TSTP Solution File: COL075-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COL075-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:45:48 EDT 2024
% Result : Unsatisfiable 0.22s 0.54s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 90
% Syntax : Number of formulae : 274 ( 21 unt; 0 def)
% Number of atoms : 695 ( 218 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 786 ( 365 ~; 342 |; 0 &)
% ( 79 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 81 ( 79 usr; 80 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 396 ( 396 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2666,plain,
$false,
inference(avatar_sat_refutation,[],[f16,f20,f24,f28,f32,f36,f43,f47,f53,f60,f80,f87,f103,f107,f119,f127,f131,f135,f147,f173,f193,f197,f231,f235,f240,f256,f260,f264,f268,f272,f276,f280,f536,f569,f596,f600,f676,f680,f684,f810,f814,f858,f922,f926,f1124,f1243,f1247,f1259,f1263,f1299,f1303,f1338,f1343,f1380,f1384,f1388,f1392,f1396,f1400,f1404,f1408,f1412,f1416,f1420,f1424,f1428,f1432,f1436,f1440,f1926,f2095,f2099,f2103,f2107,f2111,f2116,f2120,f2124,f2642]) ).
fof(f2642,plain,
( ~ spl0_2
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f2641]) ).
fof(f2641,plain,
( $false
| ~ spl0_2
| ~ spl0_79 ),
inference(trivial_inequality_removal,[],[f2545]) ).
fof(f2545,plain,
( apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k)))
| ~ spl0_2
| ~ spl0_79 ),
inference(superposition,[],[f19,f2123]) ).
fof(f2123,plain,
( ! [X0,X1] : apply(apply(apply(apply(abstraction,abstraction),k),X0),X1) = apply(X0,X0)
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f2122]) ).
fof(f2122,plain,
( spl0_79
<=> ! [X0,X1] : apply(apply(apply(apply(abstraction,abstraction),k),X0),X1) = apply(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f19,plain,
( ! [X1] : apply(apply(X1,b(X1)),c(X1)) != apply(b(X1),b(X1))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f18,plain,
( spl0_2
<=> ! [X1] : apply(apply(X1,b(X1)),c(X1)) != apply(b(X1),b(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f2124,plain,
( spl0_79
| ~ spl0_3
| ~ spl0_12
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f590,f567,f85,f22,f2122]) ).
fof(f22,plain,
( spl0_3
<=> ! [X0,X1] : apply(apply(k,X0),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f85,plain,
( spl0_12
<=> ! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f567,plain,
( spl0_34
<=> ! [X2,X0,X1] : apply(apply(apply(abstraction,X2),apply(k,X0)),X1) = apply(apply(X2,apply(k,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f590,plain,
( ! [X0,X1] : apply(apply(apply(apply(abstraction,abstraction),k),X0),X1) = apply(X0,X0)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_34 ),
inference(forward_demodulation,[],[f570,f23]) ).
fof(f23,plain,
( ! [X0,X1] : apply(apply(k,X0),X1) = X0
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f570,plain,
( ! [X0,X1] : apply(apply(apply(k,X0),apply(k,X1)),X0) = apply(apply(apply(apply(abstraction,abstraction),k),X0),X1)
| ~ spl0_12
| ~ spl0_34 ),
inference(superposition,[],[f568,f86]) ).
fof(f86,plain,
( ! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f568,plain,
( ! [X2,X0,X1] : apply(apply(apply(abstraction,X2),apply(k,X0)),X1) = apply(apply(X2,apply(k,X1)),X0)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f2120,plain,
( spl0_78
| ~ spl0_3
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f437,f270,f22,f2118]) ).
fof(f2118,plain,
( spl0_78
<=> ! [X2,X0,X1] : pair(X0,X2) = apply(pair(apply(k,X0),projection2),pair(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f270,plain,
( spl0_30
<=> ! [X2,X0,X1] : apply(pair(X2,projection2),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f437,plain,
( ! [X2,X0,X1] : pair(X0,X2) = apply(pair(apply(k,X0),projection2),pair(X1,X2))
| ~ spl0_3
| ~ spl0_30 ),
inference(superposition,[],[f271,f23]) ).
fof(f271,plain,
( ! [X2,X0,X1] : apply(pair(X2,projection2),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),X1)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f2116,plain,
( ~ spl0_77
| spl0_41
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f1621,f1390,f807,f2113]) ).
fof(f2113,plain,
( spl0_77
<=> apply(b(projection2),b(projection2)) = apply(projection1,apply(b(projection2),c(projection2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f807,plain,
( spl0_41
<=> apply(b(projection2),b(projection2)) = apply(apply(projection1,b(projection2)),c(projection2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1390,plain,
( spl0_58
<=> ! [X0,X1] : apply(apply(projection1,X0),X1) = apply(projection1,apply(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1621,plain,
( apply(b(projection2),b(projection2)) != apply(projection1,apply(b(projection2),c(projection2)))
| spl0_41
| ~ spl0_58 ),
inference(superposition,[],[f809,f1391]) ).
fof(f1391,plain,
( ! [X0,X1] : apply(apply(projection1,X0),X1) = apply(projection1,apply(X0,X1))
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1390]) ).
fof(f809,plain,
( apply(b(projection2),b(projection2)) != apply(apply(projection1,b(projection2)),c(projection2))
| spl0_41 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f2111,plain,
( spl0_76
| ~ spl0_3
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f381,f266,f22,f2109]) ).
fof(f2109,plain,
( spl0_76
<=> ! [X2,X0,X1] : pair(X0,X1) = apply(pair(apply(k,X0),projection1),pair(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f266,plain,
( spl0_29
<=> ! [X2,X0,X1] : apply(pair(X2,projection1),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f381,plain,
( ! [X2,X0,X1] : pair(X0,X1) = apply(pair(apply(k,X0),projection1),pair(X1,X2))
| ~ spl0_3
| ~ spl0_29 ),
inference(superposition,[],[f267,f23]) ).
