%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL686+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 01:08:35 PM UTC 2026
% Result : Theorem 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 5 unt; 1 def)
% Number of atoms : 904 ( 0 equ)
% Maximal formula atoms : 140 ( 28 avg)
% Number of connectives : 1414 ( 542 ~; 476 |; 395 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 14 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 3 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 4 con; 0-1 aty)
% Number of variables : 204 ( 145 !; 59 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : r1(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( ~ ( ! [Y] :
( ( p1(Y)
& p2(Y) )
| ( ~ p2(Y)
& ~ p1(Y) )
| ( p2(Y)
& p3(Y) )
| ( ~ p3(Y)
& ~ p2(Y) )
| ( p3(Y)
& p4(Y) )
| ( ~ p4(Y)
& ~ p3(Y) )
| ( p4(Y)
& p5(Y) )
| ( ~ p5(Y)
& ~ p4(Y) )
| ( p5(Y)
& p6(Y) )
| ( ~ p6(Y)
& ~ p5(Y) )
| ( p6(Y)
& p7(Y) )
| ( ~ p7(Y)
& ~ p6(Y) )
| ( p7(Y)
& p8(Y) )
| ( ~ p8(Y)
& ~ p7(Y) )
| ( p8(Y)
& p9(Y) )
| ( ~ p9(Y)
& ~ p8(Y) )
| ( p9(Y)
& p10(Y) )
| ( ~ p10(Y)
& ~ p9(Y) )
| ( p10(Y)
& p11(Y) )
| ( ~ p11(Y)
& ~ p10(Y) )
| ( p11(Y)
& p12(Y) )
| ( ~ p12(Y)
& ~ p11(Y) )
| ( p12(Y)
& p13(Y) )
| ( ~ p13(Y)
& ~ p12(Y) )
| ( p13(Y)
& p14(Y) )
| ( ~ p14(Y)
& ~ p13(Y) )
| ~ r1(X,Y) )
| ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ( p1(Y)
& ~ p2(Y) )
| ( ~ p1(Y)
& p2(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p2(X)
& ~ p3(X) )
| ( ~ p2(X)
& p3(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p3(Y)
& ~ p4(Y) )
| ( ~ p3(Y)
& p4(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p4(X)
& ~ p5(X) )
| ( ~ p4(X)
& p5(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p5(Y)
& ~ p6(Y) )
| ( ~ p5(Y)
& p6(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p6(X)
& ~ p7(X) )
| ( ~ p6(X)
& p7(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p7(Y)
& ~ p8(Y) )
| ( ~ p7(Y)
& p8(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p8(X)
& ~ p9(X) )
| ( ~ p8(X)
& p9(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p9(Y)
& ~ p10(Y) )
| ( ~ p9(Y)
& p10(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p10(X)
& ~ p11(X) )
| ( ~ p10(X)
& p11(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p11(Y)
& ~ p12(Y) )
| ( ~ p11(Y)
& p12(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p12(X)
& ~ p13(X) )
| ( ~ p12(X)
& p13(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p13(Y)
