%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO268^5 : 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 : n031.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 09:53:48 AM UTC 2026
% Result : Theorem 1.50s 1.26s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 211 ( 60 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 297 ( 60 ~; 43 |; 9 &; 163 @)
% ( 8 <=>; 13 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 101 ( 0 ^; 62 !; 39 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
r: a > b > $o ).
thf(func_def_6,type,
sK0: a ).
thf(func_def_7,type,
sK1: ( a > b ) > a ).
thf(func_def_8,type,
sK2: a > b ).
thf(func_def_9,type,
sK3: a > b ).
thf(func_def_10,type,
sK4: ( b > $o ) > b ).
thf(func_def_13,type,
ph6:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK7: b > b > b ).
thf(f69,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f32,f35,f38,f64,f68]) ).
thf(f68,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
| ~ spl5_1
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true != $true )
| ~ spl5_1
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f31,f21]) ).
thf(f21,plain,
( ! [X7: a] :
( $true
= ( r @ X7 @ ( sK3 @ X7 ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl5_1
<=> ! [X7: a] :
( $true
= ( r @ X7 @ ( sK3 @ X7 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f31,plain,
( ! [X2: a > b] :
( ( r @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) )
!= $true )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl5_4
<=> ! [X2: a > b] :
( ( r @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f64,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f63]) ).
thf(f63,plain,
( $false
| ~ spl5_2
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true != $true )
| ~ spl5_2
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f31,f24]) ).
thf(f24,plain,
( ! [X4: a] :
( $true
= ( r @ X4 @ ( sK2 @ X4 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl5_2
<=> ! [X4: a] :
( $true
= ( r @ X4 @ ( sK2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f38,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f37]) ).
thf(f37,plain,
( $false
| ~ spl5_1
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true != $true )
| ~ spl5_1
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f28,f21]) ).
thf(f28,plain,
( ! [X1: b] :
( ( r @ sK0 @ X1 )
!= $true )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl5_3
<=> ! [X1: b] :
( ( r @ sK0 @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f35,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f34]) ).
thf(f34,plain,
( $false
| ~ spl5_2
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $true != $true )
| ~ spl5_2
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f28,f24]) ).
thf(f32,plain,
( spl5_3
| spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f18,f30,f27]) ).
thf(f18,plain,
! [X2: a > b,X1: b] :
( ( ( r @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) )
!= $true )
| ( ( r @ sK0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ! [X1: b] :
( ( r @ sK0 @ X1 )
!= $true )
| ! [X2: a > b] :
( ( r @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) )
!= $true ) )
& ( ! [X4: a] :
( $true
= ( r @ X4 @ ( sK2 @ X4 ) ) )
| ! [X7: a] :
( $true
= ( r @ X7 @ ( sK3 @ X7 ) ) ) )
& ! [X9: b > $o] :
( ! [X10: b] :
( $true
!= ( X9 @ X10 ) )
| ( ( X9 @ ( sK4 @ X9 ) )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f14,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: a] :
