%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWX200-1 : TPTP v9.3.1. Released v9.3.0.
% 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 03:13:46 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX200-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 10:35:31 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.37 fof(f4,axiom,(
% 0.13/0.37 (![Y,Y2,Xs]: (aux2(Y,Y2,Xs,bfalse) = bfalse ))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f6,axiom,(
% 0.13/0.37 (![Z]: (leqNat(s(Z),z) = bfalse ))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f8,axiom,(
% 0.13/0.37 (![Y]: (merge(nil,Y) = Y ))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f11,axiom,(
% 0.13/0.37 ord(nil) = btrue ),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f13,axiom,(
% 0.13/0.37 (![Y,Y2,Xs]: (ord(cons(Y,cons(Y2,Xs))) = aux2(Y,Y2,Xs,leqNat(Y,Y2)) ))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f14,axiom,(
% 0.13/0.37 (![Q]: (impl(btrue,Q) = Q ))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f16,axiom,(
% 0.13/0.37 (![X,Y]: (prop_merge_ord_not3(X,Y) = impl(eq2(ord(X),btrue),impl(eq2(ord(Y),bfalse),eq2(ord(merge(X,Y)),btrue))) ))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f17,axiom,(
% 0.13/0.37 eq2(bfalse,btrue) = bfalse ),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f23,axiom,(
% 0.13/0.37 (![X]: (eq2(X,X) = btrue ))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f24,negated_conjecture,(
% 0.13/0.37 (![X,Y]: (eq2(prop_merge_ord_not3(X,Y),bfalse) != btrue ))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f28,plain,(
% 0.13/0.37 ![X0,X1,X2]: (aux2(X0,X1,X2,bfalse)=bfalse)),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/0.37 fof(f30,plain,(
% 0.13/0.37 ![X0]: (leqNat(s(X0),z)=bfalse)),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.37 fof(f32,plain,(
% 0.13/0.37 ![X0]: (merge(nil,X0)=X0)),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/0.37 fof(f35,plain,(
% 0.13/0.37 ord(nil)=btrue),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f11])).
% 0.13/0.37 fof(f37,plain,(
% 0.13/0.37 ![X0,X1,X2]: (ord(cons(X0,cons(X1,X2)))=aux2(X0,X1,X2,leqNat(X0,X1)))),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.37 fof(f38,plain,(
% 0.13/0.37 ![X0]: (impl(btrue,X0)=X0)),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f14])).
% 0.13/0.37 fof(f40,plain,(
% 0.13/0.37 ![X0,X1]: (prop_merge_ord_not3(X0,X1)=impl(eq2(ord(X0),btrue),impl(eq2(ord(X1),bfalse),eq2(ord(merge(X0,X1)),btrue))))),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f16])).
% 0.13/0.37 fof(f41,plain,(
% 0.13/0.37 eq2(bfalse,btrue)=bfalse),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f17])).
% 0.13/0.37 fof(f47,plain,(
% 0.13/0.37 ![X0]: (eq2(X0,X0)=btrue)),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f23])).
% 0.13/0.37 fof(f48,plain,(
% 0.13/0.37 ![X0,X1]: (~eq2(prop_merge_ord_not3(X0,X1),bfalse)=btrue)),
% 0.13/0.37 inference(cnf_transformation,[status(thm)],[f24])).
% 0.13/0.37 fof(f49,definition,(
% 0.13/0.37 ![X0,X1]: (sF0_fnc(X0,X1)=eq2(prop_merge_ord_not3(X0,X1),bfalse))),
% 0.13/0.37 introduced(definition,[new_symbols(definition,[sF0_fnc(X0,X1)])],[function_definition])).
% 0.13/0.37 fof(f50,plain,(
% 0.13/0.37 ![X0,X1]: (~sF0_fnc(X0,X1)=btrue)),
% 0.13/0.37 inference(definition_folding,[],[f48,f49])).
% 0.13/0.37 fof(f51,plain,(
% 0.13/0.37 ![X0]: (prop_merge_ord_not3(nil,X0)=impl(eq2(ord(nil),btrue),impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue))))),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f32,f40])).
% 0.13/0.37 fof(f52,plain,(
% 0.13/0.37 ![X0]: (prop_merge_ord_not3(nil,X0)=impl(eq2(btrue,btrue),impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue))))),
% 0.13/0.37 inference(backward_demodulation,[status(thm)],[f35,f51])).
% 0.13/0.37 fof(f55,plain,(
% 0.13/0.37 ![X0]: (prop_merge_ord_not3(nil,X0)=impl(btrue,impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue))))),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f47,f52])).
% 0.13/0.37 fof(f77,plain,(
% 0.13/0.37 ![X0]: (prop_merge_ord_not3(nil,X0)=impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue)))),
% 0.13/0.37 inference(backward_demodulation,[status(thm)],[f38,f55])).
% 0.13/0.37 fof(f147,plain,(
% 0.13/0.37 ![X0,X1]: (ord(cons(s(X0),cons(z,X1)))=aux2(s(X0),z,X1,bfalse))),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f30,f37])).
% 0.13/0.37 fof(f149,plain,(
% 0.13/0.37 ![X0,X1]: (ord(cons(s(X0),cons(z,X1)))=bfalse)),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f28,f147])).
% 0.13/0.37 fof(f181,plain,(
% 0.13/0.37 ![X0,X1]: (prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1)))=impl(eq2(ord(cons(s(X0),cons(z,X1))),bfalse),eq2(bfalse,btrue)))),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f149,f77])).
% 0.13/0.37 fof(f189,plain,(
% 0.13/0.37 ![X0,X1]: (prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1)))=impl(eq2(bfalse,bfalse),eq2(bfalse,btrue)))),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f149,f181])).
% 0.13/0.37 fof(f190,plain,(
% 0.13/0.37 ![X0,X1]: (prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1)))=impl(btrue,eq2(bfalse,btrue)))),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f47,f189])).
% 0.13/0.37 fof(f191,plain,(
% 0.13/0.37 ![X0,X1]: (prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1)))=eq2(bfalse,btrue))),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f38,f190])).
% 0.13/0.37 fof(f192,plain,(
% 0.13/0.37 ![X0,X1]: (prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1)))=bfalse)),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f41,f191])).
% 0.13/0.37 fof(f218,plain,(
% 0.13/0.37 ![X0,X1]: (sF0_fnc(nil,cons(s(X0),cons(z,X1)))=eq2(bfalse,bfalse))),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f192,f49])).
% 0.13/0.37 fof(f219,plain,(
% 0.13/0.37 ![X0,X1]: (sF0_fnc(nil,cons(s(X0),cons(z,X1)))=btrue)),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f47,f218])).
% 0.13/0.37 fof(f220,plain,(
% 0.13/0.37 $false),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f219,f50])).
% 0.13/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.39 % Elapsed time: 0.026731 seconds
% 0.13/0.39 % CPU time: 0.044565 seconds
% 0.13/0.39 % Total memory used: 1.499 MB
% 0.13/0.39 % Net memory used: 1.463 MB
%------------------------------------------------------------------------------