TSTP Solution File: SEU477^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU477^1 : 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 : n026.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 : Tue Jul 19 13:52:22 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(def_subrel,definition,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) ).
thf(def_inv,definition,
( inv
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_idem,definition,
( idem
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ ( X1 @ X2 ) )
= ( X1 @ X2 ) ) ) ) ).
thf(def_infl,definition,
( infl
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] : ( subrel @ X2 @ ( X1 @ X2 ) ) ) ) ).
thf(def_mono,definition,
( mono
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o] :
( ( subrel @ X2 @ X3 )
=> ( subrel @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) ) ) ) ).
thf(def_refl,definition,
( refl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_irrefl,definition,
( irrefl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) ).
thf(def_rc,definition,
( rc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_symm,definition,
( symm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_antisymm,definition,
( antisymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) ).
thf(def_asymm,definition,
( asymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_sc,definition,
( sc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_trans,definition,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_tc,definition,
( tc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ( trans @ X4 )
=> ~ ( subrel @ X1 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ).
thf(def_trc,definition,
( trc
= ( ^ [X1: $i > $i > $o] : ( rc @ ( tc @ X1 ) ) ) ) ).
thf(def_trsc,definition,
( trsc
= ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ) ).
thf(def_po,definition,
( po
= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ( refl @ X1 )
=> ~ ( antisymm @ X1 ) )
=> ~ ( trans @ X1 ) ) ) ) ).
thf(def_so,definition,
( so
= ( ^ [X1: $i > $i > $o] :
~ ( ( asymm @ X1 )
=> ~ ( trans @ X1 ) ) ) ) ).
thf(def_total,definition,
( total
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_term,definition,
( term
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ) ).
thf(def_ind,definition,
( ind
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( tc @ X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) )
=> ( !! @ X2 ) ) ) ) ).
thf(def_innf,definition,
( innf
= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_nfof,definition,
( nfof
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( trc @ X1 @ X3 @ X2 )
=> ~ ( innf @ X1 @ X2 ) ) ) ) ).
thf(def_norm,definition,
( norm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( nfof @ X1 @ X3 @ X2 ) ) ) ).
thf(def_join,definition,
( join
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ! [X4: $i] :
( ( trc @ X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X3 @ X4 ) ) ) ) ).
thf(def_lconfl,definition,
( lconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_sconfl,definition,
( sconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_confl,definition,
( confl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( trc @ X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_cr,definition,
( cr
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( trsc @ X1 @ X2 @ X3 )
=> ( join @ X1 @ X2 @ X3 ) ) ) ) ).
thf(alternative_formulation_of_terminating,conjecture,
( ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) )
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) )
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[alternative_formulation_of_terminating]) ).
thf(1,plain,
$false,
inference(tab_negrefl,[status(thm),assumptions([h0])],[h0]) ).
thf(0,theorem,
( ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) )
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SEU477^1 : TPTP v8.1.0. Released v3.6.0.
% 0.13/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 23:18:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 0
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------