TSTP Solution File: NUM638^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM638^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 : Mon Jul 18 13:54:26 EDT 2022
% Result : Theorem 34.82s 34.91s
% Output : Proof 34.82s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_eigen__1,type,
eigen__1: nat ).
thf(ty_eigen__0,type,
eigen__0: nat ).
thf(ty_suc,type,
suc: nat > nat ).
thf(ty_some,type,
some: ( nat > $o ) > $o ).
thf(ty_n_1,type,
n_1: nat ).
thf(ty_x,type,
x: nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat] :
( ( eigen__1 = X1 )
=> ( X1 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat,X2: nat] :
( ( ( suc @ X1 )
= ( suc @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( suc @ eigen__1 )
= ( suc @ eigen__0 ) )
=> ( eigen__1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( suc @ x )
= ( suc @ ( suc @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( suc @ x )
= ( suc @ ( suc @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( x
= ( suc @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: nat] :
( ( ( suc @ ( suc @ eigen__1 ) )
= ( suc @ X1 ) )
=> ( ( suc @ eigen__1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( x
= ( suc @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( some
@ ^ [X1: nat] :
( x
= ( suc @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP9
=> ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: nat] :
( ( ( suc @ eigen__1 )
= ( suc @ X1 ) )
=> ( eigen__1 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: nat] :
( ( X1 != n_1 )
=> ( some
@ ^ [X2: nat] :
( X1
= ( suc @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( suc @ ( suc @ eigen__1 ) )
= ( suc @ ( suc @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( x = n_1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: nat,X2: nat] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP15
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP14
=> ( ( suc @ eigen__1 )
= ( suc @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( suc @ x )
= ( suc @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( suc @ eigen__1 )
= ( suc @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(satz3a,conjecture,
~ ( ! [X1: nat,X2: nat] :
( ( x
= ( suc @ X1 ) )
=> ( ( x
= ( suc @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ sP10 ) ).
thf(h0,negated_conjecture,
( ! [X1: nat,X2: nat] :
( ( x
= ( suc @ X1 ) )
=> ( ( x
= ( suc @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ sP10 ),
inference(assume_negation,[status(cth)],[satz3a]) ).
thf(h1,assumption,
~ ! [X1: nat,X2: nat] :
( ( x
= ( suc @ X1 ) )
=> ( ( x
= ( suc @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: nat] :
( sP8
=> ( ( x
= ( suc @ X1 ) )
=> ( eigen__0 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP8
=> ( sP6
=> sP19 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP8,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP6
=> sP19 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP6,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP20
| sP14
| ~ sP5
| ~ sP4 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
sP20,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP4
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP5
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP18
| ~ sP14
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP3
| ~ sP21
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP12
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP2
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP11
| ~ sP9
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP1
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP16
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
sP16,
inference(eq_sym,[status(thm)],]) ).
thf(ax4,axiom,
sP2 ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h5,h7,h8,ax4]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,15,h7,h8]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,16,h5,h6]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,17,h4]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h1,18,h3]) ).
thf(20,plain,
( ~ sP17
| sP15
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP13
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(satz3,axiom,
sP13 ).
thf(n,axiom,
~ sP15 ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h0])],[20,21,h2,satz3,n]) ).
thf(23,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,19,22,h1,h2]) ).
thf(0,theorem,
~ ( ! [X1: nat,X2: nat] :
( ( x
= ( suc @ X1 ) )
=> ( ( x
= ( suc @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ sP10 ),
inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM638^1 : TPTP v8.1.0. Released v3.7.0.
% 0.00/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 23:06:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 34.82/34.91 % SZS status Theorem
% 34.82/34.91 % Mode: mode473
% 34.82/34.91 % Inferences: 28427
% 34.82/34.91 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------