%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO148^5 : 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 : n009.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 09:53:29 AM UTC 2026
% Result : Theorem 1.64s 1.47s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 4 unt; 0 typ; 5 def)
% Number of atoms : 363 ( 102 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 283 ( 63 ~; 73 |; 3 &; 122 @)
% ( 17 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 22 ( 9 ^; 13 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cZ: a > $o ).
thf(func_def_2,type,
cY: a > $o ).
thf(func_def_3,type,
cX: a > $o ).
thf(func_def_12,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sK2: a ).
thf(f105,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f37,f47,f52,f53,f59,f82,f99,f104]) ).
thf(f104,plain,
( spl0_1
| spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
| spl0_1
| spl0_3
| ~ spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f102,f31]) ).
thf(f31,plain,
( ( ( cY @ sK2 )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl0_1
<=> ( ( cY @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f102,plain,
( ( ( cY @ sK2 )
= $true )
| spl0_3
| ~ spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f73,f41]) ).
thf(f41,plain,
( ( ( cZ @ sK2 )
!= $false )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl0_3
<=> ( ( cZ @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f73,plain,
( ( ( cZ @ sK2 )
= $false )
| ( ( cY @ sK2 )
= $true )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( cY @ sK2 )
= $true )
| ( ( cZ @ sK2 )
= $false )
| ( $true = $false )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f51,f14]) ).
thf(f14,plain,
! [X0: a] :
( ( ( cX @ X0 )
= $true )
| ( ( cY @ X0 )
= $true )
| ( ( cZ @ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: a] :
( ( ( cY @ X0 )
= ( cZ @ X0 ) )
| ( ( cX @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( cX
!= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) ) ) )
& ! [X0: a] :
( ( ( ( cY @ X0 )
= ( cZ @ X0 ) )
| ( ( cX @ X0 )
= $true ) )
& ( ( ( cX @ X0 )
!= $true )
| ( ( cY @ X0 )
!= ( cZ @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( cX
!= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) ) ) )
& ! [X0: a] :
( ( ( cY @ X0 )
= ( cZ @ X0 ) )
<=> ( ( cX @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: a] :
( ( ( cY @ X0 )
= ( cZ @ X0 ) )
<=> ( ( cX @ X0 )
!= $true ) )
=> ( cX
= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a] :
( ( ( cY @ X0 )
= ( cZ @ X0 ) )
<=> ( ( cX @ X0 )
!= $true ) )
=> ( cX
= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a] :
( ( ( cZ @ X0 )
<=> ( cY @ X0 ) )
<=> ~ ( cX @ X0 ) )
=> ( ( ^ [X1: a] :
~ ( ( cY @ X1 )
<=> ( cZ @ X1 ) ) )
= cX ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a] :
( ( ( cZ @ X0 )
<=> ( cY @ X0 ) )
<=> ~ ( cX @ X0 ) )
=> ( ( ^ [X0: a] :
~ ( ( cY @ X0 )
<=> ( cZ @ X0 ) ) )
= cX ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a] :
( ( ( cZ @ X0 )
<=> ( cY @ X0 ) )
<=> ~ ( cX @ X0 ) )
=> ( ( ^ [X0: a] :
~ ( ( cY @ X0 )
<=> ( cZ @ X0 ) ) )
= cX ) ),
file('/export/starexec/sandbox/tmp/tmp.Hpr68m6mtt/DTF2THF_25602.p',cBOOL25) ).
thf(f51,plain,
( ( ( cX @ sK2 )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl0_5
<=> ( ( cX @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f99,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f98]) ).
thf(f98,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f32,f46]) ).
thf(f46,plain,
( ( ( cY @ sK2 )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl0_4
<=> ( ( cY @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f32,plain,
( ( ( cY @ sK2 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f82,plain,
( spl0_4
| spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f81,f49,f34,f44]) ).
thf(f34,definition,
( spl0_2
<=> ( $true
= ( cZ @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f81,plain,
( ( ( cY @ sK2 )
= $false )
| spl0_2
| ~ spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f77,f35]) ).
