%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU829^1 : 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 : n011.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 09:37:32 AM UTC 2026
% Result : Theorem 1.49s 1.27s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 22 unt; 0 typ; 3 def)
% Number of atoms : 224 ( 65 equ; 2 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 174 ( 42 ~; 29 |; 0 &; 81 @)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 10 usr; 9 con; 0-2 aty)
% ( 12 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 78 ( 69 ^; 9 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
subseteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_2,type,
powerset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK2: $i > $o ).
thf(f60,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f40,f45,f48,f54,f59]) ).
thf(f59,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f57,f35]) ).
thf(f35,plain,
( ! [X1: $i] :
( $false
= ( sK2 @ X1 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl0_1
<=> ! [X1: $i] :
( $false
= ( sK2 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f57,plain,
( ( $false
!= ( sK2 @ sK4 ) )
| spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( ^ [Y0: $i] : $false
@ sK4 )
!= ( sK2 @ sK4 ) )
| spl0_2 ),
inference(negative_extensionality,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK2 )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl0_2
<=> ( ( ^ [Y0: $i] : $false )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f54,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f53]) ).
thf(f53,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f44,f35]) ).
thf(f44,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl0_3
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f48,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f47,f37,f34]) ).
thf(f47,plain,
( ! [X1: $i] :
( $false
= ( sK2 @ X1 ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $false
@ X1 )
= ( sK2 @ X1 ) )
| ~ spl0_2 ),
inference(argument_congruence,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( ^ [Y0: $i] : $false )
= sK2 )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f45,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f28,f42,f37]) ).
thf(f28,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( ^ [Y0: $i] : $false )
!= sK2 ) ),
inference(not_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK2 )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $false
= ( ^ [Y0: $i] :
~ ( sK2 @ Y0 )
@ sK3 ) )
| ( ( ^ [Y0: $i] : $false )
!= sK2 ) ),
inference(sigma_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK2 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $false
= ( ( ^ [Y0: $i] : $false )
= sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) )
!= ( ( ^ [Y0: $i] : $false )
= sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) )
@ sK2 )
!= ( ( ^ [Y0: $i] : $false )
= sK2 ) ),
inference(negative_extensionality,[status(thm)],[f20]) ).
thf(f20,plain,
( ( (=)
@ ^ [Y0: $i] : $false )
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( (=)
@ ^ [Y0: $i] : $false )
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> $false ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: $i > $o] :
( ( ^ [Y1: $i] : $false )
= Y0 ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
@ Y1
@ Y0 )
@ ^ [Y0: $i] : $false ) ),
inference(definition_unfolding,[status(thm)],[f13,f17,f16,f16]) ).
thf(f16,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i] : $false )
= emptyset ),
file('/export/starexec/sandbox/tmp/tmp.cQR7NxgZt1/DTF2THF_5788.p',emptyset) ).
thf(f17,plain,
( powerset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
@ Y1
@ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f15,f14]) ).
thf(f14,plain,
( subseteq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( subseteq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( subseteq
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subseteq
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cQR7NxgZt1/DTF2THF_5788.p',subseteq) ).
thf(f15,plain,
( powerset
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( subseteq @ Y1 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( powerset
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( subseteq @ Y1 @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
( powerset
= ( ^ [X0: $i > $o,X1: $i > $o] : ( subseteq @ X1 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cQR7NxgZt1/DTF2THF_5788.p',poserset) ).
thf(f13,plain,
( ( powerset @ emptyset )
!= ( ^ [Y0: $i > $o] : ( emptyset = Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( powerset @ emptyset )
!= ( ^ [Y0: $i > $o] : ( emptyset = Y0 ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( powerset @ emptyset )
!= ( ^ [Y0: $i > $o] : ( emptyset = Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
( ( ^ [X0: $i > $o] : ( emptyset = X0 ) )
!= ( powerset @ emptyset ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( ( ^ [X0: $i > $o] : ( emptyset = X0 ) )
= ( powerset @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.cQR7NxgZt1/DTF2THF_5788.p',conj) ).
