TSTP Solution File: SYN045^7 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN045^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n015.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 11:40:43 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__14,type,
eigen__14: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_p,type,
p: $i > $o ).
thf(ty_eigen__12,type,
eigen__12: $i ).
thf(ty_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__16,type,
eigen__16: $i ).
thf(ty_q,type,
q: $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__21,type,
eigen__21: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_r,type,
r: $i > $o ).
thf(ty_eigen__19,type,
eigen__19: $i ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__17,type,
eigen__17: $i ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__13,type,
eigen__13: $i ).
thf(ty_eigen__20,type,
eigen__20: $i ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(ty_eigen__18,type,
eigen__18: $i ).
thf(ty_eigen__22,type,
eigen__22: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__10 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( rel_s4 @ eigen__1 @ eigen__9 )
=> ( r @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( r @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( r @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( rel_s4 @ eigen__10 @ eigen__21 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( p @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( rel_s4 @ eigen__10 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( rel_s4 @ eigen__10 @ eigen__14 )
=> ( p @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( rel_s4 @ eigen__10 @ eigen__11 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP8
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( rel_s4 @ eigen__10 @ eigen__17 )
=> ( p @ eigen__17 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( rel_s4 @ eigen__1 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( p @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( q @ eigen__21 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( q @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( rel_s4 @ eigen__1 @ eigen__2 )
=> ( p @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP5
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__10 @ X1 )
=> ( r @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( rel_s4 @ eigen__1 @ eigen__7 )
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( r @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( rel_s4 @ eigen__1 @ eigen__4 )
=> ( p @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( p @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( p @ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( rel_s4 @ eigen__10 @ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( rel_s4 @ eigen__10 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( r @ eigen__22 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__10 @ X1 )
=> ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( rel_s4 @ eigen__10 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( rel_s4 @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( p @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( rel_s4 @ eigen__10 @ eigen__22 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP33
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( rel_s4 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( rel_s4 @ eigen__1 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
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_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ) ).
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_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ( 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_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_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_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_mdia_s4,definition,
( mdia_s4
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X1 ) ) ) ) ) ).
thf(pel13,conjecture,
! [X1: $i] :
~ ( ~ ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) )
=> ~ ( ~ ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ~ ~ ( ~ ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) )
=> ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) )
=> ~ ( ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ( ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) )
=> ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[pel13]) ).
thf(h1,assumption,
( ! [X1: $i] :
( ( rel_s4 @ eigen__0 @ X1 )
=> ( ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( r @ X2 ) ) ) )
=> ~ ( ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ~ ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__0 @ X1 )
=> ( ~ ( ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ~ ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( r @ X2 ) ) ) )
=> ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__0 @ X1 )
=> ( ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( r @ X2 ) ) ) )
=> ~ ( ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ~ ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__0 @ X1 )
=> ( ~ ( ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ~ ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( r @ X2 ) ) ) )
=> ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( rel_s4 @ eigen__0 @ eigen__1 )
=> ( ( ~ sP6
=> ~ ( sP9
=> ~ sP22 ) )
=> ~ ( ( ~ sP6
=> sP9 )
=> ~ ( ~ sP6
=> sP22 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
rel_s4 @ eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( ~ sP6
=> ~ ( sP9
=> ~ sP22 ) )
=> ~ ( ( ~ sP6
=> sP9 )
=> ~ ( ~ sP6
=> sP22 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
( ~ sP6
=> ~ ( sP9
=> ~ sP22 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ( ~ sP6
=> sP9 )
=> ~ ( ~ sP6
=> sP22 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP6,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP9
=> ~ sP22 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ sP6
=> sP9 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ~ sP6
=> sP22 ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h16,assumption,
sP35,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ( rel_s4 @ eigen__1 @ eigen__3 )
=> ( q @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
rel_s4 @ eigen__1 @ eigen__3,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( q @ eigen__3 ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP18
| ~ sP35
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h20,h18,h16,h17,h15,h13,h14,h11,h9,h7,h8,h5,h6,h4,h2,h1,h0])],[1,2,h9,h16,h17]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h15,h13,h14,h11,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,3,h19,h20]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h15,h13,h14,h11,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__3)],[h14,4,h18]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h11,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,5,h16,h17]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h11,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__2)],[h13,6,h15]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,7,h13,h14]) ).
