TSTP Solution File: ITP115^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP115^1 : 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 : n027.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 04:02:11 EDT 2023
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_set_b,type,
set_b: $tType ).
thf(ty_thesis,type,
thesis: $o ).
thf(ty_eigen__0,type,
eigen__0: set_b ).
thf(ty_a2,type,
a2: b ).
thf(ty_f,type,
f: a > b ).
thf(ty_eigen__1,type,
eigen__1: set_b ).
thf(ty_member_b,type,
member_b: b > set_b > $o ).
thf(ty_x0,type,
x0: a ).
thf(ty_inf_inf_set_b,type,
inf_inf_set_b: set_b > set_b > set_b ).
thf(ty_bot_bot_set_b,type,
bot_bot_set_b: set_b ).
thf(ty_topolo1276428102open_b,type,
topolo1276428102open_b: set_b > $o ).
thf(sP1,plain,
( sP1
<=> ( ( inf_inf_set_b @ eigen__0 @ eigen__1 )
= bot_bot_set_b ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: set_b,X2: set_b] :
( ~ ( ~ ( ~ ( ~ ( ( topolo1276428102open_b @ X1 )
=> ~ ( topolo1276428102open_b @ X2 ) )
=> ~ ( member_b @ ( f @ x0 ) @ X1 ) )
=> ~ ( member_b @ a2 @ X2 ) )
=> ( ( inf_inf_set_b @ X1 @ X2 )
!= bot_bot_set_b ) )
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( topolo1276428102open_b @ eigen__0 )
=> ~ ( topolo1276428102open_b @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ sP3
=> ~ ( member_b @ ( f @ x0 ) @ eigen__0 ) )
=> ~ ( member_b @ a2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( topolo1276428102open_b @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> thesis ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( topolo1276428102open_b @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP3
=> ~ ( member_b @ ( f @ x0 ) @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP4
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( member_b @ a2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: set_b] :
( ~ ( ~ ( ~ ( ~ ( sP7
=> ~ ( topolo1276428102open_b @ X1 ) )
=> ~ ( member_b @ ( f @ x0 ) @ eigen__0 ) )
=> ~ ( member_b @ a2 @ X1 ) )
=> ( ( inf_inf_set_b @ eigen__0 @ X1 )
!= bot_bot_set_b ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( a2
= ( f @ x0 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( f @ x0 )
= a2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP9
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( member_b @ ( f @ x0 ) @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(conj_1,conjecture,
sP6 ).
thf(h0,negated_conjecture,
~ sP6,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(h1,assumption,
sP13,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: set_b,X2: set_b] :
( ~ ( ~ ( ~ ( ( topolo1276428102open_b @ X1 )
=> ~ ( topolo1276428102open_b @ X2 ) )
=> ~ ( member_b @ ( f @ x0 ) @ X1 ) )
=> ~ ( member_b @ a2 @ X2 ) )
=> ( ( inf_inf_set_b @ X1 @ X2 )
!= bot_bot_set_b ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP12 ),
inference(symeq,[status(thm)],]) ).
thf(fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062,axiom,
~ sP12 ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,h1,fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062]) ).
thf(h3,assumption,
~ ! [X1: set_b] :
( ~ ( ~ ( ~ ( sP7
=> ~ ( topolo1276428102open_b @ X1 ) )
=> ~ sP15 )
=> ~ ( member_b @ a2 @ X1 ) )
=> ( ( inf_inf_set_b @ eigen__0 @ X1 )
!= bot_bot_set_b ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h8,assumption,
sP10,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h10,assumption,
sP15,
introduced(assumption,[]) ).
thf(h11,assumption,
sP7,
introduced(assumption,[]) ).
thf(h12,assumption,
sP5,
introduced(assumption,[]) ).
thf(3,plain,
( ~ sP8
| sP3
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP8
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| ~ sP7
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP4
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| sP9
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP11
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP2
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(conj_0,axiom,
sP2 ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h4,h3,h2,h0])],[3,4,5,6,7,8,9,h0,conj_0,h11,h12,h10,h8,h6]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h3,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,10,h11,h12]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,11,h9,h10]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,12,h7,h8]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,13,h5,h6]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,14,h4]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,15,h3]) ).
thf(fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,axiom,
( ~ sP13
=> ~ ! [X1: set_b,X2: set_b] :
( ~ ( ~ ( ~ ( ( topolo1276428102open_b @ X1 )
=> ~ ( topolo1276428102open_b @ X2 ) )
=> ~ ( member_b @ ( f @ x0 ) @ X1 ) )
=> ~ ( member_b @ a2 @ X2 ) )
=> ( ( inf_inf_set_b @ X1 @ X2 )
!= bot_bot_set_b ) ) ) ).
thf(17,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,2,16,h1,h2]) ).
thf(0,theorem,
sP6,
inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP115^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n027.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 : Sun Aug 27 11:48:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % Mode: cade22sinegrackle2x6978
% 0.19/0.45 % Steps: 339
% 0.19/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------