%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB038+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:29:44 AM UTC 2025
% Result : Theorem 78.67s 78.83s
% Output : Proof 78.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWB038+1 : TPTP v9.0.0. Released v5.2.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 07:52:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 78.67/78.83 % SZS status Theorem
% 78.67/78.83 % SZS output start Proof
% 78.67/78.83 tff(icext_type, type, (
% 78.67/78.83 icext: ( $i * $i ) > $o)).
% 78.67/78.83 tff(tptp_fun_X_67_type, type, (
% 78.67/78.83 tptp_fun_X_67: ( $i * $i ) > $i)).
% 78.67/78.83 tff(uri_ex_c1_type, type, (
% 78.67/78.83 uri_ex_c1: $i)).
% 78.67/78.83 tff(uri_ex_c2_type, type, (
% 78.67/78.83 uri_ex_c2: $i)).
% 78.67/78.83 tff(uri_ex_y_type, type, (
% 78.67/78.83 uri_ex_y: $i)).
% 78.67/78.83 tff(uri_ex_x_type, type, (
% 78.67/78.83 uri_ex_x: $i)).
% 78.67/78.83 tff(tptp_fun_X6_140_type, type, (
% 78.67/78.83 tptp_fun_X6_140: $i)).
% 78.67/78.83 tff(tptp_fun_X1_146_type, type, (
% 78.67/78.83 tptp_fun_X1_146: $i)).
% 78.67/78.83 tff(tptp_fun_X5_142_type, type, (
% 78.67/78.83 tptp_fun_X5_142: $i)).
% 78.67/78.83 tff(ic_type, type, (
% 78.67/78.83 ic: $i > $o)).
% 78.67/78.83 tff(iext_type, type, (
% 78.67/78.83 iext: ( $i * $i * $i ) > $o)).
% 78.67/78.83 tff(tptp_fun_X0_144_type, type, (
% 78.67/78.83 tptp_fun_X0_144: $i)).
% 78.67/78.83 tff(uri_owl_intersectionOf_type, type, (
% 78.67/78.83 uri_owl_intersectionOf: $i)).
% 78.67/78.83 tff(tptp_fun_X_3_type, type, (
% 78.67/78.83 tptp_fun_X_3: ( $i * $i * $i ) > $i)).
% 78.67/78.83 tff(uri_rdf_nil_type, type, (
% 78.67/78.83 uri_rdf_nil: $i)).
% 78.67/78.83 tff(tptp_fun_X2_143_type, type, (
% 78.67/78.83 tptp_fun_X2_143: $i)).
% 78.67/78.83 tff(uri_rdf_rest_type, type, (
% 78.67/78.83 uri_rdf_rest: $i)).
% 78.67/78.83 tff(uri_rdf_first_type, type, (
% 78.67/78.83 uri_rdf_first: $i)).
% 78.67/78.83 tff(tptp_fun_X3_141_type, type, (
% 78.67/78.83 tptp_fun_X3_141: $i)).
% 78.67/78.83 tff(uri_owl_unionOf_type, type, (
% 78.67/78.83 uri_owl_unionOf: $i)).
% 78.67/78.83 tff(tptp_fun_X4_145_type, type, (
% 78.67/78.83 tptp_fun_X4_145: $i)).
% 78.67/78.83 tff(uri_owl_complementOf_type, type, (
% 78.67/78.83 uri_owl_complementOf: $i)).
% 78.67/78.83 tff(uri_owl_equivalentClass_type, type, (
% 78.67/78.83 uri_owl_equivalentClass: $i)).
% 78.67/78.83 tff(uri_rdf_List_type, type, (
% 78.67/78.83 uri_rdf_List: $i)).
% 78.67/78.83 tff(tptp_fun_X_6_type, type, (
% 78.67/78.83 tptp_fun_X_6: ( $i * $i * $i ) > $i)).
% 78.67/78.83 tff(1,assumption,(~icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))), introduced(assumption)).
% 78.67/78.83 tff(2,plain,
% 78.67/78.83 (?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> ?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 78.67/78.83 inference(rewrite,[status(thm)],[])).
% 78.67/78.83 tff(3,plain,
% 78.67/78.83 (^[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1))), ((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2))), ((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2)))), (((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x))), (((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x)))), ((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4))), ((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4)))), (((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y))), (((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y)))), ((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6))), ((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6)))), (((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y))), (((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y)))), ((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil))), ((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil)))), (((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3))), (((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3)))), ((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5))), ((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5)))), (((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))), (((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))))),
% 78.67/78.84 inference(bind,[status(th)],[])).
% 78.67/78.84 tff(4,plain,
% 78.67/78.84 (?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : ((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> ?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 78.67/78.84 inference(quant_intro,[status(thm)],[3])).
% 78.67/78.84 tff(5,axiom,(?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : ((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','premise_rdfbased_sem_bool_demorgan')).
% 78.67/78.84 tff(6,plain,
% 78.67/78.84 (?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 78.67/78.84 inference(modus_ponens,[status(thm)],[5, 4])).
% 78.67/78.84 tff(7,plain,
% 78.67/78.84 (?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 78.67/78.84 inference(modus_ponens,[status(thm)],[6, 2])).
% 78.67/78.84 tff(8,plain,(
% 78.67/78.84 iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) & iext(uri_owl_complementOf, X1!146, uri_ex_x) & iext(uri_rdf_first, X0!144, X1!146) & iext(uri_rdf_rest, X0!144, X2!143) & iext(uri_rdf_first, X3!141, uri_ex_x) & iext(uri_rdf_rest, X3!141, X4!145) & iext(uri_owl_complementOf, X5!142, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6!140) & iext(uri_rdf_first, X4!145, uri_ex_y) & iext(uri_rdf_rest, X4!145, uri_rdf_nil) & iext(uri_owl_unionOf, X6!140, X3!141) & iext(uri_rdf_first, X2!143, X5!142) & iext(uri_rdf_rest, X2!143, uri_rdf_nil)),
% 78.67/78.84 inference(skolemize,[status(sab)],[7])).
% 78.67/78.84 tff(9,plain,
% 78.67/78.84 (iext(uri_rdf_rest, X2!143, uri_rdf_nil)),
% 78.67/78.84 inference(and_elim,[status(thm)],[8])).
