%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO504^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 09:54:24 AM UTC 2026
% Result : Theorem 1.46s 1.28s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 6 unt; 0 typ; 6 def)
% Number of atoms : 454 ( 92 equ; 0 cnn)
% Maximal formula atoms : 15 ( 11 avg)
% Number of connectives : 284 ( 53 ~; 51 |; 42 &; 122 @)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_2,type,
h: $o > $o > $o ).
thf(func_def_3,type,
i: $o > $o > $o ).
thf(func_def_4,type,
g: ( $o > $o > $o ) > $o ).
thf(func_def_5,type,
f: ( ( $o > $o > $o ) > $o ) > $o ).
thf(func_def_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f75,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f29,f35,f41,f42,f57,f58,f74]) ).
thf(f74,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f73]) ).
thf(f73,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f71,f60]) ).
thf(f60,plain,
( ( ( i @ $true @ $true )
= $false )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f59,f28]) ).
thf(f28,plain,
( ( b = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl0_2
<=> ( b = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f59,plain,
( ( $false
= ( i @ $true @ b ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f52,f32]) ).
thf(f32,plain,
( ( a = $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl0_3
<=> ( a = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f52,plain,
( ( ( i @ a @ b )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl0_6
<=> ( ( i @ a @ b )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f71,plain,
( ( ( i @ $true @ $true )
= $true )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f65,f32]) ).
thf(f65,plain,
( ( ( i @ a @ $true )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f38,f28]) ).
thf(f38,plain,
( ( ( i @ a @ b )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl0_4
<=> ( ( i @ a @ b )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f58,plain,
~ spl0_7,
inference(avatar_split_clause,[status(thm)],[f15,f54]) ).
thf(f54,definition,
( spl0_7
<=> ( ( f @ g )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f15,plain,
( ( f @ g )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( b = $true )
| ( a = $true )
| ( ( i @ a @ b )
!= $true ) )
& ( ( ( i @ a @ b )
= $true )
| ( ( b != $true )
& ( a != $true ) ) )
& ( ( f @ g )
!= $true )
& ( ( h @ a @ b )
= $true )
& ( ( ( b = $true )
& ( a = $true ) )
| ( ( h @ a @ b )
!= $true ) )
& ( ( ( h @ a @ b )
= $true )
| ( b != $true )
| ( a != $true ) )
& ( ( i @ a @ b )
= ( f @ g ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( b = $true )
| ( a = $true )
| ( ( i @ a @ b )
!= $true ) )
& ( ( ( i @ a @ b )
= $true )
| ( ( b != $true )
& ( a != $true ) ) )
& ( ( f @ g )
!= $true )
& ( ( h @ a @ b )
= $true )
& ( ( ( b = $true )
& ( a = $true ) )
| ( ( h @ a @ b )
!= $true ) )
& ( ( ( h @ a @ b )
= $true )
| ( b != $true )
| ( a != $true ) )
& ( ( i @ a @ b )
= ( f @ g ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( b = $true )
| ( a = $true ) )
<=> ( ( i @ a @ b )
= $true ) )
& ( ( f @ g )
!= $true )
& ( ( h @ a @ b )
= $true )
& ( ( ( b = $true )
& ( a = $true ) )
<=> ( ( h @ a @ b )
= $true ) )
& ( ( i @ a @ b )
= ( f @ g ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( f @ g )
!= $true )
& ( ( i @ a @ b )
= ( f @ g ) )
& ( ( ( b = $true )
| ( a = $true ) )
<=> ( ( i @ a @ b )
= $true ) )
& ( ( h @ a @ b )
= $true )
& ( ( ( b = $true )
& ( a = $true ) )
<=> ( ( h @ a @ b )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( i @ a @ b )
= ( f @ g ) )
& ( ( ( b = $true )
| ( a = $true ) )
<=> ( ( i @ a @ b )
= $true ) )
& ( ( h @ a @ b )
= $true )
& ( ( ( b = $true )
& ( a = $true ) )
<=> ( ( h @ a @ b )
= $true ) ) )
=> ( ( f @ g )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ( i @ a @ b )
= ( f @ g ) )
& ( ( ( i @ a @ b )
= b )
| a )
& b
& ( a
= ( h @ a @ b ) )
& ( h @ a @ b ) )
=> ( f @ g ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ( i @ a @ b )
= ( f @ g ) )
& ( ( ( i @ a @ b )
= b )
| a )
& b
& ( a
= ( h @ a @ b ) )
& ( h @ a @ b ) )
=> ( f @ g ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ( i @ a @ b )
= ( f @ g ) )
& ( ( ( i @ a @ b )
= b )
| a )
& b
& ( a
= ( h @ a @ b ) )
& ( h @ a @ b ) )
=> ( f @ g ) ),
file('/export/starexec/sandbox2/tmp/tmp.jQQZ8fe7EZ/DTF2THF_32053.p',claim) ).
