%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB031+2 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:29:42 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWB031+2 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 07:54:03 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(icext_type, type, (
% 0.21/0.43 icext: ( $i * $i ) > $o)).
% 0.21/0.43 tff(uri_owl_equivalentClass_type, type, (
% 0.21/0.43 uri_owl_equivalentClass: $i)).
% 0.21/0.43 tff(uri_owl_Nothing_type, type, (
% 0.21/0.43 uri_owl_Nothing: $i)).
% 0.21/0.43 tff(tptp_fun_BNODE_x_3_type, type, (
% 0.21/0.43 tptp_fun_BNODE_x_3: $i)).
% 0.21/0.43 tff(uri_ex_w_type, type, (
% 0.21/0.43 uri_ex_w: $i)).
% 0.21/0.43 tff(ic_type, type, (
% 0.21/0.43 ic: $i > $o)).
% 0.21/0.43 tff(iext_type, type, (
% 0.21/0.43 iext: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(tptp_fun_BNODE_l_2_type, type, (
% 0.21/0.43 tptp_fun_BNODE_l_2: $i)).
% 0.21/0.43 tff(uri_owl_oneOf_type, type, (
% 0.21/0.43 uri_owl_oneOf: $i)).
% 0.21/0.43 tff(tptp_fun_X_0_type, type, (
% 0.21/0.43 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.21/0.43 tff(uri_rdf_nil_type, type, (
% 0.21/0.43 uri_rdf_nil: $i)).
% 0.21/0.43 tff(uri_rdf_rest_type, type, (
% 0.21/0.43 uri_rdf_rest: $i)).
% 0.21/0.43 tff(uri_rdf_first_type, type, (
% 0.21/0.43 uri_rdf_first: $i)).
% 0.21/0.43 tff(uri_owl_Thing_type, type, (
% 0.21/0.43 uri_owl_Thing: $i)).
% 0.21/0.43 tff(tptp_fun_X_1_type, type, (
% 0.21/0.43 tptp_fun_X_1: ( $i * $i ) > $i)).
% 0.21/0.43 tff(ir_type, type, (
% 0.21/0.43 ir: $i > $o)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 (?[BNODE_x: $i, BNODE_l: $i] : (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_w) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)) <=> ?[BNODE_x: $i, BNODE_l: $i] : (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_w) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (^[BNODE_x: $i, BNODE_l: $i] : trans(monotonicity(rewrite(((iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_w)) <=> (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_w))), ((((iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)) <=> ((iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)))), rewrite(((iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)) <=> (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_w) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))), ((((iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)) <=> (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_w) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (?[BNODE_x: $i, BNODE_l: $i] : (((iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil)) <=> ?[BNODE_x: $i, BNODE_l: $i] : (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_w) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.43 tff(4,axiom,(?[BNODE_x: $i, BNODE_l: $i] : (((iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l)) & iext(uri_rdf_first, BNODE_l, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_premise_fullish_031_Large_Universe')).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (?[BNODE_x: $i, BNODE_l: $i] : (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_w) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (?[BNODE_x: $i, BNODE_l: $i] : (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x) & iext(uri_owl_oneOf, BNODE_x, BNODE_l) & iext(uri_rdf_first, BNODE_l, uri_ex_w) & iext(uri_rdf_rest, BNODE_l, uri_rdf_nil))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.43 tff(7,plain,(
% 0.21/0.43 iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) & iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2) & iext(uri_rdf_first, BNODE_l!2, uri_ex_w) & iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)),
% 0.21/0.43 inference(skolemize,[status(sab)],[6])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 (iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)),
% 0.21/0.43 inference(and_elim,[status(thm)],[7])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 (iext(uri_rdf_first, BNODE_l!2, uri_ex_w)),
% 0.21/0.43 inference(and_elim,[status(thm)],[7])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (^[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)))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (![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))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (^[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)))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (![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))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (^[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)))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 (![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))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (![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))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[15, 13])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (^[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))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (![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))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (^[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)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 (^[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)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.44 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/sandbox/benchmark/theBenchmark.p','owl_enum_class_001')).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.44 tff(27,plain,(
% 0.21/0.44 ![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)))))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[26])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 (![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))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (![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))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (![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))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (![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))))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (((~![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!2, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2) | (~ic(BNODE_x!3)) | (~(icext(BNODE_x!3, tptp_fun_X_0(uri_ex_w, BNODE_x!3)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x!3) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))))))))))) <=> ((~![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!2, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2) | (~ic(BNODE_x!3)) | (~(icext(BNODE_x!3, tptp_fun_X_0(uri_ex_w, BNODE_x!3)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x!3) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 ((~![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!2, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2) | (~ic(BNODE_x!3)) | (~(icext(BNODE_x!3, tptp_fun_X_0(uri_ex_w, BNODE_x!3)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x!3) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 ((~![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!2, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2) | (~ic(BNODE_x!3)) | (~(icext(BNODE_x!3, tptp_fun_X_0(uri_ex_w, BNODE_x!3)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x!3) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w)))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (~((~(iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2) | (~ic(BNODE_x!3)) | (~(icext(BNODE_x!3, tptp_fun_X_0(uri_ex_w, BNODE_x!3)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x!3) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[34, 31, 9, 8])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (((~(iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2) | (~ic(BNODE_x!3)) | (~(icext(BNODE_x!3, tptp_fun_X_0(uri_ex_w, BNODE_x!3)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x!3) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w)))))))) | ((~iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 ((~iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)),