& ~ p14(Y) )
| ( ~ p13(Y)
& p14(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( $false
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ p15(Y)
| ~ r1(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( ~ ( ! [Y] :
( ( p1(Y)
& p2(Y) )
| ( ~ p2(Y)
& ~ p1(Y) )
| ( p2(Y)
& p3(Y) )
| ( ~ p3(Y)
& ~ p2(Y) )
| ( p3(Y)
& p4(Y) )
| ( ~ p4(Y)
& ~ p3(Y) )
| ( p4(Y)
& p5(Y) )
| ( ~ p5(Y)
& ~ p4(Y) )
| ( p5(Y)
& p6(Y) )
| ( ~ p6(Y)
& ~ p5(Y) )
| ( p6(Y)
& p7(Y) )
| ( ~ p7(Y)
& ~ p6(Y) )
| ( p7(Y)
& p8(Y) )
| ( ~ p8(Y)
& ~ p7(Y) )
| ( p8(Y)
& p9(Y) )
| ( ~ p9(Y)
& ~ p8(Y) )
| ( p9(Y)
& p10(Y) )
| ( ~ p10(Y)
& ~ p9(Y) )
| ( p10(Y)
& p11(Y) )
| ( ~ p11(Y)
& ~ p10(Y) )
| ( p11(Y)
& p12(Y) )
| ( ~ p12(Y)
& ~ p11(Y) )
| ( p12(Y)
& p13(Y) )
| ( ~ p13(Y)
& ~ p12(Y) )
| ( p13(Y)
& p14(Y) )
| ( ~ p14(Y)
& ~ p13(Y) )
| ~ r1(X,Y) )
| ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ( p1(Y)
& ~ p2(Y) )
| ( ~ p1(Y)
& p2(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p2(X)
& ~ p3(X) )
| ( ~ p2(X)
& p3(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p3(Y)
& ~ p4(Y) )
| ( ~ p3(Y)
& p4(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p4(X)
& ~ p5(X) )
| ( ~ p4(X)
& p5(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p5(Y)
& ~ p6(Y) )
| ( ~ p5(Y)
& p6(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p6(X)
& ~ p7(X) )
| ( ~ p6(X)
& p7(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p7(Y)
& ~ p8(Y) )
| ( ~ p7(Y)
& p8(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p8(X)
& ~ p9(X) )
| ( ~ p8(X)
& p9(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p9(Y)
& ~ p10(Y) )
| ( ~ p9(Y)
& p10(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p10(X)
& ~ p11(X) )
| ( ~ p10(X)
& p11(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p11(Y)
& ~ p12(Y) )
| ( ~ p11(Y)
& p12(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( ~ ! [X] :
( ~ ( ( p12(X)
& ~ p13(X) )
| ( ~ p12(X)
& p13(X) ) )
| ~ r1(Y,X) )
| ! [X] :
( ~ ! [Y] :
( ~ ( ( p13(Y)
& ~ p14(Y) )
| ( ~ p13(Y)
& p14(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( $false
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ p15(Y)
| ~ r1(X,Y) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
? [X] :
( ? [Y] :
( ! [X] :
( ( ? [Y] :
( ( ~ p1(Y)
| ~ p2(Y) )
& ( p2(Y)
| p1(Y) )
& ( ~ p2(Y)
| ~ p3(Y) )
& ( p3(Y)
| p2(Y) )
& ( ~ p3(Y)
| ~ p4(Y) )
& ( p4(Y)