thf(f57,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f20,f54,f50]) ).
thf(f20,plain,
( ( ( f @ g )
= $true )
| ( ( i @ a @ b )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( i @ a @ b )
= ( f @ g ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f42,plain,
spl0_1,
inference(avatar_split_clause,[status(thm)],[f14,f22]) ).
thf(f22,definition,
( spl0_1
<=> ( ( h @ a @ b )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f14,plain,
( ( h @ a @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f41,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f16,f37,f31]) ).
thf(f16,plain,
( ( ( i @ a @ b )
= $true )
| ( a != $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f35,plain,
( spl0_3
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f12,f22,f31]) ).
thf(f12,plain,
( ( a = $true )
| ( ( h @ a @ b )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f29,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f26,f22]) ).
thf(f13,plain,
( ( b = $true )
| ( ( h @ a @ b )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO504^1 : TPTP v9.2.1. Released v4.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n016.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % 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 14:33:21 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO504^1 : TPTP v9.2.1. Released v4.1.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : Hoeschele p.21
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % : [Hoe09] Hoeschele (2009), Towards a Semi-Automatic Higher-Orde
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : basic17 [Bro09]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 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 v4.1.0
% 0.30/0.46 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.30/0.46 % Number of atoms : 23 ( 3 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 8 ( 23 avg)
% 0.30/0.46 % Number of connectives : 16 ( 0 ~; 1 |; 4 &; 10 @)
% 0.30/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.30/0.46 % Number of types : 1 ( 0 usr)
% 0.30/0.46 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments :
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(a,type,
% 0.30/0.46 a: $o ).
% 0.30/0.46
% 0.30/0.46 thf(b,type,
% 0.30/0.46 b: $o ).
% 0.30/0.46
% 0.30/0.46 thf(h,type,
% 0.30/0.46 h: $o > $o > $o ).
% 0.30/0.46
% 0.30/0.46 thf(i,type,
% 0.30/0.46 i: $o > $o > $o ).
% 0.30/0.46
% 0.30/0.46 thf(g,type,
% 0.30/0.46 g: ( $o > $o > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(f,type,
% 0.30/0.46 f: ( ( $o > $o > $o ) > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(claim,conjecture,
% 0.30/0.46 ( ( ( ( h @ a @ b )
% 0.30/0.46 = ( a
% 0.30/0.46 & b ) )
% 0.30/0.46 & ( ( i @ a @ b )
% 0.30/0.46 = ( a
% 0.30/0.46 | b ) )
% 0.30/0.46 & ( ( f @ g )
% 0.30/0.46 = ( i @ a @ b ) )
% 0.30/0.46 & ( h @ a @ b ) )
% 0.30/0.46 => ( f @ g ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.46/1.25 ---- Embedded in THF ---
% 1.46/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.25 %%% Generated on Tue Feb 24 14:33:22 EST 2026
% 1.46/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.25 %%% Logic specification used:
% 1.46/1.25 %%% thf(spec, logic, $$dhol).
% 1.46/1.25
% 1.46/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jQQZ8fe7EZ/DTF2DTF32053.p
% See solution above
% 1.46/1.25 ------------------------
% 1.46/1.26 ---- Cleaned THF ---
% 1.46/1.26 thf(a,type,
% 1.46/1.26 a: $o ).
% 1.46/1.26
% 1.46/1.26 thf(b,type,
% 1.46/1.26 b: $o ).