! [X1: b] :
( ( r @ X0 @ X1 )
!= $true )
=> ! [X1: b] :
( ( r @ sK0 @ X1 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X2: a > b] :
( ? [X3: a] :
( ( r @ X3 @ ( X2 @ X3 ) )
!= $true )
=> ( ( r @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X4: a] :
( ? [X5: b] :
( $true
= ( r @ X4 @ X5 ) )
=> ( $true
= ( r @ X4 @ ( sK2 @ X4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X6: a > b] :
! [X7: a] :
( ( r @ X7 @ ( X6 @ X7 ) )
= $true )
=> ! [X7: a] :
( $true
= ( r @ X7 @ ( sK3 @ X7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X8: ( b > $o ) > b] :
! [X9: b > $o] :
( ! [X10: b] :
( $true
!= ( X9 @ X10 ) )
| ( ( X9 @ ( X8 @ X9 ) )
= $true ) )
=> ! [X9: b > $o] :
( ! [X10: b] :
( $true
!= ( X9 @ X10 ) )
| ( ( X9 @ ( sK4 @ X9 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( ? [X0: a] :
! [X1: b] :
( ( r @ X0 @ X1 )
!= $true )
| ! [X2: a > b] :
? [X3: a] :
( ( r @ X3 @ ( X2 @ X3 ) )
!= $true ) )
& ( ! [X4: a] :
? [X5: b] :
( $true
= ( r @ X4 @ X5 ) )
| ? [X6: a > b] :
! [X7: a] :
( ( r @ X7 @ ( X6 @ X7 ) )
= $true ) )
& ? [X8: ( b > $o ) > b] :
! [X9: b > $o] :
( ! [X10: b] :
( $true
!= ( X9 @ X10 ) )
| ( ( X9 @ ( X8 @ X9 ) )
= $true ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ? [X5: a] :
! [X6: b] :
( ( r @ X5 @ X6 )
!= $true )
| ! [X3: a > b] :
? [X4: a] :
( ( r @ X4 @ ( X3 @ X4 ) )
!= $true ) )
& ( ! [X5: a] :
? [X6: b] :
( ( r @ X5 @ X6 )
= $true )
| ? [X3: a > b] :
! [X4: a] :
( ( r @ X4 @ ( X3 @ X4 ) )
= $true ) )
& ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ! [X2: b] :
( ( X1 @ X2 )
!= $true )
| ( ( X1 @ ( X0 @ X1 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ? [X5: a] :
! [X6: b] :
( ( r @ X5 @ X6 )
!= $true )
| ! [X3: a > b] :
? [X4: a] :
( ( r @ X4 @ ( X3 @ X4 ) )
!= $true ) )
& ( ! [X5: a] :
? [X6: b] :
( ( r @ X5 @ X6 )
= $true )
| ? [X3: a > b] :
! [X4: a] :
( ( r @ X4 @ ( X3 @ X4 ) )
= $true ) )
& ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ! [X2: b] :
( ( X1 @ X2 )
!= $true )
| ( ( X1 @ ( X0 @ X1 ) )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ? [X3: a > b] :
! [X4: a] :
( ( r @ X4 @ ( X3 @ X4 ) )
= $true )
<~> ! [X5: a] :
? [X6: b] :
( ( r @ X5 @ X6 )
= $true ) )
& ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ! [X2: b] :
( ( X1 @ X2 )
!= $true )
| ( ( X1 @ ( X0 @ X1 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ? [X2: b] :
( ( X1 @ X2 )
= $true )
=> ( ( X1 @ ( X0 @ X1 ) )
= $true ) )
=> ( ? [X3: a > b] :
! [X4: a] :
( ( r @ X4 @ ( X3 @ X4 ) )
= $true )
<=> ! [X5: a] :
? [X6: b] :
( ( r @ X5 @ X6 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ? [X2: b] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ( ? [X3: a > b] :
! [X4: a] : ( r @ X4 @ ( X3 @ X4 ) )
<=> ! [X5: a] :
? [X6: b] : ( r @ X5 @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ? [X2: b] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ( ? [X4: a > b] :
! [X2: a] : ( r @ X2 @ ( X4 @ X2 ) )
<=> ! [X2: a] :
? [X3: b] : ( r @ X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ? [X0: ( b > $o ) > b] :
! [X1: b > $o] :
( ? [X2: b] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ( ? [X4: a > b] :
! [X2: a] : ( r @ X2 @ ( X4 @ X2 ) )
<=> ! [X2: a] :
? [X3: b] : ( r @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.n2L1Pil8ZL/DTF2THF_14884.p',cX5308) ).
thf(f25,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f17,f23,f20]) ).
