%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL674+1.010 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 01:08:31 PM UTC 2026
% Result : Theorem 2.68s 1.08s
% Output : CNFRefutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 112 ( 8 unt; 19 def)
% Number of atoms : 1225 ( 0 equ)
% Maximal formula atoms : 226 ( 10 avg)
% Number of connectives : 1954 ( 841 ~; 654 |; 439 &)
% ( 19 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 44 ( 43 usr; 20 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 1 con; 0-1 aty)
% Number of variables : 196 ( 173 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : r1(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] :
( ( r1(Y,Z)
& r1(X,Y) )
=> r1(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p103(Y)
| p102(Y) )
& ( ~ p104(Y)
| p103(Y) )
& ( ~ p105(Y)
| p104(Y) )
& ( ~ p106(Y)
| p105(Y) )
& ( ~ p107(Y)
| p106(Y) )
& ( ~ p108(Y)
| p107(Y) )
& ( ~ p109(Y)
| p108(Y) )
& ( ~ p110(Y)
| p109(Y) )
& ( ~ p111(Y)
| p110(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| ( ( ~ p3(Y)
| ! [X] :
( ~ p102(X)
| p3(X)
| ~ r1(Y,X) ) )
& ( p3(Y)
| ! [X] :
( ~ p102(X)
| ~ p3(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p103(Y)
| ( ( ~ p4(Y)
| ! [X] :
( ~ p103(X)
| p4(X)
| ~ r1(Y,X) ) )
& ( p4(Y)
| ! [X] :
( ~ p103(X)
| ~ p4(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p104(Y)
| ( ( ~ p5(Y)
| ! [X] :
( ~ p104(X)
| p5(X)
| ~ r1(Y,X) ) )
& ( p5(Y)
| ! [X] :
( ~ p104(X)
| ~ p5(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p105(Y)
| ( ( ~ p6(Y)
| ! [X] :
( ~ p105(X)
| p6(X)
| ~ r1(Y,X) ) )
& ( p6(Y)
| ! [X] :
( ~ p105(X)
| ~ p6(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p106(Y)
| ( ( ~ p7(Y)
| ! [X] :
( ~ p106(X)
| p7(X)
| ~ r1(Y,X) ) )
& ( p7(Y)
| ! [X] :
( ~ p106(X)
| ~ p7(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p107(Y)
| ( ( ~ p8(Y)
| ! [X] :
( ~ p107(X)
| p8(X)
| ~ r1(Y,X) ) )
& ( p8(Y)
| ! [X] :
( ~ p107(X)
| ~ p8(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p108(Y)
| ( ( ~ p9(Y)
| ! [X] :
( ~ p108(X)
| p9(X)
| ~ r1(Y,X) ) )
& ( p9(Y)
| ! [X] :
( ~ p108(X)
| ~ p9(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p109(Y)
| ( ( ~ p10(Y)
| ! [X] :
( ~ p109(X)
| p10(X)
| ~ r1(Y,X) ) )
& ( p10(Y)
| ! [X] :
( ~ p109(X)
| ~ p10(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p110(Y)
| ( ( ~ p11(Y)
| ! [X] :
( ~ p110(X)
| p11(X)
| ~ r1(Y,X) ) )
& ( p11(Y)
| ! [X] :
( ~ p110(X)
| ~ p11(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ ( p100(Y)
& ~ p101(Y) )
| ( ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& p2(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& ~ p2(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p101(Y)
& ~ p102(Y) )
| ( ~ ! [X] :
( ~ ( p102(X)
& ~ p103(X)
& p3(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p102(X)
& ~ p103(X)
& ~ p3(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p102(Y)
& ~ p103(Y) )
| ( ~ ! [X] :
( ~ ( p103(X)
& ~ p104(X)
& p4(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p103(X)
& ~ p104(X)
& ~ p4(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p103(Y)
& ~ p104(Y) )
| ( ~ ! [X] :
( ~ ( p104(X)
& ~ p105(X)
& p5(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p104(X)
& ~ p105(X)