% 78.67/78.84 tff(10,plain,
% 78.67/78.84 (iext(uri_rdf_first, X2!143, X5!142)),
% 78.67/78.84 inference(and_elim,[status(thm)],[8])).
% 78.67/78.84 tff(11,plain,
% 78.67/78.84 (iext(uri_rdf_rest, X0!144, X2!143)),
% 78.67/78.84 inference(and_elim,[status(thm)],[8])).
% 78.67/78.84 tff(12,plain,
% 78.67/78.84 (iext(uri_rdf_first, X0!144, X1!146)),
% 78.67/78.84 inference(and_elim,[status(thm)],[8])).
% 78.67/78.84 tff(13,plain,
% 78.67/78.84 (^[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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))))) <=> (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, 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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, 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(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, 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(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, 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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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)))))))))))))),
% 78.69/78.84 inference(bind,[status(th)],[])).
% 78.69/78.84 tff(14,plain,
% 78.69/78.84 (![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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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)))))))))))),
% 78.69/78.84 inference(quant_intro,[status(thm)],[13])).
% 78.69/78.84 tff(15,plain,
% 78.69/78.84 (^[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_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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z)))))))))),
% 78.69/78.84 inference(bind,[status(th)],[])).
% 78.69/78.84 tff(16,plain,
% 78.69/78.84 (![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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))))))),
% 78.69/78.84 inference(quant_intro,[status(thm)],[15])).
% 78.69/78.84 tff(17,plain,
% 78.69/78.84 (^[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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z)))))))))),
% 78.69/78.84 inference(bind,[status(th)],[])).
% 78.69/78.84 tff(18,plain,
% 78.69/78.84 (![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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))))))),
% 78.69/78.84 inference(quant_intro,[status(thm)],[17])).
% 78.69/78.84 tff(19,plain,
% 78.69/78.84 (![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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))))))),
% 78.69/78.85 inference(transitivity,[status(thm)],[18, 16])).
% 78.69/78.85 tff(20,plain,
% 78.69/78.85 (^[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_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_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))), ((icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (~((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))), rewrite((icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (~((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))) <=> (~(((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))), ((icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z)))))), rewrite((~(((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))), ((icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z)))))), ((~(icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))) <=> (~(~(((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))))), rewrite((~(~(((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))) <=> (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z)))), ((~(icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))) <=> (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z)))))), rewrite((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z)))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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_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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))))))))),
% 78.69/78.85 inference(bind,[status(th)],[])).
% 78.69/78.85 tff(21,plain,
% 78.69/78.85 (![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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))))))),
% 78.69/78.85 inference(quant_intro,[status(thm)],[20])).
% 78.69/78.85 tff(22,plain,
% 78.69/78.85 (^[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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))),
% 78.69/78.85 inference(bind,[status(th)],[])).
% 78.69/78.85 tff(23,plain,
% 78.69/78.85 (![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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))))))),
% 78.69/78.85 inference(quant_intro,[status(thm)],[22])).
% 78.69/78.85 tff(24,plain,
% 78.69/78.85 (![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))))))),
% 78.69/78.85 inference(rewrite,[status(thm)],[])).
% 78.69/78.85 tff(25,plain,
% 78.69/78.85 (^[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))))))))),
% 78.69/78.85 inference(bind,[status(th)],[])).
% 78.69/78.85 tff(26,plain,
% 78.69/78.85 (![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))))))),
% 78.69/78.85 inference(quant_intro,[status(thm)],[25])).
% 78.69/78.85 tff(27,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/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_intersectionof_class_002')).
% 78.69/78.85 tff(28,plain,
% 78.69/78.85 (![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))))))),
% 78.69/78.85 inference(modus_ponens,[status(thm)],[27, 26])).
% 78.69/78.85 tff(29,plain,
% 78.69/78.85 (![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))))))),
% 78.69/78.85 inference(modus_ponens,[status(thm)],[28, 24])).
% 78.69/78.85 tff(30,plain,(
% 78.69/78.85 ![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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))),
% 78.69/78.85 inference(skolemize,[status(sab)],[29])).
% 78.69/78.85 tff(31,plain,
% 78.69/78.85 (![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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))))))),
% 78.69/78.85 inference(modus_ponens,[status(thm)],[30, 23])).
% 78.69/78.85 tff(32,plain,
% 78.69/78.85 (![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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))))))),
% 78.69/78.85 inference(modus_ponens,[status(thm)],[31, 21])).
% 78.69/78.85 tff(33,plain,
% 78.69/78.85 (![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(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_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(C2, C1, Z))))))))),
% 78.69/78.85 inference(modus_ponens,[status(thm)],[32, 19])).
% 78.69/78.85 tff(34,plain,
% 78.69/78.85 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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)))))))))))),
% 78.69/78.85 inference(modus_ponens,[status(thm)],[33, 14])).
% 78.69/78.85 tff(35,plain,
% 78.69/78.85 (((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, 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_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))))))))),
% 78.69/78.85 inference(rewrite,[status(thm)],[])).
% 78.69/78.85 tff(36,plain,
% 78.69/78.85 (((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X))))))))))) <=> ((~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))))))))),
% 78.69/78.85 inference(rewrite,[status(thm)],[])).
% 78.69/78.85 tff(37,plain,
% 78.69/78.85 ((~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))))))) <=> (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X))))))))))),
% 78.69/78.85 inference(rewrite,[status(thm)],[])).
% 78.69/78.85 tff(38,plain,
% 78.69/78.85 (((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X))))))))))) <=> ((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))))))))),
% 78.69/78.85 inference(monotonicity,[status(thm)],[37])).
% 78.69/78.85 tff(39,plain,
% 78.69/78.85 (((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X))))))))))) <=> ((~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))))))))),
% 78.69/78.85 inference(transitivity,[status(thm)],[38, 36])).
% 78.69/78.85 tff(40,plain,
% 78.69/78.85 (((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, 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_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X))))))))))))),
% 78.69/78.86 inference(monotonicity,[status(thm)],[39])).
% 78.69/78.86 tff(41,plain,
% 78.69/78.86 (((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, 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_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))))))))),
% 78.69/78.86 inference(transitivity,[status(thm)],[40, 35])).
