TSTP Solution File: ITP078^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP078^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 04:01:55 EDT 2023
% Result : Theorem 22.08s 22.27s
% Output : Proof 22.08s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_set_nat,type,
set_nat: $tType ).
thf(ty_image_mset_nat_a,type,
image_mset_nat_a: ( nat > a ) > multiset_nat > multiset_a ).
thf(ty_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(ty_mset_set_nat,type,
mset_set_nat: set_nat > multiset_nat ).
thf(ty_image_nat_nat,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(ty_image_mset_nat_nat,type,
image_mset_nat_nat: ( nat > nat ) > multiset_nat > multiset_nat ).
thf(ty_ys,type,
ys: list_a ).
thf(ty_inj_on_nat_nat,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(ty_f,type,
f: nat > nat ).
thf(ty_set_or562006527an_nat,type,
set_or562006527an_nat: nat > nat > set_nat ).
thf(ty_xs,type,
xs: list_a ).
thf(ty_nth_a,type,
nth_a: list_a > nat > a ).
thf(ty_size_size_list_a,type,
size_size_list_a: list_a > nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: set_nat] :
( ( inj_on_nat_nat @ f @ X1 )
=> ( ( image_mset_nat_nat @ f @ ( mset_set_nat @ X1 ) )
= ( mset_set_nat @ ( image_nat_nat @ f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
=> ( ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) )
= ( mset_set_nat @ ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( mset_set_nat @ ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) )
= ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: nat > nat,X2: set_nat] :
( ( inj_on_nat_nat @ X1 @ X2 )
=> ( ( image_mset_nat_nat @ X1 @ ( mset_set_nat @ X2 ) )
= ( mset_set_nat @ ( image_nat_nat @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) )
= ( mset_set_nat @ ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) )
= ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(conj_0,conjecture,
sP6 ).
thf(h0,negated_conjecture,
~ sP6,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( sP4
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP10
| sP2
| ~ sP4 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| ~ sP7
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
~ sP2,
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP6
| ~ sP10
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP5
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_71_image__mset__mset__set,axiom,
sP5 ).
thf(fact_3__C2_C,axiom,
sP8 ).
thf(fact_0__C1_C,axiom,
sP7 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,h0,fact_71_image__mset__mset__set,fact_3__C2_C,fact_0__C1_C]) ).
thf(0,theorem,
sP6,
inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP078^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 15:58:49 EDT 2023
% 0.12/0.34 % CPUTime :
% 22.08/22.27 % SZS status Theorem
% 22.08/22.27 % Mode: cade22sinegrackle2xfaf3
% 22.08/22.27 % Steps: 8332
% 22.08/22.27 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------