% 1.46/1.26
% 1.46/1.26 thf(h,type,
% 1.46/1.26 h: $o > $o > $o ).
% 1.46/1.26
% 1.46/1.26 thf(i,type,
% 1.46/1.26 i: $o > $o > $o ).
% 1.46/1.26
% 1.46/1.26 thf(g,type,
% 1.46/1.26 g: ( $o > $o > $o ) > $o ).
% 1.46/1.26
% 1.46/1.26 thf(f,type,
% 1.46/1.26 f: ( ( $o > $o > $o ) > $o ) > $o ).
% 1.46/1.26
% 1.46/1.26 thf(claim,conjecture,
% 1.46/1.26 ( ( ( ( h @ a @ b )
% 1.46/1.26 = ( a
% 1.46/1.26 & b ) )
% 1.46/1.26 & ( ( i @ a @ b )
% 1.46/1.26 = ( a
% 1.46/1.26 | b ) )
% 1.46/1.26 & ( ( f @ g )
% 1.46/1.26 = ( i @ a @ b ) )
% 1.46/1.26 & ( h @ a @ b ) )
% 1.46/1.26 => ( f @ g ) ) ).
% 1.46/1.26 ------------------------
% 1.46/1.28 % (32266)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_32053 for (2999ds/275Mi)
% 1.46/1.28 % (32265)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_32053 for (2999ds/2Mi)
% 1.46/1.28 % (32265)Instruction limit reached!
% 1.46/1.28 % (32265)------------------------------
% 1.46/1.28 % (32265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (32265)Termination reason: Unknown
% 1.46/1.28 % (32265)Termination phase: Saturation
% 1.46/1.28
% 1.46/1.28 % (32265)Memory used [KB]: 5500
% 1.46/1.28 % (32265)Time elapsed: 0.002 s
% 1.46/1.28 % (32265)Instructions burned: 2 (million)
% 1.46/1.28 % (32265)------------------------------
% 1.46/1.28 % (32265)------------------------------
% 1.46/1.28 % (32266)First to succeed.
% 1.46/1.28 % (32266)Refutation found. Thanks to Tanya!
% 1.46/1.28 % SZS status Theorem for DTF2THF_32053
% 1.46/1.28 % SZS output start Proof for DTF2THF_32053
% 1.46/1.28 thf(func_def_2, type, h: $o > $o > $o).
% 1.46/1.28 thf(func_def_3, type, i: $o > $o > $o).
% 1.46/1.28 thf(func_def_4, type, g: ($o > $o > $o) > $o).
% 1.46/1.28 thf(func_def_5, type, f: (($o > $o > $o) > $o) > $o).
% 1.46/1.28 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.46/1.28 thf(f75,plain,(
% 1.46/1.28 $false),
% 1.46/1.28 inference(avatar_sat_refutation,[status(thm)],[f29,f35,f41,f42,f57,f58,f74])).
% 1.46/1.28 thf(f74,plain,(
% 1.46/1.28 ~spl0_2 | ~spl0_3 | ~spl0_4 | ~spl0_6),
% 1.46/1.28 inference(avatar_contradiction_clause,[status(thm)],[f73])).
% 1.46/1.28 thf(f73,plain,(
% 1.46/1.28 $false | (~spl0_2 | ~spl0_3 | ~spl0_4 | ~spl0_6)),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.46/1.28 thf(f72,plain,(
% 1.46/1.28 ($true = $false) | (~spl0_2 | ~spl0_3 | ~spl0_4 | ~spl0_6)),
% 1.46/1.28 inference(forward_demodulation,[status(thm)],[f71,f60])).
% 1.46/1.28 thf(f60,plain,(
% 1.46/1.28 ((i @ $true @ $true) = $false) | (~spl0_2 | ~spl0_3 | ~spl0_6)),
% 1.46/1.28 inference(forward_demodulation,[status(thm)],[f59,f28])).
