%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWX187+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 03:13:44 PM UTC 2026
% Result : Theorem 0.13s 5.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n003.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 10:33:21 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.13/5.65 % Refutation found
% 0.13/5.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.65 % SZS output start CNFRefutation for theBenchmark
% 0.13/5.65 fof(f1,axiom,(
% 0.13/5.65 (! [X,X2] : head(cons(X,X2)) = X )),
% 0.13/5.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f3,axiom,(
% 0.13/5.65 (! [X,X2] : nil != cons(X,X2) )),
% 0.13/5.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f5,axiom,(
% 0.13/5.65 (! [X] : s(X) != z )),
% 0.13/5.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f7,axiom,(
% 0.13/5.65 (! [Y,Xs] : length(cons(Y,Xs)) = s(length(Xs)) )),
% 0.13/5.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f8,axiom,(
% 0.13/5.65 (! [Z,Y2] :( x2(s(Z),s(Y2))<=> x2(Z,Y2) ) )),
% 0.13/5.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f10,axiom,(
% 0.13/5.65 (! [X2] : x2(z,s(X2)) )),
% 0.13/5.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f12,axiom,(
% 0.13/5.65 (! [Y] : x(nil,Y) = Y )),
% 0.13/5.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f13,axiom,(
% 0.13/5.65 (! [Y,Z,Xs] : x(cons(Z,Xs),Y) = cons(Z,x(Xs,Y)) )),
% 0.13/5.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f15,axiom,(
% 0.13/5.65 (! [Z,X2,X3] : rotate(s(Z),cons(X2,X3)) = rotate(Z,x(X3,cons(X2,nil))) )),
% 0.13/5.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f16,axiom,(
% 0.13/5.65 (! [Y] : rotate(z,Y) = Y )),
% 0.13/5.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f17,conjecture,(
% 0.13/5.65 (? [N,M,Ys,Xs] :~ ( x2(N,length(Xs))=> ( x2(M,length(Ys))=> ( Xs = Ys=> ( rotate(s(z),Xs) != Xs=> ( rotate(N,Xs) = rotate(M,Ys)=> N = M ) ) ) ) ) )),
% 0.13/5.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f18,negated_conjecture,(
% 0.13/5.65 ~((? [N,M,Ys,Xs] :~ ( x2(N,length(Xs))=> ( x2(M,length(Ys))=> ( Xs = Ys=> ( rotate(s(z),Xs) != Xs=> ( rotate(N,Xs) = rotate(M,Ys)=> N = M ) ) ) ) ) ))),
% 0.13/5.65 inference(negated_conjecture,[status(cth)],[f17])).
% 0.13/5.65 fof(f19,plain,(
% 0.13/5.65 ![X0,X1]: (head(cons(X0,X1))=X0)),
% 0.13/5.65 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/5.65 fof(f21,plain,(
% 0.13/5.65 ![X0,X1]: (~nil=cons(X0,X1))),
% 0.13/5.65 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/5.65 fof(f23,plain,(
% 0.13/5.65 ![X0]: (~s(X0)=z)),
% 0.13/5.65 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/5.65 fof(f25,plain,(
% 0.13/5.65 ![X0,X1]: (length(cons(X0,X1))=s(length(X1)))),
% 0.13/5.65 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/5.65 fof(f26,plain,(
% 0.13/5.65 ![Z,Y2]: ((~x2(s(Z),s(Y2))|x2(Z,Y2))&(x2(s(Z),s(Y2))|~x2(Z,Y2)))),
% 0.13/5.65 inference(NNF_transformation,[status(thm)],[f8])).
% 0.13/5.65 fof(f27,plain,(
% 0.13/5.65 (![Z,Y2]: (~x2(s(Z),s(Y2))|x2(Z,Y2)))&(![Z,Y2]: (x2(s(Z),s(Y2))|~x2(Z,Y2)))),
% 0.13/5.65 inference(miniscoping,[status(thm)],[f26])).
% 0.13/5.65 fof(f29,plain,(
% 0.13/5.65 ![X0,X1]: (x2(s(X0),s(X1))|~x2(X0,X1))),
% 0.13/5.65 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/5.65 fof(f31,plain,(
% 0.13/5.65 ![X0]: (x2(z,s(X0)))),
% 0.13/5.65 inference(cnf_transformation,[status(thm)],[f10])).
% 0.13/5.65 fof(f33,plain,(
% 0.13/5.65 ![X0]: (x(nil,X0)=X0)),
% 0.13/5.65 inference(cnf_transformation,[status(thm)],[f12])).
