TPTP Problem File: NUM377+1.010.p
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%------------------------------------------------------------------------------
% File : NUM377+1.010 : TPTP v8.2.0. Released v3.2.0.
% Domain : Number Theory
% Problem : Find assignment in 0-10 to satisfy inequalities, very hard
% Version : [Cim05] axioms.
% English : Find an assignment to two variables which are in range, so that
% several pairs complex terms are not equal (and they are).
% Refs : [Cim05] Cimatti (2006), Email to G. Sutcliffe
% Source : [Cim05]
% Names :
% Status : Unsatisfiable
% Rating : 0.00 v5.2.0, 0.33 v5.0.0, 0.00 v3.4.0, 0.33 v3.3.0, 0.00 v3.2.0
% Syntax : Number of formulae : 1 ( 0 unt; 0 def)
% Number of atoms : 250 ( 250 equ)
% Maximal formula atoms : 250 ( 250 avg)
% Number of connectives : 314 ( 65 ~; 29 |; 220 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 244 ( 244 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 22 ( 0 !; 22 ?)
% SPC : FOF_UNS_RFO_PEQ
% Comments :
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fof(try_satisfy_this,axiom,
? [X0,Y0,X1,Y1,X2,Y2,X3,Y3,X4,Y4,X5,Y5,X6,Y6,X7,Y7,X8,Y8,X9,Y9,X10,Y10] :
( succ(n0) = n1
& succ(n1) = n2
& succ(n2) = n3
& succ(n3) = n4
& succ(n4) = n5
& succ(n5) = n6
& succ(n6) = n7
& succ(n7) = n8
& succ(n8) = n9
& succ(n9) = n10
& succ(n10) = n0
& pred(n0) = n10
& pred(n1) = n0
& pred(n2) = n1
& pred(n3) = n2
& pred(n4) = n3
& pred(n5) = n4
& pred(n6) = n5
& pred(n7) = n6
& pred(n8) = n7
& pred(n9) = n8
& pred(n10) = n9
& sum(n0,n0) = n0
& sum(n0,n1) = n1
& sum(n0,n2) = n2
& sum(n0,n3) = n3
& sum(n0,n4) = n4
& sum(n0,n5) = n5
& sum(n0,n6) = n6
& sum(n0,n7) = n7
& sum(n0,n8) = n8
& sum(n0,n9) = n9
& sum(n0,n10) = n10
& sum(n1,n0) = n1
& sum(n1,n1) = n2
& sum(n1,n2) = n3
& sum(n1,n3) = n4
& sum(n1,n4) = n5
& sum(n1,n5) = n6
& sum(n1,n6) = n7
& sum(n1,n7) = n8
& sum(n1,n8) = n9
& sum(n1,n9) = n10
& sum(n1,n10) = n0
& sum(n2,n0) = n2
& sum(n2,n1) = n3
& sum(n2,n2) = n4
& sum(n2,n3) = n5
& sum(n2,n4) = n6
& sum(n2,n5) = n7
& sum(n2,n6) = n8
& sum(n2,n7) = n9
& sum(n2,n8) = n10
& sum(n2,n9) = n0
& sum(n2,n10) = n1
& sum(n3,n0) = n3
& sum(n3,n1) = n4
& sum(n3,n2) = n5
& sum(n3,n3) = n6
& sum(n3,n4) = n7
& sum(n3,n5) = n8
& sum(n3,n6) = n9
& sum(n3,n7) = n10
& sum(n3,n8) = n0
& sum(n3,n9) = n1
& sum(n3,n10) = n2
& sum(n4,n0) = n4
& sum(n4,n1) = n5
& sum(n4,n2) = n6
& sum(n4,n3) = n7
& sum(n4,n4) = n8
& sum(n4,n5) = n9
& sum(n4,n6) = n10
& sum(n4,n7) = n0
& sum(n4,n8) = n1
& sum(n4,n9) = n2
& sum(n4,n10) = n3
& sum(n5,n0) = n5
& sum(n5,n1) = n6
& sum(n5,n2) = n7
& sum(n5,n3) = n8
& sum(n5,n4) = n9
& sum(n5,n5) = n10
& sum(n5,n6) = n0
& sum(n5,n7) = n1
& sum(n5,n8) = n2
& sum(n5,n9) = n3
& sum(n5,n10) = n4
& sum(n6,n0) = n6
& sum(n6,n1) = n7
& sum(n6,n2) = n8
& sum(n6,n3) = n9
& sum(n6,n4) = n10
& sum(n6,n5) = n0
& sum(n6,n6) = n1
& sum(n6,n7) = n2
& sum(n6,n8) = n3
& sum(n6,n9) = n4
& sum(n6,n10) = n5
