%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET592^5 : 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 : n028.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 09:31:50 AM UTC 2026
% Result : Theorem 1.48s 1.28s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 222 ( 86 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 210 ( 31 ~; 24 |; 42 &; 97 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 97 ( 39 ^; 46 !; 12 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a > $o ).
thf(func_def_11,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK5: a ).
thf(f48,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f38,f46]) ).
thf(f46,plain,
( ( sK0 @ sK5 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true = $false )
| ( ( sK0 @ sK5 )
= $false ) ),
inference(superposition,[status(thm)],[f30,f25]) ).
thf(f25,plain,
! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( sK0 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: a] :
( ( ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 )
= ( ^ [Y0: a] : $false
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X3: a] :
( ( ( sK2 @ X3 )
!= $true )
| ( $true
= ( sK0 @ X3 ) ) )
& ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( ( sK2 @ X4 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( ( ^ [Y0: a] : $false )
!= sK2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
| ( ( X2 @ X4 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( ( ^ [Y0: a] : $false )
!= X2 ) )
=> ( ! [X3: a] :
( ( ( sK2 @ X3 )
!= $true )
| ( $true
= ( sK0 @ X3 ) ) )
& ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( ( sK2 @ X4 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( ( ^ [Y0: a] : $false )
!= sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
| ( ( X2 @ X4 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( ( ^ [Y0: a] : $false )
!= X2 ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X4: a] :
( ( ( X2 @ X4 )
!= $true )
| ( $true
= ( X0 @ X4 ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( ( ^ [Y0: a] : $false )
!= X2 ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X2 )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
!= $true )
| ( $true
= ( X0 @ X4 ) ) )
& ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X1 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
=> ( $true
= ( X0 @ X4 ) ) )
& ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) )
=> ( ( ^ [Y0: a] : $false )
= X2 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
=> ( $true
= ( X1 @ X5 ) ) )
& ! [X6: a] :
( ( ( X2 @ X6 )
= $true )
=> ( $true
= ( X0 @ X6 ) ) ) )
=> ( ( ^ [Y0: a] : $false )
= X2 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [X3: a] : $false )
= ( ^ [X4: a] :
( ( X1 @ X4 )
& ( X0 @ X4 ) ) ) )
& ! [X5: a] :
( ( X2 @ X5 )
=> ( X1 @ X5 ) )
& ! [X6: a] :
( ( X2 @ X6 )
=> ( X0 @ X6 ) ) )
=> ( X2
= ( ^ [X7: a] : $false ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ( ( ^ [X3: a] : $false )
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ( X0
= ( ^ [X3: a] : $false ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ( ( ^ [X3: a] : $false )
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ( X0
= ( ^ [X3: a] : $false ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.T9zeh7iIUZ/DTF2THF_19238.p',cBOOL_PROP_51_pme) ).
thf(f30,plain,
( $true
= ( sK1 @ sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $false != $false )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f17,f20]) ).
thf(f20,plain,
! [X4: a] :
( ( ( sK2 @ X4 )
= $false )
| ( $true
= ( sK1 @ X4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
! [X4: a] :
( ( $true != $true )
| ( ( sK2 @ X4 )
= $false )
| ( $true
= ( sK1 @ X4 ) ) ),
inference(fool_paramodulation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X4: a] :
( ( ( sK2 @ X4 )
!= $true )
| ( $true
= ( sK1 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f17,plain,
( ( sK2 @ sK5 )
!= $false ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( sK2 @ sK5 )
!= ( ^ [Y0: a] : $false
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a] : $false )
!= sK2 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f38,plain,
( ( sK0 @ sK5 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $false != $false )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(superposition,[status(thm)],[f17,f22]) ).
