%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL656+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 01:08:24 PM UTC 2026
% Result : Theorem 0.14s 0.54s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 9 unt; 11 def)
% Number of atoms : 876 ( 0 equ)
% Maximal formula atoms : 129 ( 11 avg)
% Number of connectives : 1477 ( 680 ~; 558 |; 228 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 26 ( 25 usr; 12 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-5 aty)
% Number of variables : 267 ( 254 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : r1(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,conjecture,
~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ! [Y] :
( ! [X] :
( ! [Y] :
( ! [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) )
& ( ~ 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) ) ) ) )
& ( ~ ( 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) ) ) ) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ ~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ! [Y] :
( ! [X] :
( ! [Y] :
( ! [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) )
& ( ~ 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) ) ) ) )
& ( ~ ( 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) ) ) ) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ~ ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
? [X] :
( p100(X)
& ~ p101(X)
& ! [Y] :
( ! [X] :
( ! [Y] :
( ! [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) )
& ( ~ 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) ) ) ) )
& ( ~ 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) ) ) ) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f6,plain,
( p100(sK0_skl)
& ~ p101(sK0_skl)
& ! [Y] :
( ! [X] :
( ! [Y] :
( ! [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) )
& ( ~ 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) ) ) ) )
& ( ~ p100(Y)
| p101(Y)
| ( p101(sK10_skl(Y,X,Y,X,Y))
& ~ p102(sK10_skl(Y,X,Y,X,Y))
& p2(sK10_skl(Y,X,Y,X,Y))
& r1(Y,sK10_skl(Y,X,Y,X,Y))
& p101(sK9_skl(Y,X,Y,X,Y))
& ~ p102(sK9_skl(Y,X,Y,X,Y))
& ~ p2(sK9_skl(Y,X,Y,X,Y))
& r1(Y,sK9_skl(Y,X,Y,X,Y)) ) )
& ( ~ p101(Y)
| p102(Y)
| ( p102(sK8_skl(Y,X,Y,X,Y))
& ~ p103(sK8_skl(Y,X,Y,X,Y))
& p3(sK8_skl(Y,X,Y,X,Y))
& r1(Y,sK8_skl(Y,X,Y,X,Y))
& p102(sK7_skl(Y,X,Y,X,Y))
& ~ p103(sK7_skl(Y,X,Y,X,Y))
& ~ p3(sK7_skl(Y,X,Y,X,Y))
& r1(Y,sK7_skl(Y,X,Y,X,Y)) ) )
& ( ~ p102(Y)
| p103(Y)
| ( p103(sK6_skl(Y,X,Y,X,Y))
& ~ p104(sK6_skl(Y,X,Y,X,Y))
& p4(sK6_skl(Y,X,Y,X,Y))
& r1(Y,sK6_skl(Y,X,Y,X,Y))
& p103(sK5_skl(Y,X,Y,X,Y))
& ~ p104(sK5_skl(Y,X,Y,X,Y))
& ~ p4(sK5_skl(Y,X,Y,X,Y))
& r1(Y,sK5_skl(Y,X,Y,X,Y)) ) )
& ( ~ p103(Y)
| p104(Y)
| ( p104(sK4_skl(Y,X,Y,X,Y))
& ~ p105(sK4_skl(Y,X,Y,X,Y))
& p5(sK4_skl(Y,X,Y,X,Y))
& r1(Y,sK4_skl(Y,X,Y,X,Y))
& p104(sK3_skl(Y,X,Y,X,Y))
& ~ p105(sK3_skl(Y,X,Y,X,Y))
& ~ p5(sK3_skl(Y,X,Y,X,Y))
& r1(Y,sK3_skl(Y,X,Y,X,Y)) ) )
& ( ~ p104(Y)
| p105(Y)
| ( p105(sK2_skl(Y,X,Y,X,Y))
& ~ p106(sK2_skl(Y,X,Y,X,Y))
& p6(sK2_skl(Y,X,Y,X,Y))
& r1(Y,sK2_skl(Y,X,Y,X,Y))
& p105(sK1_skl(Y,X,Y,X,Y))
& ~ p106(sK1_skl(Y,X,Y,X,Y))
& ~ p6(sK1_skl(Y,X,Y,X,Y))
& r1(Y,sK1_skl(Y,X,Y,X,Y)) ) ) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
& ! [Y] :
( ! [X] :
( ! [Y] :
( ! [X] :
( ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ 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]),skolemize(X,sK0_skl),skolemize(X,sK1_skl(Y,X,Y,X,Y)),skolemize(X,sK2_skl(Y,X,Y,X,Y)),skolemize(X,sK3_skl(Y,X,Y,X,Y)),skolemize(X,sK4_skl(Y,X,Y,X,Y)),skolemize(X,sK5_skl(Y,X,Y,X,Y)),skolemize(X,sK6_skl(Y,X,Y,X,Y)),skolemize(X,sK7_skl(Y,X,Y,X,Y)),skolemize(X,sK8_skl(Y,X,Y,X,Y)),skolemize(X,sK9_skl(Y,X,Y,X,Y)),skolemize(X,sK10_skl(Y,X,Y,X,Y))],[f5]) ).
