TSTP Solution File: COM206^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM206^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.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 04:48:45 EDT 2024
% Result : Theorem 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 367
% Syntax : Number of formulae : 760 ( 238 unt; 186 typ; 0 def)
% Number of atoms : 3630 ( 640 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 670 ( 241 ~; 209 |; 15 &; 0 @)
% ( 90 <=>; 115 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 467 ( 462 >; 5 *; 0 +; 0 <<)
% Number of symbols : 304 ( 301 usr; 103 con; 0-8 aty)
% Number of variables : 1524 ( 32 ^ 973 !; 46 ?;1524 :)
% ( 473 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
itself: $tType > $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
set: $tType > $tType ).
thf(type_def_8,type,
product_prod: ( $tType * $tType ) > $tType ).
thf(type_def_9,type,
dtree: $tType ).
thf(type_def_10,type,
t: $tType ).
thf(type_def_11,type,
sum_sum: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
product_prod: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
sum_sum: ( $tType * $tType ) > $tType ).
thf(func_def_2,type,
dtree: $tType ).
thf(func_def_3,type,
set: $tType > $tType ).
thf(func_def_4,type,
t: $tType ).
thf(func_def_5,type,
itself: $tType > $tType ).
thf(func_def_6,type,
bounded_lattice:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_7,type,
type:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_8,type,
lattice:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_9,type,
distrib_lattice:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_10,type,
semilattice_inf:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_11,type,
semilattice_sup:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_12,type,
bounded_lattice_top:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_13,type,
bounde1561333602nf_top:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_14,type,
bNF_Greatest_image2:
!>[X0: $tType,X1: $tType,X2: $tType] : ( set(X0) > ( X0 > X1 ) > ( X0 > X2 ) > set(product_prod(X1,X2)) ) ).
thf(func_def_15,type,
cont: dtree > set(sum_sum(t,dtree)) ).
thf(func_def_16,type,
comp:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 ) > ( X2 > X0 ) > X2 > X1 ) ).
thf(func_def_17,type,
if:
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_18,type,
inf_inf:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_19,type,
sup_sup:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_20,type,
top_top:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
parall1899940088le_par: product_prod(dtree,dtree) > dtree ).
thf(func_def_22,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > product_prod(X0,X1) ) ).
thf(func_def_23,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X1) > X2 ) > X0 > X1 > X2 ) ).
thf(func_def_24,type,
produc2004651681e_prod:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).
thf(func_def_25,type,
product_map_prod:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( X0 > X1 ) > ( X2 > X3 ) > product_prod(X0,X2) > product_prod(X1,X3) ) ).
thf(func_def_26,type,
product_rec_prod:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).
thf(func_def_27,type,
product_case_prod:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).
thf(func_def_28,type,
product_swap:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > product_prod(X1,X0) ) ).
thf(func_def_29,type,
product_scomp:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( X0 > product_prod(X1,X2) ) > ( X1 > X2 > X3 ) > X0 > X3 ) ).
thf(func_def_30,type,
type2:
!>[X0: $tType] : itself(X0) ).
thf(func_def_31,type,
collect:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).
thf(func_def_32,type,
image:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > set(X0) > set(X1) ) ).
thf(func_def_33,type,
vimage:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > set(X1) > set(X0) ) ).
thf(func_def_34,type,
sum_Inl:
!>[X0: $tType,X1: $tType] : ( X0 > sum_sum(X0,X1) ) ).
thf(func_def_35,type,
sum_Inr:
!>[X0: $tType,X1: $tType] : ( X0 > sum_sum(X1,X0) ) ).
thf(func_def_36,type,
sum_Plus:
!>[X0: $tType,X1: $tType] : ( set(X0) > set(X1) > set(sum_sum(X0,X1)) ) ).
thf(func_def_37,type,
sum_Suml:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 ) > sum_sum(X0,X2) > X1 ) ).
thf(func_def_38,type,
sum_Sumr:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 ) > sum_sum(X2,X0) > X1 ) ).
thf(func_def_39,type,
sum_rec_sum:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 ) > ( X2 > X1 ) > sum_sum(X0,X2) > X1 ) ).
thf(func_def_40,type,
sum_case_sum:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 ) > ( X2 > X1 ) > sum_sum(X0,X2) > X1 ) ).
thf(func_def_41,type,
type_definition:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X1 > X0 ) > set(X1) > $o ) ).
thf(func_def_42,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_43,type,
tr1: dtree ).
thf(func_def_44,type,
tr1a: dtree ).
thf(func_def_45,type,
tr2: dtree ).
thf(func_def_46,type,
tr2a: dtree ).
thf(func_def_47,type,
trA: dtree ).
thf(func_def_48,type,
trA2: dtree ).
thf(func_def_49,type,
trB: dtree ).
thf(func_def_53,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_54,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_55,type,
vAND: $o > $o > $o ).
thf(func_def_56,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_58,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_59,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_60,type,
vOR: $o > $o > $o ).
thf(func_def_61,type,
vIMP: $o > $o > $o ).
thf(func_def_62,type,
sK0: dtree ).
thf(func_def_63,type,
sK1: dtree ).
thf(func_def_64,type,
sK2:
!>[X0: $tType] : X0 ).
thf(func_def_65,type,
sK3:
!>[X0: $tType] : X0 ).
thf(func_def_66,type,
sK4:
!>[X0: $tType] : X0 ).
thf(func_def_67,type,
sK5:
!>[X0: $tType] : X0 ).
thf(func_def_68,type,
sK6:
!>[X0: $tType] : X0 ).
thf(func_def_69,type,
sK7:
!>[X0: $tType] : X0 ).
thf(func_def_70,type,
sK8: product_prod(dtree,dtree) > dtree ).
thf(func_def_71,type,
sK9: product_prod(dtree,dtree) > dtree ).
thf(func_def_72,type,
sK10:
!>[X0: $tType] : X0 ).
thf(func_def_73,type,
sK11:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_74,type,
sK12: ( product_prod(dtree,dtree) > $o ) > dtree ).
thf(func_def_75,type,
sK13: ( product_prod(dtree,dtree) > $o ) > dtree ).
thf(func_def_76,type,
sK14:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_77,type,
sK15:
!>[X0: $tType,X1: $tType] : ( sum_sum(X0,X1) > X1 ) ).
thf(func_def_78,type,
sK16:
!>[X0: $tType,X1: $tType] : ( sum_sum(X0,X1) > X0 ) ).
thf(func_def_79,type,
sK17:
!>[X0: $tType,X1: $tType] : ( sum_sum(X0,X1) > X1 ) ).
thf(func_def_80,type,
sK18:
!>[X0: $tType,X1: $tType] : ( sum_sum(X0,X1) > X0 ) ).
thf(func_def_81,type,
sK19:
!>[X0: $tType,X1: $tType] : ( sum_sum(X0,X1) > X1 ) ).
thf(func_def_82,type,
sK20:
!>[X0: $tType,X1: $tType] : ( sum_sum(X0,X1) > X0 ) ).
thf(func_def_83,type,
sK21:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
thf(func_def_84,type,
sK22:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
thf(func_def_85,type,
sK23:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
thf(func_def_86,type,
sK24:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
thf(func_def_87,type,
sK25:
!>[X0: $tType,X1: $tType] : ( X0 > ( X1 > X0 ) > X1 ) ).
thf(func_def_88,type,
sK26:
!>[X0: $tType,X1: $tType] : ( X0 > ( X1 > X0 ) > X1 ) ).
thf(func_def_89,type,
sK27:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_90,type,
sK28:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_91,type,
sK29:
!>[X0: $tType,X1: $tType] : ( ( sum_sum(X1,X0) > $o ) > X0 ) ).
thf(func_def_92,type,
sK30:
!>[X0: $tType,X1: $tType] : ( ( sum_sum(X1,X0) > $o ) > X1 ) ).
thf(func_def_93,type,
sK31:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).
thf(func_def_94,type,
sK32:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).
thf(func_def_95,type,
sK33:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).
thf(func_def_96,type,
sK34:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).
thf(func_def_97,type,
sK35:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
thf(func_def_98,type,
sK36:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
thf(func_def_99,type,
sK37:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
thf(func_def_100,type,
sK38:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > ( X0 > $o ) > X1 ) ).
thf(func_def_101,type,
sK39:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > set(X1) > ( X1 > X0 ) > X0 ) ).
thf(func_def_102,type,
sK40:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X2 ) ).
thf(func_def_103,type,
sK41:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X1 ) ).
thf(func_def_104,type,
sK42:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X0 ) ).
thf(func_def_105,type,
sK43:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > set(X1) > ( X1 > X0 ) > X1 ) ).
thf(func_def_106,type,
sK44:
!>[X0: $tType,X1: $tType] : ( X0 > ( X1 > X0 ) > X1 ) ).
thf(func_def_107,type,
sK45:
!>[X0: $tType,X1: $tType] : ( set(X1) > sum_sum(X0,X1) > X1 ) ).
thf(func_def_108,type,
sK46:
!>[X0: $tType,X1: $tType] : ( set(X0) > sum_sum(X0,X1) > X0 ) ).
thf(func_def_109,type,
sK47:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
thf(func_def_110,type,
sK48:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
thf(func_def_111,type,
sK49:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
thf(func_def_112,type,
sK50:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
thf(func_def_113,type,
sK51:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > set(X1) > X1 ) ).
thf(func_def_114,type,
sK52:
!>[X0: $tType,X1: $tType,X2: $tType] : ( $o > ( sum_sum(X0,X1) > X2 ) > X2 > X1 ) ).
thf(func_def_115,type,
sK53:
!>[X0: $tType,X1: $tType,X2: $tType] : ( $o > ( sum_sum(X0,X1) > X2 ) > X2 > X0 ) ).
thf(func_def_116,type,
sK54:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > set(X1) > X1 ) ).
thf(func_def_117,type,
sK55:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > ( X2 > X1 ) > X1 ) ).
thf(func_def_118,type,
sK56:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X3 ) ).
thf(func_def_119,type,
sK57:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X2 ) ).
thf(func_def_120,type,
sK58:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X1 ) ).
thf(func_def_121,type,
sK59:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X0 ) ).
thf(func_def_122,type,
sK60:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,X2) > ( X0 > X2 > set(X1) ) > X1 > X0 ) ).
thf(func_def_123,type,
sK61:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,X2) > ( X0 > X2 > set(X1) ) > X1 > X2 ) ).
thf(func_def_124,type,
sK62:
!>[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_125,type,
sK63:
!>[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_126,type,
sK64:
!>[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_127,type,
sK65:
!>[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_128,type,
sK66:
!>[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_129,type,
sK67:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > set(X1) > X1 ) ).
thf(func_def_130,type,
sK68:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > set(X1) > X1 ) ).
thf(func_def_131,type,
sK69:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > ( X2 > X1 ) > X1 ) ).
thf(func_def_132,type,
sK70:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 > X1 ) > ( X2 > X1 ) > set(X0) > ( X0 > X2 ) > X0 ) ).
thf(func_def_133,type,
sK71:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 > X1 > X0 ) > ( X2 > X1 > X0 ) > product_prod(X2,X1) > X2 ) ).
thf(func_def_134,type,
sK72:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 > X1 > X0 ) > ( X2 > X1 > X0 ) > product_prod(X2,X1) > X1 ) ).
thf(func_def_135,type,
sK73:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > ( X2 > X1 ) > ( X2 > X1 ) > X1 ) ).
thf(func_def_136,type,
sK74:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > ( X2 > X1 ) > ( X2 > X1 ) > X1 ) ).
thf(func_def_137,type,
sK75:
!>[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_138,type,
sK76:
!>[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_139,type,
sK77:
!>[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_140,type,
sK78:
!>[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_141,type,
sK79:
!>[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_142,type,
sK80:
!>[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_143,type,
sK81:
!>[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_144,type,
sK82:
!>[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_145,type,
sK83:
!>[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_146,type,
sK84:
!>[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_147,type,
sK85:
!>[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_148,type,
sK86:
!>[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_149,type,
sK87:
!>[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_150,type,
sK88:
!>[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_151,type,
sK89:
!>[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_152,type,
sK90:
!>[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_153,type,
sK91:
!>[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_154,type,
sK92:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( set(product_prod(X3,X2)) > ( X2 > X0 ) > ( X3 > X1 ) > product_prod(X1,X0) > X3 ) ).
thf(func_def_155,type,
sK93:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( set(product_prod(X3,X2)) > ( X2 > X0 ) > ( X3 > X1 ) > product_prod(X1,X0) > X2 ) ).
thf(func_def_156,type,
sK94:
!>[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_157,type,
sK95:
!>[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_158,type,
sK96:
!>[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_159,type,
sK97:
!>[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_160,type,
sK98:
!>[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_161,type,
sK99:
!>[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_162,type,
sK100:
!>[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_163,type,
sK101:
!>[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_164,type,
sK102:
!>[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_165,type,
sK103:
!>[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_166,type,
sK104:
!>[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_167,type,
sK105:
!>[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_168,type,
sK106:
!>[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_169,type,
sK107:
!>[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_170,type,
sK108: dtree ).
thf(func_def_171,type,
sK109: dtree ).
thf(func_def_173,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_174,type,
vNOT: $o > $o ).
thf(func_def_175,type,
sK111:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > set(X1) > X0 > X1 ) ).
