%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO161^5 : 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 : n008.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 09:53:32 AM UTC 2026
% Result : Theorem 1.48s 1.29s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 1 unt; 0 typ; 5 def)
% Number of atoms : 262 ( 62 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 216 ( 45 ~; 36 |; 22 &; 85 @)
% ( 5 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 52 ( 0 ^; 31 !; 21 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $o ).
thf(f54,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f35,f40,f41,f43,f45,f52]) ).
thf(f52,plain,
( ~ spl3_1
| spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
| ~ spl3_1
| spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $true != $true )
| ~ spl3_1
| spl3_4 ),
inference(superposition,[status(thm)],[f33,f20]) ).
thf(f20,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl3_1
<=> ! [X0: $i] :
( ( cP @ X0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f33,plain,
( ( ( cP @ sK1 )
!= $true )
| spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl3_4
<=> ( ( cP @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f45,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f44]) ).
thf(f44,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f20,f28]) ).
thf(f28,plain,
( ! [X1: $i] :
( ( cP @ X1 )
!= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl3_3
<=> ! [X1: $i] :
( ( cP @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f43,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f42]) ).
thf(f42,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f24,f28]) ).
thf(f24,plain,
( ( ( cP @ sK0 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl3_2
<=> ( ( cP @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f41,plain,
( ~ spl3_5
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f12,f19,f37]) ).
thf(f37,definition,
( spl3_5
<=> ( ( cP @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f12,plain,
! [X5: $i] :
( ( ( cP @ X5 )
= $true )
| ( ( cP @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ! [X0: $i] :
( ( cP @ X0 )
= $true )
& ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
| ( ( ( cP @ sK0 )
= $true )
& ( ( cP @ sK1 )
!= $true ) ) )
& ! [X5: $i] :
( ( ( ( cP @ sK2 )
= $true )
| ( ( cP @ X5 )
!= $true ) )
& ( ( ( cP @ sK2 )
!= $true )
| ( ( cP @ X5 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f10,f9,f8]) ).
thf(f8,plain,
( ? [X2: $i] :
( ( cP @ X2 )
= $true )
=> ( ( cP @ sK0 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X3: $i] :
( ( cP @ X3 )
!= $true )
=> ( ( cP @ sK1 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X4: $i] :
! [X5: $i] :
( ( ( ( cP @ X4 )
= $true )
| ( ( cP @ X5 )
!= $true ) )
& ( ( ( cP @ X4 )
!= $true )
| ( ( cP @ X5 )
= $true ) ) )
=> ! [X5: $i] :
( ( ( ( cP @ sK2 )
= $true )
| ( ( cP @ X5 )
!= $true ) )
& ( ( ( cP @ sK2 )
!= $true )
| ( ( cP @ X5 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ( ( ! [X0: $i] :
( ( cP @ X0 )
= $true )
& ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
| ( ? [X2: $i] :
( ( cP @ X2 )
= $true )
& ? [X3: $i] :
( ( cP @ X3 )
!= $true ) ) )
& ? [X4: $i] :
! [X5: $i] :
( ( ( ( cP @ X4 )
= $true )
| ( ( cP @ X5 )
!= $true ) )
& ( ( ( cP @ X4 )
!= $true )
| ( ( cP @ X5 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( ! [X4: $i] :
( ( cP @ X4 )
= $true )
& ! [X5: $i] :
( ( cP @ X5 )
!= $true ) )
| ( ? [X2: $i] :
( ( cP @ X2 )
= $true )
& ? [X3: $i] :
( ( cP @ X3 )
!= $true ) ) )
& ? [X0: $i] :
! [X1: $i] :
( ( ( ( cP @ X0 )
= $true )
| ( ( cP @ X1 )
!= $true ) )
& ( ( ( cP @ X0 )
!= $true )
| ( ( cP @ X1 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( ( ( cP @ X1 )
= $true )
=> ( ( cP @ X0 )
= $true ) )
& ( ( ( cP @ X0 )
= $true )
=> ( ( cP @ X1 )
= $true ) ) )
=> ( ( ? [X2: $i] :
( ( cP @ X2 )
= $true )
=> ! [X3: $i] :
( ( cP @ X3 )
= $true ) )
& ( ! [X4: $i] :
( ( cP @ X4 )
= $true )
=> ? [X5: $i] :
( ( cP @ X5 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( ( cP @ X0 )
=> ( cP @ X1 ) )
& ( ( cP @ X1 )
=> ( cP @ X0 ) ) )
=> ( ( ? [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,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( ( cP @ X0 )
=> ( cP @ X1 ) )
& ( ( cP @ X1 )
=> ( 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,
( ? [X0: $i] :
! [X1: $i] :
( ( ( cP @ X0 )
=> ( cP @ X1 ) )
& ( ( cP @ X1 )
=> ( cP @ X0 ) ) )
=> ( ( ? [X0: $i] : ( cP @ X0 )
=> ! [X1: $i] : ( cP @ X1 ) )
& ( ! [X1: $i] : ( cP @ X1 )
=> ? [X0: $i] : ( cP @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZjgawJxVMO/DTF2THF_24593.p',cX2125_HALF) ).
