TSTP Solution File: SWW473^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SWW473^2 : TPTP v8.1.2. Released v5.3.0.
% 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 : Fri Sep 1 00:45:08 EDT 2023
% Result : Theorem 27.22s 27.44s
% Output : Proof 27.22s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_pname,type,
pname: $tType ).
thf(ty_x_a,type,
x_a: $tType ).
thf(ty_ord_less_eq_a_o,type,
ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(ty_member_a,type,
member_a: x_a > ( x_a > $o ) > $o ).
thf(ty_image_pname_a,type,
image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
thf(ty_member_pname,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(ty_g,type,
g: x_a > $o ).
thf(ty_insert_a,type,
insert_a: x_a > ( x_a > $o ) > x_a > $o ).
thf(ty_pn,type,
pn: pname ).
thf(ty_u,type,
u: pname > $o ).
thf(ty_mgt_call,type,
mgt_call: pname > x_a ).
thf(sP1,plain,
( sP1
<=> ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( member_pname @ pn @ u ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
=> ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: x_a > $o] :
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ X1 )
= ( ~ ( ( member_a @ ( mgt_call @ pn ) @ X1 )
=> ~ ( ord_less_eq_a_o @ g @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP1
= ( ~ ( ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) )
=> ~ sP3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: pname > x_a,X2: pname,X3: pname > $o] :
( ( member_pname @ X2 @ X3 )
=> ( member_a @ ( X1 @ X2 ) @ ( image_pname_a @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP8
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: pname,X2: pname > $o] :
( ( member_pname @ X1 @ X2 )
=> ( member_a @ ( mgt_call @ X1 ) @ ( image_pname_a @ mgt_call @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: pname > $o] :
( ( member_pname @ pn @ X1 )
=> ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: x_a > $o,X2: x_a > $o] :
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ X1 ) @ X2 )
= ( ~ ( ( member_a @ ( mgt_call @ pn ) @ X2 )
=> ~ ( ord_less_eq_a_o @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: x_a,X2: x_a > $o,X3: x_a > $o] :
( ( ord_less_eq_a_o @ ( insert_a @ X1 @ X2 ) @ X3 )
= ( ~ ( ( member_a @ X1 @ X3 )
=> ~ ( ord_less_eq_a_o @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(conj_6,conjecture,
sP1 ).
thf(h0,negated_conjecture,
~ sP1,
inference(assume_negation,[status(cth)],[conj_6]) ).
thf(1,plain,
( ~ sP9
| ~ sP8
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP1
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| ~ sP2
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP11
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP12
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP10
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP13
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP7
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(conj_4,axiom,
sP2 ).
thf(conj_1,axiom,
sP3 ).
thf(fact_324_insert__subset,axiom,
sP13 ).
thf(fact_307_imageI,axiom,
sP7 ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,h0,conj_4,conj_1,fact_324_insert__subset,fact_307_imageI]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473^2 : TPTP v8.1.2. Released v5.3.0.
% 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 19:07:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 27.22/27.44 % SZS status Theorem
% 27.22/27.44 % Mode: cade22sinegrackle2xfaf3
% 27.22/27.44 % Steps: 34137
% 27.22/27.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------