thf(func_def_176,type,
sK112:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_177,type,
sK113:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_178,type,
sK114:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_179,type,
sK115:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_180,type,
sK116:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_181,type,
sK117:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_182,type,
sK118:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X1 ) ).
thf(f2305,plain,
$false,
inference(avatar_sat_refutation,[],[f1590,f1594,f1627,f1632,f1637,f1642,f1647,f1652,f1657,f1661,f1665,f1669,f1673,f1677,f1681,f1685,f1689,f1696,f1700,f1704,f1708,f1712,f1716,f1720,f1729,f1733,f1737,f1742,f1747,f1752,f1756,f1776,f1780,f1784,f1788,f1792,f1796,f1800,f1836,f1840,f1844,f1848,f1852,f1856,f1860,f1864,f1868,f1872,f1876,f1902,f1942,f1950,f1959,f1963,f1967,f1971,f1975,f1979,f2001,f2013,f2017,f2037,f2041,f2049,f2059,f2063,f2067,f2071,f2075,f2079,f2088,f2096,f2101,f2106,f2111,f2115,f2119,f2169,f2173,f2177,f2223,f2227,f2231,f2235,f2239,f2243,f2247,f2291,f2303,f2304]) ).
thf(f2304,plain,
spl110_31,
inference(avatar_split_clause,[],[f1344,f1749]) ).
thf(f1749,plain,
( spl110_31
<=> ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr1),tr2)) = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),sK0),sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_31])]) ).
thf(f1344,plain,
vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr1),tr2)) = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),sK0),sK1)),
inference(definition_unfolding,[],[f1035,f1034]) ).
thf(f1034,plain,
trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr1),tr2)),
inference(cnf_transformation,[],[f4]) ).
thf(f4,axiom,
trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr1),tr2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062trA_H_A_061_Atr1_H_A_092_060parallel_062_Atr2_H_092_060close_062) ).
thf(f1035,plain,
trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),sK0),sK1)),
inference(cnf_transformation,[],[f924]) ).
thf(f924,plain,
( ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),sK1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) )
& ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),sK0)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)) )
& ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),sK0),sK1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f741,f923]) ).
thf(f923,plain,
( ? [X0: dtree,X1: dtree] :
( ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) )
& ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X0)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)) )
& ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) ) )
=> ( ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),sK1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) )
& ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),sK0)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)) )
& ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),sK0),sK1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f741,plain,
? [X0: dtree,X1: dtree] :
( ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) )
& ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X0)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)) )
& ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) ) ),
inference(flattening,[],[f740]) ).
thf(f740,plain,
? [X0: dtree,X1: dtree] :
( ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) )
& ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X0)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)) )
& ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) ) ),
inference(ennf_transformation,[],[f619]) ).
thf(f619,plain,
~ ! [X0: dtree,X1: dtree] :
( ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) )
=> ( ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X0)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)) )
=> ( $true != vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) ) ) ),
inference(flattening,[],[f289]) ).
thf(f289,plain,
~ ! [X0: dtree,X1: dtree] :
( ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) )
=> ( ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X0)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)) )
=> ( $true != vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) ) ) ),
inference(fool_elimination,[],[f288]) ).
thf(f288,plain,
~ ! [X0: dtree,X1: dtree] :
( ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) )
=> ( vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X0)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a))
=> ~ vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) ) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
~ ! [X7: dtree,X8: dtree] :
( ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X7),X8)) )
=> ( vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X7)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a))
=> ~ vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),X8)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062tr1_H_Atr2_H_O_A_092_060lbrakk_062trA_H_A_061_Atr1_H_A_092_060parallel_062_Atr2_H_059_AInr_Atr1_H_A_092_060in_062_Acont_Atr1_059_AInr_Atr2_H_A_092_060in_062_Acont_Atr2_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(f2303,plain,
spl110_90,
inference(avatar_split_clause,[],[f1155,f2301]) ).
thf(f2301,plain,
( spl110_90
<=> ! [X1: $tType,X0: $tType,X3: X0,X2: X1] : ( vAPP(product_prod(X1,X0),product_prod(X0,X1),product_swap(X1,X0),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X2),X3)) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_90])]) ).
thf(f1155,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0] : ( vAPP(product_prod(X1,X0),product_prod(X0,X1),product_swap(X1,X0),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X2),X3)) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ),
inference(cnf_transformation,[],[f651]) ).
thf(f651,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0] : ( vAPP(product_prod(X1,X0),product_prod(X0,X1),product_swap(X1,X0),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X2),X3)) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
! [X0: $tType,X2: $tType,X9: X2,X20: X0] : ( vAPP(product_prod(X2,X0),product_prod(X0,X2),product_swap(X2,X0),vAPP(X0,product_prod(X2,X0),vAPP(X2,sTfun(X0,product_prod(X2,X0)),product_Pair(X2,X0),X9),X20)) = vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X20),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_swap__simp) ).
thf(f2291,plain,
( spl110_89
| ~ spl110_9
| ~ spl110_49 ),
inference(avatar_split_clause,[],[f1938,f1870,f1654,f2289]) ).
thf(f2289,plain,
( spl110_89
<=> ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,semilattice_inf(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_89])]) ).
thf(f1654,plain,
( spl110_9
<=> ( vAPP(itself($o),$o,semilattice_inf($o),type2($o)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_9])]) ).
thf(f1870,plain,
( spl110_49
<=> ! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_49])]) ).
thf(f1938,plain,
( ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,semilattice_inf(sTfun(X0,$o)),type2(sTfun(X0,$o))) )
| ~ spl110_9
| ~ spl110_49 ),
inference(trivial_inequality_removal,[],[f1933]) ).
thf(f1933,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = vAPP(itself(sTfun(X0,$o)),$o,semilattice_inf(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) )
| ~ spl110_9
| ~ spl110_49 ),
inference(superposition,[],[f1871,f1656]) ).
thf(f1656,plain,
( ( vAPP(itself($o),$o,semilattice_inf($o),type2($o)) = $true )
| ~ spl110_9 ),
inference(avatar_component_clause,[],[f1654]) ).
thf(f1871,plain,
( ! [X1: $tType,X0: $tType] :
( ( $true != vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1)) )
| ( $true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) )
| ~ spl110_49 ),
inference(avatar_component_clause,[],[f1870]) ).
thf(f2247,plain,
spl110_88,
inference(avatar_split_clause,[],[f1082,f2245]) ).
thf(f2245,plain,
( spl110_88
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)),X2) )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_88])]) ).
thf(f1082,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)),X2) )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f782]) ).
thf(f782,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)),X2) )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f377]) ).
thf(f377,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) = $true )
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)),X2) ) ),
inference(fool_elimination,[],[f376]) ).
thf(f376,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0))
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)),X2) ) ),
inference(rectify,[],[f191]) ).
thf(f191,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0))
=> ! [X18: X0,X14: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X18),X14) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X18),X14)),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_inf_Oright__idem) ).
thf(f2243,plain,
spl110_87,
inference(avatar_split_clause,[],[f1080,f2241]) ).
thf(f2241,plain,
( spl110_87
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_87])]) ).
thf(f1080,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f780]) ).
thf(f780,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f373]) ).
thf(f373,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) = $true )
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) ) ),
inference(fool_elimination,[],[f372]) ).
thf(f372,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0))
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) ) ),
inference(rectify,[],[f192]) ).
thf(f192,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0))
=> ! [X9: X0,X20: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X9),X20) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X9),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_inf__left__idem) ).
thf(f2239,plain,
spl110_86,
inference(avatar_split_clause,[],[f1071,f2237]) ).
thf(f2237,plain,
( spl110_86
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X2) )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_86])]) ).
thf(f1071,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X2) )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f771]) ).
thf(f771,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X2) )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f355]) ).
thf(f355,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) = $true )
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X2) ) ),
inference(fool_elimination,[],[f354]) ).
thf(f354,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0))
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)),X2) ) ),
inference(rectify,[],[f86]) ).
thf(f86,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0))
=> ! [X18: X0,X14: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X18),X14) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X18),X14)),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_sup_Oright__idem) ).
thf(f2235,plain,
spl110_85,
inference(avatar_split_clause,[],[f1069,f2233]) ).
thf(f2233,plain,
( spl110_85
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_85])]) ).
thf(f1069,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f769]) ).
thf(f769,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f351]) ).
thf(f351,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) = $true )
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) ) ),
inference(fool_elimination,[],[f350]) ).
thf(f350,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0))
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) ) ),
inference(rectify,[],[f88]) ).
thf(f88,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0))
=> ! [X18: X0,X14: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X18),X14) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X18),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X18),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_sup_Oleft__idem) ).
thf(f2231,plain,
spl110_84,
inference(avatar_split_clause,[],[f1058,f2229]) ).
thf(f2229,plain,
( spl110_84
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_84])]) ).
thf(f1058,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f758]) ).
thf(f758,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f329]) ).
thf(f329,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) = $true )
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) ) ),
inference(fool_elimination,[],[f328]) ).
thf(f328,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) ) ),
inference(rectify,[],[f239]) ).
thf(f239,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ! [X9: X0,X20: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X9),X20) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X9),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_inf__sup__aci_I4_J) ).
thf(f2227,plain,
( spl110_83
| ~ spl110_8
| ~ spl110_48 ),
inference(avatar_split_clause,[],[f1932,f1866,f1649,f2225]) ).
thf(f2225,plain,
( spl110_83
<=> ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,semilattice_sup(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_83])]) ).
thf(f1649,plain,
( spl110_8
<=> ( vAPP(itself($o),$o,semilattice_sup($o),type2($o)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_8])]) ).
thf(f1866,plain,
( spl110_48
<=> ! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_sup(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,semilattice_sup(X1),type2(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_48])]) ).
thf(f1932,plain,
( ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,semilattice_sup(sTfun(X0,$o)),type2(sTfun(X0,$o))) )
| ~ spl110_8
| ~ spl110_48 ),
inference(trivial_inequality_removal,[],[f1927]) ).
thf(f1927,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = vAPP(itself(sTfun(X0,$o)),$o,semilattice_sup(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) )
| ~ spl110_8
| ~ spl110_48 ),
inference(superposition,[],[f1867,f1651]) ).
thf(f1651,plain,
( ( vAPP(itself($o),$o,semilattice_sup($o),type2($o)) = $true )
| ~ spl110_8 ),
inference(avatar_component_clause,[],[f1649]) ).
thf(f1867,plain,
( ! [X1: $tType,X0: $tType] :
( ( $true != vAPP(itself(X1),$o,semilattice_sup(X1),type2(X1)) )
| ( $true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_sup(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) )
| ~ spl110_48 ),
inference(avatar_component_clause,[],[f1866]) ).
thf(f2223,plain,
spl110_82,
inference(avatar_split_clause,[],[f1057,f2221]) ).
thf(f2221,plain,
( spl110_82
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_82])]) ).
thf(f1057,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f757]) ).
thf(f757,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f327]) ).
thf(f327,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) = $true )
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) ) ),
inference(fool_elimination,[],[f326]) ).
thf(f326,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) ) ),
inference(rectify,[],[f101]) ).
thf(f101,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ! [X9: X0,X20: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X9),X20) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X9),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_inf__sup__aci_I8_J) ).
thf(f2177,plain,
spl110_81,
inference(avatar_split_clause,[],[f1144,f2175]) ).
thf(f2175,plain,
( spl110_81
<=> ! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK19(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK20(X0,X1),X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_81])]) ).
thf(f1144,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK19(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK20(X0,X1),X2)) = X2 ) ),
inference(cnf_transformation,[],[f950]) ).
thf(f950,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK19(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK20(X0,X1),X2)) = X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f947,f949,f948]) ).
thf(f948,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ? [X3: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) = X2 )
=> ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK19(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f949,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ? [X4: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X4) = X2 )
=> ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK20(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f947,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ? [X3: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) = X2 )
| ? [X4: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X4) = X2 ) ),
inference(rectify,[],[f805]) ).
thf(f805,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ? [X4: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4) = X2 )
| ? [X3: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X3) = X2 ) ),
inference(ennf_transformation,[],[f640]) ).
thf(f640,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ! [X3: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X3) != X2 )
=> ~ ! [X4: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4) != X2 ) ),
inference(rectify,[],[f26]) ).
thf(f26,axiom,
! [X0: $tType,X2: $tType,X20: sum_sum(X0,X2)] :
( ! [X27: X0] : ( vAPP(X0,sum_sum(X0,X2),sum_Inl(X0,X2),X27) != X20 )
=> ~ ! [X28: X2] : ( vAPP(X2,sum_sum(X0,X2),sum_Inr(X2,X0),X28) != X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_old_Osum_Oexhaust) ).
thf(f2173,plain,
spl110_80,
inference(avatar_split_clause,[],[f1143,f2171]) ).
thf(f2171,plain,
( spl110_80
<=> ! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK17(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK18(X0,X1),X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_80])]) ).
thf(f1143,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK17(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK18(X0,X1),X2)) = X2 ) ),
inference(cnf_transformation,[],[f946]) ).
thf(f946,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK17(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK18(X0,X1),X2)) = X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f943,f945,f944]) ).
thf(f944,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ? [X3: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) = X2 )
=> ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK17(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f945,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ? [X4: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X4) = X2 )
=> ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK18(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f943,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ? [X3: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) = X2 )
| ? [X4: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X4) = X2 ) ),
inference(rectify,[],[f804]) ).
