%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO084^5 : 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 : n024.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 1.45s 1.26s
% Output : Refutation 1.45s
% 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 : 80 ( 20 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 147 ( 9 ~; 9 |; 4 &; 120 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 25 ( 0 ^; 15 !; 10 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $i > $i > $o ).
thf(func_def_1,type,
k: $i > $i ).
thf(func_def_2,type,
h: $i > $i ).
thf(func_def_7,type,
sK0: $i > $i ).
thf(f13,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
$true != $true,
inference(superposition,[status(thm)],[f9,f11]) ).
thf(f11,plain,
! [X0: $i] :
( $true
= ( cP @ a @ ( sK0 @ X0 ) @ ( h @ ( sK0 @ X0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f10,f9]) ).
thf(f10,plain,
! [X0: $i] :
( ( ( cP @ X0 @ ( sK0 @ X0 ) @ ( k @ ( sK0 @ X0 ) ) )
= $true )
| ( $true
= ( cP @ a @ ( sK0 @ X0 ) @ ( h @ ( sK0 @ X0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X2: $i] :
( ( ( ( cP @ X0 @ ( sK0 @ X0 ) @ ( k @ ( sK0 @ X0 ) ) )
= $true )
| ( $true
= ( cP @ a @ ( sK0 @ X0 ) @ ( h @ ( sK0 @ X0 ) ) ) ) )
& ( ( cP @ X0 @ ( sK0 @ X0 ) @ X2 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
! [X0: $i] :
( ? [X1: $i] :
! [X2: $i] :
( ( ( ( cP @ X0 @ X1 @ ( k @ X1 ) )
= $true )
| ( ( cP @ a @ X1 @ ( h @ X1 ) )
= $true ) )
& ( ( cP @ X0 @ X1 @ X2 )
!= $true ) )
=> ! [X2: $i] :
( ( ( ( cP @ X0 @ ( sK0 @ X0 ) @ ( k @ ( sK0 @ X0 ) ) )
= $true )
| ( $true
= ( cP @ a @ ( sK0 @ X0 ) @ ( h @ ( sK0 @ X0 ) ) ) ) )
& ( ( cP @ X0 @ ( sK0 @ X0 ) @ X2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
! [X0: $i] :
? [X1: $i] :
! [X2: $i] :
( ( ( ( cP @ X0 @ X1 @ ( k @ X1 ) )
= $true )
| ( ( cP @ a @ X1 @ ( h @ X1 ) )
= $true ) )
& ( ( cP @ X0 @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
( ( ( ( cP @ X0 @ X1 @ ( k @ X1 ) )
= $true )
| ( ( cP @ a @ X1 @ ( h @ X1 ) )
= $true ) )
=> ( ( cP @ X0 @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
( ( ( cP @ X0 @ X1 @ ( k @ X1 ) )
| ( cP @ a @ X1 @ ( h @ X1 ) ) )
=> ( cP @ X0 @ X1 @ X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
( ( ( cP @ X0 @ X1 @ ( k @ X1 ) )
| ( cP @ a @ X1 @ ( h @ X1 ) ) )
=> ( cP @ X0 @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i] :
! [X1: $i] :
? [X2: $i] :
( ( ( cP @ X0 @ X1 @ ( k @ X1 ) )
| ( cP @ a @ X1 @ ( h @ X1 ) ) )
=> ( cP @ X0 @ X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.f1rXCClesY/DTF2THF_28111.p',cTHM75) ).
thf(f9,plain,
! [X2: $i,X0: $i] :
( ( cP @ X0 @ ( sK0 @ X0 ) @ X2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SYO084^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue Feb 24 09:23:40 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SYO084^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.32 % Domain : Syntactic
% 0.07/0.32 % Problem : TPS problem THM75
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English : Related to THM87, which was used for CADE-6.
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bro09]
% 0.07/0.32 % Names : tps_0116 [Bro09]
% 0.07/0.32 % : THM75 [TPS]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.5.0, 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
% 0.07/0.32 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.07/0.32 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 3 ( 3 avg)
% 0.07/0.32 % Number of connectives : 13 ( 0 ~; 1 |; 0 &; 11 @)
% 0.07/0.32 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 9 ( 9 avg)
% 0.07/0.32 % Number of types : 2 ( 0 usr)
% 0.07/0.32 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 4 ( 4 usr; 1 con; 0-3 aty)
% 0.07/0.32 % Number of variables : 3 ( 0 ^; 1 !; 2 ?; 3 :)
% 0.07/0.32 % SPC : TH0_THM_NEQ_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.32 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.32 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.32 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(cP,type,
% 0.07/0.32 cP: $i > $i > $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(k,type,
% 0.07/0.32 k: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(h,type,
% 0.07/0.32 h: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(a,type,
% 0.07/0.32 a: $i ).
