%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL644+1.015 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:08:18 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 46
% Syntax : Number of formulae : 53 ( 3 unt; 45 def)
% Number of atoms : 3023 ( 0 equ)
% Maximal formula atoms : 655 ( 57 avg)
% Number of connectives : 4455 (1485 ~;1580 |;1345 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 12 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 63 ( 62 usr; 1 prp; 0-2 aty)
% Number of functors : 48 ( 48 usr; 18 con; 0-1 aty)
% Number of variables : 1057 ( 839 !; 218 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X] :
~ ( ~ ( ~ ( ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p1(X)
& ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& p1(X) )
| p2(X)
| ~ r1(Y,X) )
| p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| ! [X] :
( p1(X)
| ~ ( ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p2(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X) )
| p3(X)
| ~ r1(Y,X) )
| p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| ! [X] :
( p2(X)
| ~ ( ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p3(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X) )
| p4(X)
| ~ r1(Y,X) )
| p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| ! [X] :
( p3(X)
| ~ ( ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p4(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X) )
| p5(X)
| ~ r1(Y,X) )
| p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| ! [X] :
( p4(X)
| ~ ( ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p5(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X) )
| p6(X)
| ~ r1(Y,X) )
| p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| ! [X] :
( p5(X)
| ~ ( ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) ) )
| p15(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ~ ( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) ) )
| p15(Y)
| ~ r1(X,Y) )
| ~ ( ~ ( ! [Y] :
( ~ ( p6(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| p7(Y)
| p6(Y)
| ~ ( ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p6(X)
& ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X) )
| p7(X)
| ~ r1(Y,X) )
| p6(Y)
| ~ ( ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p6(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| p7(Y)
| ! [X] :
( p6(X)
| ~ ( ! [Y] :
( p7(Y)
| ~ r1(X,Y) )
& p7(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p6(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| p7(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p6(Y)
| ~ ( ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p7(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| p8(Y)
| p7(Y)
| ~ ( ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p7(X)
& ! [Y] :
( p7(Y)
| ~ r1(X,Y) )
& p7(X) )
| p8(X)
| ~ r1(Y,X) )
| p7(Y)
| ~ ( ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p7(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| p8(Y)
| ! [X] :
( p7(X)
| ~ ( ! [Y] :
( p8(Y)
| ~ r1(X,Y) )
& p8(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p7(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| p8(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p7(Y)
| ~ ( ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p8(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| p9(Y)
| p8(Y)
| ~ ( ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p8(X)
& ! [Y] :
( p8(Y)
| ~ r1(X,Y) )
& p8(X) )
| p9(X)
| ~ r1(Y,X) )
| p8(Y)
| ~ ( ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p8(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| p9(Y)
| ! [X] :
( p8(X)
| ~ ( ! [Y] :
( p9(Y)
| ~ r1(X,Y) )
& p9(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p8(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| p9(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p8(Y)
| ~ ( ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p9(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| p10(Y)
| p9(Y)
| ~ ( ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p9(X)
& ! [Y] :
( p9(Y)
| ~ r1(X,Y) )
& p9(X) )
| p10(X)
| ~ r1(Y,X) )
| p9(Y)
| ~ ( ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p9(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| p10(Y)
| ! [X] :
( p9(X)
| ~ ( ! [Y] :
( p10(Y)
| ~ r1(X,Y) )
& p10(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p9(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| p10(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p9(Y)
| ~ ( ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p10(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| p11(Y)
| p10(Y)
| ~ ( ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p10(X)
& ! [Y] :
( p10(Y)
| ~ r1(X,Y) )
& p10(X) )
| p11(X)
| ~ r1(Y,X) )
| p10(Y)
| ~ ( ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p10(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| p11(Y)
| ! [X] :
( p10(X)
| ~ ( ! [Y] :
( p11(Y)
| ~ r1(X,Y) )
& p11(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p10(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| p11(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p10(Y)
| ~ ( ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p11(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| p12(Y)
| p11(Y)
| ~ ( ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p11(X)
& ! [Y] :
( p11(Y)
| ~ r1(X,Y) )
& p11(X) )
| p12(X)
| ~ r1(Y,X) )
| p11(Y)
| ~ ( ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p11(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| p12(Y)
| ! [X] :
( p11(X)
| ~ ( ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
& p12(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p11(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| p12(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p11(Y)
| ~ ( ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p12(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| p13(Y)
| p12(Y)
| ~ ( ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p12(X)
& ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
& p12(X) )
| p13(X)
| ~ r1(Y,X) )
| p12(Y)
| ~ ( ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p12(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| p13(Y)
| ! [X] :
( p12(X)
| ~ ( ! [Y] :
( p13(Y)
| ~ r1(X,Y) )
& p13(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p12(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| p13(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p12(Y)
| ~ ( ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p13(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| p14(Y)
| p13(Y)
| ~ ( ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p13(X)
& ! [Y] :
( p13(Y)
| ~ r1(X,Y) )
& p13(X) )
| p14(X)
| ~ r1(Y,X) )
| p13(Y)
| ~ ( ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p13(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| p14(Y)
| ! [X] :
( p13(X)
| ~ ( ! [Y] :
( p14(Y)
| ~ r1(X,Y) )
& p14(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p13(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| p14(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p13(Y)
| ~ ( ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p14(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| p15(Y)
| p14(Y)
| ~ ( ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p14(X)
& ! [Y] :
( p14(Y)
| ~ r1(X,Y) )
& p14(X) )
| p15(X)
| ~ r1(Y,X) )
| p14(Y)
| ~ ( ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p14(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| p15(Y)
