%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB023+2 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:39 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB023+2 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:51:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(iext_type, type, (
% 0.12/0.37 iext: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(uri_ex_v_type, type, (
% 0.12/0.37 uri_ex_v: $i)).
% 0.12/0.37 tff(uri_ex_w_type, type, (
% 0.12/0.37 uri_ex_w: $i)).
% 0.12/0.37 tff(uri_owl_sameAs_type, type, (
% 0.12/0.37 uri_owl_sameAs: $i)).
% 0.12/0.37 tff(uri_ex_u_type, type, (
% 0.12/0.37 uri_ex_u: $i)).
% 0.12/0.37 tff(icext_type, type, (
% 0.12/0.37 icext: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_BNODE_o_5_type, type, (
% 0.12/0.37 tptp_fun_BNODE_o_5: $i)).
% 0.12/0.37 tff(ic_type, type, (
% 0.12/0.37 ic: $i > $o)).
% 0.12/0.37 tff(tptp_fun_BNODE_l_4_type, type, (
% 0.12/0.37 tptp_fun_BNODE_l_4: $i)).
% 0.12/0.37 tff(uri_owl_oneOf_type, type, (
% 0.12/0.37 uri_owl_oneOf: $i)).
% 0.12/0.37 tff(tptp_fun_X_0_type, type, (
% 0.12/0.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.37 tff(uri_rdf_nil_type, type, (
% 0.12/0.37 uri_rdf_nil: $i)).
% 0.12/0.37 tff(uri_rdf_rest_type, type, (
% 0.12/0.37 uri_rdf_rest: $i)).
% 0.12/0.37 tff(uri_rdf_first_type, type, (
% 0.12/0.37 uri_rdf_first: $i)).
% 0.12/0.37 tff(uri_owl_Class_type, type, (
% 0.12/0.37 uri_owl_Class: $i)).
% 0.12/0.37 tff(uri_rdf_type_type, type, (
% 0.12/0.37 uri_rdf_type: $i)).
% 0.12/0.37 tff(uri_owl_FunctionalProperty_type, type, (
% 0.12/0.37 uri_owl_FunctionalProperty: $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (?[BNODE_o: $i, BNODE_l: $i] : (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u) & iext(uri_rdf_first, BNODE_l, uri_ex_v) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)) <=> ?[BNODE_o: $i, BNODE_l: $i] : (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u) & iext(uri_rdf_first, BNODE_l, uri_ex_v) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (^[BNODE_o: $i, BNODE_l: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o)) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) <=> (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class))), ((((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o)) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) <=> ((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)))), rewrite(((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) <=> (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l))), ((((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o)) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) <=> (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)))), (((((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o)) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_u)) <=> ((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_u)))), rewrite(((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_u)) <=> (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u))), (((((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o)) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_u)) <=> (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u)))), ((((((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o)) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_u)) & iext(uri_rdf_first, BNODE_l, uri_ex_v)) <=> ((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u)) & iext(uri_rdf_first, BNODE_l, uri_ex_v)))), rewrite(((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u)) & iext(uri_rdf_first, BNODE_l, uri_ex_v)) <=> (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u) & iext(uri_rdf_first, BNODE_l, uri_ex_v))), ((((((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o)) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_u)) & iext(uri_rdf_first, BNODE_l, uri_ex_v)) <=> (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u) & iext(uri_rdf_first, BNODE_l, uri_ex_v)))), (((((((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o)) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_u)) & iext(uri_rdf_first, BNODE_l, uri_ex_v)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)) <=> ((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u) & iext(uri_rdf_first, BNODE_l, uri_ex_v)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)))), rewrite(((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u) & iext(uri_rdf_first, BNODE_l, uri_ex_v)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u) & iext(uri_rdf_first, BNODE_l, uri_ex_v) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))), (((((((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o)) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_u)) & iext(uri_rdf_first, BNODE_l, uri_ex_v)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u) & iext(uri_rdf_first, BNODE_l, uri_ex_v) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (?[BNODE_o: $i, BNODE_l: $i] : ((((((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o)) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_u)) & iext(uri_rdf_first, BNODE_l, uri_ex_v)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)) <=> ?