%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB021+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 05:29:38 AM UTC 2025
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB021+2 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 07:49:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(uri_ex_w2_type, type, (
% 0.11/0.38 uri_ex_w2: $i)).
% 0.11/0.38 tff(tptp_fun_X_3_type, type, (
% 0.11/0.38 tptp_fun_X_3: ( $i * $i ) > $i)).
% 0.11/0.38 tff(uri_ex_c3_type, type, (
% 0.11/0.38 uri_ex_c3: $i)).
% 0.11/0.38 tff(uri_ex_c4_type, type, (
% 0.11/0.38 uri_ex_c4: $i)).
% 0.11/0.38 tff(uri_ex_w1_type, type, (
% 0.11/0.38 uri_ex_w1: $i)).
% 0.11/0.38 tff(icext_type, type, (
% 0.11/0.38 icext: ( $i * $i ) > $o)).
% 0.11/0.38 tff(uri_ex_c1_type, type, (
% 0.11/0.38 uri_ex_c1: $i)).
% 0.11/0.38 tff(ic_type, type, (
% 0.11/0.38 ic: $i > $o)).
% 0.11/0.38 tff(iext_type, type, (
% 0.11/0.38 iext: ( $i * $i * $i ) > $o)).
% 0.11/0.38 tff(tptp_fun_BNODE_l11_12_type, type, (
% 0.11/0.38 tptp_fun_BNODE_l11_12: $i)).
% 0.11/0.38 tff(uri_owl_oneOf_type, type, (
% 0.11/0.38 uri_owl_oneOf: $i)).
% 0.11/0.38 tff(tptp_fun_X_1_type, type, (
% 0.11/0.38 tptp_fun_X_1: ( $i * $i * $i ) > $i)).
% 0.11/0.38 tff(uri_rdf_nil_type, type, (
% 0.11/0.38 uri_rdf_nil: $i)).
% 0.11/0.38 tff(tptp_fun_BNODE_l12_11_type, type, (
% 0.11/0.38 tptp_fun_BNODE_l12_11: $i)).
% 0.11/0.38 tff(uri_rdf_rest_type, type, (
% 0.11/0.38 uri_rdf_rest: $i)).
% 0.11/0.38 tff(tptp_fun_BNODE_l42_4_type, type, (
% 0.11/0.38 tptp_fun_BNODE_l42_4: $i)).
% 0.11/0.38 tff(uri_ex_c2_type, type, (
% 0.11/0.38 uri_ex_c2: $i)).
% 0.11/0.38 tff(uri_rdf_first_type, type, (
% 0.11/0.38 uri_rdf_first: $i)).
% 0.11/0.38 tff(tptp_fun_BNODE_l41_5_type, type, (
% 0.11/0.38 tptp_fun_BNODE_l41_5: $i)).
% 0.11/0.38 tff(uri_owl_unionOf_type, type, (
% 0.11/0.38 uri_owl_unionOf: $i)).
% 0.11/0.38 tff(tptp_fun_BNODE_l33_6_type, type, (
% 0.11/0.38 tptp_fun_BNODE_l33_6: $i)).
% 0.11/0.38 tff(uri_ex_w3_type, type, (
% 0.11/0.38 uri_ex_w3: $i)).
% 0.11/0.38 tff(tptp_fun_BNODE_l32_7_type, type, (
% 0.11/0.38 tptp_fun_BNODE_l32_7: $i)).
% 0.11/0.38 tff(tptp_fun_BNODE_l31_8_type, type, (
% 0.11/0.38 tptp_fun_BNODE_l31_8: $i)).
% 0.11/0.38 tff(tptp_fun_BNODE_l22_9_type, type, (
% 0.11/0.38 tptp_fun_BNODE_l22_9: $i)).
% 0.11/0.38 tff(tptp_fun_BNODE_l21_10_type, type, (
% 0.11/0.38 tptp_fun_BNODE_l21_10: $i)).
% 0.11/0.38 tff(tptp_fun_X_2_type, type, (
% 0.11/0.38 tptp_fun_X_2: ( $i * $i * $i * $i ) > $i)).