thf(f40,plain,
( spl3_3
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f13,f37,f27]) ).
thf(f13,plain,
! [X5: $i] :
( ( ( cP @ X5 )
!= $true )
| ( ( cP @ sK2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f35,plain,
( ~ spl3_4
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f14,f27,f31]) ).
thf(f14,plain,
! [X1: $i] :
( ( ( cP @ X1 )
!= $true )
| ( ( cP @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f25,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f17,f22,f19]) ).
thf(f17,plain,
! [X0: $i] :
( ( ( cP @ X0 )
= $true )
| ( ( cP @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO161^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n008.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:25:09 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYO161^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : TPS problem from BASIC-FO-THMS
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0868 [Bro09]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % 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 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.19/0.46 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 8 ( 8 avg)
% 0.19/0.46 % Number of connectives : 15 ( 0 ~; 0 |; 2 &; 8 @)
% 0.19/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.19/0.46 % Number of variables : 6 ( 0 ^; 3 !; 3 ?; 6 :)
% 0.19/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(cP,type,
% 0.19/0.46 cP: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cX2125_HALF,conjecture,
% 0.19/0.46 ( ? [Xx: $i] :
% 0.19/0.46 ! [Xy: $i] :
% 0.19/0.46 ( ( ( cP @ Xx )
% 0.19/0.46 => ( cP @ Xy ) )
% 0.19/0.46 & ( ( cP @ Xy )
% 0.19/0.46 => ( cP @ Xx ) ) )
% 0.19/0.46 => ( ( ? [Xx: $i] : ( cP @ Xx )
% 0.19/0.46 => ! [Xy: $i] : ( cP @ Xy ) )
% 0.19/0.46 & ( ! [Xy: $i] : ( cP @ Xy )
% 0.19/0.46 => ? [Xx: $i] : ( cP @ Xx ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 14:25:10 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ZjgawJxVMO/DTF2DTF24593.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf(cP,type,
% 1.48/1.26 cP: $i > $o ).
% 1.48/1.26
% 1.48/1.26 thf(cX2125_HALF,conjecture,
% 1.48/1.26 ( ? [Xx: $i] :
% 1.48/1.26 ! [Xy: $i] :
% 1.48/1.26 ( ( ( cP @ Xx )
% 1.48/1.26 => ( cP @ Xy ) )
% 1.48/1.26 & ( ( cP @ Xy )
% 1.48/1.26 => ( cP @ Xx ) ) )
% 1.48/1.26 => ( ( ? [Xx: $i] : ( cP @ Xx )
% 1.48/1.26 => ! [Xy: $i] : ( cP @ Xy ) )
% 1.48/1.26 & ( ! [Xy: $i] : ( cP @ Xy )
% 1.48/1.26 => ? [Xx: $i] : ( cP @ Xx ) ) ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.28 % (24784)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24593 for (2999ds/2Mi)
% 1.48/1.28 % (24784)Instruction limit reached!
% 1.48/1.28 % (24784)------------------------------
% 1.48/1.28 % (24784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (24784)Termination reason: Unknown
% 1.48/1.28 % (24784)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (24784)Memory used [KB]: 5373
% 1.48/1.28 % (24784)Time elapsed: 0.002 s
% 1.48/1.28 % (24784)Instructions burned: 2 (million)
% 1.48/1.28 % (24784)------------------------------
% 1.48/1.28 % (24784)------------------------------
% 1.48/1.28 % (24782)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_24593 for (2999ds/4Mi)
% 1.48/1.29 % (24782)First to succeed.
% 1.48/1.29 % (24782)Refutation found. Thanks to Tanya!
% 1.48/1.29 % SZS status Theorem for DTF2THF_24593
% 1.48/1.29 % SZS output start Proof for DTF2THF_24593
% 1.48/1.29 thf(func_def_0, type, cP: $i > $o).
