%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV162^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.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 09:40:26 AM UTC 2026
% Result : Theorem 1.78s 1.52s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 4 unt; 0 typ; 2 def)
% Number of atoms : 115 ( 40 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 193 ( 26 ~; 20 |; 5 &; 132 @)
% ( 6 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 151 ( 92 ^; 40 !; 19 ?; 151 :)
% 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(f36,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f24,f33,f35]) ).
thf(f35,plain,
spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f34]) ).
thf(f34,plain,
( $false
| spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f23,f15]) ).
thf(f15,plain,
! [X0: ( a > a > a ) > a] :
( ( sK0
@ ( X0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X0
@ ^ [Y0: a,Y1: a] : Y1 ) )
= $true ),
inference(condensation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X6: a,X4: ( a > a > a ) > a,X5: a] :
( ( $true
= ( sK0
@ ( X4
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X4
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ( $true
= ( sK0 @ X5 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( $true
!= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ( $true
!= ( sK0 @ sK2 @ sK3 ) ) )
& ( ! [X4: ( a > a > a ) > a] :
( $true
= ( sK0
@ ( X4
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X4
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ! [X5: a,X6: a] :
( $true
= ( sK0 @ X5 @ X6 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > a > $o] :
( ( ? [X1: ( a > a > a ) > a] :
( ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) )
!= $true )
| ? [X2: a,X3: a] :
( $true
!= ( X0 @ X2 @ X3 ) ) )
& ( ! [X4: ( a > a > a ) > a] :
( ( X0
@ ( X4
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X4
@ ^ [Y0: a,Y1: a] : Y1 ) )
= $true )
| ! [X5: a,X6: a] :
( $true
= ( X0 @ X5 @ X6 ) ) ) )
=> ( ( ? [X1: ( a > a > a ) > a] :
( $true
!= ( sK0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ? [X3: a,X2: a] :
( $true
!= ( sK0 @ X2 @ X3 ) ) )
& ( ! [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 @ X5 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X1: ( a > a > a ) > a] :
( $true
!= ( sK0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
=> ( $true
!= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X3: a,X2: a] :
( $true
!= ( sK0 @ X2 @ X3 ) )
=> ( $true
!= ( sK0 @ sK2 @ sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > $o] :
( ( ? [X1: ( a > a > a ) > a] :
( ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) )
!= $true )
| ? [X2: a,X3: a] :
( $true
!= ( X0 @ X2 @ X3 ) ) )
& ( ! [X4: ( a > a > a ) > a] :
( ( X0
@ ( X4
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X4
@ ^ [Y0: a,Y1: a] : Y1 ) )
= $true )
| ! [X5: a,X6: a] :
( $true
= ( X0 @ X5 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > a > $o] :
( ( ? [X3: ( a > a > a ) > a] :
( $true
!= ( X0
@ ( X3
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ? [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
!= $true ) )
& ( ! [X3: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X3
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > a > $o] :
( ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
= $true )
<~> ! [X3: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X3
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > a > $o] :
( ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
= $true )
<=> ! [X3: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X3
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ! [X1: a,X2: a] : ( X0 @ X1 @ X2 )
<=> ! [X3: ( a > a > a ) > a] :
( X0
@ ( X3
@ ^ [X4: a,X5: a] : X4 )
@ ( X3
@ ^ [X6: a,X7: a] : X7 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ! [X1: a,X2: a] : ( X0 @ X1 @ X2 )
<=> ! [X3: ( a > a > a ) > a] :
( X0
@ ( X3
@ ^ [X1: a,X2: a] : X1 )
@ ( X3
@ ^ [X1: a,X2: a] : X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ! [X1: a,X2: a] : ( X0 @ X1 @ X2 )
<=> ! [X3: ( a > a > a ) > a] :
( X0
@ ( X3
@ ^ [X1: a,X2: a] : X1 )
@ ( X3
@ ^ [X1: a,X2: a] : X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RBxxanHNVC/DTF2THF_26495.p',cTHM184_pme) ).
thf(f23,plain,
( ( $true
!= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,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(f33,plain,
spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f31]) ).
thf(f31,plain,
( $false
| spl4_1 ),
inference(equality_resolution,[status(thm)],[f28]) ).
