TSTP Solution File: SET724^4 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET724^4 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 Aug 31 15:18:22 EDT 2023
% Result : Theorem 0.20s 0.58s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 50
% Syntax : Number of formulae : 63 ( 26 unt; 5 typ; 10 def)
% Number of atoms : 123 ( 46 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 192 ( 49 ~; 17 |; 3 &; 92 @)
% ( 14 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 27 con; 0-2 aty)
% Number of variables : 72 ( 36 ^; 33 !; 3 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i > $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
( ( eigen__2 @ eigen__3 )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
( eigen__3
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
~ ! [X2: $i] :
( X1
!= ( eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__3
= ( eigen__0 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__2 @ ( eigen__0 @ eigen__4 ) )
= ( eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__1 @ ( eigen__0 @ eigen__4 ) )
= ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0 @ eigen__4 )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( eigen__3
!= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__2 @ eigen__3 )
= ( eigen__0 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ^ [X1: $i] : ( eigen__1 @ ( eigen__0 @ X1 ) ) )
= ( ^ [X1: $i] : ( eigen__2 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__1 @ eigen__3 )
= ( eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__2 @ eigen__3 )
= ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eigen__2 @ eigen__3 )
!= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( eigen__1 @ ( eigen__0 @ X1 ) )
= ( eigen__2 @ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> $false ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__1 @ ( eigen__0 @ eigen__4 ) )
= ( eigen__2 @ ( eigen__0 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(def_fun_image,definition,
( fun_image
= ( ^ [X1: $i > $i,X2: $i > $o,X3: $i] :
? [X4: $i] :
( ( X2 @ X4 )
& ( X3
= ( X1 @ X4 ) ) ) ) ) ).
thf(def_fun_composition,definition,
( fun_composition
= ( ^ [X1: $i > $i,X2: $i > $i,X3: $i] : ( X2 @ ( X1 @ X3 ) ) ) ) ).
thf(def_fun_inv_image,definition,
( fun_inv_image
= ( ^ [X1: $i > $i,X2: $i > $o,X3: $i] :
? [X4: $i] :
( ( X2 @ X4 )
& ( X4
= ( X1 @ X3 ) ) ) ) ) ).
thf(def_fun_injective,definition,
( fun_injective
= ( ^ [X1: $i > $i] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( ( X1 @ X2 )
= ( X1 @ X3 ) )
@ ( X2 = X3 ) ) ) ) ).
thf(def_fun_surjective,definition,
( fun_surjective
= ( ^ [X1: $i > $i] :
! [X2: $i] :
? [X3: $i] :
( X2
= ( X1 @ X3 ) ) ) ) ).
thf(def_fun_bijective,definition,
( fun_bijective
= ( ^ [X1: $i > $i] :
( ( fun_injective @ X1 )
& ( fun_surjective @ X1 ) ) ) ) ).
thf(def_fun_decreasing,definition,
( fun_decreasing
= ( ^ [X1: $i > $i,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X2 @ X3 @ X4 )
@ ( X2 @ ( X1 @ X4 ) @ ( X1 @ X3 ) ) ) ) ) ).
thf(def_fun_increasing,definition,
( fun_increasing
= ( ^ [X1: $i > $i,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X2 @ X3 @ X4 )
@ ( X2 @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) ) ) ) ).
thf(thm,conjecture,
! [X1: $i > $i,X2: $i > $i,X3: $i > $i] :
( ~ ( ( ( ^ [X4: $i] : ( X2 @ ( X1 @ X4 ) ) )
= ( ^ [X4: $i] : ( X3 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X1 @ X5 ) ) )
=> ( X2 = X3 ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $i,X2: $i > $i,X3: $i > $i] :
( ~ ( ( ( ^ [X4: $i] : ( X2 @ ( X1 @ X4 ) ) )
= ( ^ [X4: $i] : ( X3 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X1 @ X5 ) ) )
=> ( X2 = X3 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h2,assumption,
~ ! [X1: $i > $i,X2: $i > $i] :
( ~ ( ( ( ^ [X3: $i] : ( X1 @ ( eigen__0 @ X3 ) ) )
= ( ^ [X3: $i] : ( X2 @ ( eigen__0 @ X3 ) ) ) )
=> ~ sP1 )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $i] :
( ~ ( ( ( ^ [X2: $i] : ( eigen__1 @ ( eigen__0 @ X2 ) ) )
= ( ^ [X2: $i] : ( X1 @ ( eigen__0 @ X2 ) ) ) )
=> ~ sP1 )
=> ( eigen__1 = X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( sP8
=> ~ sP1 )
=> ( eigen__1 = eigen__2 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP8
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h6,assumption,
eigen__1 != eigen__2,
introduced(assumption,[]) ).
thf(h7,assumption,
sP8,
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( eigen__1 @ X1 )
= ( eigen__2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(1,plain,
( sP3
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP4
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP14
| sP10
| ~ sP3
| ~ sP4 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP5
| ~ sP2
| sP13 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP7
| sP9
| ~ sP10
| sP13 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(7,plain,
~ sP13,
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP11
| sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(9,plain,
( ~ sP1
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( sP6
| sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(11,plain,
( ~ sP1
| ~ sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP8
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h7,h8,h10]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,13,h10]) ).
thf(15,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_fe(discharge,[h9])],[h6,14,h9]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,15,h7,h8]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,16,h5,h6]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,17,h4]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,18,h3]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,19,h2]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[20,h0]) ).
thf(0,theorem,
! [X1: $i > $i,X2: $i > $i,X3: $i > $i] :
( ~ ( ( ( ^ [X4: $i] : ( X2 @ ( X1 @ X4 ) ) )
= ( ^ [X4: $i] : ( X3 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( X4
!= ( X1 @ X5 ) ) )
=> ( X2 = X3 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[20,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.17 % Problem : SET724^4 : TPTP v8.1.2. Released v3.6.0.
% 0.14/0.17 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.38 % Computer : n026.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sat Aug 26 16:17:19 EDT 2023
% 0.14/0.38 % CPUTime :
% 0.20/0.58 % SZS status Theorem
% 0.20/0.58 % Mode: cade22grackle2xfee4
% 0.20/0.58 % Steps: 3535
% 0.20/0.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------