% 1.48/1.29 thf(f54,plain,(
% 1.48/1.29 $false),
% 1.48/1.29 inference(avatar_sat_refutation,[status(thm)],[f25,f35,f40,f41,f43,f45,f52])).
% 1.48/1.29 thf(f52,plain,(
% 1.48/1.29 ~spl3_1 | spl3_4),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 1.48/1.29 thf(f51,plain,(
% 1.48/1.29 $false | (~spl3_1 | spl3_4)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.48/1.29 thf(f49,plain,(
% 1.48/1.29 ($true != $true) | (~spl3_1 | spl3_4)),
% 1.48/1.29 inference(superposition,[status(thm)],[f33,f20])).
% 1.48/1.29 thf(f20,plain,(
% 1.48/1.29 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | ~spl3_1),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.48/1.29 thf(f19,definition,(
% 1.48/1.29 spl3_1 <=> ! [X0 : $i] : ((cP @ X0) = $true)),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.48/1.29 thf(f33,plain,(
% 1.48/1.29 ((cP @ sK1) != $true) | spl3_4),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.48/1.29 thf(f31,definition,(
% 1.48/1.29 spl3_4 <=> ((cP @ sK1) = $true)),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.48/1.29 thf(f45,plain,(
% 1.48/1.29 ~spl3_1 | ~spl3_3),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f44])).
% 1.48/1.29 thf(f44,plain,(
% 1.48/1.29 $false | (~spl3_1 | ~spl3_3)),
% 1.48/1.29 inference(subsumption_resolution,[status(thm)],[f20,f28])).
% 1.48/1.29 thf(f28,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (((cP @ X1) != $true)) ) | ~spl3_3),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.48/1.29 thf(f27,definition,(
% 1.48/1.29 spl3_3 <=> ! [X1 : $i] : ((cP @ X1) != $true)),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.48/1.29 thf(f43,plain,(
% 1.48/1.29 ~spl3_2 | ~spl3_3),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f42])).
% 1.48/1.29 thf(f42,plain,(
% 1.48/1.29 $false | (~spl3_2 | ~spl3_3)),
% 1.48/1.29 inference(subsumption_resolution,[status(thm)],[f24,f28])).
% 1.48/1.29 thf(f24,plain,(
% 1.48/1.29 ((cP @ sK0) = $true) | ~spl3_2),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.48/1.29 thf(f22,definition,(
% 1.48/1.29 spl3_2 <=> ((cP @ sK0) = $true)),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.48/1.29 thf(f41,plain,(
% 1.48/1.29 ~spl3_5 | spl3_1),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f12,f19,f37])).
% 1.48/1.29 thf(f37,definition,(
% 1.48/1.29 spl3_5 <=> ((cP @ sK2) = $true)),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.48/1.29 thf(f12,plain,(
% 1.48/1.29 ( ! [X5 : $i] : (((cP @ X5) = $true) | ((cP @ sK2) != $true)) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.29 thf(f11,plain,(
% 1.48/1.29 ((! [X0 : $i] : ((cP @ X0) = $true) & ! [X1 : $i] : ((cP @ X1) != $true)) | (((cP @ sK0) = $true) & ((cP @ sK1) != $true))) & ! [X5 : $i] : ((((cP @ sK2) = $true) | ((cP @ X5) != $true)) & (((cP @ sK2) != $true) | ((cP @ X5) = $true)))),
% 1.48/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f10,f9,f8])).
% 1.48/1.29 thf(f8,plain,(
% 1.48/1.29 ? [X2 : $i] : ((cP @ X2) = $true) => ((cP @ sK0) = $true)),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f9,plain,(
% 1.48/1.29 ? [X3 : $i] : ((cP @ X3) != $true) => ((cP @ sK1) != $true)),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f10,plain,(
% 1.48/1.29 ? [X4 : $i] : ! [X5 : $i] : ((((cP @ X4) = $true) | ((cP @ X5) != $true)) & (((cP @ X4) != $true) | ((cP @ X5) = $true))) => ! [X5 : $i] : ((((cP @ sK2) = $true) | ((cP @ X5) != $true)) & (((cP @ sK2) != $true) | ((cP @ X5) = $true)))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f7,plain,(
% 1.48/1.29 ((! [X0 : $i] : ((cP @ X0) = $true) & ! [X1 : $i] : ((cP @ X1) != $true)) | (? [X2 : $i] : ((cP @ X2) = $true) & ? [X3 : $i] : ((cP @ X3) != $true))) & ? [X4 : $i] : ! [X5 : $i] : ((((cP @ X4) = $true) | ((cP @ X5) != $true)) & (((cP @ X4) != $true) | ((cP @ X5) = $true)))),
% 1.48/1.29 inference(rectify,[status(thm)],[f6])).
