%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET196^5 : 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 : n013.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 09:31:24 AM UTC 2026
% Result : Theorem 1.63s 1.32s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 13 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 118 ( 4 ~; 0 |; 14 &; 73 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 4 con; 0-2 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 27 ( 18 ^; 9 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_13,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK2: a > $o ).
thf(func_def_15,type,
sK3: a ).
thf(func_def_16,type,
sK4: a > $o ).
thf(f18,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f17]) ).
thf(f17,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( $false
& ( sK4 @ sK3 ) ) ),
inference(forward_demodulation,[status(thm)],[f15,f14]) ).
thf(f14,plain,
( $false
= ( sK2 @ sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( sK2 @ sK3 )
& ( sK4 @ sK3 ) )
=> ( sK2 @ sK3 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > $o] :
( ( ( sK2 @ sK3 )
& ( Y0 @ sK3 ) )
=> ( sK2 @ sK3 ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( sK2 @ sK3 )
& ( Y0 @ sK3 ) )
=> ( sK2 @ sK3 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( sK2 @ Y0 )
& ( Y1 @ Y0 ) )
=> ( sK2 @ Y0 ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( sK2 @ Y0 )
& ( Y1 @ Y0 ) )
=> ( sK2 @ Y0 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y0 @ Y1 )
& ( Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y0 @ Y1 )
& ( Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y0 @ Y1 )
& ( Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y0 @ Y1 )
& ( Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a,X2: a > $o] :
( ( ( X0 @ X1 )
& ( X2 @ X1 ) )
=> ( X2 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a,X0: a > $o] :
( ( ( X1 @ X2 )
& ( X0 @ X2 ) )
=> ( X0 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X2: a,X0: a > $o] :
( ( ( X1 @ X2 )
& ( X0 @ X2 ) )
=> ( X0 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.DJZ6GkGw9l/DTF2THF_10941.p',cBOOL_PROP_37_pme) ).
thf(f15,plain,
( $true
= ( ( sK2 @ sK3 )
& ( sK4 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET196^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n013.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 11:54:23 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SET196^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : TPS problem BOOL-PROP-37
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : Trybulec's 37th Boolean property of sets
% 0.29/0.46
% 0.29/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.29/0.46 % : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.29/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0074 [Bro09]
% 0.29/0.46 % : tps_0078 [Bro09]
% 0.29/0.46 % : 20 [Bar92]
% 0.29/0.46 % : GAZING-THM20 [TPS]
% 0.29/0.46 % : BOOL-PROP-37 [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.29/0.46 % Number of connectives : 5 ( 0 ~; 0 |; 1 &; 3 @)
% 0.29/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.29/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_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 % : Polymorphic definitions expanded.
% 0.29/0.46 % :
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(a_type,type,
% 0.29/0.46 a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(cBOOL_PROP_37_pme,conjecture,
% 0.29/0.46 ! [X: a > $o,Y: a > $o,Xx: a] :
% 0.29/0.46 ( ( ( X @ Xx )
% 0.29/0.46 & ( Y @ Xx ) )
% 0.29/0.46 => ( X @ Xx ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.46/1.29 ---- Embedded in THF ---
% 1.46/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.29 %%% Generated on Tue Feb 24 11:54:24 EST 2026
% 1.46/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.29 %%% Logic specification used:
% 1.46/1.29 %%% thf(spec, logic, $$dhol).
% 1.46/1.29
% 1.46/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.DJZ6GkGw9l/DTF2DTF10941.p
% See solution above
% 1.46/1.29 ------------------------
% 1.63/1.30 ---- Cleaned THF ---
% 1.63/1.30 thf(a_type,type,
% 1.63/1.30 a: $tType ).
% 1.63/1.30
% 1.63/1.30 thf(cBOOL_PROP_37_pme,conjecture,
% 1.63/1.30 ! [X: a > $o,Y: a > $o,Xx: a] :
% 1.63/1.30 ( ( ( X @ Xx )
% 1.63/1.30 & ( Y @ Xx ) )
% 1.63/1.30 => ( X @ Xx ) ) ).
% 1.63/1.30 ------------------------
% 1.63/1.32 % (11165)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_10941 for (2999ds/2Mi)
% 1.63/1.32 % (11165)First to succeed.
% 1.63/1.32 % (11165)Refutation found. Thanks to Tanya!
% 1.63/1.32 % SZS status Theorem for DTF2THF_10941
% 1.63/1.32 % SZS output start Proof for DTF2THF_10941
% 1.63/1.32 thf(type_def_5, type, a: $tType).
% 1.63/1.32 thf(func_def_0, type, a: $tType).
% 1.63/1.32 thf(func_def_13, type, ph1: !>[X0: $tType]:(X0)).
% 1.63/1.32 thf(func_def_14, type, sK2: a > $o).
