%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN355^5 : 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 : n031.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 09:50:49 AM UTC 2026
% Result : Theorem 1.47s 1.29s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 185 ( 52 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 152 ( 32 ~; 17 |; 19 &; 68 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 ^; 25 !; 4 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $o ).
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_2,type,
cR: $i > $o ).
thf(f20,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f19,f13]) ).
thf(f13,plain,
( $true
!= ( cQ @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 )
= $true )
| ( ( cR @ X0 )
= $true ) )
& ( $true
!= ( cP @ sK0 ) )
& ( $true
!= ( cQ @ sK0 ) )
& ! [X2: $i] :
( ( $true
!= ( cR @ X2 ) )
| ( $true
= ( cP @ X2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X1: $i] :
( ( $true
!= ( cP @ X1 ) )
& ( $true
!= ( cQ @ X1 ) ) )
=> ( ( $true
!= ( cP @ sK0 ) )
& ( $true
!= ( cQ @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 )
= $true )
| ( ( cR @ X0 )
= $true ) )
& ? [X1: $i] :
( ( $true
!= ( cP @ X1 ) )
& ( $true
!= ( cQ @ X1 ) ) )
& ! [X2: $i] :
( ( $true
!= ( cR @ X2 ) )
| ( $true
= ( cP @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X1: $i] :
( ( $true
= ( cQ @ X1 ) )
| ( $true
= ( cR @ X1 ) ) )
& ? [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
& ( $true
!= ( cQ @ X2 ) ) )
& ! [X0: $i] :
( ( ( cR @ X0 )
!= $true )
| ( ( cP @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
& ( $true
!= ( cQ @ X2 ) ) )
& ! [X0: $i] :
( ( ( cR @ X0 )
!= $true )
| ( ( cP @ X0 )
= $true ) )
& ! [X1: $i] :
( ( $true
= ( cQ @ X1 ) )
| ( $true
= ( cR @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
=> ( ( cP @ X0 )
= $true ) )
& ! [X1: $i] :
( ( $true
!= ( cQ @ X1 ) )
=> ( $true
= ( cR @ X1 ) ) ) )
=> ! [X2: $i] :
( ( $true
= ( cQ @ X2 ) )
| ( $true
= ( cP @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
=> ( ( cP @ X0 )
= $true ) )
& ! [X1: $i] :
( ( $true
!= ( cQ @ X1 ) )
=> ( $true
= ( cR @ X1 ) ) ) )
=> ! [X2: $i] :
( ( $true
= ( cQ @ X2 ) )
| ( $true
= ( cP @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( cR @ X0 )
=> ( cP @ X0 ) )
& ! [X1: $i] :
( ~ ( cQ @ X1 )
=> ( cR @ X1 ) ) )
=> ! [X2: $i] :
( ( cP @ X2 )
| ( cQ @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cR @ X0 )
=> ( cP @ X0 ) )
& ! [X0: $i] :
( ~ ( cQ @ X0 )
=> ( cR @ X0 ) ) )
=> ! [X0: $i] :
( ( cP @ X0 )
| ( cQ @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cR @ X0 )
=> ( cP @ X0 ) )
& ! [X0: $i] :
( ~ ( cQ @ X0 )
=> ( cR @ X0 ) ) )
=> ! [X0: $i] :
( ( cP @ X0 )
| ( cQ @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bJ7XcOM27N/DTF2THF_22815.p',cX2106) ).
thf(f19,plain,
( $true
= ( cQ @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true != $true )
| ( $true
= ( cQ @ sK0 ) ) ),
inference(superposition,[status(thm)],[f17,f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( ( cR @ X0 )
= $true )
| ( ( cQ @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f17,plain,
( $true
!= ( cR @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
!= ( cR @ sK0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f14,f12]) ).
