TSTP Solution File: SET716^4 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET716^4 : 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 : n025.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 15:18:19 EDT 2023
% Result : Theorem 0.17s 0.38s
% Output : Proof 0.17s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__1 @ ( eigen__0 @ eigen__2 ) )
= ( eigen__1 @ ( eigen__0 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ( ( eigen__0 @ eigen__2 )
= ( eigen__0 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( ( eigen__0 @ eigen__2 )
= ( eigen__0 @ X1 ) )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0 @ eigen__2 )
= ( eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP4
=> ( eigen__2 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( ( eigen__1 @ ( eigen__0 @ eigen__2 ) )
= ( eigen__1 @ X1 ) )
=> ( ( eigen__0 @ eigen__2 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ( ( eigen__1 @ X1 )
= ( eigen__1 @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__2 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( ( eigen__0 @ X1 )
= ( eigen__0 @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
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,X4: $i] :
( ( ( X1 @ X3 )
= ( X1 @ X4 ) )
=> ( X3 = X4 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( ( X2 @ X3 )
= ( X2 @ X4 ) )
=> ( X3 = X4 ) ) )
=> ! [X3: $i,X4: $i] :
( ( ( X2 @ ( X1 @ X3 ) )
= ( X2 @ ( X1 @ X4 ) ) )
=> ( X3 = X4 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i,X2: $i > $i] :
( ~ ( ! [X3: $i,X4: $i] :
( ( ( X1 @ X3 )
= ( X1 @ X4 ) )
=> ( X3 = X4 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( ( X2 @ X3 )
= ( X2 @ X4 ) )
=> ( X3 = X4 ) ) )
=> ! [X3: $i,X4: $i] :
( ( ( X2 @ ( X1 @ X3 ) )
= ( X2 @ ( X1 @ X4 ) ) )
=> ( X3 = X4 ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ! [X1: $i > $i] :
( ~ ( sP9
=> ~ ! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) ) )
=> ! [X2: $i,X3: $i] :
( ( ( X1 @ ( eigen__0 @ X2 ) )
= ( X1 @ ( eigen__0 @ X3 ) ) )
=> ( X2 = X3 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ( sP9
=> ~ sP7 )
=> ! [X1: $i,X2: $i] :
( ( ( eigen__1 @ ( eigen__0 @ X1 ) )
= ( eigen__1 @ ( eigen__0 @ X2 ) ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP9
=> ~ sP7 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i] :
( ( ( eigen__1 @ ( eigen__0 @ X1 ) )
= ( eigen__1 @ ( eigen__0 @ X2 ) ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP9,
introduced(assumption,[]) ).
thf(h6,assumption,
sP7,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( ( eigen__1 @ ( eigen__0 @ eigen__2 ) )
= ( eigen__1 @ ( eigen__0 @ X1 ) ) )
=> ( eigen__2 = X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP1
=> sP8 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP1
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| ~ sP4
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,h5,h6,h9,h10]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,7,h9,h10]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,8,h8]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h4,9,h7]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,10,h5,h6]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,11,h3,h4]) ).
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 > $i,X2: $i > $i] :
( ~ ( ! [X3: $i,X4: $i] :
( ( ( X1 @ X3 )
= ( X1 @ X4 ) )
=> ( X3 = X4 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( ( X2 @ X3 )
= ( X2 @ X4 ) )
=> ( X3 = X4 ) ) )
=> ! [X3: $i,X4: $i] :
( ( ( X2 @ ( X1 @ X3 ) )
= ( X2 @ ( X1 @ X4 ) ) )
=> ( X3 = X4 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET716^4 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.32 % Computer : n025.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat Aug 26 14:19:52 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.17/0.38 % SZS status Theorem
% 0.17/0.38 % Mode: cade22grackle2xfee4
% 0.17/0.38 % Steps: 57
% 0.17/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------