% 0.11/0.38 tff(uri_owl_equivalentClass_type, type, (
% 0.11/0.38 uri_owl_equivalentClass: $i)).
% 0.11/0.38 tff(uri_rdf_List_type, type, (
% 0.11/0.38 uri_rdf_List: $i)).
% 0.11/0.38 tff(tptp_fun_X_0_type, type, (
% 0.11/0.38 tptp_fun_X_0: ( $i * $i * $i ) > $i)).
% 0.11/0.38 tff(1,assumption,(~(icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1)))), introduced(assumption)).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i, BNODE_l41: $i, BNODE_l42: $i] : (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil)) <=> ?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i, BNODE_l41: $i, BNODE_l42: $i] : (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (^[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i, BNODE_l41: $i, BNODE_l42: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12))), ((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2))), ((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)))), (((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil))), (((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)))), ((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21))), ((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)))), (((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2))), (((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)))), ((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22))), ((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)))), (((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3))), (((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)))), ((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil))), ((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)))), (((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31))), (((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)))), ((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1))), ((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)))), (((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32))), (((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)))), ((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2))), ((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)))), (((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33))), (((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)))), ((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3))), ((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)))), (((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil))), (((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)))), ((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41))), ((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)))), (((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1))), (((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)))), ((((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42))), ((((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)))), (((((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2))), (((((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2)))), ((((((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil)) <=> ((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil))), ((((((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i, BNODE_l41: $i, BNODE_l42: $i] : (((((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil)) <=> ?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i, BNODE_l41: $i, BNODE_l42: $i] : (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.43 tff(5,axiom,(?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i, BNODE_l41: $i, BNODE_l42: $i] : (((((((((((((((((((((iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41)) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42)) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_021_Composite_Enumerations')).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i, BNODE_l41: $i, BNODE_l42: $i] : (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i, BNODE_l41: $i, BNODE_l42: $i] : (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41) & iext(uri_rdf_first, BNODE_l41, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41, BNODE_l42) & iext(uri_rdf_first, BNODE_l42, uri_ex_c2) & iext(uri_rdf_rest, BNODE_l42, uri_rdf_nil))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.43 tff(8,plain,(
% 0.20/0.43 iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) & iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11) & iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) & iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9) & iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil) & iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) & iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1) & iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7) & iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2) & iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6) & iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3) & iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) & iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1) & iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4) & iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2) & iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)),
% 0.20/0.43 inference(skolemize,[status(sab)],[7])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)),
% 0.20/0.43 inference(and_elim,[status(thm)],[8])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)),
% 0.20/0.43 inference(and_elim,[status(thm)],[8])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 (iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)),
% 0.20/0.43 inference(and_elim,[status(thm)],[8])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)),
% 0.20/0.43 inference(and_elim,[status(thm)],[8])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))) <=> (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))))))), (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))))))))), rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))), (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : refl(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[18, 16])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) <=> ((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))) <=> (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) <=> (((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))), rewrite((((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))) <=> (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))))), rewrite((((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : rewrite(((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2))), ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A1) | (X = A2))))) <=> (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))), (((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A1) | (X = A2)))))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))), (((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A1) | (X = A2)))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A1) | (X = A2)))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.44 tff(27,axiom,(![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A1) | (X = A2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_enum_class_002')).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.45 tff(30,plain,(
% 0.20/0.45 ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1))))))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[29])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[32, 19])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[33, 14])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 (((~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 ((~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))))) <=> (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (((~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (((~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1))))))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 (((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[40, 35])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!12, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l12!11, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!11, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l11!12, BNODE_l12!11)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1))))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (~((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[43, 34, 12, 11, 10, 9])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (((~(iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1)) <=> ((tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w1) | (tptp_fun_X_1(uri_ex_w2, uri_ex_w1, uri_ex_c1) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1))))))))) | ((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 ((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 (iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)),
% 0.20/0.46 inference(and_elim,[status(thm)],[8])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 ((~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))) | (~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 ((~((~iext(uri_owl_oneOf, uri_ex_c1, BNODE_l11!12)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))))) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1))))) | ![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 ((~![X: $i] : (icext(uri_ex_c1, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1)))) | (icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[53, 52, 1])).
