%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN049^5 : 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 : n016.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 09:50:25 AM UTC 2026
% Result : Theorem 0.23s 1.33s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 30 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 94 ( 17 ~; 6 |; 10 &; 48 @)
% ( 0 <=>; 13 =>; 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 : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 16 !; 10 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $o ).
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_5,type,
sK0: $i > $i ).
thf(func_def_6,type,
sK1: $i > $i ).
thf(f15,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
$true != $true,
inference(superposition,[status(thm)],[f13,f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( cP @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i] :
( ( ( cP @ X0 )
= $true )
& ( ( ( cP @ ( sK1 @ X0 ) )
!= $true )
| ( ( cQ @ ( sK0 @ X0 ) )
= $true ) )
& ( ( cQ @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i] :
( ? [X1: $i,X2: $i] :
( ( ( cP @ X0 )
= $true )
& ( ( ( cP @ X2 )
!= $true )
| ( ( cQ @ X1 )
= $true ) )
& ( ( cQ @ X0 )
!= $true ) )
=> ( ( ( cP @ X0 )
= $true )
& ( ( ( cP @ ( sK1 @ X0 ) )
!= $true )
| ( ( cQ @ ( sK0 @ X0 ) )
= $true ) )
& ( ( cQ @ X0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
! [X0: $i] :
? [X1: $i,X2: $i] :
( ( ( cP @ X0 )
= $true )
& ( ( ( cP @ X2 )
!= $true )
| ( ( cQ @ X1 )
= $true ) )
& ( ( cQ @ X0 )
!= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i] :
? [X1: $i,X2: $i] :
( ( ( cQ @ X0 )
!= $true )
& ( ( cP @ X0 )
= $true )
& ( ( ( cP @ X2 )
!= $true )
| ( ( cQ @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i] :
! [X1: $i,X2: $i] :
( ( ( ( cP @ X2 )
= $true )
=> ( ( cQ @ X1 )
= $true ) )
=> ( ( ( cP @ X0 )
= $true )
=> ( ( cQ @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i] :
! [X1: $i,X2: $i] :
( ( ( cP @ X2 )
=> ( cQ @ X1 ) )
=> ( ( cP @ X0 )
=> ( cQ @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i] :
! [X2: $i,X1: $i] :
( ( ( cP @ X1 )
=> ( cQ @ X2 ) )
=> ( ( cP @ X0 )
=> ( cQ @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i] :
! [X2: $i,X1: $i] :
( ( ( cP @ X1 )
=> ( cQ @ X2 ) )
=> ( ( cP @ X0 )
=> ( cQ @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XMq2pOWeVF/DTF2THF_25211.p',cPELL19) ).
thf(f13,plain,
! [X0: $i] :
( ( cP @ ( sK1 @ X0 ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f11,f10]) ).
thf(f10,plain,
! [X0: $i] :
( ( cQ @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
! [X0: $i] :
( ( ( cP @ ( sK1 @ X0 ) )
!= $true )
| ( ( cQ @ ( sK0 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYN049^5 : 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 : n016.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 13:51:06 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
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SYN049^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.39 % Domain : Syntactic
% 0.17/0.39 % Problem : TPS problem PELL19
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English :
% 0.17/0.39
% 0.17/0.39 % Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.17/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Bro09]
% 0.17/0.39 % Names : tps_0188 [Bro09]
% 0.17/0.39 % : PELL19 [TPS]
% 0.17/0.39 % : Pelletier 19 [Pel86]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % 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
% 0.17/0.39 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.17/0.39 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 4 ( 4 avg)
% 0.17/0.39 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% 0.17/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 7 ( 7 avg)
% 0.17/0.39 % Number of types : 2 ( 0 usr)
% 0.17/0.39 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.17/0.39 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.17/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.39 % :
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(cQ,type,
% 0.17/0.39 cQ: $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(cP,type,
% 0.17/0.39 cP: $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(cPELL19,conjecture,
% 0.17/0.39 ? [Xx: $i] :
% 0.17/0.39 ! [Xy: $i,Xz: $i] :
% 0.17/0.39 ( ( ( cP @ Xy )
% 0.17/0.39 => ( cQ @ Xz ) )
% 0.17/0.39 => ( ( cP @ Xx )
% 0.17/0.39 => ( cQ @ Xx ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 0.23/1.30 ---- Embedded in THF ---
% 0.23/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.23/1.30 %%% Generated on Tue Feb 24 13:51:06 EST 2026
% 0.23/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.23/1.30 %%% Logic specification used:
% 0.23/1.30 %%% thf(spec, logic, $$dhol).