% 78.69/78.86 tff(42,plain,
% 78.69/78.86 ((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))))))))),
% 78.69/78.86 inference(quant_inst,[status(thm)],[])).
% 78.69/78.86 tff(43,plain,
% 78.69/78.86 ((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_3(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, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X))))))))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[42, 41])).
% 78.69/78.86 tff(44,plain,
% 78.69/78.86 (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))))))),
% 78.69/78.86 inference(unit_resolution,[status(thm)],[43, 34, 12, 11, 10, 9])).
% 78.69/78.86 tff(45,plain,
% 78.69/78.86 (((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)))) <=> icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X))))))))) | ((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))))),
% 78.69/78.86 inference(tautology,[status(thm)],[])).
% 78.69/78.86 tff(46,plain,
% 78.69/78.86 ((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X))))))),
% 78.69/78.86 inference(unit_resolution,[status(thm)],[45, 44])).
% 78.69/78.86 tff(47,plain,
% 78.69/78.86 (iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)),
% 78.69/78.86 inference(and_elim,[status(thm)],[8])).
% 78.69/78.86 tff(48,plain,
% 78.69/78.86 ((~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))))) | (~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X))))))),
% 78.69/78.86 inference(tautology,[status(thm)],[])).
% 78.69/78.86 tff(49,plain,
% 78.69/78.86 ((~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))))) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X))))))),
% 78.69/78.86 inference(unit_resolution,[status(thm)],[48, 47])).
% 78.69/78.86 tff(50,plain,
% 78.69/78.86 (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))))),
% 78.69/78.86 inference(unit_resolution,[status(thm)],[49, 46])).
% 78.69/78.86 tff(51,plain,
% 78.69/78.86 (((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X))))) | ![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))),
% 78.69/78.86 inference(tautology,[status(thm)],[])).
% 78.69/78.86 tff(52,plain,
% 78.69/78.86 (![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))),
% 78.69/78.86 inference(unit_resolution,[status(thm)],[51, 50])).
% 78.69/78.86 tff(53,plain,
% 78.69/78.86 ((~![X: $i] : (~(((~icext(X5!142, X)) | (~icext(X1!146, X))) <=> icext(uri_ex_c2, X)))) | (~(((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 78.69/78.86 inference(quant_inst,[status(thm)],[])).
% 78.69/78.86 tff(54,plain,
% 78.69/78.86 (~(((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.86 inference(unit_resolution,[status(thm)],[53, 52])).
% 78.69/78.86 tff(55,plain,
% 78.69/78.86 ((((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | ((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) | icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.86 inference(tautology,[status(thm)],[])).
% 78.69/78.86 tff(56,plain,
% 78.69/78.86 (((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) | icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.86 inference(unit_resolution,[status(thm)],[55, 54])).
% 78.69/78.86 tff(57,plain,
% 78.69/78.86 ((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.86 inference(unit_resolution,[status(thm)],[56, 1])).
% 78.69/78.86 tff(58,plain,
% 78.69/78.86 (iext(uri_owl_complementOf, X5!142, uri_ex_y)),
% 78.69/78.86 inference(and_elim,[status(thm)],[8])).
% 78.69/78.86 tff(59,plain,
% 78.69/78.86 (^[Z: $i, C: $i] : refl(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 78.69/78.86 inference(bind,[status(th)],[])).
% 78.69/78.86 tff(60,plain,
% 78.69/78.86 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 78.69/78.86 inference(quant_intro,[status(thm)],[59])).
% 78.69/78.86 tff(61,plain,
% 78.69/78.86 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 78.69/78.86 inference(bind,[status(th)],[])).
% 78.69/78.86 tff(62,plain,
% 78.69/78.86 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 78.69/78.86 inference(quant_intro,[status(thm)],[61])).
% 78.69/78.86 tff(63,plain,
% 78.69/78.86 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 78.69/78.86 inference(transitivity,[status(thm)],[62, 60])).
% 78.69/78.86 tff(64,plain,
% 78.69/78.86 (^[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)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 78.69/78.86 inference(bind,[status(th)],[])).
% 78.69/78.86 tff(65,plain,
% 78.69/78.86 (![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)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 78.69/78.86 inference(quant_intro,[status(thm)],[64])).
% 78.69/78.86 tff(66,plain,
% 78.69/78.86 (![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)))))),
% 78.69/78.86 inference(rewrite,[status(thm)],[])).
% 78.69/78.86 tff(67,plain,
% 78.69/78.86 (^[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)))))))),
% 78.69/78.86 inference(bind,[status(th)],[])).
% 78.69/78.86 tff(68,plain,
% 78.69/78.86 (![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)))))),
% 78.69/78.86 inference(quant_intro,[status(thm)],[67])).
% 78.69/78.86 tff(69,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/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_complementof_class')).
% 78.69/78.86 tff(70,plain,
% 78.69/78.86 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[69, 68])).
% 78.69/78.86 tff(71,plain,
% 78.69/78.86 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[70, 66])).
% 78.69/78.86 tff(72,plain,(
% 78.69/78.86 ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 78.69/78.86 inference(skolemize,[status(sab)],[71])).
% 78.69/78.86 tff(73,plain,
% 78.69/78.86 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[72, 65])).
% 78.69/78.86 tff(74,plain,
% 78.69/78.86 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[73, 63])).
% 78.69/78.86 tff(75,plain,
% 78.69/78.86 (((~![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, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, 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, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X)))))))),
% 78.69/78.86 inference(rewrite,[status(thm)],[])).
% 78.69/78.86 tff(76,plain,
% 78.69/78.86 (((~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(uri_ex_y)) | (~ic(X5!142)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X))))))) <=> ((~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X)))))))),
% 78.69/78.86 inference(rewrite,[status(thm)],[])).
% 78.69/78.86 tff(77,plain,
% 78.69/78.86 (((~![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, X5!142, uri_ex_y)) | (~((~ic(uri_ex_y)) | (~ic(X5!142)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, 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, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X))))))))),
% 78.69/78.86 inference(monotonicity,[status(thm)],[76])).