& sum(n7,n0) = n7
& sum(n7,n1) = n8
& sum(n7,n2) = n9
& sum(n7,n3) = n10
& sum(n7,n4) = n0
& sum(n7,n5) = n1
& sum(n7,n6) = n2
& sum(n7,n7) = n3
& sum(n7,n8) = n4
& sum(n7,n9) = n5
& sum(n7,n10) = n6
& sum(n8,n0) = n8
& sum(n8,n1) = n9
& sum(n8,n2) = n10
& sum(n8,n3) = n0
& sum(n8,n4) = n1
& sum(n8,n5) = n2
& sum(n8,n6) = n3
& sum(n8,n7) = n4
& sum(n8,n8) = n5
& sum(n8,n9) = n6
& sum(n8,n10) = n7
& sum(n9,n0) = n9
& sum(n9,n1) = n10
& sum(n9,n2) = n0
& sum(n9,n3) = n1
& sum(n9,n4) = n2
& sum(n9,n5) = n3
& sum(n9,n6) = n4
& sum(n9,n7) = n5
& sum(n9,n8) = n6
& sum(n9,n9) = n7
& sum(n9,n10) = n8
& sum(n10,n0) = n10
& sum(n10,n1) = n0
& sum(n10,n2) = n1
& sum(n10,n3) = n2
& sum(n10,n4) = n3
& sum(n10,n5) = n4
& sum(n10,n6) = n5
& sum(n10,n7) = n6
& sum(n10,n8) = n7
& sum(n10,n9) = n8
& sum(n10,n10) = n9
& ( X0 = n0
| X0 = n1
| X0 = n2
| X0 = n3
| X0 = n4
| X0 = n5
| X0 = n6
| X0 = n7
| X0 = n8
| X0 = n9
| X0 = n10 )
& ( Y0 = n0
| Y0 = n1
| Y0 = n2
| Y0 = n3
| Y0 = n4
| Y0 = n5
| Y0 = n6
| Y0 = n7
| Y0 = n8
| Y0 = n9
| Y0 = n10 )
& X1 = sum(sum(pred(X0),succ(Y0)),sum(pred(Y0),succ(X0)))
& Y1 = sum(sum(pred(X0),succ(X0)),sum(pred(Y0),succ(Y0)))
& X2 = sum(sum(pred(X1),succ(Y1)),sum(pred(Y1),succ(X1)))
& Y2 = sum(sum(pred(X1),succ(X1)),sum(pred(Y1),succ(Y1)))
& X3 = sum(sum(pred(X2),succ(Y2)),sum(pred(Y2),succ(X2)))
& Y3 = sum(sum(pred(X2),succ(X2)),sum(pred(Y2),succ(Y2)))
& X4 = sum(sum(pred(X3),succ(Y3)),sum(pred(Y3),succ(X3)))
& Y4 = sum(sum(pred(X3),succ(X3)),sum(pred(Y3),succ(Y3)))
& X5 = sum(sum(pred(X4),succ(Y4)),sum(pred(Y4),succ(X4)))
& Y5 = sum(sum(pred(X4),succ(X4)),sum(pred(Y4),succ(Y4)))
& X6 = sum(sum(pred(X5),succ(Y5)),sum(pred(Y5),succ(X5)))
& Y6 = sum(sum(pred(X5),succ(X5)),sum(pred(Y5),succ(Y5)))
& X7 = sum(sum(pred(X6),succ(Y6)),sum(pred(Y6),succ(X6)))
& Y7 = sum(sum(pred(X6),succ(X6)),sum(pred(Y6),succ(Y6)))
& X8 = sum(sum(pred(X7),succ(Y7)),sum(pred(Y7),succ(X7)))
& Y8 = sum(sum(pred(X7),succ(X7)),sum(pred(Y7),succ(Y7)))
& X9 = sum(sum(pred(X8),succ(Y8)),sum(pred(Y8),succ(X8)))
& Y9 = sum(sum(pred(X8),succ(X8)),sum(pred(Y8),succ(Y8)))
& X10 = sum(sum(pred(X9),succ(Y9)),sum(pred(Y9),succ(X9)))
& Y10 = sum(sum(pred(X9),succ(X9)),sum(pred(Y9),succ(Y9)))
& ( X1 != Y1
| X2 != Y2
| X3 != Y3
| X4 != Y4
| X5 != Y5
| X6 != Y6
| X7 != Y7
| X8 != Y8
| X9 != Y9
| X10 != Y10 )
& n0 != n1
& n0 != n2
& n0 != n3
& n0 != n4
& n0 != n5
& n0 != n6
& n0 != n7
& n0 != n8
& n0 != n9
& n0 != n10
& n1 != n2
& n1 != n3
& n1 != n4
& n1 != n5
& n1 != n6
& n1 != n7
& n1 != n8
& n1 != n9
& n1 != n10
& n2 != n3
& n2 != n4
& n2 != n5
& n2 != n6
& n2 != n7
& n2 != n8
& n2 != n9
& n2 != n10
& n3 != n4
& n3 != n5
& n3 != n6
& n3 != n7
& n3 != n8
& n3 != n9
& n3 != n10
& n4 != n5
& n4 != n6
& n4 != n7
& n4 != n8
& n4 != n9
& n4 != n10
& n5 != n6
& n5 != n7
& n5 != n8
& n5 != n9
& n5 != n10
& n6 != n7
& n6 != n8
& n6 != n9
& n6 != n10
& n7 != n8
& n7 != n9
& n7 != n10
& n8 != n9
& n8 != n10
& n9 != n10 ) ).