%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU845^5 : 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 : n027.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 09:37:34 AM UTC 2026
% Result : Theorem 1.53s 1.37s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 214 ( 64 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 244 ( 61 ~; 36 |; 34 &; 101 @)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 10 ^; 17 !; 4 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_8,type,
sK0: a > $o ).
thf(func_def_9,type,
sK1: a > $o ).
thf(func_def_11,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK4: a ).
thf(f58,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f35,f41,f47,f57]) ).
thf(f57,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $true = $false )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f36,f30]) ).
thf(f30,plain,
( ( ( sK0 @ sK4 )
= $false )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl2_1
<=> ( ( sK0 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f36,plain,
( ( sK0 @ sK4 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f22,f9]) ).
thf(f9,plain,
! [X2: a] :
( ( ( sK0 @ X2 )
= $true )
| ( ( sK1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( sK1
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
& ! [X2: a] :
( ( ( sK1 @ X2 )
!= $true )
| ( ( sK0 @ X2 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
!= X1 )
& ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
= $true ) ) )
=> ( ( sK1
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
& ! [X2: a] :
( ( ( sK1 @ X2 )
!= $true )
| ( ( sK0 @ X2 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
!= X1 )
& ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
=> ( ( X0 @ X2 )
= $true ) )
=> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
= X1 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) )
=> ( X1
= ( ^ [X3: a] :
( ~ ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
& ( X0 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ( X0
= ( ^ [X2: a] :
( ~ ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
& ( X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ( X0
= ( ^ [X2: a] :
( ~ ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
& ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rqGzcGTLmx/DTF2THF_3769.p',cGAZING_THM12_pme) ).
thf(f22,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( ( ( sK0 @ sK4 )
& ~ ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( sK0 @ sK4 )
& ~ ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
!= ( sK1 @ sK4 ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK4 )
!= ( sK1 @ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f10]) ).
thf(f10,plain,
( sK1
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f47,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f46]) ).
thf(f46,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f34,f40]) ).
thf(f40,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl2_3
<=> ( $false
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f34,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl2_2
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f41,plain,
( spl2_3
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f20,f28,f38]) ).
thf(f20,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ( ( sK0 @ sK4 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ( ( sK0 @ sK4 )
= $false )
| ( $false
= ( sK1 @ sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( ~ ( sK1 @ sK4 ) )
= $true )
| ( ( sK0 @ sK4 )
= $false )
| ( $false
= ( sK1 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
= $true )
| ( $false
= ( sK1 @ sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ~ ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $false )
| ( ( sK0 @ sK4 )
= $false )
| ( $false
= ( sK1 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( ( sK0 @ sK4 )
& ~ ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $false )
| ( $false
= ( sK1 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f35,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f26,f32,f28]) ).
thf(f26,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( ( sK0 @ sK4 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK4 ) )
| ( ( sK0 @ sK4 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( ~ ( sK1 @ sK4 ) )
= $false )
| ( $true
= ( sK1 @ sK4 ) )
| ( ( sK0 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) )
= $false )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( ( ~ ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU845^5 : 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
% 0.18/0.34 % Computer : n027.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:35:52 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.45 ---- Original DTF file ---
% 0.21/0.45 thf(spec,logic,$$dhol).
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 % File : SEU845^5 : TPTP v9.2.1. Released v4.0.0.
% 0.21/0.45 % Domain : Set Theory
% 0.21/0.45 % Problem : TPS problem GAZING-THM12
% 0.21/0.45 % Version : Especial.
