TSTP Solution File: ITP180^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP180^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.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 : Sun May 5 07:05:02 EDT 2024
% Result : Theorem 175.36s 25.47s
% Output : Refutation 175.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 206
% Syntax : Number of formulae : 224 ( 16 unt; 202 typ; 0 def)
% Number of atoms : 479 ( 20 equ; 0 cnn)
% Maximal formula atoms : 3 ( 21 avg)
% Number of connectives : 24 ( 12 ~; 6 |; 0 &; 0 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 322 ( 317 >; 5 *; 0 +; 0 <<)
% Number of symbols : 203 ( 200 usr; 19 con; 0-8 aty)
% Number of variables : 492 ( 0 ^ 42 !; 0 ?; 492 :)
% ( 450 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set: $tType > $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
product_prod: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
standard_Constant: $tType > $tType ).
thf(type_def_9,type,
labeled_graph: ( $tType * $tType ) > $tType ).
thf(type_def_10,type,
allegorical_term: $tType > $tType ).
thf(type_def_11,type,
itself: $tType > $tType ).
thf(type_def_12,type,
nat: $tType ).
thf(type_def_13,type,
v2: $tType ).
thf(type_def_14,type,
v: $tType ).
thf(func_def_0,type,
standard_Constant: $tType > $tType ).
thf(func_def_1,type,
allegorical_term: $tType > $tType ).
thf(func_def_2,type,
labeled_graph: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
product_prod: ( $tType * $tType ) > $tType ).
thf(func_def_4,type,
set: $tType > $tType ).
thf(func_def_5,type,
nat: $tType ).
thf(func_def_6,type,
itself: $tType > $tType ).
thf(func_def_7,type,
v: $tType ).
thf(func_def_8,type,
v2: $tType ).
thf(func_def_9,type,
bounded_lattice:
!>[X0: $tType] : $o ).
thf(func_def_10,type,
type:
!>[X0: $tType] : $o ).
thf(func_def_11,type,
bot:
!>[X0: $tType] : $o ).
thf(func_def_12,type,
lattice:
!>[X0: $tType] : $o ).
thf(func_def_13,type,
preorder:
!>[X0: $tType] : $o ).
thf(func_def_14,type,
semilattice_sup:
!>[X0: $tType] : $o ).
thf(func_def_15,type,
bounde1808546759up_bot:
!>[X0: $tType] : $o ).
thf(func_def_16,type,
bNF_Gr:
!>[X0: $tType,X1: $tType] : ( set(X0) > ( X0 > X1 ) > set(product_prod(X0,X1)) ) ).
thf(func_def_17,type,
comp:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 ) > ( X2 > X0 ) > X2 > X1 ) ).
thf(func_def_18,type,
standard_S_Bot:
!>[X0: $tType] : standard_Constant(X0) ).
thf(func_def_19,type,
standard_S_Const:
!>[X0: $tType] : ( X0 > standard_Constant(X0) ) ).
thf(func_def_20,type,
standard_S_Top:
!>[X0: $tType] : standard_Constant(X0) ).
thf(func_def_21,type,
getRel:
!>[X0: $tType,X1: $tType] : ( X0 > labeled_graph(X0,X1) > set(product_prod(X1,X1)) ) ).
thf(func_def_22,type,
semantics:
!>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > allegorical_term(X0) > set(product_prod(X1,X1)) ) ).
thf(func_def_23,type,
edge_preserving:
!>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(X0,X1)) > set(product_prod(X2,product_prod(X0,X0))) > set(product_prod(X2,product_prod(X1,X1))) > $o ) ).
thf(func_def_24,type,
graph_homomorphism:
!>[X0: $tType,X1: $tType,X2: $tType] : ( labeled_graph(X0,X1) > labeled_graph(X0,X2) > set(product_prod(X1,X2)) > $o ) ).
thf(func_def_25,type,
graph_union:
!>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > labeled_graph(X0,X1) > labeled_graph(X0,X1) ) ).
thf(func_def_26,type,
labeled_LG:
!>[X0: $tType,X1: $tType] : ( set(product_prod(X0,product_prod(X1,X1))) > set(X1) > labeled_graph(X0,X1) ) ).
thf(func_def_27,type,
labele1974067554_graph:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( set(product_prod(X0,product_prod(X1,X1))) > set(X1) > X2 ) > labeled_graph(X0,X1) > X2 ) ).
thf(func_def_28,type,
labeled_edges:
!>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > set(product_prod(X0,product_prod(X1,X1))) ) ).
thf(func_def_29,type,
labeled_vertices:
!>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > set(X1) ) ).
