TSTP Solution File: SYO260^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO260^5 : 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 : n025.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 19:31:08 EDT 2022
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% 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 ).
thf(ty_eigen__3,type,
eigen__3: $i > $o ).
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o] :
( ~ ( ( sP1
=> ( X1 @ eigen__0 ) )
=> ~ ( ~ ( eigen__3 @ eigen__1 )
=> ( X1 @ eigen__1 ) ) )
=> ~ ( sP1
=> ~ ( eigen__3 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( sP2
=> ~ ( ~ ( eigen__3 @ eigen__1 )
=> ~ sP1 ) )
=> ~ ( sP1
=> ~ ( eigen__3 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ( ~ ( X1 @ eigen__0 )
=> ( X2 @ eigen__0 ) )
=> ~ ( ~ ( eigen__3 @ eigen__1 )
=> ( X2 @ eigen__1 ) ) )
=> ~ ( ~ ( X1 @ eigen__2 )
=> ~ ( eigen__3 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP1
=> ~ ( eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( eigen__3 @ eigen__1 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP2
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cTHM125A,conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i > $o] :
~ ! [X5: $i > $o,X6: $i > $o] :
( ~ ( ( ~ ( X5 @ X1 )
=> ( X6 @ X1 ) )
=> ~ ( ~ ( X4 @ X2 )
=> ( X6 @ X2 ) ) )
=> ~ ( ~ ( X5 @ X3 )
=> ~ ( X4 @ X3 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i,X4: $i > $o] :
~ ! [X5: $i > $o,X6: $i > $o] :
( ~ ( ( ~ ( X5 @ X1 )
=> ( X6 @ X1 ) )
=> ~ ( ~ ( X4 @ X2 )
=> ( X6 @ X2 ) ) )
=> ~ ( ~ ( X5 @ X3 )
=> ~ ( X4 @ X3 ) ) ),
inference(assume_negation,[status(cth)],[cTHM125A]) ).
thf(h1,assumption,
~ ! [X1: $i,X2: $i,X3: $i > $o] :
~ ! [X4: $i > $o,X5: $i > $o] :
( ~ ( ( ~ ( X4 @ eigen__0 )
=> ( X5 @ eigen__0 ) )
=> ~ ( ~ ( X3 @ X1 )
=> ( X5 @ X1 ) ) )
=> ~ ( ~ ( X4 @ X2 )
=> ~ ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i > $o] :
~ ! [X3: $i > $o,X4: $i > $o] :
( ~ ( ( ~ ( X3 @ eigen__0 )
=> ( X4 @ eigen__0 ) )
=> ~ ( ~ ( X2 @ eigen__1 )
=> ( X4 @ eigen__1 ) ) )
=> ~ ( ~ ( X3 @ X1 )
=> ~ ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ( ~ ( X2 @ eigen__0 )
=> ( X3 @ eigen__0 ) )
=> ~ ( ~ ( X1 @ eigen__1 )
=> ( X3 @ eigen__1 ) ) )
=> ~ ( ~ ( X2 @ eigen__2 )
=> ~ ( X1 @ eigen__2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP5,
introduced(assumption,[]) ).
thf(1,plain,
( sP2
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| ~ sP2
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP8
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP6
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
~ sP1,
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP7
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,h4]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,9,h4]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,10,h3]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,11,h2]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,12,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i,X4: $i > $o] :
~ ! [X5: $i > $o,X6: $i > $o] :
( ~ ( ( ~ ( X5 @ X1 )
=> ( X6 @ X1 ) )
=> ~ ( ~ ( X4 @ X2 )
=> ( X6 @ X2 ) ) )
=> ~ ( ~ ( X5 @ X3 )
=> ~ ( X4 @ X3 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[13,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO260^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n025.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 02:22:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % Mode: mode213
% 0.20/0.37 % Inferences: 128
% 0.20/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------