TSTP Solution File: SEV060^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV060^5 : 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 : 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 : 600s
% DateTime : Tue Jul 19 18:04:40 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__2,type,
eigen__2: b > a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: b ).
thf(ty_eigen__4,type,
eigen__4: b ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__3,type,
eigen__3: b > a > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__3 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ( ~ ( eigen__2 @ eigen__4 @ eigen__5 )
=> ~ ( ( eigen__4 = eigen__0 )
=> ( eigen__5 != eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__5 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__4 = eigen__0 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( eigen__2 @ eigen__4 @ eigen__5 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__4 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__3 @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__2 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ( eigen__3 @ eigen__4 @ X1 )
=> ( ~ ( eigen__2 @ eigen__4 @ X1 )
=> ~ ( sP6
=> ( X1 != eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: b,X2: a] :
( ( eigen__3 @ X1 @ X2 )
=> ( ~ ( eigen__2 @ X1 @ X2 )
=> ~ ( ( X1 = eigen__0 )
=> ( X2 != eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(cTHM173_pme,conjecture,
! [X1: b,X2: a,X3: b > a > $o,X4: b > a > $o] :
( ~ ( ! [X5: b,X6: a] :
( ( X4 @ X5 @ X6 )
=> ( ~ ( X3 @ X5 @ X6 )
=> ~ ( ( X5 = X1 )
=> ( X6 != X2 ) ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ! [X5: b,X6: a] :
( ( X4 @ X5 @ X6 )
=> ( X3 @ X5 @ X6 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: b,X2: a,X3: b > a > $o,X4: b > a > $o] :
( ~ ( ! [X5: b,X6: a] :
( ( X4 @ X5 @ X6 )
=> ( ~ ( X3 @ X5 @ X6 )
=> ~ ( ( X5 = X1 )
=> ( X6 != X2 ) ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ! [X5: b,X6: a] :
( ( X4 @ X5 @ X6 )
=> ( X3 @ X5 @ X6 ) ) ),
inference(assume_negation,[status(cth)],[cTHM173_pme]) ).
thf(h1,assumption,
~ ! [X1: a,X2: b > a > $o,X3: b > a > $o] :
( ~ ( ! [X4: b,X5: a] :
( ( X3 @ X4 @ X5 )
=> ( ~ ( X2 @ X4 @ X5 )
=> ~ ( ( X4 = eigen__0 )
=> ( X5 != X1 ) ) ) )
=> ( X3 @ eigen__0 @ X1 ) )
=> ! [X4: b,X5: a] :
( ( X3 @ X4 @ X5 )
=> ( X2 @ X4 @ X5 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: b > a > $o,X2: b > a > $o] :
( ~ ( ! [X3: b,X4: a] :
( ( X2 @ X3 @ X4 )
=> ( ~ ( X1 @ X3 @ X4 )
=> ~ ( ( X3 = eigen__0 )
=> ( X4 != eigen__1 ) ) ) )
=> ( X2 @ eigen__0 @ eigen__1 ) )
=> ! [X3: b,X4: a] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X3 @ X4 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: b > a > $o] :
( ~ ( ! [X2: b,X3: a] :
( ( X1 @ X2 @ X3 )
=> ( ~ ( eigen__2 @ X2 @ X3 )
=> ~ ( ( X2 = eigen__0 )
=> ( X3 != eigen__1 ) ) ) )
=> ( X1 @ eigen__0 @ eigen__1 ) )
=> ! [X2: b,X3: a] :
( ( X1 @ X2 @ X3 )
=> ( eigen__2 @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( sP10
=> sP7 )
=> ! [X1: b,X2: a] :
( ( eigen__3 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP10
=> sP7 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: b,X2: a] :
( ( eigen__3 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP10,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: a] :
( ( eigen__3 @ eigen__4 @ X1 )
=> ( eigen__2 @ eigen__4 @ X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP1
=> sP8 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( sP4
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP4
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP7
| ~ sP6
| ~ sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP2
| ~ sP1
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP5
| sP8
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,h7,h8,h11,h12]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,8,h11,h12]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__5)],[h9,9,h10]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__4)],[h6,10,h9]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,11,h7,h8]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,12,h5,h6]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,13,h4]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,14,h3]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,15,h2]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,16,h1]) ).
thf(0,theorem,
! [X1: b,X2: a,X3: b > a > $o,X4: b > a > $o] :
( ~ ( ! [X5: b,X6: a] :
( ( X4 @ X5 @ X6 )
=> ( ~ ( X3 @ X5 @ X6 )
=> ~ ( ( X5 = X1 )
=> ( X6 != X2 ) ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ! [X5: b,X6: a] :
( ( X4 @ X5 @ X6 )
=> ( X3 @ X5 @ X6 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV060^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 28 17:16:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 7
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------