% 1.48/1.29 thf(f6,plain,(
% 1.48/1.29 ((! [X4 : $i] : ((cP @ X4) = $true) & ! [X5 : $i] : ((cP @ X5) != $true)) | (? [X2 : $i] : ((cP @ X2) = $true) & ? [X3 : $i] : ((cP @ X3) != $true))) & ? [X0 : $i] : ! [X1 : $i] : ((((cP @ X0) = $true) | ((cP @ X1) != $true)) & (((cP @ X0) != $true) | ((cP @ X1) = $true)))),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.29 thf(f5,plain,(
% 1.48/1.29 ~(? [X0 : $i] : ! [X1 : $i] : ((((cP @ X1) = $true) => ((cP @ X0) = $true)) & (((cP @ X0) = $true) => ((cP @ X1) = $true))) => ((? [X2 : $i] : ((cP @ X2) = $true) => ! [X3 : $i] : ((cP @ X3) = $true)) & (! [X4 : $i] : ((cP @ X4) = $true) => ? [X5 : $i] : ((cP @ X5) = $true))))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.29 thf(f4,plain,(
% 1.48/1.29 ~(? [X0 : $i] : ! [X1 : $i] : (((cP @ X0) => (cP @ X1)) & ((cP @ X1) => (cP @ X0))) => ((? [X2 : $i] : (cP @ X2) => ! [X3 : $i] : (cP @ X3)) & (! [X4 : $i] : (cP @ X4) => ? [X5 : $i] : (cP @ X5))))),
% 1.48/1.29 inference(rectify,[status(thm)],[f2])).
% 1.48/1.29 thf(f2,negated_conjecture,(
% 1.48/1.29 ~(? [X0 : $i] : ! [X1 : $i] : (((cP @ X0) => (cP @ X1)) & ((cP @ X1) => (cP @ X0))) => ((? [X0 : $i] : (cP @ X0) => ! [X1 : $i] : (cP @ X1)) & (! [X1 : $i] : (cP @ X1) => ? [X0 : $i] : (cP @ X0))))),
% 1.48/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.29 thf(f1,conjecture,(
% 1.48/1.29 ? [X0 : $i] : ! [X1 : $i] : (((cP @ X0) => (cP @ X1)) & ((cP @ X1) => (cP @ X0))) => ((? [X0 : $i] : (cP @ X0) => ! [X1 : $i] : (cP @ X1)) & (! [X1 : $i] : (cP @ X1) => ? [X0 : $i] : (cP @ X0)))),
% 1.48/1.29 file('/export/starexec/sandbox/tmp/tmp.ZjgawJxVMO/DTF2THF_24593.p',cX2125_HALF)).
% 1.48/1.29 thf(f40,plain,(
% 1.48/1.29 spl3_3 | spl3_5),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f13,f37,f27])).
% 1.48/1.29 thf(f13,plain,(
% 1.48/1.29 ( ! [X5 : $i] : (((cP @ X5) != $true) | ((cP @ sK2) = $true)) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.29 thf(f35,plain,(
% 1.48/1.29 ~spl3_4 | spl3_3),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f14,f27,f31])).
% 1.48/1.29 thf(f14,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (((cP @ X1) != $true) | ((cP @ sK1) != $true)) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.29 thf(f25,plain,(
% 1.48/1.29 spl3_1 | spl3_2),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f17,f22,f19])).
% 1.48/1.29 thf(f17,plain,(
% 1.48/1.29 ( ! [X0 : $i] : (((cP @ X0) = $true) | ((cP @ sK0) = $true)) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.29 % SZS output end Proof for DTF2THF_24593
% 1.48/1.29 % (24782)------------------------------
% 1.48/1.29 % (24782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (24782)Termination reason: Refutation
% 1.48/1.29
% 1.48/1.29 % (24782)Memory used [KB]: 5500
% 1.48/1.29 % (24782)Time elapsed: 0.003 s
% 1.48/1.29 % (24782)Instructions burned: 2 (million)
% 1.48/1.29 % (24782)------------------------------
% 1.48/1.29 % (24782)------------------------------
% 1.48/1.29 % (24780)Success in time 0.017 s
%------------------------------------------------------------------------------