& ~ p5(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p104(Y)
& ~ p105(Y) )
| ( ~ ! [X] :
( ~ ( p105(X)
& ~ p106(X)
& p6(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p105(X)
& ~ p106(X)
& ~ p6(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p105(Y)
& ~ p106(Y) )
| ( ~ ! [X] :
( ~ ( p106(X)
& ~ p107(X)
& p7(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p106(X)
& ~ p107(X)
& ~ p7(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p106(Y)
& ~ p107(Y) )
| ( ~ ! [X] :
( ~ ( p107(X)
& ~ p108(X)
& p8(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p107(X)
& ~ p108(X)
& ~ p8(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p107(Y)
& ~ p108(Y) )
| ( ~ ! [X] :
( ~ ( p108(X)
& ~ p109(X)
& p9(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p108(X)
& ~ p109(X)
& ~ p9(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p108(Y)
& ~ p109(Y) )
| ( ~ ! [X] :
( ~ ( p109(X)
& ~ p110(X)
& p10(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p109(X)
& ~ p110(X)
& ~ p10(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p109(Y)
& ~ p110(Y) )
| ( ~ ! [X] :
( ~ ( p110(X)
& ~ p111(X)
& p11(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p110(X)
& ~ p111(X)
& ~ p11(X) )
| ~ r1(Y,X) ) ) ) )
| ~ r1(X,Y) ) )
| ~ ! [Y] :
( p5(Y)
| ~ r1(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p103(Y)
| p102(Y) )
& ( ~ p104(Y)
| p103(Y) )
& ( ~ p105(Y)
| p104(Y) )
& ( ~ p106(Y)
| p105(Y) )
& ( ~ p107(Y)
| p106(Y) )
& ( ~ p108(Y)
| p107(Y) )
& ( ~ p109(Y)
| p108(Y) )
& ( ~ p110(Y)
| p109(Y) )
& ( ~ p111(Y)
| p110(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| ( ( ~ p3(Y)
| ! [X] :
( ~ p102(X)
| p3(X)
| ~ r1(Y,X) ) )
& ( p3(Y)
| ! [X] :
( ~ p102(X)
| ~ p3(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p103(Y)
| ( ( ~ p4(Y)
| ! [X] :
( ~ p103(X)
| p4(X)
| ~ r1(Y,X) ) )
& ( p4(Y)
| ! [X] :
( ~ p103(X)
| ~ p4(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p104(Y)
| ( ( ~ p5(Y)
| ! [X] :
( ~ p104(X)
| p5(X)
| ~ r1(Y,X) ) )
& ( p5(Y)
| ! [X] :
( ~ p104(X)
| ~ p5(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p105(Y)
| ( ( ~ p6(Y)
| ! [X] :
( ~ p105(X)
| p6(X)
| ~ r1(Y,X) ) )
& ( p6(Y)
| ! [X] :
( ~ p105(X)
| ~ p6(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p106(Y)
| ( ( ~ p7(Y)
| ! [X] :
( ~ p106(X)
| p7(X)
| ~ r1(Y,X) ) )
& ( p7(Y)
| ! [X] :
( ~ p106(X)
| ~ p7(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p107(Y)
| ( ( ~ p8(Y)
| ! [X] :
( ~ p107(X)
| p8(X)
| ~ r1(Y,X) ) )
& ( p8(Y)
| ! [X] :
( ~ p107(X)
| ~ p8(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p108(Y)
| ( ( ~ p9(Y)
| ! [X] :
( ~ p108(X)
| p9(X)
| ~ r1(Y,X) ) )
& ( p9(Y)
| ! [X] :
( ~ p108(X)
| ~ p9(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p109(Y)
| ( ( ~ p10(Y)
| ! [X] :
( ~ p109(X)
| p10(X)
| ~ r1(Y,X) ) )
& ( p10(Y)
| ! [X] :
( ~ p109(X)
| ~ p10(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p110(Y)
| ( ( ~ p11(Y)
| ! [X] :
( ~ p110(X)
| p11(X)
| ~ r1(Y,X) ) )
& ( p11(Y)
| ! [X] :
( ~ p110(X)
| ~ p11(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ ( p100(Y)
& ~ p101(Y) )
| ( ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& p2(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& ~ p2(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p101(Y)
