%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN051^5 : 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 : n023.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 09:50:25 AM UTC 2026
% Result : Theorem 1.68s 1.44s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 1 unt; 0 typ; 5 def)
% Number of atoms : 257 ( 65 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 175 ( 42 ~; 34 |; 24 &; 48 @)
% ( 5 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 10 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 10 !; 20 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cF: $i > $o ).
thf(f44,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f30,f35,f39,f41,f43]) ).
thf(f43,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f42]) ).
thf(f42,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(subsumption_resolution,[status(thm)],[f34,f24]) ).
thf(f24,plain,
( ! [X0: $i] :
( ( cF @ X0 )
!= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl2_2
<=> ! [X0: $i] :
( ( cF @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f34,plain,
( ( ( cF @ sK1 )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl2_4
<=> ( ( cF @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f41,plain,
( spl2_3
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f40]) ).
thf(f40,plain,
( $false
| spl2_3
| ~ spl2_5 ),
inference(subsumption_resolution,[status(thm)],[f29,f38]) ).
thf(f38,plain,
( ! [X0: $i] :
( ( cF @ X0 )
= $true )
| ~ spl2_5 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl2_5
<=> ! [X0: $i] :
( ( cF @ X0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f29,plain,
( ( ( cF @ sK0 )
!= $true )
| spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl2_3
<=> ( ( cF @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f39,plain,
( spl2_5
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f17,f19,f37]) ).
thf(f19,definition,
( spl2_1
<=> ( p = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f17,plain,
! [X0: $i] :
( ( p = $true )
| ( ( cF @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i] :
( ( ( ( cF @ X0 )
= $true )
& ( p != $true ) )
| ( ( p = $true )
& ( ( cF @ X0 )
!= $true ) ) )
& ( ( ( cF @ sK0 )
!= $true )
| ( p = $true ) )
& ( ( ( cF @ sK1 )
= $true )
| ( p != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X1: $i] :
( ( ( cF @ X1 )
!= $true )
| ( p = $true ) )
=> ( ( ( cF @ sK0 )
!= $true )
| ( p = $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: $i] :
( ( ( cF @ X2 )
= $true )
| ( p != $true ) )
=> ( ( ( cF @ sK1 )
= $true )
| ( p != $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( ( ( cF @ X0 )
= $true )
& ( p != $true ) )
| ( ( p = $true )
& ( ( cF @ X0 )
!= $true ) ) )
& ? [X1: $i] :
( ( ( cF @ X1 )
!= $true )
| ( p = $true ) )
& ? [X2: $i] :
( ( ( cF @ X2 )
= $true )
| ( p != $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X2: $i] :
( ( ( ( cF @ X2 )
= $true )
& ( p != $true ) )
| ( ( p = $true )
& ( ( cF @ X2 )
!= $true ) ) )
& ? [X0: $i] :
( ( ( cF @ X0 )
!= $true )
| ( p = $true ) )
& ? [X1: $i] :
( ( ( cF @ X1 )
= $true )
| ( p != $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i] :
( ( ( ( cF @ X2 )
= $true )
& ( p != $true ) )
| ( ( p = $true )
& ( ( cF @ X2 )
!= $true ) ) )
& ? [X0: $i] :
( ( ( cF @ X0 )
!= $true )
| ( p = $true ) )
& ? [X1: $i] :
( ( ( cF @ X1 )
= $true )
| ( p != $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ? [X0: $i] :
( ( ( cF @ X0 )
= $true )
=> ( p = $true ) )
& ? [X1: $i] :
( ( p = $true )
=> ( ( cF @ X1 )
= $true ) ) )
=> ? [X2: $i] :
( ( ( p = $true )
=> ( ( cF @ X2 )
= $true ) )
& ( ( ( cF @ X2 )
= $true )
=> ( p = $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ? [X0: $i] :
( ( cF @ X0 )
=> p )
& ? [X1: $i] :
( p
=> ( cF @ X1 ) ) )
=> ? [X2: $i] :
( ( p
=> ( cF @ X2 ) )
& ( ( cF @ X2 )
=> p ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ? [X0: $i] :
( ( cF @ X0 )
=> p )
& ? [X0: $i] :
( p
=> ( cF @ X0 ) ) )
=> ? [X0: $i] :
( ( p
=> ( cF @ X0 ) )
& ( ( cF @ X0 )
=> p ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ? [X0: $i] :
( ( cF @ X0 )
=> p )
& ? [X0: $i] :
( p
=> ( cF @ X0 ) ) )
=> ? [X0: $i] :
( ( p
=> ( cF @ X0 ) )
& ( ( cF @ X0 )
=> p ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nauUPBkBk8/DTF2THF_30350.p',cPELL21) ).
