%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWX197+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 : n015.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 : Theorem 91.49s 12.03s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX197+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n015.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 10:35:52 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 91.49/12.03 % Refutation found
% 91.49/12.03 % SZS status Theorem for theBenchmark: Theorem is valid
% 91.49/12.03 % SZS output start CNFRefutation for theBenchmark
% 91.49/12.03 fof(f2,axiom,(
% 91.49/12.03 (! [X] : zero != suc(X) )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f47,axiom,(
% 91.49/12.03 (! [C,Q,R] : opti2(if(C,Q,R)) = if(add(n(suc(zero)),C),R,Q) )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f48,axiom,(
% 91.49/12.03 (! [Y] : fetch(nil,Y) = zero )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f49,axiom,(
% 91.49/12.03 (! [N,St] : fetch(cons(N,St),zero) = N )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f51,axiom,(
% 91.49/12.03 (! [Y] : addNat(zero,Y) = Y )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f53,axiom,(
% 91.49/12.03 (! [Z,X2] : addNat(suc(Z),suc(X2)) = suc(addNat(Z,suc(X2))) )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f57,axiom,(
% 91.49/12.03 (! [X,N] : eval(X,n(N)) = N )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f58,axiom,(
% 91.49/12.03 (! [X,A,B] : eval(X,add(A,B)) = addNat(eval(X,A),eval(X,B)) )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f60,axiom,(
% 91.49/12.03 (! [X,A2,B3] :( eval(X,A2) = eval(X,B3)=> eval(X,eq(A2,B3)) = suc(zero) ) )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f63,axiom,(
% 91.49/12.03 (! [X] : run(X,nil2) = nil )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f64,axiom,(
% 91.49/12.03 (! [X,R,E] : run(X,cons2(print(E),R)) = cons(eval(X,E),run(X,R)) )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f66,axiom,(
% 91.49/12.03 (! [X,R,E3,P] : run(X,cons2(while(E3,P),R)) = run(X,cons2(if(E3,append(P,cons2(while(E3,P),nil2)),nil2),R)) )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f68,axiom,(
% 91.49/12.03 (! [X,R,E4,Q,Q2,X3] :( eval(X,E4) = suc(X3)=> run(X,cons2(if(E4,Q,Q2),R)) = run(X,append(Q,R)) ) )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f71,axiom,(
% 91.49/12.03 (! [Y] : append(nil2,Y) = Y )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f72,axiom,(
% 91.49/12.03 (! [Y,Z,Xs] : append(cons2(Z,Xs),Y) = cons2(Z,append(Xs,Y)) )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f74,conjecture,(
% 91.49/12.03 (? [P] : run(nil,cons2(P,nil2)) != run(nil,cons2(opti2(P),nil2)) )),
% 91.49/12.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 91.49/12.03 fof(f75,negated_conjecture,(
% 91.49/12.03 ~((? [P] : run(nil,cons2(P,nil2)) != run(nil,cons2(opti2(P),nil2)) ))),
% 91.49/12.03 inference(negated_conjecture,[status(cth)],[f74])).
% 91.49/12.03 fof(f77,plain,(
% 91.49/12.03 ![X0]: (~zero=suc(X0))),
% 91.49/12.03 inference(cnf_transformation,[status(thm)],[f2])).
% 91.49/12.03 fof(f123,plain,(
% 91.49/12.03 ![X0,X1,X2]: (opti2(if(X0,X1,X2))=if(add(n(suc(zero)),X0),X2,X1))),
% 91.49/12.03 inference(cnf_transformation,[status(thm)],[f47])).
% 91.49/12.03 fof(f124,plain,(
% 91.49/12.03 ![X0]: (fetch(nil,X0)=zero)),
% 91.49/12.03 inference(cnf_transformation,[status(thm)],[f48])).
% 91.49/12.03 fof(f125,plain,(
% 91.49/12.03 ![X0,X1]: (fetch(cons(X0,X1),zero)=X0)),
% 91.49/12.03 inference(cnf_transformation,[status(thm)],[f49])).
% 91.49/12.03 fof(f127,plain,(
% 91.49/12.03 ![X0]: (addNat(zero,X0)=X0)),
% 91.49/12.03 inference(cnf_transformation,[status(thm)],[f51])).
% 91.49/12.03 fof(f129,plain,(
% 91.49/12.03 ![X0,X1]: (addNat(suc(X0),suc(X1))=suc(addNat(X0,suc(X1))))),
% 91.49/12.03 inference(cnf_transformation,[status(thm)],[f53])).
% 91.49/12.03 fof(f133,plain,(
% 91.49/12.03 ![X0,X1]: (eval(X0,n(X1))=X1)),
% 91.49/12.03 inference(cnf_transformation,[status(thm)],[f57])).