% 0.21/0.44 inference(and_elim,[status(thm)],[7])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 ((~((~iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))))))) | (~iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 ((~((~iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))))))) | (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (~((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (((~ic(BNODE_x!3)) | (~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w)))) | ![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 ((~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))) | (icext(BNODE_x!3, BNODE_x!3) <=> (BNODE_x!3 = uri_ex_w))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (icext(BNODE_x!3, BNODE_x!3) <=> (BNODE_x!3 = uri_ex_w)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))) <=> (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (^[C1: $i, C2: $i] : refl((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[51, 49])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (^[C1: $i, C2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))), trans(monotonicity(rewrite((~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))) <=> (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))), rewrite((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))), ((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) <=> (((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))), rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))))), ((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (^[C1: $i, C2: $i] : rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))) <=> (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))) <=> ![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (^[C1: $i, C2: $i] : rewrite((iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.45 tff(60,axiom,(![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_eqdis_equivalentclass')).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.21/0.45 tff(63,plain,(
% 0.21/0.45 ![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[62])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[65, 52])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[66, 47])).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 ((~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(uri_owl_Thing)) | (~ic(BNODE_x!3)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~ic(uri_owl_Thing)) | (~ic(BNODE_x!3)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))))))))) <=> (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(uri_owl_Thing)) | (~ic(BNODE_x!3)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~ic(uri_owl_Thing)) | (~ic(BNODE_x!3)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(uri_owl_Thing)) | (~ic(BNODE_x!3)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~ic(uri_owl_Thing)) | (~ic(BNODE_x!3)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[70, 68])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(uri_owl_Thing)) | (~ic(BNODE_x!3)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~ic(uri_owl_Thing)) | (~ic(BNODE_x!3)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X)))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[73, 67])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (((~(iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)) <=> icext(BNODE_x!3, tptp_fun_X_1(BNODE_x!3, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing))))))) | ((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 ((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)),
% 0.21/0.45 inference(and_elim,[status(thm)],[7])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 ((~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)))))) | (~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 ((~((~iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)))))) | (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (~((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[79, 76])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 (((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing))) | ![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (icext(uri_owl_Thing, BNODE_x!3) <=> icext(BNODE_x!3, BNODE_x!3))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (icext(uri_owl_Thing, BNODE_x!3) <=> icext(BNODE_x!3, BNODE_x!3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (^[X: $i] : refl((icext(uri_owl_Thing, X) <=> ir(X)) <=> (icext(uri_owl_Thing, X) <=> ir(X)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X)) <=> ![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X)) <=> ![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(88,axiom,(![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_class_thing_ext')).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.45 tff(90,plain,(
% 0.21/0.45 ![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.21/0.45 inference(skolemize,[status(sab)],[89])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))) | (icext(uri_owl_Thing, BNODE_x!3) <=> ir(BNODE_x!3))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (icext(uri_owl_Thing, BNODE_x!3) <=> ir(BNODE_x!3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (^[X: $i] : refl(ir(X) <=> ir(X))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (![X: $i] : ir(X) <=> ![X: $i] : ir(X)),
% 0.21/0.45 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 (![X: $i] : ir(X) <=> ![X: $i] : ir(X)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(97,axiom,(![X: $i] : ir(X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','simple_ir')).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 (![X: $i] : ir(X)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.45 tff(99,plain,(
% 0.21/0.45 ![X: $i] : ir(X)),
% 0.21/0.45 inference(skolemize,[status(sab)],[98])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (![X: $i] : ir(X)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 ((~![X: $i] : ir(X)) | ir(BNODE_x!3)),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 (ir(BNODE_x!3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 ((~(icext(uri_owl_Thing, BNODE_x!3) <=> ir(BNODE_x!3))) | icext(uri_owl_Thing, BNODE_x!3) | (~ir(BNODE_x!3))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 (icext(uri_owl_Thing, BNODE_x!3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[103, 102, 93])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 ((~(icext(uri_owl_Thing, BNODE_x!3) <=> icext(BNODE_x!3, BNODE_x!3))) | (~icext(uri_owl_Thing, BNODE_x!3)) | icext(BNODE_x!3, BNODE_x!3)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 (icext(BNODE_x!3, BNODE_x!3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[105, 104, 84])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 ((~(icext(BNODE_x!3, BNODE_x!3) <=> (BNODE_x!3 = uri_ex_w))) | (~icext(BNODE_x!3, BNODE_x!3)) | (BNODE_x!3 = uri_ex_w)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(108,plain,
% 0.21/0.45 (BNODE_x!3 = uri_ex_w),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[107, 106, 45])).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 (uri_ex_w = BNODE_x!3),
% 0.21/0.45 inference(symmetry,[status(thm)],[108])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 ((~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))) | (icext(BNODE_x!3, uri_owl_equivalentClass) <=> (uri_owl_equivalentClass = uri_ex_w))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 (icext(BNODE_x!3, uri_owl_equivalentClass) <=> (uri_owl_equivalentClass = uri_ex_w)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[110, 43])).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (icext(uri_owl_Thing, uri_owl_equivalentClass) <=> icext(BNODE_x!3, uri_owl_equivalentClass))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 (icext(uri_owl_Thing, uri_owl_equivalentClass) <=> icext(BNODE_x!3, uri_owl_equivalentClass)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[112, 82])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))) | (icext(uri_owl_Thing, uri_owl_equivalentClass) <=> ir(uri_owl_equivalentClass))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (icext(uri_owl_Thing, uri_owl_equivalentClass) <=> ir(uri_owl_equivalentClass)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[114, 91])).
% 0.21/0.45 tff(116,plain,
% 0.21/0.46 ((~![X: $i] : ir(X)) | ir(uri_owl_equivalentClass)),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(117,plain,
% 0.21/0.46 (ir(uri_owl_equivalentClass)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[116, 100])).
% 0.21/0.46 tff(118,plain,
% 0.21/0.46 ((~(icext(uri_owl_Thing, uri_owl_equivalentClass) <=> ir(uri_owl_equivalentClass))) | icext(uri_owl_Thing, uri_owl_equivalentClass) | (~ir(uri_owl_equivalentClass))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(119,plain,
% 0.21/0.46 (icext(uri_owl_Thing, uri_owl_equivalentClass)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[118, 117, 115])).
% 0.21/0.46 tff(120,plain,
% 0.21/0.46 ((~(icext(uri_owl_Thing, uri_owl_equivalentClass) <=> icext(BNODE_x!3, uri_owl_equivalentClass))) | (~icext(uri_owl_Thing, uri_owl_equivalentClass)) | icext(BNODE_x!3, uri_owl_equivalentClass)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(121,plain,
% 0.21/0.46 (icext(BNODE_x!3, uri_owl_equivalentClass)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[120, 119, 113])).