thf(f35,plain,
( spl2_4
| ~ spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f12,f19,f32]) ).
thf(f12,plain,
( ( p != $true )
| ( ( cF @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f30,plain,
( spl2_1
| ~ spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f13,f27,f19]) ).
thf(f13,plain,
( ( p = $true )
| ( ( cF @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f25,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f23,f19]) ).
thf(f14,plain,
! [X0: $i] :
( ( p != $true )
| ( ( cF @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN051^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n023.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 13:51:19 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.46 ---- Original DTF file ---
% 0.18/0.46 thf(spec,logic,$$dhol).
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 % File : SYN051^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.46 % Domain : Syntactic
% 0.18/0.46 % Problem : TPS problem PELL21
% 0.18/0.46 % Version : Especial.
% 0.18/0.46 % English :
% 0.18/0.46
% 0.18/0.46 % Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.18/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.46 % Source : [Bro09]
% 0.18/0.46 % Names : tps_0129 [Bro09]
% 0.18/0.46 % : PELL21 [TPS]
% 0.18/0.46 % : Pelletier 21 [Pel86]
% 0.18/0.46
% 0.18/0.46 % Status : Theorem
% 0.18/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 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 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.18/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.18/0.46 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.18/0.46 % Maximal formula atoms : 8 ( 8 avg)
% 0.18/0.46 % Number of connectives : 11 ( 0 ~; 0 |; 2 &; 4 @)
% 0.18/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.18/0.46 % Maximal formula depth : 6 ( 6 avg)
% 0.18/0.46 % Number of types : 2 ( 0 usr)
% 0.18/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.18/0.46 % Number of symbols : 2 ( 2 usr; 1 con; 0-1 aty)
% 0.18/0.46 % Number of variables : 3 ( 0 ^; 0 !; 3 ?; 3 :)
% 0.18/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.46
% 0.18/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.46 % :
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 thf(p,type,
% 0.18/0.46 p: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cF,type,
% 0.18/0.46 cF: $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(cPELL21,conjecture,
% 0.18/0.46 ( ( ? [Xx: $i] :
% 0.18/0.46 ( p
% 0.18/0.46 => ( cF @ Xx ) )
% 0.18/0.46 & ? [Xx: $i] :
% 0.18/0.46 ( ( cF @ Xx )
% 0.18/0.46 => p ) )
% 0.18/0.46 => ? [Xx: $i] :
% 0.18/0.46 ( ( p
% 0.18/0.46 => ( cF @ Xx ) )
% 0.18/0.46 & ( ( cF @ Xx )
% 0.18/0.46 => p ) ) ) ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 1.68/1.41 ---- Embedded in THF ---
% 1.68/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.41 %%% Generated on Tue Feb 24 13:51:20 EST 2026
% 1.68/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.41 %%% Logic specification used:
% 1.68/1.41 %%% thf(spec, logic, $$dhol).
% 1.68/1.41
% 1.68/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.nauUPBkBk8/DTF2DTF30350.p
% See solution above
% 1.68/1.41 ------------------------
% 1.68/1.42 ---- Cleaned THF ---
% 1.68/1.42 thf(p,type,
% 1.68/1.42 p: $o ).
