%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO093^5 : 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 : 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 09:53:22 AM UTC 2026
% Result : Theorem 1.54s 1.36s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 21 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 87 ( 11 ~; 9 |; 3 &; 59 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 37 !; 7 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $i > $o ).
thf(func_def_4,type,
sK0: $i > $i ).
thf(f17,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
$true != $true,
inference(superposition,[status(thm)],[f11,f15]) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( cP @ X1 @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP @ X1 @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f11,f10]) ).
thf(f10,plain,
! [X2: $i,X3: $i,X4: $i] :
( ( $true
= ( cP @ X2 @ X3 ) )
| ( ( cP @ X4 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( cP @ X0 @ ( sK0 @ X0 ) )
!= $true )
& ! [X2: $i,X3: $i,X4: $i] :
( ( $true
= ( cP @ X2 @ X3 ) )
| ( ( cP @ X4 @ X2 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( cP @ X0 @ X1 )
!= $true )
=> ( ( cP @ X0 @ ( sK0 @ X0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i] :
? [X1: $i] :
( ( cP @ X0 @ X1 )
!= $true )
& ! [X2: $i,X3: $i,X4: $i] :
( ( $true
= ( cP @ X2 @ X3 ) )
| ( ( cP @ X4 @ X2 )
= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X3: $i] :
? [X4: $i] :
( ( cP @ X3 @ X4 )
!= $true )
& ! [X0: $i,X1: $i,X2: $i] :
( ( ( cP @ X0 @ X1 )
= $true )
| ( ( cP @ X2 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( cP @ X0 @ X1 )
= $true )
| ( ( cP @ X2 @ X0 )
= $true ) )
=> ? [X3: $i] :
! [X4: $i] :
( ( cP @ X3 @ X4 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i,X1: $i,X2: $i] :
( ( cP @ X2 @ X0 )
| ( cP @ X0 @ X1 ) )
=> ? [X3: $i] :
! [X4: $i] : ( cP @ X3 @ X4 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: $i,X2: $i,X0: $i] :
( ( cP @ X0 @ X1 )
| ( cP @ X1 @ X2 ) )
=> ? [X3: $i] :
! [X4: $i] : ( cP @ X3 @ X4 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: $i,X2: $i,X0: $i] :
( ( cP @ X0 @ X1 )
| ( cP @ X1 @ X2 ) )
=> ? [X3: $i] :
! [X4: $i] : ( cP @ X3 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Njc1ny9sLv/DTF2THF_18921.p',cTHM63) ).
thf(f11,plain,
! [X0: $i] :
( ( cP @ X0 @ ( sK0 @ X0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO093^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n022.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 14:24:06 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.40 ---- Original DTF file ---
% 0.18/0.40 thf(spec,logic,$$dhol).
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 % File : SYO093^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.40 % Domain : Syntactic
% 0.18/0.40 % Problem : TPS problem THM63
% 0.18/0.40 % Version : Especial.
% 0.18/0.40 % English :
% 0.18/0.40
% 0.18/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.40 % Source : [Bro09]
% 0.18/0.40 % Names : tps_0202 [Bro09]
% 0.18/0.40 % : THM63 [TPS]
% 0.18/0.40
% 0.18/0.40 % Status : Theorem
% 0.18/0.40 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.18/0.40 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.18/0.40 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.18/0.40 % Maximal formula atoms : 3 ( 3 avg)
% 0.18/0.40 % Number of connectives : 8 ( 0 ~; 1 |; 0 &; 6 @)
% 0.18/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.40 % Maximal formula depth : 8 ( 8 avg)
% 0.18/0.40 % Number of types : 2 ( 0 usr)
% 0.18/0.40 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.18/0.40 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.18/0.40 % Number of variables : 5 ( 0 ^; 4 !; 1 ?; 5 :)
% 0.18/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.40
% 0.18/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 thf(cP,type,
% 0.18/0.40 cP: $i > $i > $o ).
