%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO232^5 : 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 : n021.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 09:53:43 AM UTC 2026
% Result : Theorem 1.65s 1.31s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 21 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 44 ( 9 ~; 3 |; 4 &; 16 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 9 ( 0 ^; 5 !; 4 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cP: a > $o ).
thf(func_def_2,type,
x: a ).
thf(f17,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f10,f14]) ).
thf(f14,plain,
! [X0: a] :
( ( cP @ X0 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: a] :
( ( $true != $true )
| ( ( cP @ X0 )
= $false ) ),
inference(fool_paramodulation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: a] :
( ( cP @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cP @ x )
= $true )
& ! [X0: a] :
( ( cP @ X0 )
!= $true )
& ( ( y != y )
| ( cB = $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: a] :
( ( cP @ X0 )
!= $true )
& ( ( cP @ x )
= $true )
& ( ( y != y )
| ( cB = $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( y = y )
=> ( cB = $true ) )
=> ( ( ( cP @ x )
= $true )
=> ? [X0: a] :
( ( cP @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( y = y )
=> cB )
=> ( ( cP @ x )
=> ? [X0: a] : ( cP @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( y = y )
=> cB )
=> ( ( cP @ x )
=> ? [X0: a] : ( cP @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( y = y )
=> cB )
=> ( ( cP @ x )
=> ? [X0: a] : ( cP @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6iJrgqen6m/DTF2THF_5080.p',cADDHYP4) ).
thf(f10,plain,
( ( cP @ x )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO232^5 : 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
% 0.16/0.34 % Computer : n021.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % 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 14:26:39 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : SYO232^5 : TPTP v9.2.1. Released v4.0.0.
% 0.21/0.46 % Domain : Syntactic
% 0.21/0.46 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.21/0.46 % Version : Especial.
% 0.21/0.46 % English :
% 0.21/0.46
% 0.21/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.46 % Source : [Bro09]
% 0.21/0.46 % Names : tps_0689 [Bro09]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % 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
% 0.21/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.21/0.46 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.21/0.46 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 2 @)
% 0.21/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 5 ( 5 avg)
% 0.21/0.46 % Number of types : 3 ( 1 usr)
% 0.21/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.21/0.46 % Number of variables : 1 ( 0 ^; 0 !; 1 ?; 1 :)
% 0.21/0.46 % SPC : TH0_THM_EQU_NAR
% 0.21/0.46
% 0.21/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 thf(a_type,type,
% 0.21/0.46 a: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(cP,type,
% 0.21/0.46 cP: a > $o ).
% 0.21/0.46
% 0.21/0.46 thf(x,type,
% 0.21/0.46 x: a ).
% 0.21/0.46
% 0.21/0.46 thf(cB,type,
% 0.21/0.46 cB: $o ).
% 0.21/0.46
% 0.21/0.46 thf(y,type,
% 0.21/0.46 y: $i ).
% 0.21/0.46
% 0.21/0.46 thf(cADDHYP4,conjecture,
% 0.21/0.46 ( ( ( y = y )
% 0.21/0.46 => cB )
% 0.21/0.46 => ( ( cP @ x )
% 0.21/0.46 => ? [Xx0: a] : ( cP @ Xx0 ) ) ) ).
% 0.21/0.46
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 ------------------------
% 1.46/1.28 ---- Embedded in THF ---
% 1.46/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.28 %%% Generated on Tue Feb 24 14:26:40 EST 2026
% 1.46/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.28 %%% Logic specification used:
% 1.46/1.28 %%% thf(spec, logic, $$dhol).
% 1.46/1.28
% 1.46/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6iJrgqen6m/DTF2DTF5080.p
% See solution above
% 1.46/1.28 ------------------------
% 1.46/1.29 ---- Cleaned THF ---
% 1.46/1.29 thf(a_type,type,
% 1.46/1.29 a: $tType ).
% 1.46/1.29
% 1.46/1.29 thf(cP,type,
% 1.46/1.29 cP: a > $o ).
% 1.46/1.29
% 1.46/1.29 thf(x,type,
% 1.46/1.29 x: a ).
% 1.46/1.29
% 1.46/1.29 thf(cB,type,
% 1.46/1.29 cB: $o ).
% 1.46/1.29
% 1.46/1.29 thf(y,type,
% 1.46/1.29 y: $i ).