% 1.68/1.42
% 1.68/1.42 thf(cF,type,
% 1.68/1.42 cF: $i > $o ).
% 1.68/1.42
% 1.68/1.42 thf(cPELL21,conjecture,
% 1.68/1.42 ( ( ? [Xx: $i] :
% 1.68/1.42 ( p
% 1.68/1.42 => ( cF @ Xx ) )
% 1.68/1.42 & ? [Xx: $i] :
% 1.68/1.42 ( ( cF @ Xx )
% 1.68/1.42 => p ) )
% 1.68/1.42 => ? [Xx: $i] :
% 1.68/1.42 ( ( p
% 1.68/1.42 => ( cF @ Xx ) )
% 1.68/1.42 & ( ( cF @ Xx )
% 1.68/1.42 => p ) ) ) ).
% 1.68/1.42 ------------------------
% 1.68/1.44 % (30487)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30350 for (3000ds/2Mi)
% 1.68/1.44 % (30486)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_30350 for (3000ds/27Mi)
% 1.68/1.44 % (30485)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_30350 for (3000ds/4Mi)
% 1.68/1.44 % (30489)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_30350 for (3000ds/275Mi)
% 1.68/1.44 % (30484)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30350 for (3000ds/183Mi)
% 1.68/1.44 % (30490)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30350 for (3000ds/18Mi)
% 1.68/1.44 % (30488)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_30350 for (3000ds/2Mi)
% 1.68/1.44 % (30488)Instruction limit reached!
% 1.68/1.44 % (30488)------------------------------
% 1.68/1.44 % (30488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.44 % (30488)Termination reason: Unknown
% 1.68/1.44 % (30488)Termination phase: Saturation
% 1.68/1.44
% 1.68/1.44 % (30488)Memory used [KB]: 5373
% 1.68/1.44 % (30488)Time elapsed: 0.003 s
% 1.68/1.44 % (30488)Instructions burned: 2 (million)
% 1.68/1.44 % (30488)------------------------------
% 1.68/1.44 % (30488)------------------------------
% 1.68/1.44 % (30485)First to succeed.
% 1.68/1.44 % (30490)Also succeeded, but the first one will report.
% 1.68/1.44 % (30484)Also succeeded, but the first one will report.
% 1.68/1.44 % (30485)Refutation found. Thanks to Tanya!
% 1.68/1.44 % SZS status Theorem for DTF2THF_30350
% 1.68/1.44 % SZS output start Proof for DTF2THF_30350
% 1.68/1.44 thf(func_def_1, type, cF: $i > $o).
% 1.68/1.44 thf(f44,plain,(
% 1.68/1.44 $false),
% 1.68/1.44 inference(avatar_sat_refutation,[status(thm)],[f25,f30,f35,f39,f41,f43])).
% 1.68/1.44 thf(f43,plain,(
% 1.68/1.44 ~spl2_2 | ~spl2_4),
% 1.68/1.44 inference(avatar_contradiction_clause,[status(thm)],[f42])).
% 1.68/1.44 thf(f42,plain,(
% 1.68/1.44 $false | (~spl2_2 | ~spl2_4)),
% 1.68/1.44 inference(subsumption_resolution,[status(thm)],[f34,f24])).
% 1.68/1.44 thf(f24,plain,(
% 1.68/1.44 ( ! [X0 : $i] : (((cF @ X0) != $true)) ) | ~spl2_2),
% 1.68/1.44 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.68/1.44 thf(f23,definition,(
% 1.68/1.44 spl2_2 <=> ! [X0 : $i] : ((cF @ X0) != $true)),
% 1.68/1.44 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.68/1.44 thf(f34,plain,(
% 1.68/1.44 ((cF @ sK1) = $true) | ~spl2_4),
% 1.68/1.44 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.68/1.44 thf(f32,definition,(
% 1.68/1.44 spl2_4 <=> ((cF @ sK1) = $true)),
% 1.68/1.44 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.68/1.44 thf(f41,plain,(
% 1.68/1.44 spl2_3 | ~spl2_5),
% 1.68/1.44 inference(avatar_contradiction_clause,[status(thm)],[f40])).
