%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP001^3 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 08:53:00 AM UTC 2026
% Result : Theorem 1.98s 1.67s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 15 ( 8 ~; 3 |; 1 &; 0 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 12 ( 12 ^; 0 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
tyop_2Emin_2Ebool: $tType ).
thf(func_def_1,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
thf(func_def_2,type,
c_2Ebool_2E_21:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_4,type,
c_2Emin_2E_3D:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_5,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_6,type,
c_2Ebool_2E_3F:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_9,type,
c_2Ebool_2E_7E: $o > $o ).
thf(func_def_16,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f79,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f78,f56]) ).
thf(f56,plain,
c_2Ebool_2ET != $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
c_2Ebool_2ET != $true,
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
c_2Ebool_2ET != $true,
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ c_2Ebool_2ET,
inference(rectify,[status(thm)],[f10]) ).
thf(f10,negated_conjecture,
~ c_2Ebool_2ET,
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f9,conjecture,
c_2Ebool_2ET,
file('/export/starexec/sandbox2/tmp/tmp.dFFSnK7xOV/DTF2THF_28936.p',thm_2Ebool_2ETRUTH) ).
thf(f78,plain,
c_2Ebool_2ET = $true,
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( c_2Ebool_2ET = $true )
| ( ( ^ [Y0: $o] : Y0 )
!= ( ^ [Y0: $o] : Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( ( ^ [Y0: $o] : Y0 )
= ( ^ [Y0: $o] : Y0 ) )
| ( c_2Ebool_2ET != $true ) )
& ( ( c_2Ebool_2ET = $true )
| ( ( ^ [Y0: $o] : Y0 )
!= ( ^ [Y0: $o] : Y0 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ^ [Y0: $o] : Y0 )
= ( ^ [Y0: $o] : Y0 ) )
<=> ( c_2Ebool_2ET = $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( c_2Ebool_2ET
<=> ( ( ^ [X0: $o] : X0 )
= ( ^ [X1: $o] : X1 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( c_2Ebool_2ET
<=> ( ( ^ [X5: $o] : X5 )
= ( ^ [X4: $o] : X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dFFSnK7xOV/DTF2THF_28936.p',thm_2Ebool_2ET__DEF) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP001^3 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.10/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.35 % Computer : n007.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Feb 24 08:15:09 EST 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.25/0.46 ---- Original DTF file ---
% 0.25/0.46 thf(spec,logic,$$dhol).
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 % File : ITP001^3 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.25/0.46 % Domain : Interactive Theorem Proving
% 0.25/0.46 % Problem : HOL4 syntactic export of thm_2Ebool_2ETRUTH.p, bushy mode
% 0.25/0.46 % Version : [BG+19] axioms.
% 0.25/0.46 % English :
% 0.25/0.46
% 0.25/0.46 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.25/0.46 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.25/0.46 % Source : [BG+19]
% 0.25/0.46 % Names : thm_2Ebool_2ETRUTH.p [Gau19]
% 0.25/0.46 % : HL400001^3.p [TPAP]
% 0.25/0.46
% 0.25/0.46 % Status : Theorem
% 0.25/0.46 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.25/0.46 % Syntax : Number of formulae : 19 ( 6 unt; 10 typ; 0 def)
% 0.25/0.46 % Number of atoms : 12 ( 2 equ; 1 cnn)
% 0.25/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.25/0.46 % Number of connectives : 29 ( 1 ~; 1 |; 1 &; 17 @)
% 0.25/0.46 % ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% 0.25/0.46 % Maximal formula depth : 8 ( 5 avg)
% 0.25/0.46 % Number of types : 2 ( 1 usr)
% 0.25/0.46 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.25/0.46 % Number of symbols : 11 ( 9 usr; 2 con; 0-3 aty)
% 0.25/0.46 % Number of variables : 21 ( 2 ^; 15 !; 1 ?; 21 :)
% 0.25/0.46 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.25/0.46 % SPC : TH1_THM_EQU_NAR
% 0.25/0.46
% 0.25/0.46 % Comments :
% 0.25/0.46 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 thf(tyop_2Emin_2Ebool,type,
% 0.25/0.46 tyop_2Emin_2Ebool: $tType ).
% 0.25/0.46
% 0.25/0.46 thf(tyop_2Emin_2Efun,type,
% 0.25/0.46 tyop_2Emin_2Efun: $tType > $tType > $tType ).