fof(f267,plain,
( ! [X2,X0,X1] : apply(pair(X2,projection1),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),X0)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f2107,plain,
( spl0_75
| ~ spl0_3
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f322,f258,f22,f2105]) ).
fof(f2105,plain,
( spl0_75
<=> ! [X2,X0,X1] : pair(X2,X0) = apply(pair(projection2,apply(k,X0)),pair(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f258,plain,
( spl0_27
<=> ! [X2,X0,X1] : apply(pair(projection2,X2),pair(X0,X1)) = pair(X1,apply(X2,pair(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f322,plain,
( ! [X2,X0,X1] : pair(X2,X0) = apply(pair(projection2,apply(k,X0)),pair(X1,X2))
| ~ spl0_3
| ~ spl0_27 ),
inference(superposition,[],[f259,f23]) ).
fof(f259,plain,
( ! [X2,X0,X1] : apply(pair(projection2,X2),pair(X0,X1)) = pair(X1,apply(X2,pair(X0,X1)))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f2103,plain,
( spl0_74
| ~ spl0_3
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f286,f254,f22,f2101]) ).
fof(f2101,plain,
( spl0_74
<=> ! [X2,X0,X1] : apply(pair(projection1,apply(k,X0)),pair(X1,X2)) = pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f254,plain,
( spl0_26
<=> ! [X2,X0,X1] : apply(pair(projection1,X2),pair(X0,X1)) = pair(X0,apply(X2,pair(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f286,plain,
( ! [X2,X0,X1] : apply(pair(projection1,apply(k,X0)),pair(X1,X2)) = pair(X1,X0)
| ~ spl0_3
| ~ spl0_26 ),
inference(superposition,[],[f255,f23]) ).
fof(f255,plain,
( ! [X2,X0,X1] : apply(pair(projection1,X2),pair(X0,X1)) = pair(X0,apply(X2,pair(X0,X1)))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f2099,plain,
( spl0_73
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f110,f105,f58,f2097]) ).
fof(f2097,plain,
( spl0_73
<=> ! [X0,X1] : apply(pair(pair(projection1,projection2),X1),X0) = pair(X0,apply(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f58,plain,
( spl0_10
<=> ! [X2,X0,X1] : apply(pair(X0,X1),X2) = pair(apply(X0,X2),apply(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f105,plain,
( spl0_14
<=> ! [X0] : apply(pair(projection1,projection2),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f110,plain,
( ! [X0,X1] : apply(pair(pair(projection1,projection2),X1),X0) = pair(X0,apply(X1,X0))
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f59,f106]) ).
fof(f106,plain,
( ! [X0] : apply(pair(projection1,projection2),X0) = X0
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f59,plain,
( ! [X2,X0,X1] : apply(pair(X0,X1),X2) = pair(apply(X0,X2),apply(X1,X2))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f2095,plain,
( spl0_72
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f109,f105,f58,f2093]) ).
fof(f2093,plain,
( spl0_72
<=> ! [X0,X1] : apply(pair(X1,pair(projection1,projection2)),X0) = pair(apply(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f109,plain,
( ! [X0,X1] : apply(pair(X1,pair(projection1,projection2)),X0) = pair(apply(X1,X0),X0)
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f59,f106]) ).
fof(f1926,plain,
( ~ spl0_71
| ~ spl0_2
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f1554,f1386,f18,f1923]) ).
fof(f1923,plain,
( spl0_71
<=> apply(b(projection2),b(projection2)) = apply(projection2,apply(b(projection2),c(projection2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1386,plain,
( spl0_57
<=> ! [X0,X1] : apply(apply(projection2,X0),X1) = apply(projection2,apply(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1554,plain,
( apply(b(projection2),b(projection2)) != apply(projection2,apply(b(projection2),c(projection2)))
| ~ spl0_2
| ~ spl0_57 ),
inference(superposition,[],[f19,f1387]) ).
fof(f1387,plain,
( ! [X0,X1] : apply(apply(projection2,X0),X1) = apply(projection2,apply(X0,X1))
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1386]) ).
fof(f1440,plain,
( spl0_70
| ~ spl0_3
| ~ spl0_18
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f1368,f1341,f133,f22,f1438]) ).
fof(f1438,plain,
( spl0_70
<=> ! [X0] : apply(b(apply(apply(abstraction,apply(abstraction,k)),apply(k,X0))),b(apply(apply(abstraction,apply(abstraction,k)),apply(k,X0)))) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f133,plain,
( spl0_18
<=> ! [X0,X1] : apply(k,X0) = apply(apply(apply(abstraction,k),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1341,plain,
( spl0_54
<=> ! [X0,X1] : apply(b(apply(apply(abstraction,X0),apply(k,X1))),b(apply(apply(abstraction,X0),apply(k,X1)))) != apply(apply(apply(X0,apply(k,b(apply(apply(abstraction,X0),apply(k,X1))))),X1),c(apply(apply(abstraction,X0),apply(k,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1368,plain,
( ! [X0] : apply(b(apply(apply(abstraction,apply(abstraction,k)),apply(k,X0))),b(apply(apply(abstraction,apply(abstraction,k)),apply(k,X0)))) != X0
| ~ spl0_3
| ~ spl0_18
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1353,f23]) ).
fof(f1353,plain,
( ! [X0] : apply(b(apply(apply(abstraction,apply(abstraction,k)),apply(k,X0))),b(apply(apply(abstraction,apply(abstraction,k)),apply(k,X0)))) != apply(apply(k,X0),c(apply(apply(abstraction,apply(abstraction,k)),apply(k,X0))))
| ~ spl0_18
| ~ spl0_54 ),
inference(superposition,[],[f1342,f134]) ).
