TSTP Solution File: PUZ140^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : PUZ140^1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 : Mon Jul 18 18:26:06 EDT 2022
% Result : Theorem 33.24s 33.48s
% Output : Proof 33.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 36
% Syntax : Number of formulae : 43 ( 14 unt; 7 typ; 4 def)
% Number of atoms : 90 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 95 ( 26 ~; 11 |; 0 &; 39 @)
% ( 12 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 22 con; 0-2 aty)
% Number of variables : 27 ( 4 ^ 14 !; 0 ?; 27 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_syrup,type,
syrup: $tType ).
thf(ty_beverage,type,
beverage: $tType ).
thf(ty_eigen__0,type,
eigen__0: beverage ).
thf(ty_heat,type,
heat: beverage > beverage ).
thf(ty_eigen__3,type,
eigen__3: beverage ).
thf(ty_coffee,type,
coffee: beverage ).
thf(ty_hot,type,
hot: beverage > $o ).
thf(h0,assumption,
! [X1: beverage > $o,X2: beverage] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: beverage] :
( ( hot @ X1 )
!= ( hot @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: syrup > $o,X2: syrup] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: syrup] :
~ ~ ! [X2: beverage] :
( ( ( @+[X3: beverage] : ( hot @ X3 ) )
= X2 )
=> ~ ( hot @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: beverage] : ( hot @ ( heat @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( @+[X1: beverage] : ( hot @ X1 ) )
= ( @+[X1: beverage] : ( hot @ X1 ) ) )
=> ~ ( hot
@ @+[X1: beverage] : ( hot @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: beverage] :
( ( hot @ X1 )
= ( hot @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: syrup] :
~ ! [X2: beverage] :
( ( ( @+[X3: beverage] : ( hot @ X3 ) )
= X2 )
=> ~ ( hot @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( @+[X1: beverage] : ( hot @ X1 ) )
= ( @+[X1: beverage] : ( hot @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: beverage] :
( ( ( @+[X2: beverage] : ( hot @ X2 ) )
= X1 )
=> ~ ( hot @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( hot = hot ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( hot @ eigen__3 )
= ( hot @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: beverage > syrup > beverage] :
~ ! [X2: syrup] :
~ ! [X3: beverage] :
( ( ( X1 @ coffee @ X2 )
= X3 )
=> ~ ( hot @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: beverage] :
~ ( hot @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( hot
@ @+[X1: beverage] : ( hot @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( hot @ ( heat @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(def_cold_mixture,definition,
cold_mixture = mix ).
thf(def_hot_mixture,definition,
( hot_mixture
= ( ^ [X1: beverage,X2: syrup] : ( heat @ ( mix @ X1 @ X2 ) ) ) ) ).
thf(hot_coffee,conjecture,
~ sP9 ).
thf(h2,negated_conjecture,
sP9,
inference(assume_negation,[status(cth)],[hot_coffee]) ).
thf(1,plain,
( ~ sP2
| ~ sP5
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
sP8,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP3
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(4,plain,
( sP7
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP5
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| ~ sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP11
| sP10 ),
inference(choice_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP4
| sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(10,plain,
( ~ sP9
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(its_hot,axiom,
sP1 ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,its_hot,h2]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[12,h1]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[13,h0]) ).
thf(0,theorem,
~ sP9,
inference(contra,[status(thm),contra(discharge,[h2])],[12,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : PUZ140^1 : TPTP v8.1.0. Released v6.1.0.
% 0.09/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun May 29 02:33:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 33.24/33.48 % SZS status Theorem
% 33.24/33.48 % Mode: mode448
% 33.24/33.48 % Inferences: 1979
% 33.24/33.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------