%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO257^5 : 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 : n018.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 09:53:47 AM UTC 2026
% Result : Theorem 1.47s 1.28s
% Output : Refutation 1.47s
% 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 : 73 ( 21 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 125 ( 10 ~; 0 |; 14 &; 96 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 0 ^; 30 !; 7 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
h: $i > $i ).
thf(func_def_1,type,
g: $i > $i ).
thf(func_def_2,type,
cP: $i > $i > $o ).
thf(func_def_6,type,
sK0: $i > $i ).
thf(func_def_8,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f19,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
$true != $true,
inference(superposition,[status(thm)],[f10,f12]) ).
thf(f12,plain,
! [X2: $i > $i,X3: $i,X0: $i] :
( ( cP @ X3 @ ( X2 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i] :
( ! [X2: $i > $i,X3: $i] :
( ( ( cP @ X3 @ ( X2 @ X0 ) )
= $true )
& ( ( cP @ X0 @ ( sK0 @ X0 ) )
= $true ) )
& ( $true
!= ( cP @ ( sK0 @ X0 ) @ ( g @ ( h @ ( sK0 @ X0 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i] :
( ? [X1: $i] :
( ! [X2: $i > $i,X3: $i] :
( ( ( cP @ X3 @ ( X2 @ X0 ) )
= $true )
& ( ( cP @ X0 @ X1 )
= $true ) )
& ( ( cP @ X1 @ ( g @ ( h @ X1 ) ) )
!= $true ) )
=> ( ! [X3: $i,X2: $i > $i] :
( ( ( cP @ X3 @ ( X2 @ X0 ) )
= $true )
& ( ( cP @ X0 @ ( sK0 @ X0 ) )
= $true ) )
& ( $true
!= ( cP @ ( sK0 @ X0 ) @ ( g @ ( h @ ( sK0 @ X0 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
! [X0: $i] :
? [X1: $i] :
( ! [X2: $i > $i,X3: $i] :
( ( ( cP @ X3 @ ( X2 @ X0 ) )
= $true )
& ( ( cP @ X0 @ X1 )
= $true ) )
& ( ( cP @ X1 @ ( g @ ( h @ X1 ) ) )
!= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i] :
? [X1: $i] :
( ! [X3: $i > $i,X2: $i] :
( ( $true
= ( cP @ X2 @ ( X3 @ X0 ) ) )
& ( ( cP @ X0 @ X1 )
= $true ) )
& ( ( cP @ X1 @ ( g @ ( h @ X1 ) ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i] :
! [X1: $i] :
( ! [X3: $i > $i,X2: $i] :
( ( $true
= ( cP @ X2 @ ( X3 @ X0 ) ) )
& ( ( cP @ X0 @ X1 )
= $true ) )
=> ( ( cP @ X1 @ ( g @ ( h @ X1 ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i] :
! [X1: $i] :
( ! [X2: $i,X3: $i > $i] :
( ( cP @ X2 @ ( X3 @ X0 ) )
& ( cP @ X0 @ X1 ) )
=> ( cP @ X1 @ ( g @ ( h @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i] :
! [X1: $i] :
( ! [X3: $i,X2: $i > $i] :
( ( cP @ X3 @ ( X2 @ X0 ) )
& ( cP @ X0 @ X1 ) )
=> ( cP @ X1 @ ( g @ ( h @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i] :
! [X1: $i] :
( ! [X3: $i,X2: $i > $i] :
( ( cP @ X3 @ ( X2 @ X0 ) )
& ( cP @ X0 @ X1 ) )
=> ( cP @ X1 @ ( g @ ( h @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nfxcw9oHF1/DTF2THF_5004.p',cTHM84) ).
thf(f10,plain,
! [X0: $i] :
( $true
!= ( cP @ ( sK0 @ X0 ) @ ( g @ ( h @ ( sK0 @ X0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO257^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n018.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 14:26:46 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
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SYO257^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Syntactic
% 0.28/0.46 % Problem : TPS problem THM84
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0113 [Bro09]
% 0.28/0.46 % : THM84 [TPS]
% 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, 0.17 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 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.28/0.46 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.28/0.46 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 9 @)
% 0.28/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.28/0.46 % Number of variables : 4 ( 0 ^; 3 !; 1 ?; 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 thf(h,type,
% 0.28/0.46 h: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(g,type,
% 0.28/0.46 g: $i > $i ).