& ~ p102(Y) )
| ( ~ ! [X] :
( ~ ( p102(X)
& ~ p103(X)
& p3(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p102(X)
& ~ p103(X)
& ~ p3(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p102(Y)
& ~ p103(Y) )
| ( ~ ! [X] :
( ~ ( p103(X)
& ~ p104(X)
& p4(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p103(X)
& ~ p104(X)
& ~ p4(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p103(Y)
& ~ p104(Y) )
| ( ~ ! [X] :
( ~ ( p104(X)
& ~ p105(X)
& p5(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p104(X)
& ~ p105(X)
& ~ p5(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p104(Y)
& ~ p105(Y) )
| ( ~ ! [X] :
( ~ ( p105(X)
& ~ p106(X)
& p6(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p105(X)
& ~ p106(X)
& ~ p6(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p105(Y)
& ~ p106(Y) )
| ( ~ ! [X] :
( ~ ( p106(X)
& ~ p107(X)
& p7(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p106(X)
& ~ p107(X)
& ~ p7(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p106(Y)
& ~ p107(Y) )
| ( ~ ! [X] :
( ~ ( p107(X)
& ~ p108(X)
& p8(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p107(X)
& ~ p108(X)
& ~ p8(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p107(Y)
& ~ p108(Y) )
| ( ~ ! [X] :
( ~ ( p108(X)
& ~ p109(X)
& p9(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p108(X)
& ~ p109(X)
& ~ p9(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p108(Y)
& ~ p109(Y) )
| ( ~ ! [X] :
( ~ ( p109(X)
& ~ p110(X)
& p10(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p109(X)
& ~ p110(X)
& ~ p10(X) )
| ~ r1(Y,X) ) ) )
& ( ~ ( p109(Y)
& ~ p110(Y) )
| ( ~ ! [X] :
( ~ ( p110(X)
& ~ p111(X)
& p11(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p110(X)
& ~ p111(X)
& ~ p11(X) )
| ~ r1(Y,X) ) ) ) )
| ~ r1(X,Y) ) )
| ~ ! [Y] :
( p5(Y)
| ~ r1(X,Y) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X,Y,Z] :
( r1(X,Z)
| ~ r1(Y,Z)
| ~ r1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X,Z] :
( r1(X,Z)
| ! [Y] :
( ~ r1(Y,Z)
| ~ r1(X,Y) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( r1(X0,X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
? [X] :
( p100(X)
& ~ p101(X)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p103(Y)
| p102(Y) )
& ( ~ p104(Y)
| p103(Y) )
& ( ~ p105(Y)
| p104(Y) )
& ( ~ p106(Y)
| p105(Y) )
& ( ~ p107(Y)
| p106(Y) )
& ( ~ p108(Y)
| p107(Y) )
& ( ~ p109(Y)
| p108(Y) )
& ( ~ p110(Y)
| p109(Y) )
& ( ~ p111(Y)
| p110(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| ( ( ~ p3(Y)
| ! [X] :
( ~ p102(X)
| p3(X)
| ~ r1(Y,X) ) )
& ( p3(Y)
| ! [X] :
( ~ p102(X)
| ~ p3(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p103(Y)
| ( ( ~ p4(Y)
| ! [X] :
( ~ p103(X)
| p4(X)
| ~ r1(Y,X) ) )
& ( p4(Y)
| ! [X] :
( ~ p103(X)
| ~ p4(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p104(Y)
| ( ( ~ p5(Y)
| ! [X] :
( ~ p104(X)
| p5(X)
| ~ r1(Y,X) ) )
& ( p5(Y)
| ! [X] :
( ~ p104(X)
| ~ p5(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p105(Y)
| ( ( ~ p6(Y)
| ! [X] :
( ~ p105(X)
| p6(X)
| ~ r1(Y,X) ) )
& ( p6(Y)
| ! [X] :
( ~ p105(X)
| ~ p6(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p106(Y)
| ( ( ~ p7(Y)
| ! [X] :
( ~ p106(X)
| p7(X)
| ~ r1(Y,X) ) )
& ( p7(Y)
| ! [X] :