fof(f7,plain,
! [X0,X1,X2,X3,X4] :
( p3(X4)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4] :
( ~ p101(X4)
| p102(X4)
| r1(X4,sK7_skl(X4,X3,X2,X1,X0))
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4] :
( ~ p101(X4)
| p102(X4)
| ~ p3(sK7_skl(X4,X3,X2,X1,X0))
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ~ p100(X4)
| p101(X4)
| r1(X4,sK10_skl(X4,X3,X2,X1,X0))
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( ~ p100(X4)
| p101(X4)
| ~ p102(sK10_skl(X4,X3,X2,X1,X0))
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4] :
( ~ p100(X4)
| p101(X4)
| p101(sK10_skl(X4,X3,X2,X1,X0))
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f64,plain,
! [X0,X1,X2,X3,X4] :
( ~ p102(X4)
| p101(X4)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f66,plain,
~ p101(sK0_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f67,plain,
p100(sK0_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( ~ p102(sK0_skl)
| ~ r1(X3,sK0_skl)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f64,f66]) ).
fof(f70,definition,
! [X0,X1,X2,X3] :
( sQ0_spl
<=> ( ~ r1(X3,sK0_skl)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ r1(X3,sK0_skl)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> p102(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f70,f73]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ r1(X2,sK0_skl)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f71,f4]) ).
fof(f78,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ r1(X1,sK0_skl)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f77,f4]) ).
fof(f79,plain,
! [X0] :
( ~ sQ0_spl
| ~ r1(X0,sK0_skl)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f78,f4]) ).
fof(f80,plain,
( ~ sQ0_spl
| ~ r1(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f79,f4]) ).
fof(f81,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f4]) ).
fof(f82,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f81]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ r1(X8,sK7_skl(X4,X3,X2,X1,X0))
| ~ r1(X7,X8)
| ~ r1(X6,X7)
| ~ r1(X5,X6)
| ~ r1(sK0_skl,X5)
| ~ p101(X4)
| p102(X4)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f33,f7]) ).
fof(f125,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ r1(X7,sK7_skl(X4,X3,X2,X1,X0))
| ~ r1(X6,X7)
| ~ r1(X5,X6)
| ~ r1(sK0_skl,X5)
| ~ p101(X4)
| p102(X4)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f97,f4]) ).
fof(f133,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ r1(X6,sK7_skl(X4,X3,X2,X1,X0))
| ~ r1(X5,X6)
| ~ r1(sK0_skl,X5)
| ~ p101(X4)
| p102(X4)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f125,f4]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r1(X5,sK7_skl(X4,X3,X2,X1,X0))
| ~ r1(sK0_skl,X5)
| ~ p101(X4)
| p102(X4)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f133,f4]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4] :
( ~ p101(X4)
| p102(X4)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0)
| ~ r1(sK0_skl,X4)
| ~ p101(X4)
| p102(X4)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f141,f32]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4] :
( ~ r1(sK0_skl,sK7_skl(X4,X3,X2,X1,X0))
| ~ p101(X4)
| p102(X4)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f141,f4]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4] :
( ~ r1(sK0_skl,X4)
| ~ p101(X4)
| p102(X4)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f148]) ).
fof(f157,definition,
( sQ5_spl
<=> p101(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f166,plain,
! [X0,X1,X2,X3] :
( ~ p101(sK0_skl)
| p102(sK0_skl)
| ~ r1(X3,sK0_skl)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0)
| ~ p101(sK0_skl)
| p102(sK0_skl)
| ~ r1(X3,sK0_skl)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f149,f32]) ).
fof(f167,definition,
! [X0,X1,X2,X3] :
( sQ6_spl
<=> ( ~ r1(X3,sK0_skl)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0)
| ~ r1(X3,sK0_skl)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f168,plain,
! [X0,X1,X2,X3] :
( ~ sQ6_spl
| ~ r1(X3,sK0_skl)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0)
| ~ r1(X3,sK0_skl)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( ~ sQ5_spl
| sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f166,f167,f73,f157]) ).
