TSTP Solution File: SYO536^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO536^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n007.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 19:33:17 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eps,type,
eps: ( $i > $o ) > $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $i ) > $i > $o ).
thf(ty_epsii,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
~ ( eigen__0 @ eigen__1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0
@ ( epsii
@ ^ [X1: $i > $i] :
~ ! [X2: $i] :
~ ( eigen__0 @ X1 @ X2 ) )
@ ( eps
@ ( eigen__0
@ ( epsii
@ ^ [X1: $i > $i] :
~ ! [X2: $i] :
~ ( eigen__0 @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $i,X2: $i] :
~ ( eigen__0 @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
~ ( eigen__0
@ ( epsii
@ ^ [X2: $i > $i] :
~ ! [X3: $i] :
~ ( eigen__0 @ X2 @ X3 ) )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(def_epsa,definition,
( epsa
= ( ^ [X1: ( $i > $i ) > $i > $o] :
( epsii
@ ^ [X2: $i > $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_epsb,definition,
( epsb
= ( ^ [X1: ( $i > $i ) > $i > $o] : ( eps @ ( X1 @ ( epsa @ X1 ) ) ) ) ) ).
thf(conj,conjecture,
! [X1: ( $i > $i ) > $i > $o] :
( ~ ! [X2: $i > $i,X3: $i] :
~ ( X1 @ X2 @ X3 )
=> ( X1
@ ( epsii
@ ^ [X2: $i > $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) )
@ ( eps
@ ( X1
@ ( epsii
@ ^ [X2: $i > $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: ( $i > $i ) > $i > $o] :
( ~ ! [X2: $i > $i,X3: $i] :
~ ( X1 @ X2 @ X3 )
=> ( X1
@ ( epsii
@ ^ [X2: $i > $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) )
@ ( eps
@ ( X1
@ ( epsii
@ ^ [X2: $i > $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
~ ( ~ sP4
=> sP3 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(choiceaxii,axiom,
! [X1: ( $i > $i ) > $o] :
( ~ ! [X2: $i > $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( epsii @ X1 ) ) ) ).
thf(3,plain,
( ~ sP5
| sP4 ),
inference(choice_rule,[status(thm)],[choiceaxii]) ).
thf(choiceax,axiom,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( eps @ X1 ) ) ) ).
thf(4,plain,
( sP3
| sP5 ),
inference(choice_rule,[status(thm)],[choiceax]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h4,h2,h3,h1,h0])],[1,2,3,4,h5,h3]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,5,h5]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,6,h4]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,7,h2,h3]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,8,h1]) ).
thf(0,theorem,
! [X1: ( $i > $i ) > $i > $o] :
( ~ ! [X2: $i > $i,X3: $i] :
~ ( X1 @ X2 @ X3 )
=> ( X1
@ ( epsii
@ ^ [X2: $i > $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) )
@ ( eps
@ ( X1
@ ( epsii
@ ^ [X2: $i > $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO536^1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n007.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 : Fri Jul 8 20:16:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 21
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------