( ~ p106(X)
| ~ p7(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p107(Y)
| ( ( ~ p8(Y)
| ! [X] :
( ~ p107(X)
| p8(X)
| ~ r1(Y,X) ) )
& ( p8(Y)
| ! [X] :
( ~ p107(X)
| ~ p8(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p108(Y)
| ( ( ~ p9(Y)
| ! [X] :
( ~ p108(X)
| p9(X)
| ~ r1(Y,X) ) )
& ( p9(Y)
| ! [X] :
( ~ p108(X)
| ~ p9(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p109(Y)
| ( ( ~ p10(Y)
| ! [X] :
( ~ p109(X)
| p10(X)
| ~ r1(Y,X) ) )
& ( p10(Y)
| ! [X] :
( ~ p109(X)
| ~ p10(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p110(Y)
| ( ( ~ p11(Y)
| ! [X] :
( ~ p110(X)
| p11(X)
| ~ r1(Y,X) ) )
& ( p11(Y)
| ! [X] :
( ~ p110(X)
| ~ p11(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p100(Y)
| p101(Y)
| ( ? [X] :
( p101(X)
& ~ p102(X)
& p2(X)
& r1(Y,X) )
& ? [X] :
( p101(X)
& ~ p102(X)
& ~ p2(X)
& r1(Y,X) ) ) )
& ( ~ p101(Y)
| p102(Y)
| ( ? [X] :
( p102(X)
& ~ p103(X)
& p3(X)
& r1(Y,X) )
& ? [X] :
( p102(X)
& ~ p103(X)
& ~ p3(X)
& r1(Y,X) ) ) )
& ( ~ p102(Y)
| p103(Y)
| ( ? [X] :
( p103(X)
& ~ p104(X)
& p4(X)
& r1(Y,X) )
& ? [X] :
( p103(X)
& ~ p104(X)
& ~ p4(X)
& r1(Y,X) ) ) )
& ( ~ p103(Y)
| p104(Y)
| ( ? [X] :
( p104(X)
& ~ p105(X)
& p5(X)
& r1(Y,X) )
& ? [X] :
( p104(X)
& ~ p105(X)
& ~ p5(X)
& r1(Y,X) ) ) )
& ( ~ p104(Y)
| p105(Y)
| ( ? [X] :
( p105(X)
& ~ p106(X)
& p6(X)
& r1(Y,X) )
& ? [X] :
( p105(X)
& ~ p106(X)
& ~ p6(X)
& r1(Y,X) ) ) )
& ( ~ p105(Y)
| p106(Y)
| ( ? [X] :
( p106(X)
& ~ p107(X)
& p7(X)
& r1(Y,X) )
& ? [X] :
( p106(X)
& ~ p107(X)
& ~ p7(X)
& r1(Y,X) ) ) )
& ( ~ p106(Y)
| p107(Y)
| ( ? [X] :
( p107(X)
& ~ p108(X)
& p8(X)
& r1(Y,X) )
& ? [X] :
( p107(X)
& ~ p108(X)
& ~ p8(X)
& r1(Y,X) ) ) )
& ( ~ p107(Y)
| p108(Y)
| ( ? [X] :
( p108(X)
& ~ p109(X)
& p9(X)
& r1(Y,X) )
& ? [X] :
( p108(X)
& ~ p109(X)
& ~ p9(X)
& r1(Y,X) ) ) )
& ( ~ p108(Y)
| p109(Y)
| ( ? [X] :
( p109(X)
& ~ p110(X)
& p10(X)
& r1(Y,X) )
& ? [X] :
( p109(X)
& ~ p110(X)
& ~ p10(X)
& r1(Y,X) ) ) )
& ( ~ p109(Y)
| p110(Y)
| ( ? [X] :
( p110(X)
& ~ p111(X)
& p11(X)
& r1(Y,X) )
& ? [X] :
( p110(X)
& ~ p111(X)
& ~ p11(X)
& r1(Y,X) ) ) ) )
| ~ r1(X,Y) )
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
( p100(sK0_skl)
& ~ p101(sK0_skl)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p103(Y)
| p102(Y) )
& ( ~ p104(Y)
| p103(Y) )
& ( ~ p105(Y)
| p104(Y) )
& ( ~ p106(Y)
| p105(Y) )
& ( ~ p107(Y)
| p106(Y) )
& ( ~ p108(Y)
| p107(Y) )
& ( ~ p109(Y)
| p108(Y) )
& ( ~ p110(Y)
| p109(Y) )
& ( ~ p111(Y)
| p110(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| ( ( ~ p3(Y)
| ! [X] :
( ~ p102(X)
| p3(X)
| ~ r1(Y,X) ) )
& ( p3(Y)
| ! [X] :
( ~ p102(X)
| ~ p3(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p103(Y)
| ( ( ~ p4(Y)
| ! [X] :
( ~ p103(X)
| p4(X)
| ~ r1(Y,X) ) )
& ( p4(Y)
| ! [X] :
( ~ p103(X)
| ~ p4(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p104(Y)
| ( ( ~ p5(Y)
| ! [X] :
( ~ p104(X)
| p5(X)
| ~ r1(Y,X) ) )
& ( p5(Y)
| ! [X] :
( ~ p104(X)
| ~ p5(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p105(Y)
| ( ( ~ p6(Y)
| ! [X] :
( ~ p105(X)
| p6(X)
| ~ r1(Y,X) ) )
& ( p6(Y)
| ! [X] :
( ~ p105(X)
| ~ p6(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p106(Y)
| ( ( ~ p7(Y)
| ! [X] :
( ~ p106(X)
| p7(X)
| ~ r1(Y,X) ) )
& ( p7(Y)