thf(func_def_30,type,
map_graph:
!>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(X0,X1)) > labeled_graph(X2,X0) > labeled_graph(X2,X1) ) ).
thf(func_def_31,type,
restrict:
!>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > labeled_graph(X0,X1) ) ).
thf(func_def_32,type,
sup_sup:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_33,type,
bot_bot:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
ord_less_eq:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_35,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > product_prod(X0,X1) ) ).
thf(func_def_36,type,
product_rec_prod:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).
thf(func_def_37,type,
field:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > set(X0) ) ).
thf(func_def_38,type,
id_on:
!>[X0: $tType] : ( set(X0) > set(product_prod(X0,X0)) ) ).
thf(func_def_39,type,
total_on:
!>[X0: $tType] : ( set(X0) > set(product_prod(X0,X0)) > $o ) ).
thf(func_def_40,type,
agree_on:
!>[X0: $tType,X1: $tType,X2: $tType] : ( labeled_graph(X0,X1) > set(product_prod(X1,X2)) > set(product_prod(X1,X2)) > $o ) ).
thf(func_def_41,type,
consequence_graph:
!>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(labeled_graph(X0,X1),labeled_graph(X0,X1))) > labeled_graph(X0,X2) > $o ) ).
thf(func_def_42,type,
extensible:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(labeled_graph(X0,X1),labeled_graph(X0,X1)) > labeled_graph(X0,X2) > set(product_prod(X1,X2)) > $o ) ).
thf(func_def_43,type,
least:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( itself(X0) > set(product_prod(labeled_graph(X1,X2),labeled_graph(X1,X2))) > labeled_graph(X1,X3) > labeled_graph(X1,X3) > $o ) ).
thf(func_def_44,type,
least_559130134_graph:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( itself(X0) > set(product_prod(labeled_graph(X1,X2),labeled_graph(X1,X2))) > labeled_graph(X1,X3) > labeled_graph(X1,X3) > $o ) ).
thf(func_def_45,type,
maintained:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(labeled_graph(X0,X1),labeled_graph(X0,X1)) > labeled_graph(X0,X2) > $o ) ).
thf(func_def_46,type,
collect:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).
thf(func_def_47,type,
insert:
!>[X0: $tType] : ( X0 > set(X0) > set(X0) ) ).
thf(func_def_48,type,
is_singleton:
!>[X0: $tType] : ( set(X0) > $o ) ).
thf(func_def_49,type,
the_elem:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_50,type,
standa1138209853_rules:
!>[X0: $tType] : ( set(X0) > set(product_prod(labeled_graph(standard_Constant(X0),nat),labeled_graph(standard_Constant(X0),nat))) ) ).
thf(func_def_51,type,
standa2002409347_rules:
!>[X0: $tType] : ( set(standard_Constant(X0)) > set(product_prod(labeled_graph(standard_Constant(X0),nat),labeled_graph(standard_Constant(X0),nat))) ) ).
thf(func_def_52,type,
standa244753842y_rule:
!>[X0: $tType] : product_prod(labeled_graph(X0,nat),labeled_graph(X0,nat)) ).
thf(func_def_53,type,
standa438229444_rules:
!>[X0: $tType] : ( set(X0) > set(standard_Constant(X0)) > set(product_prod(labeled_graph(standard_Constant(X0),nat),labeled_graph(standard_Constant(X0),nat))) ) ).
thf(func_def_54,type,
standa400804411p_rule:
!>[X0: $tType] : ( X0 > product_prod(labeled_graph(X0,nat),labeled_graph(X0,nat)) ) ).
thf(func_def_55,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_56,type,
c: set(v2) ).
thf(func_def_57,type,
g: labeled_graph(standard_Constant(v2),v) ).
thf(func_def_58,type,
l: set(standard_Constant(v2)) ).
thf(func_def_59,type,
h: v > v ).
thf(func_def_60,type,
m: v2 > v ).
thf(func_def_61,type,
x: v ).
thf(func_def_62,type,
xa: v2 ).
thf(func_def_63,type,
y: v2 ).
thf(func_def_67,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_68,type,
vNOT: $o > $o ).
thf(func_def_69,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_70,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_71,type,
vIMP: $o > $o > $o ).
thf(func_def_72,type,
vOR: $o > $o > $o ).
thf(func_def_73,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_74,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_75,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_76,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_77,type,
vAND: $o > $o > $o ).
thf(func_def_78,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_79,type,
sP0:
!>[X0: $tType] : ( set(X0) > set(product_prod(X0,X0)) > $o ) ).
thf(func_def_80,type,
sK1: v2 > v ).
thf(func_def_81,type,
sK2: v ).