% 1.63/1.32 thf(func_def_15, type, sK3: a).
% 1.63/1.32 thf(func_def_16, type, sK4: a > $o).
% 1.63/1.32 thf(f18,plain,(
% 1.63/1.32 $false),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f17])).
% 1.63/1.32 thf(f17,plain,(
% 1.63/1.32 ($true = $false)),
% 1.63/1.32 inference(boolean_simplification,[status(thm)],[f16])).
% 1.63/1.32 thf(f16,plain,(
% 1.63/1.32 ($true = ($false & (sK4 @ sK3)))),
% 1.63/1.32 inference(forward_demodulation,[status(thm)],[f15,f14])).
% 1.63/1.32 thf(f14,plain,(
% 1.63/1.32 ($false = (sK2 @ sK3))),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.63/1.32 thf(f13,plain,(
% 1.63/1.32 ((((sK2 @ sK3) & (sK4 @ sK3)) => (sK2 @ sK3)) = $false)),
% 1.63/1.32 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.63/1.32 thf(f12,plain,(
% 1.63/1.32 ($false = ((^[Y0 : a > $o]: (((sK2 @ sK3) & (Y0 @ sK3)) => (sK2 @ sK3))) @ sK4))),
% 1.63/1.32 inference(sigma_clausification,[status(thm)],[f11])).
% 1.63/1.32 thf(f11,plain,(
% 1.63/1.32 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((sK2 @ sK3) & (Y0 @ sK3)) => (sK2 @ sK3)))) = $false)),
% 1.63/1.32 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.63/1.32 thf(f10,plain,(
% 1.63/1.32 (((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((sK2 @ Y0) & (Y1 @ Y0)) => (sK2 @ Y0))))) @ sK3) = $false)),
% 1.63/1.32 inference(sigma_clausification,[status(thm)],[f9])).
% 1.63/1.32 thf(f9,plain,(
% 1.63/1.32 ((!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((sK2 @ Y0) & (Y1 @ Y0)) => (sK2 @ Y0)))))) = $false)),
% 1.63/1.32 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.63/1.32 thf(f8,plain,(
% 1.63/1.32 (((^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y0 @ Y1) & (Y2 @ Y1)) => (Y0 @ Y1))))))) @ sK2) = $false)),
% 1.63/1.32 inference(sigma_clausification,[status(thm)],[f7])).
% 1.63/1.32 thf(f7,plain,(
% 1.63/1.32 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y0 @ Y1) & (Y2 @ Y1)) => (Y0 @ Y1)))))))) = $false)),
% 1.63/1.32 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.63/1.32 thf(f6,plain,(
% 1.63/1.32 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y0 @ Y1) & (Y2 @ Y1)) => (Y0 @ Y1))))))))))),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f5])).
% 1.63/1.32 thf(f5,plain,(
% 1.63/1.32 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y0 @ Y1) & (Y2 @ Y1)) => (Y0 @ Y1))))))))))),
% 1.63/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.32 thf(f4,plain,(
% 1.63/1.32 ~! [X0 : a > $o,X1 : a,X2 : a > $o] : (((X0 @ X1) & (X2 @ X1)) => (X2 @ X1))),
% 1.63/1.32 inference(rectify,[status(thm)],[f2])).
% 1.63/1.32 thf(f2,negated_conjecture,(
% 1.63/1.32 ~! [X1 : a > $o,X2 : a,X0 : a > $o] : (((X1 @ X2) & (X0 @ X2)) => (X0 @ X2))),
% 1.63/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.32 thf(f1,conjecture,(
% 1.63/1.32 ! [X1 : a > $o,X2 : a,X0 : a > $o] : (((X1 @ X2) & (X0 @ X2)) => (X0 @ X2))),
% 1.63/1.32 file('/export/starexec/sandbox2/tmp/tmp.DJZ6GkGw9l/DTF2THF_10941.p',cBOOL_PROP_37_pme)).
% 1.63/1.32 thf(f15,plain,(
% 1.63/1.32 ($true = ((sK2 @ sK3) & (sK4 @ sK3)))),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.63/1.32 % SZS output end Proof for DTF2THF_10941
% 1.63/1.32 % (11165)------------------------------
% 1.63/1.32 % (11165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (11165)Termination reason: Refutation
% 1.63/1.32
% 1.63/1.32 % (11165)Memory used [KB]: 5500
% 1.63/1.32 % (11165)Time elapsed: 0.003 s
% 1.63/1.32 % (11165)Instructions burned: 1 (million)
% 1.63/1.32 % (11165)------------------------------
% 1.63/1.32 % (11165)------------------------------
% 1.63/1.32 % (11160)Success in time 0.013 s
%------------------------------------------------------------------------------