TSTP Solution File: SYO383^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO383^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 : Fri Sep 1 04:46:30 EDT 2023
% Result : Theorem 0.18s 0.84s
% Output : Proof 0.60s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_f,type,
f: $i > $i ).
thf(ty_b,type,
b: $i ).
thf(ty_d,type,
d: $i ).
thf(ty_c,type,
c: $i ).
thf(ty_cP_1,type,
cP_1: $i > $i > $o ).
thf(ty_cQ_2,type,
cQ_2: $i > $i > $i > $o ).
thf(ty_a,type,
a: $i ).
thf(ty_cQ_1,type,
cQ_1: $i > $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ X1 @ X2 @ X3 )
=> ~ ( cP_1 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_1 @ ( f @ X2 ) @ X5 ) )
=> ~ ( cP_1 @ ( f @ X3 ) @ X6 ) )
=> ( cQ_2 @ X4 @ X5 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( cP_1 @ c @ X1 )
=> ( cP_1 @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cP_1 @ a @ a ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ a @ b @ c )
=> ~ ( cP_1 @ ( f @ a ) @ X1 ) )
=> ~ ( cP_1 @ ( f @ b ) @ X2 ) )
=> ~ ( cP_1 @ ( f @ c ) @ X3 ) )
=> ( cQ_2 @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ a @ b @ c )
=> ~ ( cP_1 @ ( f @ a ) @ a ) )
=> ~ ( cP_1 @ ( f @ b ) @ X1 ) )
=> ~ ( cP_1 @ ( f @ c ) @ X2 ) )
=> ( cQ_2 @ a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cP_1 @ c @ c ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ~ ( ~ ( ( cQ_1 @ a @ b @ c )
=> ~ ( cP_1 @ ( f @ a ) @ a ) )
=> ~ ( cP_1 @ ( f @ b ) @ b ) )
=> ~ ( cP_1 @ ( f @ c ) @ c ) )
=> ( cQ_2 @ a @ b @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( cP_1 @ b @ X1 )
=> ( cP_1 @ ( f @ b ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cP_1 @ ( f @ c ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ( cQ_1 @ a @ b @ c )
=> ~ ( cP_1 @ ( f @ a ) @ a ) )
=> ~ ( cP_1 @ ( f @ b ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
~ ( cQ_2 @ a @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cP_1 @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( cQ_1 @ a @ b @ c )
=> ~ ( cP_1 @ ( f @ a ) @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( cQ_2 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cP_1 @ ( f @ b ) @ b ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( cP_1 @ a @ X1 )
=> ( cP_1 @ ( f @ a ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP10
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP3
=> ( cP_1 @ ( f @ a ) @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i] :
( ( cP_1 @ X1 @ X2 )
=> ( cP_1 @ ( f @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_2 @ X1 @ X2 @ X3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( cQ_1 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP12
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ a @ b @ X1 )
=> ~ ( cP_1 @ ( f @ a ) @ X2 ) )
=> ~ ( cP_1 @ ( f @ b ) @ X3 ) )
=> ~ ( cP_1 @ ( f @ X1 ) @ X4 ) )
=> ( cQ_2 @ X2 @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ~ ( ~ sP10
=> ~ ( cP_1 @ ( f @ c ) @ X1 ) )
=> ( cQ_2 @ a @ b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( cP_1 @ ( f @ a ) @ a ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
~ ( cQ_2 @ a @ b @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP6
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ a @ X1 @ X2 )
=> ~ ( cP_1 @ ( f @ a ) @ X3 ) )
=> ~ ( cP_1 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_1 @ ( f @ X2 ) @ X5 ) )
=> ( cQ_2 @ X3 @ X4 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(cTHM409_1,conjecture,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP21
=> ~ sP3 )
=> ~ sP12 )
=> ~ sP6 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP19 )
=> ~ sP1 )
=> ~ sP20 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP21
=> ~ sP3 )
=> ~ sP12 )
=> ~ sP6 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP19 )
=> ~ sP1 )
=> ~ sP20 ),
inference(assume_negation,[status(cth)],[cTHM409_1]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP21
=> ~ sP3 )
=> ~ sP12 )
=> ~ sP6 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP19 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP20,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( sP21
=> ~ sP3 )
=> ~ sP12 )
=> ~ sP6 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP19 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ( sP21
=> ~ sP3 )
=> ~ sP12 )
=> ~ sP6 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP19,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( sP21
=> ~ sP3 )
=> ~ sP12 )
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: $i] : ( cP_1 @ d @ X1 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( sP21
=> ~ sP3 )
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP6,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP21
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP12,
introduced(assumption,[]) ).
thf(h13,assumption,
sP21,
introduced(assumption,[]) ).
thf(h14,assumption,
sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| sP13
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP13
| ~ sP21
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP17
| sP10
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP17
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP24
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP23
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP28
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP26
| ~ sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP18
| ~ sP3
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP11
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP16
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP20
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP19
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP1
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP22
| ~ sP12
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP8
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP19
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP27
| ~ sP6
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP2
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP19
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h13,h14,h12,h10,h6,h4,h2]) ).
thf(24,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])],[h11,23,h13,h14]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,24,h11,h12]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,25,h9,h10]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,26,h7,h8]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,27,h5,h6]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,28,h3,h4]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,29,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP21
=> ~ sP3 )
=> ~ sP12 )
=> ~ sP6 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP19 )
=> ~ sP1 )
=> ~ sP20 ),
inference(contra,[status(thm),contra(discharge,[h0])],[30,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO383^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 05:06:05 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.84 % SZS status Theorem
% 0.18/0.84 % Mode: cade22grackle2xfee4
% 0.18/0.84 % Steps: 12040
% 0.18/0.84 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------