%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB029+3 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:42 AM UTC 2025
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SWB029+3 : TPTP v9.0.0. Released v5.2.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 07:54:42 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(icext_type, type, (
% 0.20/0.46 icext: ( $i * $i ) > $o)).
% 0.20/0.46 tff(uri_ex_w_type, type, (
% 0.20/0.46 uri_ex_w: $i)).
% 0.20/0.46 tff(tptp_fun_BNODE_y_19_type, type, (
% 0.20/0.46 tptp_fun_BNODE_y_19: $i)).
% 0.20/0.46 tff(uri_ex_A_type, type, (
% 0.20/0.46 uri_ex_A: $i)).
% 0.20/0.46 tff(tptp_fun_BNODE_x_20_type, type, (
% 0.20/0.46 tptp_fun_BNODE_x_20: $i)).
% 0.20/0.46 tff(ic_type, type, (
% 0.20/0.46 ic: $i > $o)).
% 0.20/0.46 tff(iext_type, type, (
% 0.20/0.46 iext: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(tptp_fun_BNODE_l1_18_type, type, (
% 0.20/0.46 tptp_fun_BNODE_l1_18: $i)).
% 0.20/0.46 tff(uri_owl_intersectionOf_type, type, (
% 0.20/0.46 uri_owl_intersectionOf: $i)).
% 0.20/0.46 tff(tptp_fun_X_2_type, type, (
% 0.20/0.46 tptp_fun_X_2: ( $i * $i * $i ) > $i)).
% 0.20/0.46 tff(uri_rdf_nil_type, type, (
% 0.20/0.46 uri_rdf_nil: $i)).
% 0.20/0.46 tff(tptp_fun_BNODE_l2_17_type, type, (
% 0.20/0.46 tptp_fun_BNODE_l2_17: $i)).
% 0.20/0.46 tff(uri_rdf_rest_type, type, (
% 0.20/0.46 uri_rdf_rest: $i)).
% 0.20/0.46 tff(uri_owl_complementOf_type, type, (
% 0.20/0.46 uri_owl_complementOf: $i)).
% 0.20/0.46 tff(uri_rdf_first_type, type, (
% 0.20/0.46 uri_rdf_first: $i)).
% 0.20/0.46 tff(uri_rdf_type_type, type, (
% 0.20/0.46 uri_rdf_type: $i)).
% 0.20/0.46 tff(uri_owl_Class_type, type, (
% 0.20/0.46 uri_owl_Class: $i)).
% 0.20/0.46 tff(uri_ex_B_type, type, (
% 0.20/0.46 uri_ex_B: $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (?[BNODE_x: $i, BNODE_y: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A)) <=> ?[BNODE_x: $i, BNODE_y: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (^[BNODE_x: $i, BNODE_y: $i, BNODE_l1: $i, BNODE_l2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x))), ((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) <=> ((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)))), rewrite(((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1))), ((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)))), (((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) <=> ((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)))), rewrite(((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A))), (((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)))), ((((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> ((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)))), rewrite(((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2))), ((((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)))), (((((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_y)) <=> ((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_y)))), rewrite(((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_y)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y))), (((((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_y)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y)))), ((((((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_y)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> ((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))), ((((((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_y)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)))), (((((((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_y)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A)) <=> ((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A)))), rewrite(((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A))), (((((((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_y)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A)) <=> (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (?[BNODE_x: $i, BNODE_y: $i, BNODE_l1: $i, BNODE_l2: $i] : ((((((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_y)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A)) <=> ?[BNODE_x: $i, BNODE_y: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.47 tff(4,axiom,(?[BNODE_x: $i, BNODE_y: $i, BNODE_l1: $i, BNODE_l2: $i] : ((((((((iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class)) & iext(uri_rdf_type, uri_ex_w, BNODE_x)) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_A)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_y)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_029_Ex_Falso_Quodlibet')).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (?[BNODE_x: $i, BNODE_y: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 (?[BNODE_x: $i, BNODE_y: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x) & iext(uri_owl_intersectionOf, BNODE_x, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_y) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_y, uri_ex_A))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.47 tff(7,plain,(
% 0.20/0.47 iext(uri_rdf_type, uri_ex_A, uri_owl_Class) & iext(uri_rdf_type, uri_ex_B, uri_owl_Class) & iext(uri_rdf_type, uri_ex_w, BNODE_x!20) & iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) & iext(uri_rdf_first, BNODE_l1!18, uri_ex_A) & iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17) & iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19) & iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_y!19, uri_ex_A)),
% 0.20/0.47 inference(skolemize,[status(sab)],[6])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 (iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)),
% 0.20/0.47 inference(and_elim,[status(thm)],[7])).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 (iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)),
% 0.20/0.47 inference(and_elim,[status(thm)],[7])).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)),
% 0.20/0.47 inference(and_elim,[status(thm)],[7])).