thf(f35,plain,
( ( $true
!= ( cZ @ sK2 ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f77,plain,
( ( $true
= ( cZ @ sK2 ) )
| ( ( cY @ sK2 )
= $false )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $true
= ( cZ @ sK2 ) )
| ( $true = $false )
| ( ( cY @ sK2 )
= $false )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f15,f51]) ).
thf(f15,plain,
! [X0: a] :
( ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true )
| ( ( cY @ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f59,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f42,f36]) ).
thf(f36,plain,
( ( $true
= ( cZ @ sK2 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f42,plain,
( ( ( cZ @ sK2 )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f53,plain,
( spl0_4
| spl0_2
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f23,f49,f34,f44]) ).
thf(f23,plain,
( ( $true
= ( cZ @ sK2 ) )
| ( ( cX @ sK2 )
= $false )
| ( ( cY @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( cY @ sK2 )
= ( cZ @ sK2 ) )
| ( ( cX @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( cX @ sK2 )
= $false )
| ( ( ( cY @ sK2 )
= ( cZ @ sK2 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ( cY @ sK2 )
!= ( cZ @ sK2 ) )
= $false )
| ( ( cX @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( cY @ sK2 )
!= ( cZ @ sK2 ) )
!= ( cX @ sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( cX @ sK2 )
!= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f11]) ).
thf(f11,plain,
( cX
!= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f52,plain,
( spl0_5
| spl0_3
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f22,f30,f40,f49]) ).
thf(f22,plain,
( ( ( cX @ sK2 )
= $false )
| ( ( cY @ sK2 )
= $true )
| ( ( cZ @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f47,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f38,f44,f40]) ).
thf(f38,plain,
( ( ( cY @ sK2 )
= $false )
| ( ( cZ @ sK2 )
= $false ) ),
inference(subsumption_resolution,[status(thm)],[f27,f13]) ).
thf(f13,plain,
! [X0: a] :
( ( ( cY @ X0 )
= $false )
| ( ( cZ @ X0 )
= $false )
| ( ( cX @ X0 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: a] :
( ( ( cX @ X0 )
!= $true )
| ( ( cY @ X0 )
!= ( cZ @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f27,plain,
( ( $true
= ( cX @ sK2 ) )
| ( ( cY @ sK2 )
= $false )
| ( ( cZ @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $true
= ( cX @ sK2 ) )
| ( ( cY @ sK2 )
!= ( cZ @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( ( cY @ sK2 )
= ( cZ @ sK2 ) )
= $false )
| ( $true
= ( cX @ sK2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true
= ( cX @ sK2 ) )
| ( ( ( cY @ sK2 )
!= ( cZ @ sK2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f37,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f28,f34,f30]) ).
thf(f28,plain,
( ( $true
= ( cZ @ sK2 ) )
| ( ( cY @ sK2 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f26,f12]) ).
thf(f12,plain,
! [X0: a] :
( ( ( cY @ X0 )
= $true )
| ( ( cX @ X0 )
!= $true )
| ( ( cZ @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f26,plain,
( ( $true
= ( cX @ sK2 ) )
| ( ( cY @ sK2 )
= $true )
| ( $true
= ( cZ @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO148^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.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 14:24:40 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.48 ---- Original DTF file ---
% 0.32/0.48 thf(spec,logic,$$dhol).
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 % File : SYO148^5 : TPTP v9.2.1. Released v4.0.0.
% 0.32/0.48 % Domain : Syntactic
% 0.32/0.48 % Problem : TPS problem from BASIC-FO-THMS
% 0.32/0.48 % Version : Especial.
% 0.32/0.48 % English :
% 0.32/0.48
% 0.32/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.32/0.48 % Source : [Bro09]
% 0.32/0.48 % Names : tps_0794 [Bro09]
% 0.32/0.48
% 0.32/0.48 % Status : Theorem
% 0.32/0.48 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.32/0.48 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.32/0.48 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.32/0.48 % Maximal formula atoms : 4 ( 7 avg)
% 0.32/0.48 % Number of connectives : 11 ( 2 ~; 0 |; 0 &; 5 @)
% 0.32/0.48 % ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% 0.32/0.48 % Maximal formula depth : 6 ( 6 avg)
% 0.32/0.48 % Number of types : 2 ( 1 usr)
% 0.32/0.48 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.32/0.48 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.32/0.48 % Number of variables : 2 ( 1 ^; 1 !; 0 ?; 2 :)
% 0.32/0.48 % SPC : TH0_THM_EQU_NAR
% 0.32/0.48
% 0.32/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.32/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.32/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.32/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 thf(a_type,type,
% 0.32/0.48 a: $tType ).