% 0.25/0.46
% 0.25/0.46 thf(c_2Ebool_2E_21,type,
% 0.25/0.46 c_2Ebool_2E_21:
% 0.25/0.46 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 0.25/0.46
% 0.25/0.46 thf(c_2Ebool_2E_2F_5C,type,
% 0.25/0.46 c_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.25/0.46
% 0.25/0.46 thf(c_2Emin_2E_3D,type,
% 0.25/0.46 c_2Emin_2E_3D:
% 0.25/0.46 !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
% 0.25/0.46
% 0.25/0.46 thf(c_2Emin_2E_3D_3D_3E,type,
% 0.25/0.46 c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.25/0.46
% 0.25/0.46 thf(c_2Ebool_2E_3F,type,
% 0.25/0.46 c_2Ebool_2E_3F:
% 0.25/0.46 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 0.25/0.46
% 0.25/0.46 thf(c_2Ebool_2ET,type,
% 0.25/0.46 c_2Ebool_2ET: $o ).
% 0.25/0.46
% 0.25/0.46 thf(c_2Ebool_2E_5C_2F,type,
% 0.25/0.46 c_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.25/0.46
% 0.25/0.46 thf(c_2Ebool_2E_7E,type,
% 0.25/0.46 c_2Ebool_2E_7E: $o > $o ).
% 0.25/0.46
% 0.25/0.46 thf(logicdef_2E_2F_5C,axiom,
% 0.25/0.46 ! [V0: $o,V1: $o] :
% 0.25/0.46 ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.25/0.46 <=> ( V0
% 0.25/0.46 & V1 ) ) ).
% 0.25/0.46
% 0.25/0.46 thf(logicdef_2E_5C_2F,axiom,
% 0.25/0.46 ! [V0: $o,V1: $o] :
% 0.25/0.46 ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.25/0.46 <=> ( V0
% 0.25/0.46 | V1 ) ) ).
% 0.25/0.46
% 0.25/0.46 thf(logicdef_2E_7E,axiom,
% 0.25/0.46 ! [V0: $o] :
% 0.25/0.46 ( ( c_2Ebool_2E_7E @ V0 )
% 0.25/0.46 <=> ( (~) @ V0 ) ) ).
% 0.25/0.46
% 0.25/0.46 thf(logicdef_2E_3D_3D_3E,axiom,
% 0.25/0.46 ! [V0: $o,V1: $o] :
% 0.25/0.46 ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.25/0.46 <=> ( V0
% 0.25/0.46 => V1 ) ) ).
% 0.25/0.46
% 0.25/0.46 thf(logicdef_2E_3D,axiom,
% 0.25/0.46 ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
% 0.25/0.46 ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
% 0.25/0.46 <=> ( V0 = V1 ) ) ).
% 0.25/0.46
% 0.25/0.46 thf(quantdef_2E_21,axiom,
% 0.25/0.46 ! [A_27a: $tType,V0f: A_27a > $o] :
% 0.25/0.46 ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
% 0.25/0.46 <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 0.25/0.46
% 0.25/0.46 thf(quantdef_2E_3F,axiom,
% 0.25/0.46 ! [A_27a: $tType,V0f: A_27a > $o] :
% 0.25/0.46 ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
% 0.25/0.46 <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 0.25/0.46
% 0.25/0.46 thf(thm_2Ebool_2ET__DEF,axiom,
% 0.25/0.46 ( c_2Ebool_2ET
% 0.25/0.46 <=> ( ( ^ [V0x: $o] : V0x )
% 0.25/0.46 = ( ^ [V1x: $o] : V1x ) ) ) ).
% 0.25/0.46
% 0.25/0.46 thf(thm_2Ebool_2ETRUTH,conjecture,
% 0.25/0.46 c_2Ebool_2ET ).
% 0.25/0.46
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 ------------------------
% 1.98/1.63 ---- Embedded in THF ---
% 1.98/1.64 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.98/1.64 %%% Generated on Tue Feb 24 08:15:10 EST 2026
% 1.98/1.64 %%% using '$$dhol' embedding, version 1.3.0.
% 1.98/1.64 %%% Logic specification used:
% 1.98/1.64 %%% thf(spec, logic, $$dhol).