[BNODE_o: $i, BNODE_l: $i] : (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u) & iext(uri_rdf_first, BNODE_l, uri_ex_v) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,axiom,(?[BNODE_o: $i, BNODE_l: $i] : ((((((iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o)) & iext(uri_rdf_type, BNODE_o, uri_owl_Class)) & iext(uri_owl_oneOf, BNODE_o, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_u)) & iext(uri_rdf_first, BNODE_l, uri_ex_v)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_023_Unique_List_Components')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (?[BNODE_o: $i, BNODE_l: $i] : (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u) & iext(uri_rdf_first, BNODE_l, uri_ex_v) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (?[BNODE_o: $i, BNODE_l: $i] : (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o) & iext(uri_rdf_type, BNODE_o, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_u) & iext(uri_rdf_first, BNODE_l, uri_ex_v) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.38 tff(7,plain,(
% 0.12/0.38 iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) & iext(uri_rdf_type, uri_ex_w, BNODE_o!5) & iext(uri_rdf_type, BNODE_o!5, uri_owl_Class) & iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) & iext(uri_rdf_first, BNODE_l!4, uri_ex_u) & iext(uri_rdf_first, BNODE_l!4, uri_ex_v) & iext(uri_rdf_rest, BNODE_l!4, uri_rdf_nil)),
% 0.12/0.38 inference(skolemize,[status(sab)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (iext(uri_rdf_rest, BNODE_l!4, uri_rdf_nil)),
% 0.12/0.38 inference(and_elim,[status(thm)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (iext(uri_rdf_first, BNODE_l!4, uri_ex_u)),
% 0.12/0.38 inference(and_elim,[status(thm)],[7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (^[Z: $i, S1: $i, A1: $i] : refl(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[15, 13])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> ((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))) <=> (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) <=> (((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))), rewrite((((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))) <=> (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))))), rewrite((((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(monotonicity(rewrite((ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))), ((iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.39 tff(24,axiom,(![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_enum_class_001')).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.39 tff(27,plain,(
% 0.19/0.39 ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_l!4, uri_ex_u)) | (~iext(uri_rdf_rest, BNODE_l!4, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_u, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_u, BNODE_o!5) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_l!4, uri_ex_u)) | (~iext(uri_rdf_rest, BNODE_l!4, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_u, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_u, BNODE_o!5) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_l!4, uri_ex_u)) | (~iext(uri_rdf_rest, BNODE_l!4, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_u, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_u, BNODE_o!5) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_l!4, uri_ex_u)) | (~iext(uri_rdf_rest, BNODE_l!4, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_u, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_u, BNODE_o!5) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u)))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (~((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_u, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_u, BNODE_o!5) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 31, 9, 8])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_u, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_u, BNODE_o!5) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u)))))))) | ((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 ((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)),
% 0.19/0.39 inference(and_elim,[status(thm)],[7])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u))))))) | (~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ((~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u))))))) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u)))) | ![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_u))) | (icext(BNODE_o!5, uri_ex_w) <=> (uri_ex_w = uri_ex_u))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (icext(BNODE_o!5, uri_ex_w) <=> (uri_ex_w = uri_ex_u)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rdfs_cext_def')).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,(
% 0.19/0.39 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.39 inference(skolemize,[status(sab)],[50])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_w, BNODE_o!5) <=> icext(BNODE_o!5, uri_ex_w))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (iext(uri_rdf_type, uri_ex_w, BNODE_o!5) <=> icext(BNODE_o!5, uri_ex_w)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (iext(uri_rdf_type, uri_ex_w, BNODE_o!5)),