% 0.21/0.46 tff(122,plain,
% 0.21/0.46 ((~(icext(BNODE_x!3, uri_owl_equivalentClass) <=> (uri_owl_equivalentClass = uri_ex_w))) | (~icext(BNODE_x!3, uri_owl_equivalentClass)) | (uri_owl_equivalentClass = uri_ex_w)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(123,plain,
% 0.21/0.46 (uri_owl_equivalentClass = uri_ex_w),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[122, 121, 111])).
% 0.21/0.46 tff(124,plain,
% 0.21/0.46 (uri_ex_w = uri_owl_equivalentClass),
% 0.21/0.46 inference(symmetry,[status(thm)],[123])).
% 0.21/0.46 tff(125,plain,
% 0.21/0.46 ((~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))) | (icext(BNODE_x!3, uri_rdf_first) <=> (uri_rdf_first = uri_ex_w))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(126,plain,
% 0.21/0.46 (icext(BNODE_x!3, uri_rdf_first) <=> (uri_rdf_first = uri_ex_w)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[125, 43])).
% 0.21/0.46 tff(127,plain,
% 0.21/0.46 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (icext(uri_owl_Thing, uri_rdf_first) <=> icext(BNODE_x!3, uri_rdf_first))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(128,plain,
% 0.21/0.46 (icext(uri_owl_Thing, uri_rdf_first) <=> icext(BNODE_x!3, uri_rdf_first)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[127, 82])).
% 0.21/0.46 tff(129,plain,
% 0.21/0.46 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))) | (icext(uri_owl_Thing, uri_rdf_first) <=> ir(uri_rdf_first))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(130,plain,
% 0.21/0.46 (icext(uri_owl_Thing, uri_rdf_first) <=> ir(uri_rdf_first)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[129, 91])).
% 0.21/0.46 tff(131,plain,
% 0.21/0.46 ((~![X: $i] : ir(X)) | ir(uri_rdf_first)),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(132,plain,
% 0.21/0.46 (ir(uri_rdf_first)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[131, 100])).
% 0.21/0.46 tff(133,plain,
% 0.21/0.46 ((~(icext(uri_owl_Thing, uri_rdf_first) <=> ir(uri_rdf_first))) | icext(uri_owl_Thing, uri_rdf_first) | (~ir(uri_rdf_first))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(134,plain,
% 0.21/0.46 ((~(icext(uri_owl_Thing, uri_rdf_first) <=> ir(uri_rdf_first))) | icext(uri_owl_Thing, uri_rdf_first)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.21/0.46 tff(135,plain,
% 0.21/0.46 (icext(uri_owl_Thing, uri_rdf_first)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[134, 130])).
% 0.21/0.46 tff(136,plain,
% 0.21/0.46 ((~(icext(uri_owl_Thing, uri_rdf_first) <=> icext(BNODE_x!3, uri_rdf_first))) | (~icext(uri_owl_Thing, uri_rdf_first)) | icext(BNODE_x!3, uri_rdf_first)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(137,plain,
% 0.21/0.46 ((~(icext(uri_owl_Thing, uri_rdf_first) <=> icext(BNODE_x!3, uri_rdf_first))) | icext(BNODE_x!3, uri_rdf_first)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.21/0.46 tff(138,plain,
% 0.21/0.46 (icext(BNODE_x!3, uri_rdf_first)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[137, 128])).
% 0.21/0.46 tff(139,plain,
% 0.21/0.46 ((~(icext(BNODE_x!3, uri_rdf_first) <=> (uri_rdf_first = uri_ex_w))) | (~icext(BNODE_x!3, uri_rdf_first)) | (uri_rdf_first = uri_ex_w)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(140,plain,
% 0.21/0.46 ((~(icext(BNODE_x!3, uri_rdf_first) <=> (uri_rdf_first = uri_ex_w))) | (uri_rdf_first = uri_ex_w)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.21/0.46 tff(141,plain,
% 0.21/0.46 (uri_rdf_first = uri_ex_w),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[140, 126])).
% 0.21/0.46 tff(142,plain,
% 0.21/0.46 (uri_rdf_first = uri_owl_equivalentClass),
% 0.21/0.46 inference(transitivity,[status(thm)],[141, 124])).
% 0.21/0.46 tff(143,plain,
% 0.21/0.46 (iext(uri_rdf_first, uri_owl_Thing, uri_ex_w) <=> iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[142, 109])).
% 0.21/0.46 tff(144,plain,
% 0.21/0.46 (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) <=> iext(uri_rdf_first, uri_owl_Thing, uri_ex_w)),
% 0.21/0.46 inference(symmetry,[status(thm)],[143])).
% 0.21/0.46 tff(145,plain,
% 0.21/0.46 (iext(uri_rdf_first, uri_owl_Thing, uri_ex_w)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[77, 144])).
% 0.21/0.46 tff(146,plain,
% 0.21/0.46 (uri_ex_w = uri_rdf_first),
% 0.21/0.46 inference(symmetry,[status(thm)],[141])).
% 0.21/0.46 tff(147,plain,
% 0.21/0.46 (uri_owl_equivalentClass = uri_rdf_first),
% 0.21/0.46 inference(transitivity,[status(thm)],[123, 146])).
% 0.21/0.46 tff(148,plain,
% 0.21/0.46 (iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2) <=> iext(uri_rdf_first, BNODE_l!2, BNODE_l!2)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.46 tff(149,plain,
% 0.21/0.46 (iext(uri_rdf_first, BNODE_l!2, BNODE_l!2) <=> iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)),
% 0.21/0.46 inference(symmetry,[status(thm)],[148])).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 ((~iext(uri_rdf_first, BNODE_l!2, BNODE_l!2)) <=> (~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[149])).
