%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO291^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.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 09:53:52 AM UTC 2026
% Result : Theorem 1.61s 1.37s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 11 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 48 ( 6 ~; 2 |; 9 &; 27 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 7 ( 1 ^; 6 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cQ: $i > $o ).
thf(func_def_3,type,
f: $i > $i ).
thf(func_def_4,type,
cR: $i > $o ).
thf(func_def_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f26,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
$false = $true,
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( ^ [Y0: $i] : $false
@ y ) ),
inference(primitive_instantiation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i > $o] :
( ( X0 @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( ( cQ @ y )
!= $true )
| ( ( cR @ ( f @ x ) )
!= $true )
| ( ( cR @ x )
!= $true ) )
& ! [X0: $i > $o] :
( ( X0 @ y )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i > $o] :
( ( X0 @ y )
= $true )
=> ( ( ( cQ @ y )
= $true )
& ( ( cR @ x )
= $true )
& ( ( cR @ ( f @ x ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o] : ( X0 @ y )
=> ( ( cR @ ( f @ x ) )
& ( cR @ x )
& ( cQ @ y ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i > $o] : ( X0 @ y )
=> ( ( cR @ ( f @ x ) )
& ( cR @ x )
& ( cQ @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i > $o] : ( X0 @ y )
=> ( ( cR @ ( f @ x ) )
& ( cR @ x )
& ( cQ @ y ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p8gQyRggLi/DTF2THF_23965.p',cTEST3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO291^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n028.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 14:27:42 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SYO291^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.47 % Domain : Syntactic
% 0.31/0.47 % Problem : TPS problem from BASIC-HO-THMS
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English :
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Bro09]
% 0.31/0.47 % Names : tps_0697 [Bro09]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.00 v4.0.0
% 0.31/0.47 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.31/0.47 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.31/0.47 % Number of connectives : 8 ( 0 ~; 0 |; 2 &; 5 @)
% 0.31/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 6 ( 6 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 5 ( 5 usr; 2 con; 0-1 aty)
% 0.31/0.47 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.31/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(y,type,
% 0.31/0.47 y: $i ).
% 0.31/0.47
% 0.31/0.47 thf(cQ,type,
% 0.31/0.47 cQ: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(x,type,
% 0.31/0.47 x: $i ).
% 0.31/0.47
% 0.31/0.47 thf(f,type,
% 0.31/0.47 f: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(cR,type,
% 0.31/0.47 cR: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(cTEST3,conjecture,
% 0.31/0.47 ( ! [Xp: $i > $o] : ( Xp @ y )
% 0.31/0.47 => ( ( cR @ x )
% 0.31/0.47 & ( cR @ ( f @ x ) )
% 0.31/0.47 & ( cQ @ y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.61/1.34 ---- Embedded in THF ---
% 1.61/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.34 %%% Generated on Tue Feb 24 14:27:43 EST 2026
% 1.61/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.34 %%% Logic specification used:
% 1.61/1.34 %%% thf(spec, logic, $$dhol).
% 1.61/1.34
% 1.61/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.p8gQyRggLi/DTF2DTF23965.p
% See solution above
% 1.61/1.34 ------------------------
% 1.61/1.35 ---- Cleaned THF ---
% 1.61/1.35 thf(y,type,
% 1.61/1.35 y: $i ).
% 1.61/1.35
% 1.61/1.35 thf(cQ,type,
% 1.61/1.35 cQ: $i > $o ).
% 1.61/1.35
% 1.61/1.35 thf(x,type,
% 1.61/1.35 x: $i ).
% 1.61/1.35
% 1.61/1.35 thf(f,type,
% 1.61/1.35 f: $i > $i ).
% 1.61/1.35
% 1.61/1.35 thf(cR,type,
% 1.61/1.35 cR: $i > $o ).
% 1.61/1.35
% 1.61/1.35 thf(cTEST3,conjecture,
% 1.61/1.35 ( ! [Xp: $i > $o] : ( Xp @ y )
% 1.61/1.35 => ( ( cR @ x )
% 1.61/1.35 & ( cR @ ( f @ x ) )
% 1.61/1.35 & ( cQ @ y ) ) ) ).
% 1.61/1.35 ------------------------
% 1.61/1.36 % (24129)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23965 for (2999ds/2Mi)
% 1.61/1.36 % (24129)Instruction limit reached!
% 1.61/1.36 % (24129)------------------------------
% 1.61/1.36 % (24129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.36 % (24129)Termination reason: Unknown
% 1.61/1.36 % (24129)Termination phase: Saturation
% 1.61/1.36
% 1.61/1.36 % (24129)Memory used [KB]: 5500
% 1.61/1.36 % (24129)Time elapsed: 0.002 s
% 1.61/1.36 % (24129)Instructions burned: 2 (million)
% 1.61/1.36 % (24129)------------------------------
% 1.61/1.36 % (24129)------------------------------
% 1.61/1.37 % (24126)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23965 for (2999ds/183Mi)
% 1.61/1.37 % (24127)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_23965 for (2999ds/4Mi)
% 1.61/1.37 % (24128)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_23965 for (2999ds/27Mi)
% 1.61/1.37 % (24130)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_23965 for (2999ds/2Mi)
% 1.61/1.37 % (24131)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_23965 for (2999ds/275Mi)
% 1.61/1.37 % (24132)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23965 for (2999ds/18Mi)
% 1.61/1.37 % (24126)First to succeed.