thf(f40,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f32,f37,f34]) ).
thf(f32,plain,
! [X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( ( ^ [Y0: $i] : $false )
= sK2 ) ),
inference(not_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] : $false )
= sK2 )
| ( $true
= ( ~ ( sK2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] : $false )
= sK2 )
| ( $true
= ( ^ [Y0: $i] :
~ ( sK2 @ Y0 )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( ^ [Y0: $i] : $false )
= sK2 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
= ( ( ^ [Y0: $i] : $false )
= sK2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU829^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n011.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 12:35:02 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU829^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : About powersets 2
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.18/0.45 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Ben09]
% 0.18/0.45 % Names : Example 22d [BB05]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 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 v4.0.1, 0.33 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 7 ( 4 unt; 3 typ; 3 def)
% 0.18/0.45 % Number of atoms : 13 ( 5 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 1 ( 3 avg)
% 0.18/0.45 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 5 @)
% 0.18/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 1 ( 1 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 7 ( 6 ^; 1 !; 0 ?; 7 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments :
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(subseteq_type,type,
% 0.18/0.45 subseteq: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.18/0.45
% 0.18/0.45 thf(subseteq,definition,
% 0.18/0.45 ( subseteq
% 0.18/0.45 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.18/0.45 ! [U: $i] :
% 0.18/0.45 ( ( X @ U )
% 0.18/0.45 => ( Y @ U ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(powerset_type,type,
% 0.18/0.45 powerset: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.18/0.45
% 0.18/0.45 thf(poserset,definition,
% 0.18/0.45 ( powerset
% 0.18/0.45 = ( ^ [X: $i > $o,Y: $i > $o] : ( subseteq @ Y @ X ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyset_type,type,
% 0.18/0.45 emptyset: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyset,definition,
% 0.18/0.45 ( emptyset
% 0.18/0.45 = ( ^ [X: $i] : $false ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(conj,conjecture,
% 0.29/0.45 ( ( powerset @ emptyset )
% 0.29/0.45 = ( ^ [X: $i > $o] : ( X = emptyset ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.49/1.23 ---- Embedded in THF ---
% 1.49/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.23 %%% Generated on Tue Feb 24 12:35:03 EST 2026
% 1.49/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.23 %%% Logic specification used:
% 1.49/1.23 %%% thf(spec, logic, $$dhol).
% 1.49/1.23
% 1.49/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cQR7NxgZt1/DTF2DTF5788.p
% See solution above
% 1.49/1.23 ------------------------
% 1.49/1.25 ---- Cleaned THF ---
% 1.49/1.25 thf(subseteq_type,type,
% 1.49/1.25 subseteq: ( $i > $o ) > ( $i > $o ) > $o ).
% 1.49/1.25
% 1.49/1.25 thf(subseteq,definition,
% 1.49/1.25 ( subseteq
% 1.49/1.25 = ( ^ [X: $i > $o,Y: $i > $o] :
% 1.49/1.25 ! [U: $i] :
% 1.49/1.25 ( ( X @ U )
% 1.49/1.25 => ( Y @ U ) ) ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(powerset_type,type,
% 1.49/1.25 powerset: ( $i > $o ) > ( $i > $o ) > $o ).
% 1.49/1.25
% 1.49/1.25 thf(poserset,definition,
% 1.49/1.25 ( powerset
% 1.49/1.25 = ( ^ [X: $i > $o,Y: $i > $o] : ( subseteq @ Y @ X ) ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(emptyset_type,type,
% 1.49/1.25 emptyset: $i > $o ).
% 1.49/1.25
% 1.49/1.25 thf(emptyset,definition,
% 1.49/1.25 ( emptyset
% 1.49/1.25 = ( ^ [X: $i] : $false ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(conj,conjecture,
% 1.49/1.25 ( ( powerset @ emptyset )
% 1.49/1.25 = ( ^ [X: $i > $o] : ( X = emptyset ) ) ) ).