% 78.69/78.86 tff(78,plain,
% 78.69/78.86 (((~![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, X5!142, uri_ex_y)) | (~((~ic(uri_ex_y)) | (~ic(X5!142)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, 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, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X)))))))),
% 78.69/78.86 inference(transitivity,[status(thm)],[77, 75])).
% 78.69/78.86 tff(79,plain,
% 78.69/78.86 ((~![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, X5!142, uri_ex_y)) | (~((~ic(uri_ex_y)) | (~ic(X5!142)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X)))))))),
% 78.69/78.86 inference(quant_inst,[status(thm)],[])).
% 78.69/78.86 tff(80,plain,
% 78.69/78.86 ((~![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, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X))))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[79, 78])).
% 78.69/78.86 tff(81,plain,
% 78.69/78.86 (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X)))))),
% 78.69/78.86 inference(unit_resolution,[status(thm)],[80, 74, 58])).
% 78.69/78.86 tff(82,plain,
% 78.69/78.86 (((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X))))) | ![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X)))),
% 78.69/78.86 inference(tautology,[status(thm)],[])).
% 78.69/78.86 tff(83,plain,
% 78.69/78.86 (![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X)))),
% 78.69/78.86 inference(unit_resolution,[status(thm)],[82, 81])).
% 78.69/78.86 tff(84,plain,
% 78.69/78.86 ((~![X: $i] : (~(icext(uri_ex_y, X) <=> icext(X5!142, X)))) | (~(icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 78.69/78.86 inference(quant_inst,[status(thm)],[])).
% 78.69/78.86 tff(85,plain,
% 78.69/78.86 (~(icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.86 inference(unit_resolution,[status(thm)],[84, 83])).
% 78.69/78.86 tff(86,plain,
% 78.69/78.86 (^[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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))))))),
% 78.69/78.86 inference(bind,[status(th)],[])).
% 78.69/78.86 tff(87,plain,
% 78.69/78.86 (![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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 78.69/78.86 inference(quant_intro,[status(thm)],[86])).
% 78.69/78.86 tff(88,plain,
% 78.69/78.86 (^[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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))))),
% 78.69/78.86 inference(bind,[status(th)],[])).
% 78.69/78.86 tff(89,plain,
% 78.69/78.86 (![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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 78.69/78.86 inference(quant_intro,[status(thm)],[88])).
% 78.69/78.86 tff(90,plain,
% 78.69/78.86 (^[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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))))),
% 78.69/78.86 inference(bind,[status(th)],[])).
% 78.69/78.86 tff(91,plain,
% 78.69/78.86 (![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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 78.69/78.86 inference(quant_intro,[status(thm)],[90])).
% 78.69/78.86 tff(92,plain,
% 78.69/78.86 (![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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 78.69/78.86 inference(transitivity,[status(thm)],[91, 89])).
% 78.69/78.86 tff(93,plain,
% 78.69/78.86 (^[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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))) <=> (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))), rewrite((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))))),
% 78.69/78.86 inference(bind,[status(th)],[])).
% 78.69/78.86 tff(94,plain,
% 78.69/78.86 (![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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 78.69/78.86 inference(quant_intro,[status(thm)],[93])).
% 78.69/78.86 tff(95,plain,
% 78.69/78.86 (^[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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 78.69/78.86 inference(bind,[status(th)],[])).
% 78.69/78.86 tff(96,plain,
% 78.69/78.86 (![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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))),
% 78.69/78.86 inference(quant_intro,[status(thm)],[95])).
% 78.69/78.86 tff(97,plain,
% 78.69/78.86 (![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))))),
% 78.69/78.86 inference(rewrite,[status(thm)],[])).
% 78.69/78.86 tff(98,plain,
% 78.69/78.86 (^[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)))))),
% 78.69/78.86 inference(bind,[status(th)],[])).
% 78.69/78.86 tff(99,plain,
% 78.69/78.86 (![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))))),
% 78.69/78.86 inference(quant_intro,[status(thm)],[98])).
% 78.69/78.86 tff(100,axiom,(![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_eqdis_equivalentclass')).
% 78.69/78.86 tff(101,plain,
% 78.69/78.86 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[100, 99])).
% 78.69/78.86 tff(102,plain,
% 78.69/78.86 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[101, 97])).
% 78.69/78.86 tff(103,plain,(
% 78.69/78.86 ![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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 78.69/78.86 inference(skolemize,[status(sab)],[102])).
% 78.69/78.86 tff(104,plain,
% 78.69/78.86 (![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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[103, 96])).
% 78.69/78.86 tff(105,plain,
% 78.69/78.86 (![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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[104, 94])).
% 78.69/78.86 tff(106,plain,
% 78.69/78.86 (![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_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[105, 92])).
% 78.69/78.86 tff(107,plain,
% 78.69/78.86 (![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 78.69/78.86 inference(modus_ponens,[status(thm)],[106, 87])).
% 78.69/78.86 tff(108,plain,
% 78.69/78.86 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X))) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X))) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)))))))))),
% 78.69/78.86 inference(rewrite,[status(thm)],[])).
% 78.69/78.86 tff(109,plain,
% 78.69/78.86 ((~((~(iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X))))))))) <=> (~((~(iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X))) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2))))))))),
% 78.69/78.86 inference(rewrite,[status(thm)],[])).
% 78.69/78.86 tff(110,plain,
% 78.69/78.86 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X))) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)))))))))),
% 78.69/78.86 inference(monotonicity,[status(thm)],[109])).
% 78.69/78.86 tff(111,plain,
% 78.69/78.86 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X))) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)))))))))),
% 78.69/78.87 inference(transitivity,[status(thm)],[110, 108])).
% 78.69/78.87 tff(112,plain,
% 78.69/78.87 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X)))))))))),
% 78.69/78.87 inference(quant_inst,[status(thm)],[])).
% 78.69/78.87 tff(113,plain,
% 78.69/78.87 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(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_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X))) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2))))))))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[112, 111])).
% 78.69/78.87 tff(114,plain,
% 78.69/78.87 (~((~(iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X))) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)))))))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[113, 107])).
% 78.69/78.87 tff(115,plain,
% 78.69/78.87 (((~(iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X))) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2))))))) | (iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))),
% 78.69/78.87 inference(tautology,[status(thm)],[])).