| ! [X] :
( p14(X)
| ~ ( ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
& p15(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p14(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| p15(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p14(Y)
| ~ ( ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| p16(Y)
| p15(Y)
| ~ ( ! [X] :
( p16(X)
| ~ r1(Y,X) )
& p16(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p15(X)
& ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
& p15(X) )
| p16(X)
| ~ r1(Y,X) )
| p15(Y)
| ~ ( ! [X] :
( p16(X)
| ~ r1(Y,X) )
& p16(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| p16(Y)
| ! [X] :
( p15(X)
| ~ ( ! [Y] :
( p16(Y)
| ~ r1(X,Y) )
& p16(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| p16(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p15(Y)
| ~ ( ! [X] :
( p16(X)
| ~ r1(Y,X) )
& p16(Y) )
| ~ r1(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ~ ? [X] :
~ ( ~ ( ~ ( ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p1(X)
& ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& p1(X) )
| p2(X)
| ~ r1(Y,X) )
| p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| ! [X] :
( p1(X)
| ~ ( ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p2(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X) )
| p3(X)
| ~ r1(Y,X) )
| p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| ! [X] :
( p2(X)
| ~ ( ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p3(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X) )
| p4(X)
| ~ r1(Y,X) )
| p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| ! [X] :
( p3(X)
| ~ ( ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p4(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X) )
| p5(X)
| ~ r1(Y,X) )
| p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| ! [X] :
( p4(X)
| ~ ( ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p5(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X) )
| p6(X)
| ~ r1(Y,X) )
| p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| ! [X] :
( p5(X)
| ~ ( ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) ) )
| p15(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ~ ( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) ) )
| p15(Y)
| ~ r1(X,Y) )
| ~ ( ~ ( ! [Y] :
( ~ ( p6(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| p7(Y)
| p6(Y)
| ~ ( ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p6(X)
& ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X) )
| p7(X)
| ~ r1(Y,X) )
| p6(Y)
| ~ ( ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p6(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| p7(Y)
| ! [X] :
( p6(X)
| ~ ( ! [Y] :
( p7(Y)
| ~ r1(X,Y) )
& p7(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p6(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| p7(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p6(Y)
| ~ ( ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p7(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| p8(Y)
| p7(Y)
| ~ ( ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p7(X)
& ! [Y] :
( p7(Y)
| ~ r1(X,Y) )
& p7(X) )
| p8(X)
| ~ r1(Y,X) )
| p7(Y)
| ~ ( ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p7(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| p8(Y)
| ! [X] :
( p7(X)
| ~ ( ! [Y] :
( p8(Y)
| ~ r1(X,Y) )
& p8(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p7(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y) )
| p8(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p7(Y)
| ~ ( ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p8(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| p9(Y)
| p8(Y)
| ~ ( ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p8(X)
& ! [Y] :
( p8(Y)
| ~ r1(X,Y) )
& p8(X) )
| p9(X)
| ~ r1(Y,X) )
| p8(Y)
| ~ ( ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p8(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| p9(Y)
| ! [X] :
( p8(X)
| ~ ( ! [Y] :
( p9(Y)
| ~ r1(X,Y) )
& p9(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p8(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y) )
| p9(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p8(Y)
| ~ ( ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p9(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| p10(Y)
| p9(Y)
| ~ ( ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p9(X)
& ! [Y] :
( p9(Y)
| ~ r1(X,Y) )
& p9(X) )
| p10(X)
| ~ r1(Y,X) )
| p9(Y)
| ~ ( ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p9(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| p10(Y)
| ! [X] :
( p9(X)
| ~ ( ! [Y] :
( p10(Y)
| ~ r1(X,Y) )
& p10(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p9(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y) )
| p10(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p9(Y)
| ~ ( ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p10(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| p11(Y)
| p10(Y)
| ~ ( ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p10(X)
& ! [Y] :
( p10(Y)
| ~ r1(X,Y) )
& p10(X) )
| p11(X)
| ~ r1(Y,X) )
| p10(Y)
| ~ ( ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p10(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| p11(Y)
| ! [X] :
( p10(X)
| ~ ( ! [Y] :
( p11(Y)
| ~ r1(X,Y) )
& p11(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p10(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y) )
| p11(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p10(Y)
| ~ ( ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p11(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| p12(Y)
| p11(Y)
| ~ ( ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p11(X)
& ! [Y] :
( p11(Y)
| ~ r1(X,Y) )
& p11(X) )
| p12(X)
| ~ r1(Y,X) )
| p11(Y)
| ~ ( ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p11(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| p12(Y)
| ! [X] :
( p11(X)
| ~ ( ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
& p12(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p11(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y) )
| p12(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p11(Y)
| ~ ( ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p12(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| p13(Y)
| p12(Y)
| ~ ( ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p12(X)
& ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
& p12(X) )
| p13(X)
| ~ r1(Y,X) )
| p12(Y)
| ~ ( ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p12(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| p13(Y)
| ! [X] :
( p12(X)
| ~ ( ! [Y] :
( p13(Y)
| ~ r1(X,Y) )
& p13(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p12(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y) )
| p13(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p12(Y)
| ~ ( ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p13(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| p14(Y)
| p13(Y)
| ~ ( ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p13(X)
& ! [Y] :
( p13(Y)
| ~ r1(X,Y) )
& p13(X) )
| p14(X)
| ~ r1(Y,X) )
| p13(Y)
| ~ ( ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p13(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| p14(Y)
| ! [X] :
( p13(X)
| ~ ( ! [Y] :
( p14(Y)
| ~ r1(X,Y) )
& p14(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p13(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y) )
| p14(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p13(Y)