% 1.49/1.25 ------------------------
% 1.49/1.26 % (5891)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_5788 for (2999ds/2Mi)
% 1.49/1.26 % (5891)Instruction limit reached!
% 1.49/1.26 % (5891)------------------------------
% 1.49/1.26 % (5891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (5891)Termination reason: Unknown
% 1.49/1.26 % (5891)Termination phase: Saturation
% 1.49/1.26
% 1.49/1.26 % (5891)Memory used [KB]: 5373
% 1.49/1.26 % (5891)Time elapsed: 0.002 s
% 1.49/1.26 % (5891)Instructions burned: 2 (million)
% 1.49/1.26 % (5891)------------------------------
% 1.49/1.26 % (5891)------------------------------
% 1.49/1.27 % (5889)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_5788 for (2999ds/27Mi)
% 1.49/1.27 % (5888)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_5788 for (2999ds/4Mi)
% 1.49/1.27 % (5887)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5788 for (2999ds/183Mi)
% 1.49/1.27 % (5890)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5788 for (2999ds/2Mi)
% 1.49/1.27 % (5892)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_5788 for (2999ds/275Mi)
% 1.49/1.27 % (5893)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5788 for (2999ds/18Mi)
% 1.49/1.27 % (5890)Instruction limit reached!
% 1.49/1.27 % (5890)------------------------------
% 1.49/1.27 % (5890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (5890)Termination reason: Unknown
% 1.49/1.27 % (5890)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (5890)Memory used [KB]: 895
% 1.49/1.27 % (5890)Time elapsed: 0.003 s
% 1.49/1.27 % (5890)Instructions burned: 2 (million)
% 1.49/1.27 % (5890)------------------------------
% 1.49/1.27 % (5890)------------------------------
% 1.49/1.27 % (5892)Refutation not found, incomplete strategy
% 1.49/1.27 % (5892)------------------------------
% 1.49/1.27 % (5892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (5892)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.27
% 1.49/1.27
% 1.49/1.27 % (5892)Memory used [KB]: 5500
% 1.49/1.27 % (5892)Time elapsed: 0.004 s
% 1.49/1.27 % (5892)Instructions burned: 2 (million)
% 1.49/1.27 % (5892)------------------------------
% 1.49/1.27 % (5892)------------------------------
% 1.49/1.27 % (5894)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5788 for (2999ds/3Mi)
% 1.49/1.27 % (5887)First to succeed.
% 1.49/1.27 % (5888)Instruction limit reached!
% 1.49/1.27 % (5888)------------------------------
% 1.49/1.27 % (5888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (5888)Termination reason: Unknown
% 1.49/1.27 % (5888)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (5888)Memory used [KB]: 5500
% 1.49/1.27 % (5888)Time elapsed: 0.005 s
% 1.49/1.27 % (5888)Instructions burned: 4 (million)
% 1.49/1.27 % (5888)------------------------------
% 1.49/1.27 % (5888)------------------------------
% 1.49/1.27 % (5894)Refutation not found, incomplete strategy
% 1.49/1.27 % (5894)------------------------------
% 1.49/1.27 % (5894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (5894)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.27
% 1.49/1.27
% 1.49/1.27 % (5894)Memory used [KB]: 5500
% 1.49/1.27 % (5894)Time elapsed: 0.001 s
% 1.49/1.27 % (5894)Instructions burned: 1 (million)
% 1.49/1.27 % (5894)------------------------------
% 1.49/1.27 % (5894)------------------------------
% 1.49/1.27 % (5889)Also succeeded, but the first one will report.
% 1.49/1.27 % (5887)Refutation found. Thanks to Tanya!
% 1.49/1.27 % SZS status Theorem for DTF2THF_5788
% 1.49/1.27 % SZS output start Proof for DTF2THF_5788
% 1.49/1.27 thf(func_def_0, type, subseteq: ($i > $o) > ($i > $o) > $o).