% 0.18/0.40
% 0.18/0.40 thf(cTHM63,conjecture,
% 0.18/0.40 ( ! [U: $i,V: $i,W: $i] :
% 0.18/0.40 ( ( cP @ U @ V )
% 0.18/0.40 | ( cP @ V @ W ) )
% 0.18/0.40 => ? [X: $i] :
% 0.18/0.40 ! [Y: $i] : ( cP @ X @ Y ) ) ).
% 0.18/0.40
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 ------------------------
% 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 14:24:07 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/sandbox2/tmp/tmp.Njc1ny9sLv/DTF2DTF18921.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(cTHM63,conjecture,
% 1.54/1.33 ( ! [U: $i,V: $i,W: $i] :
% 1.54/1.33 ( ( cP @ U @ V )
% 1.54/1.33 | ( cP @ V @ W ) )
% 1.54/1.33 => ? [X: $i] :
% 1.54/1.33 ! [Y: $i] : ( cP @ X @ Y ) ) ).
% 1.54/1.33 ------------------------
% 1.54/1.35 % (19020)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_18921 for (3000ds/4Mi)
% 1.54/1.35 % (19019)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18921 for (3000ds/183Mi)
% 1.54/1.35 % (19021)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_18921 for (3000ds/27Mi)
% 1.54/1.35 % (19024)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_18921 for (3000ds/275Mi)
% 1.54/1.35 % (19023)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_18921 for (3000ds/2Mi)
% 1.54/1.35 % (19025)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18921 for (3000ds/18Mi)
% 1.54/1.35 % (19022)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18921 for (3000ds/2Mi)
% 1.54/1.36 % (19024)First to succeed.
% 1.54/1.36 % (19022)Instruction limit reached!
% 1.54/1.36 % (19022)------------------------------
% 1.54/1.36 % (19022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (19022)Termination reason: Unknown
% 1.54/1.36 % (19022)Termination phase: Saturation
% 1.54/1.36
% 1.54/1.36 % (19022)Memory used [KB]: 5500
% 1.54/1.36 % (19022)Time elapsed: 0.004 s
% 1.54/1.36 % (19022)Instructions burned: 2 (million)
% 1.54/1.36 % (19022)------------------------------
% 1.54/1.36 % (19022)------------------------------
% 1.54/1.36 % (19023)Instruction limit reached!
% 1.54/1.36 % (19023)------------------------------
% 1.54/1.36 % (19023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (19023)Termination reason: Unknown
% 1.54/1.36 % (19023)Termination phase: Saturation
% 1.54/1.36
% 1.54/1.36 % (19023)Memory used [KB]: 5500
% 1.54/1.36 % (19023)Time elapsed: 0.004 s
% 1.54/1.36 % (19023)Instructions burned: 3 (million)
% 1.54/1.36 % (19023)------------------------------
% 1.54/1.36 % (19023)------------------------------
% 1.54/1.36 % (19019)Also succeeded, but the first one will report.
% 1.54/1.36 % (19021)Also succeeded, but the first one will report.
% 1.54/1.36 % (19024)Refutation found. Thanks to Tanya!
% 1.54/1.36 % SZS status Theorem for DTF2THF_18921
% 1.54/1.36 % SZS output start Proof for DTF2THF_18921
% 1.54/1.36 thf(func_def_0, type, cP: $i > $i > $o).
% 1.54/1.36 thf(func_def_4, type, sK0: $i > $i).
% 1.54/1.36 thf(f17,plain,(
% 1.54/1.36 $false),
% 1.54/1.36 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.54/1.36 thf(f16,plain,(
% 1.54/1.36 ($true != $true)),
% 1.54/1.36 inference(superposition,[status(thm)],[f11,f15])).
% 1.54/1.36 thf(f15,plain,(
% 1.54/1.36 ( ! [X0 : $i,X1 : $i] : (((cP @ X1 @ X0) = $true)) )),
% 1.54/1.36 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.54/1.36 thf(f12,plain,(
% 1.54/1.36 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((cP @ X1 @ X0) = $true)) )),
% 1.54/1.36 inference(superposition,[status(thm)],[f11,f10])).
