%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO142^5 : 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 : n009.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 09:53:28 AM UTC 2026
% Result : Theorem 1.28s 1.13s
% Output : Refutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 1 unt; 0 typ; 3 def)
% Number of atoms : 95 ( 18 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 112 ( 19 ~; 14 |; 6 &; 62 @)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 9 !; 8 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
p: $i > $o ).
thf(f28,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f18,f22,f25,f27]) ).
thf(f27,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f26]) ).
thf(f26,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f17,f21]) ).
thf(f21,plain,
( ! [X1: $i] :
( ( p @ X1 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl0_3
<=> ! [X1: $i] :
( ( p @ X1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f17,plain,
( ! [X0: $i] :
( ( p @ ( f @ ( f @ X0 ) ) )
!= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f16,definition,
( spl0_2
<=> ! [X0: $i] :
( ( p @ ( f @ ( f @ X0 ) ) )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f25,plain,
( spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f24]) ).
thf(f24,plain,
( $false
| spl0_1
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f14,f21]) ).
thf(f14,plain,
( ( ( p @ ( f @ ( f @ a ) ) )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f12]) ).
thf(f12,definition,
( spl0_1
<=> ( ( p @ ( f @ ( f @ a ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f22,plain,
( spl0_3
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f7,f20,f20]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( p @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i] :
( ( ( ( p @ ( f @ ( f @ a ) ) )
!= $true )
& ( ( p @ X0 )
= $true ) )
| ( ( ( p @ ( f @ ( f @ X0 ) ) )
!= $true )
& ( ( p @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X1: $i,X0: $i] :
( ( ( ( p @ X1 )
= $true )
=> ( ( p @ ( f @ ( f @ X0 ) ) )
= $true ) )
& ( ( ( p @ X0 )
= $true )
=> ( ( p @ ( f @ ( f @ a ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i,X1: $i] :
( ( ( p @ X0 )
=> ( p @ ( f @ ( f @ a ) ) ) )
& ( ( p @ X1 )
=> ( p @ ( f @ ( f @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X1: $i,X0: $i] :
( ( ( p @ X1 )
=> ( p @ ( f @ ( f @ a ) ) ) )
& ( ( p @ X0 )
=> ( p @ ( f @ ( f @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X1: $i,X0: $i] :
( ( ( p @ X1 )
=> ( p @ ( f @ ( f @ a ) ) ) )
& ( ( p @ X0 )
=> ( p @ ( f @ ( f @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.DwkrRU8hDz/DTF2THF_27968.p',cTEST4) ).
thf(f18,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f10,f16,f12]) ).
thf(f10,plain,
! [X0: $i] :
( ( ( p @ ( f @ ( f @ a ) ) )
!= $true )
| ( ( p @ ( f @ ( f @ X0 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SYO142^5 : TPTP v9.2.1. Released v4.0.0.
% 0.09/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.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 14:25:25 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
% 0.25/0.45 ---- Original DTF file ---
% 0.25/0.45 thf(spec,logic,$$dhol).
% 0.25/0.45 %------------------------------------------------------------------------------
% 0.25/0.45 % File : SYO142^5 : TPTP v9.2.1. Released v4.0.0.
% 0.25/0.45 % Domain : Syntactic
% 0.25/0.45 % Problem : TPS problem from BASIC-FO-THMS
% 0.25/0.45 % Version : Especial.
% 0.25/0.45 % English :
% 0.25/0.45
% 0.25/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.25/0.45 % Source : [Bro09]
% 0.25/0.45 % Names : tps_0765 [Bro09]
% 0.25/0.45
% 0.25/0.45 % Status : Theorem
% 0.25/0.45 % Rating : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.25/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.25/0.45 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.25/0.45 % Maximal formula atoms : 4 ( 4 avg)
% 0.25/0.45 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 8 @)
% 0.25/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.25/0.45 % Maximal formula depth : 8 ( 8 avg)
% 0.25/0.45 % Number of types : 2 ( 0 usr)
% 0.25/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.25/0.45 % Number of symbols : 3 ( 3 usr; 1 con; 0-1 aty)
% 0.25/0.45 % Number of variables : 2 ( 0 ^; 0 !; 2 ?; 2 :)
% 0.25/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.25/0.45
% 0.25/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.25/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.25/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.25/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.25/0.45 %------------------------------------------------------------------------------
% 0.25/0.45 thf(a,type,
% 0.25/0.45 a: $i ).
