%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SWW473^2 : TPTP v9.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n015.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 Oct 9 03:12:02 PM UTC 2025
% Result : Theorem 252.52s 252.75s
% Output : Proof 252.52s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_x_a,type,
x_a: $tType ).
thf(ty_pname,type,
pname: $tType ).
thf(ty_ord_less_eq_a_o,type,
ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(ty_mgt_call,type,
mgt_call: pname > x_a ).
thf(ty_insert_a,type,
insert_a: x_a > ( x_a > $o ) > x_a > $o ).
thf(ty_u,type,
u: pname > $o ).
thf(ty_pn,type,
pn: pname ).
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(sP1,plain,
( sP1
<=> ( ( insert_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) )
= ( image_pname_a @ mgt_call @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( member_pname @ pn @ u )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( insert_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: x_a > $o,X2: x_a > $o,X3: x_a > $o] :
( ( ord_less_eq_a_o @ X2 @ X3 )
=> ( ( X3 = X1 )
=> ( ord_less_eq_a_o @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: x_a > $o] :
( ( ord_less_eq_a_o @ g @ X1 )
=> ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( insert_a @ ( mgt_call @ pn ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: x_a > $o,X2: x_a > $o] :
( ( ord_less_eq_a_o @ X1 @ X2 )
=> ( ( X2
= ( image_pname_a @ mgt_call @ u ) )
=> ( ord_less_eq_a_o @ X1 @ ( image_pname_a @ mgt_call @ u ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: pname,X2: pname > $o] :
( ( member_pname @ X1 @ X2 )
=> ( ( insert_a @ ( mgt_call @ X1 ) @ ( image_pname_a @ mgt_call @ X2 ) )
= ( image_pname_a @ mgt_call @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: pname > x_a,X2: pname,X3: pname > $o] :
( ( member_pname @ X2 @ X3 )
=> ( ( insert_a @ ( X1 @ X2 ) @ ( image_pname_a @ X1 @ X3 ) )
= ( image_pname_a @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: x_a > $o,X2: x_a > $o] :
( ( ord_less_eq_a_o @ X1 @ X2 )
=> ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ X1 ) @ ( insert_a @ ( mgt_call @ pn ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: x_a > $o] :
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ X1 )
=> ( ( X1
= ( image_pname_a @ mgt_call @ u ) )
=> sP11 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP3
=> ( sP1
=> sP11 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP1
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: x_a,X2: x_a > $o,X3: x_a > $o] :
( ( ord_less_eq_a_o @ X2 @ X3 )
=> ( ord_less_eq_a_o @ ( insert_a @ X1 @ X2 ) @ ( insert_a @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( member_pname @ pn @ u ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: pname > $o] :
( ( member_pname @ pn @ X1 )
=> ( ( insert_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ X1 ) )
= ( image_pname_a @ mgt_call @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP9
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(conj_6,conjecture,
sP11 ).
thf(h0,negated_conjecture,
~ sP11,
inference(assume_negation,[status(cth)],[conj_6]) ).
thf(1,plain,
( ~ sP7
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP17
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| ~ sP16
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP12
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP13
| ~ sP3
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP14
| ~ sP1
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP6
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP5
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP18
| ~ sP9
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP8
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP15
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP4
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(conj_4,axiom,
sP16 ).
thf(conj_1,axiom,
sP9 ).
thf(fact_529_ord__le__eq__trans,axiom,
sP4 ).
thf(fact_343_insert__image,axiom,
sP8 ).
thf(fact_333_insert__mono,axiom,
sP15 ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,conj_4,conj_1,fact_529_ord__le__eq__trans,fact_343_insert__image,fact_333_insert__mono,h0]) ).
thf(0,theorem,
sP11,
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW473^2 : TPTP v9.2.0. Released v5.3.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 8 13:35:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 252.52/252.75 % SZS status Theorem
% 252.52/252.75 % Mode: mode407:USE_SINE=true:SINE_TOLERANCE=1.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 252.52/252.75 % Inferences: 1692
% 252.52/252.75 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------