% 0.21/0.45 % English :
% 0.21/0.45
% 0.21/0.45 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.21/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.45 % Source : [Bro09]
% 0.21/0.45 % Names : tps_0229 [Bro09]
% 0.21/0.45 % : 12 [Bar92]
% 0.21/0.45 % : GAZING-THM12 [TPS]
% 0.21/0.45
% 0.21/0.45 % Status : Theorem
% 0.21/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 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, 0.00 v6.1.0, 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
% 0.21/0.45 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.21/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.21/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.21/0.45 % Number of connectives : 11 ( 2 ~; 0 |; 2 &; 5 @)
% 0.21/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.45 % Maximal formula depth : 7 ( 7 avg)
% 0.21/0.45 % Number of types : 2 ( 1 usr)
% 0.21/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.21/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.21/0.45 % Number of variables : 4 ( 1 ^; 3 !; 0 ?; 4 :)
% 0.21/0.45 % SPC : TH0_THM_EQU_NAR
% 0.21/0.45
% 0.21/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.45 % : Polymorphic definitions expanded.
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 thf(a_type,type,
% 0.21/0.45 a: $tType ).
% 0.21/0.45
% 0.21/0.45 thf(cGAZING_THM12_pme,conjecture,
% 0.21/0.45 ! [S: a > $o,T: a > $o] :
% 0.21/0.45 ( ! [Xx: a] :
% 0.21/0.45 ( ( S @ Xx )
% 0.21/0.45 => ( T @ Xx ) )
% 0.21/0.45 => ( S
% 0.21/0.45 = ( ^ [Xx: a] :
% 0.21/0.45 ( ( T @ Xx )
% 0.21/0.45 & ~ ( ( T @ Xx )
% 0.21/0.45 & ~ ( S @ Xx ) ) ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 ------------------------
% 1.53/1.34 ---- Embedded in THF ---
% 1.53/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.34 %%% Generated on Tue Feb 24 12:35:53 EST 2026
% 1.53/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.34 %%% Logic specification used:
% 1.53/1.34 %%% thf(spec, logic, $$dhol).
% 1.53/1.34
% 1.53/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.rqGzcGTLmx/DTF2DTF3769.p
% See solution above
% 1.53/1.34 ------------------------
% 1.53/1.35 ---- Cleaned THF ---
% 1.53/1.35 thf(a_type,type,
% 1.53/1.35 a: $tType ).
% 1.53/1.35
% 1.53/1.35 thf(cGAZING_THM12_pme,conjecture,
% 1.53/1.35 ! [S: a > $o,T: a > $o] :
% 1.53/1.35 ( ! [Xx: a] :
% 1.53/1.35 ( ( S @ Xx )
% 1.53/1.35 => ( T @ Xx ) )
% 1.53/1.35 => ( S
% 1.53/1.35 = ( ^ [Xx: a] :
% 1.53/1.35 ( ( T @ Xx )
% 1.53/1.35 & ~ ( ( T @ Xx )
% 1.53/1.35 & ~ ( S @ Xx ) ) ) ) ) ) ).
% 1.53/1.35 ------------------------
% 1.53/1.37 % (3866)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3769 for (3000ds/183Mi)
% 1.53/1.37 % (3867)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_3769 for (3000ds/4Mi)
% 1.53/1.37 % (3868)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_3769 for (3000ds/27Mi)
% 1.53/1.37 % (3870)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_3769 for (3000ds/2Mi)
% 1.53/1.37 % (3869)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3769 for (3000ds/2Mi)
% 1.53/1.37 % (3871)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_3769 for (3000ds/275Mi)
% 1.53/1.37 % (3872)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3769 for (3000ds/18Mi)
% 1.53/1.37 % (3869)Instruction limit reached!
% 1.53/1.37 % (3869)------------------------------
% 1.53/1.37 % (3869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.37 % (3869)Termination reason: Unknown
% 1.53/1.37 % (3869)Termination phase: Saturation
% 1.53/1.37
% 1.53/1.37 % (3870)Instruction limit reached!