% 0.20/0.47 tff(11,plain,
% 0.20/0.47 (iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)),
% 0.20/0.47 inference(and_elim,[status(thm)],[7])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))))) <=> (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))))))), (((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))) <=> ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))))))))), rewrite(((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))))))) <=> ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))), (((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))) <=> ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : refl(((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))) <=> ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(15,plain,
% 0.20/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))) <=> ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[17, 15])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 (^[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, 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, 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, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))))))), rewrite((~(~((~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, 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, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))))), trans(monotonicity(rewrite(((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) <=> ((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))), trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite((icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))))), ((icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> (icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (~((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))))))), rewrite((icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (~((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))))) <=> (~(((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))), ((icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))), rewrite((~(((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))), ((icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))), ((~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z))))) <=> (~(~(((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))))), rewrite((~(~(((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) <=> (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))), ((~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z))))) <=> (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z)))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))), rewrite((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z)))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))), ((((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z))))))) <=> (((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))))), rewrite((((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))), ((((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(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_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z)))))))) <=> (((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))))), rewrite((((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z)))))))) <=> ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(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_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z)))))))) <=> ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (![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_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (^[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_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(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_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (![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_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(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_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (![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_intersectionOf, 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_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (^[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_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) <=> (iext(uri_owl_intersectionOf, 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_intersectionOf, 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_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, 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_intersectionOf, 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_intersectionOf, 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_intersectionOf, 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_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (![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_intersectionOf, 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_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.48 tff(26,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_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB002+0.ax','owl_bool_intersectionof_class_002')).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (![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_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (![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_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.48 tff(29,plain,(
% 0.20/0.48 ![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_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z)))))))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[28])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![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_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_2(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_2(C2, C1, Z)) & icext(C2, tptp_fun_X_2(C2, C1, Z))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[32, 13])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (((~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 ((~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (((~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))))) <=> (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (((~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (((~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (((~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (((~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[37, 35])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (((~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X))))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (((~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[39, 34])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (((~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_y!19)) | (~ic(uri_ex_A)) | (~ic(BNODE_x!20)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~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_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_2(C2, C1, Z))) | (~icext(C2, tptp_fun_X_2(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_2(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!18, uri_ex_A)) | (~iext(uri_rdf_rest, BNODE_l1!18, BNODE_l2!17)) | (~iext(uri_rdf_first, BNODE_l2!17, BNODE_y!19)) | (~iext(uri_rdf_rest, BNODE_l2!17, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 (~((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[42, 33, 11, 10, 9, 8])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 (((~(iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18) | (~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (((~icext(BNODE_y!19, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))) | (~icext(uri_ex_A, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20)))) <=> icext(BNODE_x!20, tptp_fun_X_2(BNODE_y!19, uri_ex_A, BNODE_x!20))))) | (~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X))))))))) | ((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 ((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 (iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)),