| p3(Y) )
& ( ~ p4(Y)
| ~ p5(Y) )
& ( p5(Y)
| p4(Y) )
& ( ~ p5(Y)
| ~ p6(Y) )
& ( p6(Y)
| p5(Y) )
& ( ~ p6(Y)
| ~ p7(Y) )
& ( p7(Y)
| p6(Y) )
& ( ~ p7(Y)
| ~ p8(Y) )
& ( p8(Y)
| p7(Y) )
& ( ~ p8(Y)
| ~ p9(Y) )
& ( p9(Y)
| p8(Y) )
& ( ~ p9(Y)
| ~ p10(Y) )
& ( p10(Y)
| p9(Y) )
& ( ~ p10(Y)
| ~ p11(Y) )
& ( p11(Y)
| p10(Y) )
& ( ~ p11(Y)
| ~ p12(Y) )
& ( p12(Y)
| p11(Y) )
& ( ~ p12(Y)
| ~ p13(Y) )
& ( p13(Y)
| p12(Y) )
& ( ~ p13(Y)
| ~ p14(Y) )
& ( p14(Y)
| p13(Y) )
& r1(X,Y) )
& ? [Y] :
( ~ p15(Y)
& r1(X,Y) )
& ! [Y] :
( ( ( ~ p1(Y)
| p2(Y) )
& ( p1(Y)
| ~ p2(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p2(X)
| p3(X) )
& ( p2(X)
| ~ p3(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p3(Y)
| p4(Y) )
& ( p3(Y)
| ~ p4(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p4(X)
| p5(X) )
& ( p4(X)
| ~ p5(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p5(Y)
| p6(Y) )
& ( p5(Y)
| ~ p6(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p6(X)
| p7(X) )
& ( p6(X)
| ~ p7(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p7(Y)
| p8(Y) )
& ( p7(Y)
| ~ p8(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p8(X)
| p9(X) )
& ( p8(X)
| ~ p9(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p9(Y)
| p10(Y) )
& ( p9(Y)
| ~ p10(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p10(X)
| p11(X) )
& ( p10(X)
| ~ p11(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p11(Y)
| p12(Y) )
& ( p11(Y)
| ~ p12(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p12(X)
| p13(X) )
& ( p12(X)
| ~ p13(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p13(Y)
| p14(Y) )
& ( p13(Y)
| ~ p14(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( $true
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) ) )
| ~ r1(Y,X) )
& r1(X,Y) )
& ? [Y] :
( ? [X] :
( p1(X)
& r1(Y,X) )
& p15(Y)
& r1(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
? [X] :
( ? [Y] :
( ! [X] :
( ( ? [Y] :
( ( ~ p1(Y)
| ~ p2(Y) )
& ( p2(Y)
| p1(Y) )
& ( ~ p2(Y)
| ~ p3(Y) )
& ( p3(Y)
| p2(Y) )
& ( ~ p3(Y)
| ~ p4(Y) )
& ( p4(Y)
| p3(Y) )
& ( ~ p4(Y)
| ~ p5(Y) )
& ( p5(Y)
| p4(Y) )
& ( ~ p5(Y)
| ~ p6(Y) )
& ( p6(Y)
| p5(Y) )
& ( ~ p6(Y)
| ~ p7(Y) )
& ( p7(Y)
| p6(Y) )
& ( ~ p7(Y)
| ~ p8(Y) )
& ( p8(Y)
| p7(Y) )
& ( ~ p8(Y)
| ~ p9(Y) )
& ( p9(Y)
| p8(Y) )
& ( ~ p9(Y)
| ~ p10(Y) )
& ( p10(Y)
| p9(Y) )
& ( ~ p10(Y)
| ~ p11(Y) )
& ( p11(Y)
| p10(Y) )
& ( ~ p11(Y)
| ~ p12(Y) )
& ( p12(Y)
| p11(Y) )