thf(f22,plain,
! [X3: a] :
( ( ( sK2 @ X3 )
= $false )
| ( $true
= ( sK0 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
! [X3: a] :
( ( $true != $true )
| ( $true
= ( sK0 @ X3 ) )
| ( ( sK2 @ X3 )
= $false ) ),
inference(fool_paramodulation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X3: a] :
( ( ( sK2 @ X3 )
!= $true )
| ( $true
= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET592^5 : 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
% 0.17/0.33 % Computer : n028.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 11:59:57 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SET592^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : TPS problem BOOL-PROP-51
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English : Trybulec's 51st Boolean property of sets
% 0.19/0.45
% 0.19/0.45 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0318 [Bro09]
% 0.19/0.45 % : BOOL-PROP-51 [TPS]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 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 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.19/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.19/0.45 % Number of atoms : 4 ( 2 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 2 ( 4 avg)
% 0.19/0.45 % Number of connectives : 12 ( 0 ~; 0 |; 3 &; 6 @)
% 0.19/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 10 ( 10 avg)
% 0.19/0.45 % Number of types : 2 ( 1 usr)
% 0.19/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.19/0.45 % Number of variables : 8 ( 3 ^; 5 !; 0 ?; 8 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 % : Polymorphic definitions expanded.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(a_type,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(cBOOL_PROP_51_pme,conjecture,
% 0.19/0.45 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.19/0.45 ( ( ! [Xx: a] :
% 0.19/0.45 ( ( X @ Xx )
% 0.19/0.45 => ( Y @ Xx ) )
% 0.19/0.45 & ! [Xx: a] :
% 0.19/0.45 ( ( X @ Xx )
% 0.19/0.45 => ( Z @ Xx ) )
% 0.19/0.45 & ( ( ^ [Xx: a] :
% 0.19/0.45 ( ( Y @ Xx )
% 0.19/0.45 & ( Z @ Xx ) ) )
% 0.19/0.45 = ( ^ [Xx: a] : $false ) ) )
% 0.19/0.45 => ( X
% 0.19/0.45 = ( ^ [Xx: a] : $false ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.48/1.24 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 11:59:57 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.T9zeh7iIUZ/DTF2DTF19238.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.25 ---- Cleaned THF ---
% 1.48/1.25 thf(a_type,type,
% 1.48/1.25 a: $tType ).
% 1.48/1.25
% 1.48/1.25 thf(cBOOL_PROP_51_pme,conjecture,
% 1.48/1.25 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.48/1.25 ( ( ! [Xx: a] :
% 1.48/1.25 ( ( X @ Xx )
% 1.48/1.25 => ( Y @ Xx ) )
% 1.48/1.25 & ! [Xx: a] :
% 1.48/1.25 ( ( X @ Xx )
% 1.48/1.25 => ( Z @ Xx ) )
% 1.48/1.25 & ( ( ^ [Xx: a] :
% 1.48/1.25 ( ( Y @ Xx )
% 1.48/1.25 & ( Z @ Xx ) ) )
% 1.48/1.25 = ( ^ [Xx: a] : $false ) ) )
% 1.48/1.25 => ( X
% 1.48/1.25 = ( ^ [Xx: a] : $false ) ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.27 % (19347)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19238 for (2999ds/183Mi)
% 1.48/1.27 % (19351)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_19238 for (2999ds/2Mi)
% 1.48/1.27 % (19347)Refutation not found, incomplete strategy
% 1.48/1.27 % (19347)------------------------------
% 1.48/1.27 % (19347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (19347)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.27
% 1.48/1.27
% 1.48/1.27 % (19347)Memory used [KB]: 5500
% 1.48/1.27 % (19347)Time elapsed: 0.002 s
% 1.48/1.27 % (19347)Instructions burned: 2 (million)
% 1.48/1.27 % (19347)------------------------------
% 1.48/1.27 % (19347)------------------------------
% 1.48/1.27 % (19351)Instruction limit reached!
% 1.48/1.27 % (19351)------------------------------
% 1.48/1.27 % (19351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (19351)Termination reason: Unknown
% 1.48/1.27 % (19351)Termination phase: Saturation
% 1.48/1.27
% 1.48/1.27 % (19351)Memory used [KB]: 5500
% 1.48/1.27 % (19351)Time elapsed: 0.002 s
% 1.48/1.27 % (19351)Instructions burned: 2 (million)
% 1.48/1.27 % (19351)------------------------------
% 1.48/1.27 % (19351)------------------------------
% 1.48/1.28 % (19348)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_19238 for (2999ds/4Mi)
% 1.48/1.28 % (19349)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_19238 for (2999ds/27Mi)
% 1.48/1.28 % (19350)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19238 for (2999ds/2Mi)
% 1.48/1.28 % (19352)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_19238 for (2999ds/275Mi)
% 1.48/1.28 % (19353)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19238 for (2999ds/18Mi)
% 1.48/1.28 % (19350)Instruction limit reached!