% 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(cTHM84,conjecture,
% 0.28/0.46 ? [Xx: $i] :
% 0.28/0.46 ! [Xy: $i] :
% 0.28/0.46 ( ! [Xf: $i > $i,Xz: $i] :
% 0.28/0.46 ( ( cP @ Xz @ ( Xf @ Xx ) )
% 0.28/0.46 & ( cP @ Xx @ Xy ) )
% 0.28/0.46 => ( cP @ Xy @ ( g @ ( h @ Xy ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.47/1.25 ---- Embedded in THF ---
% 1.47/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.25 %%% Generated on Tue Feb 24 14:26:47 EST 2026
% 1.47/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.25 %%% Logic specification used:
% 1.47/1.25 %%% thf(spec, logic, $$dhol).
% 1.47/1.25
% 1.47/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.nfxcw9oHF1/DTF2DTF5004.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.26 ---- Cleaned THF ---
% 1.47/1.26 thf(h,type,
% 1.47/1.26 h: $i > $i ).
% 1.47/1.26
% 1.47/1.26 thf(g,type,
% 1.47/1.26 g: $i > $i ).
% 1.47/1.26
% 1.47/1.26 thf(cP,type,
% 1.47/1.26 cP: $i > $i > $o ).
% 1.47/1.26
% 1.47/1.26 thf(cTHM84,conjecture,
% 1.47/1.26 ? [Xx: $i] :
% 1.47/1.26 ! [Xy: $i] :
% 1.47/1.26 ( ! [Xf: $i > $i,Xz: $i] :
% 1.47/1.26 ( ( cP @ Xz @ ( Xf @ Xx ) )
% 1.47/1.26 & ( cP @ Xx @ Xy ) )
% 1.47/1.26 => ( cP @ Xy @ ( g @ ( h @ Xy ) ) ) ) ).
% 1.47/1.26 ------------------------
% 1.47/1.27 % (5280)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_5004 for (2999ds/4Mi)
% 1.47/1.27 % (5285)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5004 for (2999ds/18Mi)
% 1.47/1.27 % (5280)First to succeed.
% 1.47/1.28 % (5285)Also succeeded, but the first one will report.
% 1.47/1.28 % (5280)Refutation found. Thanks to Tanya!
% 1.47/1.28 % SZS status Theorem for DTF2THF_5004
% 1.47/1.28 % SZS output start Proof for DTF2THF_5004
% 1.47/1.28 thf(func_def_0, type, h: $i > $i).
% 1.47/1.28 thf(func_def_1, type, g: $i > $i).
% 1.47/1.28 thf(func_def_2, type, cP: $i > $i > $o).
% 1.47/1.28 thf(func_def_6, type, sK0: $i > $i).
% 1.47/1.28 thf(func_def_8, type, ph2: !>[X0: $tType]:(X0)).
% 1.47/1.28 thf(f19,plain,(
% 1.47/1.28 $false),
% 1.47/1.28 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.47/1.28 thf(f16,plain,(
% 1.47/1.28 ($true != $true)),
% 1.47/1.28 inference(superposition,[status(thm)],[f10,f12])).