% 0.23/1.30
% 0.23/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.XMq2pOWeVF/DTF2DTF25211.p
% See solution above
% 0.23/1.30 ------------------------
% 0.23/1.31 ---- Cleaned THF ---
% 0.23/1.31 thf(cQ,type,
% 0.23/1.31 cQ: $i > $o ).
% 0.23/1.31
% 0.23/1.31 thf(cP,type,
% 0.23/1.31 cP: $i > $o ).
% 0.23/1.31
% 0.23/1.31 thf(cPELL19,conjecture,
% 0.23/1.31 ? [Xx: $i] :
% 0.23/1.31 ! [Xy: $i,Xz: $i] :
% 0.23/1.31 ( ( ( cP @ Xy )
% 0.23/1.31 => ( cQ @ Xz ) )
% 0.23/1.31 => ( ( cP @ Xx )
% 0.23/1.31 => ( cQ @ Xx ) ) ) ).
% 0.23/1.31 ------------------------
% 0.23/1.33 % (25309)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_25211 for (3000ds/4Mi)
% 0.23/1.33 % (25311)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25211 for (3000ds/2Mi)
% 0.23/1.33 % (25308)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25211 for (3000ds/183Mi)
% 0.23/1.33 % (25310)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_25211 for (3000ds/27Mi)
% 0.23/1.33 % (25312)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_25211 for (3000ds/2Mi)
% 0.23/1.33 % (25313)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_25211 for (3000ds/275Mi)
% 0.23/1.33 % (25314)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25211 for (3000ds/18Mi)
% 0.23/1.33 % (25312)Instruction limit reached!
% 0.23/1.33 % (25312)------------------------------
% 0.23/1.33 % (25312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.23/1.33 % (25312)Termination reason: Unknown
% 0.23/1.33 % (25312)Termination phase: Saturation
% 0.23/1.33
% 0.23/1.33 % (25312)Memory used [KB]: 5500
% 0.23/1.33 % (25312)Time elapsed: 0.003 s
% 0.23/1.33 % (25312)Instructions burned: 2 (million)
% 0.23/1.33 % (25312)------------------------------
% 0.23/1.33 % (25312)------------------------------
% 0.23/1.33 % (25313)First to succeed.
% 0.23/1.33 % (25314)Also succeeded, but the first one will report.
% 0.23/1.33 % (25309)Also succeeded, but the first one will report.
% 0.23/1.33 % (25313)Refutation found. Thanks to Tanya!
% 0.23/1.33 % SZS status Theorem for DTF2THF_25211
% 0.23/1.33 % SZS output start Proof for DTF2THF_25211
% 0.23/1.33 thf(func_def_0, type, cQ: $i > $o).
% 0.23/1.33 thf(func_def_1, type, cP: $i > $o).
% 0.23/1.33 thf(func_def_5, type, sK0: $i > $i).
% 0.23/1.33 thf(func_def_6, type, sK1: $i > $i).
% 0.23/1.33 thf(f15,plain,(
% 0.23/1.33 $false),
% 0.23/1.33 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 0.23/1.33 thf(f14,plain,(
% 0.23/1.33 ($true != $true)),
% 0.23/1.33 inference(superposition,[status(thm)],[f13,f12])).
