TSTP Solution File: SYO555^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO555^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n009.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 19:33:24 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% 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: $o ).
thf(ty_eps1,type,
eps1: ( $i > $o ) > $i ).
thf(ty_eps2,type,
eps2: ( $i > $o ) > $i ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__0
=> ( eigen__1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( eigen__1 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eps1
@ ^ [X1: $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__2 ) ) ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0
=> ( ( eps2
@ ^ [X1: $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__2 ) ) ) )
!= eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( ( eps2
@ ^ [X1: $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__2 ) ) ) )
!= eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__2
= ( eps1
@ ^ [X1: $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ eigen__0
=> ( eigen__2 != eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eps1
@ ^ [X1: $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__2 ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ( eps2
@ ^ [X1: $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__2 ) ) ) )
= eigen__2 )
=> ( eigen__2
= ( eps2
@ ^ [X1: $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP2
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ eigen__0
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( ( eps2
@ ^ [X2: $i] :
( ( eigen__0
=> ( X2 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X2 != eigen__2 ) ) ) )
= X1 )
=> ( X1
= ( eps2
@ ^ [X2: $i] :
( ( eigen__0
=> ( X2 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X2 != eigen__2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ( eps2
@ ^ [X1: $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__2 ) ) ) )
= eigen__1 )
=> ( eigen__1
= ( eps2
@ ^ [X1: $i] :
( ( eigen__0
=> ( X1 != eigen__1 ) )
=> ~ ( ~ eigen__0
=> ( X1 != eigen__2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> eigen__0 ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( sP13
=> ~ sP6 )
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP13
=> ( ( eps2
@ ^ [X1: $i] :
( ( sP13
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X1 != eigen__2 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP13
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP13
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__2
= ( eps2
@ ^ [X1: $i] :
( ( sP13
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X1 != eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__1
= ( eps2
@ ^ [X1: $i] :
( ( sP13
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X1 != eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( eps1
@ ^ [X1: $i] :
( ( sP13
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X1 != eigen__2 ) ) ) )
= ( eps2
@ ^ [X1: $i] :
( ( sP13
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X1 != eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
~ ( ( sP13
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X1 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP13
=> ( ( eps2
@ ^ [X1: $i] :
( ( sP13
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X1 != eigen__2 ) ) ) )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP6
=> ( eigen__1
= ( eps1
@ ^ [X1: $i] :
( ( sP13
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X1 != eigen__2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( eps2
@ ^ [X1: $i] :
( ( sP13
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X1 != eigen__2 ) ) ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( eps2
@ ^ [X1: $i] :
( ( sP13
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X1 != eigen__2 ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__1
= ( eps1
@ ^ [X1: $i] :
( ( sP13
=> ( X1 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X1 != eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( ( eps1
@ ^ [X2: $i] :
( ( sP13
=> ( X2 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X2 != eigen__2 ) ) ) )
= X1 )
=> ( X1
= ( eps1
@ ^ [X2: $i] :
( ( sP13
=> ( X2 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X2 != eigen__2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( sP13
=> ( eigen__2 != eigen__1 ) )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(def_if1,definition,
( if1
= ( ^ [X1: $o,X2: $i,X3: $i] :
( eps1
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ).
thf(def_if2,definition,
( if2
= ( ^ [X1: $o,X2: $i,X3: $i] :
( eps2
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ).
thf(conj,conjecture,
( ( ^ [X1: $o,X2: $i,X3: $i] :
( eps1
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) )
= ( ^ [X1: $o,X2: $i,X3: $i] :
( eps2
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ^ [X1: $o,X2: $i,X3: $i] :
( eps1
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) )
!= ( ^ [X1: $o,X2: $i,X3: $i] :
( eps2
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
~ ! [X1: $o] :
( ( ^ [X2: $i,X3: $i] :
( eps1
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) )
= ( ^ [X2: $i,X3: $i] :
( eps2
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ^ [X1: $i,X2: $i] :
( eps1
@ ^ [X3: $i] :
( ( sP13
=> ( X3 != X1 ) )
=> ~ ( ~ sP13
=> ( X3 != X2 ) ) ) ) )
!= ( ^ [X1: $i,X2: $i] :
( eps2
@ ^ [X3: $i] :
( ( sP13
=> ( X3 != X1 ) )
=> ~ ( ~ sP13
=> ( X3 != X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( ^ [X2: $i] :
( eps1
@ ^ [X3: $i] :
( ( sP13
=> ( X3 != X1 ) )
=> ~ ( ~ sP13
=> ( X3 != X2 ) ) ) ) )
= ( ^ [X2: $i] :
( eps2
@ ^ [X3: $i] :
( ( sP13
=> ( X3 != X1 ) )
=> ~ ( ~ sP13
=> ( X3 != X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ^ [X1: $i] :
( eps1
@ ^ [X2: $i] :
( ( sP13
=> ( X2 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X2 != X1 ) ) ) ) )
!= ( ^ [X1: $i] :
( eps2
@ ^ [X2: $i] :
( ( sP13
=> ( X2 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X2 != X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( eps1
@ ^ [X2: $i] :
( ( sP13
=> ( X2 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X2 != X1 ) ) ) )
= ( eps2
@ ^ [X2: $i] :
( ( sP13
=> ( X2 != eigen__1 ) )
=> ~ ( ~ sP13
=> ( X2 != X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP21,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP21
| ~ sP4
| ~ sP18 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP21
| ~ sP28
| ~ sP19 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( sP24
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP24
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP15
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP15
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| ~ sP15
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP10
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP10
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP16
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP16
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP14
| ~ sP16
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
sP22,
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP5
| sP13
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP30
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
sP9,
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP17
| ~ sP13
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP1
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP8
| ~ sP2
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP29
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP25
| ~ sP6
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP29
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP23
| ~ sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP7
| ~ sP26
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP11
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP23
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP12
| ~ sP27
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP11
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(choiceax2,axiom,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( eps2 @ X1 ) ) ) ).
thf(29,plain,
( sP3
| sP23 ),
inference(choice_rule,[status(thm)],[choiceax2]) ).
thf(choiceax1,axiom,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( eps1 @ X1 ) ) ) ).
thf(30,plain,
( sP14
| sP23 ),
inference(choice_rule,[status(thm)],[choiceax1]) ).
thf(31,plain,
( ~ sP20
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP20
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
sP20,
inference(eq_sym,[status(thm)],]) ).
thf(34,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,h6]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,34,h6]) ).
thf(36,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_fe(discharge,[h5])],[h4,35,h5]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,36,h4]) ).
thf(38,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,37,h3]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,38,h2]) ).
thf(40,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,39,h1]) ).
thf(0,theorem,
( ( ^ [X1: $o,X2: $i,X3: $i] :
( eps1
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) )
= ( ^ [X1: $o,X2: $i,X3: $i] :
( eps2
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[40,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO555^1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 16:18:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % Mode: mode213
% 0.12/0.37 % Inferences: 72
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------