thf(f17,plain,
! [X7: a,X4: a] :
( ( $true
= ( r @ X4 @ ( sK2 @ X4 ) ) )
| ( $true
= ( r @ X7 @ ( sK3 @ X7 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO268^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n031.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:35:03 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SYO268^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.45 % Domain : Syntactic
% 0.29/0.45 % Problem : TPS problem X5308
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_0240 [Bro09]
% 0.29/0.45 % : X5308 [TPS]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.29/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.29/0.45 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 2 ( 2 avg)
% 0.29/0.45 % Number of connectives : 11 ( 0 ~; 0 |; 0 &; 8 @)
% 0.29/0.45 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 7 ( 7 avg)
% 0.29/0.45 % Number of types : 3 ( 2 usr)
% 0.29/0.45 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.29/0.45 % Number of variables : 7 ( 0 ^; 3 !; 4 ?; 7 :)
% 0.29/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(a_type,type,
% 0.29/0.45 a: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(b_type,type,
% 0.29/0.45 b: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(r,type,
% 0.29/0.45 r: a > b > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cX5308,conjecture,
% 0.29/0.45 ( ? [Xj: ( b > $o ) > b] :
% 0.29/0.45 ! [Xp: b > $o] :
% 0.29/0.45 ( ? [Xx: b] : ( Xp @ Xx )
% 0.29/0.45 => ( Xp @ ( Xj @ Xp ) ) )
% 0.29/0.45 => ( ! [Xx: a] :
% 0.29/0.45 ? [Xy: b] : ( r @ Xx @ Xy )
% 0.29/0.45 <=> ? [Xf: a > b] :
% 0.29/0.45 ! [Xx: a] : ( r @ Xx @ ( Xf @ Xx ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.50/1.22 ---- Embedded in THF ---
% 1.50/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.23 %%% Generated on Tue Feb 24 14:35:04 EST 2026
% 1.50/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.23 %%% Logic specification used:
% 1.50/1.23 %%% thf(spec, logic, $$dhol).
% 1.50/1.23
% 1.50/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.n2L1Pil8ZL/DTF2DTF14884.p
% See solution above
% 1.50/1.23 ------------------------
% 1.50/1.23 ---- Cleaned THF ---
% 1.50/1.24 thf(a_type,type,
% 1.50/1.24 a: $tType ).
% 1.50/1.24
% 1.50/1.24 thf(b_type,type,
% 1.50/1.24 b: $tType ).
% 1.50/1.24
% 1.50/1.24 thf(r,type,
% 1.50/1.24 r: a > b > $o ).
% 1.50/1.24
% 1.50/1.24 thf(cX5308,conjecture,
% 1.50/1.24 ( ? [Xj: ( b > $o ) > b] :
% 1.50/1.24 ! [Xp: b > $o] :
% 1.50/1.24 ( ? [Xx: b] : ( Xp @ Xx )
% 1.50/1.24 => ( Xp @ ( Xj @ Xp ) ) )
% 1.50/1.24 => ( ! [Xx: a] :
% 1.50/1.24 ? [Xy: b] : ( r @ Xx @ Xy )
% 1.50/1.24 <=> ? [Xf: a > b] :
% 1.50/1.24 ! [Xx: a] : ( r @ Xx @ ( Xf @ Xx ) ) ) ) ).
% 1.50/1.24 ------------------------
% 1.50/1.25 % (14999)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_14884 for (2999ds/4Mi)
% 1.50/1.25 % (14998)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14884 for (2999ds/183Mi)
% 1.50/1.25 % (14999)Instruction limit reached!
% 1.50/1.25 % (14999)------------------------------
% 1.50/1.25 % (14999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (14999)Termination reason: Unknown
% 1.50/1.25 % (14999)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (14999)Memory used [KB]: 5500
% 1.50/1.25 % (14999)Time elapsed: 0.004 s
% 1.50/1.25 % (14999)Instructions burned: 6 (million)
% 1.50/1.25 % (14999)------------------------------
% 1.50/1.25 % (14999)------------------------------
% 1.50/1.25 % (14998)First to succeed.
% 1.50/1.26 % (14998)Refutation found. Thanks to Tanya!
% 1.50/1.26 % SZS status Theorem for DTF2THF_14884
% 1.50/1.26 % SZS output start Proof for DTF2THF_14884
% 1.50/1.26 thf(type_def_5, type, a: $tType).
% 1.50/1.26 thf(type_def_6, type, b: $tType).
% 1.50/1.26 thf(func_def_0, type, a: $tType).
% 1.50/1.26 thf(func_def_1, type, b: $tType).
% 1.50/1.26 thf(func_def_2, type, r: a > b > $o).
% 1.50/1.26 thf(func_def_6, type, sK0: a).
% 1.50/1.26 thf(func_def_7, type, sK1: (a > b) > a).
% 1.50/1.26 thf(func_def_8, type, sK2: a > b).
% 1.50/1.26 thf(func_def_9, type, sK3: a > b).
