%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV164^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 09:40:27 AM UTC 2026
% Result : Theorem 1.63s 1.35s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 125 ( 44 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 211 ( 32 ~; 22 |; 5 &; 140 @)
% ( 8 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 165 ( 100 ^; 28 !; 37 ?; 165 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_7,type,
sK0: a > a > $o ).
thf(func_def_8,type,
sK1: ( a > a > a ) > a ).
thf(func_def_9,type,
sK2: a ).
thf(func_def_10,type,
sK3: a ).
thf(func_def_12,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f45,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f27,f39,f44]) ).
thf(f44,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
| ~ spl4_3 ),
inference(equality_resolution,[status(thm)],[f34]) ).
thf(f34,plain,
( ! [X0: ( a > a > a ) > a] :
( sK2
!= ( X0
@ ^ [Y0: a,Y1: a] : Y1 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl4_3
<=> ! [X0: ( a > a > a ) > a] :
( sK2
!= ( X0
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f39,plain,
( spl4_3
| ~ spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f30,f18,f33]) ).
thf(f18,definition,
( spl4_1
<=> ( $true
= ( sK0 @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f30,plain,
( ! [X3: ( a > a > a ) > a] :
( sK2
!= ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X3: ( a > a > a ) > a] :
( ( sK2
!= ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) )
| ( $true != $true ) )
| ~ spl4_1 ),
inference(constrained_superposition,[status(thm)],[f16,f20]) ).
thf(f20,plain,
( ( $true
= ( sK0 @ sK3 @ sK2 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f16,plain,
! [X0: ( a > a > a ) > a] :
( $true
!= ( sK0
@ ( X0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X0
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(condensation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: a,X3: a,X1: ( a > a > a ) > a] :
( ( $true
!= ( sK0 @ X3 @ X2 ) )
| ( ( sK0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ! [X1: ( a > a > a ) > a] :
( ( sK0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) )
!= $true )
| ! [X2: a,X3: a] :
( $true
!= ( sK0 @ X3 @ X2 ) ) )
& ( ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ( $true
= ( sK0 @ sK3 @ sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > a > $o] :
( ( ! [X1: ( a > a > a ) > a] :
( $true
!= ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ! [X2: a,X3: a] :
( ( X0 @ X3 @ X2 )
!= $true ) )
& ( ? [X4: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X4
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X4
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ? [X5: a,X6: a] :
( $true
= ( X0 @ X6 @ X5 ) ) ) )
=> ( ( ! [X1: ( a > a > a ) > a] :
( ( sK0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) )
!= $true )
| ! [X3: a,X2: a] :
( $true
!= ( sK0 @ X3 @ X2 ) ) )
& ( ? [X4: ( a > a > a ) > a] :
( $true
= ( sK0
@ ( X4
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X4
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ? [X6: a,X5: a] :
( $true
= ( sK0 @ X6 @ X5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X4: ( a > a > a ) > a] :
( $true
= ( sK0
@ ( X4
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X4
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
=> ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X6: a,X5: a] :
( $true
= ( sK0 @ X6 @ X5 ) )
=> ( $true
= ( sK0 @ sK3 @ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > a > $o] :
( ( ! [X1: ( a > a > a ) > a] :
( $true
!= ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ! [X2: a,X3: a] :
( ( X0 @ X3 @ X2 )
!= $true ) )
& ( ? [X4: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X4
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X4
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ? [X5: a,X6: a] :
( $true
= ( X0 @ X6 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > a > $o] :
( ( ! [X1: ( a > a > a ) > a] :
( $true
!= ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ! [X2: a,X3: a] :
( ( X0 @ X3 @ X2 )
!= $true ) )
& ( ? [X1: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ? [X2: a,X3: a] :
( ( X0 @ X3 @ X2 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > a > $o] :
( ? [X2: a,X3: a] :
( ( X0 @ X3 @ X2 )
= $true )
<~> ? [X1: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > a > $o] :
( ? [X1: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
<=> ? [X2: a,X3: a] :
( ( X0 @ X3 @ X2 )
= $true ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > a > $o] :
( ? [X1: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
<=> ? [X6: a,X7: a] :
( $true
= ( X0 @ X7 @ X6 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ? [X1: ( a > a > a ) > a] :
( X0
@ ( X1
@ ^ [X2: a,X3: a] : X2 )
@ ( X1
@ ^ [X4: a,X5: a] : X5 ) )
<=> ? [X6: a,X7: a] : ( X0 @ X7 @ X6 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ? [X3: ( a > a > a ) > a] :
( X0
@ ( X3
@ ^ [X1: a,X2: a] : X1 )
@ ( X3
@ ^ [X1: a,X2: a] : X2 ) )
<=> ? [X2: a,X1: a] : ( X0 @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ? [X3: ( a > a > a ) > a] :
( X0
@ ( X3
@ ^ [X1: a,X2: a] : X1 )
@ ( X3
@ ^ [X1: a,X2: a] : X2 ) )
<=> ? [X2: a,X1: a] : ( X0 @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0yyx2xzgJU/DTF2THF_17831.p',cTHM185_pme) ).
