TSTP Solution File: SWW470^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SWW470^1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 : Thu Jul 21 01:21:51 EDT 2022
% Result : Theorem 51.21s 51.43s
% Output : Proof 51.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 53
% Syntax : Number of formulae : 60 ( 14 unt; 14 typ; 2 def)
% Number of atoms : 192 ( 2 equ; 0 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 393 ( 53 ~; 17 |; 0 &; 238 @)
% ( 18 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 24 con; 0-3 aty)
% Number of variables : 93 ( 24 ^ 69 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_com,type,
com: $tType ).
thf(ty_state,type,
state: $tType ).
thf(ty_x_a,type,
x_a: $tType ).
thf(ty_hoare_669141180iple_a,type,
hoare_669141180iple_a: $tType ).
thf(ty_p,type,
p: x_a > state > $o ).
thf(ty_insert175534902iple_a,type,
insert175534902iple_a: hoare_669141180iple_a > ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a > $o ).
thf(ty_eigen__1,type,
eigen__1: state ).
thf(ty_eigen__0,type,
eigen__0: x_a ).
thf(ty_b,type,
b: state > $o ).
thf(ty_hoare_2128652938rivs_a,type,
hoare_2128652938rivs_a: ( hoare_669141180iple_a > $o ) > ( hoare_669141180iple_a > $o ) > $o ).
thf(ty_hoare_1295064928iple_a,type,
hoare_1295064928iple_a: ( x_a > state > $o ) > com > ( x_a > state > $o ) > hoare_669141180iple_a ).
thf(ty_bot_bo280939947le_a_o,type,
bot_bo280939947le_a_o: hoare_669141180iple_a > $o ).
thf(ty_c,type,
c: com ).
thf(ty_g,type,
g: hoare_669141180iple_a > $o ).
thf(h0,assumption,
! [X1: state > $o,X2: state] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: state] :
~ ( $false
=> ~ ! [X2: x_a > state > $o,X3: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X2 @ c @ X3 ) @ bot_bo280939947le_a_o ) )
=> ~ ! [X4: state] :
( ! [X5: x_a] :
( ( X2 @ X5 @ X1 )
=> ( X3 @ X5 @ X4 ) )
=> ~ ( ( p @ eigen__0 @ X4 )
=> ( b @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: x_a > $o,X2: x_a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: x_a] :
~ ! [X2: state] :
( $false
=> ~ ! [X3: x_a > state > $o,X4: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X3 @ c @ X4 ) @ bot_bo280939947le_a_o ) )
=> ~ ! [X5: state] :
( ! [X6: x_a] :
( ( X3 @ X6 @ X2 )
=> ( X4 @ X6 @ X5 ) )
=> ~ ( ( p @ X1 @ X5 )
=> ( b @ X5 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( hoare_2128652938rivs_a @ g @ bot_bo280939947le_a_o ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: x_a > state > $o,X2: hoare_669141180iple_a > $o,X3: com,X4: x_a > state > $o] :
( ! [X5: x_a,X6: state] :
( ( X4 @ X5 @ X6 )
=> ~ ! [X7: x_a > state > $o,X8: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ X2 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X7 @ X3 @ X8 ) @ bot_bo280939947le_a_o ) )
=> ~ ! [X9: state] :
( ! [X10: x_a] :
( ( X7 @ X10 @ X6 )
=> ( X8 @ X10 @ X9 ) )
=> ( X1 @ X5 @ X9 ) ) ) )
=> ( hoare_2128652938rivs_a @ X2 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X4 @ X3 @ X1 ) @ bot_bo280939947le_a_o ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [X1: x_a,X2: state] : $false
@ c
@ ^ [X1: x_a,X2: state] :
~ ( ( p @ X1 @ X2 )
=> ( b @ X2 ) ) )
@ bot_bo280939947le_a_o ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: x_a,X2: state] :
( $false
=> ~ ! [X3: x_a > state > $o,X4: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X3 @ c @ X4 ) @ bot_bo280939947le_a_o ) )
=> ~ ! [X5: state] :
( ! [X6: x_a] :
( ( X3 @ X6 @ X2 )
=> ( X4 @ X6 @ X5 ) )
=> ~ ( ( p @ X1 @ X5 )
=> ( b @ X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: hoare_669141180iple_a > $o,X2: hoare_669141180iple_a > $o] :
( ( hoare_2128652938rivs_a @ X1 @ X2 )
=> ( ( hoare_2128652938rivs_a @ g @ X1 )
=> ( hoare_2128652938rivs_a @ g @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [X1: x_a,X2: state] : $false
@ c
@ ^ [X1: x_a,X2: state] :
~ ( ( p @ X1 @ X2 )
=> ( b @ X2 ) ) )
@ bot_bo280939947le_a_o ) )
=> ( sP1
=> sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> $false ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: state] :
( sP7
=> ~ ! [X2: x_a > state > $o,X3: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X2 @ c @ X3 ) @ bot_bo280939947le_a_o ) )
=> ~ ! [X4: state] :
( ! [X5: x_a] :
( ( X2 @ X5 @ X1 )
=> ( X3 @ X5 @ X4 ) )
=> ~ ( ( p @ eigen__0 @ X4 )
=> ( b @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: hoare_669141180iple_a > $o] :
( ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o @ X1 )
=> ( sP1
=> ( hoare_2128652938rivs_a @ g @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP1
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: x_a > state > $o] :
