%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO104^5 : 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 : n022.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 09:53:23 AM UTC 2026
% Result : Theorem 1.66s 1.42s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 1 unt; 0 typ; 6 def)
% Number of atoms : 357 ( 68 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 291 ( 49 ~; 46 |; 22 &; 160 @)
% ( 10 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 12 con; 0-2 aty)
% Number of variables : 47 ( 0 ^; 35 !; 12 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cQ: $i > $i > $o ).
thf(func_def_2,type,
cP: $i > $i > $o ).
thf(f54,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f22,f39,f43,f47,f49,f51,f53]) ).
thf(f53,plain,
( ~ spl3_1
| spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
| ~ spl3_1
| spl3_5 ),
inference(subsumption_resolution,[status(thm)],[f38,f21]) ).
thf(f21,plain,
( ! [X4: $i] :
( ( cQ @ X4 @ y )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl3_1
<=> ! [X4: $i] :
( ( cQ @ X4 @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f38,plain,
( ( $true
!= ( cQ @ sK1 @ y ) )
| spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl3_5
<=> ( $true
= ( cQ @ sK1 @ y ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f51,plain,
( spl3_4
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f50]) ).
thf(f50,plain,
( $false
| spl3_4
| ~ spl3_6 ),
inference(subsumption_resolution,[status(thm)],[f34,f42]) ).
thf(f42,plain,
( ! [X3: $i] :
( $true
= ( cP @ X3 @ y ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl3_6
<=> ! [X3: $i] :
( $true
= ( cP @ X3 @ y ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f34,plain,
( ( $true
!= ( cP @ sK2 @ y ) )
| spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl3_4
<=> ( $true
= ( cP @ sK2 @ y ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f49,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f48]) ).
thf(f48,plain,
( $false
| ~ spl3_1
| spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f30,f21]) ).
thf(f30,plain,
( ( $true
!= ( cQ @ sK0 @ y ) )
| spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl3_3
<=> ( $true
= ( cQ @ sK0 @ y ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f47,plain,
( spl3_2
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f46]) ).
thf(f46,plain,
( $false
| spl3_2
| ~ spl3_6 ),
inference(subsumption_resolution,[status(thm)],[f26,f42]) ).
thf(f26,plain,
( ( $true
!= ( cP @ sK0 @ y ) )
| spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl3_2
<=> ( $true
= ( cP @ sK0 @ y ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f43,plain,
( spl3_6
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f16,f41,f41]) ).
thf(f16,plain,
! [X3: $i,X5: $i] :
( ( $true
= ( cP @ X3 @ y ) )
| ( $true
= ( cP @ X5 @ y ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( $true
!= ( cP @ sK0 @ y ) )
| ( $true
!= ( cQ @ sK0 @ y ) )
| ( $true
!= ( cQ @ sK1 @ y ) )
| ( $true
!= ( cP @ sK2 @ y ) ) )
& ( ! [X3: $i] :
( ( $true
= ( cP @ X3 @ y ) )
& ( $true
= ( cQ @ X3 @ y ) ) )
| ( ! [X4: $i] :
( ( cQ @ X4 @ y )
= $true )
& ! [X5: $i] :
( $true
= ( cP @ X5 @ y ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: $i] :
( ( ( cP @ X0 @ y )
!= $true )
| ( ( cQ @ X0 @ y )
!= $true ) )
=> ( ( $true
!= ( cP @ sK0 @ y ) )
| ( $true
!= ( cQ @ sK0 @ y ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X1: $i] :
( $true
!= ( cQ @ X1 @ y ) )
=> ( $true
!= ( cQ @ sK1 @ y ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X2: $i] :
( $true
!= ( cP @ X2 @ y ) )
=> ( $true
!= ( cP @ sK2 @ y ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( ? [X0: $i] :
( ( ( cP @ X0 @ y )
!= $true )
