TSTP Solution File: ITP081^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP081^1 : 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 : n026.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 04:01:56 EDT 2023
% Result : Theorem 125.28s 125.81s
% Output : Proof 125.28s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_node,type,
node: $tType ).
thf(ty_g,type,
g: $tType ).
thf(ty_list_node,type,
list_node: $tType ).
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_r,type,
r: val ).
thf(ty_ri,type,
ri: list_node ).
thf(ty_g2,type,
g2: g ).
thf(ty_ns,type,
ns: list_node ).
thf(ty_n,type,
n: node ).
thf(ty_inEdges,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(ty_append_node,type,
append_node: list_node > list_node > list_node ).
thf(ty_phi_r,type,
phi_r: val ).
thf(ty_tl_node,type,
tl_node: list_node > list_node ).
thf(ty_invar,type,
invar: g > $o ).
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_phis,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(ty_defs,type,
defs: g > node > set_val ).
thf(ty_alpha_n,type,
alpha_n: g > list_node ).
thf(sP1,plain,
( sP1
<=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: node,X2: list_node,X3: node,X4: list_node,X5: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X1 @ X2 @ X3 )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X3 @ X4 @ X5 )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X1 @ ( append_node @ X2 @ ( tl_node @ X4 ) ) @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: list_node,X2: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ X1 @ X2 )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ X1 ) ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ X1 )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: g,X2: node,X3: list_node,X4: node,X5: list_node,X6: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X2 @ X3 @ X4 )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X4 @ X5 @ X6 )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X2 @ ( append_node @ X3 @ ( tl_node @ X5 ) ) @ X6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: node,X2: list_node,X3: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ X1 )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X1 @ X2 @ X3 )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ X2 ) ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( i
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP1
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: list_node,X2: node,X3: list_node,X4: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ X1 @ X2 )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X2 @ X3 @ X4 )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ X1 @ ( tl_node @ X3 ) ) @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP12
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> $false ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(conj_0,conjecture,
sP9 ).
thf(h0,negated_conjecture,
~ sP9,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP2
| sP1
| ~ sP8
| sP14
| sP14
| sP14
| sP14
| sP14
| sP14 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| ~ sP1
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
~ sP14,
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP13
| ~ sP12
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP11
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP3
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_5_old_Opath2__app,axiom,
sP6 ).
thf(fact_4_ri__props_I1_J,axiom,
sP2 ).
thf(fact_3_assms_I7_J,axiom,
sP12 ).
thf(fact_1_ri__is__valid,axiom,
sP8 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,fact_5_old_Opath2__app,fact_4_ri__props_I1_J,fact_3_assms_I7_J,fact_1_ri__is__valid,h0]) ).
thf(0,theorem,
sP9,
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP081^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.33 % Computer : n026.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Sun Aug 27 17:19:34 EDT 2023
% 0.15/0.33 % CPUTime :
% 125.28/125.81 % SZS status Theorem
% 125.28/125.81 % Mode: cade22sinegrackle2xec37
% 125.28/125.81 % Steps: 93842
% 125.28/125.81 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------