%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM637^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 : 300s
% DateTime : Thu Oct 9 02:11:34 PM UTC 2025
% Result : Theorem 13.14s 13.35s
% Output : Proof 13.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 24
% Syntax : Number of formulae : 29 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 67 ( 22 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 45 ~; 10 |; 0 &; 28 @)
% ( 11 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 16 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 18 ( 1 ^; 17 !; 0 ?; 18 :)
% 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] :
~ ( ( ( X1 != one )
=> ~ ! [X2: $i] :
( X1
!= ( succ @ X2 ) ) )
=> ( ( ( succ @ X1 )
!= one )
=> ~ ! [X2: $i] :
( ( succ @ X1 )
!= ( succ @ X2 ) ) ) ) ) ),
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
<=> ( ( one != one )
=> ~ ! [X1: $i] :
( one
!= ( succ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( ( X1 != one )
=> ~ ! [X2: $i] :
( X1
!= ( succ @ X2 ) ) )
=> ( ( ( succ @ X1 )
!= one )
=> ~ ! [X2: $i] :
( ( succ @ X1 )
!= ( succ @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( succ @ eigen__1 )
!= one )
=> ~ ! [X1: $i] :
( ( succ @ eigen__1 )
!= ( succ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( sP2
=> ~ sP3 )
=> ! [X1: $i] :
( ( X1 != one )
=> ~ ! [X2: $i] :
( X1
!= ( succ @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( succ @ eigen__1 )
!= ( succ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( X1 != one )
=> ~ ! [X2: $i] :
( X1
!= ( succ @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP2
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( succ @ eigen__1 )
= ( succ @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ( eigen__1 != one )
=> ~ ! [X1: $i] :
( eigen__1
!= ( succ @ X1 ) ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( one = one ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(satz3,conjecture,
sP7 ).
thf(h1,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[satz3]) ).
thf(1,plain,
sP9,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP6
| ~ sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
sP11,
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP2
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP4
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP10
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP3
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(8,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP5
| sP8
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP8
| ~ sP2
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
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,induction,h1]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[11,h0]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h1])],[11,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM637^2 : TPTP v9.2.0. Released v3.7.0.
% 0.13/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n019.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 : 300
% 0.13/0.34 % DateTime : Wed Oct 8 22:06:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 13.14/13.35 % SZS status Theorem
% 13.14/13.35 % Mode: mode454
% 13.14/13.35 % Inferences: 195
% 13.14/13.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------