% 1.61/1.37 % (24128)Refutation not found, incomplete strategy
% 1.61/1.37 % (24128)------------------------------
% 1.61/1.37 % (24128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.37 % (24128)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.37
% 1.61/1.37
% 1.61/1.37 % (24128)Memory used [KB]: 5500
% 1.61/1.37 % (24128)Time elapsed: 0.003 s
% 1.61/1.37 % (24128)Instructions burned: 1 (million)
% 1.61/1.37 % (24128)------------------------------
% 1.61/1.37 % (24128)------------------------------
% 1.61/1.37 % (24130)Instruction limit reached!
% 1.61/1.37 % (24130)------------------------------
% 1.61/1.37 % (24130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.37 % (24130)Termination reason: Unknown
% 1.61/1.37 % (24130)Termination phase: Saturation
% 1.61/1.37
% 1.61/1.37 % (24130)Memory used [KB]: 5500
% 1.61/1.37 % (24130)Time elapsed: 0.004 s
% 1.61/1.37 % (24130)Instructions burned: 2 (million)
% 1.61/1.37 % (24130)------------------------------
% 1.61/1.37 % (24130)------------------------------
% 1.61/1.37 % (24133)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23965 for (2999ds/3Mi)
% 1.61/1.37 % (24131)Also succeeded, but the first one will report.
% 1.61/1.37 % (24126)Refutation found. Thanks to Tanya!
% 1.61/1.37 % SZS status Theorem for DTF2THF_23965
% 1.61/1.37 % SZS output start Proof for DTF2THF_23965
% 1.61/1.37 thf(func_def_1, type, cQ: $i > $o).
% 1.61/1.37 thf(func_def_3, type, f: $i > $i).
% 1.61/1.37 thf(func_def_4, type, cR: $i > $o).
% 1.61/1.37 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.61/1.37 thf(f26,plain,(
% 1.61/1.37 $false),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.61/1.37 thf(f25,plain,(
% 1.61/1.37 ($false = $true)),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.61/1.37 thf(f20,plain,(
% 1.61/1.37 ($true = ((^[Y0 : $i]: ($false)) @ y))),
% 1.61/1.37 inference(primitive_instantiation,[status(thm)],[f7])).
% 1.61/1.37 thf(f7,plain,(
% 1.61/1.37 ( ! [X0 : $i > $o] : (((X0 @ y) = $true)) )),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f6])).
% 1.61/1.37 thf(f6,plain,(
% 1.61/1.37 (((cQ @ y) != $true) | ((cR @ (f @ x)) != $true) | ((cR @ x) != $true)) & ! [X0 : $i > $o] : ((X0 @ y) = $true)),
% 1.61/1.37 inference(ennf_transformation,[status(thm)],[f5])).
% 1.61/1.37 thf(f5,plain,(
% 1.61/1.37 ~(! [X0 : $i > $o] : ((X0 @ y) = $true) => (((cQ @ y) = $true) & ((cR @ x) = $true) & ((cR @ (f @ x)) = $true)))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f4])).
% 1.61/1.37 thf(f4,plain,(
% 1.61/1.37 ~(! [X0 : $i > $o] : (X0 @ y) => ((cR @ (f @ x)) & (cR @ x) & (cQ @ y)))),
% 1.61/1.37 inference(rectify,[status(thm)],[f2])).
% 1.61/1.37 thf(f2,negated_conjecture,(
% 1.61/1.37 ~(! [X0 : $i > $o] : (X0 @ y) => ((cR @ (f @ x)) & (cR @ x) & (cQ @ y)))),
% 1.61/1.37 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.37 thf(f1,conjecture,(
% 1.61/1.37 ! [X0 : $i > $o] : (X0 @ y) => ((cR @ (f @ x)) & (cR @ x) & (cQ @ y))),
% 1.61/1.37 file('/export/starexec/sandbox2/tmp/tmp.p8gQyRggLi/DTF2THF_23965.p',cTEST3)).
% 1.61/1.37 % SZS output end Proof for DTF2THF_23965
% 1.61/1.37 % (24126)------------------------------
% 1.61/1.37 % (24126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.37 % (24126)Termination reason: Refutation
% 1.61/1.37
% 1.61/1.37 % (24126)Memory used [KB]: 5500
% 1.61/1.37 % (24126)Time elapsed: 0.005 s
% 1.61/1.37 % (24126)Instructions burned: 1 (million)
% 1.61/1.37 % (24126)------------------------------
% 1.61/1.37 % (24126)------------------------------
% 1.61/1.37 % (24125)Success in time 0.021 s
%------------------------------------------------------------------------------