% 1.49/1.27 thf(func_def_2, type, powerset: ($i > $o) > ($i > $o) > $o).
% 1.49/1.27 thf(func_def_3, type, emptyset: $i > $o).
% 1.49/1.27 thf(func_def_15, type, ph1: !>[X0: $tType]:(X0)).
% 1.49/1.27 thf(func_def_16, type, sK2: $i > $o).
% 1.49/1.27 thf(f60,plain,(
% 1.49/1.27 $false),
% 1.49/1.27 inference(avatar_sat_refutation,[status(thm)],[f40,f45,f48,f54,f59])).
% 1.49/1.27 thf(f59,plain,(
% 1.49/1.27 ~spl0_1 | spl0_2),
% 1.49/1.27 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.49/1.27 thf(f58,plain,(
% 1.49/1.27 $false | (~spl0_1 | spl0_2)),
% 1.49/1.27 inference(subsumption_resolution,[status(thm)],[f57,f35])).
% 1.49/1.27 thf(f35,plain,(
% 1.49/1.27 ( ! [X1 : $i] : (($false = (sK2 @ X1))) ) | ~spl0_1),
% 1.49/1.27 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.49/1.27 thf(f34,definition,(
% 1.49/1.27 spl0_1 <=> ! [X1 : $i] : ($false = (sK2 @ X1))),
% 1.49/1.27 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.49/1.27 thf(f57,plain,(
% 1.49/1.27 ($false != (sK2 @ sK4)) | spl0_2),
% 1.49/1.27 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.49/1.27 thf(f56,plain,(
% 1.49/1.27 (((^[Y0 : $i]: ($false)) @ sK4) != (sK2 @ sK4)) | spl0_2),
% 1.49/1.27 inference(negative_extensionality,[status(thm)],[f38])).
% 1.49/1.27 thf(f38,plain,(
% 1.49/1.27 ((^[Y0 : $i]: ($false)) != sK2) | spl0_2),
% 1.49/1.27 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.49/1.27 thf(f37,definition,(
% 1.49/1.27 spl0_2 <=> ((^[Y0 : $i]: ($false)) = sK2)),
% 1.49/1.27 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.49/1.27 thf(f54,plain,(
% 1.49/1.27 ~spl0_1 | ~spl0_3),
% 1.49/1.27 inference(avatar_contradiction_clause,[status(thm)],[f53])).
% 1.49/1.27 thf(f53,plain,(
% 1.49/1.27 $false | (~spl0_1 | ~spl0_3)),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.49/1.27 thf(f50,plain,(
% 1.49/1.27 ($false = $true) | (~spl0_1 | ~spl0_3)),
% 1.49/1.27 inference(superposition,[status(thm)],[f44,f35])).
% 1.49/1.27 thf(f44,plain,(
% 1.49/1.27 ($true = (sK2 @ sK3)) | ~spl0_3),
% 1.49/1.27 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.49/1.27 thf(f42,definition,(
% 1.49/1.27 spl0_3 <=> ($true = (sK2 @ sK3))),
% 1.49/1.27 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.49/1.27 thf(f48,plain,(
% 1.49/1.27 spl0_1 | ~spl0_2),
% 1.49/1.27 inference(avatar_split_clause,[status(thm)],[f47,f37,f34])).
% 1.49/1.27 thf(f47,plain,(
% 1.49/1.27 ( ! [X1 : $i] : (($false = (sK2 @ X1))) ) | ~spl0_2),
% 1.49/1.27 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.49/1.27 thf(f46,plain,(
% 1.49/1.27 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($false)) @ X1) = (sK2 @ X1))) ) | ~spl0_2),
% 1.49/1.27 inference(argument_congruence,[status(thm)],[f39])).
% 1.49/1.27 thf(f39,plain,(
% 1.49/1.27 ((^[Y0 : $i]: ($false)) = sK2) | ~spl0_2),
% 1.49/1.27 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.49/1.27 thf(f45,plain,(
% 1.49/1.27 ~spl0_2 | spl0_3),
% 1.49/1.27 inference(avatar_split_clause,[status(thm)],[f28,f42,f37])).