% 0.19/0.39 inference(and_elim,[status(thm)],[7])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 ((~(iext(uri_rdf_type, uri_ex_w, BNODE_o!5) <=> icext(BNODE_o!5, uri_ex_w))) | (~iext(uri_rdf_type, uri_ex_w, BNODE_o!5)) | icext(BNODE_o!5, uri_ex_w)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((~(iext(uri_rdf_type, uri_ex_w, BNODE_o!5) <=> icext(BNODE_o!5, uri_ex_w))) | icext(BNODE_o!5, uri_ex_w)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (icext(BNODE_o!5, uri_ex_w)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ((~(icext(BNODE_o!5, uri_ex_w) <=> (uri_ex_w = uri_ex_u))) | (~icext(BNODE_o!5, uri_ex_w)) | (uri_ex_w = uri_ex_u)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((~(icext(BNODE_o!5, uri_ex_w) <=> (uri_ex_w = uri_ex_u))) | (uri_ex_w = uri_ex_u)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (uri_ex_w = uri_ex_u),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[60, 45])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (iext(uri_rdf_first, BNODE_l!4, uri_ex_v)),
% 0.19/0.39 inference(and_elim,[status(thm)],[7])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_l!4, uri_ex_v)) | (~iext(uri_rdf_rest, BNODE_l!4, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_v, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_v, BNODE_o!5) = uri_ex_v))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_l!4, uri_ex_v)) | (~iext(uri_rdf_rest, BNODE_l!4, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_v, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_v, BNODE_o!5) = uri_ex_v))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v))))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_l!4, uri_ex_v)) | (~iext(uri_rdf_rest, BNODE_l!4, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_v, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_v, BNODE_o!5) = uri_ex_v))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v))))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_l!4, uri_ex_v)) | (~iext(uri_rdf_rest, BNODE_l!4, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_v, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_v, BNODE_o!5) = uri_ex_v))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v)))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (~((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_v, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_v, BNODE_o!5) = uri_ex_v))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[65, 31, 62, 8])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (((~(iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4) | (~ic(BNODE_o!5)) | (~(icext(BNODE_o!5, tptp_fun_X_0(uri_ex_v, BNODE_o!5)) <=> (tptp_fun_X_0(uri_ex_v, BNODE_o!5) = uri_ex_v))))) | (~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v)))))))) | ((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 ((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v))))))) | (~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 ((~((~iext(uri_owl_oneOf, BNODE_o!5, BNODE_l!4)) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v))))))) | (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[69, 38])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (~((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[70, 68])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (((~ic(BNODE_o!5)) | (~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v)))) | ![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((~![X: $i] : (icext(BNODE_o!5, X) <=> (X = uri_ex_v))) | (icext(BNODE_o!5, uri_ex_w) <=> (uri_ex_w = uri_ex_v))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (icext(BNODE_o!5, uri_ex_w) <=> (uri_ex_w = uri_ex_v)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~(icext(BNODE_o!5, uri_ex_w) <=> (uri_ex_w = uri_ex_v))) | (~icext(BNODE_o!5, uri_ex_w)) | (uri_ex_w = uri_ex_v)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((~(icext(BNODE_o!5, uri_ex_w) <=> (uri_ex_w = uri_ex_v))) | (uri_ex_w = uri_ex_v)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 58])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (uri_ex_w = uri_ex_v),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[77, 75])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (uri_ex_v = uri_ex_w),
% 0.19/0.40 inference(symmetry,[status(thm)],[78])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (uri_ex_v = uri_ex_u),
% 0.19/0.40 inference(transitivity,[status(thm)],[79, 61])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (iext(uri_owl_sameAs, uri_ex_w, uri_ex_v) <=> iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[80])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) <=> iext(uri_owl_sameAs, uri_ex_w, uri_ex_v)),
% 0.19/0.40 inference(symmetry,[status(thm)],[81])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (uri_ex_u = uri_ex_w),
% 0.19/0.40 inference(symmetry,[status(thm)],[61])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (iext(uri_owl_sameAs, uri_ex_u, uri_ex_u) <=> iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) <=> iext(uri_owl_sameAs, uri_ex_u, uri_ex_u)),
