%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO175^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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 : Thu Oct 9 03:25:03 PM UTC 2025
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_p,type,
p: $tType ).
thf(ty_cVEG_EATS,type,
cVEG_EATS: a > p > $o ).
thf(ty_cBIRD,type,
cBIRD: a ).
thf(ty_cSMALLER,type,
cSMALLER: a > a > $o ).
thf(ty_cFOX,type,
cFOX: a ).
thf(ty_cWOLF,type,
cWOLF: a ).
thf(ty_cGRAIN,type,
cGRAIN: p ).
thf(ty_cCATERPILLAR,type,
cCATERPILLAR: a ).
thf(ty_eigen__1,type,
eigen__1: p ).
thf(ty_eigen__0,type,
eigen__0: p ).
thf(ty_cSNAIL,type,
cSNAIL: a ).
thf(ty_cMEAT_EATS,type,
cMEAT_EATS: a > a > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ~ ( ( cSMALLER @ X1 @ cBIRD )
=> ! [X2: p] :
~ ( cVEG_EATS @ X1 @ X2 ) )
=> ( cMEAT_EATS @ cBIRD @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cVEG_EATS @ cSNAIL @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( cSMALLER @ cBIRD @ cFOX )
=> ! [X1: p] :
~ ( cVEG_EATS @ cBIRD @ X1 ) )
=> ( cMEAT_EATS @ cFOX @ cBIRD ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ( cSMALLER @ cFOX @ cWOLF )
=> ! [X1: p] :
~ ( cVEG_EATS @ cFOX @ X1 ) )
=> ( cMEAT_EATS @ cWOLF @ cFOX ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cMEAT_EATS @ cWOLF @ cFOX ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cSMALLER @ cSNAIL @ cBIRD ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( !! @ ( cVEG_EATS @ cWOLF ) )
=> ! [X1: a] :
( ~ ( ( cSMALLER @ X1 @ cWOLF )
=> ! [X2: p] :
~ ( cVEG_EATS @ X1 @ X2 ) )
=> ( cMEAT_EATS @ cWOLF @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( !! @ ( cVEG_EATS @ cWOLF ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cVEG_EATS @ cFOX @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cSMALLER @ cBIRD @ cFOX )
=> ! [X1: p] :
~ ( cVEG_EATS @ cBIRD @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: p] :
~ ( cVEG_EATS @ cSNAIL @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cVEG_EATS @ cBIRD @ cGRAIN ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( cSMALLER @ cFOX @ cWOLF )
=> ! [X1: p] :
~ ( cVEG_EATS @ cFOX @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( !! @ ( cVEG_EATS @ cFOX ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cVEG_EATS @ cWOLF @ cGRAIN ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( !! @ ( cVEG_EATS @ cBIRD ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: p] :
~ ( cVEG_EATS @ cFOX @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cSMALLER @ cBIRD @ cFOX ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: p] :
~ ( cVEG_EATS @ cBIRD @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( cVEG_EATS @ cBIRD @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
( ~ ( ( cSMALLER @ X1 @ cWOLF )
=> ! [X2: p] :
~ ( cVEG_EATS @ X1 @ X2 ) )
=> ( cMEAT_EATS @ cWOLF @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP16
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ( sP6
=> sP11 )
=> ( cMEAT_EATS @ cBIRD @ cSNAIL ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP6
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a,X2: a] :
( ( cMEAT_EATS @ X1 @ X2 )
=> ~ ( cVEG_EATS @ X2 @ cGRAIN ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( cSMALLER @ cFOX @ cWOLF ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a] :
( ~ ( !! @ ( cVEG_EATS @ X1 ) )
=> ! [X2: a] :
( ~ ( ( cSMALLER @ X2 @ X1 )
=> ! [X3: p] :
~ ( cVEG_EATS @ X2 @ X3 ) )
=> ( cMEAT_EATS @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP14
=> ! [X1: a] :
( ~ ( ( cSMALLER @ X1 @ cFOX )
=> ! [X2: p] :
~ ( cVEG_EATS @ X1 @ X2 ) )
=> ( cMEAT_EATS @ cFOX @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a] :
( ~ ( ( cSMALLER @ X1 @ cFOX )
=> ! [X2: p] :
~ ( cVEG_EATS @ X1 @ X2 ) )
=> ( cMEAT_EATS @ cFOX @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( cMEAT_EATS @ cBIRD @ cSNAIL ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( cMEAT_EATS @ cFOX @ cBIRD )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( cMEAT_EATS @ cFOX @ cBIRD ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a] :
( ( cMEAT_EATS @ cFOX @ X1 )
=> ~ ( cVEG_EATS @ X1 @ cGRAIN ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(cPUZ031_1_HO,conjecture,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 )
=> ~ sP18 )
=> ~ sP26 )
=> sP5 )
=> sP15 )
=> ~ ( cMEAT_EATS @ cBIRD @ cCATERPILLAR ) )
=> sP30 )
=> ! [X1: p] :
~ ( cVEG_EATS @ cCATERPILLAR @ X1 ) )
=> sP11 )
=> ~ sP25 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 )
=> ~ sP18 )
=> ~ sP26 )
=> sP5 )
=> sP15 )
=> ~ ( cMEAT_EATS @ cBIRD @ cCATERPILLAR ) )
=> sP30 )
=> ! [X1: p] :
~ ( cVEG_EATS @ cCATERPILLAR @ X1 ) )
=> sP11 )
=> ~ sP25 ),
inference(assume_negation,[status(cth)],[cPUZ031_1_HO]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 )
