%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : PHI045^6 : TPTP v9.2.0. Released v9.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n008.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 02:13:41 PM UTC 2025
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 30
% Syntax : Number of formulae : 35 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 84 ( 6 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 106 ( 38 ~; 14 |; 0 &; 21 @)
% ( 14 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 17 con; 0-2 aty)
% Number of variables : 18 ( 5 ^; 13 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_entity,type,
entity: $tType ).
thf(ty_eigen__1,type,
eigen__1: entity ).
thf(ty_positive_property,type,
positive_property: ( entity > $o ) > $o ).
thf(ty_god_like,type,
god_like: entity > $o ).
thf(h0,assumption,
! [X1: entity > $o,X2: entity] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: entity] :
~ ( $false
=> ( X1 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( positive_property @ god_like ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( sP1
=> ~ ! [X1: entity] :
~ ( god_like @ X1 ) )
=> ( positive_property
@ ^ [X1: entity] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( positive_property
@ ^ [X1: entity] : $false ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> ~ ! [X1: entity] :
~ ( god_like @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: entity] :
( $false
=> ( X1 != X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( sP3
=> ~ sP5 )
=> ( positive_property
@ ^ [X1: entity] : ( X1 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: entity > $o,X2: entity > $o] :
( ~ ( ( positive_property @ X1 )
=> ~ ! [X3: entity] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( positive_property @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( $false
=> ( eigen__1 != eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: entity] :
~ ( god_like @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: entity > $o] :
( ~ ( sP1
=> ~ ! [X2: entity] :
( ( god_like @ X2 )
=> ( X1 @ X2 ) ) )
=> ( positive_property @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: entity > $o] :
( ~ ( sP3
=> ~ ! [X2: entity] :
( $false
=> ( X1 @ X2 ) ) )
=> ( positive_property @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> $false ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( positive_property
@ ^ [X1: entity] : ( X1 != X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP3
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(conj_1,conjecture,
~ sP9 ).
thf(h1,negated_conjecture,
sP9,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(1,plain,
( sP8
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP5
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(3,plain,
( ~ sP11
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP6
| sP14
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP14
| ~ sP3
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
~ sP12,
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP7
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP2
| sP4
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP4
| ~ sP1
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(coro1,axiom,
~ sP13 ).
thf(coro2,axiom,
sP7 ).
thf(axiom3,axiom,
sP1 ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,coro1,coro2,axiom3,h1]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0]) ).
thf(0,theorem,
~ sP9,
inference(contra,[status(thm),contra(discharge,[h1])],[12,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : PHI045^6 : TPTP v9.2.0. Released v9.0.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n008.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 23:18:08 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % Mode: mode213
% 0.14/0.39 % Inferences: 22
% 0.14/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------