%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWX222+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 03:13:50 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX222+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
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 10:35:27 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.41 fof(f26,axiom,(
% 0.13/0.41 (! [E] :( nf(lam(E))<=> nf(E) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f27,axiom,(
% 0.13/0.41 (! [X4] : nf(var(X4)) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f29,axiom,(
% 0.13/0.41 (! [Z,Xs] : index(cons(Z,Xs),zero) = just(Z) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f33,axiom,(
% 0.13/0.41 (! [X,E,Tx2,T1] :( tc(X,lam(E),arr(Tx2,T1))<=> tc(cons(Tx2,X),E,T1) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f35,axiom,(
% 0.13/0.41 (! [X,Z,X3,Tx3] :( index(X,X3) = just(Tx3)=> ( tc(X,var(X3),Z)<=> Tx3 = Z ) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f36,conjecture,(
% 0.13/0.41 (? [E] :( nf(E)& tc(nil,E,arr(a,arr(b,b))) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f37,negated_conjecture,(
% 0.13/0.41 ~((? [E] :( nf(E)& tc(nil,E,arr(a,arr(b,b))) ) ))),
% 0.13/0.41 inference(negated_conjecture,[status(cth)],[f36])).
% 0.13/0.41 fof(f68,plain,(
% 0.13/0.41 ![E]: ((~nf(lam(E))|nf(E))&(nf(lam(E))|~nf(E)))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f26])).
% 0.13/0.41 fof(f69,plain,(
% 0.13/0.41 (![E]: (~nf(lam(E))|nf(E)))&(![E]: (nf(lam(E))|~nf(E)))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f68])).
% 0.13/0.41 fof(f71,plain,(
% 0.13/0.41 ![X0]: (nf(lam(X0))|~nf(X0))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f69])).
% 0.13/0.41 fof(f72,plain,(
% 0.13/0.41 ![X0]: (nf(var(X0)))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.41 fof(f74,plain,(
% 0.13/0.41 ![X0,X1]: (index(cons(X0,X1),zero)=just(X0))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f29])).
% 0.13/0.41 fof(f84,plain,(
% 0.13/0.41 ![X,E,Tx2,T1]: ((~tc(X,lam(E),arr(Tx2,T1))|tc(cons(Tx2,X),E,T1))&(tc(X,lam(E),arr(Tx2,T1))|~tc(cons(Tx2,X),E,T1)))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f33])).
% 0.13/0.41 fof(f85,plain,(
% 0.13/0.41 (![X,E,Tx2,T1]: (~tc(X,lam(E),arr(Tx2,T1))|tc(cons(Tx2,X),E,T1)))&(![X,E,Tx2,T1]: (tc(X,lam(E),arr(Tx2,T1))|~tc(cons(Tx2,X),E,T1)))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f84])).
% 0.13/0.41 fof(f87,plain,(
% 0.13/0.41 ![X0,X1,X2,X3]: (tc(X0,lam(X1),arr(X2,X3))|~tc(cons(X2,X0),X1,X3))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f85])).
% 0.13/0.41 fof(f91,plain,(
% 0.13/0.41 ![X,Z,X3,Tx3]: (~index(X,X3)=just(Tx3)|(tc(X,var(X3),Z)<=>Tx3=Z))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f35])).
% 0.13/0.41 fof(f92,plain,(
% 0.13/0.41 ![X,Z,X3,Tx3]: (~index(X,X3)=just(Tx3)|((~tc(X,var(X3),Z)|Tx3=Z)&(tc(X,var(X3),Z)|~Tx3=Z)))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f91])).
% 0.13/0.41 fof(f93,plain,(
% 0.13/0.41 ![X,X3,Tx3]: (~index(X,X3)=just(Tx3)|((![Z]: (~tc(X,var(X3),Z)|Tx3=Z))&(![Z]: (tc(X,var(X3),Z)|~Tx3=Z))))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f92])).
% 0.13/0.41 fof(f95,plain,(
% 0.13/0.41 ![X0,X1,X2,X3]: (~index(X0,X1)=just(X2)|tc(X0,var(X1),X3)|~X2=X3)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f93])).
% 0.13/0.41 fof(f96,plain,(
% 0.13/0.41 (![E]: (~nf(E)|~tc(nil,E,arr(a,arr(b,b)))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.13/0.41 fof(f97,plain,(
% 0.13/0.41 ![X0]: (~nf(X0)|~tc(nil,X0,arr(a,arr(b,b))))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f96])).
% 0.13/0.41 fof(f98,plain,(
% 0.13/0.41 ![X0,X1,X2]: (~index(X0,X1)=just(X2)|tc(X0,var(X1),X2))),
% 0.13/0.41 inference(destructive_equality_resolution,[status(thm)],[f95])).
% 0.13/0.41 fof(f99,plain,(
% 0.13/0.41 ![X0]: (nf(lam(var(X0))))),
% 0.13/0.41 inference(resolution,[status(thm)],[f71,f72])).
% 0.13/0.41 fof(f101,plain,(
% 0.13/0.41 ![X0]: (nf(lam(lam(var(X0)))))),
% 0.13/0.41 inference(resolution,[status(thm)],[f99,f71])).
% 0.13/0.41 fof(f113,plain,(
% 0.13/0.41 ![X0,X1]: (tc(cons(X0,X1),var(zero),X0))),
% 0.13/0.41 inference(resolution,[status(thm)],[f98,f74])).
% 0.13/0.41 fof(f130,plain,(
% 0.13/0.41 ![X0,X1]: (tc(X0,lam(var(zero)),arr(X1,X1)))),
% 0.13/0.41 inference(resolution,[status(thm)],[f87,f113])).
% 0.13/0.41 fof(f155,plain,(
% 0.13/0.41 ![X0,X1,X2]: (tc(X0,lam(lam(var(zero))),arr(X1,arr(X2,X2))))),
% 0.13/0.41 inference(resolution,[status(thm)],[f130,f87])).
% 0.13/0.41 fof(f184,plain,(
% 0.13/0.41 ~nf(lam(lam(var(zero))))),
% 0.13/0.41 inference(resolution,[status(thm)],[f155,f97])).
% 0.13/0.41 fof(f188,plain,(
% 0.13/0.41 $false),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f184,f101])).
% 0.13/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.43 % Elapsed time: 0.065995 seconds
% 0.13/0.43 % CPU time: 0.168421 seconds
% 0.13/0.43 % Total memory used: 102.820 MB
% 0.13/0.43 % Net memory used: 102.666 MB
%------------------------------------------------------------------------------