thf(f804,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ? [X4: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4) = X2 )
| ? [X3: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X3) = X2 ) ),
inference(ennf_transformation,[],[f639]) ).
thf(f639,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ! [X3: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X3) != X2 )
=> ~ ! [X4: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4) != X2 ) ),
inference(rectify,[],[f24]) ).
thf(f24,axiom,
! [X0: $tType,X2: $tType,X31: sum_sum(X0,X2)] :
( ! [X25: X0] : ( vAPP(X0,sum_sum(X0,X2),sum_Inl(X0,X2),X25) != X31 )
=> ~ ! [X25: X2] : ( vAPP(X2,sum_sum(X0,X2),sum_Inr(X2,X0),X25) != X31 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_obj__sumE) ).
thf(f2169,plain,
spl110_79,
inference(avatar_split_clause,[],[f1142,f2167]) ).
thf(f2167,plain,
( spl110_79
<=> ! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK15(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK16(X0,X1),X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_79])]) ).
thf(f1142,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK15(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK16(X0,X1),X2)) = X2 ) ),
inference(cnf_transformation,[],[f942]) ).
thf(f942,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK15(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK16(X0,X1),X2)) = X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f939,f941,f940]) ).
thf(f940,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ? [X3: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) = X2 )
=> ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK15(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f941,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ? [X4: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X4) = X2 )
=> ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK16(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f939,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ? [X3: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) = X2 )
| ? [X4: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X4) = X2 ) ),
inference(rectify,[],[f803]) ).
thf(f803,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ? [X4: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4) = X2 )
| ? [X3: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X3) = X2 ) ),
inference(ennf_transformation,[],[f638]) ).
thf(f638,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ! [X3: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X3) != X2 )
=> ~ ! [X4: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4) != X2 ) ),
inference(rectify,[],[f30]) ).
thf(f30,axiom,
! [X0: $tType,X2: $tType,X31: sum_sum(X0,X2)] :
( ! [X25: X0] : ( vAPP(X0,sum_sum(X0,X2),sum_Inl(X0,X2),X25) != X31 )
=> ~ ! [X26: X2] : ( vAPP(X2,sum_sum(X0,X2),sum_Inr(X2,X0),X26) != X31 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_sumE) ).
thf(f2119,plain,
spl110_78,
inference(avatar_split_clause,[],[f1200,f2117]) ).
thf(f2117,plain,
( spl110_78
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X1 > X0] : ( $true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X1,X0,X2,X3)),vAPP(set(X1),set(X0),vAPP(sTfun(X1,X0),sTfun(set(X1),set(X0)),image(X1,X0),X2),top_top(set(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_78])]) ).
thf(f1200,plain,
! [X1: $tType,X0: $tType,X2: X1 > X0,X3: X1] : ( $true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X1,X0,X2,X3)),vAPP(set(X1),set(X0),vAPP(sTfun(X1,X0),sTfun(set(X1),set(X0)),image(X1,X0),X2),top_top(set(X1)))) ),
inference(cnf_transformation,[],[f503]) ).
thf(f503,plain,
! [X0: $tType,X1: $tType,X2: X1 > X0,X3: X1] : ( $true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X1,X0,X2,X3)),vAPP(set(X1),set(X0),vAPP(sTfun(X1,X0),sTfun(set(X1),set(X0)),image(X1,X0),X2),top_top(set(X1)))) ),
inference(fool_elimination,[],[f502]) ).
thf(f502,plain,
! [X0: $tType,X1: $tType,X2: X1 > X0,X3: X1] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X1,X0,X2,X3)),vAPP(set(X1),set(X0),vAPP(sTfun(X1,X0),sTfun(set(X1),set(X0)),image(X1,X0),X2),top_top(set(X1)))),
inference(rectify,[],[f165]) ).
thf(f165,axiom,
! [X0: $tType,X2: $tType,X50: X2 > X0,X9: X2] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X2,X0,X50,X9)),vAPP(set(X2),set(X0),vAPP(sTfun(X2,X0),sTfun(set(X2),set(X0)),image(X2,X0),X50),top_top(set(X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_rangeI) ).
thf(f2115,plain,
( spl110_77
| ~ spl110_7
| ~ spl110_47 ),
inference(avatar_split_clause,[],[f1926,f1862,f1644,f2113]) ).
thf(f2113,plain,
( spl110_77
<=> ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_77])]) ).
thf(f1644,plain,
( spl110_7
<=> ( vAPP(itself($o),$o,lattice($o),type2($o)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_7])]) ).
thf(f1862,plain,
( spl110_47
<=> ! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,lattice(X1),type2(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_47])]) ).
thf(f1926,plain,
( ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))) )
| ~ spl110_7
| ~ spl110_47 ),
inference(trivial_inequality_removal,[],[f1921]) ).
thf(f1921,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = vAPP(itself(sTfun(X0,$o)),$o,lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) )
| ~ spl110_7
| ~ spl110_47 ),
inference(superposition,[],[f1863,f1646]) ).
thf(f1646,plain,
( ( vAPP(itself($o),$o,lattice($o),type2($o)) = $true )
| ~ spl110_7 ),
inference(avatar_component_clause,[],[f1644]) ).
thf(f1863,plain,
( ! [X1: $tType,X0: $tType] :
( ( $true != vAPP(itself(X1),$o,lattice(X1),type2(X1)) )
| ( $true = vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) )
| ~ spl110_47 ),
inference(avatar_component_clause,[],[f1862]) ).
thf(f2111,plain,
spl110_76,
inference(avatar_split_clause,[],[f1341,f2108]) ).
thf(f2108,plain,
( spl110_76
<=> ( vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),tr1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_76])]) ).
thf(f1341,plain,
vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),tr1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)) = $true,
inference(cnf_transformation,[],[f615]) ).
thf(f615,plain,
vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),tr1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)) = $true,
inference(fool_elimination,[],[f614]) ).
thf(f614,plain,
vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),tr1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),tr1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062Inr_Atr1_H_A_092_060in_062_Acont_Atr1_092_060close_062) ).
thf(f2106,plain,
spl110_75,
inference(avatar_split_clause,[],[f1340,f2103]) ).
thf(f2103,plain,
( spl110_75
<=> ( vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),tr2)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_75])]) ).
thf(f1340,plain,
vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),tr2)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) = $true,
inference(cnf_transformation,[],[f613]) ).
thf(f613,plain,
vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),tr2)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) = $true,
inference(fool_elimination,[],[f612]) ).
thf(f612,plain,
vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),tr2)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),tr2)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062Inr_Atr2_H_A_092_060in_062_Acont_Atr2_092_060close_062) ).
thf(f2101,plain,
spl110_74,
inference(avatar_split_clause,[],[f1037,f2098]) ).
thf(f2098,plain,
( spl110_74
<=> ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),sK1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_74])]) ).
thf(f1037,plain,
$true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),sK1)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr2a)),
inference(cnf_transformation,[],[f924]) ).
thf(f2096,plain,
spl110_73,
inference(avatar_split_clause,[],[f1036,f2093]) ).
thf(f2093,plain,
( spl110_73
<=> ( $true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),sK0)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_73])]) ).
thf(f1036,plain,
$true = vAPP(set(sum_sum(t,dtree)),$o,vAPP(sum_sum(t,dtree),sTfun(set(sum_sum(t,dtree)),$o),member(sum_sum(t,dtree)),vAPP(dtree,sum_sum(t,dtree),sum_Inr(dtree,t),sK0)),vAPP(dtree,set(sum_sum(t,dtree)),cont,tr1a)),
inference(cnf_transformation,[],[f924]) ).
thf(f2088,plain,
( spl110_72
| ~ spl110_5
| ~ spl110_46 ),
inference(avatar_split_clause,[],[f1920,f1858,f1634,f2086]) ).
thf(f2086,plain,
( spl110_72
<=> ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,distrib_lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_72])]) ).
thf(f1634,plain,
( spl110_5
<=> ( vAPP(itself($o),$o,distrib_lattice($o),type2($o)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_5])]) ).
thf(f1858,plain,
( spl110_46
<=> ! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,distrib_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,distrib_lattice(X1),type2(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_46])]) ).
thf(f1920,plain,
( ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,distrib_lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))) )
| ~ spl110_5
| ~ spl110_46 ),
inference(trivial_inequality_removal,[],[f1915]) ).
thf(f1915,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = vAPP(itself(sTfun(X0,$o)),$o,distrib_lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) )
| ~ spl110_5
| ~ spl110_46 ),
inference(superposition,[],[f1859,f1636]) ).
thf(f1636,plain,
( ( vAPP(itself($o),$o,distrib_lattice($o),type2($o)) = $true )
| ~ spl110_5 ),
inference(avatar_component_clause,[],[f1634]) ).
thf(f1859,plain,
( ! [X1: $tType,X0: $tType] :
( ( $true != vAPP(itself(X1),$o,distrib_lattice(X1),type2(X1)) )
| ( $true = vAPP(itself(sTfun(X0,X1)),$o,distrib_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) )
| ~ spl110_46 ),
inference(avatar_component_clause,[],[f1858]) ).
thf(f2079,plain,
spl110_71,
inference(avatar_split_clause,[],[f1430,f2077]) ).
thf(f2077,plain,
( spl110_71
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X1,X4: X2 > X0,X6: X2] : ( vAPP(X0,X1,X3,vAPP(X2,X0,X4,X6)) = vAPP(X2,X1,vAPP(sTfun(X2,X0),sTfun(X2,X1),vAPP(sTfun(X0,X1),sTfun(sTfun(X2,X0),sTfun(X2,X1)),bCOMB,X3),X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_71])]) ).
thf(f1430,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X1,X6: X2,X4: X2 > X0] : ( vAPP(X0,X1,X3,vAPP(X2,X0,X4,X6)) = vAPP(X2,X1,vAPP(sTfun(X2,X0),sTfun(X2,X1),vAPP(sTfun(X0,X1),sTfun(sTfun(X2,X0),sTfun(X2,X1)),bCOMB,X3),X4),X6) ),
inference(equality_resolution,[],[f1383]) ).
thf(f1383,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X1,X6: X2,X4: X2 > X0,X5: X2 > X1] :
( ( vAPP(X0,X1,X3,vAPP(X2,X0,X4,X6)) = vAPP(X2,X1,X5,X6) )
| ( vAPP(sTfun(X2,X0),sTfun(X2,X1),vAPP(sTfun(X0,X1),sTfun(sTfun(X2,X0),sTfun(X2,X1)),bCOMB,X3),X4) != X5 ) ),
inference(definition_unfolding,[],[f1290,f1136]) ).
thf(f1136,plain,
! [X1: $tType,X0: $tType,X2: $tType] : ( comp(X2,X1,X0) = bCOMB ),
inference(cnf_transformation,[],[f451]) ).
thf(f451,plain,
! [X0: $tType,X1: $tType,X2: $tType] : ( comp(X2,X1,X0) = bCOMB ),
inference(fool_elimination,[],[f450]) ).
thf(f450,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( comp(X2,X1,X0)
= ( ^ [X3: X2 > X1,X4: X0 > X2,X5: X0] : vAPP(X2,X1,X3,vAPP(X0,X2,X4,X5)) ) ),
inference(rectify,[],[f148]) ).
thf(f148,axiom,
! [X0: $tType,X1: $tType,X2: $tType] :
( comp(X2,X1,X0)
= ( ^ [X59: X2 > X1,X68: X0 > X2,X36: X0] : vAPP(X2,X1,X59,vAPP(X0,X2,X68,X36)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_comp__def) ).
thf(f1290,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X1,X6: X2,X4: X2 > X0,X5: X2 > X1] :
( ( vAPP(X0,X1,X3,vAPP(X2,X0,X4,X6)) = vAPP(X2,X1,X5,X6) )
| ( vAPP(sTfun(X2,X0),sTfun(X2,X1),vAPP(sTfun(X0,X1),sTfun(sTfun(X2,X0),sTfun(X2,X1)),comp(X0,X1,X2),X3),X4) != X5 ) ),
inference(cnf_transformation,[],[f887]) ).
thf(f887,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X1,X4: X2 > X0,X5: X2 > X1,X6: X2] :
( ( vAPP(X0,X1,X3,vAPP(X2,X0,X4,X6)) = vAPP(X2,X1,X5,X6) )
| ( vAPP(sTfun(X2,X0),sTfun(X2,X1),vAPP(sTfun(X0,X1),sTfun(sTfun(X2,X0),sTfun(X2,X1)),comp(X0,X1,X2),X3),X4) != X5 ) ),
inference(ennf_transformation,[],[f714]) ).
thf(f714,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X1,X4: X2 > X0,X5: X2 > X1,X6: X2] :
( ( vAPP(sTfun(X2,X0),sTfun(X2,X1),vAPP(sTfun(X0,X1),sTfun(sTfun(X2,X0),sTfun(X2,X1)),comp(X0,X1,X2),X3),X4) = X5 )
=> ( vAPP(X0,X1,X3,vAPP(X2,X0,X4,X6)) = vAPP(X2,X1,X5,X6) ) ),
inference(rectify,[],[f144]) ).
thf(f144,axiom,
! [X1: $tType,X2: $tType,X0: $tType,X18: X1 > X2,X14: X0 > X1,X55: X0 > X2,X84: X0] :
( ( vAPP(sTfun(X0,X1),sTfun(X0,X2),vAPP(sTfun(X1,X2),sTfun(sTfun(X0,X1),sTfun(X0,X2)),comp(X1,X2,X0),X18),X14) = X55 )
=> ( vAPP(X1,X2,X18,vAPP(X0,X1,X14,X84)) = vAPP(X0,X2,X55,X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_comp__eq__dest__lhs) ).
