TSTP Solution File: SYO064^4.002 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO064^4.002 : 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 : n011.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 04:44:59 EDT 2023
% Result : Theorem 0.20s 0.75s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_a1,type,
a1: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_a,type,
a: $i > $o ).
thf(ty_b,type,
b: $i > $o ).
thf(ty_a2,type,
a2: $i > $o ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_b1,type,
b1: $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( irel @ X1 @ X2 )
=> ~ ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( irel @ eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ( ~ sP2
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( b1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( irel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( irel @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP5
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( b @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP3
=> ( b1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( b1 @ eigen__4 )
=> ~ ( a2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__0 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ~ ( sP5
=> ~ ( irel @ eigen__2 @ X1 ) )
=> ( irel @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( b1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( irel @ eigen__0 @ eigen__4 )
=> ( b1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( irel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( b1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP2
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( irel @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( a @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP6
=> ( b @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( a1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] : ( a2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP22
=> ( ~ sP18
=> sP19 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP25
=> sP30 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ ( sP5
=> ~ sP25 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( b @ eigen__3 )
=> ~ sP30 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( b @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( a2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP5
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ sP18
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( irel @ eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP5
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ sP41
=> sP44 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( irel @ X2 @ X3 )
@ ( X1 @ X3 ) ) ) ) ).
thf(def_iatom,definition,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_inot,definition,
( inot
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).
thf(def_itrue,definition,
( itrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
( iand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
thf(def_ior,definition,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplies,definition,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplied,definition,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).
thf(def_iequiv,definition,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).
thf(def_ixor,definition,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).
thf(def_ivalid,definition,
( ivalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(con,conjecture,
! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b @ X3 )
=> ~ ( a1 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b1 @ X3 )
=> ~ ( a2 @ X3 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b @ X3 )
=> ~ ( a1 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b1 @ X3 )
=> ~ ( a2 @ X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
~ ( ~ sP19
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b @ X2 )
=> ~ ( a1 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b1 @ X2 )
=> ~ ( a2 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b @ X2 )
=> ~ ( a1 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b1 @ X2 )
=> ~ ( a2 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(h5,assumption,
sP38,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP5
=> ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( b @ X1 )
=> ~ ( a1 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( b1 @ X1 )
=> ~ ( a2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP5,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( b @ X1 )
=> ~ ( a1 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( b1 @ X1 )
=> ~ ( a2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( b @ X1 )
=> ~ ( a1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( b1 @ X1 )
=> ~ ( a2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP25
=> ~ sP37 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP25,
introduced(assumption,[]) ).
thf(h14,assumption,
sP37,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP3
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP3,
introduced(assumption,[]) ).
thf(h17,assumption,
sP13,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP27
| ~ sP38
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP19
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| ~ sP22
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP14
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP10
| ~ sP18
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP8
| ~ sP5
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP41
| ~ sP5
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP46
| sP41
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP45
| ~ sP5
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP35
| sP45
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP32
| ~ sP22
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP17
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP17
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP36
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP42
| sP18
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP21
| ~ sP44
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP20
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP24
| sP2
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP15
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP29
| ~ sP6
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP18
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP16
| sP36
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP34
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP1
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP9
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP43
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP33
| ~ sP25
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP28
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP12
| ~ sP3
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP11
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP7
| sP11
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP31
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP37
| ~ sP39
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP13
| ~ sP23
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(axiom3,axiom,
sP9 ).
thf(axiom2,axiom,
sP43 ).
thf(axiom1,axiom,
sP31 ).
thf(trans_axiom,axiom,
sP1 ).
thf(refl_axiom,axiom,
sP34 ).
thf(36,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,h5,h6,h8,h13,h14,h16,h17,axiom3,axiom2,axiom1,trans_axiom,refl_axiom]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,36,h16,h17]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__4)],[h11,37,h15]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,38,h13,h14]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h10,39,h12]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,40,h10,h11]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,41,h8,h9]) ).
thf(43,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h3,42,h7]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,43,h5,h6]) ).
thf(45,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,44,h4]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,45,h2,h3]) ).
thf(47,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,46,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b @ X3 )
=> ~ ( a1 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b1 @ X3 )
=> ~ ( a2 @ X3 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[47,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO064^4.002 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 00:45:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.75 % SZS status Theorem
% 0.20/0.75 % Mode: cade22grackle2xfee4
% 0.20/0.75 % Steps: 3958
% 0.20/0.75 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------