%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO082^5 : 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 : n002.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 09:53:20 AM UTC 2026
% Result : Theorem 1.66s 1.42s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 12 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 56 ( 8 ~; 0 |; 4 &; 39 @)
% ( 0 <=>; 5 =>; 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 : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 9 !; 6 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $i > $i > $i ).
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_5,type,
sK0: $i > $i ).
thf(f11,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f9,f10]) ).
thf(f10,plain,
! [X0: $i] :
( ( cP @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i] :
( ( ( cP @ X0 )
= $true )
& ( ( cP @ ( f @ X0 @ ( sK0 @ X0 ) ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( ( cP @ X0 )
= $true )
& ( ( cP @ ( f @ X0 @ X1 ) )
!= $true ) )
=> ( ( ( cP @ X0 )
= $true )
& ( ( cP @ ( f @ X0 @ ( sK0 @ X0 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
! [X0: $i] :
? [X1: $i] :
( ( ( cP @ X0 )
= $true )
& ( ( cP @ ( f @ X0 @ X1 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i] :
! [X1: $i] :
( ( ( cP @ X0 )
= $true )
=> ( ( cP @ ( f @ X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i] :
! [X1: $i] :
( ( cP @ X0 )
=> ( cP @ ( f @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i] :
! [X1: $i] :
( ( cP @ X0 )
=> ( cP @ ( f @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i] :
! [X1: $i] :
( ( cP @ X0 )
=> ( cP @ ( f @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ggziES8l9t/DTF2THF_7187.p',cBAFFLER_VARIANT) ).
thf(f9,plain,
! [X0: $i] :
( ( cP @ ( f @ X0 @ ( sK0 @ X0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO082^5 : 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
% 0.16/0.34 % Computer : n002.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:24:03 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.48 ---- Original DTF file ---
% 0.28/0.49 thf(spec,logic,$$dhol).
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 % File : SYO082^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.49 % Domain : Syntactic
% 0.28/0.49 % Problem : TPS problem BAFFLER-VARIANT
% 0.28/0.49 % Version : Especial.
% 0.28/0.49 % English :
% 0.28/0.49
% 0.28/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.49 % Source : [Bro09]
% 0.28/0.49 % Names : tps_0063 [Bro09]
% 0.28/0.49 % : BAFFLER-VARIANT [TPS]
% 0.28/0.49
% 0.28/0.49 % Status : Theorem
% 0.28/0.49 % 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
% 0.28/0.49 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.28/0.49 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.28/0.49 % Maximal formula atoms : 2 ( 2 avg)
% 0.28/0.49 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 4 @)
% 0.28/0.49 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.49 % Maximal formula depth : 7 ( 7 avg)
% 0.28/0.49 % Number of types : 2 ( 0 usr)
% 0.28/0.49 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.28/0.49 % Number of symbols : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.28/0.49 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.28/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.49
% 0.28/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 thf(f,type,
% 0.28/0.49 f: $i > $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(cP,type,
% 0.28/0.49 cP: $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(cBAFFLER_VARIANT,conjecture,
% 0.28/0.49 ? [Xy: $i] :
% 0.28/0.49 ! [Xx: $i] :
% 0.28/0.49 ( ( cP @ Xy )
% 0.28/0.49 => ( cP @ ( f @ Xy @ Xx ) ) ) ).
% 0.28/0.49
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 ------------------------
% 1.46/1.39 ---- Embedded in THF ---
% 1.46/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.39 %%% Generated on Tue Feb 24 14:24:04 EST 2026
% 1.46/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.39 %%% Logic specification used:
% 1.46/1.39 %%% thf(spec, logic, $$dhol).
% 1.46/1.39
% 1.46/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ggziES8l9t/DTF2DTF7187.p
% See solution above
% 1.46/1.39 ------------------------
% 1.66/1.40 ---- Cleaned THF ---
% 1.66/1.40 thf(f,type,
% 1.66/1.40 f: $i > $i > $i ).
% 1.66/1.40
% 1.66/1.40 thf(cP,type,
% 1.66/1.40 cP: $i > $o ).
% 1.66/1.40
% 1.66/1.40 thf(cBAFFLER_VARIANT,conjecture,
% 1.66/1.40 ? [Xy: $i] :
% 1.66/1.40 ! [Xx: $i] :
% 1.66/1.40 ( ( cP @ Xy )
% 1.66/1.40 => ( cP @ ( f @ Xy @ Xx ) ) ) ).