thf(f2075,plain,
spl110_70,
inference(avatar_split_clause,[],[f1217,f2073]) ).
thf(f2073,plain,
( spl110_70
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: X2 > X1,X3: X2 > X1] :
( ( X3 = X4 )
| ( vAPP(sTfun(X2,X1),sTfun(sum_sum(X2,X0),X1),sum_Suml(X2,X1,X0),X3) != vAPP(sTfun(X2,X1),sTfun(sum_sum(X2,X0),X1),sum_Suml(X2,X1,X0),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_70])]) ).
thf(f1217,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2 > X1,X4: X2 > X1] :
( ( X3 = X4 )
| ( vAPP(sTfun(X2,X1),sTfun(sum_sum(X2,X0),X1),sum_Suml(X2,X1,X0),X3) != vAPP(sTfun(X2,X1),sTfun(sum_sum(X2,X0),X1),sum_Suml(X2,X1,X0),X4) ) ),
inference(cnf_transformation,[],[f836]) ).
thf(f836,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X1,X4: X2 > X1] :
( ( X3 = X4 )
| ( vAPP(sTfun(X2,X1),sTfun(sum_sum(X2,X0),X1),sum_Suml(X2,X1,X0),X3) != vAPP(sTfun(X2,X1),sTfun(sum_sum(X2,X0),X1),sum_Suml(X2,X1,X0),X4) ) ),
inference(ennf_transformation,[],[f690]) ).
thf(f690,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X1,X4: X2 > X1] :
( ( vAPP(sTfun(X2,X1),sTfun(sum_sum(X2,X0),X1),sum_Suml(X2,X1,X0),X3) = vAPP(sTfun(X2,X1),sTfun(sum_sum(X2,X0),X1),sum_Suml(X2,X1,X0),X4) )
=> ( X3 = X4 ) ),
inference(rectify,[],[f59]) ).
thf(f59,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X50: X0 > X1,X51: X0 > X1] :
( ( vAPP(sTfun(X0,X1),sTfun(sum_sum(X0,X2),X1),sum_Suml(X0,X1,X2),X50) = vAPP(sTfun(X0,X1),sTfun(sum_sum(X0,X2),X1),sum_Suml(X0,X1,X2),X51) )
=> ( X50 = X51 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Suml__inject) ).
thf(f2071,plain,
spl110_69,
inference(avatar_split_clause,[],[f1216,f2069]) ).
thf(f2069,plain,
( spl110_69
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: X2 > X1,X3: X2 > X1] :
( ( X3 = X4 )
| ( vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X3) != vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_69])]) ).
thf(f1216,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2 > X1,X4: X2 > X1] :
( ( X3 = X4 )
| ( vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X3) != vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X4) ) ),
inference(cnf_transformation,[],[f835]) ).
thf(f835,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X1,X4: X2 > X1] :
( ( X3 = X4 )
| ( vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X3) != vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X4) ) ),
inference(ennf_transformation,[],[f689]) ).
thf(f689,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X1,X4: X2 > X1] :
( ( vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X3) = vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X4) )
=> ( X3 = X4 ) ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X50: X2 > X1,X51: X2 > X1] :
( ( vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X50) = vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X51) )
=> ( X50 = X51 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Sumr__inject) ).
thf(f2067,plain,
spl110_68,
inference(avatar_split_clause,[],[f1110,f2065]) ).
thf(f2065,plain,
( spl110_68
<=> ! [X0: $tType,X1: set(X0)] : ( vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_68])]) ).
thf(f1110,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1 ),
inference(cnf_transformation,[],[f411]) ).
thf(f411,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1 ),
inference(fool_elimination,[],[f410]) ).
thf(f410,plain,
! [X0: $tType,X1: set(X0)] :
( vAPP(sTfun(X0,$o),set(X0),collect(X0),
^ [X2: X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) = X1 ),
inference(rectify,[],[f47]) ).
thf(f47,axiom,
! [X0: $tType,X48: set(X0)] :
( vAPP(sTfun(X0,$o),set(X0),collect(X0),
^ [X36: X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X36),X48)) = X48 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(f2063,plain,
spl110_67,
inference(avatar_split_clause,[],[f1040,f2061]) ).
thf(f2061,plain,
( spl110_67
<=> ! [X0: $tType] : ( inf_inf(set(X0)) = vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,inf_inf(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_67])]) ).
thf(f1040,plain,
! [X0: $tType] : ( inf_inf(set(X0)) = vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,inf_inf(set(X0))) ),
inference(cnf_transformation,[],[f293]) ).
thf(f293,plain,
! [X0: $tType] : ( inf_inf(set(X0)) = vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,inf_inf(set(X0))) ),
inference(fool_elimination,[],[f292]) ).
thf(f292,plain,
! [X0: $tType] :
( inf_inf(set(X0))
= ( ^ [X1: set(X0),X2: set(X0)] : vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X2),X1) ) ),
inference(rectify,[],[f230]) ).
thf(f230,axiom,
! [X0: $tType] :
( inf_inf(set(X0))
= ( ^ [X71: set(X0),X72: set(X0)] : vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X72),X71) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_Int__commute) ).
thf(f2059,plain,
spl110_66,
inference(avatar_split_clause,[],[f1039,f2057]) ).
thf(f2057,plain,
( spl110_66
<=> ! [X0: $tType] : ( sup_sup(set(X0)) = vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,sup_sup(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_66])]) ).
thf(f1039,plain,
! [X0: $tType] : ( sup_sup(set(X0)) = vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,sup_sup(set(X0))) ),
inference(cnf_transformation,[],[f291]) ).
thf(f291,plain,
! [X0: $tType] : ( sup_sup(set(X0)) = vAPP(sTfun(set(X0),sTfun(set(X0),set(X0))),sTfun(set(X0),sTfun(set(X0),set(X0))),cCOMB,sup_sup(set(X0))) ),
inference(fool_elimination,[],[f290]) ).
thf(f290,plain,
! [X0: $tType] :
( sup_sup(set(X0))
= ( ^ [X1: set(X0),X2: set(X0)] : vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X2),X1) ) ),
inference(rectify,[],[f104]) ).
thf(f104,axiom,
! [X0: $tType] :
( sup_sup(set(X0))
= ( ^ [X71: set(X0),X72: set(X0)] : vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X72),X71) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Un__commute) ).
thf(f2049,plain,
( spl110_65
| ~ spl110_4
| ~ spl110_45 ),
inference(avatar_split_clause,[],[f1914,f1854,f1629,f2047]) ).
thf(f2047,plain,
( spl110_65
<=> ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,bounded_lattice_top(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_65])]) ).
thf(f1629,plain,
( spl110_4
<=> ( vAPP(itself($o),$o,bounded_lattice($o),type2($o)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_4])]) ).
thf(f1854,plain,
( spl110_45
<=> ! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_45])]) ).
thf(f1914,plain,
( ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,bounded_lattice_top(sTfun(X0,$o)),type2(sTfun(X0,$o))) )
| ~ spl110_4
| ~ spl110_45 ),
inference(trivial_inequality_removal,[],[f1909]) ).
thf(f1909,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = vAPP(itself(sTfun(X0,$o)),$o,bounded_lattice_top(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) )
| ~ spl110_4
| ~ spl110_45 ),
inference(superposition,[],[f1855,f1631]) ).
thf(f1631,plain,
( ( vAPP(itself($o),$o,bounded_lattice($o),type2($o)) = $true )
| ~ spl110_4 ),
inference(avatar_component_clause,[],[f1629]) ).
thf(f1855,plain,
( ! [X1: $tType,X0: $tType] :
( ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) )
| ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) )
| ~ spl110_45 ),
inference(avatar_component_clause,[],[f1854]) ).
thf(f2041,plain,
spl110_64,
inference(avatar_split_clause,[],[f1146,f2039]) ).
thf(f2039,plain,
( spl110_64
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK23(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK24(X0,X1),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_64])]) ).
thf(f1146,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK23(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK24(X0,X1),X2)) = X2 ),
inference(cnf_transformation,[],[f954]) ).
thf(f954,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK23(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK24(X0,X1),X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f642,f953]) ).
thf(f953,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] :
( ? [X3: X0,X4: X1] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 )
=> ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK23(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK24(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f642,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
? [X3: X0,X4: X1] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
! [X0: $tType,X2: $tType,X24: product_prod(X0,X2)] :
? [X25: X0,X26: X2] : ( vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X25),X26) = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_surj__pair) ).
thf(f2037,plain,
spl110_63,
inference(avatar_split_clause,[],[f1145,f2035]) ).
thf(f2035,plain,
( spl110_63
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK21(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK22(X0,X1),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_63])]) ).
thf(f1145,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK21(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK22(X0,X1),X2)) = X2 ),
inference(cnf_transformation,[],[f952]) ).
thf(f952,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK21(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK22(X0,X1),X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f806,f951]) ).
thf(f951,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] :
( ? [X3: X0,X4: X1] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 )
=> ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK21(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK22(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f806,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
? [X3: X0,X4: X1] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 ),
inference(ennf_transformation,[],[f641]) ).
thf(f641,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
~ ! [X3: X0,X4: X1] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) != X2 ),
inference(rectify,[],[f35]) ).
thf(f35,axiom,
! [X0: $tType,X2: $tType,X20: product_prod(X0,X2)] :
~ ! [X27: X0,X28: X2] : ( vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X27),X28) != X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_old_Oprod_Oexhaust) ).
thf(f2017,plain,
spl110_62,
inference(avatar_split_clause,[],[f1056,f2015]) ).
thf(f2015,plain,
( spl110_62
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) = X1 )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_62])]) ).
thf(f1056,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) = X1 )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f756]) ).
thf(f756,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) = X1 )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f325]) ).
thf(f325,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) = $true )
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) = X1 ) ),
inference(fool_elimination,[],[f324]) ).
thf(f324,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X2)) = X1 ) ),
inference(rectify,[],[f200]) ).
thf(f200,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ! [X9: X0,X20: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X9),X20)) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_inf__sup__absorb) ).
thf(f2013,plain,
spl110_61,
inference(avatar_split_clause,[],[f1055,f2011]) ).
thf(f2011,plain,
( spl110_61
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) = X1 )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_61])]) ).
thf(f1055,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) = X1 )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f755]) ).
thf(f755,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) = X1 )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f323]) ).
thf(f323,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) = $true )
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) = X1 ) ),
inference(fool_elimination,[],[f322]) ).
thf(f322,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ! [X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X2)) = X1 ) ),
inference(rectify,[],[f199]) ).
thf(f199,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ! [X9: X0,X20: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X9),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X9),X20)) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_sup__inf__absorb) ).
thf(f2001,plain,
( spl110_60
| ~ spl110_4
| ~ spl110_44 ),
inference(avatar_split_clause,[],[f1908,f1850,f1629,f1999]) ).
thf(f1999,plain,
( spl110_60
<=> ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,bounded_lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_60])]) ).
thf(f1850,plain,
( spl110_44
<=> ! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_44])]) ).
thf(f1908,plain,
( ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,bounded_lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))) )
| ~ spl110_4
| ~ spl110_44 ),
inference(trivial_inequality_removal,[],[f1903]) ).
thf(f1903,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = vAPP(itself(sTfun(X0,$o)),$o,bounded_lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) )
| ~ spl110_4
| ~ spl110_44 ),
inference(superposition,[],[f1851,f1631]) ).
thf(f1851,plain,
( ! [X1: $tType,X0: $tType] :
( ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) )
| ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) )
| ~ spl110_44 ),
inference(avatar_component_clause,[],[f1850]) ).
thf(f1979,plain,
spl110_59,
inference(avatar_split_clause,[],[f1202,f1977]) ).
thf(f1977,plain,
( spl110_59
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: X2,X3: X2 > X1] : ( vAPP(X2,X1,X3,X4) = vAPP(sum_sum(X0,X2),X1,vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X3),vAPP(X2,sum_sum(X0,X2),sum_Inr(X2,X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_59])]) ).
thf(f1202,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2 > X1,X4: X2] : ( vAPP(X2,X1,X3,X4) = vAPP(sum_sum(X0,X2),X1,vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X3),vAPP(X2,sum_sum(X0,X2),sum_Inr(X2,X0),X4)) ),
inference(cnf_transformation,[],[f677]) ).
thf(f677,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X1,X4: X2] : ( vAPP(X2,X1,X3,X4) = vAPP(sum_sum(X0,X2),X1,vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X3),vAPP(X2,sum_sum(X0,X2),sum_Inr(X2,X0),X4)) ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X50: X2 > X1,X9: X2] : ( vAPP(sum_sum(X0,X2),X1,vAPP(sTfun(X2,X1),sTfun(sum_sum(X0,X2),X1),sum_Sumr(X2,X1,X0),X50),vAPP(X2,sum_sum(X0,X2),sum_Inr(X2,X0),X9)) = vAPP(X2,X1,X50,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Sumr_Osimps) ).
thf(f1975,plain,
spl110_58,
inference(avatar_split_clause,[],[f1201,f1973]) ).