% 1.48/1.28 % (19350)------------------------------
% 1.48/1.28 % (19350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (19350)Termination reason: Unknown
% 1.48/1.28 % (19350)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (19350)Memory used [KB]: 5500
% 1.48/1.28 % (19350)Time elapsed: 0.004 s
% 1.48/1.28 % (19350)Instructions burned: 2 (million)
% 1.48/1.28 % (19350)------------------------------
% 1.48/1.28 % (19350)------------------------------
% 1.48/1.28 % (19349)Refutation not found, incomplete strategy
% 1.48/1.28 % (19349)------------------------------
% 1.48/1.28 % (19349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (19349)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.28
% 1.48/1.28
% 1.48/1.28 % (19349)Memory used [KB]: 5500
% 1.48/1.28 % (19349)Time elapsed: 0.004 s
% 1.48/1.28 % (19349)Instructions burned: 2 (million)
% 1.48/1.28 % (19349)------------------------------
% 1.48/1.28 % (19349)------------------------------
% 1.48/1.28 % (19353)Refutation not found, incomplete strategy
% 1.48/1.28 % (19353)------------------------------
% 1.48/1.28 % (19353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (19353)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.28
% 1.48/1.28
% 1.48/1.28 % (19353)Memory used [KB]: 5500
% 1.48/1.28 % (19353)Time elapsed: 0.004 s
% 1.48/1.28 % (19353)Instructions burned: 2 (million)
% 1.48/1.28 % (19353)------------------------------
% 1.48/1.28 % (19353)------------------------------
% 1.48/1.28 % (19352)Refutation not found, incomplete strategy
% 1.48/1.28 % (19352)------------------------------
% 1.48/1.28 % (19352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (19352)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.28
% 1.48/1.28
% 1.48/1.28 % (19352)Memory used [KB]: 5500
% 1.48/1.28 % (19352)Time elapsed: 0.004 s
% 1.48/1.28 % (19352)Instructions burned: 2 (million)
% 1.48/1.28 % (19352)------------------------------
% 1.48/1.28 % (19352)------------------------------
% 1.48/1.28 % (19354)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19238 for (2999ds/3Mi)
% 1.48/1.28 % (19348)First to succeed.
% 1.48/1.28 % (19354)Refutation not found, incomplete strategy
% 1.48/1.28 % (19354)------------------------------
% 1.48/1.28 % (19354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (19354)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.28
% 1.48/1.28
% 1.48/1.28 % (19354)Memory used [KB]: 5500
% 1.48/1.28 % (19354)Time elapsed: 0.002 s
% 1.48/1.28 % (19354)Instructions burned: 2 (million)
% 1.48/1.28 % (19354)------------------------------
% 1.48/1.28 % (19354)------------------------------
% 1.48/1.28 % (19355)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_19238 for (2999ds/37Mi)
% 1.48/1.28 % (19348)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_19238
% 1.48/1.28 % SZS output start Proof for DTF2THF_19238
% 1.48/1.28 thf(type_def_5, type, a: $tType).
% 1.48/1.28 thf(func_def_0, type, a: $tType).
% 1.48/1.28 thf(func_def_7, type, sK0: a > $o).
% 1.48/1.28 thf(func_def_8, type, sK1: a > $o).
% 1.48/1.28 thf(func_def_9, type, sK2: a > $o).
% 1.48/1.28 thf(func_def_11, type, ph4: !>[X0: $tType]:(X0)).
% 1.48/1.28 thf(func_def_12, type, sK5: a).
% 1.48/1.28 thf(f48,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.48/1.28 thf(f47,plain,(
% 1.48/1.28 ($true = $false)),
% 1.48/1.28 inference(backward_demodulation,[status(thm)],[f38,f46])).
% 1.48/1.28 thf(f46,plain,(
% 1.48/1.28 ((sK0 @ sK5) = $false)),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.48/1.28 thf(f43,plain,(
% 1.48/1.28 ($true = $false) | ((sK0 @ sK5) = $false)),
% 1.48/1.28 inference(superposition,[status(thm)],[f30,f25])).