| ! [X] :
( ~ p106(X)
| ~ p7(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p107(Y)
| ( ( ~ p8(Y)
| ! [X] :
( ~ p107(X)
| p8(X)
| ~ r1(Y,X) ) )
& ( p8(Y)
| ! [X] :
( ~ p107(X)
| ~ p8(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p108(Y)
| ( ( ~ p9(Y)
| ! [X] :
( ~ p108(X)
| p9(X)
| ~ r1(Y,X) ) )
& ( p9(Y)
| ! [X] :
( ~ p108(X)
| ~ p9(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p109(Y)
| ( ( ~ p10(Y)
| ! [X] :
( ~ p109(X)
| p10(X)
| ~ r1(Y,X) ) )
& ( p10(Y)
| ! [X] :
( ~ p109(X)
| ~ p10(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p110(Y)
| ( ( ~ p11(Y)
| ! [X] :
( ~ p110(X)
| p11(X)
| ~ r1(Y,X) ) )
& ( p11(Y)
| ! [X] :
( ~ p110(X)
| ~ p11(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p100(Y)
| p101(Y)
| ( p101(sK20_skl(Y))
& ~ p102(sK20_skl(Y))
& p2(sK20_skl(Y))
& r1(Y,sK20_skl(Y))
& p101(sK19_skl(Y))
& ~ p102(sK19_skl(Y))
& ~ p2(sK19_skl(Y))
& r1(Y,sK19_skl(Y)) ) )
& ( ~ p101(Y)
| p102(Y)
| ( p102(sK18_skl(Y))
& ~ p103(sK18_skl(Y))
& p3(sK18_skl(Y))
& r1(Y,sK18_skl(Y))
& p102(sK17_skl(Y))
& ~ p103(sK17_skl(Y))
& ~ p3(sK17_skl(Y))
& r1(Y,sK17_skl(Y)) ) )
& ( ~ p102(Y)
| p103(Y)
| ( p103(sK16_skl(Y))
& ~ p104(sK16_skl(Y))
& p4(sK16_skl(Y))
& r1(Y,sK16_skl(Y))
& p103(sK15_skl(Y))
& ~ p104(sK15_skl(Y))
& ~ p4(sK15_skl(Y))
& r1(Y,sK15_skl(Y)) ) )
& ( ~ p103(Y)
| p104(Y)
| ( p104(sK14_skl(Y))
& ~ p105(sK14_skl(Y))
& p5(sK14_skl(Y))
& r1(Y,sK14_skl(Y))
& p104(sK13_skl(Y))
& ~ p105(sK13_skl(Y))
& ~ p5(sK13_skl(Y))
& r1(Y,sK13_skl(Y)) ) )
& ( ~ p104(Y)
| p105(Y)
| ( p105(sK12_skl(Y))
& ~ p106(sK12_skl(Y))
& p6(sK12_skl(Y))
& r1(Y,sK12_skl(Y))
& p105(sK11_skl(Y))
& ~ p106(sK11_skl(Y))
& ~ p6(sK11_skl(Y))
& r1(Y,sK11_skl(Y)) ) )
& ( ~ p105(Y)
| p106(Y)
| ( p106(sK10_skl(Y))
& ~ p107(sK10_skl(Y))
& p7(sK10_skl(Y))
& r1(Y,sK10_skl(Y))
& p106(sK9_skl(Y))
& ~ p107(sK9_skl(Y))
& ~ p7(sK9_skl(Y))
& r1(Y,sK9_skl(Y)) ) )
& ( ~ p106(Y)
| p107(Y)
| ( p107(sK8_skl(Y))
& ~ p108(sK8_skl(Y))
& p8(sK8_skl(Y))
& r1(Y,sK8_skl(Y))
& p107(sK7_skl(Y))
& ~ p108(sK7_skl(Y))
& ~ p8(sK7_skl(Y))
& r1(Y,sK7_skl(Y)) ) )
& ( ~ p107(Y)
| p108(Y)
| ( p108(sK6_skl(Y))
& ~ p109(sK6_skl(Y))
& p9(sK6_skl(Y))
& r1(Y,sK6_skl(Y))
& p108(sK5_skl(Y))
& ~ p109(sK5_skl(Y))
& ~ p9(sK5_skl(Y))
& r1(Y,sK5_skl(Y)) ) )
& ( ~ p108(Y)
| p109(Y)
| ( p109(sK4_skl(Y))
& ~ p110(sK4_skl(Y))
& p10(sK4_skl(Y))
& r1(Y,sK4_skl(Y))
& p109(sK3_skl(Y))
& ~ p110(sK3_skl(Y))
& ~ p10(sK3_skl(Y))
& r1(Y,sK3_skl(Y)) ) )
& ( ~ p109(Y)
| p110(Y)
| ( p110(sK2_skl(Y))
& ~ p111(sK2_skl(Y))
& p11(sK2_skl(Y))
& r1(Y,sK2_skl(Y))
& p110(sK1_skl(Y))
& ~ p111(sK1_skl(Y))
& ~ p11(sK1_skl(Y))
& r1(Y,sK1_skl(Y)) ) ) )
| ~ r1(sK0_skl,Y) )
& ! [Y] :
( p5(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]),skolemize(X,sK0_skl),skolemize(X,sK1_skl(Y)),skolemize(X,sK2_skl(Y)),skolemize(X,sK3_skl(Y)),skolemize(X,sK4_skl(Y)),skolemize(X,sK5_skl(Y)),skolemize(X,sK6_skl(Y)),skolemize(X,sK7_skl(Y)),skolemize(X,sK8_skl(Y)),skolemize(X,sK9_skl(Y)),skolemize(X,sK10_skl(Y)),skolemize(X,sK11_skl(Y)),skolemize(X,sK12_skl(Y)),skolemize(X,sK13_skl(Y)),skolemize(X,sK14_skl(Y)),skolemize(X,sK15_skl(Y)),skolemize(X,sK16_skl(Y)),skolemize(X,sK17_skl(Y)),skolemize(X,sK18_skl(Y)),skolemize(X,sK19_skl(Y)),skolemize(X,sK20_skl(Y))],[f9]) ).
