%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO214^5 : 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 : n020.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 09:53:41 AM UTC 2026
% Result : Theorem 1.51s 1.27s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 29 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 58 ( 11 ~; 0 |; 12 &; 25 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 0 ^; 12 !; 11 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: $i > $o ).
thf(func_def_4,type,
sK1: $i > $o ).
thf(f15,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f13,f14]) ).
thf(f14,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(definition_unfolding,[status(thm)],[f12,f11]) ).
thf(f11,plain,
sK1 = sK0,
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( $true
!= ( sK0 @ sK2 ) )
& ( $true
= ( sK1 @ sK2 ) )
& ( sK1 = sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: $i > $o,X1: $i > $o] :
( ? [X2: $i] :
( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
& ( X0 = X1 ) )
=> ( ? [X2: $i] :
( ( ( sK0 @ X2 )
!= $true )
& ( $true
= ( sK1 @ X2 ) ) )
& ( sK1 = sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X2: $i] :
( ( ( sK0 @ X2 )
!= $true )
& ( $true
= ( sK1 @ X2 ) ) )
=> ( ( $true
!= ( sK0 @ sK2 ) )
& ( $true
= ( sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: $i > $o,X1: $i > $o] :
( ? [X2: $i] :
( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
& ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: $i > $o,X0: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
& ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $o,X1: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $o,X1: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: $i > $o,X0: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: $i > $o,X0: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.v26PytKqeA/DTF2THF_30671.p',cTHM12) ).
thf(f12,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f13,plain,
( $true
!= ( sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO214^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n020.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
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:26:12 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.46 thf(spec,logic,$$dhol).
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 % File : SYO214^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.46 % Domain : Syntactic
% 0.18/0.46 % Problem : TPS problem THM12
% 0.18/0.46 % Version : Especial.
% 0.18/0.46 % English :
% 0.18/0.46
% 0.18/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.46 % Source : [Bro09]
% 0.18/0.46 % Names : tps_0086 [Bro09]
% 0.18/0.46 % : THM12 [TPS]
% 0.18/0.46
% 0.18/0.46 % Status : Theorem
% 0.18/0.46 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 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
% 0.18/0.46 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.18/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.18/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.18/0.46 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 2 @)
% 0.18/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.18/0.46 % Number of types : 2 ( 0 usr)
% 0.18/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.18/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.18/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.18/0.46 % SPC : TH0_THM_EQU_NAR
% 0.18/0.46
% 0.18/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 thf(cTHM12,conjecture,
% 0.18/0.46 ! [R: $i > $o,S: $i > $o] :
% 0.18/0.46 ( ( R = S )
% 0.18/0.46 => ! [X: $i] :
% 0.18/0.46 ( ( S @ X )
% 0.18/0.46 => ( R @ X ) ) ) ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 1.51/1.24 ---- Embedded in THF ---
% 1.51/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.24 %%% Generated on Tue Feb 24 14:26:13 EST 2026
% 1.51/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.24 %%% Logic specification used:
% 1.51/1.24 %%% thf(spec, logic, $$dhol).
% 1.51/1.24
% 1.51/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.v26PytKqeA/DTF2DTF30671.p
% See solution above
% 1.51/1.24 ------------------------
% 1.51/1.25 ---- Cleaned THF ---
% 1.51/1.25 thf(cTHM12,conjecture,
% 1.51/1.25 ! [R: $i > $o,S: $i > $o] :
% 1.51/1.25 ( ( R = S )
% 1.51/1.25 => ! [X: $i] :
% 1.51/1.25 ( ( S @ X )
% 1.51/1.25 => ( R @ X ) ) ) ).
% 1.51/1.25 ------------------------
% 1.51/1.27 % (30819)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_30671 for (3000ds/4Mi)
% 1.51/1.27 % (30819)First to succeed.
% 1.51/1.27 % (30822)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_30671 for (3000ds/2Mi)
% 1.51/1.27 % (30822)Instruction limit reached!
% 1.51/1.27 % (30822)------------------------------
% 1.51/1.27 % (30822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (30822)Termination reason: Unknown
% 1.51/1.27 % (30822)Termination phase: Saturation
% 1.51/1.27
% 1.51/1.27 % (30822)Memory used [KB]: 5500
% 1.51/1.27 % (30822)Time elapsed: 0.002 s
% 1.51/1.27 % (30822)Instructions burned: 2 (million)
% 1.51/1.27 % (30822)------------------------------
% 1.51/1.27 % (30822)------------------------------
% 1.51/1.27 % (30819)Refutation found. Thanks to Tanya!