% 1.49/1.27 thf(f28,plain,(
% 1.49/1.27 ($true = (sK2 @ sK3)) | ((^[Y0 : $i]: ($false)) != sK2)),
% 1.49/1.27 inference(not_proxy_clausification,[status(thm)],[f27])).
% 1.49/1.27 thf(f27,plain,(
% 1.49/1.27 ((^[Y0 : $i]: ($false)) != sK2) | ($false = (~ (sK2 @ sK3)))),
% 1.49/1.27 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.49/1.27 thf(f26,plain,(
% 1.49/1.27 ($false = ((^[Y0 : $i]: (~ (sK2 @ Y0))) @ sK3)) | ((^[Y0 : $i]: ($false)) != sK2)),
% 1.49/1.27 inference(sigma_clausification,[status(thm)],[f25])).
% 1.49/1.27 thf(f25,plain,(
% 1.49/1.27 ((^[Y0 : $i]: ($false)) != sK2) | ($false = (!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0)))))),
% 1.49/1.27 inference(equality_proxy_clausification,[status(thm)],[f24])).
% 1.49/1.27 thf(f24,plain,(
% 1.49/1.27 ($false = ((^[Y0 : $i]: ($false)) = sK2)) | ($false = (!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0)))))),
% 1.49/1.27 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.49/1.27 thf(f22,plain,(
% 1.49/1.27 ((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0)))) != ((^[Y0 : $i]: ($false)) = sK2))),
% 1.49/1.27 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.49/1.27 thf(f21,plain,(
% 1.49/1.27 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))) @ sK2) != ((^[Y0 : $i]: ($false)) = sK2))),
% 1.49/1.27 inference(negative_extensionality,[status(thm)],[f20])).
% 1.49/1.27 thf(f20,plain,(
% 1.49/1.27 ((= @ (^[Y0 : $i]: ($false))) != (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 1.49/1.27 inference(boolean_simplification,[status(thm)],[f19])).
% 1.49/1.27 thf(f19,plain,(
% 1.49/1.27 ((= @ (^[Y0 : $i]: ($false))) != (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => $false)))))),
% 1.49/1.27 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.49/1.27 thf(f18,plain,(
% 1.49/1.27 ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ($false)) = Y0)) != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ Y1 @ Y0)))) @ (^[Y0 : $i]: ($false))))),
% 1.49/1.27 inference(definition_unfolding,[status(thm)],[f13,f17,f16,f16])).
% 1.49/1.27 thf(f16,plain,(
% 1.49/1.27 (emptyset = (^[Y0 : $i]: ($false)))),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.27 thf(f9,plain,(
% 1.49/1.27 (emptyset = (^[Y0 : $i]: ($false)))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f3])).
% 1.49/1.27 thf(f3,axiom,(
% 1.49/1.27 ((^[X0 : $i] : ($false)) = emptyset)),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.cQR7NxgZt1/DTF2THF_5788.p',emptyset)).
% 1.49/1.27 thf(f17,plain,(
% 1.49/1.27 (powerset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ Y1 @ Y0)))))),
% 1.49/1.27 inference(definition_unfolding,[status(thm)],[f15,f14])).
% 1.49/1.27 thf(f14,plain,(
% 1.49/1.27 (subseteq = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.27 thf(f11,plain,(
% 1.49/1.27 (subseteq = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f10])).
% 1.49/1.27 thf(f10,plain,(
% 1.49/1.27 (subseteq = (^[X0 : $i > $o, X1 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) => (X1 @ X2)))))),
% 1.49/1.27 inference(rectify,[status(thm)],[f1])).
% 1.49/1.27 thf(f1,axiom,(
% 1.49/1.27 (subseteq = (^[X0 : $i > $o, X1 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) => (X1 @ X2)))))),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.cQR7NxgZt1/DTF2THF_5788.p',subseteq)).