% 0.07/0.32
% 0.07/0.32 thf(cTHM75,conjecture,
% 0.07/0.32 ? [Xv: $i] :
% 0.07/0.32 ! [Xj: $i] :
% 0.07/0.32 ? [Xq: $i] :
% 0.07/0.32 ( ( ( cP @ a @ Xj @ ( h @ Xj ) )
% 0.07/0.32 | ( cP @ Xv @ Xj @ ( k @ Xj ) ) )
% 0.07/0.32 => ( cP @ Xv @ Xj @ Xq ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 1.45/1.23 ---- Embedded in THF ---
% 1.45/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.23 %%% Generated on Tue Feb 24 09:23:41 EST 2026
% 1.45/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.23 %%% Logic specification used:
% 1.45/1.23 %%% thf(spec, logic, $$dhol).
% 1.45/1.23
% 1.45/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.f1rXCClesY/DTF2DTF28111.p
% See solution above
% 1.45/1.23 ------------------------
% 1.45/1.24 ---- Cleaned THF ---
% 1.45/1.24 thf(cP,type,
% 1.45/1.24 cP: $i > $i > $i > $o ).
% 1.45/1.24
% 1.45/1.24 thf(k,type,
% 1.45/1.24 k: $i > $i ).
% 1.45/1.24
% 1.45/1.24 thf(h,type,
% 1.45/1.24 h: $i > $i ).
% 1.45/1.24
% 1.45/1.24 thf(a,type,
% 1.45/1.24 a: $i ).
% 1.45/1.24
% 1.45/1.24 thf(cTHM75,conjecture,
% 1.45/1.24 ? [Xv: $i] :
% 1.45/1.24 ! [Xj: $i] :
% 1.45/1.24 ? [Xq: $i] :
% 1.45/1.24 ( ( ( cP @ a @ Xj @ ( h @ Xj ) )
% 1.45/1.24 | ( cP @ Xv @ Xj @ ( k @ Xj ) ) )
% 1.45/1.24 => ( cP @ Xv @ Xj @ Xq ) ) ).
% 1.45/1.24 ------------------------
% 1.45/1.26 % (28225)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_28111 for (3000ds/27Mi)
% 1.45/1.26 % (28226)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28111 for (3000ds/2Mi)
% 1.45/1.26 % (28223)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28111 for (3000ds/183Mi)
% 1.45/1.26 % (28224)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_28111 for (3000ds/4Mi)
% 1.45/1.26 % (28227)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_28111 for (3000ds/2Mi)
% 1.45/1.26 % (28228)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_28111 for (3000ds/275Mi)
% 1.45/1.26 % (28229)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28111 for (3000ds/18Mi)
% 1.45/1.26 % (28226)Instruction limit reached!
% 1.45/1.26 % (28226)------------------------------
% 1.45/1.26 % (28226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.26 % (28226)Termination reason: Unknown
% 1.45/1.26 % (28226)Termination phase: Saturation
% 1.45/1.26
% 1.45/1.26 % (28226)Memory used [KB]: 5500
% 1.45/1.26 % (28226)Time elapsed: 0.003 s
% 1.45/1.26 % (28226)Instructions burned: 2 (million)
% 1.45/1.26 % (28226)------------------------------
% 1.45/1.26 % (28226)------------------------------
% 1.45/1.26 % (28228)First to succeed.
% 1.45/1.26 % (28227)Instruction limit reached!
% 1.45/1.26 % (28227)------------------------------
% 1.45/1.26 % (28227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.26 % (28227)Termination reason: Unknown
% 1.45/1.26 % (28227)Termination phase: Saturation
% 1.45/1.26
% 1.45/1.26 % (28227)Memory used [KB]: 5500
% 1.45/1.26 % (28227)Time elapsed: 0.003 s
% 1.45/1.26 % (28227)Instructions burned: 2 (million)
% 1.45/1.26 % (28227)------------------------------
% 1.45/1.26 % (28227)------------------------------
% 1.45/1.26 % (28229)Also succeeded, but the first one will report.
% 1.45/1.26 % (28228)Refutation found. Thanks to Tanya!
% 1.45/1.26 % SZS status Theorem for DTF2THF_28111
% 1.45/1.26 % SZS output start Proof for DTF2THF_28111
% 1.45/1.26 thf(func_def_0, type, cP: $i > $i > $i > $o).
% 1.45/1.26 thf(func_def_1, type, k: $i > $i).
% 1.45/1.26 thf(func_def_2, type, h: $i > $i).
% 1.45/1.26 thf(func_def_7, type, sK0: $i > $i).