thf(f27,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f26]) ).
thf(f26,plain,
( $false
| ~ spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f24,f16]) ).
thf(f24,plain,
( ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl4_2
<=> ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f25,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f22,f18]) ).
thf(f14,plain,
( ( $true
= ( sK0 @ sK3 @ sK2 ) )
| ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV164^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n015.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:41:31 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEV164^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : TPS problem THM185
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : Basic theorem about representing relations in terms of ordered
% 0.29/0.46 % pairs.
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0224 [Bro09]
% 0.29/0.46 % : THM149 [TPS]
% 0.29/0.46 % : THM185 [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.25 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.50 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.29/0.46 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 6 @)
% 0.29/0.46 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.29/0.46 % Number of variables : 8 ( 4 ^; 1 !; 3 ?; 8 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 % : Polymorphic definitions expanded.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(a_type,type,
% 0.29/0.46 a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(cTHM185_pme,conjecture,
% 0.29/0.46 ! [Xr: a > a > $o] :
% 0.29/0.46 ( ? [Xx: a,Xy: a] : ( Xr @ Xx @ Xy )
% 0.29/0.46 <=> ? [Xp: ( a > a > a ) > a] :
% 0.29/0.46 ( Xr
% 0.29/0.46 @ ( Xp
% 0.29/0.46 @ ^ [Xx: a,Xy: a] : Xx )
% 0.29/0.46 @ ( Xp
% 0.29/0.46 @ ^ [Xx: a,Xy: a] : Xy ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.63/1.31 ---- Embedded in THF ---
% 1.63/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.31 %%% Generated on Tue Feb 24 12:41:32 EST 2026
% 1.63/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.31 %%% Logic specification used:
% 1.63/1.31 %%% thf(spec, logic, $$dhol).
% 1.63/1.31
% 1.63/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.0yyx2xzgJU/DTF2DTF17831.p
% See solution above
% 1.63/1.31 ------------------------
% 1.63/1.32 ---- Cleaned THF ---
% 1.63/1.32 thf(a_type,type,
% 1.63/1.32 a: $tType ).
% 1.63/1.32
% 1.63/1.32 thf(cTHM185_pme,conjecture,
% 1.63/1.32 ! [Xr: a > a > $o] :
% 1.63/1.32 ( ? [Xx: a,Xy: a] : ( Xr @ Xx @ Xy )
% 1.63/1.32 <=> ? [Xp: ( a > a > a ) > a] :
% 1.63/1.32 ( Xr
% 1.63/1.32 @ ( Xp
% 1.63/1.32 @ ^ [Xx: a,Xy: a] : Xx )
% 1.63/1.32 @ ( Xp
% 1.63/1.32 @ ^ [Xx: a,Xy: a] : Xy ) ) ) ).
% 1.63/1.32 ------------------------
% 1.63/1.34 % (18041)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17831 for (2999ds/2Mi)
% 1.63/1.34 % (18041)Instruction limit reached!
% 1.63/1.34 % (18041)------------------------------
% 1.63/1.34 % (18041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (18041)Termination reason: Unknown
% 1.63/1.34 % (18041)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (18041)Memory used [KB]: 5500
% 1.63/1.34 % (18041)Time elapsed: 0.002 s
% 1.63/1.34 % (18041)Instructions burned: 2 (million)
% 1.63/1.34 % (18041)------------------------------
% 1.63/1.34 % (18041)------------------------------
% 1.63/1.34 % (18038)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17831 for (2999ds/183Mi)
% 1.63/1.34 % (18039)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_17831 for (2999ds/4Mi)
% 1.63/1.34 % (18040)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_17831 for (2999ds/27Mi)
% 1.63/1.34 % (18042)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_17831 for (2999ds/2Mi)
% 1.63/1.34 % (18044)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17831 for (2999ds/18Mi)
% 1.63/1.34 % (18043)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_17831 for (2999ds/275Mi)
% 1.63/1.34 % (18042)Instruction limit reached!