% 78.69/78.87 tff(116,plain,
% 78.69/78.87 (iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[115, 114])).
% 78.69/78.87 tff(117,plain,
% 78.69/78.87 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 78.69/78.87 inference(bind,[status(th)],[])).
% 78.69/78.87 tff(118,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 78.69/78.87 inference(quant_intro,[status(thm)],[117])).
% 78.69/78.87 tff(119,plain,
% 78.69/78.87 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 78.69/78.87 inference(bind,[status(th)],[])).
% 78.69/78.87 tff(120,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 78.69/78.87 inference(quant_intro,[status(thm)],[119])).
% 78.69/78.87 tff(121,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 78.69/78.87 inference(rewrite,[status(thm)],[])).
% 78.69/78.87 tff(122,plain,
% 78.69/78.87 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_intersectionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))))),
% 78.69/78.87 inference(bind,[status(th)],[])).
% 78.69/78.87 tff(123,plain,
% 78.69/78.87 (![X: $i, Y: $i] : (iext(uri_owl_intersectionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 78.69/78.87 inference(quant_intro,[status(thm)],[122])).
% 78.69/78.87 tff(124,axiom,(![X: $i, Y: $i] : (iext(uri_owl_intersectionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_intersectionof_ext')).
% 78.69/78.87 tff(125,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[124, 123])).
% 78.69/78.87 tff(126,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[125, 121])).
% 78.69/78.87 tff(127,plain,(
% 78.69/78.87 ![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 78.69/78.87 inference(skolemize,[status(sab)],[126])).
% 78.69/78.87 tff(128,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[127, 120])).
% 78.69/78.87 tff(129,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[128, 118])).
% 78.69/78.87 tff(130,plain,
% 78.69/78.87 (((~![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144)))))),
% 78.69/78.87 inference(rewrite,[status(thm)],[])).
% 78.69/78.87 tff(131,plain,
% 78.69/78.87 ((~![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144)))))),
% 78.69/78.87 inference(quant_inst,[status(thm)],[])).
% 78.69/78.87 tff(132,plain,
% 78.69/78.87 ((~![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144))))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[131, 130])).
% 78.69/78.87 tff(133,plain,
% 78.69/78.87 (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144)))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[132, 129, 47])).
% 78.69/78.87 tff(134,plain,
% 78.69/78.87 (((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144))) | ic(uri_ex_c2)),
% 78.69/78.87 inference(tautology,[status(thm)],[])).
% 78.69/78.87 tff(135,plain,
% 78.69/78.87 (ic(uri_ex_c2)),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[134, 133])).
% 78.69/78.87 tff(136,plain,
% 78.69/78.87 (iext(uri_owl_complementOf, uri_ex_c1, X6!140)),
% 78.69/78.87 inference(and_elim,[status(thm)],[8])).
% 78.69/78.87 tff(137,plain,
% 78.69/78.87 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 78.69/78.87 inference(bind,[status(th)],[])).
% 78.69/78.87 tff(138,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 78.69/78.87 inference(quant_intro,[status(thm)],[137])).
% 78.69/78.87 tff(139,plain,
% 78.69/78.87 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))) <=> ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 78.69/78.87 inference(bind,[status(th)],[])).
% 78.69/78.87 tff(140,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 78.69/78.87 inference(quant_intro,[status(thm)],[139])).
% 78.69/78.87 tff(141,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 78.69/78.87 inference(rewrite,[status(thm)],[])).
% 78.69/78.87 tff(142,plain,
% 78.69/78.87 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_complementOf, X, Y) => (ic(X) & ic(Y))) <=> ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))))),
% 78.69/78.87 inference(bind,[status(th)],[])).
% 78.69/78.87 tff(143,plain,
% 78.69/78.87 (![X: $i, Y: $i] : (iext(uri_owl_complementOf, X, Y) => (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 78.69/78.87 inference(quant_intro,[status(thm)],[142])).
% 78.69/78.87 tff(144,axiom,(![X: $i, Y: $i] : (iext(uri_owl_complementOf, X, Y) => (ic(X) & ic(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_complementof_ext')).
% 78.69/78.87 tff(145,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[144, 143])).
% 78.69/78.87 tff(146,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[145, 141])).
% 78.69/78.87 tff(147,plain,(
% 78.69/78.87 ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 78.69/78.87 inference(skolemize,[status(sab)],[146])).
% 78.69/78.87 tff(148,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[147, 140])).
% 78.69/78.87 tff(149,plain,
% 78.69/78.87 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[148, 138])).
% 78.69/78.87 tff(150,plain,
% 78.69/78.87 (((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)))))),
% 78.69/78.87 inference(rewrite,[status(thm)],[])).
% 78.69/78.87 tff(151,plain,
% 78.69/78.87 ((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)))))),
% 78.69/78.87 inference(quant_inst,[status(thm)],[])).
% 78.69/78.87 tff(152,plain,
% 78.69/78.87 ((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1))))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[151, 150])).
% 78.69/78.87 tff(153,plain,
% 78.69/78.87 (~((~ic(X6!140)) | (~ic(uri_ex_c1)))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[152, 149, 136])).
% 78.69/78.87 tff(154,plain,
% 78.69/78.87 (((~ic(X6!140)) | (~ic(uri_ex_c1))) | ic(uri_ex_c1)),
% 78.69/78.87 inference(tautology,[status(thm)],[])).
% 78.69/78.87 tff(155,plain,
% 78.69/78.87 (ic(uri_ex_c1)),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[154, 153])).
% 78.69/78.87 tff(156,plain,
% 78.69/78.87 ((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) <=> (~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2))),
% 78.69/78.87 inference(rewrite,[status(thm)],[])).
% 78.69/78.87 tff(157,axiom,(~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion_rdfbased_sem_bool_demorgan')).
% 78.69/78.87 tff(158,plain,
% 78.69/78.87 (~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[157, 156])).
% 78.69/78.87 tff(159,plain,
% 78.69/78.87 ((~(iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 78.69/78.87 inference(tautology,[status(thm)],[])).
% 78.69/78.87 tff(160,plain,
% 78.69/78.87 ((~(iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[159, 158])).