thf(f1973,plain,
( spl110_58
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: X2,X3: X2 > X1] : ( vAPP(sum_sum(X2,X0),X1,vAPP(sTfun(X2,X1),sTfun(sum_sum(X2,X0),X1),sum_Suml(X2,X1,X0),X3),vAPP(X2,sum_sum(X2,X0),sum_Inl(X2,X0),X4)) = vAPP(X2,X1,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_58])]) ).
thf(f1201,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2 > X1,X4: X2] : ( vAPP(sum_sum(X2,X0),X1,vAPP(sTfun(X2,X1),sTfun(sum_sum(X2,X0),X1),sum_Suml(X2,X1,X0),X3),vAPP(X2,sum_sum(X2,X0),sum_Inl(X2,X0),X4)) = vAPP(X2,X1,X3,X4) ),
inference(cnf_transformation,[],[f676]) ).
thf(f676,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X1,X4: X2] : ( vAPP(sum_sum(X2,X0),X1,vAPP(sTfun(X2,X1),sTfun(sum_sum(X2,X0),X1),sum_Suml(X2,X1,X0),X3),vAPP(X2,sum_sum(X2,X0),sum_Inl(X2,X0),X4)) = vAPP(X2,X1,X3,X4) ),
inference(rectify,[],[f55]) ).
thf(f55,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X50: X0 > X1,X9: X0] : ( vAPP(sum_sum(X0,X2),X1,vAPP(sTfun(X0,X1),sTfun(sum_sum(X0,X2),X1),sum_Suml(X0,X1,X2),X50),vAPP(X0,sum_sum(X0,X2),sum_Inl(X0,X2),X9)) = vAPP(X0,X1,X50,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Suml_Osimps) ).
thf(f1971,plain,
spl110_57,
inference(avatar_split_clause,[],[f1076,f1969]) ).
thf(f1969,plain,
( spl110_57
<=> ! [X0: $tType] :
( ( inf_inf(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,inf_inf(X0)) )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_57])]) ).
thf(f1076,plain,
! [X0: $tType] :
( ( inf_inf(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,inf_inf(X0)) )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f776]) ).
thf(f776,plain,
! [X0: $tType] :
( ( inf_inf(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,inf_inf(X0)) )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f365]) ).
thf(f365,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) = $true )
=> ( inf_inf(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,inf_inf(X0)) ) ),
inference(fool_elimination,[],[f364]) ).
thf(f364,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0))
=> ( inf_inf(X0)
= ( ^ [X1: X0,X2: X0] : vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X2),X1) ) ) ),
inference(rectify,[],[f224]) ).
thf(f224,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0))
=> ( inf_inf(X0)
= ( ^ [X60: X0,X61: X0] : vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X61),X60) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_inf_Ocommute) ).
thf(f1967,plain,
spl110_56,
inference(avatar_split_clause,[],[f1065,f1965]) ).
thf(f1965,plain,
( spl110_56
<=> ! [X0: $tType] :
( ( sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0)) )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_56])]) ).
thf(f1065,plain,
! [X0: $tType] :
( ( sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0)) )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f765]) ).
thf(f765,plain,
! [X0: $tType] :
( ( sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0)) )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f343]) ).
thf(f343,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) = $true )
=> ( sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0)) ) ),
inference(fool_elimination,[],[f342]) ).
thf(f342,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0))
=> ( sup_sup(X0)
= ( ^ [X1: X0,X2: X0] : vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X1) ) ) ),
inference(rectify,[],[f94]) ).
thf(f94,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0))
=> ( sup_sup(X0)
= ( ^ [X60: X0,X61: X0] : vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X61),X60) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_sup_Ocommute) ).
thf(f1963,plain,
spl110_55,
inference(avatar_split_clause,[],[f1054,f1961]) ).
thf(f1961,plain,
( spl110_55
<=> ! [X0: $tType] :
( ( inf_inf(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,inf_inf(X0)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_55])]) ).
thf(f1054,plain,
! [X0: $tType] :
( ( inf_inf(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,inf_inf(X0)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f754]) ).
thf(f754,plain,
! [X0: $tType] :
( ( inf_inf(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,inf_inf(X0)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f321]) ).
thf(f321,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) = $true )
=> ( inf_inf(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,inf_inf(X0)) ) ),
inference(fool_elimination,[],[f320]) ).
thf(f320,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ( inf_inf(X0)
= ( ^ [X1: X0,X2: X0] : vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X2),X1) ) ) ),
inference(rectify,[],[f236]) ).
thf(f236,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ( inf_inf(X0)
= ( ^ [X36: X0,X69: X0] : vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X69),X36) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_inf__sup__aci_I1_J) ).
thf(f1959,plain,
spl110_54,
inference(avatar_split_clause,[],[f1053,f1957]) ).
thf(f1957,plain,
( spl110_54
<=> ! [X0: $tType] :
( ( sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_54])]) ).
thf(f1053,plain,
! [X0: $tType] :
( ( sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f753]) ).
thf(f753,plain,
! [X0: $tType] :
( ( sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0)) )
| ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f319]) ).
thf(f319,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,lattice(X0),type2(X0)) = $true )
=> ( sup_sup(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,sup_sup(X0)) ) ),
inference(fool_elimination,[],[f318]) ).
thf(f318,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ( sup_sup(X0)
= ( ^ [X1: X0,X2: X0] : vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X2),X1) ) ) ),
inference(rectify,[],[f98]) ).
thf(f98,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,lattice(X0),type2(X0))
=> ( sup_sup(X0)
= ( ^ [X36: X0,X69: X0] : vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X69),X36) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_inf__sup__aci_I5_J) ).
thf(f1950,plain,
spl110_53,
inference(avatar_split_clause,[],[f1088,f1948]) ).
thf(f1948,plain,
( spl110_53
<=> ! [X0: product_prod(dtree,dtree)] : ( vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),vAPP(product_prod(dtree,dtree),dtree,sK8,X0)),vAPP(product_prod(dtree,dtree),dtree,sK9,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_53])]) ).
thf(f1088,plain,
! [X0: product_prod(dtree,dtree)] : ( vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),vAPP(product_prod(dtree,dtree),dtree,sK8,X0)),vAPP(product_prod(dtree,dtree),dtree,sK9,X0)) = X0 ),
inference(cnf_transformation,[],[f930]) ).
thf(f930,plain,
! [X0: product_prod(dtree,dtree)] : ( vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),vAPP(product_prod(dtree,dtree),dtree,sK8,X0)),vAPP(product_prod(dtree,dtree),dtree,sK9,X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f788,f929]) ).
thf(f929,plain,
! [X0: product_prod(dtree,dtree)] :
( ? [X1: dtree,X2: dtree] : ( vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X2) = X0 )
=> ( vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),vAPP(product_prod(dtree,dtree),dtree,sK8,X0)),vAPP(product_prod(dtree,dtree),dtree,sK9,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f788,plain,
! [X0: product_prod(dtree,dtree)] :
? [X1: dtree,X2: dtree] : ( vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X2) = X0 ),
inference(ennf_transformation,[],[f620]) ).
thf(f620,plain,
! [X0: product_prod(dtree,dtree)] :
~ ! [X1: dtree,X2: dtree] : ( vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X2) != X0 ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X9: product_prod(dtree,dtree)] :
~ ! [X5: dtree,X6: dtree] : ( vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X5),X6) != X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_par__r_Ocases) ).
thf(f1942,plain,
spl110_52,
inference(avatar_split_clause,[],[f1111,f1940]) ).
thf(f1940,plain,
( spl110_52
<=> ! [X0: $tType,X1: set(X0)] :
( ( top_top(set(X0)) = X1 )
| ( $true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK11(X0),X1)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_52])]) ).
thf(f1111,plain,
! [X0: $tType,X1: set(X0)] :
( ( top_top(set(X0)) = X1 )
| ( $true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK11(X0),X1)),X1) ) ),
inference(cnf_transformation,[],[f934]) ).
thf(f934,plain,
! [X0: $tType,X1: set(X0)] :
( ( top_top(set(X0)) = X1 )
| ( $true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK11(X0),X1)),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f789,f933]) ).
thf(f933,plain,
! [X0: $tType,X1: set(X0)] :
( ? [X2: X0] : ( $true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1) )
=> ( $true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK11(X0),X1)),X1) ) ),
introduced(choice_axiom,[]) ).
thf(f789,plain,
! [X0: $tType,X1: set(X0)] :
( ( top_top(set(X0)) = X1 )
| ? [X2: X0] : ( $true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1) ) ),
inference(ennf_transformation,[],[f413]) ).
thf(f413,plain,
! [X0: $tType,X1: set(X0)] :
( ! [X2: X0] : ( $true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1) )
=> ( top_top(set(X0)) = X1 ) ),
inference(fool_elimination,[],[f412]) ).
thf(f412,plain,
! [X0: $tType,X1: set(X0)] :
( ! [X2: X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)
=> ( top_top(set(X0)) = X1 ) ),
inference(rectify,[],[f171]) ).
thf(f171,axiom,
! [X0: $tType,X48: set(X0)] :
( ! [X25: X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X25),X48)
=> ( top_top(set(X0)) = X48 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_UNIV__eq__I) ).
thf(f1902,plain,
( spl110_51
| ~ spl110_4
| ~ spl110_42 ),
inference(avatar_split_clause,[],[f1898,f1842,f1629,f1900]) ).
thf(f1900,plain,
( spl110_51
<=> ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,bounde1561333602nf_top(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_51])]) ).
thf(f1842,plain,
( spl110_42
<=> ! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounde1561333602nf_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_42])]) ).
thf(f1898,plain,
( ! [X0: $tType] : ( $true = vAPP(itself(sTfun(X0,$o)),$o,bounde1561333602nf_top(sTfun(X0,$o)),type2(sTfun(X0,$o))) )
| ~ spl110_4
| ~ spl110_42 ),
inference(trivial_inequality_removal,[],[f1893]) ).
thf(f1893,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = vAPP(itself(sTfun(X0,$o)),$o,bounde1561333602nf_top(sTfun(X0,$o)),type2(sTfun(X0,$o))) ) )
| ~ spl110_4
| ~ spl110_42 ),
inference(superposition,[],[f1843,f1631]) ).
thf(f1843,plain,
( ! [X1: $tType,X0: $tType] :
( ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) )
| ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounde1561333602nf_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) )
| ~ spl110_42 ),
inference(avatar_component_clause,[],[f1842]) ).
thf(f1876,plain,
spl110_50,
inference(avatar_split_clause,[],[f1127,f1874]) ).
thf(f1874,plain,
( spl110_50
<=> ! [X1: $tType,X0: $tType,X2: X1 > X0] : ( top_top(set(X1)) = vAPP(set(X0),set(X1),vAPP(sTfun(X1,X0),sTfun(set(X0),set(X1)),vimage(X1,X0),X2),top_top(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_50])]) ).
thf(f1127,plain,
! [X1: $tType,X0: $tType,X2: X1 > X0] : ( top_top(set(X1)) = vAPP(set(X0),set(X1),vAPP(sTfun(X1,X0),sTfun(set(X0),set(X1)),vimage(X1,X0),X2),top_top(set(X0))) ),
inference(cnf_transformation,[],[f633]) ).
thf(f633,plain,
! [X0: $tType,X1: $tType,X2: X1 > X0] : ( top_top(set(X1)) = vAPP(set(X0),set(X1),vAPP(sTfun(X1,X0),sTfun(set(X0),set(X1)),vimage(X1,X0),X2),top_top(set(X0))) ),
inference(rectify,[],[f160]) ).
thf(f160,axiom,
! [X2: $tType,X0: $tType,X50: X0 > X2] : ( top_top(set(X0)) = vAPP(set(X2),set(X0),vAPP(sTfun(X0,X2),sTfun(set(X2),set(X0)),vimage(X0,X2),X50),top_top(set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_vimage__UNIV) ).
thf(f1872,plain,
spl110_49,
inference(avatar_split_clause,[],[f1123,f1870]) ).
thf(f1123,plain,
! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1)) ) ),
inference(cnf_transformation,[],[f801]) ).
thf(f801,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1)) ) ),
inference(ennf_transformation,[],[f437]) ).
thf(f437,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1)) )
=> ( $true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) ),
inference(fool_elimination,[],[f436]) ).
thf(f436,plain,
! [X0: $tType,X1: $tType] :
( vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1))
=> vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1))) ),
inference(rectify,[],[f263]) ).
thf(f263,axiom,
! [X38: $tType,X110: $tType] :
( vAPP(itself(X110),$o,semilattice_inf(X110),type2(X110))
=> vAPP(itself(sTfun(X38,X110)),$o,semilattice_inf(sTfun(X38,X110)),type2(sTfun(X38,X110))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf) ).
thf(f1868,plain,
spl110_48,
inference(avatar_split_clause,[],[f1120,f1866]) ).
thf(f1120,plain,
! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_sup(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,semilattice_sup(X1),type2(X1)) ) ),
inference(cnf_transformation,[],[f798]) ).
thf(f798,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_sup(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,semilattice_sup(X1),type2(X1)) ) ),
inference(ennf_transformation,[],[f431]) ).
thf(f431,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(X1),$o,semilattice_sup(X1),type2(X1)) )
=> ( $true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_sup(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) ),
inference(fool_elimination,[],[f430]) ).
thf(f430,plain,
! [X0: $tType,X1: $tType] :
( vAPP(itself(X1),$o,semilattice_sup(X1),type2(X1))
=> vAPP(itself(sTfun(X0,X1)),$o,semilattice_sup(sTfun(X0,X1)),type2(sTfun(X0,X1))) ),
inference(rectify,[],[f262]) ).