thf(f12,plain,
! [X2: $i] :
( ( $true
= ( cP @ X2 ) )
| ( $true
!= ( cR @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f14,plain,
( $true
!= ( cP @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN355^5 : 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
% 0.17/0.34 % Computer : n031.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 13:56:48 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYN355^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : TPS problem X2106
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0120 [Bro09]
% 0.29/0.46 % : X2106 [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % 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 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.29/0.46 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 6 ( 6 avg)
% 0.29/0.46 % Number of connectives : 12 ( 1 ~; 1 |; 1 &; 6 @)
% 0.29/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 3 ( 3 usr; 0 con; 1-1 aty)
% 0.29/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 % :
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(cQ,type,
% 0.29/0.46 cQ: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(cP,type,
% 0.29/0.46 cP: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(cR,type,
% 0.29/0.46 cR: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(cX2106,conjecture,
% 0.29/0.46 ( ( ! [Xx: $i] :
% 0.29/0.46 ( ( cR @ Xx )
% 0.29/0.46 => ( cP @ Xx ) )
% 0.29/0.46 & ! [Xx: $i] :
% 0.29/0.46 ( ~ ( cQ @ Xx )
% 0.29/0.46 => ( cR @ Xx ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( cP @ Xx )
% 0.29/0.46 | ( cQ @ Xx ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.27 %%% Generated on Tue Feb 24 13:56:49 EST 2026
% 1.47/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.27 %%% Logic specification used:
% 1.47/1.27 %%% thf(spec, logic, $$dhol).
% 1.47/1.27
% 1.47/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bJ7XcOM27N/DTF2DTF22815.p
% See solution above
% 1.47/1.27 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.28 thf(cQ,type,
% 1.47/1.28 cQ: $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(cP,type,
% 1.47/1.28 cP: $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(cR,type,
% 1.47/1.28 cR: $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(cX2106,conjecture,
% 1.47/1.28 ( ( ! [Xx: $i] :
% 1.47/1.28 ( ( cR @ Xx )
% 1.47/1.28 => ( cP @ Xx ) )
% 1.47/1.28 & ! [Xx: $i] :
% 1.47/1.28 ( ~ ( cQ @ Xx )
% 1.47/1.28 => ( cR @ Xx ) ) )
% 1.47/1.28 => ! [Xx: $i] :
% 1.47/1.28 ( ( cP @ Xx )
% 1.47/1.28 | ( cQ @ Xx ) ) ) ).
% 1.47/1.28 ------------------------
% 1.47/1.29 % (23091)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22815 for (2999ds/183Mi)
% 1.47/1.29 % (23092)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_22815 for (2999ds/4Mi)
% 1.47/1.29 % (23091)First to succeed.
% 1.47/1.29 % (23091)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_22815
% 1.47/1.29 % SZS output start Proof for DTF2THF_22815
% 1.47/1.29 thf(func_def_0, type, cQ: $i > $o).
% 1.47/1.29 thf(func_def_1, type, cP: $i > $o).
% 1.47/1.29 thf(func_def_2, type, cR: $i > $o).
% 1.47/1.29 thf(f20,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(subsumption_resolution,[status(thm)],[f19,f13])).
% 1.47/1.29 thf(f13,plain,(
% 1.47/1.29 ($true != (cQ @ sK0))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.29 thf(f11,plain,(
% 1.47/1.29 ! [X0 : $i] : (((cQ @ X0) = $true) | ((cR @ X0) = $true)) & (($true != (cP @ sK0)) & ($true != (cQ @ sK0))) & ! [X2 : $i] : (($true != (cR @ X2)) | ($true = (cP @ X2)))),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.47/1.29 thf(f10,plain,(
% 1.47/1.29 ? [X1 : $i] : (($true != (cP @ X1)) & ($true != (cQ @ X1))) => (($true != (cP @ sK0)) & ($true != (cQ @ sK0)))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f9,plain,(
% 1.47/1.29 ! [X0 : $i] : (((cQ @ X0) = $true) | ((cR @ X0) = $true)) & ? [X1 : $i] : (($true != (cP @ X1)) & ($true != (cQ @ X1))) & ! [X2 : $i] : (($true != (cR @ X2)) | ($true = (cP @ X2)))),
% 1.47/1.29 inference(rectify,[status(thm)],[f8])).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 ! [X1 : $i] : (($true = (cQ @ X1)) | ($true = (cR @ X1))) & ? [X2 : $i] : (($true != (cP @ X2)) & ($true != (cQ @ X2))) & ! [X0 : $i] : (((cR @ X0) != $true) | ((cP @ X0) = $true))),
% 1.47/1.29 inference(flattening,[status(thm)],[f7])).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 ? [X2 : $i] : (($true != (cP @ X2)) & ($true != (cQ @ X2))) & (! [X0 : $i] : (((cR @ X0) != $true) | ((cP @ X0) = $true)) & ! [X1 : $i] : (($true = (cQ @ X1)) | ($true = (cR @ X1))))),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f6])).