& ( ~ p12(Y)
| ~ p13(Y) )
& ( p13(Y)
| p12(Y) )
& ( ~ p13(Y)
| ~ p14(Y) )
& ( p14(Y)
| p13(Y) )
& r1(X,Y) )
& ? [Y] :
( ~ p15(Y)
& r1(X,Y) )
& ! [Y] :
( ( ( ~ p1(Y)
| p2(Y) )
& ( p1(Y)
| ~ p2(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p2(X)
| p3(X) )
& ( p2(X)
| ~ p3(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p3(Y)
| p4(Y) )
& ( p3(Y)
| ~ p4(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p4(X)
| p5(X) )
& ( p4(X)
| ~ p5(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p5(Y)
| p6(Y) )
& ( p5(Y)
| ~ p6(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p6(X)
| p7(X) )
& ( p6(X)
| ~ p7(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p7(Y)
| p8(Y) )
& ( p7(Y)
| ~ p8(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p8(X)
| p9(X) )
& ( p8(X)
| ~ p9(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p9(Y)
| p10(Y) )
& ( p9(Y)
| ~ p10(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p10(X)
| p11(X) )
& ( p10(X)
| ~ p11(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p11(Y)
| p12(Y) )
& ( p11(Y)
| ~ p12(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p12(X)
| p13(X) )
& ( p12(X)
| ~ p13(X) ) )
| ~ r1(Y,X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p13(Y)
| p14(Y) )
& ( p13(Y)
| ~ p14(Y) ) )
| ~ r1(X,Y) )
& $true
& ? [Y] : r1(X,Y)
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) )
& r1(Y,X) )
& r1(X,Y) ) )
| ~ r1(Y,X) )
& r1(X,Y) )
& ? [Y] :
( ? [X] :
( p1(X)
& r1(Y,X) )
& p15(Y)
& r1(X,Y) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f11,plain,
( ! [X] :
( ( ( ~ p1(sK18_skl(X))
| ~ p2(sK18_skl(X)) )
& ( p2(sK18_skl(X))
| p1(sK18_skl(X)) )
& ( ~ p2(sK18_skl(X))
| ~ p3(sK18_skl(X)) )
& ( p3(sK18_skl(X))
| p2(sK18_skl(X)) )
& ( ~ p3(sK18_skl(X))
| ~ p4(sK18_skl(X)) )
& ( p4(sK18_skl(X))
| p3(sK18_skl(X)) )
& ( ~ p4(sK18_skl(X))
| ~ p5(sK18_skl(X)) )
& ( p5(sK18_skl(X))
| p4(sK18_skl(X)) )
& ( ~ p5(sK18_skl(X))
| ~ p6(sK18_skl(X)) )
& ( p6(sK18_skl(X))
| p5(sK18_skl(X)) )
& ( ~ p6(sK18_skl(X))
| ~ p7(sK18_skl(X)) )
& ( p7(sK18_skl(X))
| p6(sK18_skl(X)) )
& ( ~ p7(sK18_skl(X))
| ~ p8(sK18_skl(X)) )
& ( p8(sK18_skl(X))
| p7(sK18_skl(X)) )
& ( ~ p8(sK18_skl(X))
| ~ p9(sK18_skl(X)) )
& ( p9(sK18_skl(X))
| p8(sK18_skl(X)) )
& ( ~ p9(sK18_skl(X))
| ~ p10(sK18_skl(X)) )
& ( p10(sK18_skl(X))
| p9(sK18_skl(X)) )
& ( ~ p10(sK18_skl(X))
| ~ p11(sK18_skl(X)) )
& ( p11(sK18_skl(X))
| p10(sK18_skl(X)) )