% 0.32/0.48
% 0.32/0.48 thf(cZ,type,
% 0.32/0.48 cZ: a > $o ).
% 0.32/0.48
% 0.32/0.48 thf(cY,type,
% 0.32/0.48 cY: a > $o ).
% 0.32/0.48
% 0.32/0.48 thf(cX,type,
% 0.32/0.48 cX: a > $o ).
% 0.32/0.48
% 0.32/0.48 thf(cBOOL25,conjecture,
% 0.32/0.48 ( ! [U: a] :
% 0.32/0.48 ( ~ ( cX @ U )
% 0.32/0.48 <=> ( ( cY @ U )
% 0.32/0.48 <=> ( cZ @ U ) ) )
% 0.32/0.48 => ( cX
% 0.32/0.48 = ( ^ [U: a] :
% 0.32/0.48 ~ ( ( cY @ U )
% 0.32/0.48 <=> ( cZ @ U ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 1.64/1.43 ---- Embedded in THF ---
% 1.64/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.43 %%% Generated on Tue Feb 24 14:24:41 EST 2026
% 1.64/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.43 %%% Logic specification used:
% 1.64/1.43 %%% thf(spec, logic, $$dhol).
% 1.64/1.43
% 1.64/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Hpr68m6mtt/DTF2DTF25602.p
% See solution above
% 1.64/1.43 ------------------------
% 1.64/1.44 ---- Cleaned THF ---
% 1.64/1.44 thf(a_type,type,
% 1.64/1.44 a: $tType ).
% 1.64/1.44
% 1.64/1.44 thf(cZ,type,
% 1.64/1.44 cZ: a > $o ).
% 1.64/1.44
% 1.64/1.44 thf(cY,type,
% 1.64/1.44 cY: a > $o ).
% 1.64/1.44
% 1.64/1.44 thf(cX,type,
% 1.64/1.44 cX: a > $o ).
% 1.64/1.44
% 1.64/1.44 thf(cBOOL25,conjecture,
% 1.64/1.44 ( ! [U: a] :
% 1.64/1.44 ( ~ ( cX @ U )
% 1.64/1.44 <=> ( ( cY @ U )
% 1.64/1.44 <=> ( cZ @ U ) ) )
% 1.64/1.44 => ( cX
% 1.64/1.44 = ( ^ [U: a] :
% 1.64/1.44 ~ ( ( cY @ U )
% 1.64/1.44 <=> ( cZ @ U ) ) ) ) ) ).
% 1.64/1.44 ------------------------
% 1.64/1.46 % (25706)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25602 for (3000ds/183Mi)
% 1.64/1.46 % (25707)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_25602 for (3000ds/4Mi)
% 1.64/1.46 % (25710)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_25602 for (3000ds/2Mi)
% 1.64/1.46 % (25708)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_25602 for (3000ds/27Mi)
% 1.64/1.46 % (25709)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25602 for (3000ds/2Mi)
% 1.64/1.46 % (25711)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_25602 for (3000ds/275Mi)
% 1.64/1.46 % (25712)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25602 for (3000ds/18Mi)
% 1.64/1.46 % (25710)Instruction limit reached!
% 1.64/1.46 % (25710)------------------------------
% 1.64/1.46 % (25710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.46 % (25710)Termination reason: Unknown
% 1.64/1.46 % (25710)Termination phase: Saturation
% 1.64/1.46
% 1.64/1.46 % (25710)Memory used [KB]: 5500
% 1.64/1.46 % (25710)Time elapsed: 0.003 s
% 1.64/1.46 % (25710)Instructions burned: 2 (million)
% 1.64/1.46 % (25710)------------------------------
% 1.64/1.46 % (25710)------------------------------
% 1.64/1.46 % (25709)Instruction limit reached!