% 0.20/0.46 tff(55,plain,(icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(56,assumption,(~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))), introduced(assumption)).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 (iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)),
% 0.20/0.46 inference(and_elim,[status(thm)],[8])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 (iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)),
% 0.20/0.46 inference(and_elim,[status(thm)],[8])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 (iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)),
% 0.20/0.46 inference(and_elim,[status(thm)],[8])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 (iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)),
% 0.20/0.46 inference(and_elim,[status(thm)],[8])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)),
% 0.20/0.46 inference(and_elim,[status(thm)],[8])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 (iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)),
% 0.20/0.46 inference(and_elim,[status(thm)],[8])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))) <=> (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))))))))), (((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))) <=> ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))))))))))), rewrite(((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))))))))) <=> ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))), (((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))) <=> ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : refl(((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))) <=> ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : rewrite(((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))) <=> ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[68, 66])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))))))), rewrite((~(~((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))))) <=> ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))))), trans(monotonicity(rewrite(((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) <=> ((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))) <=> (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) <=> (((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))), rewrite((((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))) <=> (((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))))), rewrite((((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))) <=> ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : rewrite(((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2))), ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3))), ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3)))), (((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3))), (((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3)))), ((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))), ((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), rewrite((iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (((X = A1) | (X = A2)) | (X = A3))))) <=> (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))), (((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (((X = A1) | (X = A2)) | (X = A3)))))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))))), (((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (((X = A1) | (X = A2)) | (X = A3)))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (((X = A1) | (X = A2)) | (X = A3)))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.47 tff(77,axiom,(![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (((X = A1) | (X = A2)) | (X = A3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_enum_class_003')).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.47 tff(80,plain,(
% 0.20/0.47 ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1))))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[79])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[82, 69])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[83, 64])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))))) | (~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)))) <=> ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))) | (~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))))) | (~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (((~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))))) | (~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 ((~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2) | (X = uri_ex_w1)))))))))) <=> (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 (((~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2) | (X = uri_ex_w1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[87])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (((~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2) | (X = uri_ex_w1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))))) | (~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[88, 86])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 (((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2) | (X = uri_ex_w1)))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))))) | (~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2) | (X = uri_ex_w1)))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))) | (~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))))) | (~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[90, 85])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2) | (X = uri_ex_w1)))))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(A3, A2, A1, Z)) <=> ((tptp_fun_X_2(A3, A2, A1, Z) = A3) | (tptp_fun_X_2(A3, A2, A1, Z) = A2) | (tptp_fun_X_2(A3, A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A3) | (X = A2) | (X = A1)))))))))))) | (~iext(uri_rdf_first, BNODE_l31!8, uri_ex_w1)) | (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))))) | (~iext(uri_rdf_first, BNODE_l32!7, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l31!8, BNODE_l32!7)) | (~iext(uri_rdf_rest, BNODE_l33!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l33!6, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l32!7, BNODE_l33!6))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 (~((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[93, 84, 62, 61, 60, 59, 58, 57])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 (((~(iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3)) <=> ((tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_2(uri_ex_w3, uri_ex_w2, uri_ex_w1, uri_ex_c3) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3))))))))) | ((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 ((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 (iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)),
% 0.20/0.48 inference(and_elim,[status(thm)],[8])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 ((~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))) | (~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(99,plain,
% 0.20/0.48 ((~((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))))) | (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 (~((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (((~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3))))) | ![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 (![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 ((~![X: $i] : (icext(uri_ex_c3, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w1) | (X = uri_ex_w3)))) | (icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 (icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 ((~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)))) | (~icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 ((~icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 (~icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[106, 56])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))) <=> (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(109,plain,
% 0.20/0.48 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.48 tff(110,plain,
% 0.20/0.48 (^[C1: $i, C2: $i] : refl((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.48 tff(112,plain,
% 0.20/0.48 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[113, 111])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 (^[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(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))), trans(monotonicity(rewrite((~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))) <=> (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))), rewrite((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) <=> (((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))), rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 (![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(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[115])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 (^[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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 (![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 (^[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)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.48 tff(122,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/sandbox2/benchmark/theBenchmark.p','owl_eqdis_equivalentclass')).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.20/0.49 tff(125,plain,(
% 0.20/0.49 ![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[124])).