% 0.13/5.65 fof(f34,plain,(
% 0.13/5.65 ![X0,X1,X2]: (x(cons(X0,X1),X2)=cons(X0,x(X1,X2)))),
% 0.13/5.65 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/5.65 fof(f36,plain,(
% 0.13/5.65 ![X0,X1,X2]: (rotate(s(X0),cons(X1,X2))=rotate(X0,x(X2,cons(X1,nil))))),
% 0.13/5.65 inference(cnf_transformation,[status(thm)],[f15])).
% 0.13/5.65 fof(f37,plain,(
% 0.13/5.65 ![X0]: (rotate(z,X0)=X0)),
% 0.13/5.65 inference(cnf_transformation,[status(thm)],[f16])).
% 0.13/5.65 fof(f38,plain,(
% 0.13/5.65 (![N,M,Ys,Xs]: (~x2(N,length(Xs))|(~x2(M,length(Ys))|(~Xs=Ys|(rotate(s(z),Xs)=Xs|(~rotate(N,Xs)=rotate(M,Ys)|N=M))))))),
% 0.13/5.65 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.13/5.65 fof(f39,plain,(
% 0.13/5.65 ![N,Xs]: (~x2(N,length(Xs))|(![M,Ys]: (~x2(M,length(Ys))|(~Xs=Ys|(rotate(s(z),Xs)=Xs|(~rotate(N,Xs)=rotate(M,Ys)|N=M))))))),
% 0.13/5.65 inference(miniscoping,[status(thm)],[f38])).
% 0.13/5.65 fof(f40,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (~x2(X0,length(X1))|~x2(X2,length(X3))|~X1=X3|rotate(s(z),X1)=X1|~rotate(X0,X1)=rotate(X2,X3)|X0=X2)),
% 0.13/5.65 inference(cnf_transformation,[status(thm)],[f39])).
% 0.13/5.65 fof(f41,plain,(
% 0.13/5.65 ![X0,X1,X2]: (~x2(X0,length(X1))|~x2(X2,length(X1))|rotate(s(z),X1)=X1|~rotate(X0,X1)=rotate(X2,X1)|X0=X2)),
% 0.13/5.65 inference(destructive_equality_resolution,[status(thm)],[f40])).
% 0.13/5.65 fof(f47,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (~x2(X0,length(cons(X1,X2)))|~x2(X3,s(length(X2)))|rotate(s(z),cons(X1,X2))=cons(X1,X2)|~rotate(X0,cons(X1,X2))=rotate(X3,cons(X1,X2))|X0=X3)),
% 0.13/5.65 inference(paramodulation,[status(thm)],[f25,f41])).
% 0.13/5.65 fof(f49,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (~x2(X0,s(length(X1)))|~x2(X2,s(length(X1)))|rotate(s(z),cons(X3,X1))=cons(X3,X1)|~rotate(X0,cons(X3,X1))=rotate(X2,cons(X3,X1))|X0=X2)),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f25,f47])).
% 0.13/5.65 fof(f51,plain,(
% 0.13/5.65 ![X0]: (x2(s(z),s(s(X0))))),
% 0.13/5.65 inference(resolution,[status(thm)],[f31,f29])).
% 0.13/5.65 fof(f52,plain,(
% 0.13/5.65 ![X0,X1]: (rotate(s(z),cons(X0,X1))=x(X1,cons(X0,nil)))),
% 0.13/5.65 inference(paramodulation,[status(thm)],[f37,f36])).
% 0.13/5.65 fof(f53,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (rotate(s(X0),cons(X1,cons(X2,X3)))=rotate(X0,cons(X2,x(X3,cons(X1,nil)))))),
% 0.13/5.65 inference(paramodulation,[status(thm)],[f34,f36])).
% 0.13/5.65 fof(f57,plain,(
% 0.13/5.65 ![X0,X1,X2]: (~x2(X0,s(length(X1)))|rotate(s(z),cons(X2,X1))=cons(X2,X1)|~rotate(z,cons(X2,X1))=rotate(X0,cons(X2,X1))|z=X0)),
% 0.13/5.65 inference(resolution,[status(thm)],[f49,f31])).
% 0.13/5.65 fof(f64,plain,(
% 0.13/5.65 ![X0,X1,X2]: (~x2(X0,s(length(X1)))|rotate(s(z),cons(X2,X1))=cons(X2,X1)|~cons(X2,X1)=rotate(X0,cons(X2,X1))|z=X0)),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f37,f57])).