% 1.64/1.46 % (25709)------------------------------
% 1.64/1.46 % (25709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.46 % (25709)Termination reason: Unknown
% 1.64/1.46 % (25709)Termination phase: Saturation
% 1.64/1.46
% 1.64/1.46 % (25709)Memory used [KB]: 5500
% 1.64/1.46 % (25709)Time elapsed: 0.004 s
% 1.64/1.46 % (25709)Instructions burned: 2 (million)
% 1.64/1.46 % (25709)------------------------------
% 1.64/1.46 % (25709)------------------------------
% 1.64/1.47 % (25707)Instruction limit reached!
% 1.64/1.47 % (25707)------------------------------
% 1.64/1.47 % (25707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.47 % (25707)Termination reason: Unknown
% 1.64/1.47 % (25707)Termination phase: Saturation
% 1.64/1.47
% 1.64/1.47 % (25707)Memory used [KB]: 5500
% 1.64/1.47 % (25707)Time elapsed: 0.005 s
% 1.64/1.47 % (25707)Instructions burned: 5 (million)
% 1.64/1.47 % (25707)------------------------------
% 1.64/1.47 % (25707)------------------------------
% 1.64/1.47 % (25706)First to succeed.
% 1.64/1.47 % (25711)Also succeeded, but the first one will report.
% 1.64/1.47 % (25706)Refutation found. Thanks to Tanya!
% 1.64/1.47 % SZS status Theorem for DTF2THF_25602
% 1.64/1.47 % SZS output start Proof for DTF2THF_25602
% 1.64/1.47 thf(type_def_5, type, a: $tType).
% 1.64/1.47 thf(func_def_0, type, a: $tType).
% 1.64/1.47 thf(func_def_1, type, cZ: a > $o).
% 1.64/1.47 thf(func_def_2, type, cY: a > $o).
% 1.64/1.47 thf(func_def_3, type, cX: a > $o).
% 1.64/1.47 thf(func_def_12, type, ph1: !>[X0: $tType]:(X0)).
% 1.64/1.47 thf(func_def_13, type, sK2: a).
% 1.64/1.47 thf(f105,plain,(
% 1.64/1.47 $false),
% 1.64/1.47 inference(avatar_sat_refutation,[status(thm)],[f37,f47,f52,f53,f59,f82,f99,f104])).
% 1.64/1.47 thf(f104,plain,(
% 1.64/1.47 spl0_1 | spl0_3 | ~spl0_5),
% 1.64/1.47 inference(avatar_contradiction_clause,[status(thm)],[f103])).
% 1.64/1.47 thf(f103,plain,(
% 1.64/1.47 $false | (spl0_1 | spl0_3 | ~spl0_5)),
% 1.64/1.47 inference(subsumption_resolution,[status(thm)],[f102,f31])).
% 1.64/1.47 thf(f31,plain,(
% 1.64/1.47 ((cY @ sK2) != $true) | spl0_1),
% 1.64/1.47 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.64/1.47 thf(f30,definition,(
% 1.64/1.47 spl0_1 <=> ((cY @ sK2) = $true)),
% 1.64/1.47 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.64/1.47 thf(f102,plain,(
% 1.64/1.47 ((cY @ sK2) = $true) | (spl0_3 | ~spl0_5)),
% 1.64/1.47 inference(subsumption_resolution,[status(thm)],[f73,f41])).
% 1.64/1.47 thf(f41,plain,(
% 1.64/1.47 ((cZ @ sK2) != $false) | spl0_3),
% 1.64/1.47 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.64/1.47 thf(f40,definition,(
% 1.64/1.47 spl0_3 <=> ((cZ @ sK2) = $false)),
% 1.64/1.47 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.64/1.47 thf(f73,plain,(
% 1.64/1.47 ((cZ @ sK2) = $false) | ((cY @ sK2) = $true) | ~spl0_5),
% 1.64/1.47 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.64/1.47 thf(f72,plain,(
% 1.64/1.47 ((cY @ sK2) = $true) | ((cZ @ sK2) = $false) | ($true = $false) | ~spl0_5),
% 1.64/1.47 inference(superposition,[status(thm)],[f51,f14])).