% 1.63/1.34 % (18042)------------------------------
% 1.63/1.34 % (18042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (18042)Termination reason: Unknown
% 1.63/1.34 % (18042)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (18042)Memory used [KB]: 5500
% 1.63/1.34 % (18042)Time elapsed: 0.004 s
% 1.63/1.34 % (18042)Instructions burned: 2 (million)
% 1.63/1.34 % (18042)------------------------------
% 1.63/1.34 % (18042)------------------------------
% 1.63/1.34 % (18040)Refutation not found, incomplete strategy
% 1.63/1.34 % (18040)------------------------------
% 1.63/1.34 % (18040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (18040)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.34
% 1.63/1.34
% 1.63/1.34 % (18040)Memory used [KB]: 5500
% 1.63/1.34 % (18040)Time elapsed: 0.004 s
% 1.63/1.34 % (18040)Instructions burned: 2 (million)
% 1.63/1.34 % (18040)------------------------------
% 1.63/1.34 % (18040)------------------------------
% 1.63/1.34 % (18039)Instruction limit reached!
% 1.63/1.34 % (18039)------------------------------
% 1.63/1.34 % (18039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (18039)Termination reason: Unknown
% 1.63/1.34 % (18039)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (18039)Memory used [KB]: 5500
% 1.63/1.34 % (18039)Time elapsed: 0.005 s
% 1.63/1.34 % (18039)Instructions burned: 4 (million)
% 1.63/1.34 % (18039)------------------------------
% 1.63/1.34 % (18039)------------------------------
% 1.63/1.34 % (18043)Refutation not found, incomplete strategy
% 1.63/1.34 % (18043)------------------------------
% 1.63/1.34 % (18043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (18043)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.34
% 1.63/1.34
% 1.63/1.34 % (18043)Memory used [KB]: 5500
% 1.63/1.34 % (18043)Time elapsed: 0.004 s
% 1.63/1.34 % (18043)Instructions burned: 2 (million)
% 1.63/1.34 % (18043)------------------------------
% 1.63/1.34 % (18043)------------------------------
% 1.63/1.35 % (18044)First to succeed.
% 1.63/1.35 % (18045)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17831 for (2999ds/3Mi)
% 1.63/1.35 % (18038)Refutation not found, incomplete strategy
% 1.63/1.35 % (18038)------------------------------
% 1.63/1.35 % (18038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (18038)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.35
% 1.63/1.35
% 1.63/1.35 % (18038)Memory used [KB]: 5500
% 1.63/1.35 % (18038)Time elapsed: 0.007 s
% 1.63/1.35 % (18038)Instructions burned: 8 (million)
% 1.63/1.35 % (18038)------------------------------
% 1.63/1.35 % (18038)------------------------------
% 1.63/1.35 % (18044)Refutation found. Thanks to Tanya!
% 1.63/1.35 % SZS status Theorem for DTF2THF_17831
% 1.63/1.35 % SZS output start Proof for DTF2THF_17831
% 1.63/1.35 thf(type_def_5, type, a: $tType).
% 1.63/1.35 thf(func_def_0, type, a: $tType).
% 1.63/1.35 thf(func_def_7, type, sK0: a > a > $o).
% 1.63/1.35 thf(func_def_8, type, sK1: (a > a > a) > a).
% 1.63/1.35 thf(func_def_9, type, sK2: a).
% 1.63/1.35 thf(func_def_10, type, sK3: a).
% 1.63/1.35 thf(func_def_12, type, ph5: !>[X0: $tType]:(X0)).
% 1.63/1.35 thf(f45,plain,(
% 1.63/1.35 $false),
% 1.63/1.35 inference(avatar_sat_refutation,[status(thm)],[f25,f27,f39,f44])).
% 1.63/1.35 thf(f44,plain,(
% 1.63/1.35 ~spl4_3),
% 1.63/1.35 inference(avatar_contradiction_clause,[status(thm)],[f41])).
% 1.63/1.35 thf(f41,plain,(
% 1.63/1.35 $false | ~spl4_3),
% 1.63/1.35 inference(equality_resolution,[status(thm)],[f34])).