% 1.46/1.29
% 1.46/1.29 thf(cADDHYP4,conjecture,
% 1.46/1.29 ( ( ( y = y )
% 1.46/1.29 => cB )
% 1.46/1.29 => ( ( cP @ x )
% 1.46/1.29 => ? [Xx0: a] : ( cP @ Xx0 ) ) ) ).
% 1.46/1.29 ------------------------
% 1.65/1.31 % (5233)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_5080 for (2999ds/4Mi)
% 1.65/1.31 % (5238)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5080 for (2999ds/18Mi)
% 1.65/1.31 % (5233)First to succeed.
% 1.65/1.31 % (5238)Also succeeded, but the first one will report.
% 1.65/1.31 % (5233)Refutation found. Thanks to Tanya!
% 1.65/1.31 % SZS status Theorem for DTF2THF_5080
% 1.65/1.31 % SZS output start Proof for DTF2THF_5080
% 1.65/1.31 thf(type_def_5, type, a: $tType).
% 1.65/1.31 thf(func_def_0, type, a: $tType).
% 1.65/1.31 thf(func_def_1, type, cP: a > $o).
% 1.65/1.31 thf(func_def_2, type, x: a).
% 1.65/1.31 thf(f17,plain,(
% 1.65/1.31 $false),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.65/1.31 thf(f15,plain,(
% 1.65/1.31 ($true = $false)),
% 1.65/1.31 inference(backward_demodulation,[status(thm)],[f10,f14])).
% 1.65/1.31 thf(f14,plain,(
% 1.65/1.31 ( ! [X0 : a] : (((cP @ X0) = $false)) )),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.65/1.31 thf(f13,plain,(
% 1.65/1.31 ( ! [X0 : a] : (($true != $true) | ((cP @ X0) = $false)) )),
% 1.65/1.31 inference(fool_paramodulation,[status(thm)],[f9])).
% 1.65/1.31 thf(f9,plain,(
% 1.65/1.31 ( ! [X0 : a] : (((cP @ X0) != $true)) )),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f7])).
% 1.65/1.31 thf(f7,plain,(
% 1.65/1.31 ((cP @ x) = $true) & ! [X0 : a] : ((cP @ X0) != $true) & ((y != y) | (cB = $true))),
% 1.65/1.31 inference(flattening,[status(thm)],[f6])).
% 1.65/1.31 thf(f6,plain,(
% 1.65/1.31 (! [X0 : a] : ((cP @ X0) != $true) & ((cP @ x) = $true)) & ((y != y) | (cB = $true))),
% 1.65/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.65/1.31 thf(f5,plain,(
% 1.65/1.31 ~(((y = y) => (cB = $true)) => (((cP @ x) = $true) => ? [X0 : a] : ((cP @ X0) = $true)))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.31 thf(f4,plain,(
% 1.65/1.31 ~(((y = y) => cB) => ((cP @ x) => ? [X0 : a] : (cP @ X0)))),
% 1.65/1.31 inference(rectify,[status(thm)],[f2])).
% 1.65/1.31 thf(f2,negated_conjecture,(
% 1.65/1.31 ~(((y = y) => cB) => ((cP @ x) => ? [X0 : a] : (cP @ X0)))),
% 1.65/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.31 thf(f1,conjecture,(
% 1.65/1.31 ((y = y) => cB) => ((cP @ x) => ? [X0 : a] : (cP @ X0))),
% 1.65/1.31 file('/export/starexec/sandbox2/tmp/tmp.6iJrgqen6m/DTF2THF_5080.p',cADDHYP4)).
% 1.65/1.31 thf(f10,plain,(
% 1.65/1.31 ((cP @ x) = $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f7])).
% 1.65/1.31 % SZS output end Proof for DTF2THF_5080
% 1.65/1.31 % (5233)------------------------------
% 1.65/1.31 % (5233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (5233)Termination reason: Refutation
% 1.65/1.31
% 1.65/1.31 % (5233)Memory used [KB]: 5500
% 1.65/1.31 % (5233)Time elapsed: 0.003 s
% 1.65/1.31 % (5233)Instructions burned: 2 (million)
% 1.65/1.31 % (5233)------------------------------
% 1.65/1.31 % (5233)------------------------------
% 1.65/1.31 % (5231)Success in time 0.013 s
%------------------------------------------------------------------------------