% 0.20/0.49 tff(126,plain,
% 0.20/0.49 (![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(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.20/0.49 tff(128,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[127, 114])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[128, 109])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X))) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X))) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 ((~((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X))))))))) <=> (~((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X))) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X))) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[131])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X))) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[132, 130])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X)))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X))) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 (~((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X))) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[135, 129])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 (((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) | (~((~![X: $i] : (icext(uri_ex_c3, X) <=> icext(uri_ex_c4, X))) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4))))))) | (iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 (iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_oneOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 (![X: $i, Y: $i] : (iext(uri_owl_oneOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[144])).
% 0.20/0.49 tff(146,axiom,(![X: $i, Y: $i] : (iext(uri_owl_oneOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_prop_oneof_ext')).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.20/0.49 tff(149,plain,(
% 0.20/0.49 ![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[148])).
% 0.20/0.49 tff(150,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.20/0.49 tff(151,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[150, 140])).
% 0.20/0.49 tff(152,plain,
% 0.20/0.49 (((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, BNODE_l31!8)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, BNODE_l31!8)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(153,plain,
% 0.20/0.49 ((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, BNODE_l31!8)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(154,plain,
% 0.20/0.49 ((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_oneOf, uri_ex_c3, BNODE_l31!8)) | (~((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, BNODE_l31!8))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.49 tff(155,plain,
% 0.20/0.49 (~((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, BNODE_l31!8)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[154, 151, 97])).
% 0.20/0.49 tff(156,plain,
% 0.20/0.49 (((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, BNODE_l31!8))) | ic(uri_ex_c3)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(157,plain,
% 0.20/0.49 (ic(uri_ex_c3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.20/0.49 tff(158,plain,
% 0.20/0.49 (iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)),
% 0.20/0.49 inference(and_elim,[status(thm)],[8])).
% 0.20/0.49 tff(159,plain,
% 0.20/0.49 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.49 tff(161,plain,
% 0.20/0.49 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(162,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[161])).
% 0.20/0.49 tff(163,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(164,plain,
% 0.20/0.49 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_unionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(165,plain,
% 0.20/0.49 (![X: $i, Y: $i] : (iext(uri_owl_unionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.49 tff(166,axiom,(![X: $i, Y: $i] : (iext(uri_owl_unionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_prop_unionof_ext')).
% 0.20/0.49 tff(167,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.49 tff(168,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.20/0.49 tff(169,plain,(
% 0.20/0.49 ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[168])).
% 0.20/0.49 tff(170,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.20/0.49 tff(171,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[170, 160])).
% 0.20/0.49 tff(172,plain,
% 0.20/0.49 (((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~icext(uri_rdf_List, BNODE_l41!5)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~icext(uri_rdf_List, BNODE_l41!5)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(173,plain,
% 0.20/0.49 ((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~icext(uri_rdf_List, BNODE_l41!5)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(174,plain,
% 0.20/0.49 ((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~icext(uri_rdf_List, BNODE_l41!5))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.49 tff(175,plain,
% 0.20/0.49 (~((~ic(uri_ex_c4)) | (~icext(uri_rdf_List, BNODE_l41!5)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[174, 171, 158])).
% 0.20/0.49 tff(176,plain,
% 0.20/0.49 (((~ic(uri_ex_c4)) | (~icext(uri_rdf_List, BNODE_l41!5))) | ic(uri_ex_c4)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(177,plain,
% 0.20/0.49 (ic(uri_ex_c4)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 ((~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)) <=> (~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(179,axiom,(~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_021_Composite_Enumerations')).
