%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM635^2 : 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 : n014.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 02:11:33 PM UTC 2025
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_succ,type,
succ: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( succ @ eigen__0 )
= ( succ @ eigen__1 ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( succ @ eigen__0 )
= ( succ @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ( ( succ @ X1 )
= ( succ @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( ( succ @ eigen__0 )
= ( succ @ X1 ) )
=> ( eigen__0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(satz1,conjecture,
! [X1: $i,X2: $i] :
( ( X1 != X2 )
=> ( ( succ @ X1 )
!= ( succ @ X2 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( X1 != X2 )
=> ( ( succ @ X1 )
!= ( succ @ X2 ) ) ),
inference(assume_negation,[status(cth)],[satz1]) ).
thf(h1,assumption,
~ ! [X1: $i] :
( ( eigen__0 != X1 )
=> ( ( succ @ eigen__0 )
!= ( succ @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ sP1
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| ~ sP3
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(succ_injective,axiom,
sP4 ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h1,h0])],[1,2,3,succ_injective,h3,h4]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,4,h3,h4]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,5,h2]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( X1 != X2 )
=> ( ( succ @ X1 )
!= ( succ @ X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM635^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 22:24:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % Mode: mode213
% 0.14/0.38 % Inferences: 5
% 0.14/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------