& ( ~ p11(sK18_skl(X))
| ~ p12(sK18_skl(X)) )
& ( p12(sK18_skl(X))
| p11(sK18_skl(X)) )
& ( ~ p12(sK18_skl(X))
| ~ p13(sK18_skl(X)) )
& ( p13(sK18_skl(X))
| p12(sK18_skl(X)) )
& ( ~ p13(sK18_skl(X))
| ~ p14(sK18_skl(X)) )
& ( p14(sK18_skl(X))
| p13(sK18_skl(X)) )
& r1(X,sK18_skl(X))
& ~ p15(sK17_skl(X))
& r1(X,sK17_skl(X))
& ! [Y] :
( ( ( ~ p1(Y)
| p2(Y) )
& ( p1(Y)
| ~ p2(Y) ) )
| ~ r1(X,Y) )
& ! [X] :
( ( ( ~ p2(X)
| p3(X) )
& ( p2(X)
| ~ p3(X) ) )
| ~ r1(sK4_skl(X),X) )
& ! [Y] :
( ( ( ~ p3(Y)
| p4(Y) )
& ( p3(Y)
| ~ p4(Y) ) )
| ~ r1(sK5_skl(X),Y) )
& ! [X] :
( ( ( ~ p4(X)
| p5(X) )
& ( p4(X)
| ~ p5(X) ) )
| ~ r1(sK6_skl(X),X) )
& ! [Y] :
( ( ( ~ p5(Y)
| p6(Y) )
& ( p5(Y)
| ~ p6(Y) ) )
| ~ r1(sK7_skl(X),Y) )
& ! [X] :
( ( ( ~ p6(X)
| p7(X) )
& ( p6(X)
| ~ p7(X) ) )
| ~ r1(sK8_skl(X),X) )
& ! [Y] :
( ( ( ~ p7(Y)
| p8(Y) )
& ( p7(Y)
| ~ p8(Y) ) )
| ~ r1(sK9_skl(X),Y) )
& ! [X] :
( ( ( ~ p8(X)
| p9(X) )
& ( p8(X)
| ~ p9(X) ) )
| ~ r1(sK10_skl(X),X) )
& ! [Y] :
( ( ( ~ p9(Y)
| p10(Y) )
& ( p9(Y)
| ~ p10(Y) ) )
| ~ r1(sK11_skl(X),Y) )
& ! [X] :
( ( ( ~ p10(X)
| p11(X) )
& ( p10(X)
| ~ p11(X) ) )
| ~ r1(sK12_skl(X),X) )
& ! [Y] :
( ( ( ~ p11(Y)
| p12(Y) )
& ( p11(Y)
| ~ p12(Y) ) )
| ~ r1(sK13_skl(X),Y) )
& ! [X] :
( ( ( ~ p12(X)
| p13(X) )
& ( p12(X)
| ~ p13(X) ) )
| ~ r1(sK14_skl(X),X) )
& ! [Y] :
( ( ( ~ p13(Y)
| p14(Y) )
& ( p13(Y)
| ~ p14(Y) ) )
| ~ r1(sK15_skl(X),Y) )
& $true
& r1(sK15_skl(X),sK16_skl(X))
& r1(sK14_skl(X),sK15_skl(X))
& r1(sK13_skl(X),sK14_skl(X))
& r1(sK12_skl(X),sK13_skl(X))
& r1(sK11_skl(X),sK12_skl(X))
& r1(sK10_skl(X),sK11_skl(X))
& r1(sK9_skl(X),sK10_skl(X))
& r1(sK8_skl(X),sK9_skl(X))
& r1(sK7_skl(X),sK8_skl(X))
& r1(sK6_skl(X),sK7_skl(X))
& r1(sK5_skl(X),sK6_skl(X))
& r1(sK4_skl(X),sK5_skl(X))
& r1(X,sK4_skl(X)) )
| ~ r1(sK3_skl,X) )
& r1(sK0_skl,sK3_skl)
& p1(sK2_skl)
& r1(sK1_skl,sK2_skl)
& p15(sK1_skl)
& r1(sK0_skl,sK1_skl) ),
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]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(X,sK2_skl),skolemize(Y,sK3_skl),skolemize(Y,sK4_skl(X)),skolemize(X,sK5_skl(X)),skolemize(Y,sK6_skl(X)),skolemize(X,sK7_skl(X)),skolemize(Y,sK8_skl(X)),skolemize(X,sK9_skl(X)),skolemize(Y,sK10_skl(X)),skolemize(X,sK11_skl(X)),skolemize(Y,sK12_skl(X)),skolemize(X,sK13_skl(X)),skolemize(Y,sK14_skl(X)),skolemize(X,sK15_skl(X)),skolemize(Y,sK16_skl(X)),skolemize(Y,sK17_skl(X)),skolemize(Y,sK18_skl(X))],[f10]) ).