% 0.19/0.40 inference(symmetry,[status(thm)],[84])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 ((~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)) <=> (~iext(uri_owl_sameAs, uri_ex_u, uri_ex_u))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.40 tff(87,assumption,(~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)), introduced(assumption)).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (~iext(uri_owl_sameAs, uri_ex_u, uri_ex_u)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : refl((iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> (iext(uri_owl_sameAs, X, Y) <=> (X = Y)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(92,axiom,(![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_eqdis_sameas')).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.40 tff(94,plain,(
% 0.19/0.40 ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.40 inference(skolemize,[status(sab)],[93])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | iext(uri_owl_sameAs, uri_ex_u, uri_ex_u)) <=> ((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | iext(uri_owl_sameAs, uri_ex_u, uri_ex_u))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((iext(uri_owl_sameAs, uri_ex_u, uri_ex_u) <=> $true) <=> iext(uri_owl_sameAs, uri_ex_u, uri_ex_u)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((uri_ex_u = uri_ex_u) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ((iext(uri_owl_sameAs, uri_ex_u, uri_ex_u) <=> (uri_ex_u = uri_ex_u)) <=> (iext(uri_owl_sameAs, uri_ex_u, uri_ex_u) <=> $true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[98])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 ((iext(uri_owl_sameAs, uri_ex_u, uri_ex_u) <=> (uri_ex_u = uri_ex_u)) <=> iext(uri_owl_sameAs, uri_ex_u, uri_ex_u)),
% 0.19/0.40 inference(transitivity,[status(thm)],[99, 97])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | (iext(uri_owl_sameAs, uri_ex_u, uri_ex_u) <=> (uri_ex_u = uri_ex_u))) <=> ((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | iext(uri_owl_sameAs, uri_ex_u, uri_ex_u))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[100])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | (iext(uri_owl_sameAs, uri_ex_u, uri_ex_u) <=> (uri_ex_u = uri_ex_u))) <=> ((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | iext(uri_owl_sameAs, uri_ex_u, uri_ex_u))),
% 0.19/0.40 inference(transitivity,[status(thm)],[101, 96])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | (iext(uri_owl_sameAs, uri_ex_u, uri_ex_u) <=> (uri_ex_u = uri_ex_u))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | iext(uri_owl_sameAs, uri_ex_u, uri_ex_u)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (iext(uri_owl_sameAs, uri_ex_u, uri_ex_u)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[104, 95])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[105, 88])).
% 0.19/0.40 tff(107,plain,(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (iext(uri_owl_sameAs, uri_ex_w, uri_ex_v)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[107, 82])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 ((~(~((~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)) | (~iext(uri_owl_sameAs, uri_ex_w, uri_ex_v))))) <=> ((~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)) | (~iext(uri_owl_sameAs, uri_ex_w, uri_ex_v)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 ((iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) & iext(uri_owl_sameAs, uri_ex_w, uri_ex_v)) <=> (~((~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)) | (~iext(uri_owl_sameAs, uri_ex_w, uri_ex_v))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 ((~(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) & iext(uri_owl_sameAs, uri_ex_w, uri_ex_v))) <=> (~(~((~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)) | (~iext(uri_owl_sameAs, uri_ex_w, uri_ex_v)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[110])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 ((~(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) & iext(uri_owl_sameAs, uri_ex_w, uri_ex_v))) <=> ((~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)) | (~iext(uri_owl_sameAs, uri_ex_w, uri_ex_v)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[111, 109])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 ((~(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) & iext(uri_owl_sameAs, uri_ex_w, uri_ex_v))) <=> (~(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) & iext(uri_owl_sameAs, uri_ex_w, uri_ex_v)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(114,axiom,(~(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) & iext(uri_owl_sameAs, uri_ex_w, uri_ex_v))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_023_Unique_List_Components')).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (~(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) & iext(uri_owl_sameAs, uri_ex_w, uri_ex_v))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 ((~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)) | (~iext(uri_owl_sameAs, uri_ex_w, uri_ex_v))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[115, 112])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (~iext(uri_owl_sameAs, uri_ex_w, uri_ex_v)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[116, 107])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[117, 108])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------