% 1.68/1.44 thf(f40,plain,(
% 1.68/1.44 $false | (spl2_3 | ~spl2_5)),
% 1.68/1.44 inference(subsumption_resolution,[status(thm)],[f29,f38])).
% 1.68/1.44 thf(f38,plain,(
% 1.68/1.44 ( ! [X0 : $i] : (((cF @ X0) = $true)) ) | ~spl2_5),
% 1.68/1.44 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.68/1.44 thf(f37,definition,(
% 1.68/1.44 spl2_5 <=> ! [X0 : $i] : ((cF @ X0) = $true)),
% 1.68/1.44 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 1.68/1.44 thf(f29,plain,(
% 1.68/1.44 ((cF @ sK0) != $true) | spl2_3),
% 1.68/1.44 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.68/1.44 thf(f27,definition,(
% 1.68/1.44 spl2_3 <=> ((cF @ sK0) = $true)),
% 1.68/1.44 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.68/1.44 thf(f39,plain,(
% 1.68/1.44 spl2_5 | spl2_1),
% 1.68/1.44 inference(avatar_split_clause,[status(thm)],[f17,f19,f37])).
% 1.68/1.44 thf(f19,definition,(
% 1.68/1.44 spl2_1 <=> (p = $true)),
% 1.68/1.44 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.68/1.44 thf(f17,plain,(
% 1.68/1.44 ( ! [X0 : $i] : ((p = $true) | ((cF @ X0) = $true)) )),
% 1.68/1.44 inference(cnf_transformation,[status(thm)],[f11])).
% 1.68/1.44 thf(f11,plain,(
% 1.68/1.44 ! [X0 : $i] : ((((cF @ X0) = $true) & (p != $true)) | ((p = $true) & ((cF @ X0) != $true))) & (((cF @ sK0) != $true) | (p = $true)) & (((cF @ sK1) = $true) | (p != $true))),
% 1.68/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.68/1.44 thf(f9,plain,(
% 1.68/1.44 ? [X1 : $i] : (((cF @ X1) != $true) | (p = $true)) => (((cF @ sK0) != $true) | (p = $true))),
% 1.68/1.44 introduced(definition,[],[choice_axiom])).
% 1.68/1.44 thf(f10,plain,(
% 1.68/1.44 ? [X2 : $i] : (((cF @ X2) = $true) | (p != $true)) => (((cF @ sK1) = $true) | (p != $true))),
% 1.68/1.44 introduced(definition,[],[choice_axiom])).
% 1.68/1.44 thf(f8,plain,(
% 1.68/1.44 ! [X0 : $i] : ((((cF @ X0) = $true) & (p != $true)) | ((p = $true) & ((cF @ X0) != $true))) & ? [X1 : $i] : (((cF @ X1) != $true) | (p = $true)) & ? [X2 : $i] : (((cF @ X2) = $true) | (p != $true))),
% 1.68/1.44 inference(rectify,[status(thm)],[f7])).
% 1.68/1.44 thf(f7,plain,(
% 1.68/1.44 ! [X2 : $i] : ((((cF @ X2) = $true) & (p != $true)) | ((p = $true) & ((cF @ X2) != $true))) & ? [X0 : $i] : (((cF @ X0) != $true) | (p = $true)) & ? [X1 : $i] : (((cF @ X1) = $true) | (p != $true))),
% 1.68/1.44 inference(flattening,[status(thm)],[f6])).
% 1.68/1.44 thf(f6,plain,(
% 1.68/1.44 ! [X2 : $i] : ((((cF @ X2) = $true) & (p != $true)) | ((p = $true) & ((cF @ X2) != $true))) & (? [X0 : $i] : (((cF @ X0) != $true) | (p = $true)) & ? [X1 : $i] : (((cF @ X1) = $true) | (p != $true)))),
% 1.68/1.44 inference(ennf_transformation,[status(thm)],[f5])).
