%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO098^5 : 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 : n028.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 09:53:22 AM UTC 2026
% Result : Theorem 1.53s 1.25s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 4 unt; 0 typ; 2 def)
% Number of atoms : 147 ( 35 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 160 ( 32 ~; 14 |; 11 &; 90 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 0 ^; 28 !; 13 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $i > $o ).
thf(func_def_1,type,
cR: $i > $i > $o ).
thf(f29,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f21,f25,f28]) ).
thf(f28,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f27]) ).
thf(f27,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true != $true )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f11,f16]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i] :
( ( cR @ X1 @ X0 )
= $true )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f15]) ).
thf(f15,definition,
( spl1_1
<=> ! [X0: $i,X1: $i] :
( ( cR @ X1 @ X0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f11,plain,
! [X3: $i] :
( ( cR @ X3 @ X3 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i] :
( ( ( cR @ X1 @ X0 )
= $true )
| ( ( $true
= ( cQ @ X0 @ X1 ) )
& ( $true
!= ( cQ @ sK0 @ sK0 ) ) ) )
& ! [X3: $i] :
( ( cR @ X3 @ X3 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X2: $i] :
( ( cQ @ X2 @ X2 )
!= $true )
=> ( $true
!= ( cQ @ sK0 @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] :
( ( ( cR @ X1 @ X0 )
= $true )
| ( ( $true
= ( cQ @ X0 @ X1 ) )
& ? [X2: $i] :
( ( cQ @ X2 @ X2 )
!= $true ) ) )
& ! [X3: $i] :
( ( cR @ X3 @ X3 )
!= $true ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X1: $i,X2: $i] :
( ( ( cR @ X2 @ X1 )
= $true )
| ( ( ( cQ @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( cQ @ X3 @ X3 )
!= $true ) ) )
& ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
=> ? [X2: $i,X1: $i] :
( ( ( cR @ X2 @ X1 )
!= $true )
& ( ( ( cQ @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( cQ @ X3 @ X3 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
=> ? [X1: $i,X2: $i] :
( ( ( ( cQ @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( cQ @ X3 @ X3 )
= $true ) )
& ( ( cR @ X2 @ X1 )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
~ ( cR @ X0 @ X0 )
=> ? [X1: $i,X2: $i] :
( ( ( cQ @ X1 @ X2 )
=> ! [X3: $i] : ( cQ @ X3 @ X3 ) )
& ~ ( cR @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
~ ( cR @ X0 @ X0 )
=> ? [X2: $i,X1: $i] :
( ( ( cQ @ X2 @ X1 )
=> ! [X3: $i] : ( cQ @ X3 @ X3 ) )
& ~ ( cR @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
~ ( cR @ X0 @ X0 )
=> ? [X2: $i,X1: $i] :
( ( ( cQ @ X2 @ X1 )
=> ! [X3: $i] : ( cQ @ X3 @ X3 ) )
& ~ ( cR @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.geQnrpfqye/DTF2THF_11205.p',cTHM65) ).
thf(f25,plain,
spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f24]) ).
thf(f24,plain,
( $false
| spl1_2 ),
inference(subsumption_resolution,[status(thm)],[f23,f11]) ).
thf(f23,plain,
( ( ( cR @ sK0 @ sK0 )
= $true )
| spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true != $true )
| ( ( cR @ sK0 @ sK0 )
= $true )
| spl1_2 ),
inference(superposition,[status(thm)],[f20,f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( cQ @ X0 @ X1 ) )
| ( ( cR @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f20,plain,
( ( $true
!= ( cQ @ sK0 @ sK0 ) )
| spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl1_2
<=> ( $true
= ( cQ @ sK0 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f21,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f12,f18,f15]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cQ @ sK0 @ sK0 ) )
| ( ( cR @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO098^5 : 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 : n028.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 14:24:27 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO098^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : TPS problem THM65
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0289 [Bro09]
% 0.30/0.46 % : THM65 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % 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
% 0.30/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.30/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.30/0.46 % Number of connectives : 13 ( 2 ~; 0 |; 1 &; 8 @)
% 0.30/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.30/0.46 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(cQ,type,
% 0.30/0.46 cQ: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cR,type,
% 0.30/0.46 cR: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cTHM65,conjecture,
% 0.30/0.46 ( ! [W: $i] :
% 0.30/0.46 ~ ( cR @ W @ W )
% 0.30/0.46 => ? [X: $i,Y: $i] :
% 0.30/0.46 ( ~ ( cR @ X @ Y )
% 0.30/0.46 & ( ( cQ @ Y @ X )
% 0.30/0.46 => ! [Z: $i] : ( cQ @ Z @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.53/1.22 ---- Embedded in THF ---
% 1.53/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.22 %%% Generated on Tue Feb 24 14:24:27 EST 2026
% 1.53/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.22 %%% Logic specification used:
% 1.53/1.22 %%% thf(spec, logic, $$dhol).