% 91.49/12.03 fof(f134,plain,(
% 91.49/12.03 ![X0,X1,X2]: (eval(X0,add(X1,X2))=addNat(eval(X0,X1),eval(X0,X2)))),
% 91.49/12.03 inference(cnf_transformation,[status(thm)],[f58])).
% 91.49/12.03 fof(f136,plain,(
% 91.49/12.03 ![X,A2,B3]: (~eval(X,A2)=eval(X,B3)|eval(X,eq(A2,B3))=suc(zero))),
% 91.49/12.03 inference(pre_NNF_transformation,[status(thm)],[f60])).
% 91.49/12.03 fof(f137,plain,(
% 91.49/12.03 ![X0,X1,X2]: (~eval(X0,X1)=eval(X0,X2)|eval(X0,eq(X1,X2))=suc(zero))),
% 91.49/12.03 inference(cnf_transformation,[status(thm)],[f136])).
% 91.49/12.03 fof(f141,plain,(
% 91.49/12.03 ![X0]: (run(X0,nil2)=nil)),
% 91.49/12.03 inference(cnf_transformation,[status(thm)],[f63])).
% 91.49/12.03 fof(f142,plain,(
% 91.49/12.03 ![X0,X1,X2]: (run(X0,cons2(print(X1),X2))=cons(eval(X0,X1),run(X0,X2)))),
% 91.49/12.03 inference(cnf_transformation,[status(thm)],[f64])).
% 91.49/12.03 fof(f144,plain,(
% 91.49/12.03 ![X0,X1,X2,X3]: (run(X0,cons2(while(X1,X2),X3))=run(X0,cons2(if(X1,append(X2,cons2(while(X1,X2),nil2)),nil2),X3)))),
% 91.49/12.05 inference(cnf_transformation,[status(thm)],[f66])).
% 91.49/12.05 fof(f148,plain,(
% 91.49/12.05 ![X,R,E4,Q,Q2,X3]: (~eval(X,E4)=suc(X3)|run(X,cons2(if(E4,Q,Q2),R))=run(X,append(Q,R)))),
% 91.49/12.05 inference(pre_NNF_transformation,[status(thm)],[f68])).
% 91.49/12.05 fof(f149,plain,(
% 91.49/12.05 ![X,E4]: ((![X3]: ~eval(X,E4)=suc(X3))|(![R,Q,Q2]: run(X,cons2(if(E4,Q,Q2),R))=run(X,append(Q,R))))),
% 91.49/12.05 inference(miniscoping,[status(thm)],[f148])).
% 91.49/12.05 fof(f150,plain,(
% 91.49/12.05 ![X0,X1,X2,X3,X4,X5]: (~eval(X0,X1)=suc(X2)|run(X0,cons2(if(X1,X3,X4),X5))=run(X0,append(X3,X5)))),
% 91.49/12.05 inference(cnf_transformation,[status(thm)],[f149])).
% 91.49/12.05 fof(f153,plain,(
% 91.49/12.05 ![X0]: (append(nil2,X0)=X0)),
% 91.49/12.05 inference(cnf_transformation,[status(thm)],[f71])).
% 91.49/12.05 fof(f154,plain,(
% 91.49/12.05 ![X0,X1,X2]: (append(cons2(X0,X1),X2)=cons2(X0,append(X1,X2)))),
% 91.49/12.05 inference(cnf_transformation,[status(thm)],[f72])).
% 91.49/12.05 fof(f156,plain,(
% 91.49/12.05 (![P]: run(nil,cons2(P,nil2))=run(nil,cons2(opti2(P),nil2)))),
% 91.49/12.05 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 91.49/12.05 fof(f157,plain,(
% 91.49/12.05 ![X0]: (run(nil,cons2(X0,nil2))=run(nil,cons2(opti2(X0),nil2)))),
% 91.49/12.05 inference(cnf_transformation,[status(thm)],[f156])).
% 91.49/12.05 fof(f1217,plain,(
% 91.49/12.05 ![X0]: (addNat(suc(zero),suc(X0))=suc(suc(X0)))),
% 91.49/12.05 inference(paramodulation,[status(thm)],[f127,f129])).
% 91.49/12.05 fof(f1396,plain,(
% 91.49/12.05 ![X0,X1]: (append(cons2(X0,nil2),X1)=cons2(X0,X1))),
% 91.49/12.05 inference(paramodulation,[status(thm)],[f153,f154])).
% 91.49/12.05 fof(f1443,plain,(
% 91.49/12.05 ![X0,X1,X2]: (append(cons2(X0,cons2(X1,nil2)),X2)=cons2(X0,cons2(X1,X2)))),
% 91.49/12.05 inference(paramodulation,[status(thm)],[f1396,f154])).
