%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV225^5 : TPTP v9.2.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 02:56:29 PM UTC 2025
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_r,type,
r: $tType ).
thf(ty_eigen__0,type,
eigen__0: r ).
thf(ty_less,type,
less: r > r > $o ).
thf(ty_c0,type,
c0: r ).
thf(sP1,plain,
( sP1
<=> ( less @ eigen__0 @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 = c0 )
=> ( c0 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: r,X2: r] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: r] :
( ( eigen__0 = X1 )
=> ( X1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( less @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: r] :
~ ( less @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 = c0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( c0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(def_cIRREFLEXIVE_LAW,definition,
cIRREFLEXIVE_LAW = sP6 ).
thf(cPARNAS_FIG3_A,conjecture,
( sP6
=> ! [X1: r] :
( ( less @ X1 @ c0 )
=> ( X1 != c0 ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP6
=> ! [X1: r] :
( ( less @ X1 @ c0 )
=> ( X1 != c0 ) ) ),
inference(assume_negation,[status(cth)],[cPARNAS_FIG3_A]) ).
thf(h1,assumption,
sP6,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: r] :
( ( less @ X1 @ c0 )
=> ( X1 != c0 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP1
=> ~ sP7 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
sP7,
introduced(assumption,[]) ).
thf(1,plain,
sP9,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP1
| sP5
| ~ sP9
| ~ sP8 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP6
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP2
| ~ sP7
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
sP3,
inference(eq_sym,[status(thm)],[]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h1,h2,h0])],[1,2,3,4,5,6,7,h1,h4,h5]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,8,h4,h5]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,9,h3]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,10,h1,h2]) ).
thf(0,theorem,
( sP6
=> ! [X1: r] :
( ( less @ X1 @ c0 )
=> ( X1 != c0 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEV225^5 : TPTP v9.2.0. Bugfixed v5.3.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n028.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 19:16:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 15
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------