% 1.49/1.27 thf(f15,plain,(
% 1.49/1.27 (powerset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (subseteq @ Y1 @ Y0)))))),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f8])).
% 1.49/1.27 thf(f8,plain,(
% 1.49/1.27 (powerset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (subseteq @ Y1 @ Y0)))))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f2])).
% 1.49/1.27 thf(f2,axiom,(
% 1.49/1.27 (powerset = (^[X0 : $i > $o, X1 : $i > $o] : (subseteq @ X1 @ X0)))),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.cQR7NxgZt1/DTF2THF_5788.p',poserset)).
% 1.49/1.27 thf(f13,plain,(
% 1.49/1.27 ((powerset @ emptyset) != (^[Y0 : $i > $o]: (emptyset = Y0)))),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.27 thf(f12,plain,(
% 1.49/1.27 ((powerset @ emptyset) != (^[Y0 : $i > $o]: (emptyset = Y0)))),
% 1.49/1.27 inference(flattening,[status(thm)],[f7])).
% 1.49/1.27 thf(f7,plain,(
% 1.49/1.27 ~((powerset @ emptyset) = (^[Y0 : $i > $o]: (emptyset = Y0)))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f5])).
% 1.49/1.27 thf(f5,negated_conjecture,(
% 1.49/1.27 ~((^[X0 : $i > $o] : ((emptyset = X0))) = (powerset @ emptyset))),
% 1.49/1.27 inference(negated_conjecture,[status(cth)],[f4])).
% 1.49/1.27 thf(f4,conjecture,(
% 1.49/1.27 ((^[X0 : $i > $o] : ((emptyset = X0))) = (powerset @ emptyset))),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.cQR7NxgZt1/DTF2THF_5788.p',conj)).
% 1.49/1.27 thf(f40,plain,(
% 1.49/1.27 spl0_1 | spl0_2),
% 1.49/1.27 inference(avatar_split_clause,[status(thm)],[f32,f37,f34])).
% 1.49/1.27 thf(f32,plain,(
% 1.49/1.27 ( ! [X1 : $i] : (($false = (sK2 @ X1)) | ((^[Y0 : $i]: ($false)) = sK2)) )),
% 1.49/1.27 inference(not_proxy_clausification,[status(thm)],[f31])).
% 1.49/1.27 thf(f31,plain,(
% 1.49/1.27 ( ! [X1 : $i] : (((^[Y0 : $i]: ($false)) = sK2) | ($true = (~ (sK2 @ X1)))) )),
% 1.49/1.27 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.49/1.27 thf(f30,plain,(
% 1.49/1.27 ( ! [X1 : $i] : (((^[Y0 : $i]: ($false)) = sK2) | ($true = ((^[Y0 : $i]: (~ (sK2 @ Y0))) @ X1))) )),
% 1.49/1.27 inference(pi_clausification,[status(thm)],[f29])).
% 1.49/1.27 thf(f29,plain,(
% 1.49/1.27 ((^[Y0 : $i]: ($false)) = sK2) | ((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0)))) = $true)),
% 1.49/1.27 inference(equality_proxy_clausification,[status(thm)],[f23])).
% 1.49/1.27 thf(f23,plain,(
% 1.49/1.27 ($true = ((^[Y0 : $i]: ($false)) = sK2)) | ((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0)))) = $true)),
% 1.49/1.27 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.49/1.27 % SZS output end Proof for DTF2THF_5788
% 1.49/1.27 % (5887)------------------------------
% 1.49/1.27 % (5887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (5887)Termination reason: Refutation
% 1.49/1.27
% 1.49/1.27 % (5887)Memory used [KB]: 5500
% 1.49/1.27 % (5887)Time elapsed: 0.005 s
% 1.49/1.27 % (5887)Instructions burned: 2 (million)
% 1.49/1.27 % (5887)------------------------------
% 1.49/1.27 % (5887)------------------------------
% 1.49/1.27 % (5886)Success in time 0.015 s
%------------------------------------------------------------------------------