( ! [X2: x_a,X3: state] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: x_a > state > $o,X5: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X4 @ c @ X5 ) @ bot_bo280939947le_a_o ) )
=> ~ ! [X6: state] :
( ! [X7: x_a] :
( ( X4 @ X7 @ X3 )
=> ( X5 @ X7 @ X6 ) )
=> ~ ( ( p @ X2 @ X6 )
=> ( b @ X6 ) ) ) ) )
=> ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a @ X1 @ c
@ ^ [X2: x_a,X3: state] :
~ ( ( p @ X2 @ X3 )
=> ( b @ X3 ) ) )
@ bot_bo280939947le_a_o ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP7
=> ~ ! [X1: x_a > state > $o,X2: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X1 @ c @ X2 ) @ bot_bo280939947le_a_o ) )
=> ~ ! [X3: state] :
( ! [X4: x_a] :
( ( X1 @ X4 @ eigen__1 )
=> ( X2 @ X4 @ X3 ) )
=> ~ ( ( p @ eigen__0 @ X3 )
=> ( b @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: hoare_669141180iple_a > $o,X2: com,X3: x_a > state > $o] :
( ! [X4: x_a,X5: state] :
( ( X3 @ X4 @ X5 )
=> ~ ! [X6: x_a > state > $o,X7: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ X1 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X6 @ X2 @ X7 ) @ bot_bo280939947le_a_o ) )
=> ~ ! [X8: state] :
( ! [X9: x_a] :
( ( X6 @ X9 @ X5 )
=> ( X7 @ X9 @ X8 ) )
=> ~ ( ( p @ X4 @ X8 )
=> ( b @ X8 ) ) ) ) )
=> ( hoare_2128652938rivs_a @ X1
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a @ X3 @ X2
@ ^ [X4: x_a,X5: state] :
~ ( ( p @ X4 @ X5 )
=> ( b @ X5 ) ) )
@ bot_bo280939947le_a_o ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: hoare_669141180iple_a > $o,X2: hoare_669141180iple_a > $o,X3: hoare_669141180iple_a > $o] :
( ( hoare_2128652938rivs_a @ X2 @ X3 )
=> ( ( hoare_2128652938rivs_a @ X1 @ X2 )
=> ( hoare_2128652938rivs_a @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: hoare_669141180iple_a > $o] : ( hoare_2128652938rivs_a @ X1 @ bot_bo280939947le_a_o ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP4
=> ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [X1: x_a,X2: state] : sP7
@ c
@ ^ [X1: x_a,X2: state] :
~ ( ( p @ X1 @ X2 )
=> ( b @ X2 ) ) )
@ bot_bo280939947le_a_o ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [X1: x_a,X2: state] : sP7
@ c
@ ^ [X1: x_a,X2: state] :
~ ( ( p @ X1 @ X2 )
=> ( b @ X2 ) ) )
@ bot_bo280939947le_a_o ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: com,X2: x_a > state > $o] :
( ! [X3: x_a,X4: state] :
( ( X2 @ X3 @ X4 )
=> ~ ! [X5: x_a > state > $o,X6: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X5 @ X1 @ X6 ) @ bot_bo280939947le_a_o ) )
=> ~ ! [X7: state] :
( ! [X8: x_a] :
( ( X5 @ X8 @ X4 )
=> ( X6 @ X8 @ X7 ) )
=> ~ ( ( p @ X3 @ X7 )
=> ( b @ X7 ) ) ) ) )
=> ( hoare_2128652938rivs_a @ bot_bo280939947le_a_o
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a @ X2 @ X1
@ ^ [X3: x_a,X4: state] :
~ ( ( p @ X3 @ X4 )
=> ( b @ X4 ) ) )
@ bot_bo280939947le_a_o ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(conj_0,conjecture,
sP3 ).
thf(h2,negated_conjecture,
~ sP3,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
~ sP7,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP12
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP8
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(4,plain,
( sP4
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(5,plain,
( ~ sP13
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP18
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP11
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP16
| ~ sP4
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP5
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP9
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| ~ sP17
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| ~ sP1
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP15
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP14
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP2
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_60_conseq,axiom,
sP2 ).
thf(fact_2_cut,axiom,
sP14 ).
thf(fact_0_empty,axiom,
sP15 ).
thf(16,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,h2,fact_60_conseq,fact_2_cut,fact_0_empty]) ).
thf(17,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[16,h1]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[17,h0]) ).
thf(0,theorem,
sP3,
inference(contra,[status(thm),contra(discharge,[h2])],[16,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW470^1 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 5 02:01:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 51.21/51.43 % SZS status Theorem
% 51.21/51.43 % Mode: mode94:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
% 51.21/51.43 % Inferences: 114
% 51.21/51.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------