| ~ ( ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p14(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| p15(Y)
| p14(Y)
| ~ ( ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p14(X)
& ! [Y] :
( p14(Y)
| ~ r1(X,Y) )
& p14(X) )
| p15(X)
| ~ r1(Y,X) )
| p14(Y)
| ~ ( ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p14(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| p15(Y)
| ! [X] :
( p14(X)
| ~ ( ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
& p15(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p14(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y) )
| p15(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p14(Y)
| ~ ( ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| p16(Y)
| p15(Y)
| ~ ( ! [X] :
( p16(X)
| ~ r1(Y,X) )
& p16(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p15(X)
& ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
& p15(X) )
| p16(X)
| ~ r1(Y,X) )
| p15(Y)
| ~ ( ! [X] :
( p16(X)
| ~ r1(Y,X) )
& p16(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| p16(Y)
| ! [X] :
( p15(X)
| ~ ( ! [Y] :
( p16(Y)
| ~ r1(X,Y) )
& p16(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y) )
| p16(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p15(Y)
| ~ ( ! [X] :
( p16(X)
| ~ r1(Y,X) )
& p16(Y) )
| ~ r1(X,Y) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X] :
( ( ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y)
& ~ p2(Y)
& ~ p1(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p1(X)
& ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& p1(X)
& ~ p2(X)
& r1(Y,X) )
& ~ p1(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& r1(X,Y) )
| ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y)
& ~ p2(Y)
& ? [X] :
( ~ p1(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p1(Y)
| ? [X] :
( ~ p1(X)
& r1(Y,X) )
| ~ p1(Y)
| p2(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p1(Y)
| ? [X] :
( ~ p2(X)
& r1(Y,X) )
| ~ p2(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& ~ p3(Y)
& ~ p2(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p2(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X)
& ~ p3(X)
& r1(Y,X) )
& ~ p2(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& r1(X,Y) )
| ? [Y] :
( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& ~ p3(Y)
& ? [X] :
( ~ p2(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p2(Y)
| ? [X] :
( ~ p2(X)
& r1(Y,X) )
| ~ p2(Y)
| p3(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ? [X] :
( ~ p3(X)
& r1(Y,X) )
| ~ p3(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& ~ p4(Y)
& ~ p3(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p3(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X)
& ~ p4(X)
& r1(Y,X) )
& ~ p3(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& r1(X,Y) )
| ? [Y] :
( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& ~ p4(Y)
& ? [X] :
( ~ p3(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p3(Y)
| ? [X] :
( ~ p3(X)
& r1(Y,X) )
| ~ p3(Y)
| p4(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ? [X] :
( ~ p4(X)
& r1(Y,X) )
| ~ p4(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& ~ p5(Y)
& ~ p4(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p4(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X)
& ~ p5(X)
& r1(Y,X) )
& ~ p4(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& r1(X,Y) )
| ? [Y] :
( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& ~ p5(Y)
& ? [X] :
( ~ p4(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p4(Y)
| ? [X] :
( ~ p4(X)
& r1(Y,X) )
| ~ p4(Y)
| p5(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p4(Y)
| ? [X] :
( ~ p5(X)
& r1(Y,X) )
| ~ p5(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& ~ p6(Y)
& ~ p5(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p5(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X)
& ~ p6(X)
& r1(Y,X) )
& ~ p5(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& r1(X,Y) )
| ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& ~ p6(Y)
& ? [X] :
( ~ p5(X)
& ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p5(Y)
| ? [X] :
( ~ p5(X)
& r1(Y,X) )
| ~ p5(Y)
| p6(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ? [X] :
( ~ p6(X)
& r1(Y,X) )
| ~ p6(Y)
| ~ r1(X,Y) ) )
& ? [Y] :
( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& ~ p15(Y)
& r1(X,Y) )
& ? [Y] :
( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& ~ p15(Y)
& r1(X,Y) )
& ( ? [Y] :
( p6(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& ~ p7(Y)
& ~ p6(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p6(X)
& ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X)
& ~ p7(X)
& r1(Y,X) )
& ~ p6(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y)
& r1(X,Y) )
| ? [Y] :
( p6(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& ~ p7(Y)
& ? [X] :
( ~ p6(X)
& ! [Y] :
( p7(Y)
| ~ r1(X,Y) )
& p7(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p6(Y)
| ? [X] :
( ~ p6(X)
& r1(Y,X) )
| ~ p6(Y)
| p7(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p6(Y)
| ? [X] :
( ~ p7(X)
& r1(Y,X) )
| ~ p7(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p7(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y)
& ~ p8(Y)
& ~ p7(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p7(X)
& ! [Y] :
( p7(Y)
| ~ r1(X,Y) )
& p7(X)
& ~ p8(X)
& r1(Y,X) )
& ~ p7(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y)
& r1(X,Y) )
| ? [Y] :
( p7(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y)
& ~ p8(Y)
& ? [X] :
( ~ p7(X)
& ! [Y] :
( p8(Y)
| ~ r1(X,Y) )
& p8(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p7(Y)
| ? [X] :
( ~ p7(X)
& r1(Y,X) )
| ~ p7(Y)
| p8(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p7(Y)
| ? [X] :
( ~ p8(X)
& r1(Y,X) )
| ~ p8(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p8(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y)
& ~ p9(Y)
& ~ p8(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p8(X)
& ! [Y] :
( p8(Y)
| ~ r1(X,Y) )
& p8(X)
& ~ p9(X)
& r1(Y,X) )
& ~ p8(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y)
& r1(X,Y) )
| ? [Y] :
( p8(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y)
& ~ p9(Y)
& ? [X] :
( ~ p8(X)
& ! [Y] :
( p9(Y)
| ~ r1(X,Y) )
& p9(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p8(Y)
| ? [X] :
( ~ p8(X)
& r1(Y,X) )
| ~ p8(Y)
| p9(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p8(Y)
| ? [X] :
( ~ p9(X)
& r1(Y,X) )
| ~ p9(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p9(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y)
& ~ p10(Y)
& ~ p9(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p9(X)
& ! [Y] :
( p9(Y)
| ~ r1(X,Y) )
& p9(X)
& ~ p10(X)
& r1(Y,X) )
& ~ p9(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y)
& r1(X,Y) )
| ? [Y] :
( p9(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y)
& ~ p10(Y)
& ? [X] :
( ~ p9(X)
& ! [Y] :
( p10(Y)
| ~ r1(X,Y) )
& p10(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p9(Y)
| ? [X] :
( ~ p9(X)
& r1(Y,X) )
| ~ p9(Y)
| p10(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p9(Y)
| ? [X] :
( ~ p10(X)
& r1(Y,X) )
| ~ p10(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p10(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y)
& ~ p11(Y)
& ~ p10(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p10(X)
& ! [Y] :
( p10(Y)
| ~ r1(X,Y) )
& p10(X)
& ~ p11(X)
& r1(Y,X) )
& ~ p10(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y)
& r1(X,Y) )
| ? [Y] :
( p10(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y)
& ~ p11(Y)
& ? [X] :
( ~ p10(X)
& ! [Y] :