fof(f12,plain,
? [X] :
( ? [Y] :
( ! [X] :
( ( ? [Y] :
( ( ~ p1(sK18_skl(X))
| ~ p2(sK18_skl(X)) )
& ( p2(sK18_skl(X))
| p1(sK18_skl(X)) )
& ( ~ p2(sK18_skl(X))
| ~ p3(sK18_skl(X)) )
& ( p3(sK18_skl(X))
| p2(sK18_skl(X)) )
& ( ~ p3(sK18_skl(X))
| ~ p4(sK18_skl(X)) )
& ( p4(sK18_skl(X))
| p3(sK18_skl(X)) )
& ( ~ p4(sK18_skl(X))
| ~ p5(sK18_skl(X)) )
& ( p5(sK18_skl(X))
| p4(sK18_skl(X)) )
& ( ~ p5(sK18_skl(X))
| ~ p6(sK18_skl(X)) )
& ( p6(sK18_skl(X))
| p5(sK18_skl(X)) )
& ( ~ p6(sK18_skl(X))
| ~ p7(sK18_skl(X)) )
& ( p7(sK18_skl(X))
| p6(sK18_skl(X)) )
& ( ~ p7(sK18_skl(X))
| ~ p8(sK18_skl(X)) )
& ( p8(sK18_skl(X))
| p7(sK18_skl(X)) )
& ( ~ p8(sK18_skl(X))
| ~ p9(sK18_skl(X)) )
& ( p9(sK18_skl(X))
| p8(sK18_skl(X)) )
& ( ~ p9(sK18_skl(X))
| ~ p10(sK18_skl(X)) )
& ( p10(sK18_skl(X))
| p9(sK18_skl(X)) )
& ( ~ p10(sK18_skl(X))
| ~ p11(sK18_skl(X)) )
& ( p11(sK18_skl(X))
| p10(sK18_skl(X)) )
& ( ~ p11(sK18_skl(X))
| ~ p12(sK18_skl(X)) )
& ( p12(sK18_skl(X))
| p11(sK18_skl(X)) )
& ( ~ p12(sK18_skl(X))
| ~ p13(sK18_skl(X)) )
& ( p13(sK18_skl(X))
| p12(sK18_skl(X)) )
& ( ~ p13(sK18_skl(X))
| ~ p14(sK18_skl(X)) )
& ( p14(sK18_skl(X))
| p13(sK18_skl(X)) )
& r1(X,sK18_skl(X)) )
& ? [Y] :
( ~ p15(sK17_skl(X))
& r1(X,sK17_skl(X)) )
& ! [Y] :
( ( ( ~ p1(Y)
| p2(Y) )
& ( p1(Y)
| ~ p2(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p2(X)
| p3(X) )
& ( p2(X)
| ~ p3(X) ) )
| ~ r1(sK4_skl(X),X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p3(Y)
| p4(Y) )
& ( p3(Y)
| ~ p4(Y) ) )
| ~ r1(sK5_skl(X),Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p4(X)
| p5(X) )
& ( p4(X)
| ~ p5(X) ) )
| ~ r1(sK6_skl(X),X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p5(Y)
| p6(Y) )
& ( p5(Y)
| ~ p6(Y) ) )
| ~ r1(sK7_skl(X),Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p6(X)
| p7(X) )
& ( p6(X)
| ~ p7(X) ) )
| ~ r1(sK8_skl(X),X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p7(Y)
| p8(Y) )
& ( p7(Y)
| ~ p8(Y) ) )
| ~ r1(sK9_skl(X),Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p8(X)
| p9(X) )
& ( p8(X)
| ~ p9(X) ) )
| ~ r1(sK10_skl(X),X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p9(Y)
| p10(Y) )
& ( p9(Y)
| ~ p10(Y) ) )
| ~ r1(sK11_skl(X),Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p10(X)
| p11(X) )
& ( p10(X)
| ~ p11(X) ) )
| ~ r1(sK12_skl(X),X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p11(Y)
| p12(Y) )
& ( p11(Y)
| ~ p12(Y) ) )
| ~ r1(sK13_skl(X),Y) )
& ? [Y] :
( ! [X] :
( ( ( ~ p12(X)
| p13(X) )
& ( p12(X)
| ~ p13(X) ) )
| ~ r1(sK14_skl(X),X) )
& ? [X] :
( ! [Y] :
( ( ( ~ p13(Y)
| p14(Y) )
& ( p13(Y)
| ~ p14(Y) ) )
| ~ r1(sK15_skl(X),Y) )
& ? [Y] : r1(sK15_skl(X),sK16_skl(X))
& r1(sK14_skl(X),sK15_skl(X)) )
& r1(sK13_skl(X),sK14_skl(X)) )
& r1(sK12_skl(X),sK13_skl(X)) )
& r1(sK11_skl(X),sK12_skl(X)) )
& r1(sK10_skl(X),sK11_skl(X)) )
& r1(sK9_skl(X),sK10_skl(X)) )
& r1(sK8_skl(X),sK9_skl(X)) )
& r1(sK7_skl(X),sK8_skl(X)) )
& r1(sK6_skl(X),sK7_skl(X)) )
& r1(sK5_skl(X),sK6_skl(X)) )
& r1(sK4_skl(X),sK5_skl(X)) )
& r1(X,sK4_skl(X)) ) )
| ~ r1(sK3_skl,X) )
& r1(sK0_skl,sK3_skl) )
& ? [Y] :
( ? [X] :
( p1(sK2_skl)
& r1(sK1_skl,sK2_skl) )
& p15(sK1_skl)
& r1(sK0_skl,sK1_skl) ) ),
inference(true_and_false_simplification,[status(thm)],[f11]) ).