% 0.13/5.65 fof(f71,plain,(
% 0.13/5.65 ![X0]: (x2(s(s(z)),s(s(s(X0)))))),
% 0.13/5.65 inference(resolution,[status(thm)],[f51,f29])).
% 0.13/5.65 fof(f99,plain,(
% 0.13/5.65 ![X0,X1,X2]: (rotate(s(s(z)),cons(X0,cons(X1,X2)))=x(x(X2,cons(X0,nil)),cons(X1,nil)))),
% 0.13/5.65 inference(paramodulation,[status(thm)],[f52,f53])).
% 0.13/5.65 fof(f107,plain,(
% 0.13/5.65 ![X0,X1,X2]: (~x2(X0,s(length(X1)))|x(X1,cons(X2,nil))=cons(X2,X1)|~cons(X2,X1)=rotate(X0,cons(X2,X1))|z=X0)),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f52,f64])).
% 0.13/5.65 fof(f109,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (~x2(X0,s(s(length(X1))))|x(cons(X2,X1),cons(X3,nil))=cons(X3,cons(X2,X1))|~cons(X3,cons(X2,X1))=rotate(X0,cons(X3,cons(X2,X1)))|z=X0)),
% 0.13/5.65 inference(paramodulation,[status(thm)],[f25,f107])).
% 0.13/5.65 fof(f111,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (~x2(X0,s(s(length(X1))))|cons(X2,x(X1,cons(X3,nil)))=cons(X3,cons(X2,X1))|~cons(X3,cons(X2,X1))=rotate(X0,cons(X3,cons(X2,X1)))|z=X0)),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f34,f109])).
% 0.13/5.65 fof(f148,plain,(
% 0.13/5.65 ![X0,X1,X2,X3,X4]: (~x2(X0,s(s(s(length(X1)))))|cons(X2,x(cons(X3,X1),cons(X4,nil)))=cons(X4,cons(X2,cons(X3,X1)))|~cons(X4,cons(X2,cons(X3,X1)))=rotate(X0,cons(X4,cons(X2,cons(X3,X1))))|z=X0)),
% 0.13/5.65 inference(paramodulation,[status(thm)],[f25,f111])).
% 0.13/5.65 fof(f151,plain,(
% 0.13/5.65 ![X0,X1,X2,X3,X4]: (~x2(X0,s(s(s(length(X1)))))|cons(X2,cons(X3,x(X1,cons(X4,nil))))=cons(X4,cons(X2,cons(X3,X1)))|~cons(X4,cons(X2,cons(X3,X1)))=rotate(X0,cons(X4,cons(X2,cons(X3,X1))))|z=X0)),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f34,f148])).
% 0.13/5.65 fof(f272,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (cons(X0,cons(X1,x(X2,cons(X3,nil))))=cons(X3,cons(X0,cons(X1,X2)))|~cons(X3,cons(X0,cons(X1,X2)))=rotate(s(s(z)),cons(X3,cons(X0,cons(X1,X2))))|z=s(s(z)))),
% 0.13/5.65 inference(resolution,[status(thm)],[f151,f71])).
% 0.13/5.65 fof(f277,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (cons(X0,cons(X1,x(X2,cons(X3,nil))))=cons(X3,cons(X0,cons(X1,X2)))|~cons(X3,cons(X0,cons(X1,X2)))=x(x(cons(X1,X2),cons(X3,nil)),cons(X0,nil))|z=s(s(z)))),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f99,f272])).
% 0.13/5.65 fof(f278,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (cons(X0,cons(X1,x(X2,cons(X3,nil))))=cons(X3,cons(X0,cons(X1,X2)))|~cons(X3,cons(X0,cons(X1,X2)))=x(cons(X1,x(X2,cons(X3,nil))),cons(X0,nil))|z=s(s(z)))),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f34,f277])).
% 0.13/5.65 fof(f279,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (cons(X0,cons(X1,x(X2,cons(X3,nil))))=cons(X3,cons(X0,cons(X1,X2)))|~cons(X3,cons(X0,cons(X1,X2)))=cons(X1,x(x(X2,cons(X3,nil)),cons(X0,nil)))|z=s(s(z)))),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f34,f278])).
% 0.13/5.65 fof(f280,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (cons(X0,cons(X1,x(X2,cons(X3,nil))))=cons(X3,cons(X0,cons(X1,X2)))|~cons(X3,cons(X0,cons(X1,X2)))=cons(X1,x(x(X2,cons(X3,nil)),cons(X0,nil))))),
% 0.13/5.65 inference(forward_subsumption_resolution,[status(thm)],[f279,f23])).
