%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN064^5 : 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 : n003.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 09:50:28 AM UTC 2026
% Result : Theorem 1.46s 1.29s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 54 ( 10 ~; 0 |; 3 &; 36 @)
% ( 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 : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 16 !; 14 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $i > $o ).
thf(f13,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
$true != $true,
inference(superposition,[status(thm)],[f11,f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( cP @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cP @ sK1 @ sK0 ) )
& ( ( cP @ X0 @ X1 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( cP @ X3 @ X2 ) )
=> ( $true
!= ( cP @ sK1 @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i,X3: $i] :
( $true
!= ( cP @ X3 @ X2 ) )
& ( ( cP @ X0 @ X1 )
= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
! [X1: $i,X0: $i] :
( ? [X3: $i,X2: $i] :
( ( cP @ X2 @ X3 )
!= $true )
& ( ( cP @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i,X1: $i] :
( ( ( cP @ X1 @ X0 )
= $true )
=> ! [X3: $i,X2: $i] :
( ( cP @ X2 @ X3 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i,X1: $i] :
( ( cP @ X1 @ X0 )
=> ! [X2: $i,X3: $i] : ( cP @ X2 @ X3 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X1: $i,X0: $i] :
( ( cP @ X0 @ X1 )
=> ! [X2: $i,X3: $i] : ( cP @ X2 @ X3 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X1: $i,X0: $i] :
( ( cP @ X0 @ X1 )
=> ! [X2: $i,X3: $i] : ( cP @ X2 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.rj7Xu1F9o8/DTF2THF_22011.p',cPELL35) ).
thf(f11,plain,
( $true
!= ( cP @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN064^5 : 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
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 13:50:40 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
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SYN064^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Syntactic
% 0.28/0.46 % Problem : TPS problem PELL35
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.28/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0090 [Bro09]
% 0.28/0.46 % : PELL35 [TPS]
% 0.28/0.46 % : Pelletier 35 [Pel86]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % 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
% 0.28/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.28/0.46 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.28/0.46 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 4 @)
% 0.28/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.28/0.46 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 % :
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(cP,type,
% 0.28/0.46 cP: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cPELL35,conjecture,
% 0.28/0.46 ? [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( cP @ Xx @ Xy )
% 0.28/0.46 => ! [Xx0: $i,Xy0: $i] : ( cP @ Xx0 @ Xy0 ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.46/1.26 ---- Embedded in THF ---
% 1.46/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.26 %%% Generated on Tue Feb 24 13:50:41 EST 2026
% 1.46/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.26 %%% Logic specification used:
% 1.46/1.26 %%% thf(spec, logic, $$dhol).
% 1.46/1.26
% 1.46/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rj7Xu1F9o8/DTF2DTF22011.p
% See solution above
% 1.46/1.26 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.28 thf(cP,type,
% 1.46/1.28 cP: $i > $i > $o ).
% 1.46/1.28
% 1.46/1.28 thf(cPELL35,conjecture,
% 1.46/1.28 ? [Xx: $i,Xy: $i] :
% 1.46/1.28 ( ( cP @ Xx @ Xy )
% 1.46/1.28 => ! [Xx0: $i,Xy0: $i] : ( cP @ Xx0 @ Xy0 ) ) ).
% 1.46/1.28 ------------------------
% 1.46/1.29 % (22118)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22011 for (2999ds/183Mi)
% 1.46/1.29 % (22118)First to succeed.
% 1.46/1.29 % (22123)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_22011 for (2999ds/275Mi)
% 1.46/1.29 % (22123)Also succeeded, but the first one will report.
% 1.46/1.29 % (22118)Refutation found. Thanks to Tanya!
% 1.46/1.29 % SZS status Theorem for DTF2THF_22011
% 1.46/1.29 % SZS output start Proof for DTF2THF_22011
% 1.46/1.29 thf(func_def_0, type, cP: $i > $i > $o).
% 1.46/1.29 thf(f13,plain,(
% 1.46/1.29 $false),
% 1.46/1.29 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.46/1.29 thf(f12,plain,(
% 1.46/1.29 ($true != $true)),
% 1.46/1.29 inference(superposition,[status(thm)],[f11,f10])).
% 1.46/1.29 thf(f10,plain,(
% 1.46/1.29 ( ! [X0 : $i,X1 : $i] : (((cP @ X0 @ X1) = $true)) )),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.29 thf(f9,plain,(
% 1.46/1.29 ! [X0 : $i,X1 : $i] : (($true != (cP @ sK1 @ sK0)) & ((cP @ X0 @ X1) = $true))),
% 1.46/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 1.46/1.29 thf(f8,plain,(
% 1.46/1.29 ? [X2 : $i,X3 : $i] : ($true != (cP @ X3 @ X2)) => ($true != (cP @ sK1 @ sK0))),
% 1.46/1.29 introduced(definition,[],[choice_axiom])).
% 1.46/1.29 thf(f7,plain,(
% 1.46/1.29 ! [X0 : $i,X1 : $i] : (? [X2 : $i,X3 : $i] : ($true != (cP @ X3 @ X2)) & ((cP @ X0 @ X1) = $true))),
% 1.46/1.29 inference(rectify,[status(thm)],[f6])).
% 1.46/1.29 thf(f6,plain,(
% 1.46/1.29 ! [X1 : $i,X0 : $i] : (? [X3 : $i,X2 : $i] : ((cP @ X2 @ X3) != $true) & ((cP @ X1 @ X0) = $true))),
% 1.46/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.46/1.29 thf(f5,plain,(
% 1.46/1.29 ~? [X0 : $i,X1 : $i] : (((cP @ X1 @ X0) = $true) => ! [X3 : $i,X2 : $i] : ((cP @ X2 @ X3) = $true))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.29 thf(f4,plain,(
% 1.46/1.29 ~? [X0 : $i,X1 : $i] : ((cP @ X1 @ X0) => ! [X2 : $i,X3 : $i] : (cP @ X2 @ X3))),
% 1.46/1.29 inference(rectify,[status(thm)],[f2])).
% 1.46/1.29 thf(f2,negated_conjecture,(
% 1.46/1.29 ~? [X1 : $i,X0 : $i] : ((cP @ X0 @ X1) => ! [X2 : $i,X3 : $i] : (cP @ X2 @ X3))),
% 1.46/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.29 thf(f1,conjecture,(
% 1.46/1.29 ? [X1 : $i,X0 : $i] : ((cP @ X0 @ X1) => ! [X2 : $i,X3 : $i] : (cP @ X2 @ X3))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.rj7Xu1F9o8/DTF2THF_22011.p',cPELL35)).
% 1.46/1.29 thf(f11,plain,(
% 1.46/1.29 ($true != (cP @ sK1 @ sK0))),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.29 % SZS output end Proof for DTF2THF_22011
% 1.46/1.29 % (22118)------------------------------
% 1.46/1.29 % (22118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (22118)Termination reason: Refutation
% 1.46/1.29
% 1.46/1.29 % (22118)Memory used [KB]: 5500
% 1.46/1.29 % (22118)Time elapsed: 0.002 s
% 1.46/1.29 % (22118)Instructions burned: 1 (million)
% 1.46/1.29 % (22118)------------------------------
% 1.46/1.29 % (22118)------------------------------
% 1.46/1.29 % (22117)Success in time 0.012 s
%------------------------------------------------------------------------------