% 1.53/1.22
% 1.53/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.geQnrpfqye/DTF2DTF11205.p
% See solution above
% 1.53/1.22 ------------------------
% 1.53/1.23 ---- Cleaned THF ---
% 1.53/1.23 thf(cQ,type,
% 1.53/1.23 cQ: $i > $i > $o ).
% 1.53/1.23
% 1.53/1.23 thf(cR,type,
% 1.53/1.23 cR: $i > $i > $o ).
% 1.53/1.23
% 1.53/1.23 thf(cTHM65,conjecture,
% 1.53/1.23 ( ! [W: $i] :
% 1.53/1.23 ~ ( cR @ W @ W )
% 1.53/1.23 => ? [X: $i,Y: $i] :
% 1.53/1.23 ( ~ ( cR @ X @ Y )
% 1.53/1.23 & ( ( cQ @ Y @ X )
% 1.53/1.23 => ! [Z: $i] : ( cQ @ Z @ Z ) ) ) ) ).
% 1.53/1.23 ------------------------
% 1.53/1.24 % (11393)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11205 for (2999ds/183Mi)
% 1.53/1.24 % (11399)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11205 for (2999ds/18Mi)
% 1.53/1.24 % (11393)First to succeed.
% 1.53/1.24 % (11399)Also succeeded, but the first one will report.
% 1.53/1.25 % (11393)Refutation found. Thanks to Tanya!
% 1.53/1.25 % SZS status Theorem for DTF2THF_11205
% 1.53/1.25 % SZS output start Proof for DTF2THF_11205
% 1.53/1.25 thf(func_def_0, type, cQ: $i > $i > $o).
% 1.53/1.25 thf(func_def_1, type, cR: $i > $i > $o).
% 1.53/1.25 thf(f29,plain,(
% 1.53/1.25 $false),
% 1.53/1.25 inference(avatar_sat_refutation,[status(thm)],[f21,f25,f28])).
% 1.53/1.25 thf(f28,plain,(
% 1.53/1.25 ~spl1_1),
% 1.53/1.25 inference(avatar_contradiction_clause,[status(thm)],[f27])).
% 1.53/1.25 thf(f27,plain,(
% 1.53/1.25 $false | ~spl1_1),
% 1.53/1.25 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.53/1.25 thf(f26,plain,(
% 1.53/1.25 ($true != $true) | ~spl1_1),
% 1.53/1.25 inference(superposition,[status(thm)],[f11,f16])).
% 1.53/1.25 thf(f16,plain,(
% 1.53/1.25 ( ! [X0 : $i,X1 : $i] : (((cR @ X1 @ X0) = $true)) ) | ~spl1_1),
% 1.53/1.25 inference(avatar_component_clause,[status(thm)],[f15])).
% 1.53/1.25 thf(f15,definition,(
% 1.53/1.25 spl1_1 <=> ! [X0 : $i,X1 : $i] : ((cR @ X1 @ X0) = $true)),
% 1.53/1.25 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.53/1.25 thf(f11,plain,(
% 1.53/1.25 ( ! [X3 : $i] : (((cR @ X3 @ X3) != $true)) )),
% 1.53/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.25 thf(f10,plain,(
% 1.53/1.25 ! [X0 : $i,X1 : $i] : (((cR @ X1 @ X0) = $true) | (($true = (cQ @ X0 @ X1)) & ($true != (cQ @ sK0 @ sK0)))) & ! [X3 : $i] : ((cR @ X3 @ X3) != $true)),
% 1.53/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.53/1.25 thf(f9,plain,(
% 1.53/1.25 ? [X2 : $i] : ((cQ @ X2 @ X2) != $true) => ($true != (cQ @ sK0 @ sK0))),
% 1.53/1.25 introduced(definition,[],[choice_axiom])).
% 1.53/1.25 thf(f8,plain,(
% 1.53/1.25 ! [X0 : $i,X1 : $i] : (((cR @ X1 @ X0) = $true) | (($true = (cQ @ X0 @ X1)) & ? [X2 : $i] : ((cQ @ X2 @ X2) != $true))) & ! [X3 : $i] : ((cR @ X3 @ X3) != $true)),
% 1.53/1.25 inference(rectify,[status(thm)],[f7])).
% 1.53/1.25 thf(f7,plain,(
% 1.53/1.25 ! [X1 : $i,X2 : $i] : (((cR @ X2 @ X1) = $true) | (((cQ @ X1 @ X2) = $true) & ? [X3 : $i] : ((cQ @ X3 @ X3) != $true))) & ! [X0 : $i] : ((cR @ X0 @ X0) != $true)),
% 1.53/1.25 inference(ennf_transformation,[status(thm)],[f6])).