% 1.54/1.36 thf(f10,plain,(
% 1.54/1.36 ( ! [X2 : $i,X3 : $i,X4 : $i] : (($true = (cP @ X2 @ X3)) | ((cP @ X4 @ X2) = $true)) )),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.54/1.36 thf(f9,plain,(
% 1.54/1.36 ! [X0 : $i] : ((cP @ X0 @ (sK0 @ X0)) != $true) & ! [X2 : $i,X3 : $i,X4 : $i] : (($true = (cP @ X2 @ X3)) | ((cP @ X4 @ X2) = $true))),
% 1.54/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.54/1.36 thf(f8,plain,(
% 1.54/1.36 ! [X0 : $i] : (? [X1 : $i] : ((cP @ X0 @ X1) != $true) => ((cP @ X0 @ (sK0 @ X0)) != $true))),
% 1.54/1.36 introduced(definition,[],[choice_axiom])).
% 1.54/1.36 thf(f7,plain,(
% 1.54/1.36 ! [X0 : $i] : ? [X1 : $i] : ((cP @ X0 @ X1) != $true) & ! [X2 : $i,X3 : $i,X4 : $i] : (($true = (cP @ X2 @ X3)) | ((cP @ X4 @ X2) = $true))),
% 1.54/1.36 inference(rectify,[status(thm)],[f6])).
% 1.54/1.36 thf(f6,plain,(
% 1.54/1.36 ! [X3 : $i] : ? [X4 : $i] : ((cP @ X3 @ X4) != $true) & ! [X0 : $i,X1 : $i,X2 : $i] : (((cP @ X0 @ X1) = $true) | ((cP @ X2 @ X0) = $true))),
% 1.54/1.36 inference(ennf_transformation,[status(thm)],[f5])).
% 1.54/1.36 thf(f5,plain,(
% 1.54/1.36 ~(! [X0 : $i,X1 : $i,X2 : $i] : (((cP @ X0 @ X1) = $true) | ((cP @ X2 @ X0) = $true)) => ? [X3 : $i] : ! [X4 : $i] : ((cP @ X3 @ X4) = $true))),
% 1.54/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.54/1.36 thf(f4,plain,(
% 1.54/1.36 ~(! [X0 : $i,X1 : $i,X2 : $i] : ((cP @ X2 @ X0) | (cP @ X0 @ X1)) => ? [X3 : $i] : ! [X4 : $i] : (cP @ X3 @ X4))),
% 1.54/1.36 inference(rectify,[status(thm)],[f2])).
% 1.54/1.36 thf(f2,negated_conjecture,(
% 1.54/1.36 ~(! [X1 : $i,X2 : $i,X0 : $i] : ((cP @ X0 @ X1) | (cP @ X1 @ X2)) => ? [X3 : $i] : ! [X4 : $i] : (cP @ X3 @ X4))),
% 1.54/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.54/1.36 thf(f1,conjecture,(
% 1.54/1.36 ! [X1 : $i,X2 : $i,X0 : $i] : ((cP @ X0 @ X1) | (cP @ X1 @ X2)) => ? [X3 : $i] : ! [X4 : $i] : (cP @ X3 @ X4)),
% 1.54/1.36 file('/export/starexec/sandbox2/tmp/tmp.Njc1ny9sLv/DTF2THF_18921.p',cTHM63)).
% 1.54/1.36 thf(f11,plain,(
% 1.54/1.36 ( ! [X0 : $i] : (((cP @ X0 @ (sK0 @ X0)) != $true)) )),
% 1.54/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.54/1.36 % SZS output end Proof for DTF2THF_18921
% 1.54/1.36 % (19024)------------------------------
% 1.54/1.36 % (19024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (19024)Termination reason: Refutation
% 1.54/1.36
% 1.54/1.36 % (19024)Memory used [KB]: 5500
% 1.54/1.36 % (19024)Time elapsed: 0.004 s
% 1.54/1.36 % (19024)Instructions burned: 1 (million)
% 1.54/1.36 % (19024)------------------------------
% 1.54/1.36 % (19024)------------------------------
% 1.54/1.36 % (19018)Success in time 0.017 s
%------------------------------------------------------------------------------