%---------------- iProver v3.0 (CASC-27) ----------------% ------ iProver source info git: date: 2019-08-21 14:25:56 +0100 git: sha1: aef4729e525848973f587b098cdb2be67e368c05 git: non_committed_changes: true git: last_make_outside_of_git: false ------ Parsing... ------ Clausification by vclausify_rel & Parsing by iProver... ------ Preprocessing... sf_s rm: 1 0s sf_e ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e ------ Proving... ------ Problem Properties clauses 27 conjectures 12 EPR 8 Horn 23 unary 11 binary 4 lits 68 lits eq 16 ------ Input Options Time Limit: Unbounded ------ Current options: ------ Proving... % SZS status Theorem for HL400543+2.p % SZS output start CNFRefutation for HL400543+2.p fof(f27,conjecture,( ! [X8] : (ne(X8) => ! [X10] : (ne(X10) => ! [X18] : (mem(X18,X10) => ! [X19] : (mem(X19,arr(X8,X10)) => ! [X20] : (mem(X20,ty_2Eoption_2Eoption(X8)) => ! [X21] : (mem(X21,ty_2Eoption_2Eoption(X8)) => ! [X22] : (mem(X22,X10) => ! [X23] : (mem(X23,arr(X8,X10)) => ((! [X24] : (mem(X24,X8) => (ap(c_2Eoption_2ESOME(X8),X24) = X21 => ap(X19,X24) = ap(X23,X24))) & (c_2Eoption_2ENONE(X8) = X21 => X18 = X22) & X20 = X21) => ap(ap(ap(c_2Eoption_2Eoption__CASE(X8,X8),X20),X22),X23) = ap(ap(ap(c_2Eoption_2Eoption__CASE(X8,X8),X21),X18),X19))))))))))), file('/export/starexec/sandbox/benchmark/Problems/HL400543+2.p',unknown)). fof(f28,negated_conjecture,( ~! [X8] : (ne(X8) => ! [X10] : (ne(X10) => ! [X18] : (mem(X18,X10) => ! [X19] : (mem(X19,arr(X8,X10)) => ! [X20] : (mem(X20,ty_2Eoption_2Eoption(X8)) => ! [X21] : (mem(X21,ty_2Eoption_2Eoption(X8)) => ! [X22] : (mem(X22,X10) => ! [X23] : (mem(X23,arr(X8,X10)) => ((! [X24] : (mem(X24,X8) => (ap(c_2Eoption_2ESOME(X8),X24) = X21 => ap(X19,X24) = ap(X23,X24))) & (c_2Eoption_2ENONE(X8) = X21 => X18 = X22) & X20 = X21) => ap(ap(ap(c_2Eoption_2Eoption__CASE(X8,X8),X20),X22),X23) = ap(ap(ap(c_2Eoption_2Eoption__CASE(X8,X8),X21),X18),X19))))))))))), inference(negated_conjecture,[],[f27])). fof(f30,plain,( ~! [X0] : (ne(X0) => ! [X1] : (ne(X1) => ! [X2] : (mem(X2,X1) => ! [X3] : (mem(X3,arr(X0,X1)) => ! [X4] : (mem(X4,ty_2Eoption_2Eoption(X0)) => ! [X5] : (mem(X5,ty_2Eoption_2Eoption(X0)) => ! [X6] : (mem(X6,X1) => ! [X7] : (mem(X7,arr(X0,X1)) => ((! [X8] : (mem(X8,X0) => (ap(c_2Eoption_2ESOME(X0),X8) = X5 => ap(X3,X8) = ap(X7,X8))) & (c_2Eoption_2ENONE(X0) = X5 => X2 = X6) & X4 = X5) => ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) = ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3))))))))))), inference(rectify,[],[f28])). fof(f40,plain,( ? [X0] : (? [X1] : (? [X2] : (? [X3] : (? [X4] : (? [X5] : (? [X6] : (? [X7] : ((ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & (! [X8] : ((ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5) | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5)) & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(X0))) & mem(X4,ty_2Eoption_2Eoption(X0))) & mem(X3,arr(X0,X1))) & mem(X2,X1)) & ne(X1)) & ne(X0))), inference(ennf_transformation,[],[f30])). fof(f41,plain,( ? [X0] : (? [X1] : (? [X2] : (? [X3] : (? [X4] : (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(X0))) & mem(X4,ty_2Eoption_2Eoption(X0))) & mem(X3,arr(X0,X1))) & mem(X2,X1)) & ne(X1)) & ne(X0))), inference(flattening