%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO083^5 : 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 : n007.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 09:53:20 AM UTC 2026
% Result : Theorem 1.54s 1.35s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 4 unt; 0 typ; 2 def)
% Number of atoms : 85 ( 15 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 79 ( 15 ~; 13 |; 1 &; 44 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 18 !; 4 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $i > $o ).
thf(f22,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f15,f18,f21]) ).
thf(f21,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $true != $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f7,f11]) ).
thf(f11,plain,
( ! [X1: $i] :
( $true
= ( cP @ cA @ X1 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f10]) ).
thf(f10,definition,
( spl0_1
<=> ! [X1: $i] :
( $true
= ( cP @ cA @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f7,plain,
! [X2: $i] :
( ( cP @ X2 @ X2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ! [X0: $i] :
( ( cP @ X0 @ cB )
= $true )
| ! [X1: $i] :
( $true
= ( cP @ cA @ X1 ) ) )
& ! [X2: $i] :
( ( cP @ X2 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( cP @ X0 @ cB )
= $true )
| ! [X1: $i] :
( $true
= ( cP @ cA @ X1 ) ) )
=> ? [X2: $i] :
( ( cP @ X2 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] : ( cP @ X0 @ cB )
| ! [X1: $i] : ( cP @ cA @ X1 ) )
=> ? [X2: $i] : ( cP @ X2 @ X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: $i] : ( cP @ X1 @ cB )
| ! [X0: $i] : ( cP @ cA @ X0 ) )
=> ? [X2: $i] : ( cP @ X2 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: $i] : ( cP @ X1 @ cB )
| ! [X0: $i] : ( cP @ cA @ X0 ) )
=> ? [X2: $i] : ( cP @ X2 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.qKgMKeqkNy/DTF2THF_6359.p',cTHM62) ).
thf(f18,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f7,f14]) ).
thf(f14,plain,
( ! [X0: $i] :
( ( cP @ X0 @ cB )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f13]) ).
thf(f13,definition,
( spl0_2
<=> ! [X0: $i] :
( ( cP @ X0 @ cB )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f15,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f8,f13,f10]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( cP @ cA @ X1 ) )
| ( ( cP @ X0 @ cB )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO083^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n007.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 14:23:08 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.39 ---- Original DTF file ---
% 0.18/0.39 thf(spec,logic,$$dhol).
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 % File : SYO083^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.39 % Domain : Syntactic
% 0.18/0.39 % Problem : TPS problem THM62
% 0.18/0.39 % Version : Especial.
% 0.18/0.39 % English :
% 0.18/0.39
% 0.18/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.39 % Source : [Bro09]
% 0.18/0.39 % Names : tps_0092 [Bro09]
% 0.18/0.39 % : THM62 [TPS]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.18/0.39 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.18/0.39 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 3 ( 3 avg)
% 0.18/0.39 % Number of connectives : 8 ( 0 ~; 1 |; 0 &; 6 @)
% 0.18/0.39 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 6 ( 6 avg)
% 0.18/0.39 % Number of types : 2 ( 0 usr)
% 0.18/0.39 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 3 ( 3 usr; 2 con; 0-2 aty)
% 0.18/0.39 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.18/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.39
% 0.18/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 thf(cP,type,
% 0.18/0.39 cP: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cB,type,
% 0.18/0.39 cB: $i ).
% 0.18/0.39
% 0.18/0.39 thf(cA,type,
% 0.18/0.39 cA: $i ).
% 0.18/0.39
% 0.18/0.39 thf(cTHM62,conjecture,
% 0.18/0.39 ( ( ! [U: $i] : ( cP @ cA @ U )
% 0.18/0.39 | ! [V: $i] : ( cP @ V @ cB ) )
% 0.18/0.39 => ? [X: $i] : ( cP @ X @ X ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 1.54/1.32 ---- Embedded in THF ---
% 1.54/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.32 %%% Generated on Tue Feb 24 14:23:09 EST 2026
% 1.54/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.32 %%% Logic specification used:
% 1.54/1.32 %%% thf(spec, logic, $$dhol).