% 1.47/1.28 thf(f12,plain,(
% 1.47/1.28 ( ! [X2 : $i > $i,X3 : $i,X0 : $i] : (((cP @ X3 @ (X2 @ X0)) = $true)) )),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.47/1.28 thf(f9,plain,(
% 1.47/1.28 ! [X0 : $i] : (! [X2 : $i > $i,X3 : $i] : (((cP @ X3 @ (X2 @ X0)) = $true) & ((cP @ X0 @ (sK0 @ X0)) = $true)) & ($true != (cP @ (sK0 @ X0) @ (g @ (h @ (sK0 @ X0))))))),
% 1.47/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.47/1.28 thf(f8,plain,(
% 1.47/1.28 ! [X0 : $i] : (? [X1 : $i] : (! [X2 : $i > $i,X3 : $i] : (((cP @ X3 @ (X2 @ X0)) = $true) & ((cP @ X0 @ X1) = $true)) & ((cP @ X1 @ (g @ (h @ X1))) != $true)) => (! [X3 : $i,X2 : $i > $i] : (((cP @ X3 @ (X2 @ X0)) = $true) & ((cP @ X0 @ (sK0 @ X0)) = $true)) & ($true != (cP @ (sK0 @ X0) @ (g @ (h @ (sK0 @ X0)))))))),
% 1.47/1.28 introduced(definition,[],[choice_axiom])).
% 1.47/1.28 thf(f7,plain,(
% 1.47/1.28 ! [X0 : $i] : ? [X1 : $i] : (! [X2 : $i > $i,X3 : $i] : (((cP @ X3 @ (X2 @ X0)) = $true) & ((cP @ X0 @ X1) = $true)) & ((cP @ X1 @ (g @ (h @ X1))) != $true))),
% 1.47/1.28 inference(rectify,[status(thm)],[f6])).
% 1.47/1.28 thf(f6,plain,(
% 1.47/1.28 ! [X0 : $i] : ? [X1 : $i] : (! [X3 : $i > $i,X2 : $i] : (($true = (cP @ X2 @ (X3 @ X0))) & ((cP @ X0 @ X1) = $true)) & ((cP @ X1 @ (g @ (h @ X1))) != $true))),
% 1.47/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.47/1.28 thf(f5,plain,(
% 1.47/1.28 ~? [X0 : $i] : ! [X1 : $i] : (! [X3 : $i > $i,X2 : $i] : (($true = (cP @ X2 @ (X3 @ X0))) & ((cP @ X0 @ X1) = $true)) => ((cP @ X1 @ (g @ (h @ X1))) = $true))),
% 1.47/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.28 thf(f4,plain,(
% 1.47/1.28 ~? [X0 : $i] : ! [X1 : $i] : (! [X2 : $i,X3 : $i > $i] : ((cP @ X2 @ (X3 @ X0)) & (cP @ X0 @ X1)) => (cP @ X1 @ (g @ (h @ X1))))),
% 1.47/1.28 inference(rectify,[status(thm)],[f2])).
% 1.47/1.28 thf(f2,negated_conjecture,(
% 1.47/1.28 ~? [X0 : $i] : ! [X1 : $i] : (! [X3 : $i,X2 : $i > $i] : ((cP @ X3 @ (X2 @ X0)) & (cP @ X0 @ X1)) => (cP @ X1 @ (g @ (h @ X1))))),
% 1.47/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.28 thf(f1,conjecture,(
% 1.47/1.28 ? [X0 : $i] : ! [X1 : $i] : (! [X3 : $i,X2 : $i > $i] : ((cP @ X3 @ (X2 @ X0)) & (cP @ X0 @ X1)) => (cP @ X1 @ (g @ (h @ X1))))),
% 1.47/1.28 file('/export/starexec/sandbox2/tmp/tmp.nfxcw9oHF1/DTF2THF_5004.p',cTHM84)).
% 1.47/1.28 thf(f10,plain,(
% 1.47/1.28 ( ! [X0 : $i] : (($true != (cP @ (sK0 @ X0) @ (g @ (h @ (sK0 @ X0)))))) )),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.47/1.28 % SZS output end Proof for DTF2THF_5004
% 1.47/1.28 % (5280)------------------------------
% 1.47/1.28 % (5280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (5280)Termination reason: Refutation
% 1.47/1.28
% 1.47/1.28 % (5280)Memory used [KB]: 5500
% 1.47/1.28 % (5280)Time elapsed: 0.003 s
% 1.47/1.28 % (5280)Instructions burned: 3 (million)
% 1.47/1.28 % (5280)------------------------------
% 1.47/1.28 % (5280)------------------------------
% 1.47/1.28 % (5278)Success in time 0.013 s
%------------------------------------------------------------------------------