fof(f11,plain,
! [X0] :
( p5(X0)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f60,plain,
! [X0] :
( ~ p103(X0)
| p104(X0)
| r1(X0,sK13_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f61,plain,
! [X0] :
( ~ p103(X0)
| p104(X0)
| ~ p5(sK13_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f63,plain,
! [X0] :
( ~ p103(X0)
| p104(X0)
| p104(sK13_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f72,plain,
! [X0] :
( ~ p102(X0)
| p103(X0)
| r1(X0,sK16_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f74,plain,
! [X0] :
( ~ p102(X0)
| p103(X0)
| ~ p104(sK16_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f75,plain,
! [X0] :
( ~ p102(X0)
| p103(X0)
| p103(sK16_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f80,plain,
! [X0] :
( ~ p101(X0)
| p102(X0)
| r1(X0,sK18_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f82,plain,
! [X0] :
( ~ p101(X0)
| p102(X0)
| ~ p103(sK18_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f83,plain,
! [X0] :
( ~ p101(X0)
| p102(X0)
| p102(sK18_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f88,plain,
! [X0] :
( ~ p100(X0)
| p101(X0)
| r1(X0,sK20_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f90,plain,
! [X0] :
( ~ p100(X0)
| p101(X0)
| ~ p102(sK20_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f91,plain,
! [X0] :
( ~ p100(X0)
| p101(X0)
| p101(sK20_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f105,plain,
! [X0,X1] :
( ~ p104(X0)
| ~ p5(X0)
| ~ p104(X1)
| p5(X1)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f125,plain,
~ p101(sK0_skl),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f126,plain,
p100(sK0_skl),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f127,plain,
! [X0,X1] :
( ~ p104(X0)
| ~ p104(X1)
| p5(X1)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f11]) ).
fof(f163,plain,
( p101(sK0_skl)
| r1(sK0_skl,sK20_skl(sK0_skl))
| ~ r1(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f126,f88]) ).
fof(f165,plain,
( p101(sK0_skl)
| p101(sK20_skl(sK0_skl))
| ~ r1(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f126,f91]) ).
fof(f168,definition,
( sQ7_spl
<=> r1(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ7_spl
| ~ r1(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ8_spl
<=> r1(sK0_skl,sK20_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ8_spl
| r1(sK0_skl,sK20_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
( sQ9_spl
<=> p101(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ9_spl
| p101(sK0_skl) ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( sQ9_spl
| sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f163,f168,f171,f174]) ).
fof(f182,definition,
( sQ11_spl
<=> p101(sK20_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ11_spl
| p101(sK20_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( sQ9_spl
| sQ11_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f165,f168,f182,f174]) ).
fof(f194,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f125]) ).
fof(f195,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f196,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f5]) ).
fof(f197,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f196]) ).
fof(f198,plain,
( ~ sQ11_spl
| p102(sK20_skl(sK0_skl))
| r1(sK20_skl(sK0_skl),sK18_skl(sK20_skl(sK0_skl)))
| ~ r1(sK0_skl,sK20_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f183,f80]) ).
fof(f200,plain,
( ~ sQ11_spl
| p102(sK20_skl(sK0_skl))
| p102(sK18_skl(sK20_skl(sK0_skl)))
| ~ r1(sK0_skl,sK20_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f183,f83]) ).
fof(f204,definition,
( sQ14_spl
<=> r1(sK20_skl(sK0_skl),sK18_skl(sK20_skl(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( ~ sQ14_spl
| r1(sK20_skl(sK0_skl),sK18_skl(sK20_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,definition,
( sQ15_spl
<=> p102(sK20_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( ~ sQ15_spl
| p102(sK20_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( ~ sQ11_spl
| sQ15_spl
| sQ14_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f198,f171,f204,f207,f182]) ).
fof(f215,definition,
( sQ17_spl
<=> p102(sK18_skl(sK20_skl(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( ~ sQ17_spl
| p102(sK18_skl(sK20_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( ~ sQ11_spl
| sQ15_spl
| sQ17_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f200,f171,f215,f207,f182]) ).
fof(f274,plain,
( ~ sQ15_spl
| ~ p100(sK0_skl)
| p101(sK0_skl)
| ~ r1(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f208,f90]) ).
fof(f281,definition,
( sQ30_spl
<=> p100(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( sQ30_spl
| ~ p100(sK0_skl) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,plain,
( ~ sQ15_spl
| ~ sQ30_spl
| sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f274,f168,f174,f281,f207]) ).
fof(f309,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f126]) ).