% 0.20/0.49 tff(180,plain,
% 0.20/0.49 (~iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.20/0.49 tff(181,plain,
% 0.20/0.49 ((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(182,plain,
% 0.20/0.49 ((~(iext(uri_owl_equivalentClass, uri_ex_c3, uri_ex_c4) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))))) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c4)) | (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.20/0.49 tff(183,plain,
% 0.20/0.49 (~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[182, 177, 157, 138])).
% 0.20/0.49 tff(184,plain,
% 0.20/0.49 ((icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 (icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 (icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[185, 107])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 (iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)),
% 0.20/0.49 inference(and_elim,[status(thm)],[8])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)),
% 0.20/0.49 inference(and_elim,[status(thm)],[8])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 (iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)),
% 0.20/0.49 inference(and_elim,[status(thm)],[8])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 (iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)),
% 0.20/0.49 inference(and_elim,[status(thm)],[8])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))) <=> (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))))), rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(192,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[191])).
% 0.20/0.50 tff(193,plain,
% 0.20/0.50 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : refl(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(194,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[193])).
% 0.20/0.50 tff(195,plain,
% 0.20/0.50 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(196,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[195])).
% 0.20/0.50 tff(197,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[196, 194])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) <=> ((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))) <=> (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))), rewrite((iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) <=> (((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))), rewrite((((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))) <=> (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))))), rewrite((((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[198])).
% 0.20/0.50 tff(200,plain,
% 0.20/0.50 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(201,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[200])).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(203,plain,
% 0.20/0.50 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X))))) <=> (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(204,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[203])).
% 0.20/0.50 tff(205,axiom,(![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_bool_unionof_class_002')).
% 0.20/0.50 tff(206,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.20/0.50 tff(208,plain,(
% 0.20/0.50 ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z)))))))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[207])).
% 0.20/0.50 tff(209,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[208, 201])).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[209, 199])).
% 0.20/0.50 tff(211,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[210, 197])).
% 0.20/0.50 tff(212,plain,
% 0.20/0.50 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[211, 192])).
% 0.20/0.50 tff(213,plain,
% 0.20/0.50 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(214,plain,
% 0.20/0.51 (((~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X))))))))))) <=> ((~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(215,plain,
% 0.20/0.51 ((~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))) <=> (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(216,plain,
% 0.20/0.51 (((~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[215])).
% 0.20/0.51 tff(217,plain,
% 0.20/0.51 (((~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))) <=> ((~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[216, 214])).
% 0.20/0.51 tff(218,plain,
% 0.20/0.51 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X))))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[217])).
% 0.20/0.51 tff(219,plain,
% 0.20/0.51 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[218, 213])).
% 0.20/0.51 tff(220,plain,
% 0.20/0.51 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(221,plain,
% 0.20/0.51 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_0(C2, C1, Z)) | icext(C1, tptp_fun_X_0(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_rest, BNODE_l42!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l42!4, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_l41!5, BNODE_l42!4)) | (~iext(uri_rdf_first, BNODE_l41!5, uri_ex_c1)) | (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.20/0.51 tff(222,plain,
% 0.20/0.51 (~((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[221, 212, 190, 189, 188, 187])).
% 0.20/0.51 tff(223,plain,
% 0.20/0.51 (((~(iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5) | (~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c4, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) <=> (icext(uri_ex_c1, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4)) | icext(uri_ex_c2, tptp_fun_X_0(uri_ex_c2, uri_ex_c1, uri_ex_c4))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X))))))))) | ((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(224,plain,
% 0.20/0.51 ((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.20/0.51 tff(225,plain,
% 0.20/0.51 ((~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))))))) | (~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(226,plain,
% 0.20/0.51 ((~((~iext(uri_owl_unionOf, uri_ex_c4, BNODE_l41!5)) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))))))) | (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[225, 158])).
% 0.20/0.51 tff(227,plain,
% 0.20/0.51 (~((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[226, 224])).
