%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM740^1 : 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 : n002.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 02:12:00 PM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_frac,type,
frac: $tType ).
thf(ty_y,type,
y: frac ).
thf(ty_eq,type,
eq: frac > frac > $o ).
thf(ty_moref,type,
moref: frac > frac > $o ).
thf(ty_lessf,type,
lessf: frac > frac > $o ).
thf(ty_x,type,
x: frac ).
thf(sP1,plain,
( sP1
<=> ( lessf @ y @ x ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eq @ x @ y )
=> ( eq @ y @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( moref @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eq @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP3
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: frac,X2: frac] :
( ( moref @ X1 @ X2 )
=> ( lessf @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eq @ y @ x ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: frac] :
( ( eq @ x @ X1 )
=> ( eq @ X1 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: frac] :
( ( moref @ x @ X1 )
=> ( lessf @ X1 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: frac,X2: frac] :
( ( eq @ X1 @ X2 )
=> ( eq @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(satz48,conjecture,
( ~ sP1
=> sP7 ) ).
thf(h0,negated_conjecture,
~ ( ~ sP1
=> sP7 ),
inference(assume_negation,[status(cth)],[satz48]) ).
thf(h1,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h3,assumption,
sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP9
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP5
| ~ sP3
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(satz42,axiom,
sP6 ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h1,h2,h0])],[1,2,3,h3,satz42,h1]) ).
thf(5,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP2
| ~ sP4
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(satz38,axiom,
sP10 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h1,h2,h0])],[5,6,7,h4,satz38,h2]) ).
thf(m,axiom,
( ~ sP3
=> sP4 ) ).
thf(9,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[m,4,8,h3,h4]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2]) ).
thf(0,theorem,
( ~ sP1
=> sP7 ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM740^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n002.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 : 300
% 0.12/0.33 % DateTime : Wed Oct 8 22:41:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 8
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------