% 1.50/1.26 thf(func_def_10, type, sK4: (b > $o) > b).
% 1.50/1.26 thf(func_def_13, type, ph6: !>[X0: $tType]:(X0)).
% 1.50/1.26 thf(func_def_17, type, sK7: b > b > b).
% 1.50/1.26 thf(f69,plain,(
% 1.50/1.26 $false),
% 1.50/1.26 inference(avatar_sat_refutation,[status(thm)],[f25,f32,f35,f38,f64,f68])).
% 1.50/1.26 thf(f68,plain,(
% 1.50/1.26 ~spl5_1 | ~spl5_4),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f67])).
% 1.50/1.26 thf(f67,plain,(
% 1.50/1.26 $false | (~spl5_1 | ~spl5_4)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.50/1.26 thf(f66,plain,(
% 1.50/1.26 ($true != $true) | (~spl5_1 | ~spl5_4)),
% 1.50/1.26 inference(superposition,[status(thm)],[f31,f21])).
% 1.50/1.26 thf(f21,plain,(
% 1.50/1.26 ( ! [X7 : a] : (($true = (r @ X7 @ (sK3 @ X7)))) ) | ~spl5_1),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.50/1.26 thf(f20,definition,(
% 1.50/1.26 spl5_1 <=> ! [X7 : a] : ($true = (r @ X7 @ (sK3 @ X7)))),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.50/1.26 thf(f31,plain,(
% 1.50/1.26 ( ! [X2 : a > b] : (((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))) != $true)) ) | ~spl5_4),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.50/1.26 thf(f30,definition,(
% 1.50/1.26 spl5_4 <=> ! [X2 : a > b] : ((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))) != $true)),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.50/1.26 thf(f64,plain,(
% 1.50/1.26 ~spl5_2 | ~spl5_4),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f63])).
% 1.50/1.26 thf(f63,plain,(
% 1.50/1.26 $false | (~spl5_2 | ~spl5_4)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.50/1.26 thf(f59,plain,(
% 1.50/1.26 ($true != $true) | (~spl5_2 | ~spl5_4)),
% 1.50/1.26 inference(superposition,[status(thm)],[f31,f24])).
% 1.50/1.26 thf(f24,plain,(
% 1.50/1.26 ( ! [X4 : a] : (($true = (r @ X4 @ (sK2 @ X4)))) ) | ~spl5_2),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.50/1.26 thf(f23,definition,(
% 1.50/1.26 spl5_2 <=> ! [X4 : a] : ($true = (r @ X4 @ (sK2 @ X4)))),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.50/1.26 thf(f38,plain,(
% 1.50/1.26 ~spl5_1 | ~spl5_3),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f37])).
% 1.50/1.26 thf(f37,plain,(
% 1.50/1.26 $false | (~spl5_1 | ~spl5_3)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.50/1.26 thf(f36,plain,(
% 1.50/1.26 ($true != $true) | (~spl5_1 | ~spl5_3)),
% 1.50/1.26 inference(superposition,[status(thm)],[f28,f21])).
% 1.50/1.26 thf(f28,plain,(
% 1.50/1.26 ( ! [X1 : b] : (((r @ sK0 @ X1) != $true)) ) | ~spl5_3),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.50/1.26 thf(f27,definition,(
% 1.50/1.26 spl5_3 <=> ! [X1 : b] : ((r @ sK0 @ X1) != $true)),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.50/1.26 thf(f35,plain,(
% 1.50/1.26 ~spl5_2 | ~spl5_3),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f34])).
% 1.50/1.26 thf(f34,plain,(
% 1.50/1.26 $false | (~spl5_2 | ~spl5_3)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.50/1.26 thf(f33,plain,(
% 1.50/1.26 ($true != $true) | (~spl5_2 | ~spl5_3)),
% 1.50/1.26 inference(superposition,[status(thm)],[f28,f24])).
% 1.50/1.26 thf(f32,plain,(
% 1.50/1.26 spl5_3 | spl5_4),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f18,f30,f27])).
% 1.50/1.26 thf(f18,plain,(
% 1.50/1.26 ( ! [X2 : a > b,X1 : b] : (((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))) != $true) | ((r @ sK0 @ X1) != $true)) )),
% 1.50/1.26 inference(cnf_transformation,[status(thm)],[f15])).