% 91.49/12.05 fof(f1578,plain,(
% 91.49/12.05 ![X0,X1,X2]: (eval(X0,add(n(X1),X2))=addNat(X1,eval(X0,X2)))),
% 91.49/12.05 inference(paramodulation,[status(thm)],[f133,f134])).
% 91.49/12.05 fof(f1811,plain,(
% 91.49/12.05 ![X0,X1]: (eval(X0,eq(X1,n(eval(X0,X1))))=suc(zero))),
% 91.49/12.05 inference(resolution,[status(thm)],[f137,f133])).
% 91.49/12.05 fof(f1816,plain,(
% 91.49/12.05 ![X0,X1]: (eval(X0,eq(X1,X1))=suc(zero))),
% 91.49/12.05 inference(equality_resolution,[status(thm)],[f137])).
% 91.49/12.05 fof(f1878,plain,(
% 91.49/12.05 ![X0,X1,X2]: (fetch(run(X0,cons2(print(X1),X2)),zero)=eval(X0,X1))),
% 91.49/12.05 inference(paramodulation,[status(thm)],[f142,f125])).
% 91.49/12.05 fof(f2518,plain,(
% 91.49/12.05 ![X0,X1,X2,X3,X4]: (~eval(X0,X1)=suc(X2)|run(X0,cons2(while(X1,X3),X4))=run(X0,append(append(X3,cons2(while(X1,X3),nil2)),X4)))),
% 91.49/12.05 inference(paramodulation,[status(thm)],[f144,f150])).
% 91.49/12.05 fof(f2521,plain,(
% 91.49/12.05 ![X0,X1,X2,X3,X4,X5]: (~eval(X0,add(n(suc(zero)),X1))=suc(X2)|run(X0,cons2(opti2(if(X1,X3,X4)),X5))=run(X0,append(X4,X5)))),
% 91.49/12.05 inference(paramodulation,[status(thm)],[f123,f150])).
% 91.49/12.05 fof(f2560,plain,(
% 91.49/12.05 ![X0,X1,X2,X3,X4,X5]: (~addNat(suc(zero),eval(X0,X1))=suc(X2)|run(X0,cons2(opti2(if(X1,X3,X4)),X5))=run(X0,append(X4,X5)))),
% 91.49/12.05 inference(forward_demodulation,[status(thm)],[f1578,f2521])).
% 91.49/12.05 fof(f2710,plain,(
% 91.49/12.05 ![X0,X1,X2,X3]: (~addNat(suc(zero),eval(nil,X0))=suc(X1)|run(nil,cons2(if(X0,X2,X3),nil2))=run(nil,append(X3,nil2)))),
% 91.49/12.05 inference(paramodulation,[status(thm)],[f157,f2560])).
% 91.49/12.05 fof(f3331,plain,(
% 91.49/12.05 ![X0,X1,X2]: (~addNat(suc(zero),eval(nil,X0))=suc(X1)|run(nil,cons2(while(X0,X2),nil2))=run(nil,append(nil2,nil2)))),
% 91.49/12.05 inference(paramodulation,[status(thm)],[f144,f2710])).
% 91.49/12.05 fof(f3369,plain,(
% 91.49/12.05 ![X0,X1,X2]: (~addNat(suc(zero),eval(nil,X0))=suc(X1)|run(nil,cons2(while(X0,X2),nil2))=run(nil,nil2))),
% 91.49/12.05 inference(forward_demodulation,[status(thm)],[f153,f3331])).
% 91.49/12.05 fof(f3370,plain,(
% 91.49/12.05 ![X0,X1,X2]: (~addNat(suc(zero),eval(nil,X0))=suc(X1)|run(nil,cons2(while(X0,X2),nil2))=nil)),
% 91.49/12.05 inference(forward_demodulation,[status(thm)],[f141,f3369])).
% 91.49/12.05 fof(f22772,plain,(
% 91.49/12.05 ![X0,X1,X2,X3]: (run(X0,cons2(while(eq(X1,X1),X2),X3))=run(X0,append(append(X2,cons2(while(eq(X1,X1),X2),nil2)),X3)))),
% 91.49/12.05 inference(resolution,[status(thm)],[f1816,f2518])).
% 91.49/12.05 fof(f24475,plain,(
% 91.49/12.05 ![X0,X1,X2,X3]: (run(X0,cons2(while(eq(X1,X1),cons2(X2,nil2)),X3))=run(X0,append(cons2(X2,cons2(while(eq(X1,X1),cons2(X2,nil2)),nil2)),X3)))),
% 91.49/12.05 inference(paramodulation,[status(thm)],[f1396,f22772])).
% 91.49/12.05 fof(f24522,plain,(
% 91.49/12.05 ![X0,X1,X2,X3]: (run(X0,cons2(while(eq(X1,X1),cons2(X2,nil2)),X3))=run(X0,cons2(X2,cons2(while(eq(X1,X1),cons2(X2,nil2)),X3))))),
% 91.49/12.05 inference(forward_demodulation,[status(thm)],[f1443,f24475])).