thf(func_def_82,type,
sK3: v2 > v ).
thf(func_def_83,type,
sK4: v2 > v ).
thf(func_def_84,type,
sK5:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_85,type,
sK6:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_86,type,
sK7:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_87,type,
sK8:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_88,type,
sK9:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_89,type,
sK10:
!>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).
thf(func_def_90,type,
sK11:
!>[X0: $tType] : ( set(X0) > set(product_prod(X0,X0)) > X0 ) ).
thf(func_def_91,type,
sK12:
!>[X0: $tType] : ( set(X0) > set(product_prod(X0,X0)) > X0 ) ).
thf(func_def_92,type,
sK13:
!>[X0: $tType] : ( set(X0) > X0 > set(X0) ) ).
thf(func_def_93,type,
sK14:
!>[X0: $tType] : ( set(X0) > X0 > set(X0) ) ).
thf(func_def_94,type,
sK15:
!>[X0: $tType] : ( set(X0) > product_prod(X0,X0) > X0 ) ).
thf(func_def_95,type,
sK16:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
thf(func_def_96,type,
sK17:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
thf(func_def_97,type,
sK18:
!>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > set(product_prod(X0,product_prod(X1,X1))) ) ).
thf(func_def_98,type,
sK19:
!>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > set(X1) ) ).
thf(func_def_99,type,
sK20:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
thf(func_def_100,type,
sK21:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
thf(func_def_101,type,
sK22:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_102,type,
sK23:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).
thf(func_def_103,type,
sK24:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).
thf(func_def_104,type,
sK25:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).
thf(func_def_105,type,
sK26:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).
thf(func_def_106,type,
sK27:
!>[X0: $tType,X1: $tType] : ( ( labeled_graph(X1,X0) > $o ) > set(product_prod(X1,product_prod(X0,X0))) ) ).
thf(func_def_107,type,
sK28:
!>[X0: $tType,X1: $tType] : ( ( labeled_graph(X1,X0) > $o ) > set(X0) ) ).
thf(func_def_108,type,
sK29:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
thf(func_def_109,type,
sK30:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
thf(func_def_110,type,
sK31:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
thf(func_def_111,type,
sK32:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X2 ) ).
thf(func_def_112,type,
sK33:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X1 ) ).
thf(func_def_113,type,
sK34:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X0 ) ).
thf(func_def_114,type,
sK35:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
thf(func_def_115,type,
sK36:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
thf(func_def_116,type,
sK37:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
thf(func_def_117,type,
sK38:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
thf(func_def_118,type,
sK39:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > labeled_graph(X2,X1) > X1 ) ).
thf(func_def_119,type,
sK40:
!>[X0: $tType,X1: $tType,X2: $tType] : ( labeled_graph(X2,X0) > labeled_graph(X2,X1) > labeled_graph(X2,X0) > set(product_prod(X0,X1)) ) ).
thf(func_def_120,type,
sK41:
!>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(X2,product_prod(X1,X1))) > ( X0 > X1 ) > labeled_graph(X2,X0) > X2 ) ).
thf(func_def_121,type,
sK42:
!>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(X2,product_prod(X1,X1))) > ( X0 > X1 ) > labeled_graph(X2,X0) > X0 ) ).
thf(func_def_122,type,
sK43:
!>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(X2,product_prod(X1,X1))) > ( X0 > X1 ) > labeled_graph(X2,X0) > X0 ) ).
thf(func_def_123,type,
sK44:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X3 ) ).
thf(func_def_124,type,
sK45:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X2 ) ).
thf(func_def_125,type,
sK46:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X1 ) ).
thf(func_def_126,type,
sK47:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X0 ) ).
thf(func_def_127,type,
sK48:
!>[X0: $tType,X1: $tType] : ( ( X0 > X0 ) > labeled_graph(X1,X0) > X0 ) ).
thf(func_def_128,type,
sK49:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0 ) ).
thf(func_def_129,type,
sK50:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1 ) ).
thf(func_def_130,type,
sK51:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2 ) ).
thf(func_def_131,type,
sK52:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).
thf(func_def_132,type,
sK53:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).
thf(func_def_133,type,
sK54:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X4 ) ).
thf(func_def_134,type,
sK55:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X3 ) ).
thf(func_def_135,type,
sK56:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X2 ) ).
thf(func_def_136,type,
sK57:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X1 ) ).
thf(func_def_137,type,
sK58:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X0 ) ).
thf(func_def_138,type,
sK59:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).
thf(func_def_139,type,
sK60:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).
thf(func_def_140,type,
sK61:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).
thf(func_def_141,type,
sK62:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).
thf(func_def_142,type,
sK63:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).