% 0.20/0.49 inference(and_elim,[status(thm)],[7])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 ((~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))) | (~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 ((~((~iext(uri_owl_intersectionOf, BNODE_x!20, BNODE_l1!18)) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))))) | (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (~((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 (((~ic(BNODE_x!20)) | (~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X))))) | ![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 (![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 ((~![X: $i] : (~(((~icext(BNODE_y!19, X)) | (~icext(uri_ex_A, X))) <=> icext(BNODE_x!20, X)))) | (~(((~icext(BNODE_y!19, uri_ex_w)) | (~icext(uri_ex_A, uri_ex_w))) <=> icext(BNODE_x!20, uri_ex_w)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (~(((~icext(BNODE_y!19, uri_ex_w)) | (~icext(uri_ex_A, uri_ex_w))) <=> icext(BNODE_x!20, uri_ex_w))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(57,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB002+0.ax','rdfs_cext_def')).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.49 tff(59,plain,(
% 0.20/0.49 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.20/0.49 inference(skolemize,[status(sab)],[58])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_w, BNODE_x!20) <=> icext(BNODE_x!20, uri_ex_w))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(62,plain,
% 0.20/0.49 (iext(uri_rdf_type, uri_ex_w, BNODE_x!20) <=> icext(BNODE_x!20, uri_ex_w)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (iext(uri_rdf_type, uri_ex_w, BNODE_x!20)),
% 0.20/0.49 inference(and_elim,[status(thm)],[7])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 ((~(iext(uri_rdf_type, uri_ex_w, BNODE_x!20) <=> icext(BNODE_x!20, uri_ex_w))) | (~iext(uri_rdf_type, uri_ex_w, BNODE_x!20)) | icext(BNODE_x!20, uri_ex_w)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 ((~(iext(uri_rdf_type, uri_ex_w, BNODE_x!20) <=> icext(BNODE_x!20, uri_ex_w))) | icext(BNODE_x!20, uri_ex_w)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (icext(BNODE_x!20, uri_ex_w)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[65, 62])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 ((((~icext(BNODE_y!19, uri_ex_w)) | (~icext(uri_ex_A, uri_ex_w))) <=> icext(BNODE_x!20, uri_ex_w)) | (~((~icext(BNODE_y!19, uri_ex_w)) | (~icext(uri_ex_A, uri_ex_w)))) | (~icext(BNODE_x!20, uri_ex_w))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 ((((~icext(BNODE_y!19, uri_ex_w)) | (~icext(uri_ex_A, uri_ex_w))) <=> icext(BNODE_x!20, uri_ex_w)) | (~((~icext(BNODE_y!19, uri_ex_w)) | (~icext(uri_ex_A, uri_ex_w))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (~((~icext(BNODE_y!19, uri_ex_w)) | (~icext(uri_ex_A, uri_ex_w)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[68, 53])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (((~icext(BNODE_y!19, uri_ex_w)) | (~icext(uri_ex_A, uri_ex_w))) | icext(uri_ex_A, uri_ex_w)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 (icext(uri_ex_A, uri_ex_w)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (((~icext(BNODE_y!19, uri_ex_w)) | (~icext(uri_ex_A, uri_ex_w))) | icext(BNODE_y!19, uri_ex_w)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (icext(BNODE_y!19, uri_ex_w)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 ((icext(uri_ex_A, uri_ex_w) <=> icext(BNODE_y!19, uri_ex_w)) | (~icext(uri_ex_A, uri_ex_w)) | (~icext(BNODE_y!19, uri_ex_w))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (icext(uri_ex_A, uri_ex_w) <=> icext(BNODE_y!19, uri_ex_w)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[74, 73, 71])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (iext(uri_owl_complementOf, BNODE_y!19, uri_ex_A)),
% 0.20/0.49 inference(and_elim,[status(thm)],[7])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (^[Z: $i, C: $i] : refl(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[82, 80])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (^[Z: $i, C: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(rewrite((icext(Z, X) <=> (~icext(C, X))) <=> (~(icext(C, X) <=> icext(Z, X)))), rewrite((~(icext(C, X) <=> icext(Z, X))) <=> (~(icext(C, X) <=> icext(Z, X)))), ((icext(Z, X) <=> (~icext(C, X))) <=> (~(icext(C, X) <=> icext(Z, X)))))), (![X: $i] : (icext(Z, X) <=> (~icext(C, X))) <=> ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))), (((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> ((ic(Z) & ic(C)) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), rewrite(((ic(Z) & ic(C)) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) <=> (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))), (((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> (iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))), rewrite((iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 (![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.49 tff(89,axiom,(![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB002+0.ax','owl_bool_complementof_class')).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.49 tff(92,plain,(
% 0.20/0.49 ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[91])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) | (~ic(Z)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[94, 78])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_y!19, uri_ex_A)) | (~((~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(icext(uri_ex_A, X) <=> icext(BNODE_y!19, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, BNODE_y!19, uri_ex_A)) | (~((~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(icext(uri_ex_A, X) <=> icext(BNODE_y!19, X)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_y!19, uri_ex_A)) | (~((~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(icext(uri_ex_A, X) <=> icext(BNODE_y!19, X)))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, BNODE_y!19, uri_ex_A)) | (~((~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(icext(uri_ex_A, X) <=> icext(BNODE_y!19, X))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 (~((~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(icext(uri_ex_A, X) <=> icext(BNODE_y!19, X)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[98, 95, 76])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 (((~ic(uri_ex_A)) | (~ic(BNODE_y!19)) | (~![X: $i] : (~(icext(uri_ex_A, X) <=> icext(BNODE_y!19, X))))) | ![X: $i] : (~(icext(uri_ex_A, X) <=> icext(BNODE_y!19, X)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 (![X: $i] : (~(icext(uri_ex_A, X) <=> icext(BNODE_y!19, X)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 ((~![X: $i] : (~(icext(uri_ex_A, X) <=> icext(BNODE_y!19, X)))) | (~(icext(uri_ex_A, uri_ex_w) <=> icext(BNODE_y!19, uri_ex_w)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[102, 101, 75])).
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------