% 1.46/1.28 thf(f28,plain,(
% 1.46/1.28 (b = $true) | ~spl0_2),
% 1.46/1.28 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.46/1.28 thf(f26,definition,(
% 1.46/1.28 spl0_2 <=> (b = $true)),
% 1.46/1.28 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.46/1.28 thf(f59,plain,(
% 1.46/1.28 ($false = (i @ $true @ b)) | (~spl0_3 | ~spl0_6)),
% 1.46/1.28 inference(forward_demodulation,[status(thm)],[f52,f32])).
% 1.46/1.28 thf(f32,plain,(
% 1.46/1.28 (a = $true) | ~spl0_3),
% 1.46/1.28 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.46/1.28 thf(f31,definition,(
% 1.46/1.28 spl0_3 <=> (a = $true)),
% 1.46/1.28 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.46/1.28 thf(f52,plain,(
% 1.46/1.28 ((i @ a @ b) = $false) | ~spl0_6),
% 1.46/1.28 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.46/1.28 thf(f50,definition,(
% 1.46/1.28 spl0_6 <=> ((i @ a @ b) = $false)),
% 1.46/1.28 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.46/1.28 thf(f71,plain,(
% 1.46/1.28 ((i @ $true @ $true) = $true) | (~spl0_2 | ~spl0_3 | ~spl0_4)),
% 1.46/1.28 inference(forward_demodulation,[status(thm)],[f65,f32])).
% 1.46/1.28 thf(f65,plain,(
% 1.46/1.28 ((i @ a @ $true) = $true) | (~spl0_2 | ~spl0_4)),
% 1.46/1.28 inference(superposition,[status(thm)],[f38,f28])).
% 1.46/1.28 thf(f38,plain,(
% 1.46/1.28 ((i @ a @ b) = $true) | ~spl0_4),
% 1.46/1.28 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.46/1.28 thf(f37,definition,(
% 1.46/1.28 spl0_4 <=> ((i @ a @ b) = $true)),
% 1.46/1.28 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.46/1.28 thf(f58,plain,(
% 1.46/1.28 ~spl0_7),
% 1.46/1.28 inference(avatar_split_clause,[status(thm)],[f15,f54])).
% 1.46/1.28 thf(f54,definition,(
% 1.46/1.28 spl0_7 <=> ((f @ g) = $true)),
% 1.46/1.28 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.46/1.28 thf(f15,plain,(
% 1.46/1.28 ((f @ g) != $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.28 thf(f9,plain,(
% 1.46/1.28 ((b = $true) | (a = $true) | ((i @ a @ b) != $true)) & (((i @ a @ b) = $true) | ((b != $true) & (a != $true))) & ((f @ g) != $true) & ((h @ a @ b) = $true) & (((b = $true) & (a = $true)) | ((h @ a @ b) != $true)) & (((h @ a @ b) = $true) | (b != $true) | (a != $true)) & ((i @ a @ b) = (f @ g))),
% 1.46/1.28 inference(flattening,[status(thm)],[f8])).
% 1.46/1.28 thf(f8,plain,(
% 1.46/1.28 ((((b = $true) | (a = $true)) | ((i @ a @ b) != $true)) & (((i @ a @ b) = $true) | ((b != $true) & (a != $true)))) & ((f @ g) != $true) & ((h @ a @ b) = $true) & ((((b = $true) & (a = $true)) | ((h @ a @ b) != $true)) & (((h @ a @ b) = $true) | ((b != $true) | (a != $true)))) & ((i @ a @ b) = (f @ g))),
% 1.46/1.28 inference(nnf_transformation,[status(thm)],[f7])).
% 1.46/1.28 thf(f7,plain,(
% 1.46/1.28 (((b = $true) | (a = $true)) <=> ((i @ a @ b) = $true)) & ((f @ g) != $true) & ((h @ a @ b) = $true) & (((b = $true) & (a = $true)) <=> ((h @ a @ b) = $true)) & ((i @ a @ b) = (f @ g))),
% 1.46/1.28 inference(flattening,[status(thm)],[f6])).