% 1.68/1.44 thf(f5,plain,(
% 1.68/1.44 ~((? [X0 : $i] : (((cF @ X0) = $true) => (p = $true)) & ? [X1 : $i] : ((p = $true) => ((cF @ X1) = $true))) => ? [X2 : $i] : (((p = $true) => ((cF @ X2) = $true)) & (((cF @ X2) = $true) => (p = $true))))),
% 1.68/1.44 inference(fool_elimination,[status(thm)],[f4])).
% 1.68/1.44 thf(f4,plain,(
% 1.68/1.44 ~((? [X0 : $i] : ((cF @ X0) => p) & ? [X1 : $i] : (p => (cF @ X1))) => ? [X2 : $i] : ((p => (cF @ X2)) & ((cF @ X2) => p)))),
% 1.68/1.44 inference(rectify,[status(thm)],[f2])).
% 1.68/1.44 thf(f2,negated_conjecture,(
% 1.68/1.44 ~((? [X0 : $i] : ((cF @ X0) => p) & ? [X0 : $i] : (p => (cF @ X0))) => ? [X0 : $i] : ((p => (cF @ X0)) & ((cF @ X0) => p)))),
% 1.68/1.44 inference(negated_conjecture,[status(cth)],[f1])).
% 1.68/1.44 thf(f1,conjecture,(
% 1.68/1.44 (? [X0 : $i] : ((cF @ X0) => p) & ? [X0 : $i] : (p => (cF @ X0))) => ? [X0 : $i] : ((p => (cF @ X0)) & ((cF @ X0) => p))),
% 1.68/1.44 file('/export/starexec/sandbox/tmp/tmp.nauUPBkBk8/DTF2THF_30350.p',cPELL21)).
% 1.68/1.44 thf(f35,plain,(
% 1.68/1.44 spl2_4 | ~spl2_1),
% 1.68/1.44 inference(avatar_split_clause,[status(thm)],[f12,f19,f32])).
% 1.68/1.44 thf(f12,plain,(
% 1.68/1.44 (p != $true) | ((cF @ sK1) = $true)),
% 1.68/1.44 inference(cnf_transformation,[status(thm)],[f11])).
% 1.68/1.44 thf(f30,plain,(
% 1.68/1.44 spl2_1 | ~spl2_3),
% 1.68/1.44 inference(avatar_split_clause,[status(thm)],[f13,f27,f19])).
% 1.68/1.44 thf(f13,plain,(
% 1.68/1.44 (p = $true) | ((cF @ sK0) != $true)),
% 1.68/1.44 inference(cnf_transformation,[status(thm)],[f11])).
% 1.68/1.44 thf(f25,plain,(
% 1.68/1.44 ~spl2_1 | spl2_2),
% 1.68/1.44 inference(avatar_split_clause,[status(thm)],[f14,f23,f19])).
% 1.68/1.44 thf(f14,plain,(
% 1.68/1.44 ( ! [X0 : $i] : ((p != $true) | ((cF @ X0) != $true)) )),
% 1.68/1.44 inference(cnf_transformation,[status(thm)],[f11])).
% 1.68/1.44 % SZS output end Proof for DTF2THF_30350
% 1.68/1.44 % (30485)------------------------------
% 1.68/1.44 % (30485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.44 % (30485)Termination reason: Refutation
% 1.68/1.44
% 1.68/1.44 % (30485)Memory used [KB]: 5500
% 1.68/1.44 % (30485)Time elapsed: 0.004 s
% 1.68/1.44 % (30485)Instructions burned: 2 (million)
% 1.68/1.44 % (30485)------------------------------
% 1.68/1.44 % (30485)------------------------------
% 1.68/1.44 % (30483)Success in time 0.018 s
%------------------------------------------------------------------------------