thf(h21,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(h23,assumption,
sP31,
introduced(assumption,[]) ).
thf(h24,assumption,
~ sP32,
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( ( rel_s4 @ eigen__1 @ eigen__5 )
=> ( r @ eigen__5 ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
rel_s4 @ eigen__1 @ eigen__5,
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( r @ eigen__5 ),
introduced(assumption,[]) ).
thf(9,plain,
( ~ sP6
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP23
| ~ sP31
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h27,h25,h23,h24,h22,h13,h21,h12,h9,h7,h8,h5,h6,h4,h2,h1,h0])],[9,10,h9,h23,h24]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h23,h24,h22,h13,h21,h12,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h26,h27])],[h25,11,h26,h27]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h24,h22,h13,h21,h12,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__5)],[h21,12,h25]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h13,h21,h12,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h22,13,h23,h24]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h21,h12,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__4)],[h13,14,h22]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h21])],[h12,15,h13,h21]) ).
thf(17,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h7,h8,h5,h6,h4,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h8,8,16,h11,h12]) ).
thf(h28,assumption,
sP9,
introduced(assumption,[]) ).
thf(h29,assumption,
sP22,
introduced(assumption,[]) ).
thf(h30,assumption,
~ ( ( rel_s4 @ eigen__1 @ eigen__6 )
=> ( p @ eigen__6 ) ),
introduced(assumption,[]) ).
thf(h31,assumption,
rel_s4 @ eigen__1 @ eigen__6,
introduced(assumption,[]) ).
thf(h32,assumption,
~ ( p @ eigen__6 ),
introduced(assumption,[]) ).
thf(h33,assumption,
~ sP21,
introduced(assumption,[]) ).
thf(h34,assumption,
sP36,
introduced(assumption,[]) ).
thf(h35,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(18,plain,
( ~ sP9
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP21
| ~ sP36
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h34,h35,h33,h31,h32,h30,h13,h14,h11,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0])],[18,19,h28,h34,h35]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h31,h32,h30,h13,h14,h11,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h34,h35])],[h33,20,h34,h35]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h31,h32,h30,h13,h14,h11,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__7)],[h14,21,h33]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h13,h14,h11,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h30,22,h31,h32]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h11,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__6)],[h13,23,h30]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,24,h13,h14]) ).
thf(h36,assumption,
~ ( ( rel_s4 @ eigen__1 @ eigen__8 )
=> ( p @ eigen__8 ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
rel_s4 @ eigen__1 @ eigen__8,
introduced(assumption,[]) ).
thf(h38,assumption,
~ ( p @ eigen__8 ),
introduced(assumption,[]) ).
thf(h39,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h40,assumption,
sP14,
introduced(assumption,[]) ).
thf(h41,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(26,plain,
( ~ sP22
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP2
| ~ sP14
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h40,h41,h39,h37,h38,h36,h13,h21,h12,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0])],[26,27,h29,h40,h41]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h39,h37,h38,h36,h13,h21,h12,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h40,h41])],[h39,28,h40,h41]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h37,h38,h36,h13,h21,h12,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negall(discharge,[h39]),tab_negall(eigenvar,eigen__9)],[h21,29,h39]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h13,h21,h12,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h37,h38])],[h36,30,h37,h38]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h21,h12,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negall(discharge,[h36]),tab_negall(eigenvar,eigen__8)],[h13,31,h36]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h21])],[h12,32,h13,h21]) ).
thf(34,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h28,h29,h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h8,25,33,h11,h12]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h7,h8,h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h10,34,h28,h29]) ).
thf(36,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h7,17,35,h9,h10]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,36,h7,h8]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,37,h5,h6]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,38,h4]) ).
