TSTP Solution File: SET752^4 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET752^4 : 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 : n018.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 15:18:30 EDT 2023
% Result : Theorem 0.20s 0.63s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 83
% Syntax : Number of formulae : 99 ( 53 unt; 7 typ; 24 def)
% Number of atoms : 235 ( 74 equ; 5 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 351 ( 100 ~; 27 |; 9 &; 138 @)
% ( 20 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 50 usr; 49 con; 0-2 aty)
% Number of variables : 122 ( 70 ^; 47 !; 5 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i > $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__1 @ X1 )
=> ( eigen__3
!= ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__3
!= ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__0 @ eigen__5 )
=> ( eigen__3
!= ( eigen__2 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__3
!= ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( eigen__0 @ eigen__6 )
=> ( eigen__1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> ( eigen__3
!= ( eigen__2 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP4
=> ( eigen__3
!= ( eigen__2 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__1 @ eigen__6 )
=> ( eigen__3
!= ( eigen__2 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ( eigen__3
!= ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__1 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__3
= ( eigen__2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__3
= ( eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( eigen__3
!= ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP5
=> ( eigen__1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP2
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP7
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP15
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP4
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__3
= ( eigen__2 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(def_in,definition,
( in
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_is_a,definition,
( is_a
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_emptyset,definition,
( emptyset
= ( ^ [X1: $i] : $false ) ) ).
thf(def_unord_pair,definition,
( unord_pair
= ( ^ [X1: $i,X2: $i,X3: $i] :
( ( X3 = X1 )
| ( X3 = X2 ) ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).
thf(def_union,definition,
( union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_excl_union,definition,
( excl_union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
& ( (~) @ ( X2 @ X3 ) ) )
| ( ( (~) @ ( X1 @ X3 ) )
& ( X2 @ X3 ) ) ) ) ) ).
thf(def_intersection,definition,
( intersection
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_setminus,definition,
( setminus
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( (~) @ ( X2 @ X3 ) ) ) ) ) ).
thf(def_complement,definition,
( complement
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_disjoint,definition,
( disjoint
= ( ^ [X1: $i > $o,X2: $i > $o] :
( ( intersection @ X1 @ X2 )
= emptyset ) ) ) ).
thf(def_subset,definition,
( subset
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_meets,definition,
( meets
= ( ^ [X1: $i > $o,X2: $i > $o] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_misses,definition,
( misses
= ( ^ [X1: $i > $o,X2: $i > $o] :
( (~)
@ ? [X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ) ).
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 > $o,X2: $i > $o,X3: $i > $i] :
( ( ^ [X4: $i] :
~ ! [X5: $i] :
( ( ~ ( X1 @ X5 )
=> ( X2 @ X5 ) )
=> ( X4
!= ( X3 @ X5 ) ) ) )
= ( ^ [X4: $i] :
( ! [X5: $i] :
( ( X1 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $i] :
( ( ^ [X4: $i] :
~ ! [X5: $i] :
( ( ~ ( X1 @ X5 )
=> ( X2 @ X5 ) )
=> ( X4
!= ( X3 @ X5 ) ) ) )
= ( ^ [X4: $i] :
( ! [X5: $i] :
( ( X1 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h2,assumption,
~ ! [X1: $i > $o,X2: $i > $i] :
( ( ^ [X3: $i] :
~ ! [X4: $i] :
( ( ~ ( eigen__0 @ X4 )
=> ( X1 @ X4 ) )
=> ( X3
!= ( X2 @ X4 ) ) ) )
= ( ^ [X3: $i] :
( ! [X4: $i] :
( ( eigen__0 @ X4 )
=> ( X3
!= ( X2 @ X4 ) ) )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $i] :
( ( ^ [X2: $i] :
~ ! [X3: $i] :
( ( ~ ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 ) )
=> ( X2
!= ( X1 @ X3 ) ) ) )
= ( ^ [X2: $i] :
( ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( X2
!= ( X1 @ X3 ) ) )
=> ~ ! [X3: $i] :
( ( eigen__1 @ X3 )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ( ^ [X1: $i] :
~ ! [X2: $i] :
( ( ~ ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ( X1
!= ( eigen__2 @ X2 ) ) ) )
!= ( ^ [X1: $i] :
( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1
!= ( eigen__2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1
!= ( eigen__2 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( ~ ! [X2: $i] :
( ( ~ ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ( X1
!= ( eigen__2 @ X2 ) ) ) )
= ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1
!= ( eigen__2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1
!= ( eigen__2 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ sP10 != sP16 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h8,assumption,
sP16,
introduced(assumption,[]) ).
thf(h9,assumption,
sP10,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP19
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP19,
introduced(assumption,[]) ).
thf(h13,assumption,
sP12,
introduced(assumption,[]) ).
thf(h14,assumption,
sP2,
introduced(assumption,[]) ).
thf(h15,assumption,
sP14,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP17
| ~ sP7
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| ~ sP4
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP14
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP19
| sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h12,h13,h11,h7,h8,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,h12,h13,h14,h15]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h8,6,h14,h15]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,7,h12,h13]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__4)],[h7,8,h11]) ).
thf(10,plain,
( sP3
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| ~ sP3
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP15
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP18
| ~ sP15
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP10
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( sP9
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP9
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP1
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP1
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP14
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(21,plain,
( sP2
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(22,plain,
( ~ sP16
| ~ sP2
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h6,h5,h4,h3,h2,h1,h0])],[10,11,12,13,14,15,16,17,18,19,20,21,22,h9,h10]) ).
thf(24,plain,
$false,
inference(tab_be,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h7,h8]),tab_be(discharge,[h9,h10])],[h6,9,23,h7,h8,h9,h10]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,24,h6]) ).
thf(26,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_fe(discharge,[h5])],[h4,25,h5]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,26,h4]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,27,h3]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,28,h2]) ).
thf(30,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[29,h0]) ).
thf(0,theorem,
! [X1: $i > $o,X2: $i > $o,X3: $i > $i] :
( ( ^ [X4: $i] :
~ ! [X5: $i] :
( ( ~ ( X1 @ X5 )
=> ( X2 @ X5 ) )
=> ( X4
!= ( X3 @ X5 ) ) ) )
= ( ^ [X4: $i] :
( ! [X5: $i] :
( ( X1 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[29,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET752^4 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.17/0.35 % Computer : n018.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sat Aug 26 15:06:00 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.63 % SZS status Theorem
% 0.20/0.63 % Mode: cade22grackle2xfee4
% 0.20/0.63 % Steps: 3578
% 0.20/0.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------