| ( ( cQ @ X0 @ y )
!= $true ) )
| ? [X1: $i] :
( $true
!= ( cQ @ X1 @ y ) )
| ? [X2: $i] :
( $true
!= ( cP @ X2 @ y ) ) )
& ( ! [X3: $i] :
( ( $true
= ( cP @ X3 @ y ) )
& ( $true
= ( cQ @ X3 @ y ) ) )
| ( ! [X4: $i] :
( ( cQ @ X4 @ y )
= $true )
& ! [X5: $i] :
( $true
= ( cP @ X5 @ y ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ? [X2: $i] :
( ( $true
!= ( cP @ X2 @ y ) )
| ( $true
!= ( cQ @ X2 @ y ) ) )
| ? [X0: $i] :
( ( cQ @ X0 @ y )
!= $true )
| ? [X1: $i] :
( $true
!= ( cP @ X1 @ y ) ) )
& ( ! [X2: $i] :
( ( $true
= ( cP @ X2 @ y ) )
& ( $true
= ( cQ @ X2 @ y ) ) )
| ( ! [X0: $i] :
( ( cQ @ X0 @ y )
= $true )
& ! [X1: $i] :
( $true
= ( cP @ X1 @ y ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ? [X2: $i] :
( ( $true
!= ( cP @ X2 @ y ) )
| ( $true
!= ( cQ @ X2 @ y ) ) )
| ? [X0: $i] :
( ( cQ @ X0 @ y )
!= $true )
| ? [X1: $i] :
( $true
!= ( cP @ X1 @ y ) ) )
& ( ! [X2: $i] :
( ( $true
= ( cP @ X2 @ y ) )
& ( $true
= ( cQ @ X2 @ y ) ) )
| ( ! [X0: $i] :
( ( cQ @ X0 @ y )
= $true )
& ! [X1: $i] :
( $true
= ( cP @ X1 @ y ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ! [X0: $i] :
( ( cQ @ X0 @ y )
= $true )
& ! [X1: $i] :
( $true
= ( cP @ X1 @ y ) ) )
<~> ! [X2: $i] :
( ( $true
= ( cP @ X2 @ y ) )
& ( $true
= ( cQ @ X2 @ y ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( cQ @ X0 @ y )
= $true )
& ! [X1: $i] :
( $true
= ( cP @ X1 @ y ) ) )
<=> ! [X2: $i] :
( ( $true
= ( cP @ X2 @ y ) )
& ( $true
= ( cQ @ X2 @ y ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] : ( cQ @ X0 @ y )
& ! [X1: $i] : ( cP @ X1 @ y ) )
<=> ! [X2: $i] :
( ( cQ @ X2 @ y )
& ( cP @ X2 @ y ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] : ( cQ @ X0 @ y )
& ! [X0: $i] : ( cP @ X0 @ y ) )
<=> ! [X0: $i] :
( ( cQ @ X0 @ y )
& ( cP @ X0 @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] : ( cQ @ X0 @ y )
& ! [X0: $i] : ( cP @ X0 @ y ) )
<=> ! [X0: $i] :
( ( cQ @ X0 @ y )
& ( cP @ X0 @ y ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xFRpfb1oG6/DTF2THF_20226.p',cTTTP2129) ).
thf(f39,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_4
| ~ spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f18,f36,f32,f28,f24]) ).
thf(f18,plain,
( ( $true
!= ( cP @ sK2 @ y ) )
| ( $true
!= ( cQ @ sK1 @ y ) )
| ( $true
!= ( cP @ sK0 @ y ) )
| ( $true
!= ( cQ @ sK0 @ y ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f22,plain,
( spl3_1
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f15,f20,f20]) ).
thf(f15,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( cQ @ X3 @ y ) )
| ( ( cQ @ X4 @ y )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO104^5 : 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
% 0.15/0.34 % Computer : n022.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:24:21 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 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 : SYO104^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.47 % Domain : Syntactic
% 0.19/0.47 % Problem : TPS problem TTTP2129
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 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_0380 [Bro09]
% 0.19/0.47 % : TTTP2129 [TPS]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.19/0.47 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.47 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.19/0.47 % Number of connectives : 11 ( 0 ~; 0 |; 2 &; 8 @)
% 0.19/0.47 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 6 ( 6 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 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 %------------------------------------------------------------------------------
% 0.19/0.47 thf(y,type,
% 0.19/0.47 y: $i ).