( p11(Y)
| ~ r1(X,Y) )
& p11(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p10(Y)
| ? [X] :
( ~ p10(X)
& r1(Y,X) )
| ~ p10(Y)
| p11(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p10(Y)
| ? [X] :
( ~ p11(X)
& r1(Y,X) )
| ~ p11(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p11(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y)
& ~ p12(Y)
& ~ p11(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p11(X)
& ! [Y] :
( p11(Y)
| ~ r1(X,Y) )
& p11(X)
& ~ p12(X)
& r1(Y,X) )
& ~ p11(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y)
& r1(X,Y) )
| ? [Y] :
( p11(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y)
& ~ p12(Y)
& ? [X] :
( ~ p11(X)
& ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
& p12(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p11(Y)
| ? [X] :
( ~ p11(X)
& r1(Y,X) )
| ~ p11(Y)
| p12(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p11(Y)
| ? [X] :
( ~ p12(X)
& r1(Y,X) )
| ~ p12(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p12(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y)
& ~ p13(Y)
& ~ p12(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p12(X)
& ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
& p12(X)
& ~ p13(X)
& r1(Y,X) )
& ~ p12(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y)
& r1(X,Y) )
| ? [Y] :
( p12(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y)
& ~ p13(Y)
& ? [X] :
( ~ p12(X)
& ! [Y] :
( p13(Y)
| ~ r1(X,Y) )
& p13(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p12(Y)
| ? [X] :
( ~ p12(X)
& r1(Y,X) )
| ~ p12(Y)
| p13(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p12(Y)
| ? [X] :
( ~ p13(X)
& r1(Y,X) )
| ~ p13(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p13(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y)
& ~ p14(Y)
& ~ p13(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p13(X)
& ! [Y] :
( p13(Y)
| ~ r1(X,Y) )
& p13(X)
& ~ p14(X)
& r1(Y,X) )
& ~ p13(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y)
& r1(X,Y) )
| ? [Y] :
( p13(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y)
& ~ p14(Y)
& ? [X] :
( ~ p13(X)
& ! [Y] :
( p14(Y)
| ~ r1(X,Y) )
& p14(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p13(Y)
| ? [X] :
( ~ p13(X)
& r1(Y,X) )
| ~ p13(Y)
| p14(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p13(Y)
| ? [X] :
( ~ p14(X)
& r1(Y,X) )
| ~ p14(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p14(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y)
& ~ p15(Y)
& ~ p14(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p14(X)
& ! [Y] :
( p14(Y)
| ~ r1(X,Y) )
& p14(X)
& ~ p15(X)
& r1(Y,X) )
& ~ p14(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y)
& r1(X,Y) )
| ? [Y] :
( p14(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y)
& ~ p15(Y)
& ? [X] :
( ~ p14(X)
& ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
& p15(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p14(Y)
| ? [X] :
( ~ p14(X)
& r1(Y,X) )
| ~ p14(Y)
| p15(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p14(Y)
| ? [X] :
( ~ p15(X)
& r1(Y,X) )
| ~ p15(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y)
& ~ p16(Y)
& ~ p15(Y)
& ! [X] :
( p16(X)
| ~ r1(Y,X) )
& p16(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p15(X)
& ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
& p15(X)
& ~ p16(X)
& r1(Y,X) )
& ~ p15(Y)
& ! [X] :
( p16(X)
| ~ r1(Y,X) )
& p16(Y)
& r1(X,Y) )
| ? [Y] :
( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y)
& ~ p16(Y)
& ? [X] :
( ~ p15(X)
& ! [Y] :
( p16(Y)
| ~ r1(X,Y) )
& p16(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p15(Y)
| ? [X] :
( ~ p15(X)
& r1(Y,X) )
| ~ p15(Y)
| p16(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p15(Y)
| ? [X] :
( ~ p16(X)
& r1(Y,X) )
| ~ p16(Y)
| ~ r1(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [Y,X] :
( sP0_prd(X,Y)
<=> ( ~ p16(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,definition,
! [Y,X] :
( sP1_prd(X,Y)
<=> ( ~ p15(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f6,definition,
! [X] :
( sP2_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p15(X)
& ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
& p15(X)
& ~ p16(X)
& r1(Y,X) )
& ~ p15(Y)
& ! [X] :
( p16(X)
| ~ r1(Y,X) )
& p16(Y)
& r1(X,Y) )
| ? [Y] :
( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y)
& ~ p16(Y)
& ? [X] :
( ~ p15(X)
& ! [Y] :
( p16(Y)
| ~ r1(X,Y) )
& p16(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f7,definition,
! [Y,X] :
( sP3_prd(X,Y)
<=> ( ~ p15(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f8,definition,
! [Y,X] :
( sP4_prd(X,Y)
<=> ( ~ p14(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f9,definition,
! [X] :
( sP5_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p14(X)
& ! [Y] :
( p14(Y)
| ~ r1(X,Y) )
& p14(X)
& ~ p15(X)
& r1(Y,X) )
& ~ p14(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y)
& r1(X,Y) )
| ? [Y] :
( p14(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y)
& ~ p15(Y)
& ? [X] :
( ~ p14(X)
& ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
& p15(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f10,definition,
! [Y,X] :
( sP6_prd(X,Y)
<=> ( ~ p14(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f11,definition,
! [Y,X] :
( sP7_prd(X,Y)
<=> ( ~ p13(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f12,definition,
! [X] :
( sP8_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p13(X)
& ! [Y] :
( p13(Y)
| ~ r1(X,Y) )
& p13(X)
& ~ p14(X)
& r1(Y,X) )
& ~ p13(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y)
& r1(X,Y) )
| ? [Y] :
( p13(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y)
& ~ p14(Y)
& ? [X] :
( ~ p13(X)
& ! [Y] :
( p14(Y)
| ~ r1(X,Y) )
& p14(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP8_prd])],[]) ).
fof(f13,definition,
! [Y,X] :
( sP9_prd(X,Y)
<=> ( ~ p13(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f14,definition,
! [Y,X] :
( sP10_prd(X,Y)
<=> ( ~ p12(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP10_prd])],[]) ).
fof(f15,definition,
! [X] :
( sP11_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p12(X)
& ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
& p12(X)
& ~ p13(X)
& r1(Y,X) )
& ~ p12(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y)
& r1(X,Y) )
| ? [Y] :
( p12(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y)
& ~ p13(Y)
& ? [X] :
( ~ p12(X)
& ! [Y] :
( p13(Y)
| ~ r1(X,Y) )
& p13(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP11_prd])],[]) ).
fof(f16,definition,
! [Y,X] :
( sP12_prd(X,Y)
<=> ( ~ p12(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP12_prd])],[]) ).
fof(f17,definition,
! [Y,X] :
( sP13_prd(X,Y)
<=> ( ~ p11(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP13_prd])],[]) ).
fof(f18,definition,
! [X] :
( sP14_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p11(X)
& ! [Y] :
( p11(Y)
| ~ r1(X,Y) )
& p11(X)
& ~ p12(X)
& r1(Y,X) )
& ~ p11(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y)
& r1(X,Y) )
| ? [Y] :
( p11(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y)
& ~ p12(Y)
& ? [X] :
( ~ p11(X)
& ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
& p12(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP14_prd])],[]) ).
fof(f19,definition,
! [Y,X] :
( sP15_prd(X,Y)
<=> ( ~ p11(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP15_prd])],[]) ).
fof(f20,definition,
! [Y,X] :
( sP16_prd(X,Y)
<=> ( ~ p10(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP16_prd])],[]) ).
