TSTP Solution File: SYO238^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO238^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 : 600s
% DateTime : Thu Jul 21 19:31:02 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cB,type,
cB: $o ).
thf(ty_f,type,
f: $i > $i ).
thf(ty_x,type,
x: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( ( f @ ( f @ eigen__0 ) )
= X1 )
=> ( X1
= ( f @ ( f @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( f @ ( f @ eigen__0 ) )
= ( f @ eigen__0 ) )
=> ( ( f @ eigen__0 )
= ( f @ ( f @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( f @ eigen__0 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( f @ eigen__0 )
= ( f @ ( f @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( f @ ( f @ eigen__0 ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> cB ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( f @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( f @ ( f @ eigen__0 ) )
= ( f @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(cADDHYP5,conjecture,
( ( ~ $false
=> sP8 )
=> ( ( ( ( ^ [X1: $i] : ( f @ ( f @ X1 ) ) )
= ( ^ [X1: $i] : X1 ) )
=> sP7 )
=> ( ( cP @ x )
=> sP7 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ( ~ $false
=> sP8 )
=> ( ( ( ( ^ [X1: $i] : ( f @ ( f @ X1 ) ) )
= ( ^ [X1: $i] : X1 ) )
=> sP7 )
=> ( ( cP @ x )
=> sP7 ) ) ),
inference(assume_negation,[status(cth)],[cADDHYP5]) ).
thf(h1,assumption,
( ~ $false
=> sP8 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ( ( ( ^ [X1: $i] : ( f @ ( f @ X1 ) ) )
= ( ^ [X1: $i] : X1 ) )
=> sP7 )
=> ( ( cP @ x )
=> sP7 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
$false,
introduced(assumption,[]) ).
thf(h4,assumption,
sP8,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_false,[status(thm),assumptions([h3,h1,h2,h0])],[h3]) ).
thf(h5,assumption,
( ( ( ^ [X1: $i] : ( f @ ( f @ X1 ) ) )
= ( ^ [X1: $i] : X1 ) )
=> sP7 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( cP @ x )
=> sP7 ),
introduced(assumption,[]) ).
thf(h7,assumption,
( ^ [X1: $i] : ( f @ ( f @ X1 ) ) )
!= ( ^ [X1: $i] : X1 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP7,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( f @ ( f @ X1 ) )
= X1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h11,assumption,
cP @ x,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(2,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| ~ sP9
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP6
| ~ sP5
| ~ sP4 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
sP3,
inference(eq_sym,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h9,h7,h5,h6,h4,h1,h2,h0])],[2,3,4,5,6,7,8,h4,h10]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h9,h7,h5,h6,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h6,9,h11,h12]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h5,h6,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__0)],[h9,10,h10]) ).
thf(12,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h7,h5,h6,h4,h1,h2,h0]),tab_fe(discharge,[h9])],[h7,11,h9]) ).
thf(13,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h11,h12,h8,h5,h6,h4,h1,h2,h0])],[h8,h12]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h5,h6,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h6,13,h11,h12]) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h4,h1,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,12,14,h7,h8]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h2,15,h5,h6]) ).
thf(17,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h1,1,16,h3,h4]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,17,h1,h2]) ).
thf(0,theorem,
( ( ~ $false
=> sP8 )
=> ( ( ( ( ^ [X1: $i] : ( f @ ( f @ X1 ) ) )
= ( ^ [X1: $i] : X1 ) )
=> sP7 )
=> ( ( cP @ x )
=> sP7 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO238^5 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n019.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 : 600
% 0.13/0.34 % DateTime : Sat Jul 9 00:12:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % Mode: mode213
% 0.19/0.37 % Inferences: 10
% 0.19/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------