TSTP Solution File: SEV055^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV055^5 : 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 : n005.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 19:32:28 EDT 2023
% Result : Theorem 20.23s 20.45s
% Output : Proof 20.23s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__1,type,
eigen__1: ( a > $o ) > a ).
thf(ty_eigen__2,type,
eigen__2: a > a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o] :
~ ( ! [X2: a] :
( ( X1 @ X2 )
=> ( eigen__0 @ X2 @ ( eigen__1 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 @ X2 ) )
=> ( eigen__0 @ ( eigen__1 @ X1 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
~ ( eigen__0 @ X1 @ ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( eigen__0
@ ( eigen__1
@ ^ [X2: a] : $false )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0
@ ( eigen__1
@ ^ [X1: a] : $false )
@ ( eigen__2
@ ( eigen__1
@ ^ [X1: a] : $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(cTHM402_pme,conjecture,
! [X1: a > a > $o,X2: ( a > $o ) > a] :
( ~ ( ! [X3: a,X4: a,X5: a] :
( ~ ( ( X1 @ X3 @ X4 )
=> ~ ( X1 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X5 ) )
=> ~ ! [X3: a > $o] :
~ ( ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X3 ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X3 @ X5 )
=> ( X1 @ X5 @ X4 ) )
=> ( X1 @ ( X2 @ X3 ) @ X4 ) ) ) )
=> ! [X3: a > a] :
( ! [X4: a,X5: a] :
( ( X1 @ X4 @ X5 )
=> ( X1 @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) )
=> ~ ! [X4: a] :
~ ( X1 @ X4 @ ( X3 @ X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > $o,X2: ( a > $o ) > a] :
( ~ ( ! [X3: a,X4: a,X5: a] :
( ~ ( ( X1 @ X3 @ X4 )
=> ~ ( X1 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X5 ) )
=> ~ ! [X3: a > $o] :
~ ( ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X3 ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X3 @ X5 )
=> ( X1 @ X5 @ X4 ) )
=> ( X1 @ ( X2 @ X3 ) @ X4 ) ) ) )
=> ! [X3: a > a] :
( ! [X4: a,X5: a] :
( ( X1 @ X4 @ X5 )
=> ( X1 @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) )
=> ~ ! [X4: a] :
~ ( X1 @ X4 @ ( X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM402_pme]) ).
thf(h1,assumption,
~ ! [X1: ( a > $o ) > a] :
( ~ ( ! [X2: a,X3: a,X4: a] :
( ~ ( ( eigen__0 @ X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( eigen__0 @ X2 @ X4 ) )
=> ~ ! [X2: a > $o] :
~ ( ! [X3: a] :
( ( X2 @ X3 )
=> ( eigen__0 @ X3 @ ( X1 @ X2 ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( X2 @ X4 )
=> ( eigen__0 @ X4 @ X3 ) )
=> ( eigen__0 @ ( X1 @ X2 ) @ X3 ) ) ) )
=> ! [X2: a > a] :
( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__0 @ ( X2 @ X3 ) @ ( X2 @ X4 ) ) )
=> ~ ! [X3: a] :
~ ( eigen__0 @ X3 @ ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) )
=> ~ sP1 )
=> ! [X1: a > a] :
( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__0 @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) )
=> ~ ! [X2: a] :
~ ( eigen__0 @ X2 @ ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a > a] :
( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__0 @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) )
=> ~ ! [X2: a] :
~ ( eigen__0 @ X2 @ ( X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ ( eigen__2 @ X1 ) @ ( eigen__2 @ X2 ) ) )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ ( eigen__2 @ X1 ) @ ( eigen__2 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,h6,h9]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,4,h8,h9]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h4,5,h7]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,6,h5,h6]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,7,h3,h4]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,8,h2]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: ( a > $o ) > a] :
( ~ ( ! [X3: a,X4: a,X5: a] :
( ~ ( ( X1 @ X3 @ X4 )
=> ~ ( X1 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X5 ) )
=> ~ ! [X3: a > $o] :
~ ( ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X3 ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X3 @ X5 )
=> ( X1 @ X5 @ X4 ) )
=> ( X1 @ ( X2 @ X3 ) @ X4 ) ) ) )
=> ! [X3: a > a] :
( ! [X4: a,X5: a] :
( ( X1 @ X4 @ X5 )
=> ( X1 @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) )
=> ~ ! [X4: a] :
~ ( X1 @ X4 @ ( X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV055^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n005.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 : 300
% 0.13/0.35 % DateTime : Thu Aug 24 02:28:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 20.23/20.45 % SZS status Theorem
% 20.23/20.45 % Mode: cade22grackle2x798d
% 20.23/20.45 % Steps: 249
% 20.23/20.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------