%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:12:56 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:47:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.39 fof(f4,axiom,(
% 0.13/0.39 (! [A,B,C,D] :( ( disjoint(A,B)| disjoint(C,D) )=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f5,conjecture,(
% 0.13/0.39 (! [A,B,C,D] :( A != B=> ( disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D))& disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))) ) ) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f6,negated_conjecture,(
% 0.13/0.39 ~((! [A,B,C,D] :( A != B=> ( disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D))& disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))) ) ) ))),
% 0.13/0.39 inference(negated_conjecture,[status(cth)],[f5])).
% 0.13/0.39 fof(f7,axiom,(
% 0.13/0.39 (! [A,B] :( A != B=> disjoint(singleton(A),singleton(B)) ) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f14,plain,(
% 0.13/0.39 ![A,B,C,D]: ((~disjoint(A,B)&~disjoint(C,D))|disjoint(cartesian_product2(A,C),cartesian_product2(B,D)))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.13/0.39 fof(f15,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~disjoint(X0,X1)|disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f14])).
% 0.13/0.39 fof(f16,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~disjoint(X0,X1)|disjoint(cartesian_product2(X2,X0),cartesian_product2(X3,X1)))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f14])).
% 0.13/0.39 fof(f17,plain,(
% 0.13/0.39 (?[A,B,C,D]: (~A=B&(~disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D))|~disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))))))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.13/0.39 fof(f18,plain,(
% 0.13/0.39 ?[A,B]: (~A=B&((?[C,D]: ~disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)))|(?[C,D]: ~disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f17])).
% 0.13/0.39 fof(f19,plain,(
% 0.13/0.39 (~sK2_skl=sK3_skl&(~disjoint(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK5_skl))|~disjoint(cartesian_product2(sK6_skl,singleton(sK2_skl)),cartesian_product2(sK7_skl,singleton(sK3_skl)))))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl),skolemize(C,sK6_skl),skolemize(D,sK7_skl)],[f18])).
% 0.13/0.39 fof(f20,plain,(
% 0.13/0.39 ~sK2_skl=sK3_skl),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.39 fof(f21,plain,(
% 0.13/0.39 ~disjoint(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK5_skl))|~disjoint(cartesian_product2(sK6_skl,singleton(sK2_skl)),cartesian_product2(sK7_skl,singleton(sK3_skl)))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.39 fof(f22,plain,(
% 0.13/0.39 ![A,B]: (A=B|disjoint(singleton(A),singleton(B)))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.13/0.39 fof(f23,plain,(
% 0.13/0.39 ![X0,X1]: (X0=X1|disjoint(singleton(X0),singleton(X1)))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f22])).
% 0.13/0.39 fof(f25,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (disjoint(cartesian_product2(singleton(X0),X1),cartesian_product2(singleton(X2),X3))|X0=X2)),
% 0.13/0.39 inference(resolution,[status(thm)],[f15,f23])).
% 0.13/0.39 fof(f26,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (disjoint(cartesian_product2(X0,singleton(X1)),cartesian_product2(X2,singleton(X3)))|X1=X3)),
% 0.13/0.39 inference(resolution,[status(thm)],[f16,f23])).
% 0.13/0.39 fof(f27,plain,(
% 0.13/0.39 sK2_skl=sK3_skl|~disjoint(cartesian_product2(sK6_skl,singleton(sK2_skl)),cartesian_product2(sK7_skl,singleton(sK3_skl)))),
% 0.13/0.39 inference(resolution,[status(thm)],[f25,f21])).
% 0.13/0.39 fof(f31,plain,(
% 0.13/0.39 ~disjoint(cartesian_product2(sK6_skl,singleton(sK2_skl)),cartesian_product2(sK7_skl,singleton(sK3_skl)))),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f27,f20])).
% 0.13/0.39 fof(f35,plain,(
% 0.13/0.39 sK2_skl=sK3_skl),
% 0.13/0.39 inference(resolution,[status(thm)],[f31,f26])).
% 0.13/0.39 fof(f36,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f35,f20])).
% 0.13/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.42 % Elapsed time: 0.046553 seconds
% 0.13/0.42 % CPU time: 0.140030 seconds
% 0.13/0.42 % Total memory used: 79.896 MB
% 0.13/0.42 % Net memory used: 79.368 MB
%------------------------------------------------------------------------------