=> ~ sP18 )
=> ~ sP26 )
=> sP5 )
=> sP15 )
=> ~ ( cMEAT_EATS @ cBIRD @ cCATERPILLAR ) )
=> sP30 )
=> ! [X1: p] :
~ ( cVEG_EATS @ cCATERPILLAR @ X1 ) )
=> sP11 ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP25,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 )
=> ~ sP18 )
=> ~ sP26 )
=> sP5 )
=> sP15 )
=> ~ ( cMEAT_EATS @ cBIRD @ cCATERPILLAR ) )
=> sP30 )
=> ! [X1: p] :
~ ( cVEG_EATS @ cCATERPILLAR @ X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 )
=> ~ sP18 )
=> ~ sP26 )
=> sP5 )
=> sP15 )
=> ~ ( cMEAT_EATS @ cBIRD @ cCATERPILLAR ) )
=> sP30 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: p] :
~ ( cVEG_EATS @ cCATERPILLAR @ X1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 )
=> ~ sP18 )
=> ~ sP26 )
=> sP5 )
=> sP15 )
=> ~ ( cMEAT_EATS @ cBIRD @ cCATERPILLAR ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP30,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 )
=> ~ sP18 )
=> ~ sP26 )
=> sP5 )
=> sP15 ),
introduced(assumption,[]) ).
thf(h10,assumption,
cMEAT_EATS @ cBIRD @ cCATERPILLAR,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 )
=> ~ sP18 )
=> ~ sP26 )
=> sP5 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 )
=> ~ sP18 )
=> ~ sP26 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 )
=> ~ sP18 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP26,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP18,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
sP6,
introduced(assumption,[]) ).
thf(h21,assumption,
sP27,
introduced(assumption,[]) ).
thf(h22,assumption,
cSMALLER @ cCATERPILLAR @ cBIRD,
introduced(assumption,[]) ).
thf(h23,assumption,
cVEG_EATS @ cCATERPILLAR @ eigen__0,
introduced(assumption,[]) ).
thf(h24,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP16
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP8
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP16
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP19
| ~ sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP14
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP17
| ~ sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP25
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP33
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP31
| ~ sP32
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP11
| ~ sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP27
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP7
| sP8
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP21
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP4
| sP13
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP13
| ~ sP26
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP27
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP28
| sP14
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP29
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP3
| sP10
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP10
| ~ sP18
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP1
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP23
| sP24
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP24
| ~ sP6
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP27
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP22
| sP16
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,h21,h20,h18,h16,h14,h12,h8,h24,h2]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__1)],[h4,26,h24]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__0)],[h6,27,h23]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h19,28,h21,h22]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h17,29,h19,h20]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h15,30,h17,h18]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h13,31,h15,h16]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h11,32,h13,h14]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,33,h11,h12]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,34,h9,h10]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,35,h7,h8]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,36,h5,h6]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,37,h3,h4]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,38,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP27
=> ~ ( cSMALLER @ cCATERPILLAR @ cBIRD ) )
=> ~ sP6 )
=> ~ sP18 )
=> ~ sP26 )
=> sP5 )
=> sP15 )
=> ~ ( cMEAT_EATS @ cBIRD @ cCATERPILLAR ) )
=> sP30 )
=> ! [X1: p] :
~ ( cVEG_EATS @ cCATERPILLAR @ X1 ) )
=> sP11 )
=> ~ sP25 ),
inference(contra,[status(thm),contra(discharge,[h0])],[39,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO175^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Oct 9 00:58:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % Mode: mode213
% 0.20/0.46 % Inferences: 1385
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------