% 1.66/1.40 ------------------------
% 1.66/1.42 % (7343)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_7187 for (3000ds/4Mi)
% 1.66/1.42 % (7342)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7187 for (3000ds/183Mi)
% 1.66/1.42 % (7344)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_7187 for (3000ds/27Mi)
% 1.66/1.42 % (7345)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7187 for (3000ds/2Mi)
% 1.66/1.42 % (7346)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_7187 for (3000ds/2Mi)
% 1.66/1.42 % (7348)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7187 for (3000ds/18Mi)
% 1.66/1.42 % (7347)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_7187 for (3000ds/275Mi)
% 1.66/1.42 % (7342)First to succeed.
% 1.66/1.42 % (7346)Instruction limit reached!
% 1.66/1.42 % (7346)------------------------------
% 1.66/1.42 % (7346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (7347)Also succeeded, but the first one will report.
% 1.66/1.42 % (7346)Termination reason: Unknown
% 1.66/1.42 % (7346)Termination phase: Saturation
% 1.66/1.42
% 1.66/1.42 % (7346)Memory used [KB]: 5500
% 1.66/1.42 % (7346)Time elapsed: 0.003 s
% 1.66/1.42 % (7346)Instructions burned: 2 (million)
% 1.66/1.42 % (7346)------------------------------
% 1.66/1.42 % (7346)------------------------------
% 1.66/1.42 % (7343)Also succeeded, but the first one will report.
% 1.66/1.42 % (7342)Refutation found. Thanks to Tanya!
% 1.66/1.42 % SZS status Theorem for DTF2THF_7187
% 1.66/1.42 % SZS output start Proof for DTF2THF_7187
% 1.66/1.42 thf(func_def_0, type, f: $i > $i > $i).
% 1.66/1.42 thf(func_def_1, type, cP: $i > $o).
% 1.66/1.42 thf(func_def_5, type, sK0: $i > $i).
% 1.66/1.42 thf(f11,plain,(
% 1.66/1.42 $false),
% 1.66/1.42 inference(subsumption_resolution,[status(thm)],[f9,f10])).
% 1.66/1.42 thf(f10,plain,(
% 1.66/1.42 ( ! [X0 : $i] : (((cP @ X0) = $true)) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f8])).
% 1.66/1.42 thf(f8,plain,(
% 1.66/1.42 ! [X0 : $i] : (((cP @ X0) = $true) & ((cP @ (f @ X0 @ (sK0 @ X0))) != $true))),
% 1.66/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.66/1.42 thf(f7,plain,(
% 1.66/1.42 ! [X0 : $i] : (? [X1 : $i] : (((cP @ X0) = $true) & ((cP @ (f @ X0 @ X1)) != $true)) => (((cP @ X0) = $true) & ((cP @ (f @ X0 @ (sK0 @ X0))) != $true)))),
% 1.66/1.42 introduced(definition,[],[choice_axiom])).
% 1.66/1.42 thf(f6,plain,(
% 1.66/1.42 ! [X0 : $i] : ? [X1 : $i] : (((cP @ X0) = $true) & ((cP @ (f @ X0 @ X1)) != $true))),
% 1.66/1.42 inference(ennf_transformation,[status(thm)],[f5])).
% 1.66/1.42 thf(f5,plain,(
% 1.66/1.42 ~? [X0 : $i] : ! [X1 : $i] : (((cP @ X0) = $true) => ((cP @ (f @ X0 @ X1)) = $true))),
% 1.66/1.42 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.42 thf(f4,plain,(
% 1.66/1.42 ~? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) => (cP @ (f @ X0 @ X1)))),
% 1.66/1.42 inference(rectify,[status(thm)],[f2])).
% 1.66/1.42 thf(f2,negated_conjecture,(
% 1.66/1.42 ~? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) => (cP @ (f @ X0 @ X1)))),
% 1.66/1.42 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.42 thf(f1,conjecture,(
% 1.66/1.42 ? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) => (cP @ (f @ X0 @ X1)))),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.ggziES8l9t/DTF2THF_7187.p',cBAFFLER_VARIANT)).
% 1.66/1.42 thf(f9,plain,(
% 1.66/1.42 ( ! [X0 : $i] : (((cP @ (f @ X0 @ (sK0 @ X0))) != $true)) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f8])).
% 1.66/1.42 % SZS output end Proof for DTF2THF_7187
% 1.66/1.42 % (7342)------------------------------
% 1.66/1.42 % (7342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (7342)Termination reason: Refutation
% 1.66/1.42
% 1.66/1.42 % (7342)Memory used [KB]: 5373
% 1.66/1.42 % (7342)Time elapsed: 0.003 s
% 1.66/1.42 % (7342)Instructions burned: 1 (million)
% 1.66/1.42 % (7342)------------------------------
% 1.66/1.42 % (7342)------------------------------
% 1.66/1.42 % (7341)Success in time 0.017 s
%------------------------------------------------------------------------------