%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN375^5 : 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 : n024.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 09:50:52 AM UTC 2026
% Result : Theorem 1.55s 1.30s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 278 ( 72 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 222 ( 47 ~; 39 |; 20 &; 90 @)
% ( 8 <=>; 16 =>; 0 <=; 2 <~>)
% 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 : 76 ( 0 ^; 42 !; 34 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $o ).
thf(f60,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f26,f40,f45,f49,f51,f59]) ).
thf(f59,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| ~ spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f25,f22]) ).
thf(f22,plain,
( ! [X1: $i] :
( ( cP @ X1 )
!= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl4_1
<=> ! [X1: $i] :
( ( cP @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f25,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl4_2
<=> ! [X0: $i] :
( ( cP @ X0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f51,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f50]) ).
thf(f50,plain,
( $false
| ~ spl4_1
| ~ spl4_5 ),
inference(subsumption_resolution,[status(thm)],[f39,f22]) ).
thf(f39,plain,
( ( $true
= ( cP @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl4_5
<=> ( $true
= ( cP @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f49,plain,
( ~ spl4_2
| spl4_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f48]) ).
thf(f48,plain,
( $false
| ~ spl4_2
| spl4_6 ),
inference(subsumption_resolution,[status(thm)],[f44,f25]) ).
thf(f44,plain,
( ( ( cP @ sK2 )
!= $true )
| spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl4_6
<=> ( ( cP @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f45,plain,
( ~ spl4_6
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f17,f21,f42]) ).
thf(f17,plain,
! [X4: $i] :
( ( ( cP @ sK2 )
!= $true )
| ( $true
!= ( cP @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ( $true
!= ( cP @ sK0 ) )
| ( $true
= ( cP @ sK1 ) ) )
& ( ! [X4: $i] :
( $true
!= ( cP @ X4 ) )
| ( ( cP @ sK2 )
!= $true ) )
& ( ( $true
= ( cP @ sK3 ) )
| ! [X7: $i] :
( $true
= ( cP @ X7 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f14,f13,f12,f11]) ).
thf(f11,plain,
( ? [X2: $i] :
( $true
!= ( cP @ X2 ) )
=> ( $true
!= ( cP @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X3: $i] :
( ( cP @ X3 )
= $true )
=> ( $true
= ( cP @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X5: $i] :
( $true
!= ( cP @ X5 ) )
=> ( ( cP @ sK2 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X6: $i] :
( $true
= ( cP @ X6 ) )
=> ( $true
= ( cP @ sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ? [X2: $i] :
( $true
!= ( cP @ X2 ) )
| ? [X3: $i] :
( ( cP @ X3 )
= $true ) )
& ( ! [X4: $i] :
( $true
!= ( cP @ X4 ) )
| ? [X5: $i] :
( $true
!= ( cP @ X5 ) ) )
& ( ? [X6: $i] :
( $true
= ( cP @ X6 ) )
| ! [X7: $i] :
( $true
= ( cP @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ? [X2: $i] :
( $true
!= ( cP @ X2 ) )
| ? [X3: $i] :
( ( cP @ X3 )
= $true ) )
& ( ! [X4: $i] :
( $true
!= ( cP @ X4 ) )
| ? [X5: $i] :
( $true
!= ( cP @ X5 ) ) )
& ( ? [X4: $i] :
( $true
= ( cP @ X4 ) )
| ! [X5: $i] :
( $true
= ( cP @ X5 ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ? [X2: $i] :
( $true
!= ( cP @ X2 ) )
| ? [X3: $i] :
( ( cP @ X3 )
= $true ) )
& ( ! [X4: $i] :
( $true
!= ( cP @ X4 ) )
| ? [X5: $i] :
( $true
!= ( cP @ X5 ) ) )
& ( ? [X4: $i] :
( $true
= ( cP @ X4 ) )
| ! [X5: $i] :
( $true
= ( cP @ X5 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ? [X2: $i] :
( $true
!= ( cP @ X2 ) )
| ? [X3: $i] :
( ( cP @ X3 )
= $true ) )
& ( ! [X5: $i] :
( $true
= ( cP @ X5 ) )
<~> ? [X4: $i] :
( $true
= ( cP @ X4 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ! [X5: $i] :
( $true