fof(f21,definition,
! [X] :
( sP17_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p10(X)
& ! [Y] :
( p10(Y)
| ~ r1(X,Y) )
& p10(X)
& ~ p11(X)
& r1(Y,X) )
& ~ p10(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y)
& r1(X,Y) )
| ? [Y] :
( p10(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y)
& ~ p11(Y)
& ? [X] :
( ~ p10(X)
& ! [Y] :
( p11(Y)
| ~ r1(X,Y) )
& p11(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP17_prd])],[]) ).
fof(f22,definition,
! [Y,X] :
( sP18_prd(X,Y)
<=> ( ~ p10(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP18_prd])],[]) ).
fof(f23,definition,
! [Y,X] :
( sP19_prd(X,Y)
<=> ( ~ p9(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP19_prd])],[]) ).
fof(f24,definition,
! [X] :
( sP20_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p9(X)
& ! [Y] :
( p9(Y)
| ~ r1(X,Y) )
& p9(X)
& ~ p10(X)
& r1(Y,X) )
& ~ p9(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y)
& r1(X,Y) )
| ? [Y] :
( p9(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y)
& ~ p10(Y)
& ? [X] :
( ~ p9(X)
& ! [Y] :
( p10(Y)
| ~ r1(X,Y) )
& p10(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP20_prd])],[]) ).
fof(f25,definition,
! [Y,X] :
( sP21_prd(X,Y)
<=> ( ~ p9(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP21_prd])],[]) ).
fof(f26,definition,
! [Y,X] :
( sP22_prd(X,Y)
<=> ( ~ p8(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP22_prd])],[]) ).
fof(f27,definition,
! [X] :
( sP23_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p8(X)
& ! [Y] :
( p8(Y)
| ~ r1(X,Y) )
& p8(X)
& ~ p9(X)
& r1(Y,X) )
& ~ p8(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y)
& r1(X,Y) )
| ? [Y] :
( p8(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y)
& ~ p9(Y)
& ? [X] :
( ~ p8(X)
& ! [Y] :
( p9(Y)
| ~ r1(X,Y) )
& p9(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP23_prd])],[]) ).
fof(f28,definition,
! [Y,X] :
( sP24_prd(X,Y)
<=> ( ~ p8(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP24_prd])],[]) ).
fof(f29,definition,
! [Y,X] :
( sP25_prd(X,Y)
<=> ( ~ p7(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP25_prd])],[]) ).
fof(f30,definition,
! [X] :
( sP26_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p7(X)
& ! [Y] :
( p7(Y)
| ~ r1(X,Y) )
& p7(X)
& ~ p8(X)
& r1(Y,X) )
& ~ p7(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y)
& r1(X,Y) )
| ? [Y] :
( p7(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y)
& ~ p8(Y)
& ? [X] :
( ~ p7(X)
& ! [Y] :
( p8(Y)
| ~ r1(X,Y) )
& p8(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP26_prd])],[]) ).
fof(f31,definition,
! [Y,X] :
( sP27_prd(X,Y)
<=> ( ~ p7(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP27_prd])],[]) ).
fof(f32,definition,
! [Y,X] :
( sP28_prd(X,Y)
<=> ( ~ p6(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP28_prd])],[]) ).
fof(f33,definition,
! [X] :
( sP29_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p6(X)
& ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X)
& ~ p7(X)
& r1(Y,X) )
& ~ p6(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y)
& r1(X,Y) )
| ? [Y] :
( p6(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& ~ p7(Y)
& ? [X] :
( ~ p6(X)
& ! [Y] :
( p7(Y)
| ~ r1(X,Y) )
& p7(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP29_prd])],[]) ).
fof(f34,definition,
! [Y,X] :
( sP30_prd(X,Y)
<=> ( ~ p6(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP30_prd])],[]) ).
fof(f35,definition,
! [Y,X] :
( sP31_prd(X,Y)
<=> ( ~ p5(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP31_prd])],[]) ).
fof(f36,definition,
! [X] :
( sP32_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p5(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X)
& ~ p6(X)
& r1(Y,X) )
& ~ p5(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& r1(X,Y) )
| ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& ~ p6(Y)
& ? [X] :
( ~ p5(X)
& ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP32_prd])],[]) ).
fof(f37,definition,
! [Y,X] :
( sP33_prd(X,Y)
<=> ( ~ p5(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP33_prd])],[]) ).
fof(f38,definition,
! [Y,X] :
( sP34_prd(X,Y)
<=> ( ~ p4(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP34_prd])],[]) ).
fof(f39,definition,
! [X] :
( sP35_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p4(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X)
& ~ p5(X)
& r1(Y,X) )
& ~ p4(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& r1(X,Y) )
| ? [Y] :
( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& ~ p5(Y)
& ? [X] :
( ~ p4(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP35_prd])],[]) ).
fof(f40,definition,
! [Y,X] :
( sP36_prd(X,Y)
<=> ( ~ p4(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP36_prd])],[]) ).
fof(f41,definition,
! [Y,X] :
( sP37_prd(X,Y)
<=> ( ~ p3(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP37_prd])],[]) ).
fof(f42,definition,
! [X] :
( sP38_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p3(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X)
& ~ p4(X)
& r1(Y,X) )
& ~ p3(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& r1(X,Y) )
| ? [Y] :
( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& ~ p4(Y)
& ? [X] :
( ~ p3(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP38_prd])],[]) ).
fof(f43,definition,
! [Y,X] :
( sP39_prd(X,Y)
<=> ( ~ p3(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP39_prd])],[]) ).
fof(f44,definition,
! [Y,X] :
( sP40_prd(X,Y)
<=> ( ~ p2(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP40_prd])],[]) ).
fof(f45,definition,
! [X] :
( sP41_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p2(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X)
& ~ p3(X)
& r1(Y,X) )
& ~ p2(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& r1(X,Y) )
| ? [Y] :
( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& ~ p3(Y)
& ? [X] :
( ~ p2(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP41_prd])],[]) ).
fof(f46,definition,
! [Y,X] :
( sP42_prd(X,Y)
<=> ( ~ p2(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP42_prd])],[]) ).
fof(f47,definition,
! [Y,X] :
( sP43_prd(X,Y)
<=> ( ~ p1(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP43_prd])],[]) ).
fof(f48,definition,
! [X] :
( sP44_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p1(X)
& ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& p1(X)
& ~ p2(X)
& r1(Y,X) )
& ~ p1(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& r1(X,Y) )
| ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y)
& ~ p2(Y)
& ? [X] :
( ~ p1(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP44_prd])],[]) ).