% 1.98/1.64
% 1.98/1.64 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.dFFSnK7xOV/DTF2DTF28936.p
% See solution above
% 1.98/1.64 ------------------------
% 1.98/1.65 ---- Cleaned THF ---
% 1.98/1.65 thf(tyop_2Emin_2Ebool,type,
% 1.98/1.65 tyop_2Emin_2Ebool: $tType ).
% 1.98/1.65
% 1.98/1.65 thf(tyop_2Emin_2Efun,type,
% 1.98/1.65 tyop_2Emin_2Efun: $tType > $tType > $tType ).
% 1.98/1.65
% 1.98/1.65 thf(c_2Ebool_2E_21,type,
% 1.98/1.65 c_2Ebool_2E_21:
% 1.98/1.65 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 1.98/1.65
% 1.98/1.65 thf(c_2Ebool_2E_2F_5C,type,
% 1.98/1.65 c_2Ebool_2E_2F_5C: $o > $o > $o ).
% 1.98/1.65
% 1.98/1.65 thf(c_2Emin_2E_3D,type,
% 1.98/1.65 c_2Emin_2E_3D:
% 1.98/1.65 !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
% 1.98/1.65
% 1.98/1.65 thf(c_2Emin_2E_3D_3D_3E,type,
% 1.98/1.65 c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 1.98/1.65
% 1.98/1.65 thf(c_2Ebool_2E_3F,type,
% 1.98/1.65 c_2Ebool_2E_3F:
% 1.98/1.65 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 1.98/1.65
% 1.98/1.65 thf(c_2Ebool_2ET,type,
% 1.98/1.65 c_2Ebool_2ET: $o ).
% 1.98/1.65
% 1.98/1.65 thf(c_2Ebool_2E_5C_2F,type,
% 1.98/1.65 c_2Ebool_2E_5C_2F: $o > $o > $o ).
% 1.98/1.65
% 1.98/1.65 thf(c_2Ebool_2E_7E,type,
% 1.98/1.65 c_2Ebool_2E_7E: $o > $o ).
% 1.98/1.65
% 1.98/1.65 thf(logicdef_2E_2F_5C,axiom,
% 1.98/1.65 ! [V0: $o,V1: $o] :
% 1.98/1.65 ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
% 1.98/1.65 <=> ( V0
% 1.98/1.65 & V1 ) ) ).
% 1.98/1.65
% 1.98/1.65 thf(logicdef_2E_5C_2F,axiom,
% 1.98/1.65 ! [V0: $o,V1: $o] :
% 1.98/1.65 ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
% 1.98/1.65 <=> ( V0
% 1.98/1.65 | V1 ) ) ).
% 1.98/1.65
% 1.98/1.65 thf(logicdef_2E_7E,axiom,
% 1.98/1.65 ! [V0: $o] :
% 1.98/1.65 ( ( c_2Ebool_2E_7E @ V0 )
% 1.98/1.65 <=> ( (~) @ V0 ) ) ).
% 1.98/1.65
% 1.98/1.65 thf(logicdef_2E_3D_3D_3E,axiom,
% 1.98/1.65 ! [V0: $o,V1: $o] :
% 1.98/1.65 ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 1.98/1.65 <=> ( V0
% 1.98/1.65 => V1 ) ) ).
% 1.98/1.65
% 1.98/1.65 thf(logicdef_2E_3D,axiom,
% 1.98/1.65 ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
% 1.98/1.65 ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
% 1.98/1.65 <=> ( V0 = V1 ) ) ).
% 1.98/1.65
% 1.98/1.65 thf(quantdef_2E_21,axiom,
% 1.98/1.65 ! [A_27a: $tType,V0f: A_27a > $o] :
% 1.98/1.65 ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
% 1.98/1.65 <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 1.98/1.65
% 1.98/1.65 thf(quantdef_2E_3F,axiom,
% 1.98/1.65 ! [A_27a: $tType,V0f: A_27a > $o] :
% 1.98/1.65 ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
% 1.98/1.65 <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 1.98/1.65
% 1.98/1.65 thf(thm_2Ebool_2ET__DEF,axiom,
% 1.98/1.65 ( c_2Ebool_2ET
% 1.98/1.65 <=> ( ( ^ [V0x: $o] : V0x )
% 1.98/1.65 = ( ^ [V1x: $o] : V1x ) ) ) ).
% 1.98/1.65
% 1.98/1.65 thf(thm_2Ebool_2ETRUTH,conjecture,
% 1.98/1.65 c_2Ebool_2ET ).