thf(func_def_143,type,
sK64:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).
thf(func_def_144,type,
sK65:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X0 ) > ( X0 > X1 ) > labeled_graph(X2,X1) > X1 ) ).
thf(func_def_145,type,
sK66:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X5 ) ).
thf(func_def_146,type,
sK67:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X4 ) ).
thf(func_def_147,type,
sK68:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X3 ) ).
thf(func_def_148,type,
sK69:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X2 ) ).
thf(func_def_149,type,
sK70:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X1 ) ).
thf(func_def_150,type,
sK71:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X0 ) ).
thf(func_def_151,type,
sK72:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( labeled_graph(X3,X2) > labeled_graph(X3,X2) > set(product_prod(labeled_graph(X3,X1),labeled_graph(X3,X1))) > labeled_graph(X3,X0) ) ).
thf(func_def_152,type,
sK73:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( set(product_prod(labeled_graph(X3,X1),labeled_graph(X3,X1))) > labeled_graph(X3,X2) > labeled_graph(X3,X2) > labeled_graph(X3,X0) ) ).
thf(func_def_153,type,
sK74:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X0 ) ).
thf(func_def_154,type,
sK75:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X1 ) ).
thf(func_def_155,type,
sK76:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X2 ) ).
thf(func_def_156,type,
sK77:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X3 ) ).
thf(func_def_157,type,
sK78:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X4 ) ).
thf(func_def_158,type,
sK79:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X5 ) ).
thf(func_def_159,type,
sK80:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X6 ) ).
thf(func_def_160,type,
sK81:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X6 ) ).
thf(func_def_161,type,
sK82:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X5 ) ).
thf(func_def_162,type,
sK83:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X4 ) ).
thf(func_def_163,type,
sK84:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X3 ) ).
thf(func_def_164,type,
sK85:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X2 ) ).
thf(func_def_165,type,
sK86:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X1 ) ).
thf(func_def_166,type,
sK87:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X0 ) ).
thf(func_def_167,type,
sK88: v2 > v ).
thf(func_def_168,type,
sK89:
!>[X0: $tType] : ( X0 > set(X0) > X0 > set(X0) > set(X0) ) ).
thf(func_def_169,type,
sK90:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_170,type,
sK91:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_171,type,
sK92:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_172,type,
sK93:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_173,type,
sK94:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_174,type,
sK95:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_175,type,
sK96:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_176,type,
sK97:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_177,type,
sK98:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_178,type,
sK99:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_179,type,
sK100:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_180,type,
sK101:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_181,type,
sK102:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_182,type,
sK103:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_183,type,
sK104: v2 ).
thf(func_def_184,type,
sK105: v2 ).
thf(func_def_185,type,
sK106: v2 ).
thf(func_def_186,type,
sK107: v2 ).
thf(func_def_187,type,
sK108: v2 ).
thf(func_def_188,type,
sK109:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_189,type,
sK110:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_190,type,
sK111: v2 ).
thf(func_def_191,type,
sK112: v2 ).
thf(func_def_192,type,
sK113: v2 ).
thf(func_def_193,type,
sK114: v2 ).
thf(func_def_194,type,
sK115: v2 ).
thf(f477955,plain,
$false,
inference(subsumption_resolution,[],[f477949,f1344]) ).
thf(f1344,plain,
vAPP(set(product_prod(v,v)),$o,vAPP(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o),vAPP(labeled_graph(standard_Constant(v2),v),sTfun(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o)),graph_homomorphism(standard_Constant(v2),v,v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)),g),vAPP(set(v),set(product_prod(v,v)),id_on(v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)))) = $true,
inference(cnf_transformation,[],[f707]) ).
thf(f707,plain,
vAPP(set(product_prod(v,v)),$o,vAPP(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o),vAPP(labeled_graph(standard_Constant(v2),v),sTfun(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o)),graph_homomorphism(standard_Constant(v2),v,v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)),g),vAPP(set(v),set(product_prod(v,v)),id_on(v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)))) = $true,
inference(fool_elimination,[],[f706]) ).
thf(f706,plain,
vAPP(set(product_prod(v,v)),$o,vAPP(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o),vAPP(labeled_graph(standard_Constant(v2),v),sTfun(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o)),graph_homomorphism(standard_Constant(v2),v,v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)),g),vAPP(set(v),set(product_prod(v,v)),id_on(v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)))),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
vAPP(set(product_prod(v,v)),$o,vAPP(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o),vAPP(labeled_graph(standard_Constant(v2),v),sTfun(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o)),graph_homomorphism(standard_Constant(v2),v,v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)),g),vAPP(set(v),set(product_prod(v,v)),id_on(v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_h_I3_J) ).