% 1.64/1.47 thf(f14,plain,(
% 1.64/1.47 ( ! [X0 : a] : (((cX @ X0) = $true) | ((cY @ X0) = $true) | ((cZ @ X0) = $false)) )),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.64/1.47 thf(f10,plain,(
% 1.64/1.47 ( ! [X0 : a] : (((cY @ X0) = (cZ @ X0)) | ((cX @ X0) = $true)) )),
% 1.64/1.47 inference(cnf_transformation,[status(thm)],[f8])).
% 1.64/1.47 thf(f8,plain,(
% 1.64/1.47 (cX != (^[Y0 : a]: (~ ((cY @ Y0) = (cZ @ Y0))))) & ! [X0 : a] : ((((cY @ X0) = (cZ @ X0)) | ((cX @ X0) = $true)) & (((cX @ X0) != $true) | ((cY @ X0) != (cZ @ X0))))),
% 1.64/1.47 inference(nnf_transformation,[status(thm)],[f7])).
% 1.64/1.47 thf(f7,plain,(
% 1.64/1.47 (cX != (^[Y0 : a]: (~ ((cY @ Y0) = (cZ @ Y0))))) & ! [X0 : a] : (((cY @ X0) = (cZ @ X0)) <=> ((cX @ X0) != $true))),
% 1.64/1.47 inference(ennf_transformation,[status(thm)],[f6])).
% 1.64/1.47 thf(f6,plain,(
% 1.64/1.47 ~(! [X0 : a] : (((cY @ X0) = (cZ @ X0)) <=> ((cX @ X0) != $true)) => (cX = (^[Y0 : a]: (~ ((cY @ Y0) = (cZ @ Y0))))))),
% 1.64/1.47 inference(flattening,[status(thm)],[f5])).
% 1.64/1.47 thf(f5,plain,(
% 1.64/1.47 ~(! [X0 : a] : (((cY @ X0) = (cZ @ X0)) <=> ~((cX @ X0) = $true)) => (cX = (^[Y0 : a]: (~ ((cY @ Y0) = (cZ @ Y0))))))),
% 1.64/1.47 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.47 thf(f4,plain,(
% 1.64/1.47 ~(! [X0 : a] : (((cZ @ X0) <=> (cY @ X0)) <=> ~(cX @ X0)) => ((^[X1 : a] : (~((cY @ X1) <=> (cZ @ X1)))) = cX))),
% 1.64/1.47 inference(rectify,[status(thm)],[f2])).
% 1.64/1.47 thf(f2,negated_conjecture,(
% 1.64/1.47 ~(! [X0 : a] : (((cZ @ X0) <=> (cY @ X0)) <=> ~(cX @ X0)) => ((^[X0 : a] : (~((cY @ X0) <=> (cZ @ X0)))) = cX))),
% 1.64/1.47 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.47 thf(f1,conjecture,(
% 1.64/1.47 ! [X0 : a] : (((cZ @ X0) <=> (cY @ X0)) <=> ~(cX @ X0)) => ((^[X0 : a] : (~((cY @ X0) <=> (cZ @ X0)))) = cX)),
% 1.64/1.47 file('/export/starexec/sandbox/tmp/tmp.Hpr68m6mtt/DTF2THF_25602.p',cBOOL25)).
% 1.64/1.47 thf(f51,plain,(
% 1.64/1.47 ((cX @ sK2) = $false) | ~spl0_5),
% 1.64/1.47 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.64/1.47 thf(f49,definition,(
% 1.64/1.47 spl0_5 <=> ((cX @ sK2) = $false)),
% 1.64/1.47 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.64/1.47 thf(f99,plain,(
% 1.64/1.47 ~spl0_1 | ~spl0_4),
% 1.64/1.47 inference(avatar_contradiction_clause,[status(thm)],[f98])).
% 1.64/1.47 thf(f98,plain,(
% 1.64/1.47 $false | (~spl0_1 | ~spl0_4)),
% 1.64/1.47 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.64/1.47 thf(f92,plain,(
% 1.64/1.47 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 1.64/1.47 inference(superposition,[status(thm)],[f32,f46])).