% 0.19/0.47
% 0.19/0.47 thf(cQ,type,
% 0.19/0.47 cQ: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cP,type,
% 0.19/0.47 cP: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cTTTP2129,conjecture,
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( cP @ Xx @ y )
% 0.19/0.47 & ( cQ @ Xx @ y ) )
% 0.19/0.47 <=> ( ! [Xx: $i] : ( cP @ Xx @ y )
% 0.19/0.47 & ! [Xx: $i] : ( cQ @ Xx @ y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.46/1.39 ---- Embedded in THF ---
% 1.46/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.39 %%% Generated on Tue Feb 24 14:24:22 EST 2026
% 1.46/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.39 %%% Logic specification used:
% 1.46/1.39 %%% thf(spec, logic, $$dhol).
% 1.46/1.39
% 1.46/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xFRpfb1oG6/DTF2DTF20226.p
% See solution above
% 1.46/1.39 ------------------------
% 1.46/1.39 ---- Cleaned THF ---
% 1.46/1.40 thf(y,type,
% 1.46/1.40 y: $i ).
% 1.46/1.40
% 1.46/1.40 thf(cQ,type,
% 1.46/1.40 cQ: $i > $i > $o ).
% 1.46/1.40
% 1.46/1.40 thf(cP,type,
% 1.46/1.40 cP: $i > $i > $o ).
% 1.46/1.40
% 1.46/1.40 thf(cTTTP2129,conjecture,
% 1.46/1.40 ( ! [Xx: $i] :
% 1.46/1.40 ( ( cP @ Xx @ y )
% 1.46/1.40 & ( cQ @ Xx @ y ) )
% 1.46/1.40 <=> ( ! [Xx: $i] : ( cP @ Xx @ y )
% 1.46/1.40 & ! [Xx: $i] : ( cQ @ Xx @ y ) ) ) ).
% 1.46/1.40 ------------------------
% 1.66/1.42 % (20325)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_20226 for (3000ds/4Mi)
% 1.66/1.42 % (20324)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20226 for (3000ds/183Mi)
% 1.66/1.42 % (20328)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_20226 for (3000ds/2Mi)
% 1.66/1.42 % (20326)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_20226 for (3000ds/27Mi)
% 1.66/1.42 % (20327)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20226 for (3000ds/2Mi)
% 1.66/1.42 % (20329)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_20226 for (3000ds/275Mi)
% 1.66/1.42 % (20330)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20226 for (3000ds/18Mi)
% 1.66/1.42 % (20327)Instruction limit reached!
% 1.66/1.42 % (20327)------------------------------
% 1.66/1.42 % (20327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (20328)Refutation not found, incomplete strategy
% 1.66/1.42 % (20328)------------------------------
% 1.66/1.42 % (20328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (20327)Termination reason: Unknown
% 1.66/1.42 % (20327)Termination phase: Saturation
% 1.66/1.42
% 1.66/1.42 % (20327)Memory used [KB]: 5500
% 1.66/1.42 % (20327)Time elapsed: 0.003 s
% 1.66/1.42 % (20327)Instructions burned: 2 (million)
% 1.66/1.42 % (20327)------------------------------
% 1.66/1.42 % (20327)------------------------------
% 1.66/1.42 % (20328)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.42
% 1.66/1.42 % (20325)First to succeed.
