.32
% 1.66/1.32 % (8270)Memory used [KB]: 895
% 1.66/1.32 % (8270)Time elapsed: 0.003 s
% 1.66/1.32 % (8270)Instructions burned: 2 (million)
% 1.66/1.32 % (8270)------------------------------
% 1.66/1.32 % (8270)------------------------------
% 1.66/1.33 % (8266)First to succeed.
% 1.66/1.33 % (8267)Instruction limit reached!
% 1.66/1.33 % (8267)------------------------------
% 1.66/1.33 % (8267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (8267)Termination reason: Unknown
% 1.66/1.33 % (8267)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (8267)Memory used [KB]: 5500
% 1.66/1.33 % (8267)Time elapsed: 0.005 s
% 1.66/1.33 % (8267)Instructions burned: 4 (million)
% 1.66/1.33 % (8267)------------------------------
% 1.66/1.33 % (8267)------------------------------
% 1.66/1.33 % (8271)Also succeeded, but the first one will report.
% 1.66/1.33 % (8273)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7967 for (2999ds/3Mi)
% 1.66/1.33 % (8266)Refutation found. Thanks to Tanya!
% 1.66/1.33 % SZS status Theorem for DTF2THF_7967
% 1.66/1.33 % SZS output start Proof for DTF2THF_7967
% 1.66/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.33 thf(func_def_1, type, powerset: $i > $i).
% 1.66/1.33 thf(func_def_2, type, binintersect: $i > $i > $i).
% 1.66/1.33 thf(f35,plain,(
% 1.66/1.33 $false),
% 1.66/1.33 inference(subsumption_resolution,[status(thm)],[f34,f21])).
% 1.66/1.33 thf(f21,plain,(
% 1.66/1.33 ($true != (in @ sK3 @ sK2))),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f15])).
% 1.66/1.33 thf(f15,plain,(
% 1.66/1.33 (((($true != (in @ sK3 @ sK2)) & ($true = (in @ sK3 @ (binintersect @ sK1 @ sK2))) & ($true = (in @ sK3 @ sK0))) & ($true = (in @ sK2 @ (powerset @ sK0)))) & ($true = (in @ sK1 @ (powerset @ sK0)))) & (binintersectER = $true)),
% 1.66/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f14,f13,f12])).
% 1.66/1.33 thf(f12,plain,(
% 1.66/1.33 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (($true != (in @ X3 @ X2)) & ($true = (in @ X3 @ (binintersect @ X1 @ X2))) & ($true = (in @ X3 @ X0))) & ($true = (in @ X2 @ (powerset @ X0)))) & ($true = (in @ X1 @ (powerset @ X0)))) => (? [X2 : $i] : (? [X3 : $i] : (($true != (in @ X3 @ X2)) & ($true = (in @ X3 @ (binintersect @ sK1 @ X2))) & ($true = (in @ X3 @ sK0))) & ($true = (in @ X2 @ (powerset @ sK0)))) & ($true = (in @ sK1 @ (powerset @ sK0))))),
% 1.66/1.33 introduced(definition,[],[choice_axiom])).
% 1.66/1.33 thf(f13,plain,(
% 1.66/1.33 ? [X2 : $i] : (? [X3 : $i] : (($true != (in @ X3 @ X2)) & ($true = (in @ X3 @ (binintersect @ sK1 @ X2))) & ($true = (in @ X3 @ sK0))) & ($true = (in @ X2 @ (powerset @ sK0)))) => (? [X3 : $i] : (($true != (in @ X3 @ sK2)) & ($true = (in @ X3 @ (binintersect @ sK1 @ sK2))) & ($true = (in @ X3 @ sK0))) & ($true = (in @ sK2 @ (powerset @ sK0))))),
% 1.66/1.33 introduced(definition,[],[choice_axiom])).
% 1.66/1.33 thf(f14,plain,(
% 1.66/1.33 ? [X3 : $i] : (($true != (in @ X3 @ sK2)) & ($true = (in @ X3 @ (binintersect @ sK1 @ sK2))) & ($true = (in @ X3 @ sK0))) => (($true != (in @ sK3 @ sK2)) & ($true = (in @ sK3 @ (binintersect @ sK1 @ sK2))) & ($true = (in @ sK3 @ sK0)))),
% 1.66/1.33 introduced(definition,[],[choice_axiom])).
% 1.66/1.33 thf(f11,plain,(
% 1.66/1.33 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (($true != (in @ X3 @ X2)) & ($true = (in @ X3 @ (binintersect @ X1 @ X2))) & ($true = (in @ X3 @ X0))) & ($true = (in @ X2 @ (powerset @ X0)))) & ($true = (in @ X1 @ (powerset @ X0)))) & (binintersectER = $true)),
% 1.66/1.33 inference(flattening,[status(thm)],[f10])).
% 1.66/1.33 thf(f10,plain,(
% 1.66/1.33 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((($true = (in @ X3 @ (binintersect @ X1 @ X2))) & ($true != (in @ X3 @ X2))) & ($true = (in @ X3 @ X0))) & ($true = (in @ X2 @ (powerset @ X0)))) & ($true = (in @ X1 @ (powerset @ X0)))) & (binintersectER = $true)),
% 1.66/1.33 inference(ennf_transformation,[status(thm)],[f9])).