% 1.51/1.27 % SZS status Theorem for DTF2THF_30671
% 1.51/1.27 % SZS output start Proof for DTF2THF_30671
% 1.51/1.27 thf(func_def_3, type, sK0: $i > $o).
% 1.51/1.27 thf(func_def_4, type, sK1: $i > $o).
% 1.51/1.27 thf(f15,plain,(
% 1.51/1.27 $false),
% 1.51/1.27 inference(subsumption_resolution,[status(thm)],[f13,f14])).
% 1.51/1.27 thf(f14,plain,(
% 1.51/1.27 ($true = (sK0 @ sK2))),
% 1.51/1.27 inference(definition_unfolding,[status(thm)],[f12,f11])).
% 1.51/1.27 thf(f11,plain,(
% 1.51/1.27 (sK1 = sK0)),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.51/1.27 thf(f10,plain,(
% 1.51/1.27 (($true != (sK0 @ sK2)) & ($true = (sK1 @ sK2))) & (sK1 = sK0)),
% 1.51/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8])).
% 1.51/1.27 thf(f8,plain,(
% 1.51/1.27 ? [X0 : $i > $o,X1 : $i > $o] : (? [X2 : $i] : (((X0 @ X2) != $true) & ((X1 @ X2) = $true)) & (X0 = X1)) => (? [X2 : $i] : (((sK0 @ X2) != $true) & ($true = (sK1 @ X2))) & (sK1 = sK0))),
% 1.51/1.27 introduced(definition,[],[choice_axiom])).
% 1.51/1.27 thf(f9,plain,(
% 1.51/1.27 ? [X2 : $i] : (((sK0 @ X2) != $true) & ($true = (sK1 @ X2))) => (($true != (sK0 @ sK2)) & ($true = (sK1 @ sK2)))),
% 1.51/1.27 introduced(definition,[],[choice_axiom])).
% 1.51/1.27 thf(f7,plain,(
% 1.51/1.27 ? [X0 : $i > $o,X1 : $i > $o] : (? [X2 : $i] : (((X0 @ X2) != $true) & ((X1 @ X2) = $true)) & (X0 = X1))),
% 1.51/1.27 inference(rectify,[status(thm)],[f6])).
% 1.51/1.27 thf(f6,plain,(
% 1.51/1.27 ? [X1 : $i > $o,X0 : $i > $o] : (? [X2 : $i] : (((X1 @ X2) != $true) & ((X0 @ X2) = $true)) & (X0 = X1))),
% 1.51/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.27 thf(f5,plain,(
% 1.51/1.27 ~! [X0 : $i > $o,X1 : $i > $o] : ((X0 = X1) => ! [X2 : $i] : (((X0 @ X2) = $true) => ((X1 @ X2) = $true)))),
% 1.51/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.27 thf(f4,plain,(
% 1.51/1.27 ~! [X0 : $i > $o,X1 : $i > $o] : ((X0 = X1) => ! [X2 : $i] : ((X0 @ X2) => (X1 @ X2)))),
% 1.51/1.27 inference(rectify,[status(thm)],[f2])).
% 1.51/1.27 thf(f2,negated_conjecture,(
% 1.51/1.27 ~! [X1 : $i > $o,X0 : $i > $o] : ((X0 = X1) => ! [X2 : $i] : ((X1 @ X2) => (X0 @ X2)))),
% 1.51/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.27 thf(f1,conjecture,(
% 1.51/1.27 ! [X1 : $i > $o,X0 : $i > $o] : ((X0 = X1) => ! [X2 : $i] : ((X1 @ X2) => (X0 @ X2)))),
% 1.51/1.27 file('/export/starexec/sandbox2/tmp/tmp.v26PytKqeA/DTF2THF_30671.p',cTHM12)).
% 1.51/1.27 thf(f12,plain,(
% 1.51/1.27 ($true = (sK1 @ sK2))),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.51/1.27 thf(f13,plain,(
% 1.51/1.27 ($true != (sK0 @ sK2))),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.51/1.27 % SZS output end Proof for DTF2THF_30671
% 1.51/1.27 % (30819)------------------------------
% 1.51/1.27 % (30819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (30819)Termination reason: Refutation
% 1.51/1.27
% 1.51/1.27 % (30819)Memory used [KB]: 5373
% 1.51/1.27 % (30819)Time elapsed: 0.002 s
% 1.51/1.27 % (30819)------------------------------
% 1.51/1.27 % (30819)------------------------------
% 1.51/1.27 % (30817)Success in time 0.003 s
%------------------------------------------------------------------------------