TSTP Solution File: SYO308^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO308^5 : 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 : n007.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 19:31:22 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_cB,type,
cB: $i > $o ).
thf(ty_cA,type,
cA: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( cA @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ eigen__2 )
=> ( cB @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0 @ eigen__1 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cB @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( cB @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( cA @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cSET81_pme,conjecture,
! [X1: $i > $o] :
( ( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( cA @ X2 ) )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( cB @ X2 ) ) )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( ~ ( cA @ X2 )
=> ( cB @ X2 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $o] :
( ( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( cA @ X2 ) )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( cB @ X2 ) ) )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( ~ ( cA @ X2 )
=> ( cB @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cSET81_pme]) ).
thf(h1,assumption,
~ ( ( ~ sP8
=> sP5 )
=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( ~ ( cA @ X1 )
=> ( cB @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ~ sP8
=> sP5 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( ~ ( cA @ X1 )
=> ( cB @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP8,
introduced(assumption,[]) ).
thf(h5,assumption,
sP5,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP6
=> ( ~ sP1
=> ( cB @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP6,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ sP1
=> ( cB @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( cB @ eigen__1 ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| ~ sP6
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h6,h4,h2,h3,h1,h0])],[1,2,h4,h7,h9]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,3,h9,h10]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,4,h7,h8]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h3,5,h6]) ).
thf(h11,assumption,
~ ( sP7
=> ( ~ ( cA @ eigen__2 )
=> sP4 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP7,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( cA @ eigen__2 )
=> sP4 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( cA @ eigen__2 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(7,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP2
| ~ sP7
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h12,h13,h11,h5,h2,h3,h1,h0])],[7,8,h5,h12,h15]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,9,h14,h15]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,10,h12,h13]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h3,11,h11]) ).
thf(13,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h2,6,12,h4,h5]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,13,h2,h3]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,14,h1]) ).
thf(0,theorem,
! [X1: $i > $o] :
( ( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( cA @ X2 ) )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( cB @ X2 ) ) )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( ~ ( cA @ X2 )
=> ( cB @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO308^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 05:29:16 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % Mode: mode213
% 0.13/0.38 % Inferences: 8
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------