% 1.45/1.26 thf(f13,plain,(
% 1.45/1.26 $false),
% 1.45/1.26 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.45/1.26 thf(f12,plain,(
% 1.45/1.26 ($true != $true)),
% 1.45/1.26 inference(superposition,[status(thm)],[f9,f11])).
% 1.45/1.26 thf(f11,plain,(
% 1.45/1.26 ( ! [X0 : $i] : (($true = (cP @ a @ (sK0 @ X0) @ (h @ (sK0 @ X0))))) )),
% 1.45/1.26 inference(subsumption_resolution,[status(thm)],[f10,f9])).
% 1.45/1.26 thf(f10,plain,(
% 1.45/1.26 ( ! [X0 : $i] : (((cP @ X0 @ (sK0 @ X0) @ (k @ (sK0 @ X0))) = $true) | ($true = (cP @ a @ (sK0 @ X0) @ (h @ (sK0 @ X0))))) )),
% 1.45/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.45/1.26 thf(f8,plain,(
% 1.45/1.26 ! [X0 : $i] : ! [X2 : $i] : ((((cP @ X0 @ (sK0 @ X0) @ (k @ (sK0 @ X0))) = $true) | ($true = (cP @ a @ (sK0 @ X0) @ (h @ (sK0 @ X0))))) & ((cP @ X0 @ (sK0 @ X0) @ X2) != $true))),
% 1.45/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.45/1.26 thf(f7,plain,(
% 1.45/1.26 ! [X0 : $i] : (? [X1 : $i] : ! [X2 : $i] : ((((cP @ X0 @ X1 @ (k @ X1)) = $true) | ((cP @ a @ X1 @ (h @ X1)) = $true)) & ((cP @ X0 @ X1 @ X2) != $true)) => ! [X2 : $i] : ((((cP @ X0 @ (sK0 @ X0) @ (k @ (sK0 @ X0))) = $true) | ($true = (cP @ a @ (sK0 @ X0) @ (h @ (sK0 @ X0))))) & ((cP @ X0 @ (sK0 @ X0) @ X2) != $true)))),
% 1.45/1.26 introduced(definition,[],[choice_axiom])).
% 1.45/1.26 thf(f6,plain,(
% 1.45/1.26 ! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i] : ((((cP @ X0 @ X1 @ (k @ X1)) = $true) | ((cP @ a @ X1 @ (h @ X1)) = $true)) & ((cP @ X0 @ X1 @ X2) != $true))),
% 1.45/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.45/1.26 thf(f5,plain,(
% 1.45/1.26 ~? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ((((cP @ X0 @ X1 @ (k @ X1)) = $true) | ((cP @ a @ X1 @ (h @ X1)) = $true)) => ((cP @ X0 @ X1 @ X2) = $true))),
% 1.45/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.45/1.26 thf(f4,plain,(
% 1.45/1.26 ~? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : (((cP @ X0 @ X1 @ (k @ X1)) | (cP @ a @ X1 @ (h @ X1))) => (cP @ X0 @ X1 @ X2))),
% 1.45/1.26 inference(rectify,[status(thm)],[f2])).
% 1.45/1.26 thf(f2,negated_conjecture,(
% 1.45/1.26 ~? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : (((cP @ X0 @ X1 @ (k @ X1)) | (cP @ a @ X1 @ (h @ X1))) => (cP @ X0 @ X1 @ X2))),
% 1.45/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/1.26 thf(f1,conjecture,(
% 1.45/1.26 ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : (((cP @ X0 @ X1 @ (k @ X1)) | (cP @ a @ X1 @ (h @ X1))) => (cP @ X0 @ X1 @ X2))),
% 1.45/1.26 file('/export/starexec/sandbox/tmp/tmp.f1rXCClesY/DTF2THF_28111.p',cTHM75)).
% 1.45/1.26 thf(f9,plain,(
% 1.45/1.26 ( ! [X2 : $i,X0 : $i] : (((cP @ X0 @ (sK0 @ X0) @ X2) != $true)) )),
% 1.45/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.45/1.26 % SZS output end Proof for DTF2THF_28111
% 1.45/1.26 % (28228)------------------------------
% 1.45/1.26 % (28228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.26 % (28228)Termination reason: Refutation
% 1.45/1.26
% 1.45/1.26 % (28228)Memory used [KB]: 5500
% 1.45/1.26 % (28228)Time elapsed: 0.003 s
% 1.45/1.26 % (28228)Instructions burned: 1 (million)
% 1.45/1.26 % (28228)------------------------------
% 1.45/1.26 % (28228)------------------------------
% 1.45/1.26 % (28222)Success in time 0.017 s
%------------------------------------------------------------------------------