%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO154^5 : 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 : n012.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 09:53:31 AM UTC 2026
% Result : Theorem 1.01s 0.90s
% Output : Refutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 123 ( 32 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 120 ( 17 ~; 8 |; 17 &; 66 @)
% ( 0 <=>; 12 =>; 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 : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 22 !; 4 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cR: $i > $o ).
thf(func_def_1,type,
g: $i > $i ).
thf(func_def_2,type,
cQ: $i > $o ).
thf(func_def_3,type,
f: $i > $i ).
thf(func_def_4,type,
cP: $i > $o ).
thf(f15,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f10,f14]) ).
thf(f14,plain,
! [X1: $i] :
( ( cP @ X1 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f11,f13]) ).
thf(f13,plain,
! [X2: $i] :
( ( cQ @ X2 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f9,f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( cR @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( cR @ X0 )
!= $true )
& ! [X1: $i] :
( ( ( cP @ X1 )
!= $true )
| ( ( cQ @ ( f @ X1 ) )
= $true ) )
& ( ( cP @ a )
= $true )
& ! [X2: $i] :
( ( ( cQ @ X2 )
!= $true )
| ( ( cR @ ( g @ X2 ) )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X2: $i] :
( ( cR @ X2 )
!= $true )
& ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cQ @ ( f @ X0 ) )
= $true ) )
& ( ( cP @ a )
= $true )
& ! [X1: $i] :
( ( ( cQ @ X1 )
!= $true )
| ( ( cR @ ( g @ X1 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i] :
( ( cR @ X2 )
!= $true )
& ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cQ @ ( f @ X0 ) )
= $true ) )
& ! [X1: $i] :
( ( ( cQ @ X1 )
!= $true )
| ( ( cR @ ( g @ X1 ) )
= $true ) )
& ( ( cP @ a )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
=> ( ( cQ @ ( f @ X0 ) )
= $true ) )
& ! [X1: $i] :
( ( ( cQ @ X1 )
= $true )
=> ( ( cR @ ( g @ X1 ) )
= $true ) )
& ( ( cP @ a )
= $true ) )
=> ? [X2: $i] :
( ( cR @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ ( f @ X0 ) ) )
& ! [X1: $i] :
( ( cQ @ X1 )
=> ( cR @ ( g @ X1 ) ) )
& ( cP @ a ) )
=> ? [X2: $i] : ( cR @ X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ ( f @ X0 ) ) )
& ! [X1: $i] :
( ( cQ @ X1 )
=> ( cR @ ( g @ X1 ) ) )
& ( cP @ a ) )
=> ? [X2: $i] : ( cR @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ ( f @ X0 ) ) )
& ! [X1: $i] :
( ( cQ @ X1 )
=> ( cR @ ( g @ X1 ) ) )
& ( cP @ a ) )
=> ? [X2: $i] : ( cR @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.AMNcCXzoNd/DTF2THF_13197.p',cDEMO_TRIV1) ).
thf(f9,plain,
! [X2: $i] :
( ( ( cR @ ( g @ X2 ) )
= $true )
| ( ( cQ @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f11,plain,
! [X1: $i] :
( ( ( cP @ X1 )
!= $true )
| ( ( cQ @ ( f @ X1 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f10,plain,
( ( cP @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SYO154^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 14:24:45 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SYO154^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.32 % Domain : Syntactic
% 0.07/0.32 % Problem : TPS problem from BASIC-FO-THMS
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English :
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bro09]
% 0.07/0.32 % Names : tps_0818 [Bro09]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % 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
% 0.07/0.32 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.07/0.32 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 6 ( 6 avg)
% 0.07/0.32 % Number of connectives : 13 ( 0 ~; 0 |; 2 &; 8 @)
% 0.07/0.32 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 8 ( 8 avg)
% 0.07/0.32 % Number of types : 2 ( 0 usr)
% 0.07/0.32 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 6 ( 6 usr; 1 con; 0-1 aty)
% 0.07/0.32 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.07/0.32 % SPC : TH0_THM_NEQ_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.32 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.32 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.32 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(cR,type,
% 0.07/0.32 cR: $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(g,type,
% 0.07/0.32 g: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(cQ,type,
% 0.07/0.32 cQ: $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(f,type,
% 0.07/0.32 f: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(cP,type,
% 0.07/0.32 cP: $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(a,type,
% 0.07/0.32 a: $i ).
% 0.07/0.32
% 0.07/0.32 thf(cDEMO_TRIV1,conjecture,
% 0.07/0.32 ( ( ( cP @ a )
% 0.07/0.32 & ! [Xx: $i] :
% 0.07/0.32 ( ( cP @ Xx )
% 0.07/0.32 => ( cQ @ ( f @ Xx ) ) )
% 0.07/0.32 & ! [Xy: $i] :
% 0.07/0.32 ( ( cQ @ Xy )
% 0.07/0.32 => ( cR @ ( g @ Xy ) ) ) )
% 0.07/0.32 => ? [Xw: $i] : ( cR @ Xw ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.84/0.88 ---- Embedded in THF ---
% 0.84/0.88 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.84/0.88 %%% Generated on Tue Feb 24 14:24:46 EST 2026
% 0.84/0.88 %%% using '$$dhol' embedding, version 1.3.0.