thf(h42,assumption,
~ ( ( rel_s4 @ eigen__0 @ eigen__10 )
=> ( ~ ( ( ~ sP1
=> sP29 )
=> ~ ( ~ sP1
=> sP20 ) )
=> ( ~ sP1
=> ~ ( sP29
=> ~ sP20 ) ) ) ),
introduced(assumption,[]) ).
thf(h43,assumption,
rel_s4 @ eigen__0 @ eigen__10,
introduced(assumption,[]) ).
thf(h44,assumption,
~ ( ~ ( ( ~ sP1
=> sP29 )
=> ~ ( ~ sP1
=> sP20 ) )
=> ( ~ sP1
=> ~ ( sP29
=> ~ sP20 ) ) ),
introduced(assumption,[]) ).
thf(h45,assumption,
~ ( ( ~ sP1
=> sP29 )
=> ~ ( ~ sP1
=> sP20 ) ),
introduced(assumption,[]) ).
thf(h46,assumption,
~ ( ~ sP1
=> ~ ( sP29
=> ~ sP20 ) ),
introduced(assumption,[]) ).
thf(h47,assumption,
( ~ sP1
=> sP29 ),
introduced(assumption,[]) ).
thf(h48,assumption,
( ~ sP1
=> sP20 ),
introduced(assumption,[]) ).
thf(h49,assumption,
sP1,
introduced(assumption,[]) ).
thf(h50,assumption,
sP29,
introduced(assumption,[]) ).
thf(h51,assumption,
sP20,
introduced(assumption,[]) ).
thf(h52,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h53,assumption,
( sP29
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h54,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h55,assumption,
sP27,
introduced(assumption,[]) ).
thf(h56,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h57,assumption,
~ sP29,
introduced(assumption,[]) ).
thf(h58,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(h59,assumption,
~ ( ( rel_s4 @ eigen__10 @ eigen__12 )
=> ( q @ eigen__12 ) ),
introduced(assumption,[]) ).
thf(h60,assumption,
rel_s4 @ eigen__10 @ eigen__12,
introduced(assumption,[]) ).
thf(h61,assumption,
~ ( q @ eigen__12 ),
introduced(assumption,[]) ).
thf(40,plain,
( ~ sP1
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP11
| ~ sP27
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h60,h61,h59,h57,h55,h56,h54,h52,h53,h49,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0])],[40,41,h49,h55,h56]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h59,h57,h55,h56,h54,h52,h53,h49,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h60,h61])],[h59,42,h60,h61]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h57,h55,h56,h54,h52,h53,h49,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h59]),tab_negall(eigenvar,eigen__12)],[h57,43,h59]) ).
thf(h62,assumption,
~ ( ( rel_s4 @ eigen__10 @ eigen__13 )
=> ( r @ eigen__13 ) ),
introduced(assumption,[]) ).
thf(h63,assumption,
rel_s4 @ eigen__10 @ eigen__13,
introduced(assumption,[]) ).
thf(h64,assumption,
~ ( r @ eigen__13 ),
introduced(assumption,[]) ).
thf(45,plain,
( ~ sP1
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP11
| ~ sP27
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h63,h64,h62,h58,h55,h56,h54,h52,h53,h49,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0])],[45,46,h49,h55,h56]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h62,h58,h55,h56,h54,h52,h53,h49,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h63,h64])],[h62,47,h63,h64]) ).
thf(49,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h58,h55,h56,h54,h52,h53,h49,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h62]),tab_negall(eigenvar,eigen__13)],[h58,48,h62]) ).
thf(50,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h55,h56,h54,h52,h53,h49,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_imp(discharge,[h57]),tab_imp(discharge,[h58])],[h53,44,49,h57,h58]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h54,h52,h53,h49,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h55,h56])],[h54,50,h55,h56]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h52,h53,h49,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h54]),tab_negall(eigenvar,eigen__11)],[h52,51,h54]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h49,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h52,h53])],[h46,52,h52,h53]) ).
thf(h65,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h66,assumption,
sP30,
introduced(assumption,[]) ).
thf(h67,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h68,assumption,
~ ( ( rel_s4 @ eigen__10 @ eigen__15 )
=> ( q @ eigen__15 ) ),
introduced(assumption,[]) ).