% 0.20/0.51 tff(228,plain,
% 0.20/0.51 (((~ic(uri_ex_c4)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X))))) | ![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(229,plain,
% 0.20/0.51 (![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.20/0.51 tff(230,plain,
% 0.20/0.51 ((~![X: $i] : (icext(uri_ex_c4, X) <=> (icext(uri_ex_c1, X) | icext(uri_ex_c2, X)))) | (icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(231,plain,
% 0.20/0.51 (icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.20/0.51 tff(232,plain,
% 0.20/0.51 ((~(icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))))) | (~icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | (icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(233,plain,
% 0.20/0.51 ((~icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | (icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.20/0.51 tff(234,plain,
% 0.20/0.51 (icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[233, 186])).
% 0.20/0.51 tff(235,plain,
% 0.20/0.51 (((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)) | (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(236,plain,
% 0.20/0.51 (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[235, 56])).
% 0.20/0.51 tff(237,plain,
% 0.20/0.51 (((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)) | (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(238,plain,
% 0.20/0.51 (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[237, 56])).
% 0.20/0.51 tff(239,plain,
% 0.20/0.51 ((~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1))) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(240,plain,
% 0.20/0.51 (~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[239, 238, 236])).
% 0.20/0.51 tff(241,plain,
% 0.20/0.51 ((~(icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1)))) | (~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(242,plain,
% 0.20/0.51 (~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[241, 240, 55])).
% 0.20/0.51 tff(243,assumption,(~(icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)))), introduced(assumption)).
% 0.20/0.52 tff(244,plain,
% 0.20/0.52 (iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)),
% 0.20/0.52 inference(and_elim,[status(thm)],[8])).
% 0.20/0.52 tff(245,plain,
% 0.20/0.52 (iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)),
% 0.20/0.52 inference(and_elim,[status(thm)],[8])).
% 0.20/0.52 tff(246,plain,
% 0.20/0.52 (iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)),
% 0.20/0.52 inference(and_elim,[status(thm)],[8])).
% 0.20/0.52 tff(247,plain,
% 0.20/0.52 (iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)),
% 0.20/0.52 inference(and_elim,[status(thm)],[8])).
% 0.20/0.52 tff(248,plain,
% 0.20/0.52 (((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(249,plain,
% 0.20/0.52 (((~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(250,plain,
% 0.20/0.52 ((~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2)))))))))) <=> (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3))))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(251,plain,
% 0.20/0.52 (((~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[250])).
% 0.20/0.52 tff(252,plain,
% 0.20/0.52 (((~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[251, 249])).
% 0.20/0.52 tff(253,plain,
% 0.20/0.52 (((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2)))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3))))))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[252])).
% 0.20/0.52 tff(254,plain,
% 0.20/0.52 (((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2)))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[253, 248])).
% 0.20/0.52 tff(255,plain,
% 0.20/0.52 ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w3) | (X = uri_ex_w2)))))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(256,plain,
% 0.20/0.52 ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(A2, A1, Z)) <=> ((tptp_fun_X_1(A2, A1, Z) = A2) | (tptp_fun_X_1(A2, A1, Z) = A1)))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!10, uri_ex_w2)) | (~iext(uri_rdf_rest, BNODE_l22!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!9, uri_ex_w3)) | (~iext(uri_rdf_rest, BNODE_l21!10, BNODE_l22!9)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3))))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.20/0.52 tff(257,plain,
% 0.20/0.52 (~((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[256, 34, 247, 246, 245, 244])).
% 0.20/0.52 tff(258,plain,
% 0.20/0.52 (((~(iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c2, tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2)) <=> ((tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w2) | (tptp_fun_X_1(uri_ex_w3, uri_ex_w2, uri_ex_c2) = uri_ex_w3)))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3))))))))) | ((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(259,plain,
% 0.20/0.52 ((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.20/0.52 tff(260,plain,
% 0.20/0.52 (iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)),
% 0.20/0.52 inference(and_elim,[status(thm)],[8])).