% 0.21/0.46 tff(151,assumption,(~iext(uri_rdf_first, BNODE_l!2, BNODE_l!2)), introduced(assumption)).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 (~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.21/0.46 tff(153,plain,
% 0.21/0.46 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))) | (~(ic(BNODE_l!2) | (~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))) | (~(ic(BNODE_l!2) | (~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 ((~((~(iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2) | (~ic(BNODE_l!2)) | (~ic(BNODE_l!2)) | (~(icext(BNODE_l!2, tptp_fun_X_1(BNODE_l!2, BNODE_l!2)) <=> icext(BNODE_l!2, tptp_fun_X_1(BNODE_l!2, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)) | (~((~ic(BNODE_l!2)) | (~ic(BNODE_l!2)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(BNODE_l!2, X))))))))) <=> (~((~((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))) | (~(ic(BNODE_l!2) | (~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(155,plain,
% 0.21/0.46 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2) | (~ic(BNODE_l!2)) | (~ic(BNODE_l!2)) | (~(icext(BNODE_l!2, tptp_fun_X_1(BNODE_l!2, BNODE_l!2)) <=> icext(BNODE_l!2, tptp_fun_X_1(BNODE_l!2, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)) | (~((~ic(BNODE_l!2)) | (~ic(BNODE_l!2)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(BNODE_l!2, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))) | (~(ic(BNODE_l!2) | (~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[154])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2) | (~ic(BNODE_l!2)) | (~ic(BNODE_l!2)) | (~(icext(BNODE_l!2, tptp_fun_X_1(BNODE_l!2, BNODE_l!2)) <=> icext(BNODE_l!2, tptp_fun_X_1(BNODE_l!2, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)) | (~((~ic(BNODE_l!2)) | (~ic(BNODE_l!2)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(BNODE_l!2, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))) | (~(ic(BNODE_l!2) | (~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[155, 153])).
% 0.21/0.46 tff(157,plain,
% 0.21/0.46 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2) | (~ic(BNODE_l!2)) | (~ic(BNODE_l!2)) | (~(icext(BNODE_l!2, tptp_fun_X_1(BNODE_l!2, BNODE_l!2)) <=> icext(BNODE_l!2, tptp_fun_X_1(BNODE_l!2, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)) | (~((~ic(BNODE_l!2)) | (~ic(BNODE_l!2)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(BNODE_l!2, X)))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(158,plain,
% 0.21/0.46 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))) | (~(ic(BNODE_l!2) | (~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.46 tff(159,plain,
% 0.21/0.46 (~((~((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))) | (~(ic(BNODE_l!2) | (~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[158, 67])).
% 0.21/0.46 tff(160,plain,
% 0.21/0.46 (((~((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))) | (~(ic(BNODE_l!2) | (~iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))))) | ((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 ((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(uri_ex_w)) | (~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(uri_ex_w)) | (~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X))))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(163,plain,
% 0.21/0.46 ((~((~(iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X))))))))) <=> (~((~((~ic(uri_ex_w)) | (~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X)))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(164,plain,
% 0.21/0.46 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(uri_ex_w)) | (~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X))))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[163])).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(uri_ex_w)) | (~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X))))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[164, 162])).
% 0.21/0.46 tff(166,plain,
% 0.21/0.46 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X)))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(167,plain,
% 0.21/0.46 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(uri_ex_w)) | (~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X)))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.21/0.46 tff(168,plain,
% 0.21/0.46 (~((~((~ic(uri_ex_w)) | (~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X))))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[167, 67])).
% 0.21/0.46 tff(169,plain,
% 0.21/0.46 (((~((~ic(uri_ex_w)) | (~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) | (~(icext(BNODE_l!2, tptp_fun_X_1(uri_ex_w, BNODE_l!2)) <=> icext(uri_ex_w, tptp_fun_X_1(uri_ex_w, BNODE_l!2)))))) | (~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X)))))))) | ((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X))))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(170,plain,
% 0.21/0.46 ((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.21/0.46 tff(171,plain,
% 0.21/0.46 (iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w) <=> iext(uri_rdf_first, BNODE_l!2, uri_ex_w)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.46 tff(172,plain,
% 0.21/0.46 (iext(uri_rdf_first, BNODE_l!2, uri_ex_w) <=> iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)),
% 0.21/0.46 inference(symmetry,[status(thm)],[171])).
% 0.21/0.46 tff(173,plain,
% 0.21/0.46 (iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[9, 172])).
% 0.21/0.46 tff(174,plain,
% 0.21/0.46 ((~((~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X))))))) | (~iext(uri_owl_equivalentClass, BNODE_l!2, uri_ex_w)) | (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X)))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(175,plain,
% 0.21/0.46 (~((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[174, 173, 170])).
% 0.21/0.46 tff(176,plain,
% 0.21/0.46 (((~ic(BNODE_l!2)) | (~ic(uri_ex_w)) | (~![X: $i] : (icext(BNODE_l!2, X) <=> icext(uri_ex_w, X)))) | ic(BNODE_l!2)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(177,plain,
% 0.21/0.46 (ic(BNODE_l!2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.21/0.46 tff(178,plain,
% 0.21/0.46 ((~((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))) | (~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(179,plain,
% 0.21/0.46 ((~((~ic(BNODE_l!2)) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2))) | iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.21/0.46 tff(180,plain,
% 0.21/0.46 (iext(uri_owl_equivalentClass, BNODE_l!2, BNODE_l!2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[179, 161])).
% 0.21/0.46 tff(181,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[180, 152])).
% 0.21/0.46 tff(182,plain,(iext(uri_rdf_first, BNODE_l!2, BNODE_l!2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(183,plain,
% 0.21/0.46 (((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_ex_w)) | iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))))))))))) <=> ((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_ex_w)) | iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(184,plain,
% 0.21/0.46 (((~iext(uri_rdf_first, BNODE_l!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~ic(uri_ex_w)) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2)))))))))) <=> ((~iext(uri_rdf_first, BNODE_l!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_ex_w)) | iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 (((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~ic(uri_ex_w)) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))))))))))) <=> ((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_ex_w)) | iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2)))))))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[184])).
% 0.21/0.47 tff(186,plain,
% 0.21/0.47 (((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~ic(uri_ex_w)) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))))))))))) <=> ((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_ex_w)) | iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[185, 183])).
% 0.21/0.47 tff(187,plain,
% 0.21/0.47 ((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~ic(uri_ex_w)) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(188,plain,
% 0.21/0.47 ((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_ex_w)) | iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2)))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.21/0.47 tff(189,plain,
% 0.21/0.47 (~((~((~ic(uri_ex_w)) | iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[188, 31, 8, 182])).