% 1.64/1.47 thf(f46,plain,(
% 1.64/1.47 ((cY @ sK2) = $false) | ~spl0_4),
% 1.64/1.47 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.64/1.47 thf(f44,definition,(
% 1.64/1.47 spl0_4 <=> ((cY @ sK2) = $false)),
% 1.64/1.47 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.64/1.47 thf(f32,plain,(
% 1.64/1.47 ((cY @ sK2) = $true) | ~spl0_1),
% 1.64/1.47 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.64/1.47 thf(f82,plain,(
% 1.64/1.47 spl0_4 | spl0_2 | ~spl0_5),
% 1.64/1.47 inference(avatar_split_clause,[status(thm)],[f81,f49,f34,f44])).
% 1.64/1.47 thf(f34,definition,(
% 1.64/1.47 spl0_2 <=> ($true = (cZ @ sK2))),
% 1.64/1.47 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.64/1.47 thf(f81,plain,(
% 1.64/1.47 ((cY @ sK2) = $false) | (spl0_2 | ~spl0_5)),
% 1.64/1.47 inference(subsumption_resolution,[status(thm)],[f77,f35])).
% 1.64/1.47 thf(f35,plain,(
% 1.64/1.47 ($true != (cZ @ sK2)) | spl0_2),
% 1.64/1.47 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.64/1.47 thf(f77,plain,(
% 1.64/1.47 ($true = (cZ @ sK2)) | ((cY @ sK2) = $false) | ~spl0_5),
% 1.64/1.47 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.64/1.47 thf(f75,plain,(
% 1.64/1.47 ($true = (cZ @ sK2)) | ($true = $false) | ((cY @ sK2) = $false) | ~spl0_5),
% 1.64/1.47 inference(superposition,[status(thm)],[f15,f51])).
% 1.64/1.47 thf(f15,plain,(
% 1.64/1.47 ( ! [X0 : a] : (((cX @ X0) = $true) | ((cZ @ X0) = $true) | ((cY @ X0) = $false)) )),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.64/1.47 thf(f59,plain,(
% 1.64/1.47 ~spl0_2 | ~spl0_3),
% 1.64/1.47 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.64/1.47 thf(f58,plain,(
% 1.64/1.47 $false | (~spl0_2 | ~spl0_3)),
% 1.64/1.47 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.64/1.47 thf(f54,plain,(
% 1.64/1.47 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.64/1.47 inference(superposition,[status(thm)],[f42,f36])).
% 1.64/1.47 thf(f36,plain,(
% 1.64/1.47 ($true = (cZ @ sK2)) | ~spl0_2),
% 1.64/1.47 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.64/1.47 thf(f42,plain,(
% 1.64/1.47 ((cZ @ sK2) = $false) | ~spl0_3),
% 1.64/1.47 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.64/1.47 thf(f53,plain,(
% 1.64/1.47 spl0_4 | spl0_2 | spl0_5),
% 1.64/1.47 inference(avatar_split_clause,[status(thm)],[f23,f49,f34,f44])).
% 1.64/1.47 thf(f23,plain,(
% 1.64/1.47 ($true = (cZ @ sK2)) | ((cX @ sK2) = $false) | ((cY @ sK2) = $false)),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.64/1.47 thf(f21,plain,(
% 1.64/1.47 ((cY @ sK2) = (cZ @ sK2)) | ((cX @ sK2) = $false)),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.64/1.47 thf(f20,plain,(
% 1.64/1.47 ((cX @ sK2) = $false) | (((cY @ sK2) = (cZ @ sK2)) = $true)),
% 1.64/1.47 inference(not_proxy_clausification,[status(thm)],[f19])).
% 1.64/1.47 thf(f19,plain,(
% 1.64/1.47 ((~ ((cY @ sK2) = (cZ @ sK2))) = $false) | ((cX @ sK2) = $false)),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.64/1.47 thf(f17,plain,(
% 1.64/1.47 ((~ ((cY @ sK2) = (cZ @ sK2))) != (cX @ sK2))),
% 1.64/1.47 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.64/1.47 thf(f16,plain,(
% 1.64/1.47 ((cX @ sK2) != ((^[Y0 : a]: (~ ((cY @ Y0) = (cZ @ Y0)))) @ sK2))),
% 1.64/1.47 inference(negative_extensionality,[status(thm)],[f11])).