% 1.66/1.42
% 1.66/1.42 % (20328)Memory used [KB]: 5500
% 1.66/1.42 % (20328)Time elapsed: 0.003 s
% 1.66/1.42 % (20328)Instructions burned: 1 (million)
% 1.66/1.42 % (20328)------------------------------
% 1.66/1.42 % (20328)------------------------------
% 1.66/1.42 % (20324)Also succeeded, but the first one will report.
% 1.66/1.42 % (20325)Refutation found. Thanks to Tanya!
% 1.66/1.42 % SZS status Theorem for DTF2THF_20226
% 1.66/1.42 % SZS output start Proof for DTF2THF_20226
% 1.66/1.42 thf(func_def_1, type, cQ: $i > $i > $o).
% 1.66/1.42 thf(func_def_2, type, cP: $i > $i > $o).
% 1.66/1.42 thf(f54,plain,(
% 1.66/1.42 $false),
% 1.66/1.42 inference(avatar_sat_refutation,[status(thm)],[f22,f39,f43,f47,f49,f51,f53])).
% 1.66/1.42 thf(f53,plain,(
% 1.66/1.42 ~spl3_1 | spl3_5),
% 1.66/1.42 inference(avatar_contradiction_clause,[status(thm)],[f52])).
% 1.66/1.42 thf(f52,plain,(
% 1.66/1.42 $false | (~spl3_1 | spl3_5)),
% 1.66/1.42 inference(subsumption_resolution,[status(thm)],[f38,f21])).
% 1.66/1.42 thf(f21,plain,(
% 1.66/1.42 ( ! [X4 : $i] : (((cQ @ X4 @ y) = $true)) ) | ~spl3_1),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.66/1.42 thf(f20,definition,(
% 1.66/1.42 spl3_1 <=> ! [X4 : $i] : ((cQ @ X4 @ y) = $true)),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.66/1.42 thf(f38,plain,(
% 1.66/1.42 ($true != (cQ @ sK1 @ y)) | spl3_5),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.66/1.42 thf(f36,definition,(
% 1.66/1.42 spl3_5 <=> ($true = (cQ @ sK1 @ y))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.66/1.42 thf(f51,plain,(
% 1.66/1.42 spl3_4 | ~spl3_6),
% 1.66/1.42 inference(avatar_contradiction_clause,[status(thm)],[f50])).
% 1.66/1.42 thf(f50,plain,(
% 1.66/1.42 $false | (spl3_4 | ~spl3_6)),
% 1.66/1.42 inference(subsumption_resolution,[status(thm)],[f34,f42])).
% 1.66/1.42 thf(f42,plain,(
% 1.66/1.42 ( ! [X3 : $i] : (($true = (cP @ X3 @ y))) ) | ~spl3_6),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.66/1.42 thf(f41,definition,(
% 1.66/1.42 spl3_6 <=> ! [X3 : $i] : ($true = (cP @ X3 @ y))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.66/1.42 thf(f34,plain,(
% 1.66/1.42 ($true != (cP @ sK2 @ y)) | spl3_4),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.66/1.42 thf(f32,definition,(
% 1.66/1.42 spl3_4 <=> ($true = (cP @ sK2 @ y))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.66/1.42 thf(f49,plain,(
% 1.66/1.42 ~spl3_1 | spl3_3),
% 1.66/1.42 inference(avatar_contradiction_clause,[status(thm)],[f48])).
% 1.66/1.42 thf(f48,plain,(
% 1.66/1.42 $false | (~spl3_1 | spl3_3)),
% 1.66/1.42 inference(subsumption_resolution,[status(thm)],[f30,f21])).
% 1.66/1.42 thf(f30,plain,(
% 1.66/1.42 ($true != (cQ @ sK0 @ y)) | spl3_3),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.66/1.42 thf(f28,definition,(
% 1.66/1.42 spl3_3 <=> ($true = (cQ @ sK0 @ y))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.66/1.42 thf(f47,plain,(
% 1.66/1.42 spl3_2 | ~spl3_6),
% 1.66/1.42 inference(avatar_contradiction_clause,[status(thm)],[f46])).