% 0.21/0.47 tff(190,plain,
% 0.21/0.47 (((~((~ic(uri_ex_w)) | iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) | (~(icext(uri_ex_w, tptp_fun_X_0(BNODE_l!2, uri_ex_w)) <=> (tptp_fun_X_0(BNODE_l!2, uri_ex_w) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2)))))))) | ((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(191,plain,
% 0.21/0.47 ((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.21/0.47 tff(192,plain,
% 0.21/0.47 (iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2) <=> iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.47 tff(193,plain,
% 0.21/0.47 (iext(uri_owl_oneOf, BNODE_x!3, BNODE_l!2) <=> iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)),
% 0.21/0.47 inference(symmetry,[status(thm)],[192])).
% 0.21/0.47 tff(194,plain,
% 0.21/0.47 (iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[38, 193])).
% 0.21/0.47 tff(195,plain,
% 0.21/0.47 ((~((~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))))))) | (~iext(uri_owl_oneOf, uri_ex_w, BNODE_l!2)) | (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2)))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(196,plain,
% 0.21/0.47 (~((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[195, 194, 191])).
% 0.21/0.47 tff(197,plain,
% 0.21/0.47 (((~ic(uri_ex_w)) | (~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2)))) | ![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(198,plain,
% 0.21/0.47 (![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.21/0.47 tff(199,plain,
% 0.21/0.47 ((~![X: $i] : (icext(uri_ex_w, X) <=> (X = BNODE_l!2))) | (icext(uri_ex_w, uri_ex_w) <=> (uri_ex_w = BNODE_l!2))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(200,plain,
% 0.21/0.47 (icext(uri_ex_w, uri_ex_w) <=> (uri_ex_w = BNODE_l!2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.21/0.47 tff(201,plain,
% 0.21/0.47 (icext(uri_ex_w, uri_ex_w) <=> icext(BNODE_x!3, uri_owl_equivalentClass)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[109, 124])).
% 0.21/0.47 tff(202,plain,
% 0.21/0.47 (icext(BNODE_x!3, uri_owl_equivalentClass) <=> icext(uri_ex_w, uri_ex_w)),
% 0.21/0.47 inference(symmetry,[status(thm)],[201])).
% 0.21/0.47 tff(203,plain,
% 0.21/0.47 (icext(uri_ex_w, uri_ex_w)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[121, 202])).
% 0.21/0.47 tff(204,plain,
% 0.21/0.47 ((~(icext(uri_ex_w, uri_ex_w) <=> (uri_ex_w = BNODE_l!2))) | (~icext(uri_ex_w, uri_ex_w)) | (uri_ex_w = BNODE_l!2)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(205,plain,
% 0.21/0.47 ((~(icext(uri_ex_w, uri_ex_w) <=> (uri_ex_w = BNODE_l!2))) | (uri_ex_w = BNODE_l!2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.21/0.47 tff(206,plain,
% 0.21/0.47 (uri_ex_w = BNODE_l!2),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[205, 200])).
% 0.21/0.47 tff(207,plain,
% 0.21/0.47 (BNODE_l!2 = uri_ex_w),
% 0.21/0.47 inference(symmetry,[status(thm)],[206])).
% 0.21/0.47 tff(208,plain,
% 0.21/0.47 (((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))) | iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))))))))))) <=> ((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))) | iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(209,plain,
% 0.21/0.47 (((~iext(uri_rdf_first, BNODE_l!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2)))))))))) <=> ((~iext(uri_rdf_first, BNODE_l!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))) | iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(210,plain,
% 0.21/0.47 (((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))))))))))) <=> ((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))) | iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2)))))))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[209])).
% 0.21/0.47 tff(211,plain,
% 0.21/0.47 (((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))))))))))) <=> ((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))) | iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[210, 208])).
% 0.21/0.47 tff(212,plain,
% 0.21/0.47 ((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(213,plain,
% 0.21/0.47 ((~![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!2, BNODE_l!2)) | (~iext(uri_rdf_rest, BNODE_l!2, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))) | iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2)))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.21/0.47 tff(214,plain,
% 0.21/0.47 ((~iext(uri_rdf_first, BNODE_l!2, BNODE_l!2)) | (~((~((~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))) | iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2)))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[213, 31, 8])).
% 0.21/0.47 tff(215,plain,
% 0.21/0.47 (~((~((~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))) | iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[214, 182])).
% 0.21/0.47 tff(216,plain,
% 0.21/0.47 (((~((~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(BNODE_l!2, uri_owl_Thing)) <=> (tptp_fun_X_0(BNODE_l!2, uri_owl_Thing) = BNODE_l!2))) | iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2)))))))) | ((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(217,plain,
% 0.21/0.47 ((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.21/0.47 tff(218,plain,
% 0.21/0.47 (BNODE_l!2 = BNODE_x!3),
% 0.21/0.47 inference(transitivity,[status(thm)],[207, 109])).
% 0.21/0.47 tff(219,plain,
% 0.21/0.47 ((~![X: $i] : (icext(BNODE_x!3, X) <=> (X = uri_ex_w))) | (icext(BNODE_x!3, uri_owl_oneOf) <=> (uri_owl_oneOf = uri_ex_w))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(220,plain,
% 0.21/0.47 (icext(BNODE_x!3, uri_owl_oneOf) <=> (uri_owl_oneOf = uri_ex_w)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[219, 43])).
% 0.21/0.47 tff(221,plain,
% 0.21/0.47 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (icext(uri_owl_Thing, uri_owl_oneOf) <=> icext(BNODE_x!3, uri_owl_oneOf))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(222,plain,
% 0.21/0.47 (icext(uri_owl_Thing, uri_owl_oneOf) <=> icext(BNODE_x!3, uri_owl_oneOf)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[221, 82])).
% 0.21/0.47 tff(223,plain,
% 0.21/0.47 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))) | (icext(uri_owl_Thing, uri_owl_oneOf) <=> ir(uri_owl_oneOf))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(224,plain,
% 0.21/0.47 (icext(uri_owl_Thing, uri_owl_oneOf) <=> ir(uri_owl_oneOf)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[223, 91])).
% 0.21/0.47 tff(225,plain,
% 0.21/0.47 ((~![X: $i] : ir(X)) | ir(uri_owl_oneOf)),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(226,plain,
% 0.21/0.47 (ir(uri_owl_oneOf)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[225, 100])).