fof(f134,plain,
( ! [X0,X1] : apply(k,X0) = apply(apply(apply(abstraction,k),X1),X0)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f1342,plain,
( ! [X0,X1] : apply(b(apply(apply(abstraction,X0),apply(k,X1))),b(apply(apply(abstraction,X0),apply(k,X1)))) != apply(apply(apply(X0,apply(k,b(apply(apply(abstraction,X0),apply(k,X1))))),X1),c(apply(apply(abstraction,X0),apply(k,X1))))
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f1436,plain,
( spl0_69
| ~ spl0_5
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f470,f270,f30,f1434]) ).
fof(f1434,plain,
( spl0_69
<=> ! [X2,X0,X1] : apply(projection2,apply(pair(X0,projection2),pair(X1,X2))) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f30,plain,
( spl0_5
<=> ! [X0,X1] : apply(projection2,pair(X0,X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f470,plain,
( ! [X2,X0,X1] : apply(projection2,apply(pair(X0,projection2),pair(X1,X2))) = X2
| ~ spl0_5
| ~ spl0_30 ),
inference(superposition,[],[f31,f271]) ).
fof(f31,plain,
( ! [X0,X1] : apply(projection2,pair(X0,X1)) = X1
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f1432,plain,
( spl0_68
| ~ spl0_6
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f450,f270,f34,f1430]) ).
fof(f1430,plain,
( spl0_68
<=> ! [X0] : pair(projection1,X0) = apply(pair(eq,projection2),pair(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f34,plain,
( spl0_6
<=> ! [X0] : projection1 = apply(eq,pair(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f450,plain,
( ! [X0] : pair(projection1,X0) = apply(pair(eq,projection2),pair(X0,X0))
| ~ spl0_6
| ~ spl0_30 ),
inference(superposition,[],[f271,f35]) ).
fof(f35,plain,
( ! [X0] : projection1 = apply(eq,pair(X0,X0))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f1428,plain,
( spl0_67
| ~ spl0_5
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f409,f266,f30,f1426]) ).
fof(f1426,plain,
( spl0_67
<=> ! [X2,X0,X1] : apply(projection2,apply(pair(X0,projection1),pair(X1,X2))) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f409,plain,
( ! [X2,X0,X1] : apply(projection2,apply(pair(X0,projection1),pair(X1,X2))) = X1
| ~ spl0_5
| ~ spl0_29 ),
inference(superposition,[],[f31,f267]) ).
fof(f1424,plain,
( spl0_66
| ~ spl0_6
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f393,f266,f34,f1422]) ).
fof(f1422,plain,
( spl0_66
<=> ! [X0] : pair(projection1,X0) = apply(pair(eq,projection1),pair(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f393,plain,
( ! [X0] : pair(projection1,X0) = apply(pair(eq,projection1),pair(X0,X0))
| ~ spl0_6
| ~ spl0_29 ),
inference(superposition,[],[f267,f35]) ).
fof(f1420,plain,
( spl0_65
| ~ spl0_4
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f345,f258,f26,f1418]) ).
fof(f1418,plain,
( spl0_65
<=> ! [X2,X0,X1] : apply(projection1,apply(pair(projection2,X1),pair(X2,X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f26,plain,
( spl0_4
<=> ! [X0,X1] : apply(projection1,pair(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f345,plain,
( ! [X2,X0,X1] : apply(projection1,apply(pair(projection2,X1),pair(X2,X0))) = X0
| ~ spl0_4
| ~ spl0_27 ),
inference(superposition,[],[f27,f259]) ).
fof(f27,plain,
( ! [X0,X1] : apply(projection1,pair(X0,X1)) = X0
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f1416,plain,
( spl0_64
| ~ spl0_6
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f332,f258,f34,f1414]) ).
fof(f1414,plain,
( spl0_64
<=> ! [X0] : pair(X0,projection1) = apply(pair(projection2,eq),pair(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f332,plain,
( ! [X0] : pair(X0,projection1) = apply(pair(projection2,eq),pair(X0,X0))
| ~ spl0_6
| ~ spl0_27 ),
inference(superposition,[],[f259,f35]) ).
fof(f1412,plain,
( spl0_63
| ~ spl0_5
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f330,f258,f30,f1410]) ).
fof(f1410,plain,
( spl0_63
<=> ! [X0,X1] : pair(X1,X1) = apply(pair(projection2,projection2),pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f330,plain,
( ! [X0,X1] : pair(X1,X1) = apply(pair(projection2,projection2),pair(X0,X1))
| ~ spl0_5
| ~ spl0_27 ),
inference(superposition,[],[f259,f31]) ).
fof(f1408,plain,
( spl0_62
| ~ spl0_4
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f324,f258,f26,f1406]) ).
fof(f1406,plain,
( spl0_62
<=> ! [X0,X1] : pair(X1,X0) = apply(pair(projection2,projection1),pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f324,plain,
( ! [X0,X1] : pair(X1,X0) = apply(pair(projection2,projection1),pair(X0,X1))
| ~ spl0_4
| ~ spl0_27 ),
inference(superposition,[],[f259,f27]) ).
fof(f1404,plain,
( spl0_61
| ~ spl0_4
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f310,f254,f26,f1402]) ).
fof(f1402,plain,
( spl0_61
<=> ! [X2,X0,X1] : apply(projection1,apply(pair(projection1,X1),pair(X0,X2))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f310,plain,
( ! [X2,X0,X1] : apply(projection1,apply(pair(projection1,X1),pair(X0,X2))) = X0
| ~ spl0_4
| ~ spl0_26 ),
inference(superposition,[],[f27,f255]) ).
fof(f1400,plain,
( spl0_60
| ~ spl0_6
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f295,f254,f34,f1398]) ).
fof(f1398,plain,
( spl0_60
<=> ! [X0] : pair(X0,projection1) = apply(pair(projection1,eq),pair(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f295,plain,
( ! [X0] : pair(X0,projection1) = apply(pair(projection1,eq),pair(X0,X0))
| ~ spl0_6
| ~ spl0_26 ),
inference(superposition,[],[f255,f35]) ).