fof(f310,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f787,plain,
( ~ sQ17_spl
| p103(sK18_skl(sK20_skl(sK0_skl)))
| r1(sK18_skl(sK20_skl(sK0_skl)),sK16_skl(sK18_skl(sK20_skl(sK0_skl))))
| ~ r1(sK0_skl,sK18_skl(sK20_skl(sK0_skl))) ),
inference(resolution,[status(thm)],[f216,f72]) ).
fof(f789,plain,
( ~ sQ17_spl
| p103(sK18_skl(sK20_skl(sK0_skl)))
| p103(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))
| ~ r1(sK0_skl,sK18_skl(sK20_skl(sK0_skl))) ),
inference(resolution,[status(thm)],[f216,f75]) ).
fof(f793,definition,
( sQ131_spl
<=> r1(sK0_skl,sK18_skl(sK20_skl(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f795,plain,
( sQ131_spl
| ~ r1(sK0_skl,sK18_skl(sK20_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f793]) ).
fof(f796,definition,
( sQ132_spl
<=> r1(sK18_skl(sK20_skl(sK0_skl)),sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f797,plain,
( ~ sQ132_spl
| r1(sK18_skl(sK20_skl(sK0_skl)),sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
inference(component_clause,[status(thm)],[f796]) ).
fof(f799,definition,
( sQ133_spl
<=> p103(sK18_skl(sK20_skl(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f800,plain,
( ~ sQ133_spl
| p103(sK18_skl(sK20_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f799]) ).
fof(f802,plain,
( ~ sQ17_spl
| sQ133_spl
| sQ132_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f787,f793,f796,f799,f215]) ).
fof(f807,definition,
( sQ135_spl
<=> p103(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f808,plain,
( ~ sQ135_spl
| p103(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
inference(component_clause,[status(thm)],[f807]) ).
fof(f810,plain,
( ~ sQ17_spl
| sQ133_spl
| sQ135_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f789,f793,f807,f799,f215]) ).
fof(f951,plain,
! [X0] :
( ~ sQ14_spl
| r1(X0,sK18_skl(sK20_skl(sK0_skl)))
| ~ r1(X0,sK20_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f205,f8]) ).
fof(f970,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| r1(sK0_skl,sK18_skl(sK20_skl(sK0_skl))) ),
inference(resolution,[status(thm)],[f951,f172]) ).
fof(f972,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| sQ131_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f970,f795]) ).
fof(f973,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| sQ131_spl ),
inference(contradiction_clause,[status(thm)],[f972]) ).
fof(f974,plain,
( ~ sQ133_spl
| ~ p101(sK20_skl(sK0_skl))
| p102(sK20_skl(sK0_skl))
| ~ r1(sK0_skl,sK20_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f800,f82]) ).
fof(f981,plain,
( ~ sQ133_spl
| ~ sQ11_spl
| sQ15_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f974,f171,f207,f182,f799]) ).
fof(f1149,plain,
( ~ sQ135_spl
| p104(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))
| r1(sK16_skl(sK18_skl(sK20_skl(sK0_skl))),sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))))
| ~ r1(sK0_skl,sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
inference(resolution,[status(thm)],[f808,f60]) ).
fof(f1152,plain,
( ~ sQ135_spl
| p104(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))
| p104(sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))))
| ~ r1(sK0_skl,sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
inference(resolution,[status(thm)],[f808,f63]) ).
fof(f1154,definition,
( sQ204_spl
<=> r1(sK0_skl,sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f1156,plain,
( sQ204_spl
| ~ r1(sK0_skl,sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
inference(component_clause,[status(thm)],[f1154]) ).
fof(f1160,definition,
( sQ206_spl
<=> p104(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f1161,plain,
( ~ sQ206_spl
| p104(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
inference(component_clause,[status(thm)],[f1160]) ).
fof(f1164,definition,
( sQ207_spl
<=> r1(sK16_skl(sK18_skl(sK20_skl(sK0_skl))),sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f1165,plain,
( ~ sQ207_spl
| r1(sK16_skl(sK18_skl(sK20_skl(sK0_skl))),sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))) ),
inference(component_clause,[status(thm)],[f1164]) ).
fof(f1167,plain,
( ~ sQ135_spl
| sQ206_spl
| sQ207_spl
| ~ sQ204_spl ),
inference(split_clause,[status(thm)],[f1149,f1154,f1164,f1160,f807]) ).
fof(f1176,definition,
( sQ210_spl
<=> p104(sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f1177,plain,
( ~ sQ210_spl
| p104(sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))) ),
inference(component_clause,[status(thm)],[f1176]) ).
fof(f1179,plain,
( ~ sQ135_spl
| sQ206_spl
| sQ210_spl
| ~ sQ204_spl ),
inference(split_clause,[status(thm)],[f1152,f1154,f1176,f1160,f807]) ).