,[],[f40])). fof(f62,plain,( ( ! [X6,X4,X2,X0,X5,X3,X1] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) => (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),sK8) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(sK8,X8) = ap(X3,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(sK8,arr(X0,X1)))) )), introduced(choice_axiom,[])). fof(f61,plain,( ( ! [X4,X2,X0,X5,X3,X1] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) & mem(X6,X1)) => (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),sK7),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (sK7 = X2 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) & mem(sK7,X1))) )), introduced(choice_axiom,[])). fof(f60,plain,( ( ! [X4,X2,X0,X3,X1] : (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(X0))) => (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),sK6),X2),X3) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != sK6 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != sK6) & sK6 = X4 & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(sK6,ty_2Eoption_2Eoption(X0)))) )), introduced(choice_axiom,[])). fof(f59,plain,( ( ! [X2,X0,X3,X1] : (? [X4] : (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(X0))) & mem(X4,ty_2Eoption_2Eoption(X0))) => (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),sK5),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & sK5 = X5 & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(X0))) & mem(sK5,ty_2Eoption_2Eoption(X0)))) )), introduced(choice_axiom,[])). fof(f58,plain,( ( ! [X2,X0,X1] : (? [X3] : (? [X4] : (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(X0))) & mem(X4,ty_2Eoption_2Eoption(X0))) & mem(X3,arr(X0,X1))) => (? [X4] : (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),sK4) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) & ! [X8] : (ap(sK4,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(X0))) & mem(X4,ty_2Eoption_2Eoption(X0))) & mem(sK4,arr(X0,X1)))) )), introduced(choice_axiom,[])). fof(f57,plain,( ( ! [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(X0))) & mem(X4,ty_2Eoption_2Eoption(X0))) & mem(X3,arr(X0,X1))) & mem(X2,X1)) => (? [X3] : (? [X4] : (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),sK3),X3) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (sK3 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(X0))) & mem(X4,ty_2Eoption_2Eoption(X0))) & mem(X3,arr(X0,X1))) & mem(sK3,X1))) )), introduced(choice_axiom,[])). fof(f56,plain,( ( ! [X0] : (? [X1] : (? [X2] : (? [X3] : (? [X4] : (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(X0))) & mem(X4,ty_2Eoption_2Eoption(X0))) & mem(X3,arr(X0,X1))) & mem(X2,X1)) & ne(X1)) => (? [X2] : (? [X3] : (? [X4] : (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,sK2))) & mem(X6,sK2)) & mem(X5,ty_2Eoption_2Eoption(X0))) & mem(X4,ty_2Eoption_2Eoption(X0))) & mem(X3,arr(X0,sK2))) & mem(X2,sK2)) & ne(sK2))) )), introduced(choice_axiom,[])). fof(f55,plain,( ? [X0] : (? [X1] : (? [X2] : (? [X3] : (? [X4] : (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(X0),X8) != X5 | ~mem(X8,X0)) & (X2 = X6 | c_2Eoption_2ENONE(X0) != X5) & X4 = X5 & mem(X7,arr(X0,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(X0))) & mem(X4,ty_2Eoption_2Eoption(X0))) & mem(X3,arr(X0,X1))) & mem(X2,X1)) & ne(X1)) & ne(X0)) => (? [X1] : (? [X2] : (? [X3] : (? [X4] : (? [X5] : (? [X6] : (? [X7] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),X4),X6),X7) != ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),X5),X2),X3) & ! [X8] : (ap(X3,X8) = ap(X7,X8) | ap(c_2Eoption_2ESOME(sK1),X8) != X5 | ~mem(X8,sK1)) & (X2 = X6 | c_2Eoption_2ENONE(sK1) != X5) & X4 = X5 & mem(X7,arr(sK1,X1))) & mem(X6,X1)) & mem(X5,ty_2Eoption_2Eoption(sK1))) & mem(X4,ty_2Eoption_2Eoption(sK1))) & mem(X3,arr(sK1,X1))) & mem(X2,X1)) & ne(X1)) & ne(sK1))), introduced(choice_axiom,[])). fof(f63,plain,( (((((((ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK8) != ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK6),sK3),sK4) & ! [X8] : (ap(sK4,X8) = ap(sK8,X8) | ap(c_2Eoption_2ESOME(sK1),X8) != sK6 | ~mem(X8,sK1)) & (sK3 = sK7 | c_2Eoption_2ENONE(sK1) != sK6) & sK5 = sK6 & mem(sK8,arr(sK1,sK2))) & mem(sK7,sK2)) & mem(sK6,ty_2Eoption_2Eoption(sK1))) & mem(sK5,ty_2Eoption_2Eoption(sK1))) & mem(sK4,arr(sK1,sK2))) & mem(sK3,sK2)) & ne(sK2)) & ne(sK1)), inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f41,f62,f61,f60,f59,f58,f57,f56,f55])). fof(f74,plain,( mem(sK6,ty_2Eoption_2Eoption(sK1))), inference(cnf_transformation,[],[f63])). fof(f25,axiom,( ! [X8] : (ne(X8) => ! [X11] : (mem(X11,ty_2Eoption_2Eoption(X8)) => (? [X12] : (ap(c_2Eoption_2ESOME(X8),X12) = X11 & mem(X12,X8)) | c_2Eoption_2ENONE(X8) = X11)))), file('/export/starexec/sandbox/benchmark/Problems/HL400543+2.p',unknown)). fof(f29,plain,( ! [X0] : (ne(X0) => ! [X1] : (mem(X1,ty_2Eoption_2Eoption(X0)) => (? [X2] : (ap(c_2Eoption_2ESOME(X0),X2) = X1 & mem(X2,X0)) | c_2Eoption_2ENONE(X0) = X1)))), inference(rectify,[],[f25])). fof(f38,plain,( ! [X0] : (! [X1] : ((? [X2] : (ap(c_2Eoption_2ESOME(X0),X2) = X1 & mem(X2,X0)) | c_2Eoption_2ENONE(X0) = X1) | ~mem(X1,ty_2Eoption_2Eoption(X0))) | ~ne(X0))), inference(ennf_transformation,[],[f29])). fof(f39,plain,( ! [X0] : (! [X1] : (? [X2] : (ap(c_2Eoption_2ESOME(X0),X2) = X1 & mem(X2,X0)) | c_2Eoption_2ENONE(X0) = X1 | ~mem(X1,ty_2Eoption_2Eoption(X0))) | ~ne(X0))), inference(flattening,[],[f38])). fof(f53,plain,( ! [X1,X0] : (? [X2] : (ap(c_2Eoption_2ESOME(X0),X2) = X1 & mem(X2,X0)) => (ap(c_2Eoption_2ESOME(X0),sK0(X0,X1)) = X1 & mem(sK0(X0,X1),X0)))), introduced(choice_axiom,[])). fof(f54,plain,( ! [X0] : (! [X1] : ((ap(c_2Eoption_2ESOME(X0),sK0(X0,X1)) = X1 & mem(sK0(X0,X1),X0)) | c_2Eoption_2ENONE(X0) = X1 | ~mem(X1,ty_2Eoption_2Eoption(X0))) | ~ne(X0))), inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f39,f53])). fof(f68,plain,( ( ! [X0,X1] : (ap(c_2Eoption_2ESOME(X0),sK0(X0,X1)) = X1 | c_2Eoption_2ENONE(X0) = X1 | ~mem(X1,ty_2Eoption_2Eoption(X0)) | ~ne(X0)) )), inference(cnf_transformation,[],[f54])). fof(f69,plain,( ne(sK1)), inference(cnf_transformation,[],[f63])). fof(f67,plain,( ( ! [X0,X1] : (mem(sK0(X0,X1),X0) | c_2Eoption_2ENONE(X0) = X1 | ~mem(X1,ty_2Eoption_2Eoption(X0)) | ~ne(X0)) )), inference(cnf_transformation,[],[f54])). fof(f75,plain,( mem(sK7,sK2)), inference(cnf_transformation,[],[f63])). fof(f76,plain,( mem(sK8,arr(sK1,sK2))), inference(cnf_transformation,[],[f63])). fof(f26,axiom,( ! [X8] : (ne(X8) => ! [X10] : (ne(X10) => (! [X15] : (mem(X15,X8) => ! [X16] : (mem(X16,X10) => ! [X17] : (mem(X17,arr(X8,X10)) => ap(X17,X15) = ap(ap(ap(c_2Eoption_2Eoption__CASE(X8,X8),ap(c_2Eoption_2ESOME(X8),X15)),X16),X17)))) & ! [X13] : (mem(X13,X10) => ! [X14] : (mem(X14,arr(X8,X10)) => ap(ap(ap(c_2Eoption_2Eoption__CASE(X8,X8),c_2Eoption_2ENONE(X8)),X13),X14) = X13)))))), file('/export/starexec/sandbox/benchmark/Problems/HL400543+2.p',unknown)). fof(f32,plain,( ! [X0] : (ne(X0) => ! [X1] : (ne(X1) => (! [X2] : (mem(X2,X0) => ! [X3] : (mem(X3,X1) => ! [X4] : (mem(X4,arr(X0,X1)) => ap(X4,X2) = ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),ap(c_2Eoption_2ESOME(X0),X2)),X3),X4)))) & ! [X5] : (mem(X5,X1) => ! [X6] : (mem(X6,arr(X0,X1)) => ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),c_2Eoption_2ENONE(X0)),X5),X6) = X5)))))), inference(rectify,[],[f26])). fof(f45,plain,( ! [X0] : (! [X1] : ((! [X2] : (! [X3] : (! [X4] : (ap(X4,X2) = ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),ap(c_2Eoption_2ESOME(X0),X2)),X3),X4) | ~mem(X4,arr(X0,X1))) | ~mem(X3,X1)) | ~mem(X2,X0)) & ! [X5] : (! [X6] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),c_2Eoption_2ENONE(X0)),X5),X6) = X5 | ~mem(X6,arr(X0,X1))) | ~mem(X5,X1))) | ~ne(X1)) | ~ne(X0))), inference(ennf_transformation,[],[f32])). fof(f85,plain,( ( ! [X4,X2,X0,X3,X1] : (ap(X4,X2) = ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),ap(c_2Eoption_2ESOME(X0),X2)),X3),X4) | ~mem(X4,arr(X0,X1)) | ~mem(X3,X1) | ~mem(X2,X0) | ~ne(X1) | ~ne(X0)) )), inference(cnf_transformation,[],[f45])). fof(f70,plain,( ne(sK2)), inference(cnf_transformation,[],[f63])). fof(f71,plain,( mem(sK3,sK2)), inference(cnf_transformation,[],[f63])). fof(f72,plain,( mem(sK4,arr(sK1,sK2))), inference(cnf_transformation,[],[f63])). fof(f77,plain,( sK5 = sK6), inference(cnf_transformation,[],[f63])). fof(f80,plain,( ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK8) != ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK6),sK3),sK4)), inference(cnf_transformation,[],[f63])). fof(f79,plain,( ( ! [X8] : (ap(sK4,X8) = ap(sK8,X8) | ap(c_2Eoption_2ESOME(sK1),X8) != sK6 | ~mem(X8,sK1)) )), inference(cnf_transformation,[],[f63])). fof(f84,plain,( ( ! [X6,X0,X5,X1] : (ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),c_2Eoption_2ENONE(X0)),X5),X6) = X5 | ~mem(X6,arr(X0,X1)) | ~mem(X5,X1) | ~ne(X1) | ~ne(X0)) )), inference(cnf_transformation,[],[f45])). fof(f78,plain,( sK3 = sK7 | c_2Eoption_2ENONE(sK1) != sK6), inference(cnf_transformation,[],[f63])). cnf(c_8,negated_conjecture, ( mem(sK6,ty_2Eoption_2Eoption(sK1)) ), inference(cnf_transformation,[],[f74]) ). cnf(c_230,negated_conjecture, ( mem(sK6,ty_2Eoption_2Eoption(sK1)) ), inference(subtyping,[status(esa)],[c_8]) ). cnf(c_589,plain, ( mem(sK6,ty_2Eoption_2Eoption(sK1)) = iProver_top ), inference(predicate_to_equality,[status(thm)],[c_230]) ). cnf(c_645,plain, ( mem(sK5,ty_2Eoption_2Eoption(sK1)) = iProver_top ), inference(light_normalisation,[status(thm)],[c_589]) ). cnf(c_0,plain, ( ~ mem(X0,ty_2Eoption_2Eoption(X1)) | ~ ne(X1) | X0 = ap(c_2Eoption_2ESOME(X1),sK0(X1,X0)) | X0 = c_2Eoption_2ENONE(X1) ), inference(cnf_transformation,[],[f68]) ). cnf(c_238,plain, ( ~ mem(X0,ty_2Eoption_2Eoption(X0)) | ~ ne(X0) | X0 = ap(c_2Eoption_2ESOME(X0),sK0(X0,X0)) | X0 = c_2Eoption_2ENONE(X0) ), inference(subtyping,[status(esa)],[c_0]) ). cnf(c_584,plain, ( X0 = ap(c_2Eoption_2ESOME(X0),sK0(X0,X0)) | X0 = c_2Eoption_2ENONE(X0) | mem(X0,ty_2Eoption_2Eoption(X0)) != iProver_top | ne(X0) != iProver_top ), inference(predicate_to_equality,[status(thm)],[c_238]) ). cnf(c_1224,plain, ( sK5 = ap(c_2Eoption_2ESOME(sK1),sK0(sK1,sK5)) | sK5 = c_2Eoption_2ENONE(sK1) | ne(sK1) != iProver_top ), inference(superposition,[status(thm)],[c_645,c_584]) ). cnf(c_13,negated_conjecture, ( ne(sK1) ), inference(cnf_transformation,[],[f69]) ). cnf(c_27,plain, ( ne(sK1) = iProver_top ), inference(predicate_to_equality,[status(thm)],[c_13]) ). cnf(c_1705,plain, ( sK5 = c_2Eoption_2ENONE(sK1) | sK5 = ap(c_2Eoption_2ESOME(sK1),sK0(sK1,sK5)) ), inference(global_propositional_subsumption, [status(thm)], [c_1224,c_27]) ). cnf(c_1706,plain, ( sK5 = ap(c_2Eoption_2ESOME(sK1),sK0(sK1,sK5)) | sK5 = c_2Eoption_2ENONE(sK1) ), inference(renaming,[status(thm)],[c_1705]) ). cnf(c_1,plain, ( ~ mem(X0,ty_2Eoption_2Eoption(X1)) | mem(sK0(X1,X0),X1) | ~ ne(X1) | X0 = c_2Eoption_2ENONE(X1) ), inference(cnf_transformation,[],[f67]) ). cnf(c_237,plain, ( ~ mem(X0,ty_2Eoption_2Eoption(X0)) | mem(sK0(X0,X0),X0) | ~ ne(X0) | X0 = c_2Eoption_2ENONE(X0) ), inference(subtyping,[status(esa)],[c_1]) ). cnf(c_585,plain, ( X0 = c_2Eoption_2ENONE(X0) | mem(X0,ty_2Eoption_2Eoption(X0)) != iProver_top | mem(sK0(X0,X0),X0) = iProver_top | ne(X0) != iProver_top ), inference(predicate_to_equality,[status(thm)],[c_237]) ). cnf(c_1834,plain, ( sK5 = c_2Eoption_2ENONE(sK1) | mem(sK0(sK1,sK5),sK1) = iProver_top | ne(sK1) != iProver_top ), inference(superposition,[status(thm)],[c_645,c_585]) ). cnf(c_2450,plain, ( mem(sK0(sK1,sK5),sK1) = iProver_top | sK5 = c_2Eoption_2ENONE(sK1) ), inference(global_propositional_subsumption, [status(thm)], [c_1834,c_27]) ). cnf(c_2451,plain, ( sK5 = c_2Eoption_2ENONE(sK1) | mem(sK0(sK1,sK5),sK1) = iProver_top ), inference(renaming,[status(thm)],[c_2450]) ). cnf(c_7,negated_conjecture, ( mem(sK7,sK2) ), inference(cnf_transformation,[],[f75]) ). cnf(c_231,negated_conjecture, ( mem(sK7,sK2) ), inference(subtyping,[status(esa)],[c_7]) ). cnf(c_588,plain, ( mem(sK7,sK2) = iProver_top ), inference(predicate_to_equality,[status(thm)],[c_231]) ). cnf(c_6,negated_conjecture, ( mem(sK8,arr(sK1,sK2)) ), inference(cnf_transformation,[],[f76]) ). cnf(c_232,negated_conjecture, ( mem(sK8,arr(sK1,sK2)) ), inference(subtyping,[status(esa)],[c_6]) ). cnf(c_587,plain, ( mem(sK8,arr(sK1,sK2)) = iProver_top ), inference(predicate_to_equality,[status(thm)],[c_232]) ). cnf(c_17,plain, ( ~ mem(X0,X1) | ~ mem(X2,X3) | ~ mem(X4,arr(X3,X1)) | ~ ne(X3) | ~ ne(X1) | ap(X4,X2) = ap(ap(ap(c_2Eoption_2Eoption__CASE(X3,X3),ap(c_2Eoption_2ESOME(X3),X2)),X0),X4) ), inference(cnf_transformation,[],[f85]) ). cnf(c_221,plain, ( ~ mem(X0,X0) | ~ mem(X1,X1) | ~ mem(X2,arr(X1,X0)) | ~ ne(X0) | ~ ne(X1) | ap(X2,X1) = ap(ap(ap(c_2Eoption_2Eoption__CASE(X1,X1),ap(c_2Eoption_2ESOME(X1),X1)),X0),X2) ), inference(subtyping,[status(esa)],[c_17]) ). cnf(c_598,plain, ( ap(X0,X1) = ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),ap(c_2Eoption_2ESOME(X0),X1)),X2),X0) | mem(X2,X1) != iProver_top | mem(X1,X0) != iProver_top | mem(X0,arr(X0,X1)) != iProver_top | ne(X1) != iProver_top | ne(X0) != iProver_top ), inference(predicate_to_equality,[status(thm)],[c_221]) ). cnf(c_4234,plain, ( ap(sK8,X0) = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),ap(c_2Eoption_2ESOME(sK1),X0)),X1),sK8) | mem(X1,sK2) != iProver_top | mem(X0,sK1) != iProver_top | ne(sK2) != iProver_top | ne(sK1) != iProver_top ), inference(superposition,[status(thm)],[c_587,c_598]) ). cnf(c_12,negated_conjecture, ( ne(sK2) ), inference(cnf_transformation,[],[f70]) ). cnf(c_28,plain, ( ne(sK2) = iProver_top ), inference(predicate_to_equality,[status(thm)],[c_12]) ). cnf(c_5127,plain, ( ap(sK8,X0) = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),ap(c_2Eoption_2ESOME(sK1),X0)),X1),sK8) | mem(X1,sK2) != iProver_top | mem(X0,sK1) != iProver_top ), inference(global_propositional_subsumption, [status(thm)], [c_4234,c_27,c_28,c_34,c_4626]) ). cnf(c_5136,plain, ( ap(sK8,X0) = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),ap(c_2Eoption_2ESOME(sK1),X0)),sK7),sK8) | mem(X0,sK1) != iProver_top ), inference(superposition,[status(thm)],[c_588,c_5127]) ). cnf(c_5175,plain, ( ap(sK8,sK0(sK1,sK5)) = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),ap(c_2Eoption_2ESOME(sK1),sK0(sK1,sK5))),sK7),sK8) | sK5 = c_2Eoption_2ENONE(sK1) ), inference(superposition,[status(thm)],[c_2451,c_5136]) ). cnf(c_10186,plain, ( ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK8) = ap(sK8,sK0(sK1,sK5)) | sK5 = c_2Eoption_2ENONE(sK1) ), inference(superposition,[status(thm)],[c_1706,c_5175]) ). cnf(c_11,negated_conjecture, ( mem(sK3,sK2) ), inference(cnf_transformation,[],[f71]) ). cnf(c_227,negated_conjecture, ( mem(sK3,sK2) ), inference(subtyping,[status(esa)],[c_11]) ). cnf(c_592,plain, ( mem(sK3,sK2) = iProver_top ), inference(predicate_to_equality,[status(thm)],[c_227]) ). cnf(c_10,negated_conjecture, ( mem(sK4,arr(sK1,sK2)) ), inference(cnf_transformation,[],[f72]) ). cnf(c_228,negated_conjecture, ( mem(sK4,arr(sK1,sK2)) ), inference(subtyping,[status(esa)],[c_10]) ). cnf(c_591,plain, ( mem(sK4,arr(sK1,sK2)) = iProver_top ), inference(predicate_to_equality,[status(thm)],[c_228]) ). cnf(c_4245,plain, ( ap(sK4,X0) = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),ap(c_2Eoption_2ESOME(sK1),X0)),X1),sK4) | mem(X1,sK2) != iProver_top | mem(X0,sK1) != iProver_top | ne(sK2) != iProver_top | ne(sK1) != iProver_top ), inference(superposition,[status(thm)],[c_591,c_598]) ). cnf(c_30,plain, ( mem(sK4,arr(sK1,sK2)) = iProver_top ), inference(predicate_to_equality,[status(thm)],[c_10]) ). cnf(c_4629,plain, ( ~ mem(X0,sK2) | ~ mem(X1,sK1) | ~ mem(sK4,arr(sK1,sK2)) | ~ ne(sK2) | ~ ne(sK1) | ap(sK4,X1) = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),ap(c_2Eoption_2ESOME(sK1),X1)),X0),sK4) ), inference(instantiation,[status(thm)],[c_221]) ). cnf(c_4630,plain, ( ap(sK4,X0) = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),ap(c_2Eoption_2ESOME(sK1),X0)),X1),sK4) | mem(X1,sK2) != iProver_top | mem(X0,sK1) != iProver_top | mem(sK4,arr(sK1,sK2)) != iProver_top | ne(sK2) != iProver_top | ne(sK1) != iProver_top ), inference(predicate_to_equality,[status(thm)],[c_4629]) ). cnf(c_5418,plain, ( ap(sK4,X0) = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),ap(c_2Eoption_2ESOME(sK1),X0)),X1),sK4) | mem(X1,sK2) != iProver_top | mem(X0,sK1) != iProver_top ), inference(global_propositional_subsumption, [status(thm)], [c_4245,c_27,c_28]) ). cnf(c_5432,plain, ( ap(sK4,X0) = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),ap(c_2Eoption_2ESOME(sK1),X0)),sK3),sK4) | mem(X0,sK1) != iProver_top ), inference(superposition,[status(thm)],[c_592,c_5418]) ). cnf(c_5575,plain, ( ap(sK4,sK0(sK1,sK5)) = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),ap(c_2Eoption_2ESOME(sK1),sK0(sK1,sK5))),sK3),sK4) | sK5 = c_2Eoption_2ENONE(sK1) ), inference(superposition,[status(thm)],[c_2451,c_5432]) ). cnf(c_10361,plain, ( ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK3),sK4) = ap(sK4,sK0(sK1,sK5)) | sK5 = c_2Eoption_2ENONE(sK1) ), inference(superposition,[status(thm)],[c_1706,c_5575]) ). cnf(c_5,negated_conjecture, ( sK5 = sK6 ), inference(cnf_transformation,[],[f77]) ). cnf(c_233,negated_conjecture, ( sK5 = sK6 ), inference(subtyping,[status(esa)],[c_5]) ). cnf(c_2,negated_conjecture, ( ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK8) != ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK6),sK3),sK4) ), inference(cnf_transformation,[],[f80]) ). cnf(c_236,negated_conjecture, ( ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK8) != ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK6),sK3),sK4) ), inference(subtyping,[status(esa)],[c_2]) ). cnf(c_639,plain, ( ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK8) != ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK3),sK4) ), inference(demodulation,[status(thm)],[c_233,c_236]) ). cnf(c_22685,plain, ( ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK8) != ap(sK4,sK0(sK1,sK5)) | sK5 = c_2Eoption_2ENONE(sK1) ), inference(superposition,[status(thm)],[c_10361,c_639]) ). cnf(c_22950,plain, ( ap(sK4,sK0(sK1,sK5)) != ap(sK8,sK0(sK1,sK5)) | sK5 = c_2Eoption_2ENONE(sK1) ), inference(superposition,[status(thm)],[c_10186,c_22685]) ). cnf(c_3,negated_conjecture, ( ~ mem(X0,sK1) | ap(c_2Eoption_2ESOME(sK1),X0) != sK6 | ap(sK4,X0) = ap(sK8,X0) ), inference(cnf_transformation,[],[f79]) ). cnf(c_235,negated_conjecture, ( ~ mem(X0,sK1) | ap(c_2Eoption_2ESOME(sK1),X0) != sK6 | ap(sK4,X0) = ap(sK8,X0) ), inference(subtyping,[status(esa)],[c_3]) ). cnf(c_586,plain, ( ap(c_2Eoption_2ESOME(sK1),X0) != sK6 | ap(sK4,X0) = ap(sK8,X0) | mem(X0,sK1) != iProver_top ), inference(predicate_to_equality,[status(thm)],[c_235]) ). cnf(c_638,plain, ( ap(sK4,X0) = ap(sK8,X0) | sK5 != ap(c_2Eoption_2ESOME(sK1),X0) | mem(X0,sK1) != iProver_top ), inference(demodulation,[status(thm)],[c_233,c_586]) ). cnf(c_1709,plain, ( ap(sK4,sK0(sK1,sK5)) = ap(sK8,sK0(sK1,sK5)) | sK5 = c_2Eoption_2ENONE(sK1) | mem(sK0(sK1,sK5),sK1) != iProver_top ), inference(superposition,[status(thm)],[c_1706,c_638]) ). cnf(c_2456,plain, ( ap(sK4,sK0(sK1,sK5)) = ap(sK8,sK0(sK1,sK5)) | sK5 = c_2Eoption_2ENONE(sK1) ), inference(superposition,[status(thm)],[c_2451,c_1709]) ). cnf(c_23140,plain, ( sK5 = c_2Eoption_2ENONE(sK1) ), inference(global_propositional_subsumption, [status(thm)], [c_22950,c_2456]) ). cnf(c_18,plain, ( ~ mem(X0,X1) | ~ mem(X2,arr(X3,X1)) | ~ ne(X3) | ~ ne(X1) | X0 = ap(ap(ap(c_2Eoption_2Eoption__CASE(X3,X3),c_2Eoption_2ENONE(X3)),X0),X2) ), inference(cnf_transformation,[],[f84]) ). cnf(c_220,plain, ( ~ mem(X0,X0) | ~ mem(X1,arr(X1,X0)) | ~ ne(X0) | ~ ne(X1) | X0 = ap(ap(ap(c_2Eoption_2Eoption__CASE(X1,X1),c_2Eoption_2ENONE(X1)),X0),X1) ), inference(subtyping,[status(esa)],[c_18]) ). cnf(c_599,plain, ( X0 = ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X0),c_2Eoption_2ENONE(X0)),X0),X1) | mem(X0,X1) != iProver_top | mem(X1,arr(X0,X1)) != iProver_top | ne(X1) != iProver_top | ne(X0) != iProver_top ), inference(predicate_to_equality,[status(thm)],[c_220]) ). cnf(c_3304,plain, ( X0 = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),c_2Eoption_2ENONE(sK1)),X0),sK4) | mem(X0,sK2) != iProver_top | ne(sK2) != iProver_top | ne(sK1) != iProver_top ), inference(superposition,[status(thm)],[c_591,c_599]) ). cnf(c_3817,plain, ( X0 = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),c_2Eoption_2ENONE(sK1)),X0),sK4) | mem(X0,sK2) != iProver_top ), inference(global_propositional_subsumption, [status(thm)], [c_3304,c_27,c_28]) ). cnf(c_3825,plain, ( sK7 = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),c_2Eoption_2ENONE(sK1)),sK7),sK4) ), inference(superposition,[status(thm)],[c_588,c_3817]) ). cnf(c_23179,plain, ( sK7 = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK4) ), inference(demodulation,[status(thm)],[c_23140,c_3825]) ). cnf(c_4,negated_conjecture, ( c_2Eoption_2ENONE(sK1) != sK6 | sK3 = sK7 ), inference(cnf_transformation,[],[f78]) ). cnf(c_234,negated_conjecture, ( c_2Eoption_2ENONE(sK1) != sK6 | sK3 = sK7 ), inference(subtyping,[status(esa)],[c_4]) ). cnf(c_637,plain, ( sK7 = sK3 | sK5 != c_2Eoption_2ENONE(sK1) ), inference(demodulation,[status(thm)],[c_233,c_234]) ). cnf(c_23186,plain, ( sK7 = sK3 | sK5 != sK5 ), inference(demodulation,[status(thm)],[c_23140,c_637]) ). cnf(c_23187,plain, ( sK7 = sK3 ), inference(equality_resolution_simp,[status(thm)],[c_23186]) ). cnf(c_23458,plain, ( ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK8) != ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK4) ), inference(demodulation,[status(thm)],[c_23187,c_639]) ). cnf(c_23662,plain, ( sK7 != ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK8) ), inference(demodulation,[status(thm)],[c_23179,c_23458]) ). cnf(c_3295,plain, ( X0 = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),c_2Eoption_2ENONE(sK1)),X0),sK8) | mem(X0,sK2) != iProver_top | ne(sK2) != iProver_top | ne(sK1) != iProver_top ), inference(superposition,[status(thm)],[c_587,c_599]) ). cnf(c_3348,plain, ( X0 = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),c_2Eoption_2ENONE(sK1)),X0),sK8) | mem(X0,sK2) != iProver_top ), inference(global_propositional_subsumption, [status(thm)], [c_3295,c_27,c_28]) ). cnf(c_3356,plain, ( sK7 = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),c_2Eoption_2ENONE(sK1)),sK7),sK8) ), inference(superposition,[status(thm)],[c_588,c_3348]) ). cnf(c_23182,plain, ( sK7 = ap(ap(ap(c_2Eoption_2Eoption__CASE(sK1,sK1),sK5),sK7),sK8) ), inference(demodulation,[status(thm)],[c_23140,c_3356]) ). cnf(contradiction,plain, ( $false ), inference(minisat,[status(thm)],[c_23662,c_23182]) ). % SZS output end CNFRefutation for HL400543+2.p USED TIME: 0.75 CPU 0.79 WC 13.1200000000026/1.84000000000015 EOF