TSTP Solution File: SEV168^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV168^5 : 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 : n013.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 19:32:49 EDT 2023
% Result : Theorem 0.23s 0.43s
% Output : Proof 0.23s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_q,type,
q: ( a > a > a ) > a ).
thf(ty_p,type,
p: ( a > a > a ) > a ).
thf(ty_eigen__0,type,
eigen__0: a > a > a ).
thf(sP1,plain,
( sP1
<=> ( p
= ( ^ [X1: a > a > a] :
( X1
@ ( q
@ ^ [X2: a,X3: a] : X2 )
@ ( q
@ ^ [X2: a,X3: a] : X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( p @ eigen__0 )
= ( eigen__0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > a > a] :
( ( q @ X1 )
= ( X1
@ ( q
@ ^ [X2: a,X3: a] : X2 )
@ ( q
@ ^ [X2: a,X3: a] : X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( q @ eigen__0 )
= ( eigen__0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( q
= ( ^ [X1: a > a > a] :
( X1
@ ( q
@ ^ [X2: a,X3: a] : X2 )
@ ( q
@ ^ [X2: a,X3: a] : X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( p @ eigen__0 )
= ( q @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> $false ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) )
= ( p @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > a > a] :
( ( p @ X1 )
= ( X1
@ ( q
@ ^ [X2: a,X3: a] : X2 )
@ ( q
@ ^ [X2: a,X3: a] : X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(cTHM188_PARTIAL_pme,conjecture,
( ~ ( sP5
=> ~ sP1 )
=> ( p = q ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( sP5
=> ~ sP1 )
=> ( p = q ) ),
inference(assume_negation,[status(cth)],[cTHM188_PARTIAL_pme]) ).
thf(h1,assumption,
~ ( sP5
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
p != q,
introduced(assumption,[]) ).
thf(h3,assumption,
sP5,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a > a > a] :
( ( p @ X1 )
= ( q @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP8
| ~ sP2
| sP7 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
~ sP7,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP6
| ~ sP8
| sP7 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,h3,h4,h6]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h5,8,h6]) ).
thf(10,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_fe(discharge,[h5])],[h2,9,h5]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,10,h3,h4]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,11,h1,h2]) ).
thf(0,theorem,
( ~ ( sP5
=> ~ sP1 )
=> ( p = q ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEV168^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 24 03:18:02 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.43 % SZS status Theorem
% 0.23/0.43 % Mode: cade22grackle2xfee4
% 0.23/0.43 % Steps: 58
% 0.23/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------