% 1.66/1.42 thf(f46,plain,(
% 1.66/1.42 $false | (spl3_2 | ~spl3_6)),
% 1.66/1.42 inference(subsumption_resolution,[status(thm)],[f26,f42])).
% 1.66/1.42 thf(f26,plain,(
% 1.66/1.42 ($true != (cP @ sK0 @ y)) | spl3_2),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.66/1.42 thf(f24,definition,(
% 1.66/1.42 spl3_2 <=> ($true = (cP @ sK0 @ y))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.66/1.42 thf(f43,plain,(
% 1.66/1.42 spl3_6 | spl3_6),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f16,f41,f41])).
% 1.66/1.42 thf(f16,plain,(
% 1.66/1.42 ( ! [X3 : $i,X5 : $i] : (($true = (cP @ X3 @ y)) | ($true = (cP @ X5 @ y))) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.42 thf(f13,plain,(
% 1.66/1.42 ((($true != (cP @ sK0 @ y)) | ($true != (cQ @ sK0 @ y))) | ($true != (cQ @ sK1 @ y)) | ($true != (cP @ sK2 @ y))) & (! [X3 : $i] : (($true = (cP @ X3 @ y)) & ($true = (cQ @ X3 @ y))) | (! [X4 : $i] : ((cQ @ X4 @ y) = $true) & ! [X5 : $i] : ($true = (cP @ X5 @ y))))),
% 1.66/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10])).
% 1.66/1.42 thf(f10,plain,(
% 1.66/1.42 ? [X0 : $i] : (((cP @ X0 @ y) != $true) | ((cQ @ X0 @ y) != $true)) => (($true != (cP @ sK0 @ y)) | ($true != (cQ @ sK0 @ y)))),
% 1.66/1.42 introduced(definition,[],[choice_axiom])).
% 1.66/1.42 thf(f11,plain,(
% 1.66/1.42 ? [X1 : $i] : ($true != (cQ @ X1 @ y)) => ($true != (cQ @ sK1 @ y))),
% 1.66/1.42 introduced(definition,[],[choice_axiom])).
% 1.66/1.42 thf(f12,plain,(
% 1.66/1.42 ? [X2 : $i] : ($true != (cP @ X2 @ y)) => ($true != (cP @ sK2 @ y))),
% 1.66/1.42 introduced(definition,[],[choice_axiom])).
% 1.66/1.42 thf(f9,plain,(
% 1.66/1.42 (? [X0 : $i] : (((cP @ X0 @ y) != $true) | ((cQ @ X0 @ y) != $true)) | ? [X1 : $i] : ($true != (cQ @ X1 @ y)) | ? [X2 : $i] : ($true != (cP @ X2 @ y))) & (! [X3 : $i] : (($true = (cP @ X3 @ y)) & ($true = (cQ @ X3 @ y))) | (! [X4 : $i] : ((cQ @ X4 @ y) = $true) & ! [X5 : $i] : ($true = (cP @ X5 @ y))))),
% 1.66/1.42 inference(rectify,[status(thm)],[f8])).
% 1.66/1.42 thf(f8,plain,(
% 1.66/1.42 (? [X2 : $i] : (($true != (cP @ X2 @ y)) | ($true != (cQ @ X2 @ y))) | ? [X0 : $i] : ((cQ @ X0 @ y) != $true) | ? [X1 : $i] : ($true != (cP @ X1 @ y))) & (! [X2 : $i] : (($true = (cP @ X2 @ y)) & ($true = (cQ @ X2 @ y))) | (! [X0 : $i] : ((cQ @ X0 @ y) = $true) & ! [X1 : $i] : ($true = (cP @ X1 @ y))))),
% 1.66/1.42 inference(flattening,[status(thm)],[f7])).