= ( cP @ X5 ) )
<~> ? [X4: $i] :
( $true
= ( cP @ X4 ) ) )
& ( ? [X2: $i] :
( $true
!= ( cP @ X2 ) )
| ? [X3: $i] :
( ( cP @ X3 )
= $true ) )
& ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cP @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ! [X2: $i] :
( $true
= ( cP @ X2 ) )
=> ? [X3: $i] :
( ( cP @ X3 )
= $true ) )
& ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
=> ! [X1: $i] :
( ( cP @ X1 )
= $true ) ) )
=> ( ? [X4: $i] :
( $true
= ( cP @ X4 ) )
<=> ! [X5: $i] :
( $true
= ( cP @ X5 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ? [X0: $i] : ( cP @ X0 )
=> ! [X1: $i] : ( cP @ X1 ) )
& ( ! [X2: $i] : ( cP @ X2 )
=> ? [X3: $i] : ( cP @ X3 ) ) )
=> ( ? [X4: $i] : ( cP @ X4 )
<=> ! [X5: $i] : ( cP @ X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ? [X1: $i] : ( cP @ X1 )
=> ! [X0: $i] : ( cP @ X0 ) )
& ( ! [X0: $i] : ( cP @ X0 )
=> ? [X1: $i] : ( cP @ X1 ) ) )
=> ( ? [X1: $i] : ( cP @ X1 )
<=> ! [X0: $i] : ( cP @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ? [X1: $i] : ( cP @ X1 )
=> ! [X0: $i] : ( cP @ X0 ) )
& ( ! [X0: $i] : ( cP @ X0 )
=> ? [X1: $i] : ( cP @ X1 ) ) )
=> ( ? [X1: $i] : ( cP @ X1 )
<=> ! [X0: $i] : ( cP @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lG2S70ePZl/DTF2THF_14127.p',cX2126_BUG) ).
thf(f40,plain,
( spl4_5
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f16,f24,f37]) ).
thf(f16,plain,
! [X7: $i] :
( ( $true
= ( cP @ sK3 ) )
| ( $true
= ( cP @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f26,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f24,f21]) ).
thf(f19,plain,
! [X0: $i,X1: $i] :
( ( ( cP @ X0 )
= $true )
| ( ( cP @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SYN375^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue Feb 24 08:56:10 EST 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.34 ---- Original DTF file ---
% 0.13/0.34 thf(spec,logic,$$dhol).
% 0.13/0.34 %------------------------------------------------------------------------------
% 0.13/0.34 % File : SYN375^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.34 % Domain : Syntactic
% 0.13/0.34 % Problem : TPS problem from BASIC-FO-THMS
% 0.13/0.34 % Version : Especial.
% 0.13/0.34 % English :
% 0.13/0.34
% 0.13/0.34 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.13/0.34 % Source : [Bro09]
% 0.13/0.34 % Names : tps_0832 [Bro09]
% 0.13/0.34
% 0.13/0.34 % Status : Theorem
% 0.13/0.34 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.13/0.34 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.13/0.34 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.13/0.34 % Maximal formula atoms : 6 ( 6 avg)
% 0.13/0.34 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 6 @)
% 0.13/0.34 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.13/0.34 % Maximal formula depth : 6 ( 6 avg)
% 0.13/0.34 % Number of types : 2 ( 0 usr)
% 0.13/0.34 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.13/0.34 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.13/0.34 % Number of variables : 6 ( 0 ^; 3 !; 3 ?; 6 :)
% 0.13/0.34 % SPC : TH0_THM_NEQ_NAR
% 0.13/0.34
% 0.13/0.34 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.13/0.34 % project in the Department of Mathematical Sciences at Carnegie
% 0.13/0.34 % Mellon University. Distributed under the Creative Commons copyleft
% 0.13/0.34 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.13/0.34 % :
% 0.13/0.34 %------------------------------------------------------------------------------
% 0.13/0.34 thf(cP,type,
% 0.13/0.34 cP: $i > $o ).
% 0.13/0.34
% 0.13/0.34 thf(cX2126_BUG,conjecture,
% 0.13/0.34 ( ( ( ! [Xx: $i] : ( cP @ Xx )
% 0.13/0.34 => ? [Xy: $i] : ( cP @ Xy ) )
% 0.13/0.34 & ( ? [Xy: $i] : ( cP @ Xy )
% 0.13/0.34 => ! [Xx: $i] : ( cP @ Xx ) ) )
% 0.13/0.34 => ( ? [Xy: $i] : ( cP @ Xy )
% 0.13/0.34 <=> ! [Xx: $i] : ( cP @ Xx ) ) ) ).