% 1.63/1.35 thf(f34,plain,(
% 1.63/1.35 ( ! [X0 : (a > a > a) > a] : ((sK2 != (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) ) | ~spl4_3),
% 1.63/1.35 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.63/1.35 thf(f33,definition,(
% 1.63/1.35 spl4_3 <=> ! [X0 : (a > a > a) > a] : (sK2 != (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))),
% 1.63/1.35 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.63/1.35 thf(f39,plain,(
% 1.63/1.35 spl4_3 | ~spl4_1),
% 1.63/1.35 inference(avatar_split_clause,[status(thm)],[f30,f18,f33])).
% 1.63/1.35 thf(f18,definition,(
% 1.63/1.35 spl4_1 <=> ($true = (sK0 @ sK3 @ sK2))),
% 1.63/1.35 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.63/1.35 thf(f30,plain,(
% 1.63/1.35 ( ! [X3 : (a > a > a) > a] : ((sK2 != (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) ) | ~spl4_1),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.63/1.35 thf(f29,plain,(
% 1.63/1.35 ( ! [X3 : (a > a > a) > a] : ((sK2 != (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) | ($true != $true)) ) | ~spl4_1),
% 1.63/1.35 inference(constrained_superposition,[status(thm)],[f16,f20])).
% 1.63/1.35 thf(f20,plain,(
% 1.63/1.35 ($true = (sK0 @ sK3 @ sK2)) | ~spl4_1),
% 1.63/1.35 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.63/1.35 thf(f16,plain,(
% 1.63/1.35 ( ! [X0 : (a > a > a) > a] : (($true != (sK0 @ (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))) )),
% 1.63/1.35 inference(condensation,[status(thm)],[f15])).
% 1.63/1.35 thf(f15,plain,(
% 1.63/1.35 ( ! [X2 : a,X3 : a,X1 : (a > a > a) > a] : (($true != (sK0 @ X3 @ X2)) | ((sK0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) != $true)) )),
% 1.63/1.35 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.35 thf(f13,plain,(
% 1.63/1.35 (! [X1 : (a > a > a) > a] : ((sK0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) != $true) | ! [X2 : a,X3 : a] : ($true != (sK0 @ X3 @ X2))) & (($true = (sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ($true = (sK0 @ sK3 @ sK2)))),
% 1.63/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f12,f11,f10])).
% 1.63/1.35 thf(f10,plain,(
% 1.63/1.35 ? [X0 : a > a > $o] : ((! [X1 : (a > a > a) > a] : ($true != (X0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ! [X2 : a,X3 : a] : ((X0 @ X3 @ X2) != $true)) & (? [X4 : (a > a > a) > a] : ($true = (X0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ? [X5 : a,X6 : a] : ($true = (X0 @ X6 @ X5)))) => ((! [X1 : (a > a > a) > a] : ((sK0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) != $true) | ! [X3 : a,X2 : a] : ($true != (sK0 @ X3 @ X2))) & (? [X4 : (a > a > a) > a] : ($true = (sK0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ? [X6 : a,X5 : a] : ($true = (sK0 @ X6 @ X5))))),
% 1.63/1.35 introduced(definition,[],[choice_axiom])).
% 1.63/1.35 thf(f11,plain,(
% 1.63/1.35 ? [X4 : (a > a > a) > a] : ($true = (sK0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) => ($true = (sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))),
% 1.63/1.35 introduced(definition,[],[choice_axiom])).
% 1.63/1.35 thf(f12,plain,(
% 1.63/1.35 ? [X6 : a,X5 : a] : ($true = (sK0 @ X6 @ X5)) => ($true = (sK0 @ sK3 @ sK2))),
% 1.63/1.35 introduced(definition,[],[choice_axiom])).
% 1.63/1.35 thf(f9,plain,(
% 1.63/1.35 ? [X0 : a > a > $o] : ((! [X1 : (a > a > a) > a] : ($true != (X0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ! [X2 : a,X3 : a] : ((X0 @ X3 @ X2) != $true)) & (? [X4 : (a > a > a) > a] : ($true = (X0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ? [X5 : a,X6 : a] : ($true = (X0 @ X6 @ X5))))),
% 1.63/1.35 inference(rectify,[status(thm)],[f8])).
% 1.63/1.35 thf(f8,plain,(
% 1.63/1.35 ? [X0 : a > a > $o] : ((! [X1 : (a > a > a) > a] : ($true != (X0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ! [X2 : a,X3 : a] : ((X0 @ X3 @ X2) != $true)) & (? [X1 : (a > a > a) > a] : ($true = (X0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ? [X2 : a,X3 : a] : ((X0 @ X3 @ X2) = $true)))),
% 1.63/1.35 inference(nnf_transformation,[status(thm)],[f7])).