% 1.50/1.26 thf(f15,plain,(
% 1.50/1.26 (! [X1 : b] : ((r @ sK0 @ X1) != $true) | ! [X2 : a > b] : ((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))) != $true)) & (! [X4 : a] : ($true = (r @ X4 @ (sK2 @ X4))) | ! [X7 : a] : ($true = (r @ X7 @ (sK3 @ X7)))) & ! [X9 : b > $o] : (! [X10 : b] : ($true != (X9 @ X10)) | ((X9 @ (sK4 @ X9)) = $true))),
% 1.50/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f14,f13,f12,f11,f10])).
% 1.50/1.26 thf(f10,plain,(
% 1.50/1.26 ? [X0 : a] : ! [X1 : b] : ((r @ X0 @ X1) != $true) => ! [X1 : b] : ((r @ sK0 @ X1) != $true)),
% 1.50/1.26 introduced(definition,[],[choice_axiom])).
% 1.50/1.26 thf(f11,plain,(
% 1.50/1.26 ! [X2 : a > b] : (? [X3 : a] : ((r @ X3 @ (X2 @ X3)) != $true) => ((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))) != $true))),
% 1.50/1.26 introduced(definition,[],[choice_axiom])).
% 1.50/1.26 thf(f12,plain,(
% 1.50/1.26 ! [X4 : a] : (? [X5 : b] : ($true = (r @ X4 @ X5)) => ($true = (r @ X4 @ (sK2 @ X4))))),
% 1.50/1.26 introduced(definition,[],[choice_axiom])).
% 1.50/1.26 thf(f13,plain,(
% 1.50/1.26 ? [X6 : a > b] : ! [X7 : a] : ((r @ X7 @ (X6 @ X7)) = $true) => ! [X7 : a] : ($true = (r @ X7 @ (sK3 @ X7)))),
% 1.50/1.26 introduced(definition,[],[choice_axiom])).
% 1.50/1.26 thf(f14,plain,(
% 1.50/1.26 ? [X8 : (b > $o) > b] : ! [X9 : b > $o] : (! [X10 : b] : ($true != (X9 @ X10)) | ((X9 @ (X8 @ X9)) = $true)) => ! [X9 : b > $o] : (! [X10 : b] : ($true != (X9 @ X10)) | ((X9 @ (sK4 @ X9)) = $true))),
% 1.50/1.26 introduced(definition,[],[choice_axiom])).
% 1.50/1.26 thf(f9,plain,(
% 1.50/1.26 (? [X0 : a] : ! [X1 : b] : ((r @ X0 @ X1) != $true) | ! [X2 : a > b] : ? [X3 : a] : ((r @ X3 @ (X2 @ X3)) != $true)) & (! [X4 : a] : ? [X5 : b] : ($true = (r @ X4 @ X5)) | ? [X6 : a > b] : ! [X7 : a] : ((r @ X7 @ (X6 @ X7)) = $true)) & ? [X8 : (b > $o) > b] : ! [X9 : b > $o] : (! [X10 : b] : ($true != (X9 @ X10)) | ((X9 @ (X8 @ X9)) = $true))),
% 1.50/1.26 inference(rectify,[status(thm)],[f8])).
% 1.50/1.26 thf(f8,plain,(
% 1.50/1.26 (? [X5 : a] : ! [X6 : b] : ((r @ X5 @ X6) != $true) | ! [X3 : a > b] : ? [X4 : a] : ((r @ X4 @ (X3 @ X4)) != $true)) & (! [X5 : a] : ? [X6 : b] : ((r @ X5 @ X6) = $true) | ? [X3 : a > b] : ! [X4 : a] : ((r @ X4 @ (X3 @ X4)) = $true)) & ? [X0 : (b > $o) > b] : ! [X1 : b > $o] : (! [X2 : b] : ((X1 @ X2) != $true) | ((X1 @ (X0 @ X1)) = $true))),
% 1.50/1.26 inference(flattening,[status(thm)],[f7])).