fof(f171,plain,
! [X0,X1,X2,X3] :
( ~ sQ6_spl
| ~ r1(X3,sK0_skl)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f168]) ).
fof(f172,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ r1(X2,sK0_skl)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f171,f4]) ).
fof(f173,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ r1(X1,sK0_skl)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f172,f4]) ).
fof(f174,plain,
! [X0] :
( ~ sQ6_spl
| ~ r1(X0,sK0_skl)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f173,f4]) ).
fof(f175,plain,
( ~ sQ6_spl
| ~ r1(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f174,f4]) ).
fof(f176,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f4]) ).
fof(f177,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f176]) ).
fof(f219,definition,
( sQ13_spl
<=> r1(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( sQ13_spl
| ~ r1(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f228,definition,
( sQ15_spl
<=> p100(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ15_spl
| ~ p100(sK0_skl) ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f232,definition,
! [X0,X1,X2,X3] :
( sQ16_spl
<=> ( ~ r1(X3,sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl))
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f233,plain,
! [X0,X1,X2,X3] :
( ~ sQ16_spl
| ~ r1(X3,sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl))
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f238,definition,
( sQ18_spl
<=> p101(sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( ~ sQ18_spl
| p101(sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f240,plain,
( sQ18_spl
| ~ p101(sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f242,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f221,f4]) ).
fof(f243,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f242]) ).
fof(f244,plain,
( sQ18_spl
| ~ p100(sK0_skl)
| p101(sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f240,f47]) ).
fof(f246,plain,
( sQ18_spl
| ~ sQ15_spl
| sQ5_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f244,f219,f157,f228,f238]) ).
fof(f247,definition,
( sQ19_spl
<=> p102(sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( ~ sQ19_spl
| p102(sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f251,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f67]) ).
fof(f252,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f253,plain,
! [X0,X1,X2,X3] :
( ~ sQ18_spl
| ~ r1(sK0_skl,sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl))
| p102(sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl))
| ~ r1(X3,sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl))
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f239,f150]) ).
fof(f259,definition,
( sQ20_spl
<=> r1(sK0_skl,sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( sQ20_spl
| ~ r1(sK0_skl,sK10_skl(sK0_skl,sK0_skl,sK0_skl,sK0_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( ~ sQ18_spl
| ~ sQ20_spl
| sQ19_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f253,f232,f247,f259,f238]) ).
fof(f283,plain,
( ~ sQ19_spl
| ~ p100(sK0_skl)
| p101(sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f248,f46]) ).
fof(f290,plain,
( ~ sQ19_spl
| ~ sQ15_spl
| sQ5_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f283,f219,f157,f228,f247]) ).
fof(f318,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ p100(sK0_skl)
| p101(sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(X2,sK0_skl)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f233,f44]) ).
fof(f320,definition,
! [X0,X1,X2] :
( sQ32_spl
<=> ( ~ r1(X2,sK0_skl)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f321,plain,
! [X0,X1,X2] :
( ~ sQ32_spl
| ~ r1(X2,sK0_skl)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| sQ5_spl
| ~ sQ13_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f318,f320,f219,f157,f228,f232]) ).
fof(f324,plain,
! [X0,X1] :
( ~ sQ32_spl
| ~ r1(X1,sK0_skl)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f321,f4]) ).
fof(f326,plain,
! [X0] :
( ~ sQ32_spl
| ~ r1(X0,sK0_skl)
| ~ r1(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f324,f4]) ).
fof(f327,plain,
( ~ sQ32_spl
| ~ r1(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f326,f4]) ).
fof(f328,plain,
( ~ sQ32_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f327,f219,f320]) ).
fof(f342,plain,
( sQ20_spl
| ~ p100(sK0_skl)
| p101(sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl)
| ~ r1(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f261,f44]) ).
fof(f343,plain,
( sQ20_spl
| ~ sQ15_spl
| sQ5_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f342,f219,f157,f228,f259]) ).
fof(f344,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f82,f170,f177,f243,f246,f252,f262,f290,f323,f328,f343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL656+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 00:49:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.54 % Refutation found
% 0.14/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.56 % Elapsed time: 0.179402 seconds
% 0.14/0.56 % CPU time: 1.050127 seconds
% 0.14/0.56 % Total memory used: 26.939 MB
% 0.14/0.56 % Net memory used: 25.668 MB
%------------------------------------------------------------------------------