% 1.47/1.29 thf(f6,plain,(
% 1.47/1.29 ~((! [X0 : $i] : (((cR @ X0) = $true) => ((cP @ X0) = $true)) & ! [X1 : $i] : (($true != (cQ @ X1)) => ($true = (cR @ X1)))) => ! [X2 : $i] : (($true = (cQ @ X2)) | ($true = (cP @ X2))))),
% 1.47/1.29 inference(flattening,[status(thm)],[f5])).
% 1.47/1.29 thf(f5,plain,(
% 1.47/1.29 ~((! [X0 : $i] : (((cR @ X0) = $true) => ((cP @ X0) = $true)) & ! [X1 : $i] : (~($true = (cQ @ X1)) => ($true = (cR @ X1)))) => ! [X2 : $i] : (($true = (cQ @ X2)) | ($true = (cP @ X2))))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.29 thf(f4,plain,(
% 1.47/1.29 ~((! [X0 : $i] : ((cR @ X0) => (cP @ X0)) & ! [X1 : $i] : (~(cQ @ X1) => (cR @ X1))) => ! [X2 : $i] : ((cP @ X2) | (cQ @ X2)))),
% 1.47/1.29 inference(rectify,[status(thm)],[f2])).
% 1.47/1.29 thf(f2,negated_conjecture,(
% 1.47/1.29 ~((! [X0 : $i] : ((cR @ X0) => (cP @ X0)) & ! [X0 : $i] : (~(cQ @ X0) => (cR @ X0))) => ! [X0 : $i] : ((cP @ X0) | (cQ @ X0)))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.29 thf(f1,conjecture,(
% 1.47/1.29 (! [X0 : $i] : ((cR @ X0) => (cP @ X0)) & ! [X0 : $i] : (~(cQ @ X0) => (cR @ X0))) => ! [X0 : $i] : ((cP @ X0) | (cQ @ X0))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.bJ7XcOM27N/DTF2THF_22815.p',cX2106)).
% 1.47/1.29 thf(f19,plain,(
% 1.47/1.29 ($true = (cQ @ sK0))),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.47/1.29 thf(f18,plain,(
% 1.47/1.29 ($true != $true) | ($true = (cQ @ sK0))),
% 1.47/1.29 inference(superposition,[status(thm)],[f17,f15])).
% 1.47/1.29 thf(f15,plain,(
% 1.47/1.29 ( ! [X0 : $i] : (((cR @ X0) = $true) | ((cQ @ X0) = $true)) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.29 thf(f17,plain,(
% 1.47/1.29 ($true != (cR @ sK0))),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.47/1.29 thf(f16,plain,(
% 1.47/1.29 ($true != (cR @ sK0)) | ($true != $true)),
% 1.47/1.29 inference(superposition,[status(thm)],[f14,f12])).
% 1.47/1.29 thf(f12,plain,(
% 1.47/1.29 ( ! [X2 : $i] : (($true = (cP @ X2)) | ($true != (cR @ X2))) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.29 thf(f14,plain,(
% 1.47/1.29 ($true != (cP @ sK0))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.29 % SZS output end Proof for DTF2THF_22815
% 1.47/1.29 % (23091)------------------------------
% 1.47/1.29 % (23091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (23091)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (23091)Memory used [KB]: 5500
% 1.47/1.29 % (23091)Time elapsed: 0.002 s
% 1.47/1.29 % (23091)Instructions burned: 1 (million)
% 1.47/1.29 % (23091)------------------------------
% 1.47/1.29 % (23091)------------------------------
% 1.47/1.29 % (23090)Success in time 0.012 s
%------------------------------------------------------------------------------