TSTP Solution File: SWV107^7 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SWV107^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 : Thu Aug 31 22:47:58 EDT 2023
% Result : Theorem 0.18s 0.43s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_geq,type,
geq: mu > mu > $i > $o ).
thf(ty_n6,type,
n6: mu ).
thf(ty_true,type,
true: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(ty_minus,type,
minus: mu > mu > mu ).
thf(ty_n1,type,
n1: mu ).
thf(ty_n999,type,
n999: mu ).
thf(ty_n2,type,
n2: mu ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_n0,type,
n0: mu ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_n3,type,
n3: mu ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(sP1,plain,
( sP1
<=> ( true @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( rel_s4 @ eigen__8 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] : ( rel_s4 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__8 @ X1 )
=> ( true @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
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,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( exists_in_world @ X3 @ X2 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
@ ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [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(quaternion_ds1_inuse_0019,conjecture,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ~ ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ n2 @ n0 @ X5 ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X5 ) ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X6 ) )
=> ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X7 ) )
=> ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X8 ) )
=> ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( ~ ( ! [X9: $i] :
( ( rel_s4 @ X8 @ X9 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X9 ) )
=> ~ ! [X9: $i] :
( ( rel_s4 @ X8 @ X9 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X9 ) ) )
=> ! [X9: $i] :
( ( rel_s4 @ X8 @ X9 )
=> ( true @ X9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ~ ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ n2 @ n0 @ X5 ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X5 ) ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X6 ) )
=> ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X7 ) )
=> ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X8 ) )
=> ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( ~ ( ! [X9: $i] :
( ( rel_s4 @ X8 @ X9 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X9 ) )
=> ~ ! [X9: $i] :
( ( rel_s4 @ X8 @ X9 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X9 ) ) )
=> ! [X9: $i] :
( ( rel_s4 @ X8 @ X9 )
=> ( true @ X9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0019]) ).
thf(h1,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ~ ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ n2 @ n0 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X4 ) ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X5 ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X6 ) )
=> ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X7 ) )
=> ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X8 ) ) )
=> ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( true @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ( rel_s4 @ eigen__0 @ eigen__1 )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ n2 @ n0 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X3 ) ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X5 ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X6 ) )
=> ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X7 ) ) )
=> ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( true @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
rel_s4 @ eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ n2 @ n0 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X3 ) ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X5 ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X6 ) )
=> ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X7 ) ) )
=> ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( true @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ n2 @ n0 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X3 ) ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X5 ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X6 ) )
=> ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X7 ) ) )
=> ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( true @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( rel_s4 @ eigen__1 @ eigen__2 )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ n2 @ n0 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X2 ) ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X5 ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X6 ) ) )
=> ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( true @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
rel_s4 @ eigen__1 @ eigen__2,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ n2 @ n0 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X2 ) ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X5 ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X6 ) ) )
=> ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( true @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ n2 @ n0 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X2 ) ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X5 ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X6 ) ) )
=> ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( true @ X6 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ( rel_s4 @ eigen__2 @ eigen__3 )
=> ( ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( geq @ n2 @ n0 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X1 ) ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ~ ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X5 ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X5 ) ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( true @ X5 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
rel_s4 @ eigen__2 @ eigen__3,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( geq @ n2 @ n0 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X1 ) ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ~ ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X5 ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X5 ) ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( true @ X5 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( geq @ n2 @ n0 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ~ ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X5 ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X5 ) ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( true @ X5 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( geq @ n2 @ n0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ( rel_s4 @ eigen__3 @ eigen__4 )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ~ ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X4 ) ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( true @ X4 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
rel_s4 @ eigen__3 @ eigen__4,
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ~ ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X4 ) ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( true @ X4 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ~ ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X4 ) ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( true @ X4 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( ( rel_s4 @ eigen__4 @ eigen__5 )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X3 ) ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( true @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
rel_s4 @ eigen__4 @ eigen__5,
introduced(assumption,[]) ).