thf(h69,assumption,
rel_s4 @ eigen__10 @ eigen__15,
introduced(assumption,[]) ).
thf(h70,assumption,
~ ( q @ eigen__15 ),
introduced(assumption,[]) ).
thf(54,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP10
| ~ sP30
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h69,h70,h68,h57,h66,h67,h65,h52,h53,h51,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0])],[54,55,h49,h66,h67]) ).
thf(57,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h68,h57,h66,h67,h65,h52,h53,h51,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h69,h70])],[h68,56,h69,h70]) ).
thf(58,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h57,h66,h67,h65,h52,h53,h51,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h68]),tab_negall(eigenvar,eigen__15)],[h57,57,h68]) ).
thf(h71,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h72,assumption,
sP8,
introduced(assumption,[]) ).
thf(h73,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(59,plain,
( ~ sP20
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP12
| ~ sP8
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h72,h73,h71,h58,h66,h67,h65,h52,h53,h51,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0])],[59,60,h51,h72,h73]) ).
thf(62,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h71,h58,h66,h67,h65,h52,h53,h51,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h72,h73])],[h71,61,h72,h73]) ).
thf(63,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h58,h66,h67,h65,h52,h53,h51,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h71]),tab_negall(eigenvar,eigen__16)],[h58,62,h71]) ).
thf(64,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h66,h67,h65,h52,h53,h51,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_imp(discharge,[h57]),tab_imp(discharge,[h58])],[h53,58,63,h57,h58]) ).
thf(65,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h65,h52,h53,h51,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h66,h67])],[h65,64,h66,h67]) ).
thf(66,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h52,h53,h51,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h65]),tab_negall(eigenvar,eigen__14)],[h52,65,h65]) ).
thf(67,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h51,h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h52,h53])],[h46,66,h52,h53]) ).
thf(68,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h49,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_imp(discharge,[h49]),tab_imp(discharge,[h51])],[h48,53,67,h49,h51]) ).
thf(h74,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h75,assumption,
sP26,
introduced(assumption,[]) ).
thf(h76,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(h77,assumption,
~ ( ( rel_s4 @ eigen__10 @ eigen__18 )
=> ( q @ eigen__18 ) ),
introduced(assumption,[]) ).
thf(h78,assumption,
rel_s4 @ eigen__10 @ eigen__18,
introduced(assumption,[]) ).
thf(h79,assumption,
~ ( q @ eigen__18 ),
introduced(assumption,[]) ).
thf(69,plain,
( ~ sP1
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP13
| ~ sP26
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h78,h79,h77,h57,h75,h76,h74,h52,h53,h49,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0])],[69,70,h49,h75,h76]) ).
thf(72,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h77,h57,h75,h76,h74,h52,h53,h49,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h78,h79])],[h77,71,h78,h79]) ).
thf(73,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h57,h75,h76,h74,h52,h53,h49,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h77]),tab_negall(eigenvar,eigen__18)],[h57,72,h77]) ).
thf(h80,assumption,
~ ( ( rel_s4 @ eigen__10 @ eigen__19 )
=> ( r @ eigen__19 ) ),
introduced(assumption,[]) ).
thf(h81,assumption,
rel_s4 @ eigen__10 @ eigen__19,
introduced(assumption,[]) ).
thf(h82,assumption,
~ ( r @ eigen__19 ),
introduced(assumption,[]) ).
thf(74,plain,
( ~ sP1
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP13
| ~ sP26
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(76,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h81,h82,h80,h58,h75,h76,h74,h52,h53,h49,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0])],[74,75,h49,h75,h76]) ).
thf(77,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h80,h58,h75,h76,h74,h52,h53,h49,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h81,h82])],[h80,76,h81,h82]) ).
thf(78,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h58,h75,h76,h74,h52,h53,h49,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h80]),tab_negall(eigenvar,eigen__19)],[h58,77,h80]) ).
thf(79,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h75,h76,h74,h52,h53,h49,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_imp(discharge,[h57]),tab_imp(discharge,[h58])],[h53,73,78,h57,h58]) ).