% 1.53/1.25 thf(f6,plain,(
% 1.53/1.25 ~(! [X0 : $i] : ((cR @ X0 @ X0) != $true) => ? [X2 : $i,X1 : $i] : (((cR @ X2 @ X1) != $true) & (((cQ @ X1 @ X2) = $true) => ! [X3 : $i] : ((cQ @ X3 @ X3) = $true))))),
% 1.53/1.25 inference(flattening,[status(thm)],[f5])).
% 1.53/1.25 thf(f5,plain,(
% 1.53/1.25 ~(! [X0 : $i] : ~((cR @ X0 @ X0) = $true) => ? [X1 : $i,X2 : $i] : ((((cQ @ X1 @ X2) = $true) => ! [X3 : $i] : ((cQ @ X3 @ X3) = $true)) & ~((cR @ X2 @ X1) = $true)))),
% 1.53/1.25 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.25 thf(f4,plain,(
% 1.53/1.25 ~(! [X0 : $i] : ~(cR @ X0 @ X0) => ? [X1 : $i,X2 : $i] : (((cQ @ X1 @ X2) => ! [X3 : $i] : (cQ @ X3 @ X3)) & ~(cR @ X2 @ X1)))),
% 1.53/1.25 inference(rectify,[status(thm)],[f2])).
% 1.53/1.25 thf(f2,negated_conjecture,(
% 1.53/1.25 ~(! [X0 : $i] : ~(cR @ X0 @ X0) => ? [X2 : $i,X1 : $i] : (((cQ @ X2 @ X1) => ! [X3 : $i] : (cQ @ X3 @ X3)) & ~(cR @ X1 @ X2)))),
% 1.53/1.25 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.25 thf(f1,conjecture,(
% 1.53/1.25 ! [X0 : $i] : ~(cR @ X0 @ X0) => ? [X2 : $i,X1 : $i] : (((cQ @ X2 @ X1) => ! [X3 : $i] : (cQ @ X3 @ X3)) & ~(cR @ X1 @ X2))),
% 1.53/1.25 file('/export/starexec/sandbox/tmp/tmp.geQnrpfqye/DTF2THF_11205.p',cTHM65)).
% 1.53/1.25 thf(f25,plain,(
% 1.53/1.25 spl1_2),
% 1.53/1.25 inference(avatar_contradiction_clause,[status(thm)],[f24])).
% 1.53/1.25 thf(f24,plain,(
% 1.53/1.25 $false | spl1_2),
% 1.53/1.25 inference(subsumption_resolution,[status(thm)],[f23,f11])).
% 1.53/1.25 thf(f23,plain,(
% 1.53/1.25 ((cR @ sK0 @ sK0) = $true) | spl1_2),
% 1.53/1.25 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.53/1.25 thf(f22,plain,(
% 1.53/1.25 ($true != $true) | ((cR @ sK0 @ sK0) = $true) | spl1_2),
% 1.53/1.25 inference(superposition,[status(thm)],[f20,f13])).
% 1.53/1.25 thf(f13,plain,(
% 1.53/1.25 ( ! [X0 : $i,X1 : $i] : (($true = (cQ @ X0 @ X1)) | ((cR @ X1 @ X0) = $true)) )),
% 1.53/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.25 thf(f20,plain,(
% 1.53/1.25 ($true != (cQ @ sK0 @ sK0)) | spl1_2),
% 1.53/1.25 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.53/1.25 thf(f18,definition,(
% 1.53/1.25 spl1_2 <=> ($true = (cQ @ sK0 @ sK0))),
% 1.53/1.25 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.53/1.25 thf(f21,plain,(
% 1.53/1.25 spl1_1 | ~spl1_2),
% 1.53/1.25 inference(avatar_split_clause,[status(thm)],[f12,f18,f15])).
% 1.53/1.25 thf(f12,plain,(
% 1.53/1.25 ( ! [X0 : $i,X1 : $i] : (($true != (cQ @ sK0 @ sK0)) | ((cR @ X1 @ X0) = $true)) )),
% 1.53/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.25 % SZS output end Proof for DTF2THF_11205
% 1.53/1.25 % (11393)------------------------------
% 1.53/1.25 % (11393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.25 % (11393)Termination reason: Refutation
% 1.53/1.25
% 1.53/1.25 % (11393)Memory used [KB]: 5500
% 1.53/1.25 % (11393)Time elapsed: 0.003 s
% 1.53/1.25 % (11393)Instructions burned: 1 (million)
% 1.53/1.25 % (11393)------------------------------
% 1.53/1.25 % (11393)------------------------------
% 1.53/1.25 % (11392)Success in time 0.004 s
%------------------------------------------------------------------------------