%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO220^5 : 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 : n027.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 09:53:42 AM UTC 2026
% Result : Theorem 1.48s 1.27s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 27 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 78 ( 12 ~; 0 |; 10 &; 46 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 ^; 23 !; 8 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_5,type,
sK2: $i > $i > $o ).
thf(f15,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
$true != $true,
inference(superposition,[status(thm)],[f13,f11]) ).
thf(f11,plain,
! [X3: $i] :
( ( sK2 @ X3 @ X3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( sK0 = sK1 )
& ! [X3: $i] :
( ( sK2 @ X3 @ X3 )
= $true )
& ( ( sK2 @ sK0 @ sK1 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f8,f7]) ).
thf(f7,plain,
( ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ? [X2: $i > $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true )
& ( ( X2 @ X0 @ X1 )
!= $true ) ) )
=> ( ( sK0 = sK1 )
& ? [X2: $i > $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true )
& ( $true
!= ( X2 @ sK0 @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X2: $i > $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true )
& ( $true
!= ( X2 @ sK0 @ sK1 ) ) )
=> ( ! [X3: $i] :
( ( sK2 @ X3 @ X3 )
= $true )
& ( ( sK2 @ sK0 @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ? [X2: $i > $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true )
& ( ( X2 @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X2: $i > $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true )
=> ( ( X2 @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ozEHbitmCv/DTF2THF_24703.p',cTHM47A) ).
thf(f13,plain,
( $true
!= ( sK2 @ sK1 @ sK1 ) ),
inference(definition_unfolding,[status(thm)],[f10,f12]) ).
thf(f12,plain,
sK0 = sK1,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f10,plain,
( ( sK2 @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO220^5 : 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
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % 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 14:26:37 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYO220^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : TPS problem THM47A
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0198 [Bro09]
% 0.29/0.46 % : THM47A [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.29/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.29/0.46 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 4 @)
% 0.29/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.46 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(cTHM47A,conjecture,
% 0.29/0.46 ! [X: $i,Y: $i] :
% 0.29/0.46 ( ( X = Y )
% 0.29/0.46 => ! [R: $i > $i > $o] :
% 0.29/0.46 ( ! [Z: $i] : ( R @ Z @ Z )
% 0.29/0.46 => ( R @ X @ Y ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.48/1.24 ---- Embedded in THF ---
% 1.48/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.24 %%% Generated on Tue Feb 24 14:26:38 EST 2026
% 1.48/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.24 %%% Logic specification used:
% 1.48/1.24 %%% thf(spec, logic, $$dhol).
% 1.48/1.24
% 1.48/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ozEHbitmCv/DTF2DTF24703.p
% See solution above
% 1.48/1.24 ------------------------
% 1.48/1.25 ---- Cleaned THF ---
% 1.48/1.25 thf(cTHM47A,conjecture,
% 1.48/1.25 ! [X: $i,Y: $i] :
% 1.48/1.25 ( ( X = Y )
% 1.48/1.25 => ! [R: $i > $i > $o] :
% 1.48/1.25 ( ! [Z: $i] : ( R @ Z @ Z )
% 1.48/1.25 => ( R @ X @ Y ) ) ) ).
% 1.48/1.25 ------------------------
% 1.48/1.27 % (24982)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24703 for (2999ds/183Mi)
% 1.48/1.27 % (24983)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_24703 for (2999ds/4Mi)
% 1.48/1.27 % (24982)First to succeed.
% 1.48/1.27 % (24983)Also succeeded, but the first one will report.
% 1.48/1.27 % (24982)Refutation found. Thanks to Tanya!
% 1.48/1.27 % SZS status Theorem for DTF2THF_24703
% 1.48/1.27 % SZS output start Proof for DTF2THF_24703
% 1.48/1.27 thf(func_def_5, type, sK2: $i > $i > $o).