% 91.49/12.05 fof(f37056,plain,(
% 91.49/12.05 ![X0,X1,X2]: (~addNat(suc(zero),suc(zero))=suc(X0)|run(nil,cons2(while(eq(X1,X1),X2),nil2))=nil)),
% 89.40/12.17 inference(paramodulation,[status(thm)],[f1816,f3370])).
% 89.40/12.17 fof(f37066,definition,(
% 89.40/12.17 ![X0]: (sQ127_spl <=> (~addNat(suc(zero),suc(zero))=suc(X0)))),
% 89.40/12.17 introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition])).
% 89.40/12.17 fof(f37067,plain,(
% 89.40/12.17 ![X0]: (~addNat(suc(zero),suc(zero))=suc(X0)|~sQ127_spl)),
% 89.40/12.17 inference(component_clause,[status(thm)],[f37066])).
% 89.40/12.17 fof(f37077,definition,(
% 89.40/12.17 ![X1,X2]: (sQ130_spl <=> (run(nil,cons2(while(eq(X1,X1),X2),nil2))=nil))),
% 89.40/12.17 introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition])).
% 89.40/12.17 fof(f37078,plain,(
% 89.40/12.17 ![X0,X1]: (run(nil,cons2(while(eq(X0,X0),X1),nil2))=nil|~sQ130_spl)),
% 89.40/12.17 inference(component_clause,[status(thm)],[f37077])).
% 89.40/12.17 fof(f37080,plain,(
% 89.40/12.17 sQ127_spl|sQ130_spl),
% 89.40/12.17 inference(split_clause,[status(thm)],[f37056,f37066,f37077])).
% 89.40/12.17 fof(f37085,plain,(
% 89.40/12.17 ![X0]: (~suc(suc(zero))=suc(X0)|~sQ127_spl)),
% 89.40/12.17 inference(forward_demodulation,[status(thm)],[f1217,f37067])).
% 89.40/12.17 fof(f37092,plain,(
% 89.40/12.17 $false|~sQ127_spl),
% 89.40/12.17 inference(equality_resolution,[status(thm)],[f37085])).
% 89.40/12.17 fof(f37093,plain,(
% 89.40/12.17 ~sQ127_spl),
% 89.40/12.17 inference(contradiction_clause,[status(thm)],[f37092])).
% 89.40/12.17 fof(f46521,plain,(
% 89.40/12.17 ![X0,X1,X2,X3]: (fetch(run(X0,cons2(while(eq(X1,X1),cons2(print(X2),nil2)),X3)),zero)=eval(X0,X2))),
% 89.40/12.17 inference(paramodulation,[status(thm)],[f24522,f1878])).
% 89.40/12.17 fof(f46846,plain,(
% 89.40/12.17 ![X0]: (fetch(nil,zero)=eval(nil,X0)|~sQ130_spl)),
% 89.40/12.17 inference(paramodulation,[status(thm)],[f37078,f46521])).
% 89.40/12.17 fof(f46861,plain,(
% 89.40/12.17 ![X0]: (zero=eval(nil,X0)|~sQ130_spl)),
% 89.40/12.17 inference(forward_demodulation,[status(thm)],[f124,f46846])).
% 89.40/12.17 fof(f47017,plain,(
% 89.40/12.17 ![X0]: (eval(nil,eq(X0,n(zero)))=suc(zero)|~sQ130_spl)),
% 89.40/12.17 inference(paramodulation,[status(thm)],[f46861,f1811])).
% 89.40/12.17 fof(f47132,plain,(
% 89.40/12.17 zero=suc(zero)|~sQ130_spl),
% 89.40/12.17 inference(forward_demodulation,[status(thm)],[f46861,f47017])).
% 89.40/12.17 fof(f47133,plain,(
% 89.40/12.17 $false|~sQ130_spl),
% 89.40/12.17 inference(forward_subsumption_resolution,[status(thm)],[f47132,f77])).
% 89.40/12.17 fof(f47134,plain,(
% 89.40/12.17 ~sQ130_spl),
% 89.40/12.17 inference(contradiction_clause,[status(thm)],[f47133])).
% 89.40/12.17 fof(f47135,plain,(
% 89.40/12.17 $false),
% 89.40/12.17 inference(sat_refutation,[status(thm)],[f37080,f37093,f47134])).
% 89.40/12.17 % SZS output end CNFRefutation for theBenchmark.p
% 37.70/12.28 % Elapsed time: 11.825054 seconds
% 37.70/12.28 % CPU time: 93.171978 seconds
% 37.70/12.28 % Total memory used: 1.557 GB
% 37.70/12.28 % Net memory used: 1.527 GB
%------------------------------------------------------------------------------