%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 02:11:04 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 72 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 74 ( 32 ~; 23 |; 17 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 86 ( 75 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C,D,E] :
~ ( ! [F,G] :
~ ( in(G,set_intersection2(C,E))
& in(F,set_intersection2(B,D))
& A = ordered_pair(F,G) )
& in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B,C,D] :
( ( disjoint(C,D)
| disjoint(A,B) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B,C,D] :
( ( disjoint(C,D)
| disjoint(A,B) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [A,B,C,D,E] :
( ? [F,G] :
( in(G,set_intersection2(C,E))
& in(F,set_intersection2(B,D))
& A = ordered_pair(F,G) )
| ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f29,plain,
! [A,B,C,D,E] :
( ? [G] :
( in(G,set_intersection2(C,E))
& ? [F] :
( in(F,set_intersection2(B,D))
& A = ordered_pair(F,G) ) )
| ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
! [A,B,C,D,E] :
( ( in(sK2_skl(E,D,C,B,A),set_intersection2(C,E))
& in(sK3_skl(E,D,C,B,A),set_intersection2(B,D))
& A = ordered_pair(sK3_skl(E,D,C,B,A),sK2_skl(E,D,C,B,A)) )
| ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(G,sK2_skl(E,D,C,B,A)),skolemize(F,sK3_skl(E,D,C,B,A))],[f29]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4] :
( in(sK3_skl(X4,X3,X2,X1,X0),set_intersection2(X1,X3))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4] :
( in(sK2_skl(X4,X3,X2,X1,X0),set_intersection2(X2,X4))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
? [A,B,C,D] :
( ~ disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
& ( disjoint(C,D)
| disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f35,plain,
( ~ disjoint(cartesian_product2(sK4_skl,sK6_skl),cartesian_product2(sK5_skl,sK7_skl))
& ( disjoint(sK6_skl,sK7_skl)
| disjoint(sK4_skl,sK5_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl),skolemize(C,sK6_skl),skolemize(D,sK7_skl)],[f34]) ).
fof(f36,plain,
( disjoint(sK6_skl,sK7_skl)
| disjoint(sK4_skl,sK5_skl) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
~ disjoint(cartesian_product2(sK4_skl,sK6_skl),cartesian_product2(sK5_skl,sK7_skl)),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f39,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ! [A,B] :
( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ! [A,B] :
( in(sK8_skl(B,A),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(C,sK8_skl(B,A))],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( in(sK8_skl(X1,X0),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ disjoint(X2,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(paramodulation,[status(thm)],[f17,f42]) ).
fof(f56,plain,
! [X0] :
( disjoint(sK4_skl,sK5_skl)
| ~ in(X0,set_intersection2(sK7_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f54,f36]) ).
fof(f58,plain,
! [X0] :
( disjoint(sK4_skl,sK5_skl)
| ~ in(X0,set_intersection2(sK6_skl,sK7_skl)) ),
inference(forward_demodulation,[status(thm)],[f17,f56]) ).
fof(f70,plain,
! [X0,X1] :
( ~ in(X1,set_intersection2(sK5_skl,sK4_skl))
| ~ in(X0,set_intersection2(sK6_skl,sK7_skl)) ),
inference(resolution,[status(thm)],[f58,f54]) ).
fof(f71,plain,
! [X0,X1] :
( ~ in(X1,set_intersection2(sK4_skl,sK5_skl))
| ~ in(X0,set_intersection2(sK6_skl,sK7_skl)) ),
inference(forward_demodulation,[status(thm)],[f17,f70]) ).
fof(f84,plain,
in(sK8_skl(cartesian_product2(sK5_skl,sK7_skl),cartesian_product2(sK4_skl,sK6_skl)),set_intersection2(cartesian_product2(sK4_skl,sK6_skl),cartesian_product2(sK5_skl,sK7_skl))),
inference(resolution,[status(thm)],[f41,f37]) ).
fof(f91,plain,
in(sK2_skl(sK7_skl,sK5_skl,sK6_skl,sK4_skl,sK8_skl(cartesian_product2(sK5_skl,sK7_skl),cartesian_product2(sK4_skl,sK6_skl))),set_intersection2(sK6_skl,sK7_skl)),
inference(resolution,[status(thm)],[f84,f33]) ).
fof(f92,plain,
in(sK3_skl(sK7_skl,sK5_skl,sK6_skl,sK4_skl,sK8_skl(cartesian_product2(sK5_skl,sK7_skl),cartesian_product2(sK4_skl,sK6_skl))),set_intersection2(sK4_skl,sK5_skl)),
inference(resolution,[status(thm)],[f84,f32]) ).
fof(f126,plain,
! [X0] : ~ in(X0,set_intersection2(sK4_skl,sK5_skl)),
inference(resolution,[status(thm)],[f91,f71]) ).
fof(f142,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f92,f126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 05:44:21 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.053844 seconds
% 0.12/0.40 % CPU time: 0.163470 seconds
% 0.12/0.40 % Total memory used: 102.449 MB
% 0.12/0.40 % Net memory used: 102.020 MB
%------------------------------------------------------------------------------