fof(f49,plain,
? [X] :
( ( ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y)
& ~ p2(Y)
& ~ p1(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& r1(X,Y) )
| sP44_prd(X)
| ! [Y] :
( ~ p1(Y)
| ? [X] : sP43_prd(X,Y)
| ~ p1(Y)
| p2(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p1(Y)
| ? [X] : sP42_prd(X,Y)
| ~ p2(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& ~ p3(Y)
& ~ p2(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& r1(X,Y) )
| sP41_prd(X)
| ! [Y] :
( ~ p2(Y)
| ? [X] : sP40_prd(X,Y)
| ~ p2(Y)
| p3(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ? [X] : sP39_prd(X,Y)
| ~ p3(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& ~ p4(Y)
& ~ p3(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& r1(X,Y) )
| sP38_prd(X)
| ! [Y] :
( ~ p3(Y)
| ? [X] : sP37_prd(X,Y)
| ~ p3(Y)
| p4(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ? [X] : sP36_prd(X,Y)
| ~ p4(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& ~ p5(Y)
& ~ p4(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& r1(X,Y) )
| sP35_prd(X)
| ! [Y] :
( ~ p4(Y)
| ? [X] : sP34_prd(X,Y)
| ~ p4(Y)
| p5(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p4(Y)
| ? [X] : sP33_prd(X,Y)
| ~ p5(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& ~ p6(Y)
& ~ p5(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& r1(X,Y) )
| sP32_prd(X)
| ! [Y] :
( ~ p5(Y)
| ? [X] : sP31_prd(X,Y)
| ~ p5(Y)
| p6(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ? [X] : sP30_prd(X,Y)
| ~ p6(Y)
| ~ r1(X,Y) ) )
& ? [Y] :
( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& ~ p15(Y)
& r1(X,Y) )
& ? [Y] :
( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& ~ p15(Y)
& r1(X,Y) )
& ( ? [Y] :
( p6(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& ~ p7(Y)
& ~ p6(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y)
& r1(X,Y) )
| sP29_prd(X)
| ! [Y] :
( ~ p6(Y)
| ? [X] : sP28_prd(X,Y)
| ~ p6(Y)
| p7(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p6(Y)
| ? [X] : sP27_prd(X,Y)
| ~ p7(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p7(Y)
& ! [X] :
( p7(X)
| ~ r1(Y,X) )
& p7(Y)
& ~ p8(Y)
& ~ p7(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y)
& r1(X,Y) )
| sP26_prd(X)
| ! [Y] :
( ~ p7(Y)
| ? [X] : sP25_prd(X,Y)
| ~ p7(Y)
| p8(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p7(Y)
| ? [X] : sP24_prd(X,Y)
| ~ p8(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p8(Y)
& ! [X] :
( p8(X)
| ~ r1(Y,X) )
& p8(Y)
& ~ p9(Y)
& ~ p8(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y)
& r1(X,Y) )
| sP23_prd(X)
| ! [Y] :
( ~ p8(Y)
| ? [X] : sP22_prd(X,Y)
| ~ p8(Y)
| p9(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p8(Y)
| ? [X] : sP21_prd(X,Y)
| ~ p9(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p9(Y)
& ! [X] :
( p9(X)
| ~ r1(Y,X) )
& p9(Y)
& ~ p10(Y)
& ~ p9(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y)
& r1(X,Y) )
| sP20_prd(X)
| ! [Y] :
( ~ p9(Y)
| ? [X] : sP19_prd(X,Y)
| ~ p9(Y)
| p10(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p9(Y)
| ? [X] : sP18_prd(X,Y)
| ~ p10(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p10(Y)
& ! [X] :
( p10(X)
| ~ r1(Y,X) )
& p10(Y)
& ~ p11(Y)
& ~ p10(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y)
& r1(X,Y) )
| sP17_prd(X)
| ! [Y] :
( ~ p10(Y)
| ? [X] : sP16_prd(X,Y)
| ~ p10(Y)
| p11(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p10(Y)
| ? [X] : sP15_prd(X,Y)
| ~ p11(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p11(Y)
& ! [X] :
( p11(X)
| ~ r1(Y,X) )
& p11(Y)
& ~ p12(Y)
& ~ p11(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y)
& r1(X,Y) )
| sP14_prd(X)
| ! [Y] :
( ~ p11(Y)
| ? [X] : sP13_prd(X,Y)
| ~ p11(Y)
| p12(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p11(Y)
| ? [X] : sP12_prd(X,Y)
| ~ p12(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p12(Y)
& ! [X] :
( p12(X)
| ~ r1(Y,X) )
& p12(Y)
& ~ p13(Y)
& ~ p12(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y)
& r1(X,Y) )
| sP11_prd(X)
| ! [Y] :
( ~ p12(Y)
| ? [X] : sP10_prd(X,Y)
| ~ p12(Y)
| p13(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p12(Y)
| ? [X] : sP9_prd(X,Y)
| ~ p13(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p13(Y)
& ! [X] :
( p13(X)
| ~ r1(Y,X) )
& p13(Y)
& ~ p14(Y)
& ~ p13(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y)
& r1(X,Y) )
| sP8_prd(X)
| ! [Y] :
( ~ p13(Y)
| ? [X] : sP7_prd(X,Y)
| ~ p13(Y)
| p14(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p13(Y)
| ? [X] : sP6_prd(X,Y)
| ~ p14(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p14(Y)
& ! [X] :
( p14(X)
| ~ r1(Y,X) )
& p14(Y)
& ~ p15(Y)
& ~ p14(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y)
& r1(X,Y) )
| sP5_prd(X)
| ! [Y] :
( ~ p14(Y)
| ? [X] : sP4_prd(X,Y)
| ~ p14(Y)
| p15(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p14(Y)
| ? [X] : sP3_prd(X,Y)
| ~ p15(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p15(Y)
& ! [X] :
( p15(X)
| ~ r1(Y,X) )
& p15(Y)
& ~ p16(Y)
& ~ p15(Y)
& ! [X] :
( p16(X)
| ~ r1(Y,X) )
& p16(Y)
& r1(X,Y) )
| sP2_prd(X)
| ! [Y] :
( ~ p15(Y)
| ? [X] : sP1_prd(X,Y)
| ~ p15(Y)
| p16(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p15(Y)
| ? [X] : sP0_prd(X,Y)
| ~ p16(Y)
| ~ r1(X,Y) ) ) ),
inference(formula_renaming,[status(thm)],[f3,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11,f10,f9,f8,f7,f6,f5,f4]) ).