% 1.50/1.26 thf(f7,plain,(
% 1.50/1.26 ((? [X5 : a] : ! [X6 : b] : ((r @ X5 @ X6) != $true) | ! [X3 : a > b] : ? [X4 : a] : ((r @ X4 @ (X3 @ X4)) != $true)) & (! [X5 : a] : ? [X6 : b] : ((r @ X5 @ X6) = $true) | ? [X3 : a > b] : ! [X4 : a] : ((r @ X4 @ (X3 @ X4)) = $true))) & ? [X0 : (b > $o) > b] : ! [X1 : b > $o] : (! [X2 : b] : ((X1 @ X2) != $true) | ((X1 @ (X0 @ X1)) = $true))),
% 1.50/1.26 inference(nnf_transformation,[status(thm)],[f6])).
% 1.50/1.26 thf(f6,plain,(
% 1.50/1.26 (? [X3 : a > b] : ! [X4 : a] : ((r @ X4 @ (X3 @ X4)) = $true) <~> ! [X5 : a] : ? [X6 : b] : ((r @ X5 @ X6) = $true)) & ? [X0 : (b > $o) > b] : ! [X1 : b > $o] : (! [X2 : b] : ((X1 @ X2) != $true) | ((X1 @ (X0 @ X1)) = $true))),
% 1.50/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.26 thf(f5,plain,(
% 1.50/1.26 ~(? [X0 : (b > $o) > b] : ! [X1 : b > $o] : (? [X2 : b] : ((X1 @ X2) = $true) => ((X1 @ (X0 @ X1)) = $true)) => (? [X3 : a > b] : ! [X4 : a] : ((r @ X4 @ (X3 @ X4)) = $true) <=> ! [X5 : a] : ? [X6 : b] : ((r @ X5 @ X6) = $true)))),
% 1.50/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.26 thf(f4,plain,(
% 1.50/1.26 ~(? [X0 : (b > $o) > b] : ! [X1 : b > $o] : (? [X2 : b] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (? [X3 : a > b] : ! [X4 : a] : (r @ X4 @ (X3 @ X4)) <=> ! [X5 : a] : ? [X6 : b] : (r @ X5 @ X6)))),
% 1.50/1.26 inference(rectify,[status(thm)],[f2])).
% 1.50/1.26 thf(f2,negated_conjecture,(
% 1.50/1.26 ~(? [X0 : (b > $o) > b] : ! [X1 : b > $o] : (? [X2 : b] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (? [X4 : a > b] : ! [X2 : a] : (r @ X2 @ (X4 @ X2)) <=> ! [X2 : a] : ? [X3 : b] : (r @ X2 @ X3)))),
% 1.50/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.26 thf(f1,conjecture,(
% 1.50/1.26 ? [X0 : (b > $o) > b] : ! [X1 : b > $o] : (? [X2 : b] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (? [X4 : a > b] : ! [X2 : a] : (r @ X2 @ (X4 @ X2)) <=> ! [X2 : a] : ? [X3 : b] : (r @ X2 @ X3))),
% 1.50/1.26 file('/export/starexec/sandbox2/tmp/tmp.n2L1Pil8ZL/DTF2THF_14884.p',cX5308)).
% 1.50/1.26 thf(f25,plain,(
% 1.50/1.26 spl5_1 | spl5_2),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f17,f23,f20])).
% 1.50/1.26 thf(f17,plain,(
% 1.50/1.26 ( ! [X7 : a,X4 : a] : (($true = (r @ X4 @ (sK2 @ X4))) | ($true = (r @ X7 @ (sK3 @ X7)))) )),
% 1.50/1.26 inference(cnf_transformation,[status(thm)],[f15])).
% 1.50/1.26 % SZS output end Proof for DTF2THF_14884
% 1.50/1.26 % (14998)------------------------------
% 1.50/1.26 % (14998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (14998)Termination reason: Refutation
% 1.50/1.26
% 1.50/1.26 % (14998)Memory used [KB]: 5628
% 1.50/1.26 % (14998)Time elapsed: 0.005 s
% 1.50/1.26 % (14998)Instructions burned: 7 (million)
% 1.50/1.26 % (14998)------------------------------
% 1.50/1.26 % (14998)------------------------------
% 1.50/1.26 % (14997)Success in time 0.005 s
%------------------------------------------------------------------------------