TSTP Solution File: NUM636^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM636^2 : 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 : 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 : Mon Jul 18 13:54:24 EDT 2022
% Result : Theorem 26.04s 26.23s
% Output : Proof 26.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 31
% Syntax : Number of formulae : 36 ( 10 unt; 3 typ; 1 def)
% Number of atoms : 70 ( 17 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 105 ( 30 ~; 13 |; 0 &; 35 @)
% ( 13 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 18 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 12 ( 1 ^ 11 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_succ,type,
succ: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_one,type,
one: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( ( succ @ X1 )
!= X1 )
=> ( ( succ @ ( succ @ X1 ) )
!= ( succ @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o] :
( ~ ( ( X1 @ one )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( succ @ X2 ) ) ) )
=> ( !! @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( succ @ eigen__1 )
!= eigen__1 )
=> ( ( succ @ ( succ @ eigen__1 ) )
!= ( succ @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( succ @ one )
= one ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( succ @ ( succ @ eigen__1 ) )
= ( succ @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( ( succ @ X1 )
!= X1 )
=> ( ( succ @ ( succ @ X1 ) )
!= ( succ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ~ sP3
=> ~ sP5 )
=> ! [X1: $i] :
( ( succ @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( succ @ eigen__1 )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( ( succ @ ( succ @ eigen__1 ) )
= ( succ @ X1 ) )
=> ( ( succ @ eigen__1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( ( succ @ X1 )
= ( succ @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP4
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( succ @ X1 )
!= X1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP3
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( succ @ X1 )
!= one ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(satz2,conjecture,
sP11 ).
thf(h1,negated_conjecture,
~ sP11,
inference(assume_negation,[status(cth)],[satz2]) ).
thf(1,plain,
( ~ sP13
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| ~ sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP2
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP2
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP5
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(8,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP6
| sP12
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP12
| sP3
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(one_is_first,axiom,
sP13 ).
thf(succ_injective,axiom,
sP9 ).
thf(induction,axiom,
sP1 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,one_is_first,succ_injective,induction,h1]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[11,h0]) ).
thf(0,theorem,
sP11,
inference(contra,[status(thm),contra(discharge,[h1])],[11,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM636^2 : TPTP v8.1.0. Released v3.7.0.
% 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 : Tue Jul 5 06:19:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 26.04/26.23 % SZS status Theorem
% 26.04/26.23 % Mode: mode454
% 26.04/26.23 % Inferences: 11
% 26.04/26.23 % SZS output start Proof
% See solution above
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