% 0.84/0.88 %%% Logic specification used:
% 0.84/0.88 %%% thf(spec, logic, $$dhol).
% 0.84/0.88
% 0.84/0.88 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.AMNcCXzoNd/DTF2DTF13197.p
% See solution above
% 0.84/0.88 ------------------------
% 0.84/0.89 ---- Cleaned THF ---
% 0.84/0.89 thf(cR,type,
% 0.84/0.89 cR: $i > $o ).
% 0.84/0.89
% 0.84/0.89 thf(g,type,
% 0.84/0.89 g: $i > $i ).
% 0.84/0.89
% 0.84/0.89 thf(cQ,type,
% 0.84/0.89 cQ: $i > $o ).
% 0.84/0.89
% 0.84/0.89 thf(f,type,
% 0.84/0.89 f: $i > $i ).
% 0.84/0.89
% 0.84/0.89 thf(cP,type,
% 0.84/0.89 cP: $i > $o ).
% 0.84/0.89
% 0.84/0.89 thf(a,type,
% 0.84/0.89 a: $i ).
% 0.84/0.89
% 0.84/0.89 thf(cDEMO_TRIV1,conjecture,
% 0.84/0.89 ( ( ( cP @ a )
% 0.84/0.89 & ! [Xx: $i] :
% 0.84/0.89 ( ( cP @ Xx )
% 0.84/0.89 => ( cQ @ ( f @ Xx ) ) )
% 0.84/0.89 & ! [Xy: $i] :
% 0.84/0.89 ( ( cQ @ Xy )
% 0.84/0.89 => ( cR @ ( g @ Xy ) ) ) )
% 0.84/0.89 => ? [Xw: $i] : ( cR @ Xw ) ) ).
% 0.84/0.89 ------------------------
% 1.01/0.90 % (13462)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13197 for (3000ds/2Mi)
% 1.01/0.90 % (13460)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_13197 for (3000ds/4Mi)
% 1.01/0.90 % (13459)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13197 for (3000ds/183Mi)
% 1.01/0.90 % (13463)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_13197 for (3000ds/2Mi)
% 1.01/0.90 % (13461)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_13197 for (3000ds/27Mi)
% 1.01/0.90 % (13464)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_13197 for (3000ds/275Mi)
% 1.01/0.90 % (13465)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13197 for (3000ds/18Mi)
% 1.01/0.90 % (13464)First to succeed.
% 1.01/0.90 % (13462)Instruction limit reached!
% 1.01/0.90 % (13462)------------------------------
% 1.01/0.90 % (13462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.01/0.90 % (13462)Termination reason: Unknown
% 1.01/0.90 % (13462)Termination phase: Saturation
% 1.01/0.90
% 1.01/0.90 % (13462)Memory used [KB]: 5500
% 1.01/0.90 % (13462)Time elapsed: 0.002 s
% 1.01/0.90 % (13462)Instructions burned: 2 (million)
% 1.01/0.90 % (13462)------------------------------
% 1.01/0.90 % (13462)------------------------------
% 1.01/0.90 % (13463)Instruction limit reached!
% 1.01/0.90 % (13463)------------------------------
% 1.01/0.90 % (13463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.01/0.90 % (13463)Termination reason: Unknown
% 1.01/0.90 % (13463)Termination phase: Saturation
% 1.01/0.90
% 1.01/0.90 % (13463)Memory used [KB]: 5500
% 1.01/0.90 % (13463)Time elapsed: 0.002 s
% 1.01/0.90 % (13463)Instructions burned: 2 (million)
% 1.01/0.90 % (13463)------------------------------
% 1.01/0.90 % (13463)------------------------------
% 1.01/0.90 % (13465)Also succeeded, but the first one will report.
% 1.01/0.90 % (13459)Also succeeded, but the first one will report.
% 1.01/0.90 % (13464)Refutation found. Thanks to Tanya!
% 1.01/0.90 % SZS status Theorem for DTF2THF_13197
% 1.01/0.90 % SZS output start Proof for DTF2THF_13197
% 1.01/0.90 thf(func_def_0, type, cR: $i > $o).
% 1.01/0.90 thf(func_def_1, type, g: $i > $i).
% 1.01/0.90 thf(func_def_2, type, cQ: $i > $o).
% 1.01/0.90 thf(func_def_3, type, f: $i > $i).
% 1.01/0.90 thf(func_def_4, type, cP: $i > $o).
% 1.01/0.90 thf(f15,plain,(
% 1.01/0.90 $false),
% 1.01/0.90 inference(subsumption_resolution,[status(thm)],[f10,f14])).
% 1.01/0.90 thf(f14,plain,(
% 1.01/0.90 ( ! [X1 : $i] : (((cP @ X1) != $true)) )),
% 1.01/0.90 inference(subsumption_resolution,[status(thm)],[f11,f13])).
% 1.01/0.90 thf(f13,plain,(
% 1.01/0.90 ( ! [X2 : $i] : (((cQ @ X2) != $true)) )),
% 1.01/0.90 inference(subsumption_resolution,[status(thm)],[f9,f12])).