fof(f1396,plain,
( spl0_59
| ~ spl0_4
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f288,f254,f26,f1394]) ).
fof(f1394,plain,
( spl0_59
<=> ! [X0,X1] : pair(X0,X0) = apply(pair(projection1,projection1),pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f288,plain,
( ! [X0,X1] : pair(X0,X0) = apply(pair(projection1,projection1),pair(X0,X1))
| ~ spl0_4
| ~ spl0_26 ),
inference(superposition,[],[f255,f27]) ).
fof(f1392,plain,
( spl0_58
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f148,f129,f45,f1390]) ).
fof(f45,plain,
( spl0_8
<=> ! [X0] : pair(apply(projection1,X0),apply(projection2,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f129,plain,
( spl0_17
<=> ! [X2,X0,X1] : apply(X0,X1) = apply(projection1,apply(pair(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f148,plain,
( ! [X0,X1] : apply(apply(projection1,X0),X1) = apply(projection1,apply(X0,X1))
| ~ spl0_8
| ~ spl0_17 ),
inference(superposition,[],[f130,f46]) ).
fof(f46,plain,
( ! [X0] : pair(apply(projection1,X0),apply(projection2,X0)) = X0
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f130,plain,
( ! [X2,X0,X1] : apply(X0,X1) = apply(projection1,apply(pair(X0,X2),X1))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f1388,plain,
( spl0_57
| ~ spl0_8
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f136,f125,f45,f1386]) ).
fof(f125,plain,
( spl0_16
<=> ! [X2,X0,X1] : apply(X2,X1) = apply(projection2,apply(pair(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f136,plain,
( ! [X0,X1] : apply(apply(projection2,X0),X1) = apply(projection2,apply(X0,X1))
| ~ spl0_8
| ~ spl0_16 ),
inference(superposition,[],[f126,f46]) ).
fof(f126,plain,
( ! [X2,X0,X1] : apply(X2,X1) = apply(projection2,apply(pair(X0,X2),X1))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f1384,plain,
( spl0_56
| ~ spl0_10
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f120,f117,f58,f1382]) ).
fof(f1382,plain,
( spl0_56
<=> ! [X2,X0,X1] : projection1 = apply(eq,apply(apply(pair(X0,X0),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f117,plain,
( spl0_15
<=> ! [X0,X1] : projection1 = apply(eq,apply(pair(X0,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f120,plain,
( ! [X2,X0,X1] : projection1 = apply(eq,apply(apply(pair(X0,X0),X1),X2))
| ~ spl0_10
| ~ spl0_15 ),
inference(superposition,[],[f118,f59]) ).
fof(f118,plain,
( ! [X0,X1] : projection1 = apply(eq,apply(pair(X0,X0),X1))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f1380,plain,
( spl0_55
| ~ spl0_3
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f115,f105,f85,f22,f1378]) ).
fof(f1378,plain,
( spl0_55
<=> ! [X0,X1] : apply(apply(apply(abstraction,pair(projection1,projection2)),X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f115,plain,
( ! [X0,X1] : apply(apply(apply(abstraction,pair(projection1,projection2)),X1),X0) = X0
| ~ spl0_3
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[],[f111,f23]) ).
fof(f111,plain,
( ! [X0,X1] : apply(apply(apply(abstraction,pair(projection1,projection2)),X1),X0) = apply(apply(k,X0),apply(X1,X0))
| ~ spl0_12
| ~ spl0_14 ),
inference(superposition,[],[f86,f106]) ).
fof(f1343,plain,
( spl0_54
| ~ spl0_2
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f589,f567,f18,f1341]) ).
fof(f589,plain,
( ! [X0,X1] : apply(b(apply(apply(abstraction,X0),apply(k,X1))),b(apply(apply(abstraction,X0),apply(k,X1)))) != apply(apply(apply(X0,apply(k,b(apply(apply(abstraction,X0),apply(k,X1))))),X1),c(apply(apply(abstraction,X0),apply(k,X1))))
| ~ spl0_2
| ~ spl0_34 ),
inference(superposition,[],[f19,f568]) ).
fof(f1338,plain,
( spl0_53
| ~ spl0_3
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f241,f229,f22,f1336]) ).
fof(f1336,plain,
( spl0_53
<=> ! [X0,X1] :
( X0 != X1
| apply(k,X0) = apply(k,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f229,plain,
( spl0_23
<=> ! [X0,X1] :
( apply(X1,n(apply(k,X0),X1)) != X0
| apply(k,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f241,plain,
( ! [X0,X1] :
( X0 != X1
| apply(k,X0) = apply(k,X1) )
| ~ spl0_3
| ~ spl0_23 ),
inference(superposition,[],[f230,f23]) ).
fof(f230,plain,
( ! [X0,X1] :
( apply(X1,n(apply(k,X0),X1)) != X0
| apply(k,X0) = X1 )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f1303,plain,
( spl0_52
| ~ spl0_3
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f1248,f1245,f22,f1301]) ).
fof(f1301,plain,
( spl0_52
<=> ! [X0] : apply(b(apply(abstraction,apply(k,apply(k,X0)))),b(apply(abstraction,apply(k,apply(k,X0))))) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1245,plain,
( spl0_48
<=> ! [X0] : apply(X0,apply(b(apply(abstraction,apply(k,X0))),c(apply(abstraction,apply(k,X0))))) != apply(b(apply(abstraction,apply(k,X0))),b(apply(abstraction,apply(k,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1248,plain,
( ! [X0] : apply(b(apply(abstraction,apply(k,apply(k,X0)))),b(apply(abstraction,apply(k,apply(k,X0))))) != X0
| ~ spl0_3
| ~ spl0_48 ),
inference(superposition,[],[f1246,f23]) ).