thf(f28,plain,
( ! [X3: ( a > a > a ) > a] :
( sK3
!= ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) )
| spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X3: ( a > a > a ) > a] :
( ( sK3
!= ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) )
| ( $true != $true ) )
| spl4_1 ),
inference(constrained_superposition,[status(thm)],[f19,f15]) ).
thf(f19,plain,
( ( $true
!= ( sK0 @ sK2 @ sK3 ) )
| spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl4_1
<=> ( $true
= ( sK0 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f24,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f21,f17]) ).
thf(f14,plain,
( ( $true
!= ( sK0 @ sK2 @ sK3 ) )
| ( $true
!= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV162^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n021.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 12:41:09 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEV162^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : TPS problem THM184
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English : Theorem about representing relations in terms of ordered pairs.
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : tps_0128 [Bro09]
% 0.19/0.47 % : THM148 [TPS]
% 0.19/0.47 % : THM184 [TPS]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.19/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.19/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.19/0.47 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 6 @)
% 0.19/0.47 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 9 ( 9 avg)
% 0.19/0.47 % Number of types : 2 ( 1 usr)
% 0.19/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.47 % Number of variables : 8 ( 4 ^; 4 !; 0 ?; 8 :)
% 0.19/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.47 % : Polymorphic definitions expanded.
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(a_type,type,
% 0.19/0.47 a: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(cTHM184_pme,conjecture,
% 0.19/0.47 ! [Xr: a > a > $o] :
% 0.19/0.47 ( ! [Xx: a,Xy: a] : ( Xr @ Xx @ Xy )
% 0.19/0.47 <=> ! [Xp: ( a > a > a ) > a] :
% 0.19/0.47 ( Xr
% 0.19/0.47 @ ( Xp
% 0.19/0.47 @ ^ [Xx: a,Xy: a] : Xx )
% 0.19/0.47 @ ( Xp
% 0.19/0.47 @ ^ [Xx: a,Xy: a] : Xy ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.59/1.48 ---- Embedded in THF ---
% 1.59/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.59/1.48 %%% Generated on Tue Feb 24 12:41:10 EST 2026
% 1.59/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 1.59/1.48 %%% Logic specification used:
% 1.59/1.48 %%% thf(spec, logic, $$dhol).
% 1.59/1.48
% 1.59/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RBxxanHNVC/DTF2DTF26495.p
% See solution above
% 1.59/1.48 ------------------------
% 1.59/1.49 ---- Cleaned THF ---
% 1.59/1.49 thf(a_type,type,
% 1.59/1.49 a: $tType ).
% 1.59/1.49
% 1.59/1.49 thf(cTHM184_pme,conjecture,
% 1.59/1.49 ! [Xr: a > a > $o] :
% 1.59/1.49 ( ! [Xx: a,Xy: a] : ( Xr @ Xx @ Xy )
% 1.59/1.49 <=> ! [Xp: ( a > a > a ) > a] :
% 1.59/1.49 ( Xr
% 1.59/1.49 @ ( Xp
% 1.59/1.49 @ ^ [Xx: a,Xy: a] : Xx )
% 1.59/1.49 @ ( Xp
% 1.59/1.49 @ ^ [Xx: a,Xy: a] : Xy ) ) ) ).
% 1.59/1.49 ------------------------
% 1.78/1.51 % (26641)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_26495 for (3000ds/27Mi)
% 1.78/1.51 % (26642)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26495 for (3000ds/2Mi)
% 1.78/1.51 % (26639)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26495 for (3000ds/183Mi)
% 1.78/1.51 % (26640)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_26495 for (3000ds/4Mi)
% 1.78/1.51 % (26643)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_26495 for (3000ds/2Mi)
% 1.78/1.51 % (26642)Instruction limit reached!
% 1.78/1.51 % (26642)------------------------------
% 1.78/1.51 % (26642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.51 % (26642)Termination reason: Unknown
% 1.78/1.51 % (26643)Instruction limit reached!
