%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET968+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 : 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 02:12:55 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET968+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
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:45:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.40 fof(f7,axiom,(
% 0.10/0.40 (! [A,B,C] :( cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C))& cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f8,conjecture,(
% 0.10/0.40 (! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f9,negated_conjecture,(
% 0.10/0.40 ~((! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)) ))),
% 0.10/0.40 inference(negated_conjecture,[status(cth)],[f8])).
% 0.10/0.40 fof(f10,axiom,(
% 0.10/0.40 (! [A,B,C] : set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f24,plain,(
% 0.10/0.40 (![A,B,C]: cartesian_product2(set_union2(A,B),C)=set_union2(cartesian_product2(A,C),cartesian_product2(B,C)))&(![A,B,C]: cartesian_product2(C,set_union2(A,B))=set_union2(cartesian_product2(C,A),cartesian_product2(C,B)))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f7])).
% 0.10/0.40 fof(f25,plain,(
% 0.10/0.40 ![X0,X1,X2]: (cartesian_product2(set_union2(X0,X1),X2)=set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f24])).
% 0.10/0.40 fof(f26,plain,(
% 0.10/0.40 ![X0,X1,X2]: (cartesian_product2(X0,set_union2(X1,X2))=set_union2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f24])).
% 0.10/0.40 fof(f27,plain,(
% 0.10/0.40 (?[A,B,C,D]: ~cartesian_product2(set_union2(A,B),set_union2(C,D))=set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.10/0.40 fof(f28,plain,(
% 0.10/0.40 ~cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl))=set_union2(set_union2(set_union2(cartesian_product2(sK2_skl,sK4_skl),cartesian_product2(sK2_skl,sK5_skl)),cartesian_product2(sK3_skl,sK4_skl)),cartesian_product2(sK3_skl,sK5_skl))),
% 0.10/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl)],[f27])).
% 0.10/0.40 fof(f29,plain,(
% 0.10/0.40 ~cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl))=set_union2(set_union2(set_union2(cartesian_product2(sK2_skl,sK4_skl),cartesian_product2(sK2_skl,sK5_skl)),cartesian_product2(sK3_skl,sK4_skl)),cartesian_product2(sK3_skl,sK5_skl))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f28])).
% 0.10/0.40 fof(f30,plain,(
% 0.10/0.40 ![X0,X1,X2]: (set_union2(set_union2(X0,X1),X2)=set_union2(X0,set_union2(X1,X2)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f10])).
% 0.10/0.40 fof(f31,plain,(
% 0.10/0.40 ~cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl))=set_union2(set_union2(cartesian_product2(sK2_skl,set_union2(sK4_skl,sK5_skl)),cartesian_product2(sK3_skl,sK4_skl)),cartesian_product2(sK3_skl,sK5_skl))),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f26,f29])).
% 0.10/0.40 fof(f32,plain,(
% 0.10/0.40 ~cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl))=set_union2(cartesian_product2(sK2_skl,set_union2(sK4_skl,sK5_skl)),set_union2(cartesian_product2(sK3_skl,sK4_skl),cartesian_product2(sK3_skl,sK5_skl)))),
% 0.10/0.40 inference(backward_demodulation,[status(thm)],[f30,f31])).
% 0.10/0.40 fof(f33,plain,(
% 0.10/0.40 ~cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl))=set_union2(cartesian_product2(sK2_skl,set_union2(sK4_skl,sK5_skl)),cartesian_product2(sK3_skl,set_union2(sK4_skl,sK5_skl)))),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f26,f32])).
% 0.10/0.40 fof(f34,plain,(
% 0.10/0.40 ~cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl))=cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl))),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f25,f33])).
% 0.10/0.40 fof(f35,plain,(
% 0.10/0.40 $false),
% 0.10/0.40 inference(trivial_equality_resolution,[status(thm)],[f34])).
% 0.10/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.43 % Elapsed time: 0.049019 seconds
% 0.10/0.43 % CPU time: 0.149603 seconds
% 0.10/0.43 % Total memory used: 66.624 MB
% 0.10/0.43 % Net memory used: 66.135 MB
%------------------------------------------------------------------------------