%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO559^1 : TPTP v9.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 03:26:01 PM UTC 2025
% Result : Theorem 1.09s 1.41s
% Output : Proof 1.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_epso,type,
epso: ( $o > $o ) > $o ).
thf(ty_epsoo,type,
epsoo: ( ( $o > $o ) > $o ) > $o > $o ).
thf(sP1,plain,
( sP1
<=> ( epsoo @ epso @ $false ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( epsoo @ epso @ ( epso @ ( epsoo @ epso ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( epso @ ( epsoo @ epso ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o] :
~ ( epsoo @ epso @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> $false ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3 = ( ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $o] : ~ X1 ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( epsoo @ epso @ ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( epso
@ ^ [X1: $o] : X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP1
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( epso = epso ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $o > $o] :
~ ( epso @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(c,conjecture,
sP10 ).
thf(h0,negated_conjecture,
~ sP10,
inference(assume_negation,[status(cth)],[c]) ).
thf(1,plain,
( ~ sP7
| ~ sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(choiceaxo,axiom,
! [X1: $o > $o] :
( ~ ! [X2: $o] :
~ ( X1 @ X2 )
=> ( X1 @ ( epso @ X1 ) ) ) ).
thf(2,plain,
( sP9
| sP7 ),
inference(choice_rule,[status(thm)],[choiceaxo]) ).
thf(3,plain,
( ~ sP12
| ~ sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
~ sP5,
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP6
| ~ sP3
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
sP11,
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP4
| ~ sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP2
| sP8
| ~ sP11
| ~ sP6 ),
inference(mating_rule,[status(thm)],[]) ).
thf(9,plain,
( sP2
| sP4 ),
inference(choice_rule,[status(thm)],[choiceaxo]) ).
thf(choiceaxoo,axiom,
! [X1: ( $o > $o ) > $o] :
( ~ ! [X2: $o > $o] :
~ ( X1 @ X2 )
=> ( X1 @ ( epsoo @ X1 ) ) ) ).
thf(10,plain,
( sP3
| sP12 ),
inference(choice_rule,[status(thm)],[choiceaxoo]) ).
thf(11,plain,
( sP10
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP10
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h0]) ).
thf(0,theorem,
sP10,
inference(contra,[status(thm),contra(discharge,[h0])],[13,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO559^1 : TPTP v9.2.0. Released v5.2.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n013.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 : Thu Oct 9 01:37:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.09/1.41 % SZS status Theorem
% 1.09/1.41 % Mode: mode506
% 1.09/1.41 % Inferences: 58311
% 1.09/1.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------