% 1.66/1.33 thf(f9,plain,(
% 1.66/1.33 ~((binintersectER = $true) => ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => (($true != (in @ X3 @ X2)) => ($true != (in @ X3 @ (binintersect @ X1 @ X2))))))))),
% 1.66/1.33 inference(flattening,[status(thm)],[f6])).
% 1.66/1.33 thf(f6,plain,(
% 1.66/1.33 ~((binintersectER = $true) => ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => (~($true = (in @ X3 @ X2)) => ~($true = (in @ X3 @ (binintersect @ X1 @ X2))))))))),
% 1.66/1.33 inference(fool_elimination,[status(thm)],[f5])).
% 1.66/1.33 thf(f5,plain,(
% 1.66/1.33 ~(binintersectER => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ X2) => ~(in @ X3 @ (binintersect @ X1 @ X2)))))))),
% 1.66/1.33 inference(rectify,[status(thm)],[f3])).
% 1.66/1.33 thf(f3,negated_conjecture,(
% 1.66/1.33 ~(binintersectER => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X4) => ~(in @ X2 @ (binintersect @ X3 @ X4)))))))),
% 1.66/1.33 inference(negated_conjecture,[status(cth)],[f2])).
% 1.66/1.33 thf(f2,conjecture,(
% 1.66/1.33 binintersectER => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X4) => ~(in @ X2 @ (binintersect @ X3 @ X4))))))),
% 1.66/1.33 file('/export/starexec/sandbox/tmp/tmp.5r2ewAf1sC/DTF2THF_7967.p',binintersectTERcontra)).
% 1.66/1.33 thf(f34,plain,(
% 1.66/1.33 ($true = (in @ sK3 @ sK2))),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.66/1.33 thf(f31,plain,(
% 1.66/1.33 ($true = (in @ sK3 @ sK2)) | ($true = $false)),
% 1.66/1.33 inference(superposition,[status(thm)],[f30,f20])).
% 1.66/1.33 thf(f20,plain,(
% 1.66/1.33 ($true = (in @ sK3 @ (binintersect @ sK1 @ sK2)))),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f15])).
% 1.66/1.33 thf(f30,plain,(
% 1.66/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X1 @ (binintersect @ X3 @ X2)) = $false) | ($true = (in @ X1 @ X2))) )),
% 1.66/1.33 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.66/1.33 thf(f29,plain,(
% 1.66/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X1 @ (binintersect @ X3 @ X2)) => (in @ X1 @ X2)))) )),
% 1.66/1.33 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.66/1.33 thf(f28,plain,(
% 1.66/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ X2))) @ X3))) )),
% 1.66/1.33 inference(pi_clausification,[status(thm)],[f27])).
% 1.66/1.33 thf(f27,plain,(
% 1.66/1.33 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ X2)))))) )),
% 1.66/1.33 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.66/1.33 thf(f26,plain,(
% 1.66/1.33 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y0))))) @ X2))) )),
% 1.66/1.33 inference(pi_clausification,[status(thm)],[f25])).
% 1.66/1.33 thf(f25,plain,(
% 1.66/1.33 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y0)))))))) )),
% 1.66/1.33 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.66/1.33 thf(f24,plain,(
% 1.66/1.33 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))) @ X1))) )),
% 1.66/1.33 inference(pi_clausification,[status(thm)],[f23])).
% 1.66/1.33 thf(f23,plain,(
% 1.66/1.33 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))))),
% 1.66/1.33 inference(definition_unfolding,[status(thm)],[f22,f16])).
% 1.66/1.33 thf(f16,plain,(
% 1.66/1.33 (binintersectER = $true)),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f15])).
% 1.66/1.33 thf(f22,plain,(
% 1.66/1.33 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))))),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f8])).
% 1.66/1.33 thf(f8,plain,(
% 1.66/1.33 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))))),
% 1.66/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 1.66/1.33 thf(f7,plain,(
% 1.66/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)) = binintersectER)),
% 1.66/1.33 inference(rectify,[status(thm)],[f1])).
% 1.66/1.33 thf(f1,axiom,(
% 1.66/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)) = binintersectER)),
% 1.66/1.33 file('/export/starexec/sandbox/tmp/tmp.5r2ewAf1sC/DTF2THF_7967.p',binintersectER)).
% 1.66/1.33 % SZS output end Proof for DTF2THF_7967
% 1.66/1.33 % (8266)------------------------------
% 1.66/1.33 % (8266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (8266)Termination reason: Refutation
% 1.66/1.33
% 1.66/1.33 % (8266)Memory used [KB]: 5500
% 1.66/1.33 % (8266)Time elapsed: 0.006 s
% 1.66/1.33 % (8266)Instructions burned: 3 (million)
% 1.66/1.33 % (8266)------------------------------
% 1.66/1.33 % (8266)------------------------------
% 1.66/1.33 % (8265)Success in time 0.02 s
%------------------------------------------------------------------------------