fof(f1246,plain,
( ! [X0] : apply(X0,apply(b(apply(abstraction,apply(k,X0))),c(apply(abstraction,apply(k,X0))))) != apply(b(apply(abstraction,apply(k,X0))),b(apply(abstraction,apply(k,X0))))
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1245]) ).
fof(f1299,plain,
( spl0_51
| ~ spl0_2
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f530,f278,f18,f1297]) ).
fof(f1297,plain,
( spl0_51
<=> ! [X0,X1] : apply(b(apply(apply(abstraction,apply(k,X0)),X1)),b(apply(apply(abstraction,apply(k,X0)),X1))) != apply(apply(X0,apply(X1,b(apply(apply(abstraction,apply(k,X0)),X1)))),c(apply(apply(abstraction,apply(k,X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f278,plain,
( spl0_32
<=> ! [X2,X0,X1] : apply(apply(apply(abstraction,apply(k,X0)),X2),X1) = apply(X0,apply(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f530,plain,
( ! [X0,X1] : apply(b(apply(apply(abstraction,apply(k,X0)),X1)),b(apply(apply(abstraction,apply(k,X0)),X1))) != apply(apply(X0,apply(X1,b(apply(apply(abstraction,apply(k,X0)),X1)))),c(apply(apply(abstraction,apply(k,X0)),X1)))
| ~ spl0_2
| ~ spl0_32 ),
inference(superposition,[],[f19,f279]) ).
fof(f279,plain,
( ! [X2,X0,X1] : apply(apply(apply(abstraction,apply(k,X0)),X2),X1) = apply(X0,apply(X2,X1))
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f1263,plain,
( spl0_50
| ~ spl0_2
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f223,f195,f18,f1261]) ).
fof(f1261,plain,
( spl0_50
<=> ! [X0,X1] : apply(b(pair(X0,apply(k,X1))),b(pair(X0,apply(k,X1)))) != apply(pair(apply(X0,b(pair(X0,apply(k,X1)))),X1),c(pair(X0,apply(k,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f195,plain,
( spl0_22
<=> ! [X2,X0,X1] : apply(pair(X2,apply(k,X0)),X1) = pair(apply(X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f223,plain,
( ! [X0,X1] : apply(b(pair(X0,apply(k,X1))),b(pair(X0,apply(k,X1)))) != apply(pair(apply(X0,b(pair(X0,apply(k,X1)))),X1),c(pair(X0,apply(k,X1))))
| ~ spl0_2
| ~ spl0_22 ),
inference(superposition,[],[f19,f196]) ).
fof(f196,plain,
( ! [X2,X0,X1] : apply(pair(X2,apply(k,X0)),X1) = pair(apply(X2,X1),X0)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f1259,plain,
( spl0_49
| ~ spl0_2
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f208,f191,f18,f1257]) ).
fof(f1257,plain,
( spl0_49
<=> ! [X0,X1] : apply(b(pair(apply(k,X0),X1)),b(pair(apply(k,X0),X1))) != apply(pair(X0,apply(X1,b(pair(apply(k,X0),X1)))),c(pair(apply(k,X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f191,plain,
( spl0_21
<=> ! [X2,X0,X1] : apply(pair(apply(k,X0),X2),X1) = pair(X0,apply(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f208,plain,
( ! [X0,X1] : apply(b(pair(apply(k,X0),X1)),b(pair(apply(k,X0),X1))) != apply(pair(X0,apply(X1,b(pair(apply(k,X0),X1)))),c(pair(apply(k,X0),X1)))
| ~ spl0_2
| ~ spl0_21 ),
inference(superposition,[],[f19,f192]) ).
fof(f192,plain,
( ! [X2,X0,X1] : apply(pair(apply(k,X0),X2),X1) = pair(X0,apply(X2,X1))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f1247,plain,
( spl0_48
| ~ spl0_2
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f517,f278,f18,f1245]) ).
fof(f517,plain,
( ! [X0] : apply(X0,apply(b(apply(abstraction,apply(k,X0))),c(apply(abstraction,apply(k,X0))))) != apply(b(apply(abstraction,apply(k,X0))),b(apply(abstraction,apply(k,X0))))
| ~ spl0_2
| ~ spl0_32 ),
inference(superposition,[],[f19,f279]) ).
fof(f1243,plain,
( spl0_47
| ~ spl0_2
| ~ spl0_3
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f169,f133,f22,f18,f1241]) ).
fof(f1241,plain,
( spl0_47
<=> ! [X0] : b(apply(apply(abstraction,k),X0)) != apply(b(apply(apply(abstraction,k),X0)),b(apply(apply(abstraction,k),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f169,plain,
( ! [X0] : b(apply(apply(abstraction,k),X0)) != apply(b(apply(apply(abstraction,k),X0)),b(apply(apply(abstraction,k),X0)))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f164,f23]) ).
fof(f164,plain,
( ! [X0] : apply(b(apply(apply(abstraction,k),X0)),b(apply(apply(abstraction,k),X0))) != apply(apply(k,b(apply(apply(abstraction,k),X0))),c(apply(apply(abstraction,k),X0)))
| ~ spl0_2
| ~ spl0_18 ),
inference(superposition,[],[f19,f134]) ).
fof(f1124,plain,
( spl0_46
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f91,f85,f1122]) ).
fof(f1122,plain,
( spl0_46
<=> ! [X0,X3,X2,X1] : apply(apply(apply(abstraction,X3),apply(X0,apply(k,X1))),apply(X2,X1)) = apply(apply(X3,apply(k,apply(X2,X1))),apply(apply(apply(abstraction,X0),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f91,plain,
( ! [X2,X3,X0,X1] : apply(apply(apply(abstraction,X3),apply(X0,apply(k,X1))),apply(X2,X1)) = apply(apply(X3,apply(k,apply(X2,X1))),apply(apply(apply(abstraction,X0),X2),X1))
| ~ spl0_12 ),
inference(superposition,[],[f86,f86]) ).