% 1.98/1.65 ------------------------
% 1.98/1.67 % (29034)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_28936 for (2999ds/4Mi)
% 1.98/1.67 % (29039)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28936 for (2999ds/18Mi)
% 1.98/1.67 % (29033)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28936 for (2999ds/183Mi)
% 1.98/1.67 % (29038)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_28936 for (2999ds/275Mi)
% 1.98/1.67 % (29036)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28936 for (2999ds/2Mi)
% 1.98/1.67 % (29037)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_28936 for (2999ds/2Mi)
% 1.98/1.67 % (29035)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_28936 for (2999ds/27Mi)
% 1.98/1.67 % (29038)Refutation not found, incomplete strategy
% 1.98/1.67 % (29038)------------------------------
% 1.98/1.67 % (29038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.67 % (29036)Instruction limit reached!
% 1.98/1.67 % (29036)------------------------------
% 1.98/1.67 % (29036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.67 % (29038)Termination reason: Refutation not found, incomplete strategy
% 1.98/1.67
% 1.98/1.67
% 1.98/1.67 % (29038)Memory used [KB]: 5373
% 1.98/1.67 % (29038)Time elapsed: 0.002 s
% 1.98/1.67 % (29038)Instructions burned: 1 (million)
% 1.98/1.67 % (29038)------------------------------
% 1.98/1.67 % (29038)------------------------------
% 1.98/1.67 % (29036)Termination reason: Unknown
% 1.98/1.67 % (29037)Instruction limit reached!
% 1.98/1.67 % (29037)------------------------------
% 1.98/1.67 % (29037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.67 % (29037)Termination reason: Unknown
% 1.98/1.67 % (29037)Termination phase: Preprocessing 3
% 1.98/1.67
% 1.98/1.67 % (29037)Memory used [KB]: 1023
% 1.98/1.67 % (29037)Time elapsed: 0.003 s
% 1.98/1.67 % (29037)Instructions burned: 2 (million)
% 1.98/1.67 % (29037)------------------------------
% 1.98/1.67 % (29037)------------------------------
% 1.98/1.67 % (29036)Termination phase: Property scanning
% 1.98/1.67
% 1.98/1.67 % (29036)Memory used [KB]: 1023
% 1.98/1.67 % (29036)Time elapsed: 0.003 s
% 1.98/1.67 % (29036)Instructions burned: 2 (million)
% 1.98/1.67 % (29036)------------------------------
% 1.98/1.67 % (29036)------------------------------
% 1.98/1.67 % (29039)First to succeed.
% 1.98/1.67 % (29034)Instruction limit reached!
% 1.98/1.67 % (29034)------------------------------
% 1.98/1.67 % (29034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.67 % (29034)Termination reason: Unknown
% 1.98/1.67 % (29034)Termination phase: Saturation
% 1.98/1.67
% 1.98/1.67 % (29034)Memory used [KB]: 5500
% 1.98/1.67 % (29034)Time elapsed: 0.005 s
% 1.98/1.67 % (29034)Instructions burned: 5 (million)
% 1.98/1.67 % (29034)------------------------------
% 1.98/1.67 % (29034)------------------------------
% 1.98/1.67 % (29035)Also succeeded, but the first one will report.
% 1.98/1.67 % (29039)Refutation found. Thanks to Tanya!
% 1.98/1.67 % SZS status Theorem for DTF2THF_28936
% 1.98/1.67 % SZS output start Proof for DTF2THF_28936
% 1.98/1.67 thf(func_def_0, type, tyop_2Emin_2Ebool: $tType).
% 1.98/1.67 thf(func_def_1, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 1.98/1.67 thf(func_def_2, type, c_2Ebool_2E_21: !>[X0: $tType]:((X0 > $o) > $o)).
% 1.98/1.67 thf(func_def_3, type, c_2Ebool_2E_2F_5C: $o > $o > $o).
% 1.98/1.67 thf(func_def_4, type, c_2Emin_2E_3D: !>[X0: $tType]:(X0 > X0 > $o)).
% 1.98/1.67 thf(func_def_5, type, c_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 1.98/1.67 thf(func_def_6, type, c_2Ebool_2E_3F: !>[X0: $tType]:((X0 > $o) > $o)).