% 1.63/1.35 thf(f7,plain,(
% 1.63/1.35 ? [X0 : a > a > $o] : (? [X2 : a,X3 : a] : ((X0 @ X3 @ X2) = $true) <~> ? [X1 : (a > a > a) > a] : ($true = (X0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))))),
% 1.63/1.35 inference(ennf_transformation,[status(thm)],[f6])).
% 1.63/1.35 thf(f6,plain,(
% 1.63/1.35 ~! [X0 : a > a > $o] : (? [X1 : (a > a > a) > a] : ($true = (X0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) <=> ? [X2 : a,X3 : a] : ((X0 @ X3 @ X2) = $true))),
% 1.63/1.35 inference(rectify,[status(thm)],[f5])).
% 1.63/1.35 thf(f5,plain,(
% 1.63/1.35 ~! [X0 : a > a > $o] : (? [X1 : (a > a > a) > a] : ($true = (X0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) <=> ? [X6 : a,X7 : a] : ($true = (X0 @ X7 @ X6)))),
% 1.63/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.35 thf(f4,plain,(
% 1.63/1.35 ~! [X0 : a > a > $o] : (? [X1 : (a > a > a) > a] : (X0 @ (X1 @ (^[X2 : a, X3 : a] : (X2))) @ (X1 @ (^[X4 : a, X5 : a] : (X5)))) <=> ? [X6 : a,X7 : a] : (X0 @ X7 @ X6))),
% 1.63/1.35 inference(rectify,[status(thm)],[f2])).
% 1.63/1.35 thf(f2,negated_conjecture,(
% 1.63/1.35 ~! [X0 : a > a > $o] : (? [X3 : (a > a > a) > a] : (X0 @ (X3 @ (^[X1 : a, X2 : a] : (X1))) @ (X3 @ (^[X1 : a, X2 : a] : (X2)))) <=> ? [X2 : a,X1 : a] : (X0 @ X1 @ X2))),
% 1.63/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.35 thf(f1,conjecture,(
% 1.63/1.35 ! [X0 : a > a > $o] : (? [X3 : (a > a > a) > a] : (X0 @ (X3 @ (^[X1 : a, X2 : a] : (X1))) @ (X3 @ (^[X1 : a, X2 : a] : (X2)))) <=> ? [X2 : a,X1 : a] : (X0 @ X1 @ X2))),
% 1.63/1.35 file('/export/starexec/sandbox2/tmp/tmp.0yyx2xzgJU/DTF2THF_17831.p',cTHM185_pme)).
% 1.63/1.35 thf(f27,plain,(
% 1.63/1.35 ~spl4_2),
% 1.63/1.35 inference(avatar_contradiction_clause,[status(thm)],[f26])).
% 1.63/1.35 thf(f26,plain,(
% 1.63/1.35 $false | ~spl4_2),
% 1.63/1.35 inference(subsumption_resolution,[status(thm)],[f24,f16])).
% 1.63/1.35 thf(f24,plain,(
% 1.63/1.35 ($true = (sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ~spl4_2),
% 1.63/1.35 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.63/1.35 thf(f22,definition,(
% 1.63/1.35 spl4_2 <=> ($true = (sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))),
% 1.63/1.35 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.63/1.35 thf(f25,plain,(
% 1.63/1.35 spl4_1 | spl4_2),
% 1.63/1.35 inference(avatar_split_clause,[status(thm)],[f14,f22,f18])).
% 1.63/1.35 thf(f14,plain,(
% 1.63/1.35 ($true = (sK0 @ sK3 @ sK2)) | ($true = (sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))),
% 1.63/1.35 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.35 % SZS output end Proof for DTF2THF_17831
% 1.63/1.35 % (18044)------------------------------
% 1.63/1.35 % (18044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (18044)Termination reason: Refutation
% 1.63/1.35
% 1.63/1.35 % (18044)Memory used [KB]: 5500
% 1.63/1.35 % (18044)Time elapsed: 0.006 s
% 1.63/1.35 % (18044)Instructions burned: 2 (million)
% 1.63/1.35 % (18044)------------------------------
% 1.63/1.35 % (18044)------------------------------
% 1.63/1.35 % (18037)Success in time 0.021 s
%------------------------------------------------------------------------------