%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWX204-1 : 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 : n018.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 03:13:47 PM UTC 2026
% Result : Unsatisfiable 16.39s 2.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX204-1 : 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 : n018.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 10:35:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 16.39/2.47 % Refutation found
% 16.39/2.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 16.39/2.47 % SZS output start CNFRefutation for theBenchmark
% 16.39/2.47 fof(f1,axiom,(
% 16.39/2.47 (![Y]: (x2(z,Y) = Y ))),
% 16.39/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.39/2.47 fof(f2,axiom,(
% 16.39/2.47 (![N,Y]: (x2(s(N),Y) = s(x2(N,Y)) ))),
% 16.39/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.39/2.47 fof(f3,axiom,(
% 16.39/2.47 (![Y]: (x22(z,Y) = z ))),
% 16.39/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.39/2.47 fof(f4,axiom,(
% 16.39/2.47 (![N,Y]: (x22(s(N),Y) = x2(Y,x22(N,Y)) ))),
% 16.39/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.39/2.47 fof(f5,axiom,(
% 16.39/2.47 (![X]: (mul_idem(X) = eq(x22(X,X),X) ))),
% 16.39/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.39/2.47 fof(f8,axiom,(
% 16.39/2.47 (![X,Y]: (eq(s(X),s(Y)) = eq(X,Y) ))),
% 16.39/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.39/2.47 fof(f10,axiom,(
% 16.39/2.47 (![X]: (eq(s(X),z) = bfalse ))),
% 16.39/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.39/2.47 fof(f12,axiom,(
% 16.39/2.47 (![X]: (eq2(X,X) = btrue ))),
% 16.39/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.39/2.47 fof(f13,negated_conjecture,(
% 16.39/2.47 (![X]: (eq2(mul_idem(X),bfalse) != btrue ))),
% 16.39/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.39/2.47 fof(f14,plain,(
% 16.39/2.47 ![X0]: (x2(z,X0)=X0)),
% 16.39/2.47 inference(cnf_transformation,[status(thm)],[f1])).
% 16.39/2.47 fof(f15,plain,(
% 16.39/2.47 ![X0,X1]: (x2(s(X0),X1)=s(x2(X0,X1)))),
% 16.39/2.47 inference(cnf_transformation,[status(thm)],[f2])).
% 16.39/2.47 fof(f16,plain,(
% 16.39/2.47 ![X0]: (x22(z,X0)=z)),
% 16.39/2.47 inference(cnf_transformation,[status(thm)],[f3])).
% 16.39/2.47 fof(f17,plain,(
% 16.39/2.47 ![X0,X1]: (x22(s(X0),X1)=x2(X1,x22(X0,X1)))),
% 16.39/2.47 inference(cnf_transformation,[status(thm)],[f4])).
% 16.39/2.47 fof(f18,plain,(
% 16.39/2.47 ![X0]: (mul_idem(X0)=eq(x22(X0,X0),X0))),
% 16.39/2.47 inference(cnf_transformation,[status(thm)],[f5])).
% 16.39/2.47 fof(f21,plain,(
% 16.39/2.47 ![X0,X1]: (eq(s(X0),s(X1))=eq(X0,X1))),
% 16.39/2.47 inference(cnf_transformation,[status(thm)],[f8])).
% 16.39/2.47 fof(f23,plain,(
% 16.39/2.47 ![X0]: (eq(s(X0),z)=bfalse)),
% 16.39/2.47 inference(cnf_transformation,[status(thm)],[f10])).
% 16.39/2.47 fof(f25,plain,(
% 16.39/2.47 ![X0]: (eq2(X0,X0)=btrue)),
% 16.39/2.47 inference(cnf_transformation,[status(thm)],[f12])).
% 16.39/2.47 fof(f26,plain,(
% 16.39/2.47 ![X0]: (~eq2(mul_idem(X0),bfalse)=btrue)),
% 16.39/2.47 inference(cnf_transformation,[status(thm)],[f13])).
% 16.39/2.47 fof(f27,definition,(
% 16.39/2.47 ![X0]: (sF0_fnc(X0)=eq2(mul_idem(X0),bfalse))),
% 16.39/2.47 introduced(definition,[new_symbols(definition,[sF0_fnc(X0)])],[function_definition])).
