%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV411^5 : 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 : n012.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 09:41:12 AM UTC 2026
% Result : Theorem 0.98s 0.90s
% Output : Refutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 5 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 92 ( 6 ~; 5 |; 0 &; 50 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 2 usr; 3 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 17 ( 8 ^; 9 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cB: $i > $o ).
thf(func_def_1,type,
cA: $i > $o ).
thf(f10,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f9]) ).
thf(f9,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ~ $true ) = $true ),
inference(boolean_simplification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cA @ Y0 )
=> ( cB @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( cA @ Y0 )
=> ( cB @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cA @ Y0 )
=> ( cB @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( cA @ Y0 )
=> ( cB @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( cA @ Y0 )
=> ( cB @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cA @ Y0 )
=> ( cB @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( cA @ Y0 )
=> ( cB @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( cA @ Y0 )
=> ( cB @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
| ! [X1: $i] :
( ( cA @ X1 )
=> ( cB @ X1 ) ) )
=> ! [X2: $i] :
( ( cA @ X2 )
=> ( cB @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
| ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) )
=> ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
| ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) )
=> ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WngKGbrmhH/DTF2THF_2867.p',cDUAL_EG1_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV411^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 12:46:15 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 : SEV411^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.32 % Domain : Set Theory
% 0.07/0.32 % Problem : TPS problem from SETS-THMS
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English :
% 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_0799 [Bro09]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.07/0.32 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.07/0.32 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 6 ( 6 avg)
% 0.07/0.32 % Number of connectives : 11 ( 0 ~; 1 |; 0 &; 6 @)
% 0.07/0.32 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 6 ( 6 avg)
% 0.07/0.32 % Number of types : 2 ( 0 usr)
% 0.07/0.32 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.07/0.32 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 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(cB,type,
% 0.07/0.32 cB: $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(cA,type,
% 0.07/0.32 cA: $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(cDUAL_EG1_pme,conjecture,
% 0.07/0.32 ( ( ! [Xx: $i] :
% 0.07/0.32 ( ( cA @ Xx )
% 0.07/0.32 => ( cB @ Xx ) )
% 0.07/0.32 | ! [Xx: $i] :
% 0.07/0.32 ( ( cA @ Xx )
% 0.07/0.32 => ( cB @ Xx ) ) )
% 0.07/0.32 => ! [Xx: $i] :
% 0.07/0.32 ( ( cA @ Xx )
% 0.07/0.32 => ( cB @ Xx ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.81/0.88 ---- Embedded in THF ---
% 0.81/0.88 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.81/0.88 %%% Generated on Tue Feb 24 12:46:16 EST 2026
% 0.81/0.88 %%% using '$$dhol' embedding, version 1.3.0.
% 0.81/0.88 %%% Logic specification used:
% 0.81/0.88 %%% thf(spec, logic, $$dhol).
% 0.81/0.88
% 0.81/0.88 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WngKGbrmhH/DTF2DTF2867.p
% See solution above
% 0.81/0.88 ------------------------
% 0.81/0.88 ---- Cleaned THF ---
% 0.81/0.88 thf(cB,type,
% 0.81/0.88 cB: $i > $o ).
% 0.81/0.88
% 0.81/0.88 thf(cA,type,
% 0.81/0.88 cA: $i > $o ).
% 0.81/0.88
% 0.81/0.88 thf(cDUAL_EG1_pme,conjecture,
% 0.81/0.88 ( ( ! [Xx: $i] :
% 0.81/0.88 ( ( cA @ Xx )
% 0.81/0.88 => ( cB @ Xx ) )
% 0.81/0.88 | ! [Xx: $i] :
% 0.81/0.88 ( ( cA @ Xx )
% 0.81/0.88 => ( cB @ Xx ) ) )
% 0.81/0.88 => ! [Xx: $i] :
% 0.81/0.88 ( ( cA @ Xx )
% 0.81/0.88 => ( cB @ Xx ) ) ) ).
% 0.81/0.88 ------------------------
% 0.98/0.90 % (3130)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_2867 for (3000ds/4Mi)
% 0.98/0.90 % (3133)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_2867 for (3000ds/2Mi)
% 0.98/0.90 % (3132)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2867 for (3000ds/2Mi)
% 0.98/0.90 % (3135)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2867 for (3000ds/18Mi)
% 0.98/0.90 % (3131)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_2867 for (3000ds/27Mi)
% 0.98/0.90 % (3134)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_2867 for (3000ds/275Mi)
% 0.98/0.90 % (3129)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2867 for (3000ds/183Mi)
% 0.98/0.90 % (3133)First to succeed.