% 1.66/1.42 thf(f7,plain,(
% 1.66/1.42 (? [X2 : $i] : (($true != (cP @ X2 @ y)) | ($true != (cQ @ X2 @ y))) | (? [X0 : $i] : ((cQ @ X0 @ y) != $true) | ? [X1 : $i] : ($true != (cP @ X1 @ y)))) & (! [X2 : $i] : (($true = (cP @ X2 @ y)) & ($true = (cQ @ X2 @ y))) | (! [X0 : $i] : ((cQ @ X0 @ y) = $true) & ! [X1 : $i] : ($true = (cP @ X1 @ y))))),
% 1.66/1.42 inference(nnf_transformation,[status(thm)],[f6])).
% 1.66/1.42 thf(f6,plain,(
% 1.66/1.42 (! [X0 : $i] : ((cQ @ X0 @ y) = $true) & ! [X1 : $i] : ($true = (cP @ X1 @ y))) <~> ! [X2 : $i] : (($true = (cP @ X2 @ y)) & ($true = (cQ @ X2 @ y)))),
% 1.66/1.42 inference(ennf_transformation,[status(thm)],[f5])).
% 1.66/1.42 thf(f5,plain,(
% 1.66/1.42 ~((! [X0 : $i] : ((cQ @ X0 @ y) = $true) & ! [X1 : $i] : ($true = (cP @ X1 @ y))) <=> ! [X2 : $i] : (($true = (cP @ X2 @ y)) & ($true = (cQ @ X2 @ y))))),
% 1.66/1.42 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.42 thf(f4,plain,(
% 1.66/1.42 ~((! [X0 : $i] : (cQ @ X0 @ y) & ! [X1 : $i] : (cP @ X1 @ y)) <=> ! [X2 : $i] : ((cQ @ X2 @ y) & (cP @ X2 @ y)))),
% 1.66/1.42 inference(rectify,[status(thm)],[f2])).
% 1.66/1.42 thf(f2,negated_conjecture,(
% 1.66/1.42 ~((! [X0 : $i] : (cQ @ X0 @ y) & ! [X0 : $i] : (cP @ X0 @ y)) <=> ! [X0 : $i] : ((cQ @ X0 @ y) & (cP @ X0 @ y)))),
% 1.66/1.42 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.42 thf(f1,conjecture,(
% 1.66/1.42 (! [X0 : $i] : (cQ @ X0 @ y) & ! [X0 : $i] : (cP @ X0 @ y)) <=> ! [X0 : $i] : ((cQ @ X0 @ y) & (cP @ X0 @ y))),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.xFRpfb1oG6/DTF2THF_20226.p',cTTTP2129)).
% 1.66/1.42 thf(f39,plain,(
% 1.66/1.42 ~spl3_2 | ~spl3_3 | ~spl3_4 | ~spl3_5),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f18,f36,f32,f28,f24])).
% 1.66/1.42 thf(f18,plain,(
% 1.66/1.42 ($true != (cP @ sK2 @ y)) | ($true != (cQ @ sK1 @ y)) | ($true != (cP @ sK0 @ y)) | ($true != (cQ @ sK0 @ y))),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.42 thf(f22,plain,(
% 1.66/1.42 spl3_1 | spl3_1),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f15,f20,f20])).
% 1.66/1.42 thf(f15,plain,(
% 1.66/1.42 ( ! [X3 : $i,X4 : $i] : (($true = (cQ @ X3 @ y)) | ((cQ @ X4 @ y) = $true)) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.42 % SZS output end Proof for DTF2THF_20226
% 1.66/1.42 % (20325)------------------------------
% 1.66/1.42 % (20325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (20325)Termination reason: Refutation
% 1.66/1.42
% 1.66/1.42 % (20325)Memory used [KB]: 5500
% 1.66/1.42 % (20325)Time elapsed: 0.004 s
% 1.66/1.42 % (20325)Instructions burned: 2 (million)
% 1.66/1.42 % (20325)------------------------------
% 1.66/1.42 % (20325)------------------------------
% 1.66/1.42 % (20323)Success in time 0.018 s
%------------------------------------------------------------------------------