% 16.39/2.47 fof(f28,plain,(
% 16.39/2.47 ![X0]: (~sF0_fnc(X0)=btrue)),
% 16.39/2.47 inference(definition_folding,[],[f26,f27])).
% 16.39/2.47 fof(f36,plain,(
% 16.39/2.47 ![X0,X1]: (x22(s(X0),s(X1))=s(x2(X1,x22(X0,s(X1)))))),
% 16.39/2.47 inference(paramodulation,[status(thm)],[f15,f17])).
% 16.39/2.47 fof(f38,plain,(
% 16.39/2.47 ![X0]: (x22(s(z),X0)=x2(X0,z))),
% 16.39/2.47 inference(paramodulation,[status(thm)],[f16,f17])).
% 16.39/2.47 fof(f57,plain,(
% 16.39/2.47 ![X0,X1]: (x22(s(X0),s(s(X1)))=s(s(x2(X1,x22(X0,s(s(X1)))))))),
% 16.39/2.47 inference(paramodulation,[status(thm)],[f15,f36])).
% 16.39/2.47 fof(f97,plain,(
% 16.39/2.47 ![X0]: (x22(s(X0),s(s(z)))=s(s(x22(X0,s(s(z))))))),
% 16.39/2.47 inference(paramodulation,[status(thm)],[f14,f57])).
% 16.39/2.47 fof(f2263,plain,(
% 16.39/2.47 x22(s(s(z)),s(s(z)))=s(s(x2(s(s(z)),z)))),
% 16.39/2.47 inference(paramodulation,[status(thm)],[f38,f97])).
% 16.39/2.47 fof(f2362,plain,(
% 16.39/2.47 x22(s(s(z)),s(s(z)))=s(s(s(x2(s(z),z))))),
% 16.39/2.47 inference(forward_demodulation,[status(thm)],[f15,f2263])).
% 16.39/2.47 fof(f2363,plain,(
% 16.39/2.47 x22(s(s(z)),s(s(z)))=s(s(s(s(x2(z,z)))))),
% 16.39/2.47 inference(forward_demodulation,[status(thm)],[f15,f2362])).
% 16.39/2.47 fof(f2364,plain,(
% 16.39/2.47 x22(s(s(z)),s(s(z)))=s(s(s(s(z))))),
% 16.39/2.47 inference(forward_demodulation,[status(thm)],[f14,f2363])).
% 16.39/2.47 fof(f21287,plain,(
% 16.39/2.47 mul_idem(s(s(z)))=eq(s(s(s(s(z)))),s(s(z)))),
% 16.39/2.47 inference(paramodulation,[status(thm)],[f2364,f18])).
% 16.39/2.47 fof(f23232,plain,(
% 16.39/2.47 mul_idem(s(s(z)))=eq(s(s(s(z))),s(z))),
% 16.39/2.47 inference(forward_demodulation,[status(thm)],[f21,f21287])).
% 16.39/2.47 fof(f23233,plain,(
% 16.39/2.47 mul_idem(s(s(z)))=eq(s(s(z)),z)),
% 16.39/2.47 inference(forward_demodulation,[status(thm)],[f21,f23232])).
% 16.39/2.47 fof(f23234,plain,(
% 16.39/2.47 mul_idem(s(s(z)))=bfalse),
% 16.39/2.47 inference(forward_demodulation,[status(thm)],[f23,f23233])).
% 16.39/2.47 fof(f23235,plain,(
% 16.39/2.47 sF0_fnc(s(s(z)))=eq2(bfalse,bfalse)),
% 16.39/2.47 inference(paramodulation,[status(thm)],[f23234,f27])).
% 16.39/2.47 fof(f23236,plain,(
% 16.39/2.47 sF0_fnc(s(s(z)))=btrue),
% 16.39/2.47 inference(forward_demodulation,[status(thm)],[f25,f23235])).
% 16.39/2.47 fof(f23237,plain,(
% 16.21/2.52 $false),
% 16.21/2.52 inference(forward_subsumption_resolution,[status(thm)],[f23236,f28])).
% 16.21/2.52 % SZS output end CNFRefutation for theBenchmark.p
% 16.21/2.56 % Elapsed time: 2.190506 seconds
% 16.21/2.56 % CPU time: 17.124117 seconds
% 16.21/2.56 % Total memory used: 432.183 MB
% 16.21/2.56 % Net memory used: 428.709 MB
%------------------------------------------------------------------------------