fof(f50,plain,
( ( ( p1(sK47_skl)
& ! [X] :
( p1(X)
| ~ r1(sK47_skl,X) )
& p1(sK47_skl)
& ~ p2(sK47_skl)
& ~ p1(sK47_skl)
& ! [X] :
( p2(X)
| ~ r1(sK47_skl,X) )
& p2(sK47_skl)
& r1(sK0_skl,sK47_skl) )
| sP44_prd(sK0_skl)
| ! [Y] :
( ~ p1(Y)
| sP43_prd(sK46_skl(Y),Y)
| ~ p1(Y)
| p2(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p1(Y)
| sP42_prd(sK45_skl(Y),Y)
| ~ p2(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p2(sK44_skl)
& ! [X] :
( p2(X)
| ~ r1(sK44_skl,X) )
& p2(sK44_skl)
& ~ p3(sK44_skl)
& ~ p2(sK44_skl)
& ! [X] :
( p3(X)
| ~ r1(sK44_skl,X) )
& p3(sK44_skl)
& r1(sK0_skl,sK44_skl) )
| sP41_prd(sK0_skl)
| ! [Y] :
( ~ p2(Y)
| sP40_prd(sK43_skl(Y),Y)
| ~ p2(Y)
| p3(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p2(Y)
| sP39_prd(sK42_skl(Y),Y)
| ~ p3(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p3(sK41_skl)
& ! [X] :
( p3(X)
| ~ r1(sK41_skl,X) )
& p3(sK41_skl)
& ~ p4(sK41_skl)
& ~ p3(sK41_skl)
& ! [X] :
( p4(X)
| ~ r1(sK41_skl,X) )
& p4(sK41_skl)
& r1(sK0_skl,sK41_skl) )
| sP38_prd(sK0_skl)
| ! [Y] :
( ~ p3(Y)
| sP37_prd(sK40_skl(Y),Y)
| ~ p3(Y)
| p4(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p3(Y)
| sP36_prd(sK39_skl(Y),Y)
| ~ p4(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p4(sK38_skl)
& ! [X] :
( p4(X)
| ~ r1(sK38_skl,X) )
& p4(sK38_skl)
& ~ p5(sK38_skl)
& ~ p4(sK38_skl)
& ! [X] :
( p5(X)
| ~ r1(sK38_skl,X) )
& p5(sK38_skl)
& r1(sK0_skl,sK38_skl) )
| sP35_prd(sK0_skl)
| ! [Y] :
( ~ p4(Y)
| sP34_prd(sK37_skl(Y),Y)
| ~ p4(Y)
| p5(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p4(Y)
| sP33_prd(sK36_skl(Y),Y)
| ~ p5(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p5(sK35_skl)
& ! [X] :
( p5(X)
| ~ r1(sK35_skl,X) )
& p5(sK35_skl)
& ~ p6(sK35_skl)
& ~ p5(sK35_skl)
& ! [X] :
( p6(X)
| ~ r1(sK35_skl,X) )
& p6(sK35_skl)
& r1(sK0_skl,sK35_skl) )
| sP32_prd(sK0_skl)
| ! [Y] :
( ~ p5(Y)
| sP31_prd(sK34_skl(Y),Y)
| ~ p5(Y)
| p6(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p5(Y)
| sP30_prd(sK33_skl(Y),Y)
| ~ p6(Y)
| ~ r1(sK0_skl,Y) ) )
& p15(sK32_skl)
& ! [X] :
( p15(X)
| ~ r1(sK32_skl,X) )
& ~ p15(sK32_skl)
& r1(sK0_skl,sK32_skl)
& p15(sK31_skl)
& ! [X] :
( p15(X)
| ~ r1(sK31_skl,X) )
& ~ p15(sK31_skl)
& r1(sK0_skl,sK31_skl)
& ( ( p6(sK30_skl)
& ! [X] :
( p6(X)
| ~ r1(sK30_skl,X) )
& p6(sK30_skl)
& ~ p7(sK30_skl)
& ~ p6(sK30_skl)
& ! [X] :
( p7(X)
| ~ r1(sK30_skl,X) )
& p7(sK30_skl)
& r1(sK0_skl,sK30_skl) )
| sP29_prd(sK0_skl)
| ! [Y] :
( ~ p6(Y)
| sP28_prd(sK29_skl(Y),Y)
| ~ p6(Y)
| p7(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p6(Y)
| sP27_prd(sK28_skl(Y),Y)
| ~ p7(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p7(sK27_skl)
& ! [X] :
( p7(X)
| ~ r1(sK27_skl,X) )
& p7(sK27_skl)
& ~ p8(sK27_skl)
& ~ p7(sK27_skl)
& ! [X] :
( p8(X)
| ~ r1(sK27_skl,X) )
& p8(sK27_skl)
& r1(sK0_skl,sK27_skl) )
| sP26_prd(sK0_skl)
| ! [Y] :
( ~ p7(Y)
| sP25_prd(sK26_skl(Y),Y)
| ~ p7(Y)
| p8(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p7(Y)
| sP24_prd(sK25_skl(Y),Y)
| ~ p8(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p8(sK24_skl)
& ! [X] :
( p8(X)
| ~ r1(sK24_skl,X) )
& p8(sK24_skl)
& ~ p9(sK24_skl)
& ~ p8(sK24_skl)
& ! [X] :
( p9(X)
| ~ r1(sK24_skl,X) )
& p9(sK24_skl)
& r1(sK0_skl,sK24_skl) )
| sP23_prd(sK0_skl)
| ! [Y] :
( ~ p8(Y)
| sP22_prd(sK23_skl(Y),Y)
| ~ p8(Y)
| p9(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p8(Y)
| sP21_prd(sK22_skl(Y),Y)
| ~ p9(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p9(sK21_skl)
& ! [X] :
( p9(X)
| ~ r1(sK21_skl,X) )
& p9(sK21_skl)
& ~ p10(sK21_skl)
& ~ p9(sK21_skl)
& ! [X] :
( p10(X)
| ~ r1(sK21_skl,X) )
& p10(sK21_skl)
& r1(sK0_skl,sK21_skl) )
| sP20_prd(sK0_skl)
| ! [Y] :
( ~ p9(Y)
| sP19_prd(sK20_skl(Y),Y)
| ~ p9(Y)
| p10(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p9(Y)
| sP18_prd(sK19_skl(Y),Y)
| ~ p10(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p10(sK18_skl)
& ! [X] :
( p10(X)
| ~ r1(sK18_skl,X) )
& p10(sK18_skl)
& ~ p11(sK18_skl)
& ~ p10(sK18_skl)
& ! [X] :
( p11(X)
| ~ r1(sK18_skl,X) )
& p11(sK18_skl)
& r1(sK0_skl,sK18_skl) )
| sP17_prd(sK0_skl)
| ! [Y] :
( ~ p10(Y)
| sP16_prd(sK17_skl(Y),Y)
| ~ p10(Y)
| p11(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p10(Y)
| sP15_prd(sK16_skl(Y),Y)
