TSTP Solution File: SEV223^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV223^5 : 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 : n016.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 19:33:01 EDT 2023
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 66
% Syntax : Number of formulae : 83 ( 32 unt; 10 typ; 1 def)
% Number of atoms : 175 ( 41 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 296 ( 120 ~; 20 |; 0 &; 82 @)
% ( 21 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 26 con; 0-2 aty)
% Number of variables : 63 ( 17 ^; 46 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__2,type,
eigen__2: b > $o ).
thf(ty_eigen__5,type,
eigen__5: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__1,type,
eigen__1: b ).
thf(ty_eigen__8,type,
eigen__8: b ).
thf(ty_eigen__6,type,
eigen__6: b > $o ).
thf(ty_f,type,
f: b > a ).
thf(ty_w,type,
w: ( b > $o ) > $o ).
thf(h0,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: b] :
~ ( ( eigen__6 @ X1 )
=> ( eigen__0
!= ( f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0
= ( f @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: b > $o] :
( ( w @ X1 )
=> ( ( ^ [X2: a] :
~ ! [X3: b] :
( ( eigen__2 @ X3 )
=> ( X2
!= ( f @ X3 ) ) ) )
!= ( ^ [X2: a] :
~ ! [X3: b] :
( ( X1 @ X3 )
=> ( X2
!= ( f @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( eigen__5 @ X1 )
= ( ~ ! [X2: b] :
( ( eigen__6 @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__5 @ eigen__0 )
= ( ~ ! [X1: b] :
( ( eigen__6 @ X1 )
=> ( eigen__0
!= ( f @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ! [X1: b > $o] :
( ( w @ X1 )
=> ~ ( X1 @ eigen__8 ) )
=> ( eigen__0
!= ( f @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__6 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: b] :
( ~ ! [X2: b > $o] :
( ( w @ X2 )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
!= ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0
= ( f @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: b > $o] :
( ( w @ X1 )
=> ~ ( X1 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( w @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP6
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP10
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP2
=> ! [X1: b] :
( ( eigen__2 @ X1 )
=> ( eigen__0
!= ( f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__5
= ( ^ [X1: a] :
~ ! [X2: b] :
( ( eigen__6 @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: b] :
( ( eigen__6 @ X1 )
=> ( eigen__0
!= ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: b] :
( ( eigen__2 @ X1 )
=> ( eigen__0
!= ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP17
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a > $o] :
( ~ ! [X2: b > $o] :
( ( w @ X2 )
=> ( X1
!= ( ^ [X3: a] :
~ ! [X4: b] :
( ( X2 @ X4 )
=> ( X3
!= ( f @ X4 ) ) ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( w @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__5 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(cX5204_pme,conjecture,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ~ ( X3 @ X2 ) )
=> ( X1
!= ( f @ X2 ) ) ) )
= ( ^ [X1: a] :
~ ! [X2: a > $o] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ( X2
!= ( ^ [X4: a] :
~ ! [X5: b] :
( ( X3 @ X5 )
=> ( X4
!= ( f @ X5 ) ) ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ).
thf(h1,negated_conjecture,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ~ ( X3 @ X2 ) )
=> ( X1
!= ( f @ X2 ) ) ) )
!= ( ^ [X1: a] :
~ ! [X2: a > $o] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ( X2
!= ( ^ [X4: a] :
~ ! [X5: b] :
( ( X3 @ X5 )
=> ( X4
!= ( f @ X5 ) ) ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[cX5204_pme]) ).
thf(h2,assumption,
~ ! [X1: a] :
( ( ~ ! [X2: b] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ~ ( X3 @ X2 ) )
=> ( X1
!= ( f @ X2 ) ) ) )
= ( ~ ! [X2: a > $o] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ( X2
!= ( ^ [X4: a] :
~ ! [X5: b] :
( ( X3 @ X5 )
=> ( X4
!= ( f @ X5 ) ) ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ~ sP7 != ~ sP19 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h6,assumption,
sP7,
introduced(assumption,[]) ).
thf(h7,assumption,
sP19,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ! [X1: b > $o] :
( ( w @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: b > $o] :
( ( w @ X1 )
=> ~ ( X1 @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP20
=> ~ sP17 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP20,
introduced(assumption,[]) ).
thf(h13,assumption,
sP17,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP18
| ~ sP17
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP16
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP13
| sP2
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP19
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h9,h10,h8,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,h12,h13,h10,h5]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,6,h12,h13]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h9,7,h11]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,8,h9,h10]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h4,9,h8]) ).
thf(h14,assumption,
~ ( ~ ! [X1: b > $o] :
( ( w @ X1 )
=> ( eigen__5
!= ( ^ [X2: a] :
~ ! [X3: b] :
( ( X1 @ X3 )
=> ( X2
!= ( f @ X3 ) ) ) ) ) )
=> ~ sP21 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: b > $o] :
( ( w @ X1 )
=> ( eigen__5
!= ( ^ [X2: a] :
~ ! [X3: b] :
( ( X1 @ X3 )
=> ( X2
!= ( f @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP21,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP10
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP10,
introduced(assumption,[]) ).
thf(h19,assumption,
sP14,
introduced(assumption,[]) ).
thf(11,plain,
( ~ sP12
| ~ sP10
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP5
| sP9
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP7
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( sP11
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP11
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP15
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(18,plain,
( ~ sP4
| ~ sP21
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP14
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h6,h7,h3,h2,h1,h0])],[11,12,13,14,15,16,17,18,19,20,h6,h18,h19,h16]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h6,h7,h3,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,21,h18,h19]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h6,h7,h3,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__6)],[h15,22,h17]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h6,h7,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,23,h15,h16]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h3,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h7,24,h14]) ).
thf(26,plain,
$false,
inference(tab_be,[status(thm),assumptions([h3,h2,h1,h0]),tab_be(discharge,[h4,h5]),tab_be(discharge,[h6,h7])],[h3,10,25,h4,h5,h6,h7]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,26,h3]) ).
thf(28,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h1,h0]),tab_fe(discharge,[h2])],[h1,27,h2]) ).
thf(29,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[28,h0]) ).
thf(0,theorem,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ~ ( X3 @ X2 ) )
=> ( X1
!= ( f @ X2 ) ) ) )
= ( ^ [X1: a] :
~ ! [X2: a > $o] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ( X2
!= ( ^ [X4: a] :
~ ! [X5: b] :
( ( X3 @ X5 )
=> ( X4
!= ( f @ X5 ) ) ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[28,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV223^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.35 % Computer : n016.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu Aug 24 02:31:08 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % Mode: cade22grackle2xfee4
% 0.20/0.45 % Steps: 281
% 0.20/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------