% 0.25/0.45
% 0.25/0.45 thf(f,type,
% 0.25/0.45 f: $i > $i ).
% 0.25/0.45
% 0.25/0.45 thf(p,type,
% 0.25/0.45 p: $i > $o ).
% 0.25/0.45
% 0.25/0.45 thf(cTEST4,conjecture,
% 0.25/0.45 ? [Xx: $i,Xy: $i] :
% 0.25/0.45 ( ( ( p @ Xx )
% 0.25/0.45 => ( p @ ( f @ ( f @ Xy ) ) ) )
% 0.25/0.45 & ( ( p @ Xy )
% 0.25/0.45 => ( p @ ( f @ ( f @ a ) ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 %------------------------------------------------------------------------------
% 0.25/0.45 ------------------------
% 1.10/1.10 ---- Embedded in THF ---
% 1.10/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.10/1.11 %%% Generated on Tue Feb 24 14:25:25 EST 2026
% 1.10/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 1.10/1.11 %%% Logic specification used:
% 1.10/1.11 %%% thf(spec, logic, $$dhol).
% 1.10/1.11
% 1.10/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.DwkrRU8hDz/DTF2DTF27968.p
% See solution above
% 1.10/1.11 ------------------------
% 1.10/1.11 ---- Cleaned THF ---
% 1.10/1.11 thf(a,type,
% 1.10/1.11 a: $i ).
% 1.10/1.11
% 1.10/1.11 thf(f,type,
% 1.10/1.11 f: $i > $i ).
% 1.10/1.11
% 1.10/1.11 thf(p,type,
% 1.10/1.11 p: $i > $o ).
% 1.10/1.11
% 1.10/1.11 thf(cTEST4,conjecture,
% 1.10/1.11 ? [Xx: $i,Xy: $i] :
% 1.10/1.11 ( ( ( p @ Xx )
% 1.10/1.11 => ( p @ ( f @ ( f @ Xy ) ) ) )
% 1.10/1.11 & ( ( p @ Xy )
% 1.10/1.11 => ( p @ ( f @ ( f @ a ) ) ) ) ) ).
% 1.10/1.11 ------------------------
% 1.28/1.13 % (28065)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27968 for (3000ds/183Mi)
% 1.28/1.13 % (28065)First to succeed.
% 1.28/1.13 % (28065)Refutation found. Thanks to Tanya!
% 1.28/1.13 % SZS status Theorem for DTF2THF_27968
% 1.28/1.13 % SZS output start Proof for DTF2THF_27968
% 1.28/1.13 thf(func_def_1, type, f: $i > $i).
% 1.28/1.13 thf(func_def_2, type, p: $i > $o).
% 1.28/1.13 thf(f28,plain,(
% 1.28/1.13 $false),
% 1.28/1.13 inference(avatar_sat_refutation,[status(thm)],[f18,f22,f25,f27])).
% 1.28/1.13 thf(f27,plain,(
% 1.28/1.13 ~spl0_2 | ~spl0_3),
% 1.28/1.13 inference(avatar_contradiction_clause,[status(thm)],[f26])).
% 1.28/1.13 thf(f26,plain,(
% 1.28/1.13 $false | (~spl0_2 | ~spl0_3)),
% 1.28/1.13 inference(subsumption_resolution,[status(thm)],[f17,f21])).
% 1.28/1.13 thf(f21,plain,(
% 1.28/1.13 ( ! [X1 : $i] : (((p @ X1) = $true)) ) | ~spl0_3),
% 1.28/1.13 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.28/1.13 thf(f20,definition,(
% 1.28/1.13 spl0_3 <=> ! [X1 : $i] : ((p @ X1) = $true)),
% 1.28/1.13 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.28/1.13 thf(f17,plain,(
% 1.28/1.13 ( ! [X0 : $i] : (((p @ (f @ (f @ X0))) != $true)) ) | ~spl0_2),
% 1.28/1.13 inference(avatar_component_clause,[status(thm)],[f16])).
% 1.28/1.13 thf(f16,definition,(
% 1.28/1.13 spl0_2 <=> ! [X0 : $i] : ((p @ (f @ (f @ X0))) != $true)),
% 1.28/1.13 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.28/1.13 thf(f25,plain,(
% 1.28/1.13 spl0_1 | ~spl0_3),
% 1.28/1.13 inference(avatar_contradiction_clause,[status(thm)],[f24])).