thf(h26,assumption,
~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X3 ) ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( true @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X3 ) ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( true @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( ( rel_s4 @ eigen__5 @ eigen__6 )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__6 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__6 @ X1 )
=> ( ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X2 ) ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h30,assumption,
rel_s4 @ eigen__5 @ eigen__6,
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__6 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__6 @ X1 )
=> ( ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X2 ) ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h32,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__6 @ X1 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h33,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__6 @ X1 )
=> ( ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X2 ) ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
~ ( ( rel_s4 @ eigen__6 @ eigen__7 )
=> ( ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__7 @ X1 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__7 @ X1 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X1 ) ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__7 @ X1 )
=> ( true @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
rel_s4 @ eigen__6 @ eigen__7,
introduced(assumption,[]) ).
thf(h36,assumption,
~ ( ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__7 @ X1 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__7 @ X1 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X1 ) ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__7 @ X1 )
=> ( true @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__7 @ X1 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__7 @ X1 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h38,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__7 @ X1 )
=> ( true @ X1 ) ),
introduced(assumption,[]) ).
thf(h39,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__7 @ X1 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h40,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__7 @ X1 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h41,assumption,
~ ( ( rel_s4 @ eigen__7 @ eigen__8 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h42,assumption,
rel_s4 @ eigen__7 @ eigen__8,
introduced(assumption,[]) ).
thf(h43,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP3
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(ttrue,axiom,
sP2 ).
thf(a1,axiom,
sP5 ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h42,h43,h41,h39,h40,h37,h38,h35,h36,h34,h32,h33,h30,h31,h29,h27,h28,h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,h43,ttrue,a1]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h39,h40,h37,h38,h35,h36,h34,h32,h33,h30,h31,h29,h27,h28,h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h42,h43])],[h41,5,h42,h43]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h39,h40,h37,h38,h35,h36,h34,h32,h33,h30,h31,h29,h27,h28,h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h41]),tab_negall(eigenvar,eigen__8)],[h38,6,h41]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h37,h38,h35,h36,h34,h32,h33,h30,h31,h29,h27,h28,h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h39,h40])],[h37,7,h39,h40]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h36,h34,h32,h33,h30,h31,h29,h27,h28,h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h37,h38])],[h36,8,h37,h38]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h32,h33,h30,h31,h29,h27,h28,h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h35,h36])],[h34,9,h35,h36]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h32,h33,h30,h31,h29,h27,h28,h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h34]),tab_negall(eigenvar,eigen__7)],[h33,10,h34]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h31,h29,h27,h28,h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h32,h33])],[h31,11,h32,h33]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h27,h28,h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h30,h31])],[h29,12,h30,h31]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h27,h28,h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h29]),tab_negall(eigenvar,eigen__6)],[h28,13,h29]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,14,h27,h28]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h24,15,h25,h26]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h23,h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__5)],[h23,16,h24]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,17,h22,h23]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,18,h20,h21]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__4)],[h16,19,h19]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,20,h17,h18]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,21,h15,h16]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,22,h13,h14]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h11,23,h12]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,24,h10,h11]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,25,h8,h9]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,26,h7]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,27,h5,h6]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,28,h3,h4]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,29,h2]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,30,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( ~ ( ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ n2 @ n0 @ X5 ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X5 ) ) )
=> ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X6 ) )
=> ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X7 ) )
=> ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( geq @ ( minus @ n6 @ n1 ) @ n0 @ X8 ) )
=> ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( ~ ( ! [X9: $i] :
( ( rel_s4 @ X8 @ X9 )
=> ( geq @ ( minus @ n3 @ n1 ) @ n0 @ X9 ) )
=> ~ ! [X9: $i] :
( ( rel_s4 @ X8 @ X9 )
=> ( geq @ ( minus @ n999 @ n1 ) @ n0 @ X9 ) ) )
=> ! [X9: $i] :
( ( rel_s4 @ X8 @ X9 )
=> ( true @ X9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[31,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV107^7 : TPTP v8.1.2. Released v5.5.0.
% 0.06/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n020.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 : Tue Aug 29 07:31:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 % Mode: cade22sinegrackle2x6978
% 0.18/0.43 % Steps: 242
% 0.18/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------