% 1.53/1.37 % (3870)------------------------------
% 1.53/1.37 % (3870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.37 % (3870)Termination reason: Unknown
% 1.53/1.37 % (3870)Termination phase: Saturation
% 1.53/1.37
% 1.53/1.37 % (3870)Memory used [KB]: 5500
% 1.53/1.37 % (3870)Time elapsed: 0.003 s
% 1.53/1.37 % (3870)Instructions burned: 3 (million)
% 1.53/1.37 % (3870)------------------------------
% 1.53/1.37 % (3870)------------------------------
% 1.53/1.37 % (3869)Memory used [KB]: 5500
% 1.53/1.37 % (3869)Time elapsed: 0.003 s
% 1.53/1.37 % (3869)Instructions burned: 2 (million)
% 1.53/1.37 % (3869)------------------------------
% 1.53/1.37 % (3869)------------------------------
% 1.53/1.37 % (3866)First to succeed.
% 1.53/1.37 % (3867)Also succeeded, but the first one will report.
% 1.53/1.37 % (3866)Refutation found. Thanks to Tanya!
% 1.53/1.37 % SZS status Theorem for DTF2THF_3769
% 1.53/1.37 % SZS output start Proof for DTF2THF_3769
% 1.53/1.37 thf(type_def_5, type, a: $tType).
% 1.53/1.37 thf(func_def_0, type, a: $tType).
% 1.53/1.37 thf(func_def_8, type, sK0: a > $o).
% 1.53/1.37 thf(func_def_9, type, sK1: a > $o).
% 1.53/1.37 thf(func_def_11, type, ph3: !>[X0: $tType]:(X0)).
% 1.53/1.37 thf(func_def_12, type, sK4: a).
% 1.53/1.37 thf(f58,plain,(
% 1.53/1.37 $false),
% 1.53/1.37 inference(avatar_sat_refutation,[status(thm)],[f35,f41,f47,f57])).
% 1.53/1.37 thf(f57,plain,(
% 1.53/1.37 ~spl2_1),
% 1.53/1.37 inference(avatar_contradiction_clause,[status(thm)],[f56])).
% 1.53/1.37 thf(f56,plain,(
% 1.53/1.37 $false | ~spl2_1),
% 1.53/1.37 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.53/1.37 thf(f50,plain,(
% 1.53/1.37 ($true = $false) | ~spl2_1),
% 1.53/1.37 inference(superposition,[status(thm)],[f36,f30])).
% 1.53/1.37 thf(f30,plain,(
% 1.53/1.37 ((sK0 @ sK4) = $false) | ~spl2_1),
% 1.53/1.37 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.53/1.37 thf(f28,definition,(
% 1.53/1.37 spl2_1 <=> ((sK0 @ sK4) = $false)),
% 1.53/1.37 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.53/1.37 thf(f36,plain,(
% 1.53/1.37 ((sK0 @ sK4) = $true)),
% 1.53/1.37 inference(subsumption_resolution,[status(thm)],[f22,f9])).
% 1.53/1.37 thf(f9,plain,(
% 1.53/1.37 ( ! [X2 : a] : (((sK0 @ X2) = $true) | ((sK1 @ X2) != $true)) )),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f8])).
% 1.53/1.37 thf(f8,plain,(
% 1.53/1.37 (sK1 != (^[Y0 : a]: ((sK0 @ Y0) & (~ ((sK0 @ Y0) & (~ (sK1 @ Y0))))))) & ! [X2 : a] : (((sK1 @ X2) != $true) | ((sK0 @ X2) = $true))),
% 1.53/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.53/1.37 thf(f7,plain,(
% 1.53/1.37 ? [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ((X0 @ Y0) & (~ ((X0 @ Y0) & (~ (X1 @ Y0)))))) != X1) & ! [X2 : a] : (((X1 @ X2) != $true) | ((X0 @ X2) = $true))) => ((sK1 != (^[Y0 : a]: ((sK0 @ Y0) & (~ ((sK0 @ Y0) & (~ (sK1 @ Y0))))))) & ! [X2 : a] : (((sK1 @ X2) != $true) | ((sK0 @ X2) = $true)))),
% 1.53/1.37 introduced(definition,[],[choice_axiom])).