% 1.98/1.67 thf(func_def_8, type, c_2Ebool_2E_5C_2F: $o > $o > $o).
% 1.98/1.67 thf(func_def_9, type, c_2Ebool_2E_7E: $o > $o).
% 1.98/1.67 thf(func_def_16, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.98/1.67 thf(func_def_17, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.98/1.67 thf(f79,plain,(
% 1.98/1.67 $false),
% 1.98/1.67 inference(subsumption_resolution,[status(thm)],[f78,f56])).
% 1.98/1.67 thf(f56,plain,(
% 1.98/1.67 (c_2Ebool_2ET != $true)),
% 1.98/1.67 inference(cnf_transformation,[status(thm)],[f30])).
% 1.98/1.67 thf(f30,plain,(
% 1.98/1.67 (c_2Ebool_2ET != $true)),
% 1.98/1.67 inference(flattening,[status(thm)],[f13])).
% 1.98/1.67 thf(f13,plain,(
% 1.98/1.67 ~(c_2Ebool_2ET = $true)),
% 1.98/1.67 inference(fool_elimination,[status(thm)],[f12])).
% 1.98/1.67 thf(f12,plain,(
% 1.98/1.67 ~c_2Ebool_2ET),
% 1.98/1.67 inference(rectify,[status(thm)],[f10])).
% 1.98/1.67 thf(f10,negated_conjecture,(
% 1.98/1.67 ~c_2Ebool_2ET),
% 1.98/1.67 inference(negated_conjecture,[status(cth)],[f9])).
% 1.98/1.67 thf(f9,conjecture,(
% 1.98/1.67 c_2Ebool_2ET),
% 1.98/1.67 file('/export/starexec/sandbox2/tmp/tmp.dFFSnK7xOV/DTF2THF_28936.p',thm_2Ebool_2ETRUTH)).
% 1.98/1.67 thf(f78,plain,(
% 1.98/1.67 (c_2Ebool_2ET = $true)),
% 1.98/1.67 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.98/1.67 thf(f62,plain,(
% 1.98/1.67 (c_2Ebool_2ET = $true) | ((^[Y0 : $o]: (Y0)) != (^[Y0 : $o]: (Y0)))),
% 1.98/1.67 inference(cnf_transformation,[status(thm)],[f43])).
% 1.98/1.67 thf(f43,plain,(
% 1.98/1.67 (((^[Y0 : $o]: (Y0)) = (^[Y0 : $o]: (Y0))) | (c_2Ebool_2ET != $true)) & ((c_2Ebool_2ET = $true) | ((^[Y0 : $o]: (Y0)) != (^[Y0 : $o]: (Y0))))),
% 1.98/1.67 inference(nnf_transformation,[status(thm)],[f15])).
% 1.98/1.67 thf(f15,plain,(
% 1.98/1.67 ((^[Y0 : $o]: (Y0)) = (^[Y0 : $o]: (Y0))) <=> (c_2Ebool_2ET = $true)),
% 1.98/1.67 inference(fool_elimination,[status(thm)],[f14])).
% 1.98/1.67 thf(f14,plain,(
% 1.98/1.67 c_2Ebool_2ET <=> ((^[X0 : $o] : (X0)) = (^[X1 : $o] : (X1)))),
% 1.98/1.67 inference(rectify,[status(thm)],[f8])).
% 1.98/1.67 thf(f8,axiom,(
% 1.98/1.67 c_2Ebool_2ET <=> ((^[X5 : $o] : (X5)) = (^[X4 : $o] : (X4)))),
% 1.98/1.67 file('/export/starexec/sandbox2/tmp/tmp.dFFSnK7xOV/DTF2THF_28936.p',thm_2Ebool_2ET__DEF)).
% 1.98/1.67 % SZS output end Proof for DTF2THF_28936
% 1.98/1.67 % (29039)------------------------------
% 1.98/1.67 % (29039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.67 % (29039)Termination reason: Refutation
% 1.98/1.67
% 1.98/1.67 % (29039)Memory used [KB]: 5500
% 1.98/1.67 % (29039)Time elapsed: 0.004 s
% 1.98/1.67 % (29039)Instructions burned: 3 (million)
% 1.98/1.67 % (29039)------------------------------
% 1.98/1.67 % (29039)------------------------------
% 1.98/1.67 % (29032)Success in time 0.014 s
%------------------------------------------------------------------------------