thf(f262,axiom,
! [X38: $tType,X110: $tType] :
( vAPP(itself(X110),$o,semilattice_sup(X110),type2(X110))
=> vAPP(itself(sTfun(X38,X110)),$o,semilattice_sup(sTfun(X38,X110)),type2(sTfun(X38,X110))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__sup) ).
thf(f1864,plain,
spl110_47,
inference(avatar_split_clause,[],[f1117,f1862]) ).
thf(f1117,plain,
! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,lattice(X1),type2(X1)) ) ),
inference(cnf_transformation,[],[f795]) ).
thf(f795,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,lattice(X1),type2(X1)) ) ),
inference(ennf_transformation,[],[f425]) ).
thf(f425,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(X1),$o,lattice(X1),type2(X1)) )
=> ( $true = vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) ),
inference(fool_elimination,[],[f424]) ).
thf(f424,plain,
! [X0: $tType,X1: $tType] :
( vAPP(itself(X1),$o,lattice(X1),type2(X1))
=> vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) ),
inference(rectify,[],[f265]) ).
thf(f265,axiom,
! [X38: $tType,X110: $tType] :
( vAPP(itself(X110),$o,lattice(X110),type2(X110))
=> vAPP(itself(sTfun(X38,X110)),$o,lattice(sTfun(X38,X110)),type2(sTfun(X38,X110))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(f1860,plain,
spl110_46,
inference(avatar_split_clause,[],[f1116,f1858]) ).
thf(f1116,plain,
! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,distrib_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,distrib_lattice(X1),type2(X1)) ) ),
inference(cnf_transformation,[],[f794]) ).
thf(f794,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,distrib_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,distrib_lattice(X1),type2(X1)) ) ),
inference(ennf_transformation,[],[f423]) ).
thf(f423,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(X1),$o,distrib_lattice(X1),type2(X1)) )
=> ( $true = vAPP(itself(sTfun(X0,X1)),$o,distrib_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) ),
inference(fool_elimination,[],[f422]) ).
thf(f422,plain,
! [X0: $tType,X1: $tType] :
( vAPP(itself(X1),$o,distrib_lattice(X1),type2(X1))
=> vAPP(itself(sTfun(X0,X1)),$o,distrib_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) ),
inference(rectify,[],[f264]) ).
thf(f264,axiom,
! [X38: $tType,X110: $tType] :
( vAPP(itself(X110),$o,distrib_lattice(X110),type2(X110))
=> vAPP(itself(sTfun(X38,X110)),$o,distrib_lattice(sTfun(X38,X110)),type2(sTfun(X38,X110))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Odistrib__lattice) ).
thf(f1856,plain,
spl110_45,
inference(avatar_split_clause,[],[f1115,f1854]) ).
thf(f1115,plain,
! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) ) ),
inference(cnf_transformation,[],[f793]) ).
thf(f793,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) ) ),
inference(ennf_transformation,[],[f421]) ).
thf(f421,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) )
=> ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) ),
inference(fool_elimination,[],[f420]) ).
thf(f420,plain,
! [X0: $tType,X1: $tType] :
( vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1))
=> vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) ),
inference(rectify,[],[f261]) ).
thf(f261,axiom,
! [X38: $tType,X110: $tType] :
( vAPP(itself(X110),$o,bounded_lattice(X110),type2(X110))
=> vAPP(itself(sTfun(X38,X110)),$o,bounded_lattice_top(sTfun(X38,X110)),type2(sTfun(X38,X110))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice__top) ).
thf(f1852,plain,
spl110_44,
inference(avatar_split_clause,[],[f1114,f1850]) ).
thf(f1114,plain,
! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) ) ),
inference(cnf_transformation,[],[f792]) ).
thf(f792,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) ) ),
inference(ennf_transformation,[],[f419]) ).
thf(f419,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) )
=> ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) ),
inference(fool_elimination,[],[f418]) ).
thf(f418,plain,
! [X0: $tType,X1: $tType] :
( vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1))
=> vAPP(itself(sTfun(X0,X1)),$o,bounded_lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))) ),
inference(rectify,[],[f259]) ).
thf(f259,axiom,
! [X38: $tType,X110: $tType] :
( vAPP(itself(X110),$o,bounded_lattice(X110),type2(X110))
=> vAPP(itself(sTfun(X38,X110)),$o,bounded_lattice(sTfun(X38,X110)),type2(sTfun(X38,X110))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_2) ).
thf(f1848,plain,
( spl110_43
| ~ spl110_8
| ~ spl110_30 ),
inference(avatar_split_clause,[],[f1763,f1745,f1649,f1846]) ).
thf(f1846,plain,
( spl110_43
<=> ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sup_sup($o),X0),X0) )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_43])]) ).
thf(f1745,plain,
( spl110_30
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X1) = X1 )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_30])]) ).
thf(f1763,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sup_sup($o),X0),X0) )
| ( $false = X0 ) )
| ~ spl110_8
| ~ spl110_30 ),
inference(binary_proxy_clausification,[],[f1762]) ).
thf(f1762,plain,
( ! [X0: $o] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),sup_sup($o),X0),X0) = X0 )
| ~ spl110_8
| ~ spl110_30 ),
inference(trivial_inequality_removal,[],[f1757]) ).
thf(f1757,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( vAPP($o,$o,vAPP($o,sTfun($o,$o),sup_sup($o),X0),X0) = X0 ) )
| ~ spl110_8
| ~ spl110_30 ),
inference(superposition,[],[f1746,f1651]) ).
thf(f1746,plain,
( ! [X0: $tType,X1: X0] :
( ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X1) = X1 ) )
| ~ spl110_30 ),
inference(avatar_component_clause,[],[f1745]) ).
thf(f1844,plain,
spl110_42,
inference(avatar_split_clause,[],[f1113,f1842]) ).
thf(f1113,plain,
! [X1: $tType,X0: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounde1561333602nf_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) ) ),
inference(cnf_transformation,[],[f791]) ).
thf(f791,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounde1561333602nf_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) )
| ( $true != vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) ) ),
inference(ennf_transformation,[],[f417]) ).
thf(f417,plain,
! [X0: $tType,X1: $tType] :
( ( $true = vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1)) )
=> ( $true = vAPP(itself(sTfun(X0,X1)),$o,bounde1561333602nf_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) ) ),
inference(fool_elimination,[],[f416]) ).
thf(f416,plain,
! [X0: $tType,X1: $tType] :
( vAPP(itself(X1),$o,bounded_lattice(X1),type2(X1))
=> vAPP(itself(sTfun(X0,X1)),$o,bounde1561333602nf_top(sTfun(X0,X1)),type2(sTfun(X0,X1))) ),
inference(rectify,[],[f260]) ).
thf(f260,axiom,
! [X38: $tType,X110: $tType] :
( vAPP(itself(X110),$o,bounded_lattice(X110),type2(X110))
=> vAPP(itself(sTfun(X38,X110)),$o,bounde1561333602nf_top(sTfun(X38,X110)),type2(sTfun(X38,X110))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__semilattice__inf__top) ).
thf(f1840,plain,
spl110_41,
inference(avatar_split_clause,[],[f1047,f1838]) ).
thf(f1838,plain,
( spl110_41
<=> ! [X0: $tType,X1: X0] :
( ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),top_top(X0)),X1) )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_41])]) ).
thf(f1047,plain,
! [X0: $tType,X1: X0] :
( ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),top_top(X0)),X1) )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f747]) ).
thf(f747,plain,
! [X0: $tType] :
( ! [X1: X0] : ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),top_top(X0)),X1) )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f307]) ).
thf(f307,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) = $true )
=> ! [X1: X0] : ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),top_top(X0)),X1) ) ),
inference(fool_elimination,[],[f306]) ).
thf(f306,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0))
=> ! [X1: X0] : ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),top_top(X0)),X1) ) ),
inference(rectify,[],[f158]) ).
thf(f158,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0))
=> ! [X9: X0] : ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),top_top(X0)),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_sup__top__left) ).
thf(f1836,plain,
spl110_40,
inference(avatar_split_clause,[],[f1046,f1834]) ).
thf(f1834,plain,
( spl110_40
<=> ! [X0: $tType,X1: X0] :
( ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),top_top(X0)) )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_40])]) ).
thf(f1046,plain,
! [X0: $tType,X1: X0] :
( ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),top_top(X0)) )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f746]) ).
thf(f746,plain,
! [X0: $tType] :
( ! [X1: X0] : ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),top_top(X0)) )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f305]) ).
thf(f305,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) = $true )
=> ! [X1: X0] : ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),top_top(X0)) ) ),
inference(fool_elimination,[],[f304]) ).
thf(f304,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0))
=> ! [X1: X0] : ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),top_top(X0)) ) ),
inference(rectify,[],[f159]) ).
thf(f159,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0))
=> ! [X9: X0] : ( top_top(X0) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X9),top_top(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_sup__top__right) ).
thf(f1800,plain,
spl110_39,
inference(avatar_split_clause,[],[f1126,f1798]) ).
thf(f1798,plain,
( spl110_39
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0)] : ( vAPP(product_prod(X0,X1),product_prod(X1,X0),product_swap(X0,X1),vAPP(product_prod(X1,X0),product_prod(X0,X1),product_swap(X1,X0),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_39])]) ).
thf(f1126,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X1,X0)] : ( vAPP(product_prod(X0,X1),product_prod(X1,X0),product_swap(X0,X1),vAPP(product_prod(X1,X0),product_prod(X0,X1),product_swap(X1,X0),X2)) = X2 ),
inference(cnf_transformation,[],[f632]) ).
thf(f632,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0)] : ( vAPP(product_prod(X0,X1),product_prod(X1,X0),product_swap(X0,X1),vAPP(product_prod(X1,X0),product_prod(X0,X1),product_swap(X1,X0),X2)) = X2 ),
inference(rectify,[],[f67]) ).
thf(f67,axiom,
! [X2: $tType,X0: $tType,X24: product_prod(X0,X2)] : ( vAPP(product_prod(X2,X0),product_prod(X0,X2),product_swap(X2,X0),vAPP(product_prod(X0,X2),product_prod(X2,X0),product_swap(X0,X2),X24)) = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_swap__swap) ).
thf(f1796,plain,
spl110_38,
inference(avatar_split_clause,[],[f1102,f1794]) ).
thf(f1794,plain,
( spl110_38
<=> ! [X0: $tType,X1: set(X0)] : ( top_top(set(X0)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),top_top(set(X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_38])]) ).
thf(f1102,plain,
! [X0: $tType,X1: set(X0)] : ( top_top(set(X0)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),top_top(set(X0))),X1) ),
inference(cnf_transformation,[],[f626]) ).
thf(f626,plain,
! [X0: $tType,X1: set(X0)] : ( top_top(set(X0)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),top_top(set(X0))),X1) ),
inference(rectify,[],[f172]) ).
thf(f172,axiom,
! [X0: $tType,X67: set(X0)] : ( top_top(set(X0)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),top_top(set(X0))),X67) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Un__UNIV__left) ).
thf(f1792,plain,
spl110_37,
inference(avatar_split_clause,[],[f1101,f1790]) ).
thf(f1790,plain,
( spl110_37
<=> ! [X0: $tType,X1: set(X0)] : ( top_top(set(X0)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),top_top(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_37])]) ).
thf(f1101,plain,
! [X0: $tType,X1: set(X0)] : ( top_top(set(X0)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),top_top(set(X0))) ),
inference(cnf_transformation,[],[f625]) ).
thf(f625,plain,
! [X0: $tType,X1: set(X0)] : ( top_top(set(X0)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),top_top(set(X0))) ),
inference(rectify,[],[f173]) ).
thf(f173,axiom,
! [X0: $tType,X48: set(X0)] : ( top_top(set(X0)) = vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X48),top_top(set(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Un__UNIV__right) ).
thf(f1788,plain,
spl110_36,
inference(avatar_split_clause,[],[f1045,f1786]) ).
thf(f1786,plain,
( spl110_36
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X1) = X1 )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_36])]) ).
thf(f1045,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X1) = X1 )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f745]) ).
thf(f745,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X1) = X1 )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f303]) ).
thf(f303,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X1) = X1 ) ),
inference(fool_elimination,[],[f302]) ).
thf(f302,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0))
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X1) = X1 ) ),
inference(rectify,[],[f211]) ).
thf(f211,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0))
=> ! [X9: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X9) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_inf__top__left) ).
thf(f1784,plain,
spl110_35,
inference(avatar_split_clause,[],[f1044,f1782]) ).
thf(f1782,plain,
( spl110_35
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),top_top(X0)) = X1 )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_35])]) ).
thf(f1044,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),top_top(X0)) = X1 )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f744]) ).
thf(f744,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),top_top(X0)) = X1 )
| ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f301]) ).
thf(f301,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0)) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),top_top(X0)) = X1 ) ),
inference(fool_elimination,[],[f300]) ).
thf(f300,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0))
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),top_top(X0)) = X1 ) ),
inference(rectify,[],[f210]) ).
thf(f210,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounded_lattice_top(X0),type2(X0))
=> ! [X9: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X9),top_top(X0)) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_inf__top__right) ).
thf(f1780,plain,
spl110_34,
inference(avatar_split_clause,[],[f1043,f1778]) ).
