TSTP Solution File: SEU795^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU795^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 14:05:50 EDT 2022
% Result : Theorem 25.80s 26.03s
% Output : Proof 25.80s
% 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 > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_descr,type,
descr: ( $i > $o ) > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__2
@ ( descr
@ ^ [X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( X1 @ ( descr @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ~ ! [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( X3
!= ( eigen__1 @ X4 ) ) ) ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ sP3
=> ! [X1: $i] :
( ( in @ X1
@ ( descr
@ ^ [X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X2 )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( X3
!= ( eigen__1 @ X4 ) ) ) ) ) ) )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
= ( ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__2
!= ( eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( in @ X1
@ ( descr
@ ^ [X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X2 )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( X3
!= ( eigen__1 @ X4 ) ) ) ) ) ) )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__2
= ( eigen__1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i > $i] :
~ ! [X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X4
!= ( X2 @ X5 ) ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) )
=> ( X3 = X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( in @ eigen__5 @ eigen__0 )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__2
!= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i > $i] :
~ ! [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( X3
!= ( X1 @ X4 ) ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ eigen__0 )
=> ( X4
!= ( X1 @ X5 ) ) ) ) )
=> ( X2 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in @ eigen__5 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(def_exu,definition,
( exu
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ).
thf(def_descrp,definition,
( descrp
= ( ! [X1: $i > $o] :
( ( exu @ X1 )
=> ( X1 @ ( descr @ X1 ) ) ) ) ) ).
thf(def_in__Cong,definition,
( in__Cong
= ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ) ) ) ).
thf(def_image1Ex1,definition,
( image1Ex1
= ( ! [X1: $i,X2: $i > $i] :
( exu
@ ^ [X3: $i] :
! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X4
!= ( X2 @ X5 ) ) ) ) ) ) ) ) ).
thf(def_image1,definition,
( image1
= ( ^ [X1: $i,X2: $i > $i] :
( descr
@ ^ [X3: $i] :
! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X4
!= ( X2 @ X5 ) ) ) ) ) ) ) ) ).
thf(image1Equiv,conjecture,
( sP2
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP8
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP2
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP8
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[image1Equiv]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP8
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP8
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP8,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i > $i,X2: $i] :
( ( in @ X2
@ ( descr
@ ^ [X3: $i] :
! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ eigen__0 )
=> ( X4
!= ( X1 @ X5 ) ) ) ) ) ) )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h13,assumption,
sP10,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP1
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP3
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP11
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,h1,h5,h10,h11]) ).
thf(h14,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h15,assumption,
sP12,
introduced(assumption,[]) ).
thf(h16,assumption,
sP7,
introduced(assumption,[]) ).
thf(8,plain,
( ~ sP5
| sP1
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP11
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| ~ sP12
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP4
| sP3
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[8,9,10,11,12,13,14,15,h1,h5,h12,h15,h16]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,16,h15,h16]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h13,17,h14]) ).
thf(19,plain,
$false,
inference(tab_be,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_be(discharge,[h10,h11]),tab_be(discharge,[h12,h13])],[h9,7,18,h10,h11,h12,h13]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,19,h9]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,20,h8]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,21,h7]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,22,h5,h6]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,23,h3,h4]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,24,h1,h2]) ).
thf(0,theorem,
( sP2
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP8
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[25,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU795^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n020.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 : Sat Jun 18 23:06:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 25.80/26.03 % SZS status Theorem
% 25.80/26.03 % Mode: mode461
% 25.80/26.03 % Inferences: 142
% 25.80/26.03 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------