% 78.69/78.87 tff(161,plain,
% 78.69/78.87 (~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[160, 155, 135, 116])).
% 78.69/78.87 tff(162,plain,
% 78.69/78.87 ((icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.87 inference(tautology,[status(thm)],[])).
% 78.69/78.87 tff(163,plain,
% 78.69/78.87 (icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[162, 161])).
% 78.69/78.87 tff(164,plain,
% 78.69/78.87 (icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[163, 1])).
% 78.69/78.87 tff(165,plain,
% 78.69/78.87 (((~![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, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(icext(X6!140, X) <=> icext(uri_ex_c1, 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, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(icext(X6!140, X) <=> icext(uri_ex_c1, X)))))))),
% 78.69/78.87 inference(rewrite,[status(thm)],[])).
% 78.69/78.87 tff(166,plain,
% 78.69/78.87 ((~![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, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(icext(X6!140, X) <=> icext(uri_ex_c1, X)))))))),
% 78.69/78.87 inference(quant_inst,[status(thm)],[])).
% 78.69/78.87 tff(167,plain,
% 78.69/78.87 ((~![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, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(icext(X6!140, X) <=> icext(uri_ex_c1, X))))))),
% 78.69/78.87 inference(modus_ponens,[status(thm)],[166, 165])).
% 78.69/78.87 tff(168,plain,
% 78.69/78.87 (~((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(icext(X6!140, X) <=> icext(uri_ex_c1, X)))))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[167, 74, 136])).
% 78.69/78.87 tff(169,plain,
% 78.69/78.87 (((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(icext(X6!140, X) <=> icext(uri_ex_c1, X))))) | ![X: $i] : (~(icext(X6!140, X) <=> icext(uri_ex_c1, X)))),
% 78.69/78.87 inference(tautology,[status(thm)],[])).
% 78.69/78.87 tff(170,plain,
% 78.69/78.87 (![X: $i] : (~(icext(X6!140, X) <=> icext(uri_ex_c1, X)))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[169, 168])).
% 78.69/78.87 tff(171,plain,
% 78.69/78.87 ((~![X: $i] : (~(icext(X6!140, X) <=> icext(uri_ex_c1, X)))) | (~(icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 78.69/78.87 inference(quant_inst,[status(thm)],[])).
% 78.69/78.87 tff(172,plain,
% 78.69/78.87 (~(icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[171, 170])).
% 78.69/78.87 tff(173,plain,
% 78.69/78.87 ((icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.87 inference(tautology,[status(thm)],[])).
% 78.69/78.87 tff(174,plain,
% 78.69/78.87 ((~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[173, 172])).
% 78.69/78.87 tff(175,plain,
% 78.69/78.87 (~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.87 inference(unit_resolution,[status(thm)],[174, 164])).
% 78.69/78.87 tff(176,plain,
% 78.69/78.87 (iext(uri_rdf_rest, X4!145, uri_rdf_nil)),
% 78.69/78.87 inference(and_elim,[status(thm)],[8])).
% 78.69/78.87 tff(177,plain,
% 78.69/78.87 (iext(uri_rdf_first, X4!145, uri_ex_y)),
% 78.69/78.87 inference(and_elim,[status(thm)],[8])).
% 78.69/78.87 tff(178,plain,
% 78.69/78.87 (iext(uri_rdf_rest, X3!141, X4!145)),
% 78.69/78.87 inference(and_elim,[status(thm)],[8])).
% 78.69/78.87 tff(179,plain,
% 78.69/78.87 (iext(uri_rdf_first, X3!141, uri_ex_x)),
% 78.69/78.87 inference(and_elim,[status(thm)],[8])).
% 78.69/78.87 tff(180,plain,
% 78.69/78.87 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))))),
% 78.69/78.87 inference(bind,[status(th)],[])).
% 78.69/78.87 tff(181,plain,
% 78.69/78.87 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 78.69/78.87 inference(quant_intro,[status(thm)],[180])).
% 78.69/78.87 tff(182,plain,
% 78.69/78.87 (^[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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))))),
% 78.69/78.87 inference(bind,[status(th)],[])).
% 78.69/78.87 tff(183,plain,
% 78.69/78.87 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 78.69/78.87 inference(quant_intro,[status(thm)],[182])).
% 78.69/78.87 tff(184,plain,
% 78.69/78.87 (^[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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))))),
% 78.69/78.87 inference(bind,[status(th)],[])).
% 78.69/78.87 tff(185,plain,
% 78.69/78.87 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 78.69/78.87 inference(quant_intro,[status(thm)],[184])).
% 78.69/78.87 tff(186,plain,
% 78.69/78.87 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 78.69/78.87 inference(transitivity,[status(thm)],[185, 183])).
% 78.69/78.87 tff(187,plain,
% 78.69/78.87 (^[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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))) <=> (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))), rewrite((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))), rewrite((((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))))),
% 78.69/78.87 inference(bind,[status(th)],[])).
% 78.69/78.87 tff(188,plain,
% 78.69/78.87 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 78.69/78.87 inference(quant_intro,[status(thm)],[187])).
% 78.69/78.87 tff(189,plain,
% 78.69/78.87 (^[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_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 78.69/78.88 inference(bind,[status(th)],[])).
% 78.69/78.88 tff(190,plain,
% 78.69/78.88 (![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_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))),
% 78.69/78.88 inference(quant_intro,[status(thm)],[189])).
% 78.69/78.88 tff(191,plain,
% 78.69/78.88 (![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))))))),
% 78.69/78.88 inference(rewrite,[status(thm)],[])).
% 78.69/78.88 tff(192,plain,
% 78.69/78.88 (^[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))))))))),
% 78.69/78.88 inference(bind,[status(th)],[])).
% 78.69/78.88 tff(193,plain,
% 78.69/78.88 (![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))))))),
% 78.69/78.88 inference(quant_intro,[status(thm)],[192])).
% 78.69/78.88 tff(194,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/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_unionof_class_002')).
% 78.69/78.88 tff(195,plain,
% 78.69/78.88 (![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))))))),
% 78.69/78.88 inference(modus_ponens,[status(thm)],[194, 193])).
