TSTP Solution File: NUM830^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 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 : Thu Aug 31 11:41:22 EDT 2023
% Result : Theorem 36.12s 36.31s
% Output : Proof 36.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_n,type,
n: $tType ).
thf(ty_c0,type,
c0: n ).
thf(ty_c_star,type,
c_star: n > n > n ).
thf(ty_cS,type,
cS: n > n ).
thf(ty_c_plus,type,
c_plus: n > n > n ).
thf(sP1,plain,
( sP1
<=> ! [X1: n,X2: n] :
( ( c_star @ X1 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X1 @ X2 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: n] :
( ( c_plus @ c0 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ c0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) )
= ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ c0 ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ c0 ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> $false ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( c_plus @ c0 @ ( cS @ c0 ) )
= ( cS @ ( c_plus @ c0 @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) )
= ( cS @ ( cS @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( c_plus @ c0 @ ( cS @ ( cS @ c0 ) ) )
= ( cS @ ( c_plus @ c0 @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ c0 ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ c0 @ ( cS @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( c_plus @ ( cS @ c0 ) @ c0 )
= ( c_plus @ c0 @ ( cS @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: n] :
( ( c_plus @ ( cS @ c0 ) @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ ( cS @ c0 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ c0 )
= c0 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( cS @ ( c_plus @ c0 @ c0 ) )
= ( c_plus @ ( cS @ c0 ) @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( c0
= ( c_plus @ c0 @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( c_plus @ ( cS @ c0 ) @ c0 )
= ( cS @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: n] :
( ( c_star @ X1 @ c0 )
= c0 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( c_plus @ c0 @ ( cS @ c0 ) )
= ( c_plus @ ( cS @ c0 ) @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( c_plus @ ( cS @ c0 ) @ ( cS @ c0 ) )
= ( cS @ ( c_plus @ ( cS @ c0 ) @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( cS @ ( c_plus @ ( cS @ c0 ) @ c0 ) )
= ( cS @ ( cS @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( cS @ ( c_plus @ c0 @ ( cS @ c0 ) ) )
= ( cS @ ( cS @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: n] :
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ X1 ) )
= ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ X1 ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( c_plus @ c0 @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ c0 ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( c_plus @ ( cS @ c0 ) @ ( cS @ c0 ) )
= ( cS @ ( cS @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( cS @ ( c_plus @ ( cS @ c0 ) @ c0 ) )
= ( cS @ ( c_plus @ c0 @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( cS @ c0 )
= ( cS @ ( c_plus @ c0 @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( c_plus @ c0 @ c0 )
= c0 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ c0 ) @ ( cS @ ( cS @ c0 ) ) )
= ( cS @ ( cS @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(def_cPA_1,definition,
cPA_1 = sP6 ).
thf(def_cPA_2,definition,
cPA_2 = sP30 ).
thf(def_cPA_3,definition,
cPA_3 = sP19 ).
thf(def_cPA_4,definition,
cPA_4 = sP1 ).
thf(cPA_THM1,conjecture,
( ~ ( ~ ( ~ ( sP6
=> ~ sP30 )
=> ~ sP19 )
=> ~ sP1 )
=> sP22 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( sP6
=> ~ sP30 )
=> ~ sP19 )
=> ~ sP1 )
=> sP22 ),
inference(assume_negation,[status(cth)],[cPA_THM1]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( sP6
=> ~ sP30 )
=> ~ sP19 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP6
=> ~ sP30 )
=> ~ sP19 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP6
=> ~ sP30 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP19,
introduced(assumption,[]) ).
thf(h7,assumption,
sP6,
introduced(assumption,[]) ).
thf(h8,assumption,
sP30,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP18
| sP15
| ~ sP29
| sP5 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| sP20
| sP5
| ~ sP15 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| sP32
| ~ sP26
| ~ sP24 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP21
| sP27
| sP5
| ~ sP23 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP21
| sP24
| ~ sP28
| ~ sP27 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(6,plain,
( sP29
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP28
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP11
| sP5
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP26 ),
inference(symeq,[status(thm)],]) ).
thf(10,plain,
( ~ sP3
| sP9
| ~ sP4
| ~ sP32 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP20
| sP12 ),
inference(symeq,[status(thm)],]) ).
thf(12,plain,
( sP23
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP17
| sP5
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
~ sP5,
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP8
| sP22
| sP5
| ~ sP17 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP3
| sP4 ),
inference(symeq,[status(thm)],]) ).
thf(17,plain,
( ~ sP31
| sP16 ),
inference(symeq,[status(thm)],]) ).
thf(18,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP2
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP13
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP25
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP25
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP6
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP6
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP30
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP30
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP19
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP1
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,h7,h8,h6,h4,h2]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,29,h7,h8]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,30,h5,h6]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,31,h3,h4]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,32,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( sP6
=> ~ sP30 )
=> ~ sP19 )
=> ~ sP1 )
=> sP22 ),
inference(contra,[status(thm),contra(discharge,[h0])],[33,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 16:16:20 EDT 2023
% 0.14/0.35 % CPUTime :
% 36.12/36.31 % SZS status Theorem
% 36.12/36.31 % Mode: cade22grackle2x798d
% 36.12/36.31 % Steps: 32513
% 36.12/36.31 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------