% 0.13/0.34
% 0.13/0.34 %------------------------------------------------------------------------------
% 0.13/0.34 ------------------------
% 1.40/1.27 ---- Embedded in THF ---
% 1.40/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.40/1.27 %%% Generated on Tue Feb 24 08:56:11 EST 2026
% 1.40/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.40/1.27 %%% Logic specification used:
% 1.40/1.27 %%% thf(spec, logic, $$dhol).
% 1.40/1.27
% 1.40/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lG2S70ePZl/DTF2DTF14127.p
% See solution above
% 1.40/1.27 ------------------------
% 1.40/1.27 ---- Cleaned THF ---
% 1.40/1.28 thf(cP,type,
% 1.40/1.28 cP: $i > $o ).
% 1.40/1.28
% 1.40/1.28 thf(cX2126_BUG,conjecture,
% 1.40/1.28 ( ( ( ! [Xx: $i] : ( cP @ Xx )
% 1.40/1.28 => ? [Xy: $i] : ( cP @ Xy ) )
% 1.40/1.28 & ( ? [Xy: $i] : ( cP @ Xy )
% 1.40/1.28 => ! [Xx: $i] : ( cP @ Xx ) ) )
% 1.40/1.28 => ( ? [Xy: $i] : ( cP @ Xy )
% 1.40/1.28 <=> ! [Xx: $i] : ( cP @ Xx ) ) ) ).
% 1.40/1.28 ------------------------
% 1.40/1.30 % (14238)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_14127 for (3000ds/4Mi)
% 1.40/1.30 % (14240)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14127 for (3000ds/2Mi)
% 1.40/1.30 % (14237)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14127 for (3000ds/183Mi)
% 1.40/1.30 % (14241)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_14127 for (3000ds/2Mi)
% 1.40/1.30 % (14239)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_14127 for (3000ds/27Mi)
% 1.40/1.30 % (14243)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14127 for (3000ds/18Mi)
% 1.40/1.30 % (14242)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_14127 for (3000ds/275Mi)
% 1.55/1.30 % (14241)Instruction limit reached!
% 1.55/1.30 % (14241)------------------------------
% 1.55/1.30 % (14241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.30 % (14241)Termination reason: Unknown
% 1.55/1.30 % (14241)Termination phase: Saturation
% 1.55/1.30
% 1.55/1.30 % (14241)Memory used [KB]: 5500
% 1.55/1.30 % (14242)First to succeed.
% 1.55/1.30 % (14241)Time elapsed: 0.003 s
% 1.55/1.30 % (14241)Instructions burned: 2 (million)
% 1.55/1.30 % (14241)------------------------------
% 1.55/1.30 % (14241)------------------------------
% 1.55/1.30 % (14243)Also succeeded, but the first one will report.
% 1.55/1.30 % (14237)Also succeeded, but the first one will report.
% 1.55/1.30 % (14242)Refutation found. Thanks to Tanya!
% 1.55/1.30 % SZS status Theorem for DTF2THF_14127
% 1.55/1.30 % SZS output start Proof for DTF2THF_14127
% 1.55/1.30 thf(func_def_0, type, cP: $i > $o).
% 1.55/1.30 thf(f60,plain,(
% 1.55/1.30 $false),
% 1.55/1.30 inference(avatar_sat_refutation,[status(thm)],[f26,f40,f45,f49,f51,f59])).
% 1.55/1.30 thf(f59,plain,(
% 1.55/1.30 ~spl4_1 | ~spl4_2),
% 1.55/1.30 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.55/1.30 thf(f58,plain,(
% 1.55/1.30 $false | (~spl4_1 | ~spl4_2)),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f25,f22])).
% 1.55/1.30 thf(f22,plain,(
% 1.55/1.30 ( ! [X1 : $i] : (((cP @ X1) != $true)) ) | ~spl4_1),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.55/1.30 thf(f21,definition,(
% 1.55/1.30 spl4_1 <=> ! [X1 : $i] : ((cP @ X1) != $true)),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.55/1.30 thf(f25,plain,(
% 1.55/1.30 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | ~spl4_2),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.55/1.30 thf(f24,definition,(
% 1.55/1.30 spl4_2 <=> ! [X0 : $i] : ((cP @ X0) = $true)),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.55/1.30 thf(f51,plain,(
% 1.55/1.30 ~spl4_1 | ~spl4_5),
% 1.55/1.30 inference(avatar_contradiction_clause,[status(thm)],[f50])).
% 1.55/1.30 thf(f50,plain,(
% 1.55/1.30 $false | (~spl4_1 | ~spl4_5)),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f39,f22])).