% 1.53/1.37 thf(f6,plain,(
% 1.53/1.37 ? [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ((X0 @ Y0) & (~ ((X0 @ Y0) & (~ (X1 @ Y0)))))) != X1) & ! [X2 : a] : (((X1 @ X2) != $true) | ((X0 @ X2) = $true)))),
% 1.53/1.37 inference(ennf_transformation,[status(thm)],[f5])).
% 1.53/1.37 thf(f5,plain,(
% 1.53/1.37 ~! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : (((X1 @ X2) = $true) => ((X0 @ X2) = $true)) => ((^[Y0 : a]: ((X0 @ Y0) & (~ ((X0 @ Y0) & (~ (X1 @ Y0)))))) = X1))),
% 1.53/1.37 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.37 thf(f4,plain,(
% 1.53/1.37 ~! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) => (X1 = (^[X3 : a] : (~(~(X1 @ X3) & (X0 @ X3)) & (X0 @ X3)))))),
% 1.53/1.37 inference(rectify,[status(thm)],[f2])).
% 1.53/1.37 thf(f2,negated_conjecture,(
% 1.53/1.37 ~! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => (X0 = (^[X2 : a] : (~(~(X0 @ X2) & (X1 @ X2)) & (X1 @ X2)))))),
% 1.53/1.37 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.37 thf(f1,conjecture,(
% 1.53/1.37 ! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => (X0 = (^[X2 : a] : (~(~(X0 @ X2) & (X1 @ X2)) & (X1 @ X2)))))),
% 1.53/1.37 file('/export/starexec/sandbox2/tmp/tmp.rqGzcGTLmx/DTF2THF_3769.p',cGAZING_THM12_pme)).
% 1.53/1.37 thf(f22,plain,(
% 1.53/1.37 ((sK0 @ sK4) = $true) | ($true = (sK1 @ sK4))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.53/1.37 thf(f13,plain,(
% 1.53/1.37 ($true = (sK1 @ sK4)) | (((sK0 @ sK4) & (~ ((sK0 @ sK4) & (~ (sK1 @ sK4))))) = $true)),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.53/1.37 thf(f12,plain,(
% 1.53/1.37 (((sK0 @ sK4) & (~ ((sK0 @ sK4) & (~ (sK1 @ sK4))))) != (sK1 @ sK4))),
% 1.53/1.37 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.53/1.37 thf(f11,plain,(
% 1.53/1.37 (((^[Y0 : a]: ((sK0 @ Y0) & (~ ((sK0 @ Y0) & (~ (sK1 @ Y0)))))) @ sK4) != (sK1 @ sK4))),
% 1.53/1.37 inference(negative_extensionality,[status(thm)],[f10])).
% 1.53/1.37 thf(f10,plain,(
% 1.53/1.37 (sK1 != (^[Y0 : a]: ((sK0 @ Y0) & (~ ((sK0 @ Y0) & (~ (sK1 @ Y0)))))))),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f8])).
% 1.53/1.37 thf(f47,plain,(
% 1.53/1.37 ~spl2_2 | ~spl2_3),
% 1.53/1.37 inference(avatar_contradiction_clause,[status(thm)],[f46])).
% 1.53/1.37 thf(f46,plain,(
% 1.53/1.37 $false | (~spl2_2 | ~spl2_3)),
% 1.53/1.37 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.53/1.37 thf(f43,plain,(
% 1.53/1.37 ($true = $false) | (~spl2_2 | ~spl2_3)),
% 1.53/1.37 inference(superposition,[status(thm)],[f34,f40])).
% 1.53/1.37 thf(f40,plain,(
% 1.53/1.37 ($false = (sK1 @ sK4)) | ~spl2_3),
% 1.53/1.37 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.53/1.37 thf(f38,definition,(
% 1.53/1.37 spl2_3 <=> ($false = (sK1 @ sK4))),
% 1.53/1.37 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.53/1.37 thf(f34,plain,(
% 1.53/1.37 ($true = (sK1 @ sK4)) | ~spl2_2),
% 1.53/1.37 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.53/1.37 thf(f32,definition,(
% 1.53/1.37 spl2_2 <=> ($true = (sK1 @ sK4))),
% 1.53/1.37 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.53/1.37 thf(f41,plain,(
% 1.53/1.37 spl2_3 | spl2_1),
% 1.53/1.37 inference(avatar_split_clause,[status(thm)],[f20,f28,f38])).