thf(f1778,plain,
( spl110_34
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X1) = X1 )
| ( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_34])]) ).
thf(f1043,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X1) = X1 )
| ( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f743]) ).
thf(f743,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X1) = X1 )
| ( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f299]) ).
thf(f299,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0)) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X1) = X1 ) ),
inference(fool_elimination,[],[f298]) ).
thf(f298,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0))
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X1) = X1 ) ),
inference(rectify,[],[f202]) ).
thf(f202,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0))
=> ! [X18: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),top_top(X0)),X18) = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_inf__top_Oleft__neutral) ).
thf(f1776,plain,
spl110_33,
inference(avatar_split_clause,[],[f1042,f1774]) ).
thf(f1774,plain,
( spl110_33
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),top_top(X0)) = X1 )
| ( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_33])]) ).
thf(f1042,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),top_top(X0)) = X1 )
| ( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f742]) ).
thf(f742,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),top_top(X0)) = X1 )
| ( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f297]) ).
thf(f297,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0)) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),top_top(X0)) = X1 ) ),
inference(fool_elimination,[],[f296]) ).
thf(f296,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0))
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),top_top(X0)) = X1 ) ),
inference(rectify,[],[f201]) ).
thf(f201,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,bounde1561333602nf_top(X0),type2(X0))
=> ! [X18: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X18),top_top(X0)) = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_inf__top_Oright__neutral) ).
thf(f1756,plain,
spl110_32,
inference(avatar_split_clause,[],[f1078,f1754]) ).
thf(f1754,plain,
( spl110_32
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1 )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_32])]) ).
thf(f1078,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1 )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f778]) ).
thf(f778,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1 )
| ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f369]) ).
thf(f369,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1 ) ),
inference(fool_elimination,[],[f368]) ).
thf(f368,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0))
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1 ) ),
inference(rectify,[],[f194]) ).
thf(f194,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0))
=> ! [X9: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X9),X9) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_inf__idem) ).
thf(f1752,plain,
( ~ spl110_31
| ~ spl110_29 ),
inference(avatar_split_clause,[],[f1743,f1740,f1749]) ).
thf(f1740,plain,
( spl110_29
<=> ! [X0: dtree,X1: dtree] :
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),sK0),sK1)) )
| ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr2),tr1)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_29])]) ).
thf(f1743,plain,
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr1),tr2)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),sK0),sK1)) )
| ~ spl110_29 ),
inference(equality_resolution,[],[f1741]) ).
thf(f1741,plain,
( ! [X0: dtree,X1: dtree] :
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr2),tr1)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X0)) )
| ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),sK0),sK1)) ) )
| ~ spl110_29 ),
inference(avatar_component_clause,[],[f1740]) ).
thf(f1747,plain,
spl110_30,
inference(avatar_split_clause,[],[f1067,f1745]) ).
thf(f1067,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X1) = X1 )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ),
inference(cnf_transformation,[],[f767]) ).
thf(f767,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X1) = X1 )
| ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) != $true ) ),
inference(ennf_transformation,[],[f347]) ).
thf(f347,plain,
! [X0: $tType] :
( ( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0)) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X1) = X1 ) ),
inference(fool_elimination,[],[f346]) ).
thf(f346,plain,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0))
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X1),X1) = X1 ) ),
inference(rectify,[],[f90]) ).
thf(f90,axiom,
! [X0: $tType] :
( vAPP(itself(X0),$o,semilattice_sup(X0),type2(X0))
=> ! [X18: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sup_sup(X0),X18),X18) = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_sup_Oidem) ).
thf(f1742,plain,
( spl110_29
| ~ spl110_28 ),
inference(avatar_split_clause,[],[f1738,f1735,f1740]) ).
thf(f1735,plain,
( spl110_28
<=> ! [X0: dtree,X1: dtree] :
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr2),tr1)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X0)) )
| ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr1),tr2)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_28])]) ).
thf(f1738,plain,
( ! [X0: dtree,X1: dtree] :
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),sK0),sK1)) )
| ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr2),tr1)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X0)) ) )
| ~ spl110_28 ),
inference(forward_demodulation,[],[f1736,f1344]) ).
thf(f1736,plain,
( ! [X0: dtree,X1: dtree] :
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr2),tr1)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X0)) )
| ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr1),tr2)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) ) )
| ~ spl110_28 ),
inference(avatar_component_clause,[],[f1735]) ).
thf(f1737,plain,
spl110_28,
inference(avatar_split_clause,[],[f1343,f1735]) ).
thf(f1343,plain,
! [X0: dtree,X1: dtree] :
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr2),tr1)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X0)) )
| ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr1),tr2)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) ) ),
inference(definition_unfolding,[],[f1033,f1034]) ).
thf(f1033,plain,
! [X0: dtree,X1: dtree] :
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr2),tr1)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X0)) )
| ( trA != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) ) ),
inference(cnf_transformation,[],[f739]) ).
thf(f739,plain,
! [X0: dtree,X1: dtree] :
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr2),tr1)) != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X0)) )
| ( trA != vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) ) ),
inference(ennf_transformation,[],[f618]) ).
thf(f618,plain,
~ ? [X0: dtree,X1: dtree] :
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr2),tr1)) = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X1),X0)) )
& ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X0),X1)) ) ),
inference(rectify,[],[f285]) ).
thf(f285,negated_conjecture,
~ ? [X111: dtree,X112: dtree] :
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr2),tr1)) = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X112),X111)) )
& ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X111),X112)) ) ),
inference(negated_conjecture,[],[f284]) ).
thf(f284,conjecture,
? [X111: dtree,X112: dtree] :
( ( vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),tr2),tr1)) = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X112),X111)) )
& ( trA = vAPP(product_prod(dtree,dtree),dtree,parall1899940088le_par,vAPP(dtree,product_prod(dtree,dtree),vAPP(dtree,sTfun(dtree,product_prod(dtree,dtree)),product_Pair(dtree,dtree),X111),X112)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(f1733,plain,
spl110_27,
inference(avatar_split_clause,[],[f1100,f1731]) ).
thf(f1731,plain,
( spl110_27
<=> ! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),top_top(set(X0))),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_27])]) ).
thf(f1100,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),top_top(set(X0))),X1) = X1 ),
inference(cnf_transformation,[],[f624]) ).
thf(f624,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),top_top(set(X0))),X1) = X1 ),
inference(rectify,[],[f213]) ).
thf(f213,axiom,
! [X0: $tType,X67: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),top_top(set(X0))),X67) = X67 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_Int__UNIV__left) ).
thf(f1729,plain,
spl110_26,
inference(avatar_split_clause,[],[f1099,f1727]) ).
thf(f1727,plain,
( spl110_26
<=> ! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X1),top_top(set(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_26])]) ).
thf(f1099,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X1),top_top(set(X0))) = X1 ),
inference(cnf_transformation,[],[f623]) ).
thf(f623,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X1),top_top(set(X0))) = X1 ),
inference(rectify,[],[f212]) ).
thf(f212,axiom,
! [X0: $tType,X48: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X48),top_top(set(X0))) = X48 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_Int__UNIV__right) ).
thf(f1720,plain,
spl110_25,
inference(avatar_split_clause,[],[f1140,f1718]) ).
thf(f1718,plain,
( spl110_25
<=> ! [X0: $tType,X2: X0,X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_25])]) ).
thf(f1140,plain,
! [X0: $tType,X2: X0,X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1 ),
inference(cnf_transformation,[],[f459]) ).
thf(f459,plain,
! [X0: $tType,X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1 ),
inference(fool_elimination,[],[f458]) ).
thf(f458,plain,
! [X0: $tType,X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1 ),
inference(rectify,[],[f280]) ).
thf(f280,axiom,
! [X0: $tType,X9: X0,X20: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X9),X20) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(f1716,plain,
spl110_24,
inference(avatar_split_clause,[],[f1139,f1714]) ).
thf(f1714,plain,
( spl110_24
<=> ! [X0: $tType,X2: X0,X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_24])]) ).
thf(f1139,plain,
! [X0: $tType,X2: X0,X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2 ),
inference(cnf_transformation,[],[f457]) ).
thf(f457,plain,
! [X0: $tType,X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2 ),
inference(fool_elimination,[],[f456]) ).
thf(f456,plain,
! [X0: $tType,X1: X0,X2: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2 ),
inference(rectify,[],[f279]) ).
thf(f279,axiom,
! [X0: $tType,X9: X0,X20: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X9),X20) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(f1712,plain,
spl110_23,
inference(avatar_split_clause,[],[f1147,f1710]) ).
thf(f1710,plain,
( spl110_23
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( vAPP(X1,sum_sum(X1,X0),sum_Inl(X1,X0),X3) != vAPP(X0,sum_sum(X1,X0),sum_Inr(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_23])]) ).
thf(f1147,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( vAPP(X1,sum_sum(X1,X0),sum_Inl(X1,X0),X3) != vAPP(X0,sum_sum(X1,X0),sum_Inr(X0,X1),X2) ),
inference(cnf_transformation,[],[f643]) ).
thf(f643,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( vAPP(X1,sum_sum(X1,X0),sum_Inl(X1,X0),X3) != vAPP(X0,sum_sum(X1,X0),sum_Inr(X0,X1),X2) ),
inference(rectify,[],[f32]) ).
thf(f32,axiom,
! [X37: $tType,X38: $tType,X39: X37,X40: X38] : ( vAPP(X37,sum_sum(X38,X37),sum_Inr(X37,X38),X39) != vAPP(X38,sum_sum(X38,X37),sum_Inl(X38,X37),X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_old_Osum_Odistinct_I2_J) ).
thf(f1708,plain,
spl110_22,
inference(avatar_split_clause,[],[f1098,f1706]) ).
thf(f1706,plain,
( spl110_22
<=> ! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X1),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_22])]) ).
thf(f1098,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X1),X1) = X1 ),
inference(cnf_transformation,[],[f622]) ).
thf(f622,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X1),X1) = X1 ),
inference(rectify,[],[f231]) ).
thf(f231,axiom,
! [X0: $tType,X48: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X48),X48) = X48 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_Int__absorb) ).
thf(f1704,plain,
spl110_21,
inference(avatar_split_clause,[],[f1097,f1702]) ).
thf(f1702,plain,
( spl110_21
<=> ! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_21])]) ).
thf(f1097,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X1) = X1 ),
inference(cnf_transformation,[],[f621]) ).
thf(f621,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X1),X1) = X1 ),
inference(rectify,[],[f105]) ).
thf(f105,axiom,
! [X0: $tType,X48: set(X0)] : ( vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),sup_sup(set(X0)),X48),X48) = X48 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_Un__absorb) ).
thf(f1700,plain,
spl110_20,
inference(avatar_split_clause,[],[f1124,f1698]) ).
thf(f1698,plain,
( spl110_20
<=> ! [X0: $tType,X1: X0] : ( $true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),top_top(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_20])]) ).
thf(f1124,plain,
! [X0: $tType,X1: X0] : ( $true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),top_top(set(X0))) ),
inference(cnf_transformation,[],[f439]) ).
thf(f439,plain,
! [X0: $tType,X1: X0] : ( $true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),top_top(set(X0))) ),
inference(fool_elimination,[],[f438]) ).
thf(f438,plain,
! [X0: $tType,X1: X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),top_top(set(X0))),
inference(rectify,[],[f157]) ).
thf(f157,axiom,
! [X0: $tType,X9: X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X9),top_top(set(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_UNIV__I) ).
thf(f1696,plain,
( spl110_18
| spl110_19 ),
inference(avatar_split_clause,[],[f1550,f1694,f1691]) ).
thf(f1691,plain,
( spl110_18
<=> ! [X1: $o] : ( $false = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_18])]) ).
thf(f1694,plain,
( spl110_19
<=> ! [X0: $tType,X2: X0] : ( $true = vAPP(X0,$o,top_top(sTfun(X0,$o)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_19])]) ).
thf(f1550,plain,
! [X0: $tType,X2: X0,X1: $o] :
( ( $true = vAPP(X0,$o,top_top(sTfun(X0,$o)),X2) )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[],[f1547]) ).
thf(f1547,plain,
! [X0: $tType,X2: X0,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,X1),vAPP(X0,$o,top_top(sTfun(X0,$o)),X2)) )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[],[f1133]) ).
thf(f1133,plain,
! [X0: $tType,X2: X0,X1: $o] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,X1),vAPP(X0,$o,top_top(sTfun(X0,$o)),X2)) = X1 ),
inference(cnf_transformation,[],[f445]) ).
thf(f445,plain,
! [X0: $tType,X1: $o,X2: X0] : ( vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,X1),vAPP(X0,$o,top_top(sTfun(X0,$o)),X2)) = X1 ),
inference(fool_elimination,[],[f444]) ).
thf(f444,plain,
! [X0: $tType,X1: $o,X2: X0] :
( vAPP(X0,$o,top_top(sTfun(X0,$o)),X2)
& ( X1 = X1 ) ),
inference(rectify,[],[f216]) ).
thf(f216,axiom,
! [X0: $tType,X10: $o,X9: X0] :
( vAPP(X0,$o,top_top(sTfun(X0,$o)),X9)
& ( X10 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_top__conj_I2_J) ).
thf(f1689,plain,
spl110_17,
inference(avatar_split_clause,[],[f1038,f1687]) ).
thf(f1687,plain,
( spl110_17
<=> ! [X0: $tType] : ( top_top(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),top_top(sTfun(X0,$o))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_17])]) ).