% 1.64/1.47 thf(f11,plain,(
% 1.64/1.47 (cX != (^[Y0 : a]: (~ ((cY @ Y0) = (cZ @ Y0)))))),
% 1.64/1.47 inference(cnf_transformation,[status(thm)],[f8])).
% 1.64/1.47 thf(f52,plain,(
% 1.64/1.47 spl0_5 | spl0_3 | spl0_1),
% 1.64/1.47 inference(avatar_split_clause,[status(thm)],[f22,f30,f40,f49])).
% 1.64/1.47 thf(f22,plain,(
% 1.64/1.47 ((cX @ sK2) = $false) | ((cY @ sK2) = $true) | ((cZ @ sK2) = $false)),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.64/1.47 thf(f47,plain,(
% 1.64/1.47 spl0_3 | spl0_4),
% 1.64/1.47 inference(avatar_split_clause,[status(thm)],[f38,f44,f40])).
% 1.64/1.47 thf(f38,plain,(
% 1.64/1.47 ((cY @ sK2) = $false) | ((cZ @ sK2) = $false)),
% 1.64/1.47 inference(subsumption_resolution,[status(thm)],[f27,f13])).
% 1.64/1.47 thf(f13,plain,(
% 1.64/1.47 ( ! [X0 : a] : (((cY @ X0) = $false) | ((cZ @ X0) = $false) | ((cX @ X0) != $true)) )),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.64/1.47 thf(f9,plain,(
% 1.64/1.47 ( ! [X0 : a] : (((cX @ X0) != $true) | ((cY @ X0) != (cZ @ X0))) )),
% 1.64/1.47 inference(cnf_transformation,[status(thm)],[f8])).
% 1.64/1.47 thf(f27,plain,(
% 1.64/1.47 ($true = (cX @ sK2)) | ((cY @ sK2) = $false) | ((cZ @ sK2) = $false)),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.64/1.47 thf(f25,plain,(
% 1.64/1.47 ($true = (cX @ sK2)) | ((cY @ sK2) != (cZ @ sK2))),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.64/1.47 thf(f24,plain,(
% 1.64/1.47 (((cY @ sK2) = (cZ @ sK2)) = $false) | ($true = (cX @ sK2))),
% 1.64/1.47 inference(not_proxy_clausification,[status(thm)],[f18])).
% 1.64/1.47 thf(f18,plain,(
% 1.64/1.47 ($true = (cX @ sK2)) | ((~ ((cY @ sK2) = (cZ @ sK2))) = $true)),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.64/1.47 thf(f37,plain,(
% 1.64/1.47 spl0_1 | spl0_2),
% 1.64/1.47 inference(avatar_split_clause,[status(thm)],[f28,f34,f30])).
% 1.64/1.47 thf(f28,plain,(
% 1.64/1.47 ($true = (cZ @ sK2)) | ((cY @ sK2) = $true)),
% 1.64/1.47 inference(subsumption_resolution,[status(thm)],[f26,f12])).
% 1.64/1.47 thf(f12,plain,(
% 1.64/1.47 ( ! [X0 : a] : (((cY @ X0) = $true) | ((cX @ X0) != $true) | ((cZ @ X0) = $true)) )),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.64/1.47 thf(f26,plain,(
% 1.64/1.47 ($true = (cX @ sK2)) | ((cY @ sK2) = $true) | ($true = (cZ @ sK2))),
% 1.64/1.47 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.64/1.47 % SZS output end Proof for DTF2THF_25602
% 1.64/1.47 % (25706)------------------------------
% 1.64/1.47 % (25706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.47 % (25706)Termination reason: Refutation
% 1.64/1.47
% 1.64/1.47 % (25706)Memory used [KB]: 5500
% 1.64/1.47 % (25706)Time elapsed: 0.006 s
% 1.64/1.47 % (25706)Instructions burned: 5 (million)
% 1.64/1.47 % (25706)------------------------------
% 1.64/1.47 % (25706)------------------------------
% 1.64/1.47 % (25705)Success in time 0.019 s
%------------------------------------------------------------------------------