% 1.78/1.51 % (26643)------------------------------
% 1.78/1.51 % (26643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.51 % (26642)Termination phase: Saturation
% 1.78/1.51
% 1.78/1.51 % (26642)Memory used [KB]: 5500
% 1.78/1.51 % (26642)Time elapsed: 0.003 s
% 1.78/1.51 % (26642)Instructions burned: 2 (million)
% 1.78/1.51 % (26642)------------------------------
% 1.78/1.51 % (26642)------------------------------
% 1.78/1.51 % (26643)Termination reason: Unknown
% 1.78/1.51 % (26643)Termination phase: Saturation
% 1.78/1.51
% 1.78/1.51 % (26643)Memory used [KB]: 5500
% 1.78/1.51 % (26643)Time elapsed: 0.003 s
% 1.78/1.51 % (26643)Instructions burned: 2 (million)
% 1.78/1.51 % (26643)------------------------------
% 1.78/1.51 % (26643)------------------------------
% 1.78/1.51 % (26641)Refutation not found, incomplete strategy
% 1.78/1.51 % (26641)------------------------------
% 1.78/1.51 % (26641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.51 % (26641)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.51
% 1.78/1.51
% 1.78/1.51 % (26641)Memory used [KB]: 5500
% 1.78/1.51 % (26641)Time elapsed: 0.004 s
% 1.78/1.51 % (26641)Instructions burned: 3 (million)
% 1.78/1.51 % (26641)------------------------------
% 1.78/1.51 % (26641)------------------------------
% 1.78/1.51 % (26640)Instruction limit reached!
% 1.78/1.51 % (26640)------------------------------
% 1.78/1.51 % (26640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.51 % (26640)Termination reason: Unknown
% 1.78/1.51 % (26640)Termination phase: Saturation
% 1.78/1.51
% 1.78/1.51 % (26640)Memory used [KB]: 5500
% 1.78/1.51 % (26640)Time elapsed: 0.005 s
% 1.78/1.51 % (26640)Instructions burned: 5 (million)
% 1.78/1.51 % (26640)------------------------------
% 1.78/1.51 % (26640)------------------------------
% 1.78/1.51 % (26639)Refutation not found, incomplete strategy
% 1.78/1.51 % (26639)------------------------------
% 1.78/1.51 % (26639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.51 % (26639)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.51
% 1.78/1.51
% 1.78/1.51 % (26639)Memory used [KB]: 5628
% 1.78/1.51 % (26639)Time elapsed: 0.007 s
% 1.78/1.51 % (26639)Instructions burned: 9 (million)
% 1.78/1.51 % (26639)------------------------------
% 1.78/1.51 % (26639)------------------------------
% 1.78/1.52 % (26644)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_26495 for (3000ds/275Mi)
% 1.78/1.52 % (26645)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26495 for (3000ds/18Mi)
% 1.78/1.52 % (26644)Refutation not found, incomplete strategy
% 1.78/1.52 % (26644)------------------------------
% 1.78/1.52 % (26644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.52 % (26644)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.52
% 1.78/1.52
% 1.78/1.52 % (26644)Memory used [KB]: 5500
% 1.78/1.52 % (26644)Time elapsed: 0.003 s
% 1.78/1.52 % (26644)Instructions burned: 2 (million)
% 1.78/1.52 % (26644)------------------------------
% 1.78/1.52 % (26644)------------------------------
% 1.78/1.52 % (26645)First to succeed.
% 1.78/1.52 % (26645)Refutation found. Thanks to Tanya!
% 1.78/1.52 % SZS status Theorem for DTF2THF_26495
% 1.78/1.52 % SZS output start Proof for DTF2THF_26495
% 1.78/1.52 thf(type_def_5, type, a: $tType).
% 1.78/1.52 thf(func_def_0, type, a: $tType).
% 1.78/1.52 thf(func_def_7, type, sK0: a > a > $o).
% 1.78/1.52 thf(func_def_8, type, sK1: (a > a > a) > a).
% 1.78/1.52 thf(func_def_9, type, sK2: a).
% 1.78/1.52 thf(func_def_10, type, sK3: a).
% 1.78/1.52 thf(func_def_12, type, ph5: !>[X0: $tType]:(X0)).
% 1.78/1.52 thf(f36,plain,(
% 1.78/1.52 $false),
% 1.78/1.52 inference(avatar_sat_refutation,[status(thm)],[f24,f33,f35])).
% 1.78/1.52 thf(f35,plain,(
% 1.78/1.52 spl4_2),
% 1.78/1.52 inference(avatar_contradiction_clause,[status(thm)],[f34])).