% 1.54/1.32
% 1.54/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qKgMKeqkNy/DTF2DTF6359.p
% See solution above
% 1.54/1.32 ------------------------
% 1.54/1.33 ---- Cleaned THF ---
% 1.54/1.33 thf(cP,type,
% 1.54/1.33 cP: $i > $i > $o ).
% 1.54/1.33
% 1.54/1.33 thf(cB,type,
% 1.54/1.33 cB: $i ).
% 1.54/1.33
% 1.54/1.33 thf(cA,type,
% 1.54/1.33 cA: $i ).
% 1.54/1.33
% 1.54/1.33 thf(cTHM62,conjecture,
% 1.54/1.33 ( ( ! [U: $i] : ( cP @ cA @ U )
% 1.54/1.33 | ! [V: $i] : ( cP @ V @ cB ) )
% 1.54/1.33 => ? [X: $i] : ( cP @ X @ X ) ) ).
% 1.54/1.33 ------------------------
% 1.54/1.35 % (6463)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6359 for (3000ds/18Mi)
% 1.54/1.35 % (6458)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_6359 for (3000ds/4Mi)
% 1.54/1.35 % (6460)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6359 for (3000ds/2Mi)
% 1.54/1.35 % (6457)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6359 for (3000ds/183Mi)
% 1.54/1.35 % (6459)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_6359 for (3000ds/27Mi)
% 1.54/1.35 % (6461)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_6359 for (3000ds/2Mi)
% 1.54/1.35 % (6461)Instruction limit reached!
% 1.54/1.35 % (6461)------------------------------
% 1.54/1.35 % (6461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.35 % (6461)Termination reason: Unknown
% 1.54/1.35 % (6461)Termination phase: Saturation
% 1.54/1.35
% 1.54/1.35 % (6461)Memory used [KB]: 5500
% 1.54/1.35 % (6461)Time elapsed: 0.003 s
% 1.54/1.35 % (6461)Instructions burned: 2 (million)
% 1.54/1.35 % (6461)------------------------------
% 1.54/1.35 % (6461)------------------------------
% 1.54/1.35 % (6457)First to succeed.
% 1.54/1.35 % (6463)Also succeeded, but the first one will report.
% 1.54/1.35 % (6462)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_6359 for (3000ds/275Mi)
% 1.54/1.35 % (6459)Also succeeded, but the first one will report.
% 1.54/1.35 % (6457)Refutation found. Thanks to Tanya!
% 1.54/1.35 % SZS status Theorem for DTF2THF_6359
% 1.54/1.35 % SZS output start Proof for DTF2THF_6359
% 1.54/1.35 thf(func_def_0, type, cP: $i > $i > $o).
% 1.54/1.35 thf(f22,plain,(
% 1.54/1.35 $false),
% 1.54/1.35 inference(avatar_sat_refutation,[status(thm)],[f15,f18,f21])).
% 1.54/1.35 thf(f21,plain,(
% 1.54/1.35 ~spl0_1),
% 1.54/1.35 inference(avatar_contradiction_clause,[status(thm)],[f20])).
% 1.54/1.35 thf(f20,plain,(
% 1.54/1.35 $false | ~spl0_1),
% 1.54/1.35 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.54/1.35 thf(f19,plain,(
% 1.54/1.35 ($true != $true) | ~spl0_1),
% 1.54/1.35 inference(superposition,[status(thm)],[f7,f11])).
% 1.54/1.35 thf(f11,plain,(
% 1.54/1.35 ( ! [X1 : $i] : (($true = (cP @ cA @ X1))) ) | ~spl0_1),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f10])).
% 1.54/1.35 thf(f10,definition,(
% 1.54/1.35 spl0_1 <=> ! [X1 : $i] : ($true = (cP @ cA @ X1))),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.54/1.35 thf(f7,plain,(
% 1.54/1.35 ( ! [X2 : $i] : (((cP @ X2 @ X2) != $true)) )),
% 1.54/1.35 inference(cnf_transformation,[status(thm)],[f6])).