% 0.21/0.47 tff(227,plain,
% 0.21/0.47 ((~(icext(uri_owl_Thing, uri_owl_oneOf) <=> ir(uri_owl_oneOf))) | icext(uri_owl_Thing, uri_owl_oneOf) | (~ir(uri_owl_oneOf))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(228,plain,
% 0.21/0.47 (icext(uri_owl_Thing, uri_owl_oneOf)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[227, 226, 224])).
% 0.21/0.47 tff(229,plain,
% 0.21/0.47 ((~(icext(uri_owl_Thing, uri_owl_oneOf) <=> icext(BNODE_x!3, uri_owl_oneOf))) | (~icext(uri_owl_Thing, uri_owl_oneOf)) | icext(BNODE_x!3, uri_owl_oneOf)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(230,plain,
% 0.21/0.47 (icext(BNODE_x!3, uri_owl_oneOf)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[229, 228, 222])).
% 0.21/0.47 tff(231,plain,
% 0.21/0.47 ((~(icext(BNODE_x!3, uri_owl_oneOf) <=> (uri_owl_oneOf = uri_ex_w))) | (~icext(BNODE_x!3, uri_owl_oneOf)) | (uri_owl_oneOf = uri_ex_w)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(232,plain,
% 0.21/0.47 (uri_owl_oneOf = uri_ex_w),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[231, 230, 220])).
% 0.21/0.47 tff(233,plain,
% 0.21/0.47 (uri_owl_oneOf = uri_owl_equivalentClass),
% 0.21/0.47 inference(transitivity,[status(thm)],[232, 124])).
% 0.21/0.47 tff(234,plain,
% 0.21/0.47 (iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2) <=> iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[233, 218])).
% 0.21/0.47 tff(235,plain,
% 0.21/0.47 (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) <=> iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)),
% 0.21/0.47 inference(symmetry,[status(thm)],[234])).
% 0.21/0.47 tff(236,plain,
% 0.21/0.47 (iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[77, 235])).
% 0.21/0.47 tff(237,plain,
% 0.21/0.47 ((~((~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))))))) | (~iext(uri_owl_oneOf, uri_owl_Thing, BNODE_l!2)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2)))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(238,plain,
% 0.21/0.47 (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[237, 236, 217])).
% 0.21/0.47 tff(239,plain,
% 0.21/0.47 (((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2)))) | ![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(240,plain,
% 0.21/0.47 (![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.21/0.47 tff(241,plain,
% 0.21/0.47 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))) | (icext(uri_owl_Thing, uri_rdf_nil) <=> (uri_rdf_nil = BNODE_l!2))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(242,plain,
% 0.21/0.47 (icext(uri_owl_Thing, uri_rdf_nil) <=> (uri_rdf_nil = BNODE_l!2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.21/0.47 tff(243,plain,
% 0.21/0.47 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))) | (icext(uri_owl_Thing, uri_rdf_nil) <=> ir(uri_rdf_nil))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(244,plain,
% 0.21/0.47 (icext(uri_owl_Thing, uri_rdf_nil) <=> ir(uri_rdf_nil)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[243, 91])).
% 0.21/0.47 tff(245,plain,
% 0.21/0.47 ((~![X: $i] : ir(X)) | ir(uri_rdf_nil)),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(246,plain,
% 0.21/0.47 (ir(uri_rdf_nil)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[245, 100])).
% 0.21/0.47 tff(247,plain,
% 0.21/0.47 ((~(icext(uri_owl_Thing, uri_rdf_nil) <=> ir(uri_rdf_nil))) | icext(uri_owl_Thing, uri_rdf_nil) | (~ir(uri_rdf_nil))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(248,plain,
% 0.21/0.47 (icext(uri_owl_Thing, uri_rdf_nil)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[247, 246, 244])).
% 0.21/0.47 tff(249,plain,
% 0.21/0.47 ((~(icext(uri_owl_Thing, uri_rdf_nil) <=> (uri_rdf_nil = BNODE_l!2))) | (~icext(uri_owl_Thing, uri_rdf_nil)) | (uri_rdf_nil = BNODE_l!2)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(250,plain,
% 0.21/0.47 (uri_rdf_nil = BNODE_l!2),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[249, 248, 242])).
% 0.21/0.47 tff(251,plain,
% 0.21/0.47 (uri_rdf_nil = BNODE_x!3),
% 0.21/0.47 inference(transitivity,[status(thm)],[250, 207, 109])).
% 0.21/0.47 tff(252,plain,
% 0.21/0.47 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = BNODE_l!2))) | (icext(uri_owl_Thing, uri_rdf_rest) <=> (uri_rdf_rest = BNODE_l!2))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(253,plain,
% 0.21/0.47 (icext(uri_owl_Thing, uri_rdf_rest) <=> (uri_rdf_rest = BNODE_l!2)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[252, 240])).
% 0.21/0.47 tff(254,plain,
% 0.21/0.47 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))) | (icext(uri_owl_Thing, uri_rdf_rest) <=> ir(uri_rdf_rest))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(255,plain,
% 0.21/0.47 (icext(uri_owl_Thing, uri_rdf_rest) <=> ir(uri_rdf_rest)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[254, 91])).
% 0.21/0.47 tff(256,plain,
% 0.21/0.47 ((~![X: $i] : ir(X)) | ir(uri_rdf_rest)),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(257,plain,
% 0.21/0.47 (ir(uri_rdf_rest)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[256, 100])).
% 0.21/0.47 tff(258,plain,
% 0.21/0.47 ((~(icext(uri_owl_Thing, uri_rdf_rest) <=> ir(uri_rdf_rest))) | icext(uri_owl_Thing, uri_rdf_rest) | (~ir(uri_rdf_rest))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(259,plain,
% 0.21/0.47 (icext(uri_owl_Thing, uri_rdf_rest)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[258, 257, 255])).
% 0.21/0.47 tff(260,plain,
% 0.21/0.47 ((~(icext(uri_owl_Thing, uri_rdf_rest) <=> (uri_rdf_rest = BNODE_l!2))) | (~icext(uri_owl_Thing, uri_rdf_rest)) | (uri_rdf_rest = BNODE_l!2)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(261,plain,
% 0.21/0.47 (uri_rdf_rest = BNODE_l!2),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[260, 259, 253])).