% 1.48/1.27 thf(f15,plain,(
% 1.48/1.27 $false),
% 1.48/1.27 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.48/1.27 thf(f14,plain,(
% 1.48/1.27 ($true != $true)),
% 1.48/1.27 inference(superposition,[status(thm)],[f13,f11])).
% 1.48/1.27 thf(f11,plain,(
% 1.48/1.27 ( ! [X3 : $i] : (((sK2 @ X3 @ X3) = $true)) )),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.27 thf(f9,plain,(
% 1.48/1.27 (sK0 = sK1) & (! [X3 : $i] : ((sK2 @ X3 @ X3) = $true) & ((sK2 @ sK0 @ sK1) != $true))),
% 1.48/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f8,f7])).
% 1.48/1.27 thf(f7,plain,(
% 1.48/1.27 ? [X0 : $i,X1 : $i] : ((X0 = X1) & ? [X2 : $i > $i > $o] : (! [X3 : $i] : ((X2 @ X3 @ X3) = $true) & ((X2 @ X0 @ X1) != $true))) => ((sK0 = sK1) & ? [X2 : $i > $i > $o] : (! [X3 : $i] : ((X2 @ X3 @ X3) = $true) & ($true != (X2 @ sK0 @ sK1))))),
% 1.48/1.27 introduced(definition,[],[choice_axiom])).
% 1.48/1.27 thf(f8,plain,(
% 1.48/1.27 ? [X2 : $i > $i > $o] : (! [X3 : $i] : ((X2 @ X3 @ X3) = $true) & ($true != (X2 @ sK0 @ sK1))) => (! [X3 : $i] : ((sK2 @ X3 @ X3) = $true) & ((sK2 @ sK0 @ sK1) != $true))),
% 1.48/1.27 introduced(definition,[],[choice_axiom])).
% 1.48/1.27 thf(f6,plain,(
% 1.48/1.27 ? [X0 : $i,X1 : $i] : ((X0 = X1) & ? [X2 : $i > $i > $o] : (! [X3 : $i] : ((X2 @ X3 @ X3) = $true) & ((X2 @ X0 @ X1) != $true)))),
% 1.48/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.27 thf(f5,plain,(
% 1.48/1.27 ~! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X2 : $i > $i > $o] : (! [X3 : $i] : ((X2 @ X3 @ X3) = $true) => ((X2 @ X0 @ X1) = $true)))),
% 1.48/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.27 thf(f4,plain,(
% 1.48/1.27 ~! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i > $i > $o] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)))),
% 1.48/1.27 inference(rectify,[status(thm)],[f2])).
% 1.48/1.27 thf(f2,negated_conjecture,(
% 1.48/1.27 ~! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i > $i > $o] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)))),
% 1.48/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.27 thf(f1,conjecture,(
% 1.48/1.27 ! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i > $i > $o] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)))),
% 1.48/1.27 file('/export/starexec/sandbox/tmp/tmp.ozEHbitmCv/DTF2THF_24703.p',cTHM47A)).
% 1.48/1.27 thf(f13,plain,(
% 1.48/1.27 ($true != (sK2 @ sK1 @ sK1))),
% 1.48/1.27 inference(definition_unfolding,[status(thm)],[f10,f12])).
% 1.48/1.27 thf(f12,plain,(
% 1.48/1.27 (sK0 = sK1)),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.27 thf(f10,plain,(
% 1.48/1.27 ((sK2 @ sK0 @ sK1) != $true)),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.27 % SZS output end Proof for DTF2THF_24703
% 1.48/1.27 % (24982)------------------------------
% 1.48/1.27 % (24982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (24982)Termination reason: Refutation
% 1.48/1.27
% 1.48/1.27 % (24982)Memory used [KB]: 5500
% 1.48/1.27 % (24982)Time elapsed: 0.002 s
% 1.48/1.27 % (24982)Instructions burned: 1 (million)
% 1.48/1.27 % (24982)------------------------------
% 1.48/1.27 % (24982)------------------------------
% 1.48/1.27 % (24981)Success in time 0.012 s
%------------------------------------------------------------------------------