fof(f18,plain,
! [X0] :
( r1(X0,sK4_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f53,plain,
! [X0,X1] :
( p2(X1)
| ~ p3(X1)
| ~ r1(sK4_skl(X0),X1)
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f55,plain,
! [X0,X1] :
( p1(X1)
| ~ p2(X1)
| ~ r1(X0,X1)
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f59,plain,
! [X0] :
( r1(X0,sK18_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f82,plain,
! [X0] :
( p3(sK18_skl(X0))
| p2(sK18_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f84,plain,
! [X0] :
( p2(sK18_skl(X0))
| p1(sK18_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f85,plain,
! [X0] :
( ~ p1(sK18_skl(X0))
| ~ p2(sK18_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f140,plain,
! [X0,X1] :
( p1(sK18_skl(X0))
| ~ r1(X1,sK18_skl(X0))
| ~ r1(sK3_skl,X1)
| p1(sK18_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f84,f55]) ).
fof(f142,plain,
! [X0,X1] :
( ~ r1(X1,sK18_skl(X0))
| ~ r1(sK3_skl,X1)
| p1(sK18_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f140]) ).
fof(f220,plain,
! [X0] :
( ~ r1(sK3_skl,X0)
| ~ r1(sK3_skl,X0)
| p1(sK18_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f142,f59]) ).
fof(f223,plain,
! [X0] :
( p1(sK18_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f220]) ).
fof(f224,plain,
! [X0] :
( ~ p2(sK18_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f85,f223]) ).
fof(f226,plain,
! [X0] :
( p3(sK18_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f82,f224]) ).
fof(f228,plain,
! [X0,X1] :
( p2(sK18_skl(X0))
| ~ r1(sK4_skl(X1),sK18_skl(X0))
| ~ r1(sK3_skl,X1)
| ~ r1(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f226,f53]) ).
fof(f230,plain,
! [X0,X1] :
( ~ r1(sK4_skl(X1),sK18_skl(X0))
| ~ r1(sK3_skl,X1)
| ~ r1(sK3_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f224]) ).
fof(f257,plain,
! [X0] :
( ~ r1(sK3_skl,sK4_skl(X0))
| ~ r1(sK3_skl,X0)
| ~ r1(sK3_skl,sK4_skl(X0)) ),
inference(resolution,[status(thm)],[f230,f59]) ).
fof(f259,plain,
! [X0] :
( ~ r1(sK3_skl,X0)
| ~ r1(sK3_skl,sK4_skl(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f257]) ).
fof(f264,plain,
( ~ r1(sK3_skl,sK3_skl)
| ~ r1(sK3_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f259,f18]) ).
fof(f266,definition,
( sQ2_spl
<=> r1(sK3_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( sQ2_spl
| ~ r1(sK3_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,plain,
~ sQ2_spl,
inference(split_clause,[status(thm)],[f264,f266]) ).
fof(f270,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f268,f5]) ).
fof(f271,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f272,plain,
$false,
inference(sat_refutation,[status(thm)],[f269,f271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL686+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n010.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 00:57:54 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.50 % Refutation found
% 0.17/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.53 % Elapsed time: 0.083323 seconds
% 0.24/0.53 % CPU time: 0.287264 seconds
% 0.24/0.53 % Total memory used: 20.960 MB
% 0.24/0.53 % Net memory used: 20.735 MB
%------------------------------------------------------------------------------