%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SWW474^2 : 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 : n024.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 03:12:03 PM UTC 2025
% Result : Theorem 224.93s 224.94s
% Output : Proof 224.93s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_com,type,
com: $tType ).
thf(ty_hoare_1167836817_state,type,
hoare_1167836817_state: $tType ).
thf(ty_pname,type,
pname: $tType ).
thf(ty_option_com,type,
option_com: $tType ).
thf(ty_some_com,type,
some_com: com > option_com ).
thf(ty_wt,type,
wt: com > $o ).
thf(ty_hoare_Mirabelle_MGT,type,
hoare_Mirabelle_MGT: com > hoare_1167836817_state ).
thf(ty_insert2134838167_state,type,
insert2134838167_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(ty_ord_le827224136tate_o,type,
ord_le827224136tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(ty_bot_bo70021908tate_o,type,
bot_bo70021908tate_o: hoare_1167836817_state > $o ).
thf(ty_body,type,
body: pname > option_com ).
thf(ty_y,type,
y: com ).
thf(ty_hoare_123228589_state,type,
hoare_123228589_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(ty_body_1,type,
body_1: pname > com ).
thf(ty_image_575578384_state,type,
image_575578384_state: ( pname > hoare_1167836817_state ) > ( pname > $o ) > hoare_1167836817_state > $o ).
thf(ty_pn,type,
pn: pname ).
thf(ty_hoare_1201148605gleton,type,
hoare_1201148605gleton: $o ).
thf(ty_wT_bodies,type,
wT_bodies: $o ).
thf(ty_dom_pname_com,type,
dom_pname_com: ( pname > option_com ) > pname > $o ).
thf(sP1,plain,
( sP1
<=> ( wt @ y ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> wT_bodies ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP2
=> ( ( ( body @ pn )
= ( some_com @ y ) )
=> sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: hoare_1167836817_state > $o,X2: hoare_1167836817_state > $o,X3: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ X2 @ X3 )
=> ( ( ord_le827224136tate_o @ X2 @ X1 )
=> ( hoare_123228589_state @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: com] :
( hoare_1201148605gleton
=> ( sP2
=> ( ( wt @ X1 )
=> ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ X1 ) @ bot_bo70021908tate_o ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( !! @ ( ord_le827224136tate_o @ bot_bo70021908tate_o ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ bot_bo70021908tate_o @ X1 )
=> ( ( ord_le827224136tate_o @ bot_bo70021908tate_o
@ ( image_575578384_state
@ ^ [X2: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X2 ) )
@ ( dom_pname_com @ body ) ) )
=> ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [X2: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X2 ) )
@ ( dom_pname_com @ body ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: pname,X2: com] :
( sP2
=> ( ( ( body @ X1 )
= ( some_com @ X2 ) )
=> ( wt @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( body @ pn )
= ( some_com @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ord_le827224136tate_o @ bot_bo70021908tate_o
@ ( image_575578384_state
@ ^ [X1: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X1 ) )
@ ( dom_pname_com @ body ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: com] :
( sP2
=> ( ( ( body @ pn )
= ( some_com @ X1 ) )
=> ( wt @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP9
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) )
=> ( sP10
=> ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [X1: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X1 ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> hoare_1201148605gleton ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP1
=> ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [X1: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X1 ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP10
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP2
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP14
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: hoare_1167836817_state > $o,X2: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ X1 @ X2 )
=> ( ( ord_le827224136tate_o @ X1
@ ( image_575578384_state
@ ^ [X3: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X3 ) )
@ ( dom_pname_com @ body ) ) )
=> ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [X3: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X3 ) )
@ ( dom_pname_com @ body ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(conj_7,conjecture,
sP16 ).
thf(h0,negated_conjecture,
~ sP16,
inference(assume_negation,[status(cth)],[conj_7]) ).
thf(1,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP11
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| ~ sP2
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP12
| ~ sP9
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP19
| ~ sP14
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP18
| ~ sP2
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP15
| ~ sP1
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP7
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP13
| ~ sP20
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP17
| ~ sP10
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP21
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP4
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(conj_5,axiom,
sP9 ).
thf(conj_1,axiom,
sP2 ).
thf(conj_0,axiom,
sP14 ).
thf(fact_215_WT__bodiesD,axiom,
sP8 ).
thf(fact_53_MGF,axiom,
sP5 ).
thf(fact_22_empty__subsetI,axiom,
sP6 ).
thf(fact_3_thin,axiom,
sP4 ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,conj_5,conj_1,conj_0,fact_215_WT__bodiesD,fact_53_MGF,fact_22_empty__subsetI,fact_3_thin,h0]) ).
thf(0,theorem,
sP16,
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW474^2 : TPTP v9.2.0. Released v5.3.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 13:31:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 224.93/224.94 % SZS status Theorem
% 224.93/224.94 % Mode: mode490:USE_SINE=true:SINE_TOLERANCE=5.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 224.93/224.94 % Inferences: 4895
% 224.93/224.94 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------