TSTP Solution File: LCL604^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL604^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 : Sun Jul 17 14:09:02 EDT 2022
% Result : Theorem 0.18s 0.35s
% Output : Proof 0.18s
% 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 > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__0 @ eigen__5 @ eigen__5 )
=> ( eigen__1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0 @ eigen__2 @ eigen__4 )
=> ( eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] : ( eigen__0 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__0 @ eigen__5 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__2 @ eigen__3 )
=> ~ ( eigen__0 @ eigen__3 @ X1 ) )
=> ( eigen__0 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0 @ eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__0 @ eigen__2 @ eigen__3 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP9
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__2 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(def_mfalse,definition,
( mfalse
= ( ^ [X1: $i] : $false ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : ~ $false ) ) ).
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_mimpl,definition,
( mimpl
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_miff,definition,
( miff
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimpl @ X1 @ X2 ) @ ( mimpl @ X2 @ X1 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) ).
thf(def_mall,definition,
( mall
= ( ^ [X1: individuals > $i > $o,X2: $i] :
! [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists,definition,
( mexists
= ( ^ [X1: individuals > $i > $o,X2: $i] :
~ ! [X3: individuals] :
~ ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mvalid,definition,
mvalid = !! ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_cartesian_product,definition,
( cartesian_product
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X4 ) ) ) ) ).
thf(def_pair_rel,definition,
( pair_rel
= ( ^ [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 != X1 )
=> ( X4 = X2 ) ) ) ) ).
thf(def_id_rel,definition,
( id_rel
= ( ^ [X1: $i > $o,X2: $i,X3: $i] :
~ ( ( X1 @ X2 )
=> ( X2 != X3 ) ) ) ) ).
thf(def_sub_rel,definition,
( sub_rel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) ).
thf(def_is_rel_on,definition,
( is_rel_on
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
! [X4: $i,X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ).
thf(def_restrict_rel_domain,definition,
( restrict_rel_domain
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i,X4: $i] :
~ ( ( X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_rel_diagonal,definition,
rel_diagonal = (=) ).
thf(def_rel_composition,definition,
( rel_composition
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o,X3: $i,X4: $i] :
~ ! [X5: $i] :
( ( X1 @ X3 @ X5 )
=> ~ ( X2 @ X5 @ X4 ) ) ) ) ).
thf(def_reflexive,definition,
( reflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_irreflexive,definition,
( irreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) ).
thf(def_symmetric,definition,
( symmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_transitive,definition,
( transitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_equiv_rel,definition,
( equiv_rel
= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ( reflexive @ X1 )
=> ~ ( symmetric @ X1 ) )
=> ~ ( transitive @ X1 ) ) ) ) ).
thf(def_rel_codomain,definition,
( rel_codomain
= ( ^ [X1: $i > $i > $o,X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X3 @ X2 ) ) ) ).
thf(def_rel_domain,definition,
( rel_domain
= ( ^ [X1: $i > $i > $o,X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_rel_inverse,definition,
( rel_inverse
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_equiv_classes,definition,
( equiv_classes
= ( ^ [X1: $i > $i > $o,X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
= ( X1 @ X3 @ X4 ) ) ) ) ) ).
thf(def_restrict_rel_codomain,definition,
( restrict_rel_codomain
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i,X4: $i] :
~ ( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_rel_field,definition,
( rel_field
= ( ^ [X1: $i > $i > $o,X2: $i] :
( ~ ( rel_domain @ X1 @ X2 )
=> ( rel_codomain @ X1 @ X2 ) ) ) ) ).
thf(def_well_founded,definition,
( well_founded
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X2 @ X5 ) ) ) ) ) ) ).
thf(def_upwards_well_founded,definition,
( upwards_well_founded
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X4 )
=> ~ ( X2 @ X5 ) ) ) ) ) ) ).
thf(thm,conjecture,
! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ~ ~ ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ~ ~ ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ( ~ ( sP5
=> ~ sP4 )
=> ! [X1: $i > $o] :
~ ( ! [X2: $i] :
( ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) )
=> ~ ! [X2: $i] :
( ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP5
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $o] :
~ ( ! [X2: $i] :
( ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) )
=> ~ ! [X2: $i] :
( ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP5,
introduced(assumption,[]) ).
thf(h5,assumption,
sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
( ! [X1: $i] :
( ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X3 ) ) ) )
=> ~ ! [X1: $i] :
( ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ( eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ( eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP16
=> ! [X1: $i] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP16,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP11
=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP11,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP2
=> sP12 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP2,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP15
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP13
| sP9
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP9
| ~ sP11
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP16
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| ~ sP8
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,h5,h10,h13,h16,h17]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,8,h16,h17]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__4)],[h14,9,h15]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,10,h13,h14]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h11,11,h12]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,12,h10,h11]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h7,13,h9]) ).
thf(h18,assumption,
~ ( sP10
=> sP14 ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP10,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(15,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP10
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP1
| ~ sP6
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h20,h18,h8,h6,h4,h5,h2,h3,h1,h0])],[15,16,17,h4,h19,h20]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,18,h19,h20]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__5)],[h8,19,h18]) ).
thf(21,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,14,20,h7,h8]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h3,21,h6]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,22,h4,h5]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,23,h2,h3]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,24,h1]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ~ ~ ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ~ ~ ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[25,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL604^1 : TPTP v8.1.0. Released v3.6.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jul 4 06:49:29 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.18/0.35 % SZS status Theorem
% 0.18/0.35 % Mode: mode213
% 0.18/0.35 % Inferences: 12
% 0.18/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------