% 1.48/1.28 thf(f25,plain,(
% 1.48/1.28 ( ! [X1 : a] : (($false = (sK1 @ X1)) | ((sK0 @ X1) = $false)) )),
% 1.48/1.28 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.48/1.28 thf(f24,plain,(
% 1.48/1.28 ( ! [X1 : a] : ((((sK0 @ X1) & (sK1 @ X1)) = $false)) )),
% 1.48/1.28 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.48/1.28 thf(f23,plain,(
% 1.48/1.28 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) @ X1) = ((^[Y0 : a]: ($false)) @ X1))) )),
% 1.48/1.28 inference(argument_congruence,[status(thm)],[f13])).
% 1.48/1.28 thf(f13,plain,(
% 1.48/1.28 ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) = (^[Y0 : a]: ($false)))),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.28 thf(f11,plain,(
% 1.48/1.28 ! [X3 : a] : (((sK2 @ X3) != $true) | ($true = (sK0 @ X3))) & ! [X4 : a] : (($true = (sK1 @ X4)) | ((sK2 @ X4) != $true)) & ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) = (^[Y0 : a]: ($false))) & ((^[Y0 : a]: ($false)) != sK2)),
% 1.48/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f10])).
% 1.48/1.28 thf(f10,plain,(
% 1.48/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X2 @ X3) != $true) | ((X0 @ X3) = $true)) & ! [X4 : a] : (($true = (X1 @ X4)) | ((X2 @ X4) != $true)) & ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = (^[Y0 : a]: ($false))) & ((^[Y0 : a]: ($false)) != X2)) => (! [X3 : a] : (((sK2 @ X3) != $true) | ($true = (sK0 @ X3))) & ! [X4 : a] : (($true = (sK1 @ X4)) | ((sK2 @ X4) != $true)) & ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) = (^[Y0 : a]: ($false))) & ((^[Y0 : a]: ($false)) != sK2))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f9,plain,(
% 1.48/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X2 @ X3) != $true) | ((X0 @ X3) = $true)) & ! [X4 : a] : (($true = (X1 @ X4)) | ((X2 @ X4) != $true)) & ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = (^[Y0 : a]: ($false))) & ((^[Y0 : a]: ($false)) != X2))),
% 1.48/1.28 inference(rectify,[status(thm)],[f8])).
% 1.48/1.28 thf(f8,plain,(
% 1.48/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X4 : a] : (((X2 @ X4) != $true) | ($true = (X0 @ X4))) & ! [X3 : a] : (((X1 @ X3) = $true) | ((X2 @ X3) != $true)) & ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = (^[Y0 : a]: ($false))) & ((^[Y0 : a]: ($false)) != X2))),
% 1.48/1.28 inference(flattening,[status(thm)],[f7])).
% 1.48/1.28 thf(f7,plain,(
% 1.48/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((^[Y0 : a]: ($false)) != X2) & (! [X3 : a] : (((X1 @ X3) = $true) | ((X2 @ X3) != $true)) & ! [X4 : a] : (((X2 @ X4) != $true) | ($true = (X0 @ X4))) & ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = (^[Y0 : a]: ($false)))))),
% 1.48/1.28 inference(ennf_transformation,[status(thm)],[f6])).
% 1.48/1.28 thf(f6,plain,(
% 1.48/1.28 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : (((X2 @ X3) = $true) => ((X1 @ X3) = $true)) & ! [X4 : a] : (((X2 @ X4) = $true) => ($true = (X0 @ X4))) & ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = (^[Y0 : a]: ($false)))) => ((^[Y0 : a]: ($false)) = X2))),
% 1.48/1.28 inference(rectify,[status(thm)],[f5])).