% 0.21/0.48 tff(262,plain,
% 0.21/0.48 (uri_rdf_rest = uri_owl_equivalentClass),
% 0.21/0.48 inference(transitivity,[status(thm)],[261, 207, 124])).
% 0.21/0.48 tff(263,plain,
% 0.21/0.48 (iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil) <=> iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[262, 251])).
% 0.21/0.48 tff(264,plain,
% 0.21/0.48 (iext(uri_owl_equivalentClass, uri_owl_Thing, BNODE_x!3) <=> iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)),
% 0.21/0.48 inference(symmetry,[status(thm)],[263])).
% 0.21/0.48 tff(265,plain,
% 0.21/0.48 (iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[77, 264])).
% 0.21/0.48 tff(266,plain,
% 0.21/0.48 (((~![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, uri_owl_Thing, uri_ex_w)) | (~iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))))))))) <=> ((~![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, uri_owl_Thing, uri_ex_w)) | (~iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(267,plain,
% 0.21/0.48 (((~iext(uri_rdf_first, uri_owl_Thing, uri_ex_w)) | (~iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w)))))))))) <=> ((~iext(uri_rdf_first, uri_owl_Thing, uri_ex_w)) | (~iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(268,plain,
% 0.21/0.48 (((~![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, uri_owl_Thing, uri_ex_w)) | (~iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))))))))) <=> ((~![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, uri_owl_Thing, uri_ex_w)) | (~iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w)))))))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[267])).
% 0.21/0.48 tff(269,plain,
% 0.21/0.48 (((~![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, uri_owl_Thing, uri_ex_w)) | (~iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))))))))) <=> ((~![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, uri_owl_Thing, uri_ex_w)) | (~iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[268, 266])).
% 0.21/0.48 tff(270,plain,
% 0.21/0.48 ((~![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, uri_owl_Thing, uri_ex_w)) | (~iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(271,plain,
% 0.21/0.48 ((~![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, uri_owl_Thing, uri_ex_w)) | (~iext(uri_rdf_rest, uri_owl_Thing, uri_rdf_nil)) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w)))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.21/0.48 tff(272,plain,
% 0.21/0.48 ((~iext(uri_rdf_first, uri_owl_Thing, uri_ex_w)) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w)))))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[271, 31, 265])).
% 0.21/0.48 tff(273,plain,
% 0.21/0.48 (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[272, 145])).
% 0.21/0.48 tff(274,plain,
% 0.21/0.48 (((~((~ic(uri_owl_Thing)) | iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) | (~(icext(uri_owl_Thing, tptp_fun_X_0(uri_ex_w, uri_owl_Thing)) <=> (tptp_fun_X_0(uri_ex_w, uri_owl_Thing) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w)))))))) | ((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(275,plain,
% 0.21/0.48 ((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[274, 273])).
% 0.21/0.48 tff(276,plain,
% 0.21/0.48 (uri_owl_oneOf = uri_rdf_first),
% 0.21/0.48 inference(transitivity,[status(thm)],[232, 146])).
% 0.21/0.48 tff(277,plain,
% 0.21/0.48 (iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing) <=> iext(uri_rdf_first, uri_owl_Thing, uri_owl_Thing)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[276])).
% 0.21/0.48 tff(278,plain,
% 0.21/0.48 (iext(uri_rdf_first, uri_owl_Thing, uri_owl_Thing) <=> iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)),
% 0.21/0.48 inference(symmetry,[status(thm)],[277])).
% 0.21/0.48 tff(279,plain,
% 0.21/0.48 (iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing) <=> iext(uri_rdf_first, uri_owl_Thing, uri_owl_Thing)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.48 tff(280,plain,
% 0.21/0.48 (iext(uri_rdf_first, uri_owl_Thing, uri_owl_Thing) <=> iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)),
% 0.21/0.48 inference(symmetry,[status(thm)],[279])).
% 0.21/0.48 tff(281,plain,
% 0.21/0.48 ((~iext(uri_rdf_first, uri_owl_Thing, uri_owl_Thing)) <=> (~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[280])).
% 0.21/0.48 tff(282,assumption,(~iext(uri_rdf_first, uri_owl_Thing, uri_owl_Thing)), introduced(assumption)).
% 0.21/0.48 tff(283,plain,
% 0.21/0.48 (~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.21/0.48 tff(284,plain,
% 0.21/0.48 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))) | (~(ic(uri_owl_Thing) | (~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))) | (~(ic(uri_owl_Thing) | (~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(285,plain,
% 0.21/0.48 ((~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(uri_owl_Thing, uri_owl_Thing)) <=> icext(uri_owl_Thing, tptp_fun_X_1(uri_owl_Thing, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(uri_owl_Thing, X))))))))) <=> (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))) | (~(ic(uri_owl_Thing) | (~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(286,plain,
% 0.21/0.48 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(uri_owl_Thing, uri_owl_Thing)) <=> icext(uri_owl_Thing, tptp_fun_X_1(uri_owl_Thing, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(uri_owl_Thing, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))) | (~(ic(uri_owl_Thing) | (~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[285])).
% 0.21/0.48 tff(287,plain,
% 0.21/0.48 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(uri_owl_Thing, uri_owl_Thing)) <=> icext(uri_owl_Thing, tptp_fun_X_1(uri_owl_Thing, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(uri_owl_Thing, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))) | (~(ic(uri_owl_Thing) | (~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[286, 284])).
% 0.21/0.48 tff(288,plain,
% 0.21/0.48 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~ic(uri_owl_Thing)) | (~(icext(uri_owl_Thing, tptp_fun_X_1(uri_owl_Thing, uri_owl_Thing)) <=> icext(uri_owl_Thing, tptp_fun_X_1(uri_owl_Thing, uri_owl_Thing)))))) | (~((~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(uri_owl_Thing, X)))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(289,plain,
% 0.21/0.48 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_1(C2, C1)) <=> icext(C2, tptp_fun_X_1(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))) | (~(ic(uri_owl_Thing) | (~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.21/0.48 tff(290,plain,
% 0.21/0.48 (~((~((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))) | (~(ic(uri_owl_Thing) | (~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[289, 67])).