fof(f926,plain,
( spl0_45
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f99,f85,f58,f924]) ).
fof(f924,plain,
( spl0_45
<=> ! [X0,X3,X2,X1] : apply(pair(apply(X0,apply(k,X1)),X3),apply(X2,X1)) = pair(apply(apply(apply(abstraction,X0),X2),X1),apply(X3,apply(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f99,plain,
( ! [X2,X3,X0,X1] : apply(pair(apply(X0,apply(k,X1)),X3),apply(X2,X1)) = pair(apply(apply(apply(abstraction,X0),X2),X1),apply(X3,apply(X2,X1)))
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f59,f86]) ).
fof(f922,plain,
( spl0_44
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f98,f85,f58,f920]) ).
fof(f920,plain,
( spl0_44
<=> ! [X0,X3,X2,X1] : apply(pair(X3,apply(X0,apply(k,X1))),apply(X2,X1)) = pair(apply(X3,apply(X2,X1)),apply(apply(apply(abstraction,X0),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f98,plain,
( ! [X2,X3,X0,X1] : apply(pair(X3,apply(X0,apply(k,X1))),apply(X2,X1)) = pair(apply(X3,apply(X2,X1)),apply(apply(apply(abstraction,X0),X2),X1))
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f59,f86]) ).
fof(f858,plain,
( spl0_43
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f88,f85,f856]) ).
fof(f856,plain,
( spl0_43
<=> ! [X2,X0,X1] : apply(apply(apply(abstraction,apply(X0,apply(k,X1))),X2),X1) = apply(apply(apply(apply(abstraction,X0),k),X1),apply(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f88,plain,
( ! [X2,X0,X1] : apply(apply(apply(abstraction,apply(X0,apply(k,X1))),X2),X1) = apply(apply(apply(apply(abstraction,X0),k),X1),apply(X2,X1))
| ~ spl0_12 ),
inference(superposition,[],[f86,f86]) ).
fof(f814,plain,
( spl0_42
| ~ spl0_9
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f95,f85,f51,f812]) ).
fof(f812,plain,
( spl0_42
<=> ! [X2,X0,X1] :
( apply(apply(apply(abstraction,X2),eq),pair(X0,X1)) = apply(apply(X2,apply(k,pair(X0,X1))),projection2)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f51,plain,
( spl0_9
<=> ! [X0,X1] :
( X0 = X1
| projection2 = apply(eq,pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f95,plain,
( ! [X2,X0,X1] :
( apply(apply(apply(abstraction,X2),eq),pair(X0,X1)) = apply(apply(X2,apply(k,pair(X0,X1))),projection2)
| X0 = X1 )
| ~ spl0_9
| ~ spl0_12 ),
inference(superposition,[],[f86,f52]) ).
fof(f52,plain,
( ! [X0,X1] :
( projection2 = apply(eq,pair(X0,X1))
| X0 = X1 )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f810,plain,
( spl0_40
| ~ spl0_41
| ~ spl0_2
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f185,f171,f18,f807,f803]) ).
fof(f803,plain,
( spl0_40
<=> projection2 = apply(eq,b(projection2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f171,plain,
( spl0_20
<=> ! [X0] :
( projection2 = apply(eq,X0)
| apply(projection1,X0) = apply(projection2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f185,plain,
( apply(b(projection2),b(projection2)) != apply(apply(projection1,b(projection2)),c(projection2))
| projection2 = apply(eq,b(projection2))
| ~ spl0_2
| ~ spl0_20 ),
inference(superposition,[],[f19,f172]) ).
fof(f172,plain,
( ! [X0] :
( apply(projection1,X0) = apply(projection2,X0)
| projection2 = apply(eq,X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f684,plain,
( spl0_39
| ~ spl0_6
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f94,f85,f34,f682]) ).
fof(f682,plain,
( spl0_39
<=> ! [X0,X1] : apply(apply(apply(abstraction,X1),eq),pair(X0,X0)) = apply(apply(X1,apply(k,pair(X0,X0))),projection1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f94,plain,
( ! [X0,X1] : apply(apply(apply(abstraction,X1),eq),pair(X0,X0)) = apply(apply(X1,apply(k,pair(X0,X0))),projection1)
| ~ spl0_6
| ~ spl0_12 ),
inference(superposition,[],[f86,f35]) ).
fof(f680,plain,
( spl0_38
| ~ spl0_5
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f93,f85,f30,f678]) ).
fof(f678,plain,
( spl0_38
<=> ! [X2,X0,X1] : apply(apply(apply(abstraction,X2),projection2),pair(X0,X1)) = apply(apply(X2,apply(k,pair(X0,X1))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f93,plain,
( ! [X2,X0,X1] : apply(apply(apply(abstraction,X2),projection2),pair(X0,X1)) = apply(apply(X2,apply(k,pair(X0,X1))),X1)
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[],[f86,f31]) ).
fof(f676,plain,
( spl0_37
| ~ spl0_4
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f92,f85,f26,f674]) ).
fof(f674,plain,
( spl0_37
<=> ! [X2,X0,X1] : apply(apply(apply(abstraction,X2),projection1),pair(X0,X1)) = apply(apply(X2,apply(k,pair(X0,X1))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f92,plain,
( ! [X2,X0,X1] : apply(apply(apply(abstraction,X2),projection1),pair(X0,X1)) = apply(apply(X2,apply(k,pair(X0,X1))),X0)
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f86,f27]) ).
fof(f600,plain,
( spl0_36
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f70,f58,f51,f598]) ).
fof(f598,plain,
( spl0_36
<=> ! [X2,X0,X1] :
( apply(pair(X2,eq),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),projection2)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f70,plain,
( ! [X2,X0,X1] :
( apply(pair(X2,eq),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),projection2)
| X0 = X1 )
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f59,f52]) ).