% 1.78/1.52 thf(f34,plain,(
% 1.78/1.52 $false | spl4_2),
% 1.78/1.52 inference(subsumption_resolution,[status(thm)],[f23,f15])).
% 1.78/1.52 thf(f15,plain,(
% 1.78/1.52 ( ! [X0 : (a > a > a) > a] : (((sK0 @ (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) = $true)) )),
% 1.78/1.52 inference(condensation,[status(thm)],[f13])).
% 1.78/1.52 thf(f13,plain,(
% 1.78/1.52 ( ! [X6 : a,X4 : (a > a > a) > a,X5 : a] : (($true = (sK0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ($true = (sK0 @ X5 @ X6))) )),
% 1.78/1.52 inference(cnf_transformation,[status(thm)],[f12])).
% 1.78/1.52 thf(f12,plain,(
% 1.78/1.52 (($true != (sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ($true != (sK0 @ sK2 @ sK3))) & (! [X4 : (a > a > a) > a] : ($true = (sK0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ! [X5 : a,X6 : a] : ($true = (sK0 @ X5 @ X6)))),
% 1.78/1.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f11,f10,f9])).
% 1.78/1.52 thf(f9,plain,(
% 1.78/1.52 ? [X0 : a > a > $o] : ((? [X1 : (a > a > a) > a] : ((X0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) != $true) | ? [X2 : a,X3 : a] : ($true != (X0 @ X2 @ X3))) & (! [X4 : (a > a > a) > a] : ((X0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) = $true) | ! [X5 : a,X6 : a] : ($true = (X0 @ X5 @ X6)))) => ((? [X1 : (a > a > a) > a] : ($true != (sK0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ? [X3 : a,X2 : a] : ($true != (sK0 @ X2 @ X3))) & (! [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 @ X5 @ X6))))),
% 1.78/1.52 introduced(definition,[],[choice_axiom])).
% 1.78/1.52 thf(f10,plain,(
% 1.78/1.52 ? [X1 : (a > a > a) > a] : ($true != (sK0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) => ($true != (sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))),
% 1.78/1.52 introduced(definition,[],[choice_axiom])).
% 1.78/1.52 thf(f11,plain,(
% 1.78/1.52 ? [X3 : a,X2 : a] : ($true != (sK0 @ X2 @ X3)) => ($true != (sK0 @ sK2 @ sK3))),
% 1.78/1.52 introduced(definition,[],[choice_axiom])).
% 1.78/1.52 thf(f8,plain,(
% 1.78/1.52 ? [X0 : a > a > $o] : ((? [X1 : (a > a > a) > a] : ((X0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) != $true) | ? [X2 : a,X3 : a] : ($true != (X0 @ X2 @ X3))) & (! [X4 : (a > a > a) > a] : ((X0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) = $true) | ! [X5 : a,X6 : a] : ($true = (X0 @ X5 @ X6))))),
% 1.78/1.52 inference(rectify,[status(thm)],[f7])).
% 1.78/1.52 thf(f7,plain,(
% 1.78/1.52 ? [X0 : a > a > $o] : ((? [X3 : (a > a > a) > a] : ($true != (X0 @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ? [X1 : a,X2 : a] : ((X0 @ X1 @ X2) != $true)) & (! [X3 : (a > a > a) > a] : ($true = (X0 @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | ! [X1 : a,X2 : a] : ((X0 @ X1 @ X2) = $true)))),
% 1.78/1.52 inference(nnf_transformation,[status(thm)],[f6])).
% 1.78/1.52 thf(f6,plain,(
% 1.78/1.52 ? [X0 : a > a > $o] : (! [X1 : a,X2 : a] : ((X0 @ X1 @ X2) = $true) <~> ! [X3 : (a > a > a) > a] : ($true = (X0 @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))))),
% 1.78/1.52 inference(ennf_transformation,[status(thm)],[f5])).
% 1.78/1.52 thf(f5,plain,(
% 1.78/1.52 ~! [X0 : a > a > $o] : (! [X1 : a,X2 : a] : ((X0 @ X1 @ X2) = $true) <=> ! [X3 : (a > a > a) > a] : ($true = (X0 @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))))),
% 1.78/1.52 inference(fool_elimination,[status(thm)],[f4])).
