%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 03:13:51 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.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 10:36:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.39 fof(f1,axiom,(
% 0.09/0.39 (![Y,Z,Xs]: (aux(Y,Z,Xs,btrue) = union(Xs,Y) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f3,axiom,(
% 0.09/0.39 (![Y]: (barbar(btrue,Y) = btrue ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f8,axiom,(
% 0.09/0.39 eqNat(z,z) = btrue ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f10,axiom,(
% 0.09/0.39 (![X,Z,Xs]: (elem(X,cons(Z,Xs)) = barbar(eqNat(X,Z),elem(X,Xs)) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f11,axiom,(
% 0.09/0.39 (![Y]: (union(nil,Y) = Y ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f12,axiom,(
% 0.09/0.39 (![Z,Xs,Y]: (union(cons(Z,Xs),Y) = aux(Y,Z,Xs,elem(Z,Y)) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f13,axiom,(
% 0.09/0.39 (![X,Y]: (prop_union_comm(X,Y) = eq(union(X,Y),union(Y,X)) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f20,axiom,(
% 0.09/0.40 (![X]: (eq2(X,X) = btrue ))),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f21,axiom,(
% 0.09/0.40 (![X]: (eq3(X,X) = btrue ))),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f23,axiom,(
% 0.09/0.40 (![X,Z,Y,X2]: (( eq2(X,Z) != btrue| eq(cons(X,Y),cons(Z,X2)) = eq(Y,X2) ) ))),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f25,axiom,(
% 0.09/0.40 (![X,Y]: (eq(cons(X,Y),nil) = bfalse ))),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f26,negated_conjecture,(
% 0.09/0.40 (![X,Y]: (eq3(prop_union_comm(X,Y),bfalse) != btrue ))),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f27,plain,(
% 0.09/0.40 ![X0,X1,X2]: (aux(X0,X1,X2,btrue)=union(X2,X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/0.40 fof(f29,plain,(
% 0.09/0.40 ![X0]: (barbar(btrue,X0)=btrue)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.09/0.40 fof(f34,plain,(
% 0.09/0.40 eqNat(z,z)=btrue),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f8])).
% 0.09/0.40 fof(f36,plain,(
% 0.09/0.40 ![X0,X1,X2]: (elem(X0,cons(X1,X2))=barbar(eqNat(X0,X1),elem(X0,X2)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f10])).
% 0.09/0.40 fof(f37,plain,(
% 0.09/0.40 ![X0]: (union(nil,X0)=X0)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f11])).
% 0.09/0.40 fof(f38,plain,(
% 0.09/0.40 ![X0,X1,X2]: (union(cons(X0,X1),X2)=aux(X2,X0,X1,elem(X0,X2)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f12])).
% 0.09/0.40 fof(f39,plain,(
% 0.09/0.40 ![X0,X1]: (prop_union_comm(X0,X1)=eq(union(X0,X1),union(X1,X0)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f13])).
% 0.09/0.40 fof(f46,plain,(
% 0.09/0.40 ![X0]: (eq2(X0,X0)=btrue)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f20])).
% 0.09/0.40 fof(f47,plain,(
% 0.09/0.40 ![X0]: (eq3(X0,X0)=btrue)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f21])).
% 0.09/0.40 fof(f50,plain,(
% 0.09/0.40 ![X,Z]: (~eq2(X,Z)=btrue|(![Y,X2]: eq(cons(X,Y),cons(Z,X2))=eq(Y,X2)))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f23])).
% 0.09/0.40 fof(f51,plain,(
% 0.09/0.40 ![X0,X1,X2,X3]: (~eq2(X0,X1)=btrue|eq(cons(X0,X2),cons(X1,X3))=eq(X2,X3))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f50])).
% 0.09/0.40 fof(f53,plain,(
% 0.09/0.40 ![X0,X1]: (eq(cons(X0,X1),nil)=bfalse)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f25])).
% 0.09/0.40 fof(f54,plain,(
% 0.09/0.40 ![X0,X1]: (~eq3(prop_union_comm(X0,X1),bfalse)=btrue)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f26])).
% 0.09/0.40 fof(f66,plain,(
% 0.09/0.40 ![X0]: (elem(z,cons(z,X0))=barbar(btrue,elem(z,X0)))),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f34,f36])).
% 0.09/0.40 fof(f71,plain,(
% 0.09/0.40 ![X0]: (elem(z,cons(z,X0))=btrue)),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f29,f66])).
% 0.09/0.40 fof(f78,plain,(
% 0.09/0.40 ![X0,X1,X2]: (eq(cons(X0,X1),cons(X0,X2))=eq(X1,X2))),
% 0.09/0.40 inference(resolution,[status(thm)],[f51,f46])).
% 0.09/0.40 fof(f84,plain,(
% 0.09/0.40 ![X0,X1]: (union(cons(z,X0),cons(z,X1))=aux(cons(z,X1),z,X0,btrue))),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f71,f38])).
% 0.09/0.40 fof(f86,plain,(
% 0.09/0.40 ![X0,X1]: (union(cons(z,X0),cons(z,X1))=union(X0,cons(z,X1)))),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f27,f84])).
% 0.09/0.40 fof(f137,plain,(
% 0.09/0.40 ![X0,X1]: (prop_union_comm(cons(z,X0),cons(z,X1))=eq(union(cons(z,X0),cons(z,X1)),union(X1,cons(z,X0))))),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f86,f39])).
% 0.09/0.40 fof(f139,plain,(
% 0.09/0.40 ![X0,X1]: (prop_union_comm(cons(z,X0),cons(z,X1))=eq(union(X0,cons(z,X1)),union(X1,cons(z,X0))))),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f86,f137])).
% 0.09/0.40 fof(f166,plain,(
% 0.09/0.40 ![X0]: (prop_union_comm(cons(z,nil),cons(z,X0))=eq(cons(z,X0),union(X0,cons(z,nil))))),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f37,f139])).
% 0.09/0.40 fof(f170,plain,(
% 0.09/0.40 ![X0]: (prop_union_comm(cons(z,nil),cons(z,cons(z,X0)))=eq(cons(z,cons(z,X0)),union(X0,cons(z,nil))))),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f86,f166])).
% 0.09/0.40 fof(f236,plain,(
% 0.09/0.40 prop_union_comm(cons(z,nil),cons(z,cons(z,nil)))=eq(cons(z,cons(z,nil)),cons(z,nil))),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f37,f170])).
% 0.09/0.40 fof(f237,plain,(
% 0.09/0.40 prop_union_comm(cons(z,nil),cons(z,cons(z,nil)))=eq(cons(z,nil),nil)),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f78,f236])).
% 0.09/0.40 fof(f238,plain,(
% 0.09/0.40 prop_union_comm(cons(z,nil),cons(z,cons(z,nil)))=bfalse),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f53,f237])).
% 0.09/0.40 fof(f243,plain,(
% 0.09/0.40 ~eq3(bfalse,bfalse)=btrue),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f238,f54])).
% 0.09/0.40 fof(f244,plain,(
% 0.09/0.40 ~btrue=btrue),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f47,f243])).
% 0.09/0.40 fof(f245,plain,(
% 0.09/0.40 $false),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f244])).
% 0.09/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.43 % Elapsed time: 0.062328 seconds
% 0.14/0.43 % CPU time: 0.206141 seconds
% 0.14/0.43 % Total memory used: 68.094 MB
% 0.14/0.43 % Net memory used: 67.849 MB
%------------------------------------------------------------------------------