fof(f596,plain,
( spl0_35
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f65,f58,f51,f594]) ).
fof(f594,plain,
( spl0_35
<=> ! [X2,X0,X1] :
( apply(pair(eq,X2),pair(X0,X1)) = pair(projection2,apply(X2,pair(X0,X1)))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f65,plain,
( ! [X2,X0,X1] :
( apply(pair(eq,X2),pair(X0,X1)) = pair(projection2,apply(X2,pair(X0,X1)))
| X0 = X1 )
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f59,f52]) ).
fof(f569,plain,
( spl0_34
| ~ spl0_3
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f90,f85,f22,f567]) ).
fof(f90,plain,
( ! [X2,X0,X1] : apply(apply(apply(abstraction,X2),apply(k,X0)),X1) = apply(apply(X2,apply(k,X1)),X0)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f86,f23]) ).
fof(f536,plain,
( spl0_33
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f73,f58,f51,f534]) ).
fof(f534,plain,
( spl0_33
<=> ! [X2,X0,X1] :
( projection2 = apply(eq,apply(pair(X0,X2),X1))
| apply(X0,X1) = apply(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f73,plain,
( ! [X2,X0,X1] :
( projection2 = apply(eq,apply(pair(X0,X2),X1))
| apply(X0,X1) = apply(X2,X1) )
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f52,f59]) ).
fof(f280,plain,
( spl0_32
| ~ spl0_3
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f89,f85,f22,f278]) ).
fof(f89,plain,
( ! [X2,X0,X1] : apply(apply(apply(abstraction,apply(k,X0)),X2),X1) = apply(X0,apply(X2,X1))
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f86,f23]) ).
fof(f276,plain,
( spl0_31
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f69,f58,f34,f274]) ).
fof(f274,plain,
( spl0_31
<=> ! [X0,X1] : apply(pair(X1,eq),pair(X0,X0)) = pair(apply(X1,pair(X0,X0)),projection1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f69,plain,
( ! [X0,X1] : apply(pair(X1,eq),pair(X0,X0)) = pair(apply(X1,pair(X0,X0)),projection1)
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f59,f35]) ).
fof(f272,plain,
( spl0_30
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f68,f58,f30,f270]) ).
fof(f68,plain,
( ! [X2,X0,X1] : apply(pair(X2,projection2),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),X1)
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f59,f31]) ).
fof(f268,plain,
( spl0_29
| ~ spl0_4
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f67,f58,f26,f266]) ).
fof(f67,plain,
( ! [X2,X0,X1] : apply(pair(X2,projection1),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),X0)
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f59,f27]) ).
fof(f264,plain,
( spl0_28
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f64,f58,f34,f262]) ).
fof(f262,plain,
( spl0_28
<=> ! [X0,X1] : apply(pair(eq,X1),pair(X0,X0)) = pair(projection1,apply(X1,pair(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f64,plain,
( ! [X0,X1] : apply(pair(eq,X1),pair(X0,X0)) = pair(projection1,apply(X1,pair(X0,X0)))
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f59,f35]) ).
fof(f260,plain,
( spl0_27
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f63,f58,f30,f258]) ).
fof(f63,plain,
( ! [X2,X0,X1] : apply(pair(projection2,X2),pair(X0,X1)) = pair(X1,apply(X2,pair(X0,X1)))
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f59,f31]) ).
fof(f256,plain,
( spl0_26
| ~ spl0_4
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f62,f58,f26,f254]) ).
fof(f62,plain,
( ! [X2,X0,X1] : apply(pair(projection1,X2),pair(X0,X1)) = pair(X0,apply(X2,pair(X0,X1)))
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f59,f27]) ).
fof(f240,plain,
( ~ spl0_25
| ~ spl0_2
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f157,f133,f18,f237]) ).
fof(f237,plain,
( spl0_25
<=> apply(k,c(apply(abstraction,k))) = apply(b(apply(abstraction,k)),b(apply(abstraction,k))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f157,plain,
( apply(k,c(apply(abstraction,k))) != apply(b(apply(abstraction,k)),b(apply(abstraction,k)))
| ~ spl0_2
| ~ spl0_18 ),
inference(superposition,[],[f19,f134]) ).
fof(f235,plain,
( spl0_24
| ~ spl0_3
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f82,f78,f22,f233]) ).
fof(f233,plain,
( spl0_24
<=> ! [X0,X1] :
( apply(X1,n(X1,apply(k,X0))) != X0
| apply(k,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f78,plain,
( spl0_11
<=> ! [X0,X1] :
( X0 = X1
| apply(X0,n(X0,X1)) != apply(X1,n(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f82,plain,
( ! [X0,X1] :
( apply(X1,n(X1,apply(k,X0))) != X0
| apply(k,X0) = X1 )
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f79,f23]) ).
fof(f79,plain,
( ! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f231,plain,
( spl0_23
| ~ spl0_3
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f81,f78,f22,f229]) ).
fof(f81,plain,
( ! [X0,X1] :
( apply(X1,n(apply(k,X0),X1)) != X0
| apply(k,X0) = X1 )
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f79,f23]) ).
fof(f197,plain,
( spl0_22
| ~ spl0_3
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f66,f58,f22,f195]) ).
fof(f66,plain,
( ! [X2,X0,X1] : apply(pair(X2,apply(k,X0)),X1) = pair(apply(X2,X1),X0)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f59,f23]) ).
fof(f193,plain,
( spl0_21
| ~ spl0_3
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f61,f58,f22,f191]) ).
fof(f61,plain,
( ! [X2,X0,X1] : apply(pair(apply(k,X0),X2),X1) = pair(X0,apply(X2,X1))
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f59,f23]) ).
fof(f173,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f54,f51,f45,f171]) ).
fof(f54,plain,
( ! [X0] :
( projection2 = apply(eq,X0)
| apply(projection1,X0) = apply(projection2,X0) )
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f52,f46]) ).