% 1.28/1.13 thf(f24,plain,(
% 1.28/1.13 $false | (spl0_1 | ~spl0_3)),
% 1.28/1.13 inference(subsumption_resolution,[status(thm)],[f14,f21])).
% 1.28/1.13 thf(f14,plain,(
% 1.28/1.13 ((p @ (f @ (f @ a))) != $true) | spl0_1),
% 1.28/1.13 inference(avatar_component_clause,[status(thm)],[f12])).
% 1.28/1.13 thf(f12,definition,(
% 1.28/1.13 spl0_1 <=> ((p @ (f @ (f @ a))) = $true)),
% 1.28/1.13 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.28/1.13 thf(f22,plain,(
% 1.28/1.13 spl0_3 | spl0_3),
% 1.28/1.13 inference(avatar_split_clause,[status(thm)],[f7,f20,f20])).
% 1.28/1.13 thf(f7,plain,(
% 1.28/1.13 ( ! [X0 : $i,X1 : $i] : (((p @ X1) = $true) | ((p @ X0) = $true)) )),
% 1.28/1.13 inference(cnf_transformation,[status(thm)],[f6])).
% 1.28/1.13 thf(f6,plain,(
% 1.28/1.13 ! [X0 : $i,X1 : $i] : ((((p @ (f @ (f @ a))) != $true) & ((p @ X0) = $true)) | (((p @ (f @ (f @ X0))) != $true) & ((p @ X1) = $true)))),
% 1.28/1.13 inference(ennf_transformation,[status(thm)],[f5])).
% 1.28/1.13 thf(f5,plain,(
% 1.28/1.13 ~? [X1 : $i,X0 : $i] : ((((p @ X1) = $true) => ((p @ (f @ (f @ X0))) = $true)) & (((p @ X0) = $true) => ((p @ (f @ (f @ a))) = $true)))),
% 1.28/1.13 inference(fool_elimination,[status(thm)],[f4])).
% 1.28/1.13 thf(f4,plain,(
% 1.28/1.13 ~? [X0 : $i,X1 : $i] : (((p @ X0) => (p @ (f @ (f @ a)))) & ((p @ X1) => (p @ (f @ (f @ X0)))))),
% 1.28/1.13 inference(rectify,[status(thm)],[f2])).
% 1.28/1.13 thf(f2,negated_conjecture,(
% 1.28/1.13 ~? [X1 : $i,X0 : $i] : (((p @ X1) => (p @ (f @ (f @ a)))) & ((p @ X0) => (p @ (f @ (f @ X1)))))),
% 1.28/1.13 inference(negated_conjecture,[status(cth)],[f1])).
% 1.28/1.13 thf(f1,conjecture,(
% 1.28/1.13 ? [X1 : $i,X0 : $i] : (((p @ X1) => (p @ (f @ (f @ a)))) & ((p @ X0) => (p @ (f @ (f @ X1)))))),
% 1.28/1.13 file('/export/starexec/sandbox2/tmp/tmp.DwkrRU8hDz/DTF2THF_27968.p',cTEST4)).
% 1.28/1.13 thf(f18,plain,(
% 1.28/1.13 ~spl0_1 | spl0_2),
% 1.28/1.13 inference(avatar_split_clause,[status(thm)],[f10,f16,f12])).
% 1.28/1.13 thf(f10,plain,(
% 1.28/1.13 ( ! [X0 : $i] : (((p @ (f @ (f @ a))) != $true) | ((p @ (f @ (f @ X0))) != $true)) )),
% 1.28/1.13 inference(cnf_transformation,[status(thm)],[f6])).
% 1.28/1.13 % SZS output end Proof for DTF2THF_27968
% 1.28/1.13 % (28065)------------------------------
% 1.28/1.13 % (28065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.28/1.13 % (28065)Termination reason: Refutation
% 1.28/1.13
% 1.28/1.13 % (28065)Memory used [KB]: 5500
% 1.28/1.13 % (28065)Time elapsed: 0.002 s
% 1.28/1.13 % (28065)Instructions burned: 1 (million)
% 1.28/1.13 % (28065)------------------------------
% 1.28/1.13 % (28065)------------------------------
% 1.28/1.13 % (28064)Success in time 0.011 s
%------------------------------------------------------------------------------