TSTP Solution File: SYO324^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO324^5 : 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 : n032.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 : Fri Sep 1 04:46:16 EDT 2023
% Result : Theorem 20.19s 20.40s
% Output : Proof 20.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o] :
( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0 @ eigen__1 )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o] :
( ( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
= ( eigen__0 @ X1 ) )
=> ! [X2: $i] :
( ( ~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
= ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( ( eigen__0 @ X1 )
= ( eigen__0 @ X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP2 = sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP7
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cTHM143_EXPANDB,conjecture,
! [X1: ( $i > $o ) > $i] :
( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i > $o] :
( ( X4 @ ( X1 @ X2 ) )
=> ( X4 @ ( X1 @ X3 ) ) )
=> ! [X4: $i] :
( ( X2 @ X4 )
= ( X3 @ X4 ) ) )
=> ! [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
=> ~ ! [X3: $i > $o] :
( ( X3
@ ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ~ ( X5 @ ( X1 @ X5 ) )
=> ~ ! [X6: $i > $o] :
( ( X6 @ X4 )
=> ( X6 @ ( X1 @ X5 ) ) ) ) ) )
=> ( X3 @ ( X1 @ X2 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i] :
( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i > $o] :
( ( X4 @ ( X1 @ X2 ) )
=> ( X4 @ ( X1 @ X3 ) ) )
=> ! [X4: $i] :
( ( X2 @ X4 )
= ( X3 @ X4 ) ) )
=> ! [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
=> ~ ! [X3: $i > $o] :
( ( X3
@ ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ~ ( X5 @ ( X1 @ X5 ) )
=> ~ ! [X6: $i > $o] :
( ( X6 @ X4 )
=> ( X6 @ ( X1 @ X5 ) ) ) ) ) )
=> ( X3 @ ( X1 @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM143_EXPANDB]) ).
thf(h1,assumption,
~ ( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i > $o] :
( ( X3 @ ( eigen__0 @ X1 ) )
=> ( X3 @ ( eigen__0 @ X2 ) ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) )
=> ! [X1: $i > $o] :
( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ~ ! [X2: $i > $o] :
( ( X2
@ ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( eigen__0 @ X4 ) )
=> ~ ! [X5: $i > $o] :
( ( X5 @ X3 )
=> ( X5 @ ( eigen__0 @ X4 ) ) ) ) ) )
=> ( X2 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i > $o] :
( ( X3 @ ( eigen__0 @ X1 ) )
=> ( X3 @ ( eigen__0 @ X2 ) ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $o] :
( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ~ ! [X2: $i > $o] :
( ( X2
@ ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( eigen__0 @ X4 ) )
=> ~ ! [X5: $i > $o] :
( ( X5 @ X3 )
=> ( X5 @ ( eigen__0 @ X4 ) ) ) ) ) )
=> ( X2 @ ( eigen__0 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ sP1
=> ~ ! [X1: $i > $o] :
( ( X1
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ~ ! [X4: $i > $o] :
( ( X4 @ X2 )
=> ( X4 @ ( eigen__0 @ X3 ) ) ) ) ) )
=> ( X1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: $i > $o] :
( ( X1
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ~ ! [X4: $i > $o] :
( ( X4 @ X2 )
=> ( X4 @ ( eigen__0 @ X3 ) ) ) ) ) )
=> ( X1 @ ( eigen__0 @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP2
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| ~ sP7
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h6,h4,h2,h2,h3,h1,h0])],[1,2,3,4,5,6,h2,h5,h6]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,7,h5,h6]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,8,h4]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1]) ).
thf(0,theorem,
! [X1: ( $i > $o ) > $i] :
( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i > $o] :
( ( X4 @ ( X1 @ X2 ) )
=> ( X4 @ ( X1 @ X3 ) ) )
=> ! [X4: $i] :
( ( X2 @ X4 )
= ( X3 @ X4 ) ) )
=> ! [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
=> ~ ! [X3: $i > $o] :
( ( X3
@ ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ~ ( X5 @ ( X1 @ X5 ) )
=> ~ ! [X6: $i > $o] :
( ( X6 @ X4 )
=> ( X6 @ ( X1 @ X5 ) ) ) ) ) )
=> ( X3 @ ( X1 @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO324^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Sat Aug 26 05:36:13 EDT 2023
% 0.11/0.31 % CPUTime :
% 20.19/20.40 % SZS status Theorem
% 20.19/20.40 % Mode: cade22grackle2x798d
% 20.19/20.40 % Steps: 60
% 20.19/20.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------