% 0.98/0.90 % (3135)Also succeeded, but the first one will report.
% 0.98/0.90 % (3132)Also succeeded, but the first one will report.
% 0.98/0.90 % (3133)Refutation found. Thanks to Tanya!
% 0.98/0.90 % SZS status Theorem for DTF2THF_2867
% 0.98/0.90 % SZS output start Proof for DTF2THF_2867
% 0.98/0.90 thf(func_def_0, type, cB: $i > $o).
% 0.98/0.90 thf(func_def_1, type, cA: $i > $o).
% 0.98/0.90 thf(f10,plain,(
% 0.98/0.90 $false),
% 0.98/0.90 inference(trivial_inequality_removal,[status(thm)],[f9])).
% 0.98/0.90 thf(f9,plain,(
% 0.98/0.90 ($true = $false)),
% 0.98/0.90 inference(boolean_simplification,[status(thm)],[f8])).
% 0.98/0.90 thf(f8,plain,(
% 0.98/0.90 ((~ $true) = $true)),
% 0.98/0.90 inference(boolean_simplification,[status(thm)],[f7])).
% 0.98/0.90 thf(f7,plain,(
% 0.98/0.90 ((~ ((!! @ $i @ (^[Y0 : $i]: ((cA @ Y0) => (cB @ Y0)))) => (!! @ $i @ (^[Y0 : $i]: ((cA @ Y0) => (cB @ Y0)))))) = $true)),
% 0.98/0.90 inference(boolean_simplification,[status(thm)],[f6])).
% 0.98/0.90 thf(f6,plain,(
% 0.98/0.90 ((~ (((!! @ $i @ (^[Y0 : $i]: ((cA @ Y0) => (cB @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((cA @ Y0) => (cB @ Y0))))) => (!! @ $i @ (^[Y0 : $i]: ((cA @ Y0) => (cB @ Y0)))))) = $true)),
% 0.98/0.90 inference(cnf_transformation,[status(thm)],[f5])).
% 0.98/0.90 thf(f5,plain,(
% 0.98/0.90 ((~ (((!! @ $i @ (^[Y0 : $i]: ((cA @ Y0) => (cB @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((cA @ Y0) => (cB @ Y0))))) => (!! @ $i @ (^[Y0 : $i]: ((cA @ Y0) => (cB @ Y0)))))) = $true)),
% 0.98/0.90 inference(fool_elimination,[status(thm)],[f4])).
% 0.98/0.90 thf(f4,plain,(
% 0.98/0.90 ~((! [X0 : $i] : ((cA @ X0) => (cB @ X0)) | ! [X1 : $i] : ((cA @ X1) => (cB @ X1))) => ! [X2 : $i] : ((cA @ X2) => (cB @ X2)))),
% 0.98/0.90 inference(rectify,[status(thm)],[f2])).
% 0.98/0.90 thf(f2,negated_conjecture,(
% 0.98/0.90 ~((! [X0 : $i] : ((cA @ X0) => (cB @ X0)) | ! [X0 : $i] : ((cA @ X0) => (cB @ X0))) => ! [X0 : $i] : ((cA @ X0) => (cB @ X0)))),
% 0.98/0.90 inference(negated_conjecture,[status(cth)],[f1])).
% 0.98/0.90 thf(f1,conjecture,(
% 0.98/0.90 (! [X0 : $i] : ((cA @ X0) => (cB @ X0)) | ! [X0 : $i] : ((cA @ X0) => (cB @ X0))) => ! [X0 : $i] : ((cA @ X0) => (cB @ X0))),
% 0.98/0.90 file('/export/starexec/sandbox/tmp/tmp.WngKGbrmhH/DTF2THF_2867.p',cDUAL_EG1_pme)).
% 0.98/0.90 % SZS output end Proof for DTF2THF_2867
% 0.98/0.90 % (3133)------------------------------
% 0.98/0.90 % (3133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.90 % (3133)Termination reason: Refutation
% 0.98/0.90
% 0.98/0.90 % (3133)Memory used [KB]: 5373
% 0.98/0.90 % (3133)Time elapsed: 0.002 s
% 0.98/0.90 % (3133)------------------------------
% 0.98/0.90 % (3133)------------------------------
% 0.98/0.90 % (3128)Success in time 0.011 s
%------------------------------------------------------------------------------