TSTP Solution File: SET753^4 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET753^4 : 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 : 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 : 300s
% DateTime : Thu Aug 31 15:18:30 EDT 2023
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(sP1,plain,
( sP1
<=> ( eigen__3
= ( eigen__2 @ eigen__4 ) ) ),
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
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( eigen__3
!= ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__1 @ eigen__4 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP2
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__4 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
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 ) ) )
=> ~ ( ~ ! [X5: $i] :
( ( X1 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) )
=> ! [X5: $i] :
( ( X2 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $i,X4: $i] :
( ~ ! [X5: $i] :
( ~ ( ( X1 @ X5 )
=> ~ ( X2 @ X5 ) )
=> ( X4
!= ( X3 @ X5 ) ) )
=> ~ ( ~ ! [X5: $i] :
( ( X1 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) )
=> ! [X5: $i] :
( ( X2 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ! [X1: $i > $o,X2: $i > $i,X3: $i] :
( ~ ! [X4: $i] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X1 @ X4 ) )
=> ( X3
!= ( X2 @ X4 ) ) )
=> ~ ( ~ ! [X4: $i] :
( ( eigen__0 @ X4 )
=> ( X3
!= ( X2 @ X4 ) ) )
=> ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i > $i,X2: $i] :
( ~ ! [X3: $i] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( eigen__1 @ X3 ) )
=> ( X2
!= ( X1 @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( X2
!= ( X1 @ X3 ) ) )
=> ! [X3: $i] :
( ( eigen__1 @ X3 )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,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(h4,assumption,
~ ( ~ ! [X1: $i] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) )
=> ( eigen__3
!= ( eigen__2 @ X1 ) ) )
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) )
=> ( eigen__3
!= ( eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP6,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( sP8
=> ~ sP5 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP8
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
sP8,
introduced(assumption,[]) ).
thf(h11,assumption,
sP5,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| ~ sP8
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| ~ sP5
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP6
| sP2
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,h10,h11,h9,h6]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,6,h10,h11]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,7,h8,h9]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__4)],[h5,8,h7]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,9,h5,h6]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,10,h4]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,11,h3]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,12,h2]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1]) ).
thf(0,theorem,
! [X1: $i > $o,X2: $i > $o,X3: $i > $i,X4: $i] :
( ~ ! [X5: $i] :
( ~ ( ( X1 @ X5 )
=> ~ ( X2 @ X5 ) )
=> ( X4
!= ( X3 @ X5 ) ) )
=> ~ ( ~ ! [X5: $i] :
( ( X1 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) )
=> ! [X5: $i] :
( ( X2 @ X5 )
=> ( X4
!= ( X3 @ X5 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET753^4 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 15:08:44 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % Mode: cade22grackle2xfee4
% 0.20/0.40 % Steps: 22
% 0.20/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------