thf(f1038,plain,
! [X0: $tType] : ( top_top(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),top_top(sTfun(X0,$o))) ),
inference(cnf_transformation,[],[f184]) ).
thf(f184,axiom,
! [X0: $tType] : ( top_top(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),top_top(sTfun(X0,$o))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_top__set__def) ).
thf(f1685,plain,
spl110_16,
inference(avatar_split_clause,[],[f1096,f1683]) ).
thf(f1683,plain,
( spl110_16
<=> ! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,semilattice_inf(set(X0)),type2(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_16])]) ).
thf(f1096,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,semilattice_inf(set(X0)),type2(set(X0))) ),
inference(cnf_transformation,[],[f403]) ).
thf(f403,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,semilattice_inf(set(X0)),type2(set(X0))) ),
inference(fool_elimination,[],[f402]) ).
thf(f402,plain,
! [X0: $tType] : vAPP(itself(set(X0)),$o,semilattice_inf(set(X0)),type2(set(X0))),
inference(rectify,[],[f269]) ).
thf(f269,axiom,
! [X38: $tType] : vAPP(itself(set(X38)),$o,semilattice_inf(set(X38)),type2(set(X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_6) ).
thf(f1681,plain,
spl110_15,
inference(avatar_split_clause,[],[f1095,f1679]) ).
thf(f1679,plain,
( spl110_15
<=> ! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,semilattice_sup(set(X0)),type2(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_15])]) ).
thf(f1095,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,semilattice_sup(set(X0)),type2(set(X0))) ),
inference(cnf_transformation,[],[f401]) ).
thf(f401,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,semilattice_sup(set(X0)),type2(set(X0))) ),
inference(fool_elimination,[],[f400]) ).
thf(f400,plain,
! [X0: $tType] : vAPP(itself(set(X0)),$o,semilattice_sup(set(X0)),type2(set(X0))),
inference(rectify,[],[f268]) ).
thf(f268,axiom,
! [X38: $tType] : vAPP(itself(set(X38)),$o,semilattice_sup(set(X38)),type2(set(X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__sup_5) ).
thf(f1677,plain,
spl110_14,
inference(avatar_split_clause,[],[f1094,f1675]) ).
thf(f1675,plain,
( spl110_14
<=> ! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,lattice(set(X0)),type2(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_14])]) ).
thf(f1094,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,lattice(set(X0)),type2(set(X0))) ),
inference(cnf_transformation,[],[f399]) ).
thf(f399,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,lattice(set(X0)),type2(set(X0))) ),
inference(fool_elimination,[],[f398]) ).
thf(f398,plain,
! [X0: $tType] : vAPP(itself(set(X0)),$o,lattice(set(X0)),type2(set(X0))),
inference(rectify,[],[f271]) ).
thf(f271,axiom,
! [X38: $tType] : vAPP(itself(set(X38)),$o,lattice(set(X38)),type2(set(X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_8) ).
thf(f1673,plain,
spl110_13,
inference(avatar_split_clause,[],[f1093,f1671]) ).
thf(f1671,plain,
( spl110_13
<=> ! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,distrib_lattice(set(X0)),type2(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_13])]) ).
thf(f1093,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,distrib_lattice(set(X0)),type2(set(X0))) ),
inference(cnf_transformation,[],[f397]) ).
thf(f397,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,distrib_lattice(set(X0)),type2(set(X0))) ),
inference(fool_elimination,[],[f396]) ).
thf(f396,plain,
! [X0: $tType] : vAPP(itself(set(X0)),$o,distrib_lattice(set(X0)),type2(set(X0))),
inference(rectify,[],[f270]) ).
thf(f270,axiom,
! [X38: $tType] : vAPP(itself(set(X38)),$o,distrib_lattice(set(X38)),type2(set(X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Odistrib__lattice_7) ).
thf(f1669,plain,
spl110_12,
inference(avatar_split_clause,[],[f1092,f1667]) ).
thf(f1667,plain,
( spl110_12
<=> ! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,bounded_lattice_top(set(X0)),type2(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_12])]) ).
thf(f1092,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,bounded_lattice_top(set(X0)),type2(set(X0))) ),
inference(cnf_transformation,[],[f395]) ).
thf(f395,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,bounded_lattice_top(set(X0)),type2(set(X0))) ),
inference(fool_elimination,[],[f394]) ).
thf(f394,plain,
! [X0: $tType] : vAPP(itself(set(X0)),$o,bounded_lattice_top(set(X0)),type2(set(X0))),
inference(rectify,[],[f267]) ).
thf(f267,axiom,
! [X38: $tType] : vAPP(itself(set(X38)),$o,bounded_lattice_top(set(X38)),type2(set(X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__top_4) ).
thf(f1665,plain,
spl110_11,
inference(avatar_split_clause,[],[f1091,f1663]) ).
thf(f1663,plain,
( spl110_11
<=> ! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,bounded_lattice(set(X0)),type2(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_11])]) ).
thf(f1091,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,bounded_lattice(set(X0)),type2(set(X0))) ),
inference(cnf_transformation,[],[f393]) ).
thf(f393,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,bounded_lattice(set(X0)),type2(set(X0))) ),
inference(fool_elimination,[],[f392]) ).
thf(f392,plain,
! [X0: $tType] : vAPP(itself(set(X0)),$o,bounded_lattice(set(X0)),type2(set(X0))),
inference(rectify,[],[f258]) ).
thf(f258,axiom,
! [X38: $tType] : vAPP(itself(set(X38)),$o,bounded_lattice(set(X38)),type2(set(X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_1) ).
thf(f1661,plain,
spl110_10,
inference(avatar_split_clause,[],[f1090,f1659]) ).
thf(f1659,plain,
( spl110_10
<=> ! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,bounde1561333602nf_top(set(X0)),type2(set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_10])]) ).
thf(f1090,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,bounde1561333602nf_top(set(X0)),type2(set(X0))) ),
inference(cnf_transformation,[],[f391]) ).
thf(f391,plain,
! [X0: $tType] : ( $true = vAPP(itself(set(X0)),$o,bounde1561333602nf_top(set(X0)),type2(set(X0))) ),
inference(fool_elimination,[],[f390]) ).
thf(f390,plain,
! [X0: $tType] : vAPP(itself(set(X0)),$o,bounde1561333602nf_top(set(X0)),type2(set(X0))),
inference(rectify,[],[f266]) ).
thf(f266,axiom,
! [X38: $tType] : vAPP(itself(set(X38)),$o,bounde1561333602nf_top(set(X38)),type2(set(X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_3) ).
thf(f1657,plain,
spl110_9,
inference(avatar_split_clause,[],[f1339,f1654]) ).
thf(f1339,plain,
vAPP(itself($o),$o,semilattice_inf($o),type2($o)) = $true,
inference(cnf_transformation,[],[f611]) ).
thf(f611,plain,
vAPP(itself($o),$o,semilattice_inf($o),type2($o)) = $true,
inference(fool_elimination,[],[f610]) ).
thf(f610,plain,
vAPP(itself($o),$o,semilattice_inf($o),type2($o)),
inference(rectify,[],[f275]) ).
thf(f275,axiom,
vAPP(itself($o),$o,semilattice_inf($o),type2($o)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_12) ).
thf(f1652,plain,
spl110_8,
inference(avatar_split_clause,[],[f1338,f1649]) ).
thf(f1338,plain,
vAPP(itself($o),$o,semilattice_sup($o),type2($o)) = $true,
inference(cnf_transformation,[],[f609]) ).
thf(f609,plain,
vAPP(itself($o),$o,semilattice_sup($o),type2($o)) = $true,
inference(fool_elimination,[],[f608]) ).
thf(f608,plain,
vAPP(itself($o),$o,semilattice_sup($o),type2($o)),
inference(rectify,[],[f274]) ).
thf(f274,axiom,
vAPP(itself($o),$o,semilattice_sup($o),type2($o)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__sup_11) ).
thf(f1647,plain,
spl110_7,
inference(avatar_split_clause,[],[f1337,f1644]) ).
thf(f1337,plain,
vAPP(itself($o),$o,lattice($o),type2($o)) = $true,
inference(cnf_transformation,[],[f607]) ).
thf(f607,plain,
vAPP(itself($o),$o,lattice($o),type2($o)) = $true,
inference(fool_elimination,[],[f606]) ).
thf(f606,plain,
vAPP(itself($o),$o,lattice($o),type2($o)),
inference(rectify,[],[f277]) ).
thf(f277,axiom,
vAPP(itself($o),$o,lattice($o),type2($o)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_14) ).
thf(f1642,plain,
spl110_6,
inference(avatar_split_clause,[],[f1336,f1639]) ).
thf(f1639,plain,
( spl110_6
<=> ( vAPP(itself($o),$o,bounded_lattice_top($o),type2($o)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_6])]) ).
thf(f1336,plain,
vAPP(itself($o),$o,bounded_lattice_top($o),type2($o)) = $true,
inference(cnf_transformation,[],[f605]) ).
thf(f605,plain,
vAPP(itself($o),$o,bounded_lattice_top($o),type2($o)) = $true,
inference(fool_elimination,[],[f604]) ).
thf(f604,plain,
vAPP(itself($o),$o,bounded_lattice_top($o),type2($o)),
inference(rectify,[],[f273]) ).
thf(f273,axiom,
vAPP(itself($o),$o,bounded_lattice_top($o),type2($o)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__top_10) ).
thf(f1637,plain,
spl110_5,
inference(avatar_split_clause,[],[f1335,f1634]) ).
thf(f1335,plain,
vAPP(itself($o),$o,distrib_lattice($o),type2($o)) = $true,
inference(cnf_transformation,[],[f603]) ).
thf(f603,plain,
vAPP(itself($o),$o,distrib_lattice($o),type2($o)) = $true,
inference(fool_elimination,[],[f602]) ).
thf(f602,plain,
vAPP(itself($o),$o,distrib_lattice($o),type2($o)),
inference(rectify,[],[f276]) ).
thf(f276,axiom,
vAPP(itself($o),$o,distrib_lattice($o),type2($o)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Odistrib__lattice_13) ).
thf(f1632,plain,
spl110_4,
inference(avatar_split_clause,[],[f1334,f1629]) ).
thf(f1334,plain,
vAPP(itself($o),$o,bounded_lattice($o),type2($o)) = $true,
inference(cnf_transformation,[],[f601]) ).
thf(f601,plain,
vAPP(itself($o),$o,bounded_lattice($o),type2($o)) = $true,
inference(fool_elimination,[],[f600]) ).
thf(f600,plain,
vAPP(itself($o),$o,bounded_lattice($o),type2($o)),
inference(rectify,[],[f257]) ).
thf(f257,axiom,
vAPP(itself($o),$o,bounded_lattice($o),type2($o)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice) ).
thf(f1627,plain,
spl110_3,
inference(avatar_split_clause,[],[f1333,f1624]) ).
thf(f1624,plain,
( spl110_3
<=> ( vAPP(itself($o),$o,bounde1561333602nf_top($o),type2($o)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_3])]) ).
thf(f1333,plain,
vAPP(itself($o),$o,bounde1561333602nf_top($o),type2($o)) = $true,
inference(cnf_transformation,[],[f599]) ).
thf(f599,plain,
vAPP(itself($o),$o,bounde1561333602nf_top($o),type2($o)) = $true,
inference(fool_elimination,[],[f598]) ).
thf(f598,plain,
vAPP(itself($o),$o,bounde1561333602nf_top($o),type2($o)),
inference(rectify,[],[f272]) ).
thf(f272,axiom,
vAPP(itself($o),$o,bounde1561333602nf_top($o),type2($o)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_9) ).
thf(f1594,plain,
spl110_2,
inference(avatar_split_clause,[],[f287,f1592]) ).
thf(f1592,plain,
( spl110_2
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_2])]) ).
thf(f287,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f1590,plain,
~ spl110_1,
inference(avatar_split_clause,[],[f286,f1587]) ).
thf(f1587,plain,
( spl110_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl110_1])]) ).
thf(f286,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM206^1 : TPTP v8.1.2. Released v7.0.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 21:26:38 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (3469)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (3472)WARNING: value z3 for option sas not known
% 0.15/0.39 % (3470)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (3471)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (3472)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)
% 0.15/0.39 % (3473)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (3474)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)
% 0.15/0.39 % (3475)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)
% 0.15/0.39 % (3476)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)
% 0.15/0.42 % (3476)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.43 % Exception at run slice level
% 0.21/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43 % Exception at run slice level
% 0.21/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43 % Exception at run slice level
% 0.21/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.44 % (3477)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.44 % (3478)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)
% 0.21/0.45 % (3479)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)
% 0.21/0.48 % (3477)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.48 % (3478)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.48 % Exception at run slice level
% 0.21/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.50 % (3480)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)
% 0.21/0.51 % (3474)First to succeed.
% 0.21/0.52 % (3474)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3469"
% 0.21/0.52 % (3474)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status Theorem for theBenchmark
% 0.21/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53 % (3474)------------------------------
% 0.21/0.53 % (3474)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.53 % (3474)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (3474)Memory used [KB]: 2724
% 0.21/0.53 % (3474)Time elapsed: 0.133 s
% 0.21/0.53 % (3474)Instructions burned: 269 (million)
% 0.21/0.53 % (3469)Success in time 0.171 s
%------------------------------------------------------------------------------