%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM656^1 : 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 : n003.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 02:11:39 PM UTC 2025
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_y,type,
y: nat ).
thf(ty_less,type,
less: nat > nat > $o ).
thf(ty_more,type,
more: nat > nat > $o ).
thf(ty_x,type,
x: nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat,X2: nat] :
~ ( ( ( X1 = X2 )
=> ~ ( more @ X1 @ X2 ) )
=> ( ( ( more @ X1 @ X2 )
=> ~ ( less @ X1 @ X2 ) )
=> ~ ( ( less @ X1 @ X2 )
=> ( X1 != X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( more @ x @ y )
=> ~ ( less @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( x = y )
=> ~ ( more @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( less @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP2
=> ~ ( sP5
=> ~ sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( more @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: nat] :
~ ( ( ( x = X1 )
=> ~ ( more @ x @ X1 ) )
=> ( ( ( more @ x @ X1 )
=> ~ ( less @ x @ X1 ) )
=> ~ ( ( less @ x @ X1 )
=> ( x != X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(satz10g,conjecture,
~ ( ~ sP5
=> sP4 ) ).
thf(h0,negated_conjecture,
( ~ sP5
=> sP4 ),
inference(assume_negation,[status(cth)],[satz10g]) ).
thf(h1,assumption,
sP5,
introduced(assumption,[]) ).
thf(h2,assumption,
sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP7
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP6
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP8
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP9
| ~ sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP1
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(m,axiom,
sP7 ).
thf(satz10b,axiom,
sP1 ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,m,satz10b,h1]) ).
thf(7,plain,
( ~ sP3
| ~ sP4
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP8
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP9
| ~ sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP1
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h0])],[7,8,9,10,m,satz10b,h2]) ).
thf(12,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,6,11,h1,h2]) ).
thf(0,theorem,
~ ( ~ sP5
=> sP4 ),
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM656^1 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 22:17:23 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % Mode: mode213
% 0.14/0.40 % Inferences: 119
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------