% 0.23/1.33 thf(f12,plain,(
% 0.23/1.33 ( ! [X0 : $i] : (((cP @ X0) = $true)) )),
% 0.23/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 0.23/1.33 thf(f9,plain,(
% 0.23/1.33 ! [X0 : $i] : (((cP @ X0) = $true) & (((cP @ (sK1 @ X0)) != $true) | ((cQ @ (sK0 @ X0)) = $true)) & ((cQ @ X0) != $true))),
% 0.23/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 0.23/1.33 thf(f8,plain,(
% 0.23/1.33 ! [X0 : $i] : (? [X1 : $i,X2 : $i] : (((cP @ X0) = $true) & (((cP @ X2) != $true) | ((cQ @ X1) = $true)) & ((cQ @ X0) != $true)) => (((cP @ X0) = $true) & (((cP @ (sK1 @ X0)) != $true) | ((cQ @ (sK0 @ X0)) = $true)) & ((cQ @ X0) != $true)))),
% 0.23/1.33 introduced(definition,[],[choice_axiom])).
% 0.23/1.33 thf(f7,plain,(
% 0.23/1.33 ! [X0 : $i] : ? [X1 : $i,X2 : $i] : (((cP @ X0) = $true) & (((cP @ X2) != $true) | ((cQ @ X1) = $true)) & ((cQ @ X0) != $true))),
% 0.23/1.33 inference(flattening,[status(thm)],[f6])).
% 0.23/1.33 thf(f6,plain,(
% 0.23/1.33 ! [X0 : $i] : ? [X1 : $i,X2 : $i] : ((((cQ @ X0) != $true) & ((cP @ X0) = $true)) & (((cP @ X2) != $true) | ((cQ @ X1) = $true)))),
% 0.23/1.33 inference(ennf_transformation,[status(thm)],[f5])).
% 0.23/1.33 thf(f5,plain,(
% 0.23/1.33 ~? [X0 : $i] : ! [X1 : $i,X2 : $i] : ((((cP @ X2) = $true) => ((cQ @ X1) = $true)) => (((cP @ X0) = $true) => ((cQ @ X0) = $true)))),
% 0.23/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 0.23/1.33 thf(f4,plain,(
% 0.23/1.33 ~? [X0 : $i] : ! [X1 : $i,X2 : $i] : (((cP @ X2) => (cQ @ X1)) => ((cP @ X0) => (cQ @ X0)))),
% 0.23/1.33 inference(rectify,[status(thm)],[f2])).
% 0.23/1.33 thf(f2,negated_conjecture,(
% 0.23/1.33 ~? [X0 : $i] : ! [X2 : $i,X1 : $i] : (((cP @ X1) => (cQ @ X2)) => ((cP @ X0) => (cQ @ X0)))),
% 0.23/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/1.33 thf(f1,conjecture,(
% 0.23/1.33 ? [X0 : $i] : ! [X2 : $i,X1 : $i] : (((cP @ X1) => (cQ @ X2)) => ((cP @ X0) => (cQ @ X0)))),
% 0.23/1.33 file('/export/starexec/sandbox/tmp/tmp.XMq2pOWeVF/DTF2THF_25211.p',cPELL19)).
% 0.23/1.33 thf(f13,plain,(
% 0.23/1.33 ( ! [X0 : $i] : (((cP @ (sK1 @ X0)) != $true)) )),
% 0.23/1.33 inference(subsumption_resolution,[status(thm)],[f11,f10])).
% 0.23/1.33 thf(f10,plain,(
% 0.23/1.33 ( ! [X0 : $i] : (((cQ @ X0) != $true)) )),
% 0.23/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 0.23/1.33 thf(f11,plain,(
% 0.23/1.33 ( ! [X0 : $i] : (((cP @ (sK1 @ X0)) != $true) | ((cQ @ (sK0 @ X0)) = $true)) )),
% 0.23/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 0.23/1.33 % SZS output end Proof for DTF2THF_25211
% 0.23/1.33 % (25313)------------------------------
% 0.23/1.33 % (25313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.23/1.33 % (25313)Termination reason: Refutation
% 0.23/1.33
% 0.23/1.33 % (25313)Memory used [KB]: 5500
% 0.23/1.33 % (25313)Time elapsed: 0.003 s
% 0.23/1.33 % (25313)Instructions burned: 2 (million)
% 0.23/1.33 % (25313)------------------------------
% 0.23/1.33 % (25313)------------------------------
% 0.23/1.33 % (25307)Success in time 0.018 s
%------------------------------------------------------------------------------