% 1.55/1.30 thf(f39,plain,(
% 1.55/1.30 ($true = (cP @ sK3)) | ~spl4_5),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.55/1.30 thf(f37,definition,(
% 1.55/1.30 spl4_5 <=> ($true = (cP @ sK3))),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.55/1.30 thf(f49,plain,(
% 1.55/1.30 ~spl4_2 | spl4_6),
% 1.55/1.30 inference(avatar_contradiction_clause,[status(thm)],[f48])).
% 1.55/1.30 thf(f48,plain,(
% 1.55/1.30 $false | (~spl4_2 | spl4_6)),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f44,f25])).
% 1.55/1.30 thf(f44,plain,(
% 1.55/1.30 ((cP @ sK2) != $true) | spl4_6),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.55/1.30 thf(f42,definition,(
% 1.55/1.30 spl4_6 <=> ((cP @ sK2) = $true)),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.55/1.30 thf(f45,plain,(
% 1.55/1.30 ~spl4_6 | spl4_1),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f17,f21,f42])).
% 1.55/1.30 thf(f17,plain,(
% 1.55/1.30 ( ! [X4 : $i] : (((cP @ sK2) != $true) | ($true != (cP @ X4))) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.55/1.30 thf(f15,plain,(
% 1.55/1.30 (! [X0 : $i] : ((cP @ X0) = $true) | ! [X1 : $i] : ((cP @ X1) != $true)) & (($true != (cP @ sK0)) | ($true = (cP @ sK1))) & (! [X4 : $i] : ($true != (cP @ X4)) | ((cP @ sK2) != $true)) & (($true = (cP @ sK3)) | ! [X7 : $i] : ($true = (cP @ X7)))),
% 1.55/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f14,f13,f12,f11])).
% 1.55/1.30 thf(f11,plain,(
% 1.55/1.30 ? [X2 : $i] : ($true != (cP @ X2)) => ($true != (cP @ sK0))),
% 1.55/1.30 introduced(definition,[],[choice_axiom])).
% 1.55/1.30 thf(f12,plain,(
% 1.55/1.30 ? [X3 : $i] : ((cP @ X3) = $true) => ($true = (cP @ sK1))),
% 1.55/1.30 introduced(definition,[],[choice_axiom])).
% 1.55/1.30 thf(f13,plain,(
% 1.55/1.30 ? [X5 : $i] : ($true != (cP @ X5)) => ((cP @ sK2) != $true)),
% 1.55/1.30 introduced(definition,[],[choice_axiom])).
% 1.55/1.30 thf(f14,plain,(
% 1.55/1.30 ? [X6 : $i] : ($true = (cP @ X6)) => ($true = (cP @ sK3))),
% 1.55/1.30 introduced(definition,[],[choice_axiom])).
% 1.55/1.30 thf(f10,plain,(
% 1.55/1.30 (! [X0 : $i] : ((cP @ X0) = $true) | ! [X1 : $i] : ((cP @ X1) != $true)) & (? [X2 : $i] : ($true != (cP @ X2)) | ? [X3 : $i] : ((cP @ X3) = $true)) & (! [X4 : $i] : ($true != (cP @ X4)) | ? [X5 : $i] : ($true != (cP @ X5))) & (? [X6 : $i] : ($true = (cP @ X6)) | ! [X7 : $i] : ($true = (cP @ X7)))),
% 1.55/1.30 inference(rectify,[status(thm)],[f9])).
% 1.55/1.30 thf(f9,plain,(
% 1.55/1.30 (! [X1 : $i] : ((cP @ X1) = $true) | ! [X0 : $i] : ((cP @ X0) != $true)) & (? [X2 : $i] : ($true != (cP @ X2)) | ? [X3 : $i] : ((cP @ X3) = $true)) & (! [X4 : $i] : ($true != (cP @ X4)) | ? [X5 : $i] : ($true != (cP @ X5))) & (? [X4 : $i] : ($true = (cP @ X4)) | ! [X5 : $i] : ($true = (cP @ X5)))),
% 1.55/1.30 inference(flattening,[status(thm)],[f8])).
% 1.55/1.30 thf(f8,plain,(
% 1.55/1.30 (! [X1 : $i] : ((cP @ X1) = $true) | ! [X0 : $i] : ((cP @ X0) != $true)) & (? [X2 : $i] : ($true != (cP @ X2)) | ? [X3 : $i] : ((cP @ X3) = $true)) & ((! [X4 : $i] : ($true != (cP @ X4)) | ? [X5 : $i] : ($true != (cP @ X5))) & (? [X4 : $i] : ($true = (cP @ X4)) | ! [X5 : $i] : ($true = (cP @ X5))))),
% 1.55/1.30 inference(nnf_transformation,[status(thm)],[f7])).