thf(f477949,plain,
vAPP(set(product_prod(v,v)),$o,vAPP(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o),vAPP(labeled_graph(standard_Constant(v2),v),sTfun(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o)),graph_homomorphism(standard_Constant(v2),v,v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)),g),vAPP(set(v),set(product_prod(v,v)),id_on(v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)))) != $true,
inference(unit_resulting_resolution,[],[f1342,f1041,f1303]) ).
thf(f1303,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X0,X6: labeled_graph(X1,X0),X4: X1,X5: labeled_graph(X1,X0)] :
( ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X5),X6),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X5))) )
| ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X6)) )
| ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X5)) ) ),
inference(cnf_transformation,[],[f930]) ).
thf(f930,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X0,X4: X1,X5: labeled_graph(X1,X0),X6: labeled_graph(X1,X0)] :
( ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X6)) )
| ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X5),X6),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X5))) )
| ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X5)) ) ),
inference(flattening,[],[f929]) ).
thf(f929,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X0,X4: X1,X5: labeled_graph(X1,X0),X6: labeled_graph(X1,X0)] :
( ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X6)) )
| ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X5),X6),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X5))) )
| ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X5)) ) ),
inference(ennf_transformation,[],[f639]) ).
thf(f639,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X0,X4: X1,X5: labeled_graph(X1,X0),X6: labeled_graph(X1,X0)] :
( ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X5)) )
=> ( ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X5),X6),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X5))) )
=> ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X6)) ) ) ),
inference(fool_elimination,[],[f638]) ).
thf(f638,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X0,X4: X1,X5: labeled_graph(X1,X0),X6: labeled_graph(X1,X0)] :
( vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X5))
=> ( vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X5),X6),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X5)))
=> vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X6)) ) ),
inference(rectify,[],[f30]) ).
thf(f30,axiom,
! [X0: $tType,X1: $tType,X25: X0,X26: X0,X27: X1,X28: labeled_graph(X1,X0),X36: labeled_graph(X1,X0)] :
( vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X25),X26)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X27),X28))
=> ( vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X28),X36),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X28)))
=> vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X25),X26)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X27),X36)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_getRel__subgraph) ).
thf(f1041,plain,
vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)) != $true,
inference(cnf_transformation,[],[f708]) ).
thf(f708,plain,
vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)) != $true,
inference(flattening,[],[f284]) ).
thf(f284,plain,
vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)) != $true,
inference(fool_elimination,[],[f283]) ).
thf(f283,plain,
~ vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)),
inference(rectify,[],[f280]) ).
thf(f280,negated_conjecture,
~ vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)),
inference(negated_conjecture,[],[f279]) ).
thf(f279,conjecture,
vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f1342,plain,
vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g))) = $true,
inference(cnf_transformation,[],[f703]) ).
thf(f703,plain,
vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g))) = $true,
inference(fool_elimination,[],[f702]) ).
thf(f702,plain,
vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g))),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP180^2 : TPTP v8.1.2. Released v7.5.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n009.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 : Fri May 3 19:18:53 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (24382)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.37 % (24385)WARNING: value z3 for option sas not known
% 0.17/0.37 % (24384)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.37 % (24383)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.37 % (24386)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.37 % (24385)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.17/0.37 % (24387)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.17/0.37 % (24388)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.17/0.37 % (24389)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.17/0.41 % (24389)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.42 % Exception at run slice level
% 0.17/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.42 % Exception at run slice level
% 0.17/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.43 % Exception at run slice level
% 0.17/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.43 % (24391)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.17/0.43 % (24392)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.17/0.44 % (24393)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.17/0.47 % (24391)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.47 % (24392)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.48 % Exception at run slice level
% 0.17/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.50 % (24394)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 175.36/25.46 % (24392)First to succeed.
% 175.36/25.46 % (24392)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24382"
% 175.36/25.47 % (24392)Refutation found. Thanks to Tanya!
% 175.36/25.47 % SZS status Theorem for theBenchmark
% 175.36/25.47 % SZS output start Proof for theBenchmark
% See solution above
% 175.36/25.47 % (24392)------------------------------
% 175.36/25.47 % (24392)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 175.36/25.47 % (24392)Termination reason: Refutation
% 175.36/25.47
% 175.36/25.47 % (24392)Memory used [KB]: 31752
% 175.36/25.47 % (24392)Time elapsed: 25.038 s
% 175.36/25.47 % (24392)Instructions burned: 66067 (million)
% 175.36/25.47 % (24382)Success in time 24.958 s
%------------------------------------------------------------------------------