TSTP Solution File: ITP080^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP080^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 : 600s
% DateTime : Sun Jul 17 00:29:02 EDT 2022
% Result : Theorem 278.80s 278.19s
% Output : Proof 278.80s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_val,type,
set_val: $tType ).
thf(ty_option_list_val,type,
option_list_val: $tType ).
thf(ty_val,type,
val: $tType ).
thf(ty_node,type,
node: $tType ).
thf(ty_produc1432036078de_val,type,
produc1432036078de_val: $tType ).
thf(ty_list_node,type,
list_node: $tType ).
thf(ty_g,type,
g: $tType ).
thf(ty_list_P561207620_edgeD,type,
list_P561207620_edgeD: $tType ).
thf(ty_set_node,type,
set_node: $tType ).
thf(ty_entry,type,
entry: g > node ).
thf(ty_invar,type,
invar: g > $o ).
thf(ty_alpha_n,type,
alpha_n: g > list_node ).
thf(ty_rs,type,
rs: list_node ).
thf(ty_member_val,type,
member_val: val > set_val > $o ).
thf(ty_eigen__1,type,
eigen__1: node ).
thf(ty_eigen__0,type,
eigen__0: list_node ).
thf(ty_hd_node,type,
hd_node: list_node > node ).
thf(ty_member_node,type,
member_node: node > set_node > $o ).
thf(ty_phi_r,type,
phi_r: val ).
thf(ty_r,type,
r: val ).
thf(ty_sSA_CF848637139eD_val,type,
sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(ty_graph_1012773594_edgeD,type,
graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
thf(ty_graph_272749361_edgeD,type,
graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(ty_tl_node,type,
tl_node: list_node > list_node ).
thf(ty_set_node2,type,
set_node2: list_node > set_node ).
thf(ty_distinct_node,type,
distinct_node: list_node > $o ).
thf(ty_pred_phi_r,type,
pred_phi_r: node ).
thf(ty_sSA_CF551432799de_val,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(ty_g2,type,
g2: g ).
thf(ty_defs,type,
defs: g > node > set_val ).
thf(ty_phis,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(ty_graph_1994935542_edgeD,type,
graph_1994935542_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > list_node > $o ).
thf(ty_inEdges,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(sP1,plain,
( sP1
<=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r )
= ( hd_node @ rs ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( set_node2 @ ( tl_node @ rs ) )
= ( set_node2 @ ( tl_node @ rs ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ X1 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: g,X2: list_node] :
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X1 @ X2 )
=> ( distinct_node @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: list_node] :
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ X1 )
=> ( distinct_node @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: g,X2: node,X3: list_node,X4: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X2 @ X3 @ X4 )
=> ( X2
= ( hd_node @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: list_node] :
( ( distinct_node @ X1 )
=> ~ ( member_node @ ( hd_node @ X1 ) @ ( set_node2 @ ( tl_node @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs )
=> ( distinct_node @ rs ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: list_node,X2: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ X1 @ X2 )
=> ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r )
= ( hd_node @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( distinct_node @ rs )
=> ~ ( member_node @ ( hd_node @ rs ) @ ( set_node2 @ ( tl_node @ rs ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( member_node @ ( hd_node @ rs ) @ ( set_node2 @ ( tl_node @ rs ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: node,X2: list_node,X3: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X1 @ X2 @ X3 )
=> ( X1
= ( hd_node @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( distinct_node @ rs ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(conj_0,conjecture,
~ sP8 ).
thf(h0,negated_conjecture,
sP8,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ ! [X1: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ eigen__0 @ X1 )
=> ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ eigen__0 )
=> ( ( member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ X1 ) )
=> ~ ( member_node @ X1 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ eigen__0 @ eigen__1 )
=> ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ eigen__0 )
=> ( ( member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ eigen__1 ) )
=> ~ ( member_node @ eigen__1 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ eigen__0 )
=> ( ( member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ eigen__1 ) )
=> ~ ( member_node @ eigen__1 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ eigen__0,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ eigen__1 ) )
=> ~ ( member_node @ eigen__1 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ eigen__1 ),
introduced(assumption,[]) ).
thf(h8,assumption,
member_node @ eigen__1 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| sP14
| ~ sP2
| ~ sP4 ),
inference(mating_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP13
| ~ sP17
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP9
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP15
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP12
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP3
| ~ sP1
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP11
| ~ sP16
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP6
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_30_FormalSSA__Misc_Odistinct__hd__tl,axiom,
sP10 ).
thf(fact_5_old_OEntryPath__distinct,axiom,
sP6 ).
thf(fact_4_rs_H__props_I1_J,axiom,
sP1 ).
thf(fact_3_rs_H__props_I2_J,axiom,
sP16 ).
thf(fact_0_old_Opath2__hd,axiom,
sP9 ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h0,fact_30_FormalSSA__Misc_Odistinct__hd__tl,fact_5_old_OEntryPath__distinct,fact_4_rs_H__props_I1_J,fact_3_rs_H__props_I2_J,fact_0_old_Opath2__hd]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,13,h7,h8]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,14,h5,h6]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,15,h3,h4]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,16,h2]) ).
thf(fact_26__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nrs_H_092_060rightarrow_062pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Aold_OEntryPath_Ag_Ars_H_059_Ar_A_092_060in_062_AphiUses_Ag_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_A_092_060in_062_Aset_A_Iold_Opredecessors_Ag_A_IdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: list_node,X2: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ X1 @ X2 )
=> ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ X1 )
=> ( ( member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ X2 ) )
=> ~ ( member_node @ X2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ) ) ) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_26__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nrs_H_092_060rightarrow_062pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Aold_OEntryPath_Ag_Ars_H_059_Ar_A_092_060in_062_AphiUses_Ag_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_A_092_060in_062_Aset_A_Iold_Opredecessors_Ag_A_IdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,17,h1]) ).
thf(0,theorem,
~ sP8,
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP080^1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.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 : 600
% 0.12/0.33 % DateTime : Fri Jun 3 19:31:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 278.80/278.19 % SZS status Theorem
% 278.80/278.19 % Mode: mode502:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=256:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 278.80/278.19 % Inferences: 138
% 278.80/278.19 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------