% 1.78/1.52 thf(f4,plain,(
% 1.78/1.52 ~! [X0 : a > a > $o] : (! [X1 : a,X2 : a] : (X0 @ X1 @ X2) <=> ! [X3 : (a > a > a) > a] : (X0 @ (X3 @ (^[X4 : a, X5 : a] : (X4))) @ (X3 @ (^[X6 : a, X7 : a] : (X7)))))),
% 1.78/1.52 inference(rectify,[status(thm)],[f2])).
% 1.78/1.52 thf(f2,negated_conjecture,(
% 1.78/1.52 ~! [X0 : a > a > $o] : (! [X1 : a,X2 : a] : (X0 @ X1 @ X2) <=> ! [X3 : (a > a > a) > a] : (X0 @ (X3 @ (^[X1 : a, X2 : a] : (X1))) @ (X3 @ (^[X1 : a, X2 : a] : (X2)))))),
% 1.78/1.52 inference(negated_conjecture,[status(cth)],[f1])).
% 1.78/1.52 thf(f1,conjecture,(
% 1.78/1.52 ! [X0 : a > a > $o] : (! [X1 : a,X2 : a] : (X0 @ X1 @ X2) <=> ! [X3 : (a > a > a) > a] : (X0 @ (X3 @ (^[X1 : a, X2 : a] : (X1))) @ (X3 @ (^[X1 : a, X2 : a] : (X2)))))),
% 1.78/1.52 file('/export/starexec/sandbox/tmp/tmp.RBxxanHNVC/DTF2THF_26495.p',cTHM184_pme)).
% 1.78/1.52 thf(f23,plain,(
% 1.78/1.52 ($true != (sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) | spl4_2),
% 1.78/1.52 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.78/1.52 thf(f21,definition,(
% 1.78/1.52 spl4_2 <=> ($true = (sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))),
% 1.78/1.52 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.78/1.52 thf(f33,plain,(
% 1.78/1.52 spl4_1),
% 1.78/1.52 inference(avatar_contradiction_clause,[status(thm)],[f31])).
% 1.78/1.52 thf(f31,plain,(
% 1.78/1.52 $false | spl4_1),
% 1.78/1.52 inference(equality_resolution,[status(thm)],[f28])).
% 1.78/1.52 thf(f28,plain,(
% 1.78/1.52 ( ! [X3 : (a > a > a) > a] : ((sK3 != (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) ) | spl4_1),
% 1.78/1.52 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.78/1.52 thf(f26,plain,(
% 1.78/1.52 ( ! [X3 : (a > a > a) > a] : ((sK3 != (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) | ($true != $true)) ) | spl4_1),
% 1.78/1.52 inference(constrained_superposition,[status(thm)],[f19,f15])).
% 1.78/1.52 thf(f19,plain,(
% 1.78/1.52 ($true != (sK0 @ sK2 @ sK3)) | spl4_1),
% 1.78/1.52 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.78/1.52 thf(f17,definition,(
% 1.78/1.52 spl4_1 <=> ($true = (sK0 @ sK2 @ sK3))),
% 1.78/1.52 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.78/1.52 thf(f24,plain,(
% 1.78/1.52 ~spl4_1 | ~spl4_2),
% 1.78/1.52 inference(avatar_split_clause,[status(thm)],[f14,f21,f17])).
% 1.78/1.52 thf(f14,plain,(
% 1.78/1.52 ($true != (sK0 @ sK2 @ sK3)) | ($true != (sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))),
% 1.78/1.52 inference(cnf_transformation,[status(thm)],[f12])).
% 1.78/1.52 % SZS output end Proof for DTF2THF_26495
% 1.78/1.52 % (26645)------------------------------
% 1.78/1.52 % (26645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.52 % (26645)Termination reason: Refutation
% 1.78/1.52
% 1.78/1.52 % (26645)Memory used [KB]: 5500
% 1.78/1.52 % (26645)Time elapsed: 0.004 s
% 1.78/1.52 % (26645)Instructions burned: 3 (million)
% 1.78/1.52 % (26645)------------------------------
% 1.78/1.52 % (26645)------------------------------
% 1.78/1.52 % (26638)Success in time 0.027 s
%------------------------------------------------------------------------------