%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 273 ( 118 ~; 96 |; 59 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 76 ( 53 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : r1(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( ~ ( ! [Y] :
( ( p1(Y)
& p2(Y) )
| ( ~ p2(Y)
& ~ p1(Y) )
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ( p1(Y)
& ~ p2(Y) )
| ( ~ p1(Y)
& p2(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( $false
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ p3(Y)
| ~ r1(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( ~ ( ! [Y] :
( ( p1(Y)
& p2(Y) )
| ( ~ p2(Y)
& ~ p1(Y) )
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ( p1(Y)
& ~ p2(Y) )
| ( ~ p1(Y)
& p2(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( $false
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ p3(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) )
& r1(X,Y) )
& ? [Y] :
( ~ p3(Y)
& r1(X,Y) )
& ! [Y] :
( ( ( ~ p1(Y)
| p2(Y) )
& ( p1(Y)
| ~ p2(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( $true
& r1(X,Y) ) )
| ~ r1(Y,X) )
& r1(X,Y) )
& ? [Y] :
( ? [X] :
( p1(X)
& r1(Y,X) )
& p3(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) )
& r1(X,Y) )
& ? [Y] :
( ~ p3(Y)
& r1(X,Y) )
& ! [Y] :
( ( ( ~ p1(Y)
| p2(Y) )
& ( p1(Y)
| ~ p2(Y) ) )
| ~ r1(X,Y) )
& $true
& ? [Y] : r1(X,Y) )
| ~ r1(Y,X) )
& r1(X,Y) )
& ? [Y] :
( ? [X] :
( p1(X)
& r1(Y,X) )
& p3(Y)
& r1(X,Y) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f11,plain,
( ! [X] :
( ( ( ~ p1(sK6_skl(X))
| ~ p2(sK6_skl(X)) )
& ( p2(sK6_skl(X))
| p1(sK6_skl(X)) )
& r1(X,sK6_skl(X))
& ~ p3(sK5_skl(X))
& r1(X,sK5_skl(X))
& ! [Y] :
( ( ( ~ p1(Y)
| p2(Y) )
& ( p1(Y)
| ~ p2(Y) ) )
| ~ r1(X,Y) )
& $true
& r1(X,sK4_skl(X)) )
| ~ r1(sK3_skl,X) )
& r1(sK0_skl,sK3_skl)
& p1(sK2_skl)
& r1(sK1_skl,sK2_skl)
& p3(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]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(X,sK2_skl),skolemize(Y,sK3_skl),skolemize(Y,sK4_skl(X)),skolemize(Y,sK5_skl(X)),skolemize(Y,sK6_skl(X))],[f10]) ).
fof(f12,plain,
? [X] :
( ? [Y] :
( ! [X] :
( ( ? [Y] :
( ( ~ p1(sK6_skl(X))
| ~ p2(sK6_skl(X)) )
& ( p2(sK6_skl(X))
| p1(sK6_skl(X)) )
& r1(X,sK6_skl(X)) )
& ? [Y] :
( ~ p3(sK5_skl(X))
& r1(X,sK5_skl(X)) )
& ! [Y] :
( ( ( ~ p1(Y)
| p2(Y) )
& ( p1(Y)
| ~ p2(Y) ) )
| ~ r1(X,Y) )
& ? [Y] : r1(X,sK4_skl(X)) )
| ~ r1(sK3_skl,X) )
& r1(sK0_skl,sK3_skl) )
& ? [Y] :
( ? [X] :
( p1(sK2_skl)
& r1(sK1_skl,sK2_skl) )
& p3(sK1_skl)
& r1(sK0_skl,sK1_skl) ) ),
inference(true_and_false_simplification,[status(thm)],[f11]) ).
fof(f19,plain,
! [X0,X1] :
( p1(X1)
| ~ p2(X1)
| ~ r1(X0,X1)
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( ~ p1(X1)
| p2(X1)
| ~ r1(X0,X1)
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f23,plain,
! [X0] :
( r1(X0,sK6_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f24,plain,
! [X0] :
( p2(sK6_skl(X0))
| p1(sK6_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f25,plain,
! [X0] :
( ~ p1(sK6_skl(X0))
| ~ p2(sK6_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
! [X0,X1] :
( ~ p1(sK6_skl(X0))
| ~ r1(X1,sK6_skl(X0))
| ~ r1(sK3_skl,X1)
| ~ p1(sK6_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f25,f20]) ).
fof(f28,plain,
! [X0,X1] :
( ~ r1(X1,sK6_skl(X0))
| ~ r1(sK3_skl,X1)
| ~ p1(sK6_skl(X0))
| ~ r1(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( p2(sK6_skl(X0))
| ~ r1(sK3_skl,X0)
| ~ r1(X1,sK6_skl(X0))
| ~ r1(sK3_skl,X1)
| ~ r1(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f28,f24]) ).
fof(f30,plain,
! [X0,X1] :
( p2(sK6_skl(X0))
| ~ r1(X1,sK6_skl(X0))
| ~ r1(sK3_skl,X1)
| ~ r1(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0,X1,X2] :
( p1(sK6_skl(X0))
| ~ r1(X2,sK6_skl(X0))
| ~ r1(sK3_skl,X2)
| ~ r1(X1,sK6_skl(X0))
| ~ r1(sK3_skl,X1)
| ~ r1(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f30,f19]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ r1(X2,sK6_skl(X0))
| ~ r1(sK3_skl,X2)
| ~ r1(X1,sK6_skl(X0))
| ~ r1(sK3_skl,X1)
| ~ r1(sK3_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f32,f28]) ).
fof(f35,plain,
! [X0,X1] :
( ~ r1(sK3_skl,X0)
| ~ r1(sK3_skl,X0)
| ~ r1(X1,sK6_skl(X0))
| ~ r1(sK3_skl,X1)
| ~ r1(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f34,f23]) ).
fof(f38,plain,
! [X0,X1] :
( ~ r1(X1,sK6_skl(X0))
| ~ r1(sK3_skl,X1)
| ~ r1(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f35]) ).
fof(f40,plain,
! [X0] :
( ~ r1(sK3_skl,X0)
| ~ r1(sK3_skl,X0)
| ~ r1(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f38,f23]) ).
fof(f43,plain,
! [X0] : ~ r1(sK3_skl,X0),
inference(duplicate_literals_removal,[status(thm)],[f40]) ).
fof(f45,plain,
$false,
inference(resolution,[status(thm)],[f43,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 01:00:32 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.41 % Elapsed time: 0.042771 seconds
% 0.08/0.41 % CPU time: 0.128816 seconds
% 0.08/0.41 % Total memory used: 15.015 MB
% 0.08/0.41 % Net memory used: 14.636 MB
%------------------------------------------------------------------------------