% 1.01/0.90 thf(f12,plain,(
% 1.01/0.90 ( ! [X0 : $i] : (((cR @ X0) != $true)) )),
% 1.01/0.90 inference(cnf_transformation,[status(thm)],[f8])).
% 1.01/0.90 thf(f8,plain,(
% 1.01/0.90 ! [X0 : $i] : ((cR @ X0) != $true) & ! [X1 : $i] : (((cP @ X1) != $true) | ((cQ @ (f @ X1)) = $true)) & ((cP @ a) = $true) & ! [X2 : $i] : (((cQ @ X2) != $true) | ((cR @ (g @ X2)) = $true))),
% 1.01/0.90 inference(rectify,[status(thm)],[f7])).
% 1.01/0.90 thf(f7,plain,(
% 1.01/0.90 ! [X2 : $i] : ((cR @ X2) != $true) & ! [X0 : $i] : (((cP @ X0) != $true) | ((cQ @ (f @ X0)) = $true)) & ((cP @ a) = $true) & ! [X1 : $i] : (((cQ @ X1) != $true) | ((cR @ (g @ X1)) = $true))),
% 1.01/0.90 inference(flattening,[status(thm)],[f6])).
% 1.01/0.90 thf(f6,plain,(
% 1.01/0.90 ! [X2 : $i] : ((cR @ X2) != $true) & (! [X0 : $i] : (((cP @ X0) != $true) | ((cQ @ (f @ X0)) = $true)) & ! [X1 : $i] : (((cQ @ X1) != $true) | ((cR @ (g @ X1)) = $true)) & ((cP @ a) = $true))),
% 1.01/0.90 inference(ennf_transformation,[status(thm)],[f5])).
% 1.01/0.90 thf(f5,plain,(
% 1.01/0.90 ~((! [X0 : $i] : (((cP @ X0) = $true) => ((cQ @ (f @ X0)) = $true)) & ! [X1 : $i] : (((cQ @ X1) = $true) => ((cR @ (g @ X1)) = $true)) & ((cP @ a) = $true)) => ? [X2 : $i] : ((cR @ X2) = $true))),
% 1.01/0.90 inference(fool_elimination,[status(thm)],[f4])).
% 1.01/0.90 thf(f4,plain,(
% 1.01/0.90 ~((! [X0 : $i] : ((cP @ X0) => (cQ @ (f @ X0))) & ! [X1 : $i] : ((cQ @ X1) => (cR @ (g @ X1))) & (cP @ a)) => ? [X2 : $i] : (cR @ X2))),
% 1.01/0.90 inference(rectify,[status(thm)],[f2])).
% 1.01/0.90 thf(f2,negated_conjecture,(
% 1.01/0.90 ~((! [X0 : $i] : ((cP @ X0) => (cQ @ (f @ X0))) & ! [X1 : $i] : ((cQ @ X1) => (cR @ (g @ X1))) & (cP @ a)) => ? [X2 : $i] : (cR @ X2))),
% 1.01/0.90 inference(negated_conjecture,[status(cth)],[f1])).
% 1.01/0.90 thf(f1,conjecture,(
% 1.01/0.90 (! [X0 : $i] : ((cP @ X0) => (cQ @ (f @ X0))) & ! [X1 : $i] : ((cQ @ X1) => (cR @ (g @ X1))) & (cP @ a)) => ? [X2 : $i] : (cR @ X2)),
% 1.01/0.90 file('/export/starexec/sandbox/tmp/tmp.AMNcCXzoNd/DTF2THF_13197.p',cDEMO_TRIV1)).
% 1.01/0.90 thf(f9,plain,(
% 1.01/0.90 ( ! [X2 : $i] : (((cR @ (g @ X2)) = $true) | ((cQ @ X2) != $true)) )),
% 1.01/0.90 inference(cnf_transformation,[status(thm)],[f8])).
% 1.01/0.90 thf(f11,plain,(
% 1.01/0.90 ( ! [X1 : $i] : (((cP @ X1) != $true) | ((cQ @ (f @ X1)) = $true)) )),
% 1.01/0.90 inference(cnf_transformation,[status(thm)],[f8])).
% 1.01/0.90 thf(f10,plain,(
% 1.01/0.90 ((cP @ a) = $true)),
% 1.01/0.90 inference(cnf_transformation,[status(thm)],[f8])).
% 1.01/0.90 % SZS output end Proof for DTF2THF_13197
% 1.01/0.90 % (13464)------------------------------
% 1.01/0.90 % (13464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.01/0.90 % (13464)Termination reason: Refutation
% 1.01/0.90
% 1.01/0.90 % (13464)Memory used [KB]: 5373
% 1.01/0.90 % (13464)Time elapsed: 0.002 s
% 1.01/0.90 % (13464)Instructions burned: 1 (million)
% 1.01/0.90 % (13464)------------------------------
% 1.01/0.90 % (13464)------------------------------
% 1.01/0.90 % (13458)Success in time 0.01 s
%------------------------------------------------------------------------------