TSTP Solution File: LCL868^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL868^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n012.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 14:11:43 EDT 2022
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
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(ty_eigen__8,type,
eigen__8: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X1 @ X3 ) )
=> ( eigen__0 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( eigen__0 @ eigen__4 @ eigen__3 )
=> ~ ( eigen__0 @ eigen__4 @ eigen__5 ) )
=> ( eigen__0 @ eigen__3 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__6 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ( eigen__0 @ eigen__3 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__6 @ eigen__7 )
=> ~ ( eigen__0 @ eigen__6 @ X1 ) )
=> ( eigen__0 @ eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__6 @ X1 )
=> ~ ( eigen__0 @ eigen__6 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__4 @ X1 )
=> ~ ( eigen__0 @ eigen__4 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0 @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ( eigen__0 @ eigen__6 @ eigen__7 )
=> ~ sP3 )
=> ( eigen__0 @ eigen__7 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ( eigen__0 @ eigen__3 @ eigen__4 )
=> ~ ( eigen__0 @ eigen__3 @ eigen__3 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP8
=> ~ ( eigen__0 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP12
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 @ eigen__3 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ~ ( sP8
=> ~ ( eigen__0 @ eigen__4 @ X1 ) )
=> ( eigen__0 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] : ( eigen__0 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__0 @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
~ ( eigen__0 @ eigen__1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ~ ( sP13
=> ~ ( eigen__0 @ eigen__3 @ X1 ) )
=> ( eigen__0 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__0 @ eigen__7 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP13
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__0 @ eigen__3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(def_meq_ind,definition,
( meq_ind
= ( ^ [X1: mu,X2: mu,X3: $i] : ( X1 = X2 ) ) ) ).
thf(def_meq_prop,definition,
( meq_prop
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
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] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X2 ) @ X1 ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ) ).
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] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_msymmetric,definition,
( msymmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mserial,definition,
( mserial
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_meuclidean,definition,
( meuclidean
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_mpartially_functional,definition,
( mpartially_functional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) ).
thf(def_mfunctional,definition,
( mfunctional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ).
thf(def_mweakly_dense,definition,
( mweakly_dense
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ~ ( X1 @ X5 @ X3 ) ) ) ) ) ).
thf(def_mweakly_connected,definition,
( mweakly_connected
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( ~ ( ~ ( X1 @ X3 @ X4 )
=> ( X3 = X4 ) )
=> ( X1 @ X4 @ X3 ) ) ) ) ) ).
thf(def_mweakly_directed,definition,
( mweakly_directed
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
( ( X1 @ X3 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ).
thf(def_mvalid,definition,
mvalid = !! ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(conj,conjecture,
! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
=> ~ ( ~ ( ! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
=> ~ ( ~ ( ! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
~ ( ~ ( sP18
=> ~ sP1 )
=> ~ ( ~ ( ! [X1: $i] :
~ ! [X2: $i] :
~ ( eigen__0 @ X1 @ X2 )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) )
=> ~ sP1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP18
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ~ ( ! [X1: $i] :
~ ! [X2: $i] :
~ ( eigen__0 @ X1 @ X2 )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP18,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
( ! [X1: $i] :
~ ! [X2: $i] :
~ ( eigen__0 @ X1 @ X2 )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
~ ! [X2: $i] :
~ ( eigen__0 @ X1 @ X2 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP20,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP20
| ~ sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP18
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,h4,h10]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h8,3,h10]) ).
thf(h11,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__3 @ X2 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i] :
( ~ ( sP13
=> ~ ( eigen__0 @ eigen__4 @ X1 ) )
=> ( eigen__0 @ eigen__3 @ X1 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( sP13
=> ~ sP16 )
=> sP24 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP13
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h16,assumption,
sP13,
introduced(assumption,[]) ).
thf(h17,assumption,
sP16,
introduced(assumption,[]) ).
thf(5,plain,
( ~ sP18
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP21
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP10
| sP23
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP23
| ~ sP13
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP4
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP7
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP17
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP2
| sP11
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP11
| ~ sP8
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h14,h15,h13,h12,h11,h9,h6,h4,h5,h2,h3,h1,h0])],[5,6,7,8,9,10,11,12,13,14,15,h4,h5,h16,h17,h15]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h12,h11,h9,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,16,h16,h17]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h12,h11,h9,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,17,h14,h15]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h11,h9,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__5)],[h12,18,h13]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h9,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__4)],[h11,19,h12]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h9,20,h11]) ).
thf(22,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h6,4,21,h8,h9]) ).
thf(h18,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h23,assumption,
sP12,
introduced(assumption,[]) ).
thf(h24,assumption,
sP3,
introduced(assumption,[]) ).
thf(23,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP5
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP9
| sP14
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP14
| ~ sP12
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h21,h22,h20,h19,h18,h7,h4,h5,h2,h3,h1,h0])],[23,24,25,26,27,h5,h23,h24,h22]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h20,h19,h18,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h23,h24])],[h21,28,h23,h24]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h19,h18,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,29,h21,h22]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h18,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__8)],[h19,30,h20]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__7)],[h18,31,h19]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__6)],[h7,32,h18]) ).
thf(34,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h3,22,33,h6,h7]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,34,h4,h5]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,35,h2,h3]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,36,h1]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
=> ~ ( ~ ( ! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[37,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL868^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n012.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 : Mon Jul 4 03:39:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % Mode: mode213
% 0.18/0.38 % Inferences: 65
% 0.18/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------