% 0.20/0.52 tff(261,plain,
% 0.20/0.52 ((~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))))))) | (~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3))))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(262,plain,
% 0.20/0.52 ((~((~iext(uri_owl_oneOf, uri_ex_c2, BNODE_l21!10)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))))))) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[261, 260])).
% 0.20/0.52 tff(263,plain,
% 0.20/0.52 (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[262, 259])).
% 0.20/0.52 tff(264,plain,
% 0.20/0.52 (((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3))))) | ![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(265,plain,
% 0.20/0.52 (![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.20/0.52 tff(266,plain,
% 0.20/0.52 ((~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_w2) | (X = uri_ex_w3)))) | (icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(267,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[266, 265, 243])).
% 0.20/0.52 tff(268,plain,(icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(269,plain,
% 0.20/0.52 (((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)) | (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(270,plain,
% 0.20/0.52 (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[269, 56])).
% 0.20/0.52 tff(271,plain,
% 0.20/0.52 ((~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(272,plain,
% 0.20/0.52 (~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[271, 270, 236])).
% 0.20/0.52 tff(273,plain,
% 0.20/0.52 ((~(icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)))) | (~icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(274,plain,
% 0.20/0.52 (~icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[273, 272, 268])).
% 0.20/0.52 tff(275,plain,
% 0.20/0.52 ((~(icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))) | icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(276,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[275, 274, 242, 234])).
% 0.20/0.52 tff(277,plain,((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(278,plain,
% 0.20/0.52 ((~(icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)))) | icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | (~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(279,plain,
% 0.20/0.52 (icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | (~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[278, 104])).
% 0.20/0.52 tff(280,plain,
% 0.20/0.52 (icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[279, 277])).
% 0.20/0.52 tff(281,plain,
% 0.20/0.52 ((icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | (~icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | (~icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(282,plain,
% 0.20/0.52 ((~icext(uri_ex_c3, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | (~icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[281, 183])).
% 0.20/0.52 tff(283,plain,
% 0.20/0.52 (~icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[282, 280])).
% 0.20/0.52 tff(284,plain,
% 0.20/0.52 ((~(icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))))) | icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | (~(icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(285,plain,
% 0.20/0.52 (icext(uri_ex_c4, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | (~(icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[284, 231])).
% 0.20/0.52 tff(286,plain,
% 0.20/0.52 (~(icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[285, 283])).
% 0.20/0.52 tff(287,plain,
% 0.20/0.52 ((icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | (~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(288,plain,
% 0.20/0.52 (~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[287, 286])).
% 0.20/0.52 tff(289,plain,
% 0.20/0.52 ((~(icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1)))) | icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | (~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(290,plain,
% 0.20/0.52 (~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[289, 288, 55])).
% 0.20/0.52 tff(291,plain,
% 0.20/0.52 (((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1)) | (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(292,plain,
% 0.20/0.52 (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.20/0.52 tff(293,plain,
% 0.20/0.52 (((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1)) | (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(294,plain,
% 0.20/0.52 (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[293, 290])).
% 0.20/0.52 tff(295,plain,
% 0.20/0.52 ((icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(296,plain,
% 0.20/0.52 (~icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[295, 286])).
% 0.20/0.52 tff(297,plain,
% 0.20/0.52 ((~(icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) <=> ((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)))) | icext(uri_ex_c2, tptp_fun_X_3(uri_ex_c4, uri_ex_c3)) | (~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(298,plain,
% 0.20/0.53 (~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[297, 296, 268])).
% 0.20/0.53 tff(299,plain,
% 0.20/0.53 (((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)) | (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(300,plain,
% 0.20/0.53 (~(tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[299, 298])).
% 0.20/0.53 tff(301,plain,
% 0.20/0.53 ((~((tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3))) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w2) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w1) | (tptp_fun_X_3(uri_ex_c4, uri_ex_c3) = uri_ex_w3)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(302,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[301, 300, 294, 277, 292])).
% 0.20/0.53 % SZS output end Proof
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------