% 0.21/0.48 tff(291,plain,
% 0.21/0.48 (((~((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))) | (~(ic(uri_owl_Thing) | (~iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))))) | ((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(292,plain,
% 0.21/0.48 ((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.21/0.48 tff(293,plain,
% 0.21/0.48 (((~![X: $i] : (icext(uri_owl_Thing, X) <=> icext(BNODE_x!3, X))) | (~ic(BNODE_x!3)) | (~ic(uri_owl_Thing))) | ic(uri_owl_Thing)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(294,plain,
% 0.21/0.48 (ic(uri_owl_Thing)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[293, 80])).
% 0.21/0.48 tff(295,plain,
% 0.21/0.48 ((~((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))) | (~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(296,plain,
% 0.21/0.48 ((~((~ic(uri_owl_Thing)) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing))) | iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[295, 294])).
% 0.21/0.48 tff(297,plain,
% 0.21/0.48 (iext(uri_owl_equivalentClass, uri_owl_Thing, uri_owl_Thing)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[296, 292])).
% 0.21/0.48 tff(298,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[297, 283])).
% 0.21/0.48 tff(299,plain,(iext(uri_rdf_first, uri_owl_Thing, uri_owl_Thing)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(300,plain,
% 0.21/0.48 (iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[299, 278])).
% 0.21/0.48 tff(301,plain,
% 0.21/0.48 ((~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))))) | (~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w)))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(302,plain,
% 0.21/0.48 ((~((~iext(uri_owl_oneOf, uri_owl_Thing, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))))) | (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[301, 300])).
% 0.21/0.48 tff(303,plain,
% 0.21/0.48 (~((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[302, 275])).
% 0.21/0.48 tff(304,plain,
% 0.21/0.48 (((~ic(uri_owl_Thing)) | (~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w)))) | ![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(305,plain,
% 0.21/0.48 (![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.21/0.48 tff(306,plain,
% 0.21/0.48 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> (X = uri_ex_w))) | (icext(uri_owl_Thing, uri_owl_Nothing) <=> (uri_owl_Nothing = uri_ex_w))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(307,plain,
% 0.21/0.48 (icext(uri_owl_Thing, uri_owl_Nothing) <=> (uri_owl_Nothing = uri_ex_w)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[306, 305])).
% 0.21/0.48 tff(308,plain,
% 0.21/0.48 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))) | (icext(uri_owl_Thing, uri_owl_Nothing) <=> ir(uri_owl_Nothing))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(309,plain,
% 0.21/0.48 (icext(uri_owl_Thing, uri_owl_Nothing) <=> ir(uri_owl_Nothing)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[308, 91])).
% 0.21/0.48 tff(310,plain,
% 0.21/0.48 ((~![X: $i] : ir(X)) | ir(uri_owl_Nothing)),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(311,plain,
% 0.21/0.48 (ir(uri_owl_Nothing)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[310, 100])).
% 0.21/0.48 tff(312,plain,
% 0.21/0.48 ((~(icext(uri_owl_Thing, uri_owl_Nothing) <=> ir(uri_owl_Nothing))) | icext(uri_owl_Thing, uri_owl_Nothing) | (~ir(uri_owl_Nothing))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(313,plain,
% 0.21/0.48 (icext(uri_owl_Thing, uri_owl_Nothing)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[312, 311, 309])).
% 0.21/0.48 tff(314,plain,
% 0.21/0.48 ((~(icext(uri_owl_Thing, uri_owl_Nothing) <=> (uri_owl_Nothing = uri_ex_w))) | (~icext(uri_owl_Thing, uri_owl_Nothing)) | (uri_owl_Nothing = uri_ex_w)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(315,plain,
% 0.21/0.48 (uri_owl_Nothing = uri_ex_w),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[314, 313, 307])).
% 0.21/0.48 tff(316,plain,
% 0.21/0.48 (uri_owl_Nothing = BNODE_x!3),
% 0.21/0.48 inference(transitivity,[status(thm)],[315, 109])).
% 0.21/0.48 tff(317,plain,
% 0.21/0.48 (icext(uri_owl_Nothing, uri_owl_equivalentClass) <=> icext(BNODE_x!3, uri_owl_equivalentClass)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[316])).
% 0.21/0.48 tff(318,plain,
% 0.21/0.48 (icext(BNODE_x!3, uri_owl_equivalentClass) <=> icext(uri_owl_Nothing, uri_owl_equivalentClass)),
% 0.21/0.48 inference(symmetry,[status(thm)],[317])).
% 0.21/0.48 tff(319,plain,
% 0.21/0.48 (icext(uri_owl_Nothing, uri_owl_equivalentClass)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[121, 318])).
% 0.21/0.48 tff(320,plain,
% 0.21/0.48 (^[X: $i] : refl((~icext(uri_owl_Nothing, X)) <=> (~icext(uri_owl_Nothing, X)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(321,plain,
% 0.21/0.48 (![X: $i] : (~icext(uri_owl_Nothing, X)) <=> ![X: $i] : (~icext(uri_owl_Nothing, X))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[320])).
% 0.21/0.48 tff(322,plain,
% 0.21/0.48 (![X: $i] : (~icext(uri_owl_Nothing, X)) <=> ![X: $i] : (~icext(uri_owl_Nothing, X))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(323,axiom,(![X: $i] : (~icext(uri_owl_Nothing, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_class_nothing_ext')).
% 0.21/0.48 tff(324,plain,
% 0.21/0.48 (![X: $i] : (~icext(uri_owl_Nothing, X))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.21/0.48 tff(325,plain,(
% 0.21/0.48 ![X: $i] : (~icext(uri_owl_Nothing, X))),
% 0.21/0.48 inference(skolemize,[status(sab)],[324])).
% 0.21/0.48 tff(326,plain,
% 0.21/0.48 (![X: $i] : (~icext(uri_owl_Nothing, X))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[325, 321])).
% 0.21/0.48 tff(327,plain,
% 0.21/0.48 ((~![X: $i] : (~icext(uri_owl_Nothing, X))) | (~icext(uri_owl_Nothing, uri_owl_equivalentClass))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(328,plain,
% 0.21/0.48 (~icext(uri_owl_Nothing, uri_owl_equivalentClass)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[327, 326])).
% 0.21/0.48 tff(329,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[328, 319])).
% 0.21/0.48 % SZS output end Proof
% 0.21/0.49 % E exiting
%------------------------------------------------------------------------------