| ~ p11(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p11(sK15_skl)
& ! [X] :
( p11(X)
| ~ r1(sK15_skl,X) )
& p11(sK15_skl)
& ~ p12(sK15_skl)
& ~ p11(sK15_skl)
& ! [X] :
( p12(X)
| ~ r1(sK15_skl,X) )
& p12(sK15_skl)
& r1(sK0_skl,sK15_skl) )
| sP14_prd(sK0_skl)
| ! [Y] :
( ~ p11(Y)
| sP13_prd(sK14_skl(Y),Y)
| ~ p11(Y)
| p12(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p11(Y)
| sP12_prd(sK13_skl(Y),Y)
| ~ p12(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p12(sK12_skl)
& ! [X] :
( p12(X)
| ~ r1(sK12_skl,X) )
& p12(sK12_skl)
& ~ p13(sK12_skl)
& ~ p12(sK12_skl)
& ! [X] :
( p13(X)
| ~ r1(sK12_skl,X) )
& p13(sK12_skl)
& r1(sK0_skl,sK12_skl) )
| sP11_prd(sK0_skl)
| ! [Y] :
( ~ p12(Y)
| sP10_prd(sK11_skl(Y),Y)
| ~ p12(Y)
| p13(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p12(Y)
| sP9_prd(sK10_skl(Y),Y)
| ~ p13(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p13(sK9_skl)
& ! [X] :
( p13(X)
| ~ r1(sK9_skl,X) )
& p13(sK9_skl)
& ~ p14(sK9_skl)
& ~ p13(sK9_skl)
& ! [X] :
( p14(X)
| ~ r1(sK9_skl,X) )
& p14(sK9_skl)
& r1(sK0_skl,sK9_skl) )
| sP8_prd(sK0_skl)
| ! [Y] :
( ~ p13(Y)
| sP7_prd(sK8_skl(Y),Y)
| ~ p13(Y)
| p14(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p13(Y)
| sP6_prd(sK7_skl(Y),Y)
| ~ p14(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p14(sK6_skl)
& ! [X] :
( p14(X)
| ~ r1(sK6_skl,X) )
& p14(sK6_skl)
& ~ p15(sK6_skl)
& ~ p14(sK6_skl)
& ! [X] :
( p15(X)
| ~ r1(sK6_skl,X) )
& p15(sK6_skl)
& r1(sK0_skl,sK6_skl) )
| sP5_prd(sK0_skl)
| ! [Y] :
( ~ p14(Y)
| sP4_prd(sK5_skl(Y),Y)
| ~ p14(Y)
| p15(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p14(Y)
| sP3_prd(sK4_skl(Y),Y)
| ~ p15(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p15(sK3_skl)
& ! [X] :
( p15(X)
| ~ r1(sK3_skl,X) )
& p15(sK3_skl)
& ~ p16(sK3_skl)
& ~ p15(sK3_skl)
& ! [X] :
( p16(X)
| ~ r1(sK3_skl,X) )
& p16(sK3_skl)
& r1(sK0_skl,sK3_skl) )
| sP2_prd(sK0_skl)
| ! [Y] :
( ~ p15(Y)
| sP1_prd(sK2_skl(Y),Y)
| ~ p15(Y)
| p16(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p15(Y)
| sP0_prd(sK1_skl(Y),Y)
| ~ p16(Y)
| ~ r1(sK0_skl,Y) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl,sK14_skl,sK15_skl,sK16_skl,sK17_skl,sK18_skl,sK19_skl,sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl,sK29_skl,sK30_skl,sK31_skl,sK32_skl,sK33_skl,sK34_skl,sK35_skl,sK36_skl,sK37_skl,sK38_skl,sK39_skl,sK40_skl,sK41_skl,sK42_skl,sK43_skl,sK44_skl,sK45_skl,sK46_skl,sK47_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl(Y)),skolemize(X,sK2_skl(Y)),skolemize(Y,sK3_skl),skolemize(X,sK4_skl(Y)),skolemize(X,sK5_skl(Y)),skolemize(Y,sK6_skl),skolemize(X,sK7_skl(Y)),skolemize(X,sK8_skl(Y)),skolemize(Y,sK9_skl),skolemize(X,sK10_skl(Y)),skolemize(X,sK11_skl(Y)),skolemize(Y,sK12_skl),skolemize(X,sK13_skl(Y)),skolemize(X,sK14_skl(Y)),skolemize(Y,sK15_skl),skolemize(X,sK16_skl(Y)),skolemize(X,sK17_skl(Y)),skolemize(Y,sK18_skl),skolemize(X,sK19_skl(Y)),skolemize(X,sK20_skl(Y)),skolemize(Y,sK21_skl),skolemize(X,sK22_skl(Y)),skolemize(X,sK23_skl(Y)),skolemize(Y,sK24_skl),skolemize(X,sK25_skl(Y)),skolemize(X,sK26_skl(Y)),skolemize(Y,sK27_skl),skolemize(X,sK28_skl(Y)),skolemize(X,sK29_skl(Y)),skolemize(Y,sK30_skl),skolemize(Y,sK31_skl),skolemize(Y,sK32_skl),skolemize(X,sK33_skl(Y)),skolemize(X,sK34_skl(Y)),skolemize(Y,sK35_skl),skolemize(X,sK36_skl(Y)),skolemize(X,sK37_skl(Y)),skolemize(Y,sK38_skl),skolemize(X,sK39_skl(Y)),skolemize(X,sK40_skl(Y)),skolemize(Y,sK41_skl),skolemize(X,sK42_skl(Y)),skolemize(X,sK43_skl(Y)),skolemize(Y,sK44_skl),skolemize(X,sK45_skl(Y)),skolemize(X,sK46_skl(Y)),skolemize(Y,sK47_skl)],[f49]) ).
fof(f132,plain,
~ p15(sK31_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f134,plain,
p15(sK31_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f1468,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f134,f132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL644+1.015 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 00:47:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.065795 seconds
% 0.09/0.44 % CPU time: 0.164716 seconds
% 0.09/0.44 % Total memory used: 32.296 MB
% 0.09/0.44 % Net memory used: 31.894 MB
%------------------------------------------------------------------------------