% 1.55/1.30 thf(f7,plain,(
% 1.55/1.30 (! [X1 : $i] : ((cP @ X1) = $true) | ! [X0 : $i] : ((cP @ X0) != $true)) & (? [X2 : $i] : ($true != (cP @ X2)) | ? [X3 : $i] : ((cP @ X3) = $true)) & (! [X5 : $i] : ($true = (cP @ X5)) <~> ? [X4 : $i] : ($true = (cP @ X4)))),
% 1.55/1.30 inference(flattening,[status(thm)],[f6])).
% 1.55/1.30 thf(f6,plain,(
% 1.55/1.30 (! [X5 : $i] : ($true = (cP @ X5)) <~> ? [X4 : $i] : ($true = (cP @ X4))) & ((? [X2 : $i] : ($true != (cP @ X2)) | ? [X3 : $i] : ((cP @ X3) = $true)) & (! [X1 : $i] : ((cP @ X1) = $true) | ! [X0 : $i] : ((cP @ X0) != $true)))),
% 1.55/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.55/1.30 thf(f5,plain,(
% 1.55/1.30 ~(((! [X2 : $i] : ($true = (cP @ X2)) => ? [X3 : $i] : ((cP @ X3) = $true)) & (? [X0 : $i] : ((cP @ X0) = $true) => ! [X1 : $i] : ((cP @ X1) = $true))) => (? [X4 : $i] : ($true = (cP @ X4)) <=> ! [X5 : $i] : ($true = (cP @ X5))))),
% 1.55/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.55/1.30 thf(f4,plain,(
% 1.55/1.30 ~(((? [X0 : $i] : (cP @ X0) => ! [X1 : $i] : (cP @ X1)) & (! [X2 : $i] : (cP @ X2) => ? [X3 : $i] : (cP @ X3))) => (? [X4 : $i] : (cP @ X4) <=> ! [X5 : $i] : (cP @ X5)))),
% 1.55/1.30 inference(rectify,[status(thm)],[f2])).
% 1.55/1.30 thf(f2,negated_conjecture,(
% 1.55/1.30 ~(((? [X1 : $i] : (cP @ X1) => ! [X0 : $i] : (cP @ X0)) & (! [X0 : $i] : (cP @ X0) => ? [X1 : $i] : (cP @ X1))) => (? [X1 : $i] : (cP @ X1) <=> ! [X0 : $i] : (cP @ X0)))),
% 1.55/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.55/1.30 thf(f1,conjecture,(
% 1.55/1.30 ((? [X1 : $i] : (cP @ X1) => ! [X0 : $i] : (cP @ X0)) & (! [X0 : $i] : (cP @ X0) => ? [X1 : $i] : (cP @ X1))) => (? [X1 : $i] : (cP @ X1) <=> ! [X0 : $i] : (cP @ X0))),
% 1.55/1.30 file('/export/starexec/sandbox/tmp/tmp.lG2S70ePZl/DTF2THF_14127.p',cX2126_BUG)).
% 1.55/1.30 thf(f40,plain,(
% 1.55/1.30 spl4_5 | spl4_2),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f16,f24,f37])).
% 1.55/1.30 thf(f16,plain,(
% 1.55/1.30 ( ! [X7 : $i] : (($true = (cP @ sK3)) | ($true = (cP @ X7))) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.55/1.30 thf(f26,plain,(
% 1.55/1.30 spl4_1 | spl4_2),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f19,f24,f21])).
% 1.55/1.30 thf(f19,plain,(
% 1.55/1.30 ( ! [X0 : $i,X1 : $i] : (((cP @ X0) = $true) | ((cP @ X1) != $true)) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.55/1.30 % SZS output end Proof for DTF2THF_14127
% 1.55/1.30 % (14242)------------------------------
% 1.55/1.30 % (14242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.30 % (14242)Termination reason: Refutation
% 1.55/1.30
% 1.55/1.30 % (14242)Memory used [KB]: 5500
% 1.55/1.30 % (14242)Time elapsed: 0.003 s
% 1.55/1.30 % (14242)Instructions burned: 1 (million)
% 1.55/1.30 % (14242)------------------------------
% 1.55/1.30 % (14242)------------------------------
% 1.55/1.30 % (14236)Success in time 0.018 s
%------------------------------------------------------------------------------