% 1.53/1.37 thf(f20,plain,(
% 1.53/1.37 ($false = (sK1 @ sK4)) | ((sK0 @ sK4) = $false)),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f19])).
% 1.53/1.37 thf(f19,plain,(
% 1.53/1.37 ($false = (sK1 @ sK4)) | ((sK0 @ sK4) = $false) | ($false = (sK1 @ sK4))),
% 1.53/1.37 inference(not_proxy_clausification,[status(thm)],[f17])).
% 1.53/1.37 thf(f17,plain,(
% 1.53/1.37 ((~ (sK1 @ sK4)) = $true) | ((sK0 @ sK4) = $false) | ($false = (sK1 @ sK4))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.53/1.37 thf(f16,plain,(
% 1.53/1.37 ((sK0 @ sK4) = $false) | (((sK0 @ sK4) & (~ (sK1 @ sK4))) = $true) | ($false = (sK1 @ sK4))),
% 1.53/1.37 inference(not_proxy_clausification,[status(thm)],[f15])).
% 1.53/1.37 thf(f15,plain,(
% 1.53/1.37 ((~ ((sK0 @ sK4) & (~ (sK1 @ sK4)))) = $false) | ((sK0 @ sK4) = $false) | ($false = (sK1 @ sK4))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.53/1.37 thf(f14,plain,(
% 1.53/1.37 (((sK0 @ sK4) & (~ ((sK0 @ sK4) & (~ (sK1 @ sK4))))) = $false) | ($false = (sK1 @ sK4))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.53/1.37 thf(f35,plain,(
% 1.53/1.37 spl2_1 | spl2_2),
% 1.53/1.37 inference(avatar_split_clause,[status(thm)],[f26,f32,f28])).
% 1.53/1.37 thf(f26,plain,(
% 1.53/1.37 ($true = (sK1 @ sK4)) | ((sK0 @ sK4) = $false)),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f25])).
% 1.53/1.37 thf(f25,plain,(
% 1.53/1.37 ($true = (sK1 @ sK4)) | ($true = (sK1 @ sK4)) | ((sK0 @ sK4) = $false)),
% 1.53/1.37 inference(not_proxy_clausification,[status(thm)],[f24])).
% 1.53/1.37 thf(f24,plain,(
% 1.53/1.37 ((~ (sK1 @ sK4)) = $false) | ($true = (sK1 @ sK4)) | ((sK0 @ sK4) = $false)),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.53/1.37 thf(f23,plain,(
% 1.53/1.37 (((sK0 @ sK4) & (~ (sK1 @ sK4))) = $false) | ($true = (sK1 @ sK4))),
% 1.53/1.37 inference(not_proxy_clausification,[status(thm)],[f21])).
% 1.53/1.37 thf(f21,plain,(
% 1.53/1.37 ($true = (sK1 @ sK4)) | ((~ ((sK0 @ sK4) & (~ (sK1 @ sK4)))) = $true)),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.53/1.37 % SZS output end Proof for DTF2THF_3769
% 1.53/1.37 % (3866)------------------------------
% 1.53/1.37 % (3866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.37 % (3866)Termination reason: Refutation
% 1.53/1.37
% 1.53/1.37 % (3866)Memory used [KB]: 5500
% 1.53/1.37 % (3866)Time elapsed: 0.004 s
% 1.53/1.37 % (3866)Instructions burned: 2 (million)
% 1.53/1.37 % (3866)------------------------------
% 1.53/1.37 % (3866)------------------------------
% 1.53/1.37 % (3865)Success in time 0.016 s
%------------------------------------------------------------------------------