TSTP Solution File: SEU864^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU864^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n032.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 : 600s
% DateTime : Tue Jul 19 14:10:36 EDT 2022
% Result : Theorem 35.32s 35.51s
% Output : Proof 35.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 42
% Syntax : Number of formulae : 49 ( 12 unt; 4 typ; 2 def)
% Number of atoms : 130 ( 31 equ; 5 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 147 ( 40 ~; 22 |; 0 &; 36 @)
% ( 17 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 23 con; 0-2 aty)
% Number of variables : 29 ( 14 ^ 15 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: ( a > $o ) > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_t,type,
t: a ).
thf(h0,assumption,
! [X1: ( ( a > $o ) > $o ) > $o,X2: ( a > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: ( a > $o ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ ( (=) @ t ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: a] :
( ( ~ $false
=> ( t = X1 ) )
!= ( t = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ( eigen__0
@ ^ [X1: a] : $false )
=> ~ ! [X1: a > $o] :
( ( eigen__0 @ X1 )
=> ! [X2: a] :
( ( t = X2 )
=> ( eigen__0
@ ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) )
=> ( eigen__0 @ ( (=) @ t ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( t = t )
=> ( eigen__0
@ ^ [X1: a] :
( ~ $false
=> ( t = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0
@ ^ [X1: a] : $false ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( ( eigen__0 @ X1 )
=> ! [X2: a] :
( ( t = X2 )
=> ( eigen__0
@ ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( t = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( t = t ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ~ $false
=> sP5 )
= sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( ~ $false
=> ( t = X1 ) )
= ( t = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ $false
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ^ [X1: a] :
( ~ $false
=> ( t = X1 ) ) )
= ( (=) @ t ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( t = X1 )
=> ( eigen__0
@ ^ [X2: a] :
( ~ $false
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> $false ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP3
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: ( a > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : sP12 )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ ( (=) @ t ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0
@ ^ [X1: a] :
( ~ sP12
=> ( t = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP3
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ ( (=) @ t ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cDOMLEMMA1_pme,conjecture,
sP14 ).
thf(h2,negated_conjecture,
~ sP14,
inference(assume_negation,[status(cth)],[cDOMLEMMA1_pme]) ).
thf(1,plain,
( ~ sP9
| sP12
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP9
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP7
| ~ sP9
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP7
| sP9
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP8
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(6,plain,
( sP10
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP15
| sP17
| ~ sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP2
| ~ sP6
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
~ sP12,
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
sP6,
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP11
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| ~ sP3
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP4
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP13
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP13
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP1
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP1
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP14
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h2]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[19,h1]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[20,h0]) ).
thf(0,theorem,
sP14,
inference(contra,[status(thm),contra(discharge,[h2])],[19,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : SEU864^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.10 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Sun Jun 19 01:29:32 EDT 2022
% 0.09/0.29 % CPUTime :
% 35.32/35.51 % SZS status Theorem
% 35.32/35.51 % Mode: mode466
% 35.32/35.51 % Inferences: 56912
% 35.32/35.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------