% 78.69/78.88 tff(196,plain,
% 78.69/78.88 (![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))))))),
% 78.69/78.88 inference(modus_ponens,[status(thm)],[195, 191])).
% 78.69/78.88 tff(197,plain,(
% 78.69/78.88 ![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_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 78.69/78.88 inference(skolemize,[status(sab)],[196])).
% 78.69/78.88 tff(198,plain,
% 78.69/78.88 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))),
% 78.69/78.88 inference(modus_ponens,[status(thm)],[197, 190])).
% 78.69/78.88 tff(199,plain,
% 78.69/78.88 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 78.69/78.88 inference(modus_ponens,[status(thm)],[198, 188])).
% 78.69/78.88 tff(200,plain,
% 78.69/78.88 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 78.69/78.88 inference(modus_ponens,[status(thm)],[199, 186])).
% 78.69/78.88 tff(201,plain,
% 78.69/78.88 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 78.69/78.88 inference(modus_ponens,[status(thm)],[200, 181])).
% 78.69/78.88 tff(202,plain,
% 78.69/78.88 (((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, 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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))))),
% 78.69/78.88 inference(rewrite,[status(thm)],[])).
% 78.69/78.88 tff(203,plain,
% 78.69/78.88 (((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))))))) <=> ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))))),
% 78.69/78.88 inference(rewrite,[status(thm)],[])).
% 78.69/78.88 tff(204,plain,
% 78.69/78.88 ((~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, X)))))))))) <=> (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))))))),
% 78.69/78.88 inference(rewrite,[status(thm)],[])).
% 78.69/78.88 tff(205,plain,
% 78.69/78.88 (((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, X))))))))))) <=> ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))))),
% 78.69/78.88 inference(monotonicity,[status(thm)],[204])).
% 78.69/78.88 tff(206,plain,
% 78.69/78.88 (((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, X))))))))))) <=> ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))))),
% 78.69/78.88 inference(transitivity,[status(thm)],[205, 203])).
% 78.69/78.88 tff(207,plain,
% 78.69/78.88 (((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, 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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))))))))),
% 78.69/78.88 inference(monotonicity,[status(thm)],[206])).
% 78.69/78.88 tff(208,plain,
% 78.69/78.88 (((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, 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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))))),
% 78.69/78.88 inference(transitivity,[status(thm)],[207, 202])).
% 78.69/78.88 tff(209,plain,
% 78.69/78.88 ((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, X)))))))))))),
% 78.69/78.88 inference(quant_inst,[status(thm)],[])).
% 78.69/78.88 tff(210,plain,
% 78.69/78.88 ((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))))))),
% 78.69/78.88 inference(modus_ponens,[status(thm)],[209, 208])).
% 78.69/78.88 tff(211,plain,
% 78.69/78.88 (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))),
% 78.69/78.88 inference(unit_resolution,[status(thm)],[210, 201, 179, 178, 177, 176])).
% 78.69/78.88 tff(212,plain,
% 78.69/78.88 (((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~(icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) <=> (icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))))) | ((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))),
% 78.69/78.88 inference(tautology,[status(thm)],[])).
% 78.69/78.88 tff(213,plain,
% 78.69/78.88 ((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))),
% 78.69/78.88 inference(unit_resolution,[status(thm)],[212, 211])).
% 78.69/78.88 tff(214,plain,
% 78.69/78.88 (iext(uri_owl_unionOf, X6!140, X3!141)),
% 78.69/78.88 inference(and_elim,[status(thm)],[8])).
% 78.69/78.88 tff(215,plain,
% 78.69/78.88 ((~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))) | (~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))),
% 78.69/78.88 inference(tautology,[status(thm)],[])).
% 78.69/78.88 tff(216,plain,
% 78.69/78.88 ((~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))),
% 78.69/78.88 inference(unit_resolution,[status(thm)],[215, 214])).
% 78.69/78.88 tff(217,plain,
% 78.69/78.88 (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))),
% 78.69/78.88 inference(unit_resolution,[status(thm)],[216, 213])).
% 78.69/78.88 tff(218,plain,
% 78.69/78.88 (((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))) | ![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))),
% 78.69/78.88 inference(tautology,[status(thm)],[])).
% 78.69/78.88 tff(219,plain,
% 78.69/78.88 (![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))),
% 78.69/78.88 inference(unit_resolution,[status(thm)],[218, 217])).
% 78.69/78.88 tff(220,plain,
% 78.69/78.88 ((~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))) | (icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 78.69/78.88 inference(quant_inst,[status(thm)],[])).
% 78.69/78.89 tff(221,plain,
% 78.69/78.89 (icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[220, 219])).
% 78.69/78.89 tff(222,plain,
% 78.69/78.89 ((~(icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | (~(icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 78.69/78.89 inference(tautology,[status(thm)],[])).
% 78.69/78.89 tff(223,plain,
% 78.69/78.89 (icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | (~(icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[222, 221])).
% 78.69/78.89 tff(224,plain,
% 78.69/78.89 (~(icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[223, 175])).
% 78.69/78.89 tff(225,plain,
% 78.69/78.89 ((icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.89 inference(tautology,[status(thm)],[])).
% 78.69/78.89 tff(226,plain,
% 78.69/78.89 (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[225, 224])).
% 78.69/78.89 tff(227,plain,
% 78.69/78.89 ((icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(tautology,[status(thm)],[])).
% 78.69/78.89 tff(228,plain,
% 78.69/78.89 ((icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[227, 226])).
% 78.69/78.89 tff(229,plain,
% 78.69/78.89 (icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[228, 85])).
% 78.69/78.89 tff(230,plain,
% 78.69/78.89 (iext(uri_owl_complementOf, X1!146, uri_ex_x)),
% 78.69/78.89 inference(and_elim,[status(thm)],[8])).
% 78.69/78.89 tff(231,plain,
% 78.69/78.89 (((~![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, X1!146, uri_ex_x)) | (~((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (~(icext(uri_ex_x, X) <=> icext(X1!146, 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, X1!146, uri_ex_x)) | (~((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (~(icext(uri_ex_x, X) <=> icext(X1!146, X)))))))),
% 78.69/78.89 inference(rewrite,[status(thm)],[])).
