%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 0.09s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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 05:45:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.40 fof(f8,axiom,(
% 0.09/0.40 (! [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)) ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f9,conjecture,(
% 0.09/0.40 (! [A,B,C] :( cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C))& cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))) ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f10,negated_conjecture,(
% 0.09/0.40 ~((! [A,B,C] :( cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C))& cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))) ) ))),
% 0.09/0.40 inference(negated_conjecture,[status(cth)],[f9])).
% 0.09/0.40 fof(f11,axiom,(
% 0.09/0.40 (! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f26,plain,(
% 0.09/0.40 (![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)))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f8])).
% 0.09/0.40 fof(f27,plain,(
% 0.09/0.40 ![X0,X1,X2]: (cartesian_product2(set_union2(X0,X1),X2)=set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f26])).
% 0.09/0.40 fof(f28,plain,(
% 0.09/0.40 ![X0,X1,X2]: (cartesian_product2(X0,set_union2(X1,X2))=set_union2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f26])).
% 0.09/0.40 fof(f29,plain,(
% 0.09/0.40 (?[A,B,C]: (~cartesian_product2(unordered_pair(A,B),C)=set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C))|~cartesian_product2(C,unordered_pair(A,B))=set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.09/0.40 fof(f30,plain,(
% 0.09/0.40 (?[A,B,C]: ~cartesian_product2(unordered_pair(A,B),C)=set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)))|(?[A,B,C]: ~cartesian_product2(C,unordered_pair(A,B))=set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f29])).
% 0.09/0.40 fof(f31,plain,(
% 0.09/0.40 ~cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=set_union2(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK4_skl))|~cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl))=set_union2(cartesian_product2(sK7_skl,singleton(sK5_skl)),cartesian_product2(sK7_skl,singleton(sK6_skl)))),
% 0.09/0.40 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(A,sK5_skl),skolemize(B,sK6_skl),skolemize(C,sK7_skl)],[f30])).
% 0.09/0.40 fof(f32,plain,(
% 0.09/0.40 ~cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=set_union2(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK4_skl))|~cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl))=set_union2(cartesian_product2(sK7_skl,singleton(sK5_skl)),cartesian_product2(sK7_skl,singleton(sK6_skl)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.40 fof(f33,plain,(
% 0.09/0.40 ![X0,X1]: (unordered_pair(X0,X1)=set_union2(singleton(X0),singleton(X1)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f11])).
% 0.09/0.40 fof(f34,definition,(
% 0.09/0.40 sQ0_spl <=> (cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=set_union2(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK4_skl)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f36,plain,(
% 0.09/0.40 ~cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=set_union2(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK4_skl))|sQ0_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f34])).
% 0.09/0.40 fof(f37,definition,(
% 0.09/0.40 sQ1_spl <=> (cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl))=set_union2(cartesian_product2(sK7_skl,singleton(sK5_skl)),cartesian_product2(sK7_skl,singleton(sK6_skl))))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f39,plain,(
% 0.09/0.40 ~cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl))=set_union2(cartesian_product2(sK7_skl,singleton(sK5_skl)),cartesian_product2(sK7_skl,singleton(sK6_skl)))|sQ1_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f37])).
% 0.09/0.40 fof(f40,plain,(
% 0.09/0.40 ~sQ0_spl|~sQ1_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f32,f34,f37])).
% 0.09/0.40 fof(f41,plain,(
% 0.09/0.40 ~cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=cartesian_product2(set_union2(singleton(sK2_skl),singleton(sK3_skl)),sK4_skl)|sQ0_spl),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f27,f36])).
% 0.09/0.40 fof(f42,plain,(
% 0.09/0.40 ~cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl)|sQ0_spl),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f33,f41])).
% 0.09/0.40 fof(f43,plain,(
% 0.09/0.40 $false|sQ0_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f42])).
% 0.09/0.40 fof(f44,plain,(
% 0.09/0.40 sQ0_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f43])).
% 0.09/0.40 fof(f45,plain,(
% 0.09/0.40 ~cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl))=cartesian_product2(sK7_skl,set_union2(singleton(sK5_skl),singleton(sK6_skl)))|sQ1_spl),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f28,f39])).
% 0.09/0.40 fof(f46,plain,(
% 0.09/0.40 ~cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl))=cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl))|sQ1_spl),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f33,f45])).
% 0.09/0.40 fof(f47,plain,(
% 0.09/0.40 $false|sQ1_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f46])).
% 0.09/0.40 fof(f48,plain,(
% 0.09/0.40 sQ1_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f47])).
% 0.09/0.40 fof(f49,plain,(
% 0.09/0.40 $false),
% 0.09/0.40 inference(sat_refutation,[status(thm)],[f40,f44,f48])).
% 0.09/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.42 % Elapsed time: 0.049722 seconds
% 0.09/0.42 % CPU time: 0.150037 seconds
% 0.09/0.42 % Total memory used: 66.600 MB
% 0.09/0.42 % Net memory used: 66.088 MB
%------------------------------------------------------------------------------