fof(f147,plain,
( ~ spl0_19
| ~ spl0_2
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f114,f105,f18,f144]) ).
fof(f144,plain,
( spl0_19
<=> apply(b(pair(projection1,projection2)),b(pair(projection1,projection2))) = apply(b(pair(projection1,projection2)),c(pair(projection1,projection2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f114,plain,
( apply(b(pair(projection1,projection2)),b(pair(projection1,projection2))) != apply(b(pair(projection1,projection2)),c(pair(projection1,projection2)))
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f19,f106]) ).
fof(f135,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f96,f85,f22,f133]) ).
fof(f96,plain,
( ! [X0,X1] : apply(k,X0) = apply(apply(apply(abstraction,k),X1),X0)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f86,f23]) ).
fof(f131,plain,
( spl0_17
| ~ spl0_4
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f75,f58,f26,f129]) ).
fof(f75,plain,
( ! [X2,X0,X1] : apply(X0,X1) = apply(projection1,apply(pair(X0,X2),X1))
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f27,f59]) ).
fof(f127,plain,
( spl0_16
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f74,f58,f30,f125]) ).
fof(f74,plain,
( ! [X2,X0,X1] : apply(X2,X1) = apply(projection2,apply(pair(X0,X2),X1))
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f31,f59]) ).
fof(f119,plain,
( spl0_15
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f76,f58,f34,f117]) ).
fof(f76,plain,
( ! [X0,X1] : projection1 = apply(eq,apply(pair(X0,X0),X1))
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f35,f59]) ).
fof(f107,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f71,f58,f45,f105]) ).
fof(f71,plain,
( ! [X0] : apply(pair(projection1,projection2),X0) = X0
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f59,f46]) ).
fof(f103,plain,
( spl0_13
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f38,f22,f18,f101]) ).
fof(f101,plain,
( spl0_13
<=> ! [X0] : apply(b(apply(k,X0)),b(apply(k,X0))) != apply(X0,c(apply(k,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f38,plain,
( ! [X0] : apply(b(apply(k,X0)),b(apply(k,X0))) != apply(X0,c(apply(k,X0)))
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f19,f23]) ).
fof(f87,plain,
spl0_12,
inference(avatar_split_clause,[],[f6,f85]) ).
fof(f6,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstraction) ).
fof(f80,plain,
spl0_11,
inference(avatar_split_clause,[],[f9,f78]) ).
fof(f9,axiom,
! [X0,X1] :
( X0 = X1
| apply(X0,n(X0,X1)) != apply(X1,n(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
fof(f60,plain,
spl0_10,
inference(avatar_split_clause,[],[f5,f58]) ).
fof(f5,axiom,
! [X2,X0,X1] : apply(pair(X0,X1),X2) = pair(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pairwise_application) ).
fof(f53,plain,
spl0_9,
inference(avatar_split_clause,[],[f8,f51]) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
| projection2 = apply(eq,pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).
fof(f47,plain,
spl0_8,
inference(avatar_split_clause,[],[f4,f45]) ).
fof(f4,axiom,
! [X0] : pair(apply(projection1,X0),apply(projection2,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pairing) ).
fof(f43,plain,
( ~ spl0_7
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f37,f22,f18,f40]) ).
fof(f40,plain,
( spl0_7
<=> b(k) = apply(b(k),b(k)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f37,plain,
( b(k) != apply(b(k),b(k))
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f19,f23]) ).
fof(f36,plain,
spl0_6,
inference(avatar_split_clause,[],[f7,f34]) ).
fof(f7,axiom,
! [X0] : projection1 = apply(eq,pair(X0,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality) ).
fof(f32,plain,
spl0_5,
inference(avatar_split_clause,[],[f3,f30]) ).
fof(f3,axiom,
! [X0,X1] : apply(projection2,pair(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',projection2) ).
fof(f28,plain,
spl0_4,
inference(avatar_split_clause,[],[f2,f26]) ).
fof(f2,axiom,
! [X0,X1] : apply(projection1,pair(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',projection1) ).
fof(f24,plain,
spl0_3,
inference(avatar_split_clause,[],[f1,f22]) ).
fof(f1,axiom,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f20,plain,
spl0_2,
inference(avatar_split_clause,[],[f11,f18]) ).
fof(f11,axiom,
! [X1] : apply(apply(X1,b(X1)),c(X1)) != apply(b(X1),b(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_diagonal_combinator) ).
fof(f16,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f10,f13]) ).
fof(f13,plain,
( spl0_1
<=> projection1 = projection2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f10,axiom,
projection1 != projection2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_projections) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : COL075-1 : TPTP v8.1.2. Released v1.2.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 18:31:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (22638)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (22641)WARNING: value z3 for option sas not known
% 0.22/0.38 % (22642)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (22640)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (22643)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)
% 0.22/0.38 % (22641)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)
% 0.22/0.38 % (22644)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)
% 0.22/0.38 % (22639)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (22645)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)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [3]
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.39 TRYING [4]
% 0.22/0.39 TRYING [3]
% 0.22/0.41 TRYING [5]
% 0.22/0.42 TRYING [4]
% 0.22/0.47 TRYING [6]
% 0.22/0.50 TRYING [5]
% 0.22/0.53 % (22643)First to succeed.
% 0.22/0.54 % (22643)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-22638"
% 0.22/0.54 % (22643)Refutation found. Thanks to Tanya!
% 0.22/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.54 % (22643)------------------------------
% 0.22/0.54 % (22643)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.54 % (22643)Termination reason: Refutation
% 0.22/0.54
% 0.22/0.54 % (22643)Memory used [KB]: 3542
% 0.22/0.54 % (22643)Time elapsed: 0.160 s
% 0.22/0.54 % (22643)Instructions burned: 326 (million)
% 0.22/0.54 % (22638)Success in time 0.165 s
%------------------------------------------------------------------------------