thf(80,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h74,h52,h53,h49,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h75,h76])],[h74,79,h75,h76]) ).
thf(81,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h52,h53,h49,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h74]),tab_negall(eigenvar,eigen__17)],[h52,80,h74]) ).
thf(82,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h49,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h52,h53])],[h46,81,h52,h53]) ).
thf(h83,assumption,
~ ( ( rel_s4 @ eigen__10 @ eigen__20 )
=> ( p @ eigen__20 ) ),
introduced(assumption,[]) ).
thf(h84,assumption,
rel_s4 @ eigen__10 @ eigen__20,
introduced(assumption,[]) ).
thf(h85,assumption,
~ ( p @ eigen__20 ),
introduced(assumption,[]) ).
thf(h86,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h87,assumption,
sP5,
introduced(assumption,[]) ).
thf(h88,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(83,plain,
( ~ sP29
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(84,plain,
( ~ sP19
| ~ sP5
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(85,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h87,h88,h86,h57,h84,h85,h83,h52,h53,h51,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0])],[83,84,h50,h87,h88]) ).
thf(86,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h86,h57,h84,h85,h83,h52,h53,h51,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h87,h88])],[h86,85,h87,h88]) ).
thf(87,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h57,h84,h85,h83,h52,h53,h51,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h86]),tab_negall(eigenvar,eigen__21)],[h57,86,h86]) ).
thf(h89,assumption,
~ sP34,
introduced(assumption,[]) ).
thf(h90,assumption,
sP33,
introduced(assumption,[]) ).
thf(h91,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(88,plain,
( ~ sP20
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(89,plain,
( ~ sP34
| ~ sP33
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(90,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h90,h91,h89,h58,h84,h85,h83,h52,h53,h51,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0])],[88,89,h51,h90,h91]) ).
thf(91,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h89,h58,h84,h85,h83,h52,h53,h51,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h90,h91])],[h89,90,h90,h91]) ).
thf(92,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h58,h84,h85,h83,h52,h53,h51,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h89]),tab_negall(eigenvar,eigen__22)],[h58,91,h89]) ).
thf(93,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h84,h85,h83,h52,h53,h51,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_imp(discharge,[h57]),tab_imp(discharge,[h58])],[h53,87,92,h57,h58]) ).
thf(94,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h83,h52,h53,h51,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h84,h85])],[h83,93,h84,h85]) ).
thf(95,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h52,h53,h51,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negall(discharge,[h83]),tab_negall(eigenvar,eigen__20)],[h52,94,h83]) ).
thf(96,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h51,h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h52,h53])],[h46,95,h52,h53]) ).
thf(97,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h50,h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_imp(discharge,[h49]),tab_imp(discharge,[h51])],[h48,82,96,h49,h51]) ).
thf(98,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h47,h48,h45,h46,h43,h44,h42,h3,h1,h0]),tab_imp(discharge,[h49]),tab_imp(discharge,[h50])],[h47,68,97,h49,h50]) ).
thf(99,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h46,h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h47,h48])],[h45,98,h47,h48]) ).
thf(100,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h43,h44,h42,h3,h1,h0]),tab_negimp(discharge,[h45,h46])],[h44,99,h45,h46]) ).
thf(101,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h42,h3,h1,h0]),tab_negimp(discharge,[h43,h44])],[h42,100,h43,h44]) ).
thf(102,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h0]),tab_negall(discharge,[h42]),tab_negall(eigenvar,eigen__10)],[h3,101,h42]) ).
thf(103,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[h1,39,102,h2,h3]) ).
thf(104,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,103,h1]) ).
thf(0,theorem,
! [X1: $i] :
~ ( ~ ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) )
=> ~ ( ~ ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ~ ~ ( ~ ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) )
=> ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( q @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[104,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN045^7 : TPTP v8.1.0. Released v5.5.0.
% 0.00/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jul 11 16:08:09 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 % Mode: mode213
% 0.18/0.43 % Inferences: 51
% 0.18/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------