fof(f1989,plain,
! [X0] :
( ~ sQ132_spl
| r1(X0,sK16_skl(sK18_skl(sK20_skl(sK0_skl))))
| ~ r1(X0,sK18_skl(sK20_skl(sK0_skl))) ),
inference(resolution,[status(thm)],[f797,f8]) ).
fof(f2164,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ132_spl
| r1(sK0_skl,sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
inference(resolution,[status(thm)],[f1989,f970]) ).
fof(f2166,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ132_spl
| sQ204_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2164,f1156]) ).
fof(f2167,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ132_spl
| sQ204_spl ),
inference(contradiction_clause,[status(thm)],[f2166]) ).
fof(f2168,plain,
( ~ sQ206_spl
| ~ p102(sK18_skl(sK20_skl(sK0_skl)))
| p103(sK18_skl(sK20_skl(sK0_skl)))
| ~ r1(sK0_skl,sK18_skl(sK20_skl(sK0_skl))) ),
inference(resolution,[status(thm)],[f1161,f74]) ).
fof(f2176,plain,
( ~ sQ206_spl
| ~ sQ17_spl
| sQ133_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f2168,f793,f799,f215,f1160]) ).
fof(f2458,plain,
! [X0] :
( ~ sQ210_spl
| ~ p104(X0)
| p5(sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))))
| ~ r1(X0,sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))))
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f1177,f127]) ).
fof(f2465,definition,
! [X0] :
( sQ461_spl
<=> ( ~ p104(X0)
| ~ r1(X0,sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))))
| ~ r1(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ461_spl])],[split_symbol_definition]) ).
fof(f2466,plain,
! [X0] :
( ~ sQ461_spl
| ~ p104(X0)
| ~ r1(X0,sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))))
| ~ r1(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f2465]) ).
fof(f2468,definition,
( sQ462_spl
<=> p5(sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ462_spl])],[split_symbol_definition]) ).
fof(f2469,plain,
( ~ sQ462_spl
| p5(sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))) ),
inference(component_clause,[status(thm)],[f2468]) ).
fof(f2471,plain,
( ~ sQ210_spl
| sQ462_spl
| sQ461_spl ),
inference(split_clause,[status(thm)],[f2458,f2465,f2468,f1176]) ).
fof(f2472,definition,
( sQ463_spl
<=> r1(sK0_skl,sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ463_spl])],[split_symbol_definition]) ).
fof(f2474,plain,
( sQ463_spl
| ~ r1(sK0_skl,sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))) ),
inference(component_clause,[status(thm)],[f2472]) ).
fof(f4776,plain,
! [X0] :
( ~ sQ207_spl
| r1(X0,sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))))
| ~ r1(X0,sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
inference(resolution,[status(thm)],[f1165,f8]) ).
fof(f5404,plain,
( ~ sQ461_spl
| ~ p104(sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl)))))
| ~ r1(sK0_skl,sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))) ),
inference(resolution,[status(thm)],[f2466,f5]) ).
fof(f5406,plain,
( ~ sQ461_spl
| ~ sQ210_spl
| ~ sQ463_spl ),
inference(split_clause,[status(thm)],[f5404,f2472,f1176,f2465]) ).
fof(f5824,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ132_spl
| ~ sQ207_spl
| r1(sK0_skl,sK13_skl(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))) ),
inference(resolution,[status(thm)],[f4776,f2164]) ).
fof(f5826,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ132_spl
| ~ sQ207_spl
| sQ463_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5824,f2474]) ).
fof(f5827,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ132_spl
| ~ sQ207_spl
| sQ463_spl ),
inference(contradiction_clause,[status(thm)],[f5826]) ).
fof(f5860,plain,
( ~ sQ462_spl
| ~ p103(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))
| p104(sK16_skl(sK18_skl(sK20_skl(sK0_skl))))
| ~ r1(sK0_skl,sK16_skl(sK18_skl(sK20_skl(sK0_skl)))) ),
inference(resolution,[status(thm)],[f2469,f61]) ).
fof(f5861,plain,
( ~ sQ462_spl
| ~ sQ135_spl
| sQ206_spl
| ~ sQ204_spl ),
inference(split_clause,[status(thm)],[f5860,f1154,f1160,f807,f2468]) ).
fof(f5862,plain,
$false,
inference(sat_refutation,[status(thm)],[f177,f185,f195,f197,f210,f218,f284,f310,f802,f810,f973,f981,f1167,f1179,f2167,f2176,f2471,f5406,f5827,f5861]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL674+1.010 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n001.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 00:58:58 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Drodi V4.1.1
% 2.68/1.08 % Refutation found
% 2.68/1.08 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.68/1.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.81/1.11 % Elapsed time: 0.675113 seconds
% 3.81/1.11 % CPU time: 5.088157 seconds
% 3.81/1.11 % Total memory used: 60.240 MB
% 3.81/1.11 % Net memory used: 57.301 MB
%------------------------------------------------------------------------------