TSTP Solution File: SEV197^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV197^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n009.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 18:05:19 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_iS,type,
iS: $tType ).
thf(ty_eigen__2,type,
eigen__2: iS ).
thf(ty_cP,type,
cP: iS > iS > iS ).
thf(ty_eigen__1,type,
eigen__1: iS ).
thf(ty_eigen__0,type,
eigen__0: iS ).
thf(ty_eigen__4,type,
eigen__4: iS ).
thf(ty_eigen__5,type,
eigen__5: iS ).
thf(ty_eigen__3,type,
eigen__3: iS ).
thf(ty_c0,type,
c0: iS ).
thf(sP1,plain,
( sP1
<=> ( ( cP @ eigen__0 @ eigen__2 )
= ( cP @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: iS,X2: iS] :
( ( ( cP @ eigen__0 @ X1 )
= ( cP @ eigen__1 @ X2 ) )
=> ~ ( ( eigen__0 = eigen__1 )
=> ( X1 != X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cP @ eigen__4 @ eigen__5 )
= c0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: iS] :
( ( cP @ eigen__4 @ X1 )
!= c0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0 = eigen__1 )
=> ( eigen__2 != eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: iS] :
( ( ( cP @ eigen__0 @ eigen__2 )
= ( cP @ eigen__1 @ X1 ) )
=> ~ ( ( eigen__0 = eigen__1 )
=> ( eigen__2 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: iS,X2: iS,X3: iS] :
( ( ( cP @ eigen__0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ~ ( ( eigen__0 = X1 )
=> ( X2 != X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__2 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP1
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(cS_ALG02_pme,conjecture,
( ~ ( ~ ( sP5
=> ~ sP10 )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ~ ( sP10
=> ~ sP5 ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( sP5
=> ~ sP10 )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ~ ( sP10
=> ~ sP5 ) ),
inference(assume_negation,[status(cth)],[cS_ALG02_pme]) ).
thf(h1,assumption,
~ ( ~ ( sP5
=> ~ sP10 )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( sP10
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP5
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP5,
introduced(assumption,[]) ).
thf(h6,assumption,
sP10,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
sP6,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( sP6
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP12
| ~ sP1
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h13,h14,h12,h11,h10,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,h6,h13,h15]) ).
thf(8,plain,
( sP6
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP7
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP12
| ~ sP1
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h13,h14,h12,h11,h10,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[8,9,10,11,12,13,h6,h13,h16]) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h14,h12,h11,h10,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h14,7,14,h15,h16]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h11,h10,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,15,h13,h14]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h10,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h11,16,h12]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h10,17,h11]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h9,18,h10]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h7,19,h9]) ).
thf(h17,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h18,assumption,
sP3,
introduced(assumption,[]) ).
thf(21,plain,
( ~ sP5
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP4
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h17,h8,h5,h6,h3,h4,h1,h2,h0])],[21,22,h5,h18]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__5)],[h17,23,h18]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h8,24,h17]) ).
thf(26,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h2,20,25,h7,h8]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,26,h5,h6]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,27,h3,h4]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,28,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( sP5
=> ~ sP10 )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ~ ( sP10
=> ~ sP5 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[29,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEV197^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n009.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 : 600
% 0.13/0.33 % DateTime : Mon Jun 27 23:52:22 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: 15
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------