% 1.48/1.28 thf(f5,plain,(
% 1.48/1.28 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = (^[Y0 : a]: ($false))) & ! [X5 : a] : (($true = (X2 @ X5)) => ($true = (X1 @ X5))) & ! [X6 : a] : (((X2 @ X6) = $true) => ($true = (X0 @ X6)))) => ((^[Y0 : a]: ($false)) = X2))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.28 thf(f4,plain,(
% 1.48/1.28 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((((^[X3 : a] : ($false)) = (^[X4 : a] : ((X1 @ X4) & (X0 @ X4)))) & ! [X5 : a] : ((X2 @ X5) => (X1 @ X5)) & ! [X6 : a] : ((X2 @ X6) => (X0 @ X6))) => (X2 = (^[X7 : a] : ($false))))),
% 1.48/1.28 inference(rectify,[status(thm)],[f2])).
% 1.48/1.28 thf(f2,negated_conjecture,(
% 1.48/1.28 ~! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((((^[X3 : a] : ($false)) = (^[X3 : a] : ((X2 @ X3) & (X1 @ X3)))) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))) => (X0 = (^[X3 : a] : ($false))))),
% 1.48/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.28 thf(f1,conjecture,(
% 1.48/1.28 ! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((((^[X3 : a] : ($false)) = (^[X3 : a] : ((X2 @ X3) & (X1 @ X3)))) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))) => (X0 = (^[X3 : a] : ($false))))),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.T9zeh7iIUZ/DTF2THF_19238.p',cBOOL_PROP_51_pme)).
% 1.48/1.28 thf(f30,plain,(
% 1.48/1.28 ($true = (sK1 @ sK5))),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.48/1.28 thf(f27,plain,(
% 1.48/1.28 ($false != $false) | ($true = (sK1 @ sK5))),
% 1.48/1.28 inference(superposition,[status(thm)],[f17,f20])).
% 1.48/1.28 thf(f20,plain,(
% 1.48/1.28 ( ! [X4 : a] : (((sK2 @ X4) = $false) | ($true = (sK1 @ X4))) )),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.48/1.28 thf(f19,plain,(
% 1.48/1.28 ( ! [X4 : a] : (($true != $true) | ((sK2 @ X4) = $false) | ($true = (sK1 @ X4))) )),
% 1.48/1.28 inference(fool_paramodulation,[status(thm)],[f14])).
% 1.48/1.28 thf(f14,plain,(
% 1.48/1.28 ( ! [X4 : a] : (((sK2 @ X4) != $true) | ($true = (sK1 @ X4))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.28 thf(f17,plain,(
% 1.48/1.28 ((sK2 @ sK5) != $false)),
% 1.48/1.28 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.48/1.28 thf(f16,plain,(
% 1.48/1.28 ((sK2 @ sK5) != ((^[Y0 : a]: ($false)) @ sK5))),
% 1.48/1.28 inference(negative_extensionality,[status(thm)],[f12])).
% 1.48/1.28 thf(f12,plain,(
% 1.48/1.28 ((^[Y0 : a]: ($false)) != sK2)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.28 thf(f38,plain,(
% 1.48/1.28 ((sK0 @ sK5) = $true)),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.48/1.28 thf(f34,plain,(
% 1.48/1.28 ($false != $false) | ((sK0 @ sK5) = $true)),
% 1.48/1.28 inference(superposition,[status(thm)],[f17,f22])).
% 1.48/1.28 thf(f22,plain,(
% 1.48/1.28 ( ! [X3 : a] : (((sK2 @ X3) = $false) | ($true = (sK0 @ X3))) )),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.48/1.28 thf(f21,plain,(
% 1.48/1.28 ( ! [X3 : a] : (($true != $true) | ($true = (sK0 @ X3)) | ((sK2 @ X3) = $false)) )),
% 1.48/1.28 inference(fool_paramodulation,[status(thm)],[f15])).
% 1.48/1.28 thf(f15,plain,(
% 1.48/1.28 ( ! [X3 : a] : (((sK2 @ X3) != $true) | ($true = (sK0 @ X3))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.28 % SZS output end Proof for DTF2THF_19238
% 1.48/1.28 % (19348)------------------------------
% 1.48/1.28 % (19348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (19348)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (19348)Memory used [KB]: 5500
% 1.48/1.28 % (19348)Time elapsed: 0.006 s
% 1.48/1.28 % (19348)Instructions burned: 3 (million)
% 1.48/1.28 % (19348)------------------------------
% 1.48/1.28 % (19348)------------------------------
% 1.48/1.28 % (19344)Success in time 0.018 s
%------------------------------------------------------------------------------