% 1.46/1.28 thf(f6,plain,(
% 1.46/1.28 ((f @ g) != $true) & (((i @ a @ b) = (f @ g)) & (((b = $true) | (a = $true)) <=> ((i @ a @ b) = $true)) & ((h @ a @ b) = $true) & (((b = $true) & (a = $true)) <=> ((h @ a @ b) = $true)))),
% 1.46/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.46/1.28 thf(f5,plain,(
% 1.46/1.28 ~((((i @ a @ b) = (f @ g)) & (((b = $true) | (a = $true)) <=> ((i @ a @ b) = $true)) & ((h @ a @ b) = $true) & (((b = $true) & (a = $true)) <=> ((h @ a @ b) = $true))) => ((f @ g) = $true))),
% 1.46/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.28 thf(f4,plain,(
% 1.46/1.28 ~((((i @ a @ b) = (f @ g)) & ((i @ a @ b) = b | a) & (b & a = (h @ a @ b)) & (h @ a @ b)) => (f @ g))),
% 1.46/1.28 inference(rectify,[status(thm)],[f2])).
% 1.46/1.28 thf(f2,negated_conjecture,(
% 1.46/1.28 ~((((i @ a @ b) = (f @ g)) & ((i @ a @ b) = b | a) & (b & a = (h @ a @ b)) & (h @ a @ b)) => (f @ g))),
% 1.46/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.28 thf(f1,conjecture,(
% 1.46/1.28 (((i @ a @ b) = (f @ g)) & ((i @ a @ b) = b | a) & (b & a = (h @ a @ b)) & (h @ a @ b)) => (f @ g)),
% 1.46/1.28 file('/export/starexec/sandbox2/tmp/tmp.jQQZ8fe7EZ/DTF2THF_32053.p',claim)).
% 1.46/1.28 thf(f57,plain,(
% 1.46/1.28 spl0_6 | spl0_7),
% 1.46/1.28 inference(avatar_split_clause,[status(thm)],[f20,f54,f50])).
% 1.46/1.28 thf(f20,plain,(
% 1.46/1.28 ((f @ g) = $true) | ((i @ a @ b) = $false)),
% 1.46/1.28 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.46/1.28 thf(f10,plain,(
% 1.46/1.28 ((i @ a @ b) = (f @ g))),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.28 thf(f42,plain,(
% 1.46/1.28 spl0_1),
% 1.46/1.28 inference(avatar_split_clause,[status(thm)],[f14,f22])).
% 1.46/1.28 thf(f22,definition,(
% 1.46/1.28 spl0_1 <=> ((h @ a @ b) = $true)),
% 1.46/1.28 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.46/1.28 thf(f14,plain,(
% 1.46/1.28 ((h @ a @ b) = $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.28 thf(f41,plain,(
% 1.46/1.28 ~spl0_3 | spl0_4),
% 1.46/1.28 inference(avatar_split_clause,[status(thm)],[f16,f37,f31])).
% 1.46/1.28 thf(f16,plain,(
% 1.46/1.28 ((i @ a @ b) = $true) | (a != $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.28 thf(f35,plain,(
% 1.46/1.28 spl0_3 | ~spl0_1),
% 1.46/1.28 inference(avatar_split_clause,[status(thm)],[f12,f22,f31])).
% 1.46/1.28 thf(f12,plain,(
% 1.46/1.28 (a = $true) | ((h @ a @ b) != $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.28 thf(f29,plain,(
% 1.46/1.28 ~spl0_1 | spl0_2),
% 1.46/1.28 inference(avatar_split_clause,[status(thm)],[f13,f26,f22])).
% 1.46/1.28 thf(f13,plain,(
% 1.46/1.28 (b = $true) | ((h @ a @ b) != $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.28 % SZS output end Proof for DTF2THF_32053
% 1.46/1.28 % (32266)------------------------------
% 1.46/1.28 % (32266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (32266)Termination reason: Refutation
% 1.46/1.28
% 1.46/1.28 % (32266)Memory used [KB]: 5500
% 1.46/1.28 % (32266)Time elapsed: 0.003 s
% 1.46/1.28 % (32266)Instructions burned: 2 (million)
% 1.46/1.28 % (32266)------------------------------
% 1.46/1.28 % (32266)------------------------------
% 1.46/1.28 % (32260)Success in time 0.013 s
%------------------------------------------------------------------------------