% 1.54/1.35 thf(f6,plain,(
% 1.54/1.35 (! [X0 : $i] : ((cP @ X0 @ cB) = $true) | ! [X1 : $i] : ($true = (cP @ cA @ X1))) & ! [X2 : $i] : ((cP @ X2 @ X2) != $true)),
% 1.54/1.35 inference(ennf_transformation,[status(thm)],[f5])).
% 1.54/1.35 thf(f5,plain,(
% 1.54/1.35 ~((! [X0 : $i] : ((cP @ X0 @ cB) = $true) | ! [X1 : $i] : ($true = (cP @ cA @ X1))) => ? [X2 : $i] : ((cP @ X2 @ X2) = $true))),
% 1.54/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.54/1.35 thf(f4,plain,(
% 1.54/1.35 ~((! [X0 : $i] : (cP @ X0 @ cB) | ! [X1 : $i] : (cP @ cA @ X1)) => ? [X2 : $i] : (cP @ X2 @ X2))),
% 1.54/1.35 inference(rectify,[status(thm)],[f2])).
% 1.54/1.35 thf(f2,negated_conjecture,(
% 1.54/1.35 ~((! [X1 : $i] : (cP @ X1 @ cB) | ! [X0 : $i] : (cP @ cA @ X0)) => ? [X2 : $i] : (cP @ X2 @ X2))),
% 1.54/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.54/1.35 thf(f1,conjecture,(
% 1.54/1.35 (! [X1 : $i] : (cP @ X1 @ cB) | ! [X0 : $i] : (cP @ cA @ X0)) => ? [X2 : $i] : (cP @ X2 @ X2)),
% 1.54/1.35 file('/export/starexec/sandbox/tmp/tmp.qKgMKeqkNy/DTF2THF_6359.p',cTHM62)).
% 1.54/1.35 thf(f18,plain,(
% 1.54/1.35 ~spl0_2),
% 1.54/1.35 inference(avatar_contradiction_clause,[status(thm)],[f17])).
% 1.54/1.35 thf(f17,plain,(
% 1.54/1.35 $false | ~spl0_2),
% 1.54/1.35 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.54/1.35 thf(f16,plain,(
% 1.54/1.35 ($true != $true) | ~spl0_2),
% 1.54/1.35 inference(superposition,[status(thm)],[f7,f14])).
% 1.54/1.35 thf(f14,plain,(
% 1.54/1.35 ( ! [X0 : $i] : (((cP @ X0 @ cB) = $true)) ) | ~spl0_2),
% 1.54/1.35 inference(avatar_component_clause,[status(thm)],[f13])).
% 1.54/1.35 thf(f13,definition,(
% 1.54/1.35 spl0_2 <=> ! [X0 : $i] : ((cP @ X0 @ cB) = $true)),
% 1.54/1.35 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.54/1.35 thf(f15,plain,(
% 1.54/1.35 spl0_1 | spl0_2),
% 1.54/1.35 inference(avatar_split_clause,[status(thm)],[f8,f13,f10])).
% 1.54/1.35 thf(f8,plain,(
% 1.54/1.35 ( ! [X0 : $i,X1 : $i] : (($true = (cP @ cA @ X1)) | ((cP @ X0 @ cB) = $true)) )),
% 1.54/1.35 inference(cnf_transformation,[status(thm)],[f6])).
% 1.54/1.35 % SZS output end Proof for DTF2THF_6359
% 1.54/1.35 % (6457)------------------------------
% 1.54/1.35 % (6457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.35 % (6457)Termination reason: Refutation
% 1.54/1.35
% 1.54/1.35 % (6457)Memory used [KB]: 5500
% 1.54/1.35 % (6457)Time elapsed: 0.004 s
% 1.54/1.35 % (6457)Instructions burned: 1 (million)
% 1.54/1.35 % (6457)------------------------------
% 1.54/1.35 % (6457)------------------------------
% 1.54/1.35 % (6456)Success in time 0.015 s
%------------------------------------------------------------------------------