% 0.13/5.65 fof(f821,plain,(
% 0.13/5.65 ![X0,X1,X2,X3,X4]: (cons(X0,cons(X1,x(cons(X2,X3),cons(X4,nil))))=cons(X4,cons(X0,cons(X1,cons(X2,X3))))|~cons(X4,cons(X0,cons(X1,cons(X2,X3))))=cons(X1,x(cons(X2,x(X3,cons(X4,nil))),cons(X0,nil))))),
% 0.13/5.65 inference(paramodulation,[status(thm)],[f34,f280])).
% 0.13/5.65 fof(f828,plain,(
% 0.13/5.65 ![X0,X1,X2,X3,X4]: (cons(X0,cons(X1,cons(X2,x(X3,cons(X4,nil)))))=cons(X4,cons(X0,cons(X1,cons(X2,X3))))|~cons(X4,cons(X0,cons(X1,cons(X2,X3))))=cons(X1,x(cons(X2,x(X3,cons(X4,nil))),cons(X0,nil))))),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f34,f821])).
% 0.13/5.65 fof(f829,plain,(
% 0.13/5.65 ![X0,X1,X2,X3,X4]: (cons(X0,cons(X1,cons(X2,x(X3,cons(X4,nil)))))=cons(X4,cons(X0,cons(X1,cons(X2,X3))))|~cons(X4,cons(X0,cons(X1,cons(X2,X3))))=cons(X1,cons(X2,x(x(X3,cons(X4,nil)),cons(X0,nil)))))),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f34,f828])).
% 0.13/5.65 fof(f1714,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (cons(X0,cons(X1,cons(X2,x(nil,cons(X3,nil)))))=cons(X3,cons(X0,cons(X1,cons(X2,nil))))|~cons(X3,cons(X0,cons(X1,cons(X2,nil))))=cons(X1,cons(X2,x(cons(X3,nil),cons(X0,nil)))))),
% 0.13/5.65 inference(paramodulation,[status(thm)],[f33,f829])).
% 0.13/5.65 fof(f1722,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (cons(X0,cons(X1,cons(X2,cons(X3,nil))))=cons(X3,cons(X0,cons(X1,cons(X2,nil))))|~cons(X3,cons(X0,cons(X1,cons(X2,nil))))=cons(X1,cons(X2,x(cons(X3,nil),cons(X0,nil)))))),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f33,f1714])).
% 0.13/5.65 fof(f1723,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (cons(X0,cons(X1,cons(X2,cons(X3,nil))))=cons(X3,cons(X0,cons(X1,cons(X2,nil))))|~cons(X3,cons(X0,cons(X1,cons(X2,nil))))=cons(X1,cons(X2,cons(X3,x(nil,cons(X0,nil))))))),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f34,f1722])).
% 0.13/5.65 fof(f1724,plain,(
% 0.13/5.65 ![X0,X1,X2,X3]: (cons(X0,cons(X1,cons(X2,cons(X3,nil))))=cons(X3,cons(X0,cons(X1,cons(X2,nil))))|~cons(X3,cons(X0,cons(X1,cons(X2,nil))))=cons(X1,cons(X2,cons(X3,cons(X0,nil)))))),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f33,f1723])).
% 0.13/5.65 fof(f3066,plain,(
% 0.13/5.65 ![X0,X1]: (cons(X0,cons(X1,cons(X0,cons(X1,nil))))=cons(X1,cons(X0,cons(X1,cons(X0,nil)))))),
% 0.13/5.65 inference(equality_resolution,[status(thm)],[f1724])).
% 0.13/5.65 fof(f3410,plain,(
% 0.13/5.65 ![X0,X1]: (head(cons(X0,cons(X1,cons(X0,cons(X1,nil)))))=X1)),
% 0.13/5.65 inference(paramodulation,[status(thm)],[f3066,f19])).
% 0.13/5.65 fof(f4813,plain,(
% 0.13/5.65 ![X0,X1]: (X0=X1)),
% 0.13/5.65 inference(forward_demodulation,[status(thm)],[f19,f3410])).
% 0.13/5.65 fof(f6148,plain,(
% 0.13/5.65 $false),
% 0.13/5.65 inference(backward_subsumption_resolution,[status(thm)],[f21,f4813])).
% 0.13/5.65 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/5.67 % Elapsed time: 0.288389 seconds
% 0.13/5.67 % CPU time: 2.052844 seconds
% 0.13/5.67 % Total memory used: 158.124 MB
% 0.13/5.67 % Net memory used: 155.591 MB
%------------------------------------------------------------------------------