% 78.69/78.89 tff(232,plain,
% 78.69/78.89 ((~![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, X1!146, uri_ex_x)) | (~((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (~(icext(uri_ex_x, X) <=> icext(X1!146, X)))))))),
% 78.69/78.89 inference(quant_inst,[status(thm)],[])).
% 78.69/78.89 tff(233,plain,
% 78.69/78.89 ((~![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, X1!146, uri_ex_x)) | (~((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (~(icext(uri_ex_x, X) <=> icext(X1!146, X))))))),
% 78.69/78.89 inference(modus_ponens,[status(thm)],[232, 231])).
% 78.69/78.89 tff(234,plain,
% 78.69/78.89 (~((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (~(icext(uri_ex_x, X) <=> icext(X1!146, X)))))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[233, 74, 230])).
% 78.69/78.89 tff(235,plain,
% 78.69/78.89 (((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (~(icext(uri_ex_x, X) <=> icext(X1!146, X))))) | ![X: $i] : (~(icext(uri_ex_x, X) <=> icext(X1!146, X)))),
% 78.69/78.89 inference(tautology,[status(thm)],[])).
% 78.69/78.89 tff(236,plain,
% 78.69/78.89 (![X: $i] : (~(icext(uri_ex_x, X) <=> icext(X1!146, X)))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[235, 234])).
% 78.69/78.89 tff(237,plain,
% 78.69/78.89 ((~![X: $i] : (~(icext(uri_ex_x, X) <=> icext(X1!146, X)))) | (~(icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 78.69/78.89 inference(quant_inst,[status(thm)],[])).
% 78.69/78.89 tff(238,plain,
% 78.69/78.89 (~(icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[237, 236])).
% 78.69/78.89 tff(239,plain,
% 78.69/78.89 ((icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.89 inference(tautology,[status(thm)],[])).
% 78.69/78.89 tff(240,plain,
% 78.69/78.89 (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[239, 224])).
% 78.69/78.89 tff(241,plain,
% 78.69/78.89 ((icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(tautology,[status(thm)],[])).
% 78.69/78.89 tff(242,plain,
% 78.69/78.89 ((icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[241, 240])).
% 78.69/78.89 tff(243,plain,
% 78.69/78.89 (icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[242, 238])).
% 78.69/78.89 tff(244,plain,
% 78.69/78.89 ((~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.89 inference(tautology,[status(thm)],[])).
% 78.69/78.89 tff(245,plain,
% 78.69/78.89 ($false),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[244, 243, 229, 57])).
% 78.69/78.89 tff(246,plain,(icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))), inference(lemma,lemma(discharge,[]))).
% 78.69/78.89 tff(247,plain,
% 78.69/78.89 ((icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.89 inference(tautology,[status(thm)],[])).
% 78.69/78.89 tff(248,plain,
% 78.69/78.89 ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[247, 161])).
% 78.69/78.89 tff(249,plain,
% 78.69/78.89 (~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[248, 246])).
% 78.69/78.89 tff(250,plain,
% 78.69/78.89 ((icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(tautology,[status(thm)],[])).
% 78.69/78.89 tff(251,plain,
% 78.69/78.89 (icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[250, 172])).
% 78.69/78.89 tff(252,plain,
% 78.69/78.89 (icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[251, 249])).
% 78.69/78.89 tff(253,plain,
% 78.69/78.89 ((~(icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.89 inference(tautology,[status(thm)],[])).
% 78.69/78.89 tff(254,plain,
% 78.69/78.89 ((~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[253, 221])).
% 78.69/78.89 tff(255,plain,
% 78.69/78.89 (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.69/78.89 inference(unit_resolution,[status(thm)],[254, 252])).
% 78.69/78.89 tff(256,plain,
% 78.69/78.89 ((((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.76/78.91 inference(tautology,[status(thm)],[])).
% 78.76/78.91 tff(257,plain,
% 78.76/78.91 ((~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.76/78.91 inference(unit_resolution,[status(thm)],[256, 54])).
% 78.76/78.91 tff(258,plain,
% 78.76/78.91 (~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 78.76/78.91 inference(unit_resolution,[status(thm)],[257, 246])).
% 78.76/78.91 tff(259,plain,
% 78.76/78.91 (((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) | icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.76/78.91 inference(tautology,[status(thm)],[])).
% 78.76/78.91 tff(260,plain,
% 78.76/78.91 (icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.76/78.91 inference(unit_resolution,[status(thm)],[259, 258])).
% 78.76/78.91 tff(261,plain,
% 78.76/78.91 ((icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.76/78.91 inference(tautology,[status(thm)],[])).
% 78.76/78.91 tff(262,plain,
% 78.76/78.91 ((icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.76/78.91 inference(unit_resolution,[status(thm)],[261, 260])).
% 78.76/78.91 tff(263,plain,
% 78.76/78.91 (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.76/78.91 inference(unit_resolution,[status(thm)],[262, 238])).
% 78.76/78.91 tff(264,plain,
% 78.76/78.91 (((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) | icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.76/78.91 inference(tautology,[status(thm)],[])).
% 78.76/78.91 tff(265,plain,
% 78.76/78.91 (icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.76/78.91 inference(unit_resolution,[status(thm)],[264, 258])).
% 78.76/78.91 tff(266,plain,
% 78.76/78.91 ((icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.76/78.91 inference(tautology,[status(thm)],[])).
% 78.76/78.91 tff(267,plain,
% 78.76/78.91 ((icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 78.76/78.91 inference(unit_resolution,[status(thm)],[266, 265])).
% 78.76/78.91 tff(268,plain,
% 78.76/78.91 (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.76/78.91 inference(unit_resolution,[status(thm)],[267, 85])).
% 78.76/78.91 tff(269,plain,
% 78.76/78.91 ((~(icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) | icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 78.76/78.91 inference(tautology,[status(thm)],[])).
% 78.76/78.91 tff(270,plain,
% 78.76/78.91 ($false),
% 78.76/78.91 inference(unit_resolution,[status(thm)],[269, 268, 263, 255])).
% 78.76/78.91 % SZS output end Proof
% 78.76/78.94 % E exiting
%------------------------------------------------------------------------------