%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB039+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 75.20s 75.41s
% Output : Proof 75.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWB039+1 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 07:53:56 EDT 2025
% 0.11/0.33 % CPUTime :
% 75.20/75.41 % SZS status Theorem
% 75.20/75.41 % SZS output start Proof
% 75.20/75.41 tff(icext_type, type, (
% 75.20/75.41 icext: ( $i * $i ) > $o)).
% 75.20/75.41 tff(tptp_fun_X_3_type, type, (
% 75.20/75.41 tptp_fun_X_3: ( $i * $i * $i ) > $i)).
% 75.20/75.41 tff(uri_ex_c_type, type, (
% 75.20/75.41 uri_ex_c: $i)).
% 75.20/75.41 tff(uri_ex_x_type, type, (
% 75.20/75.41 uri_ex_x: $i)).
% 75.20/75.41 tff(uri_ex_y_type, type, (
% 75.20/75.41 uri_ex_y: $i)).
% 75.20/75.41 tff(ic_type, type, (
% 75.20/75.41 ic: $i > $o)).
% 75.20/75.41 tff(iext_type, type, (
% 75.20/75.41 iext: ( $i * $i * $i ) > $o)).
% 75.20/75.41 tff(tptp_fun_X2_140_type, type, (
% 75.20/75.41 tptp_fun_X2_140: $i)).
% 75.20/75.41 tff(uri_owl_intersectionOf_type, type, (
% 75.20/75.41 uri_owl_intersectionOf: $i)).
% 75.20/75.41 tff(tptp_fun_X0_142_type, type, (
% 75.20/75.41 tptp_fun_X0_142: $i)).
% 75.20/75.41 tff(uri_rdf_rest_type, type, (
% 75.20/75.41 uri_rdf_rest: $i)).
% 75.20/75.41 tff(tptp_fun_X1_141_type, type, (
% 75.20/75.41 tptp_fun_X1_141: $i)).
% 75.20/75.41 tff(uri_owl_equivalentClass_type, type, (
% 75.20/75.41 uri_owl_equivalentClass: $i)).
% 75.20/75.41 tff(uri_rdf_first_type, type, (
% 75.20/75.41 uri_rdf_first: $i)).
% 75.20/75.41 tff(uri_rdf_nil_type, type, (
% 75.20/75.41 uri_rdf_nil: $i)).
% 75.20/75.41 tff(tptp_fun_X_67_type, type, (
% 75.20/75.41 tptp_fun_X_67: ( $i * $i ) > $i)).
% 75.20/75.41 tff(1,assumption,(~icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))), introduced(assumption)).
% 75.20/75.41 tff(2,plain,
% 75.20/75.41 (?[X0: $i, X1: $i, X2: $i] : (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x) & iext(uri_rdf_rest, X2, X0) & iext(uri_owl_equivalentClass, uri_ex_c, X1)) <=> ?[X0: $i, X1: $i, X2: $i] : (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x) & iext(uri_rdf_rest, X2, X0) & iext(uri_owl_equivalentClass, uri_ex_c, X1))),
% 75.20/75.41 inference(rewrite,[status(thm)],[])).
% 75.20/75.41 tff(3,plain,
% 75.20/75.41 (^[X0: $i, X1: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_intersectionOf, X1, X2)) <=> (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2))), ((((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_intersectionOf, X1, X2)) & iext(uri_rdf_first, X2, uri_ex_x)) <=> ((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2)) & iext(uri_rdf_first, X2, uri_ex_x)))), rewrite(((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2)) & iext(uri_rdf_first, X2, uri_ex_x)) <=> (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x))), ((((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_intersectionOf, X1, X2)) & iext(uri_rdf_first, X2, uri_ex_x)) <=> (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x)))), (((((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_intersectionOf, X1, X2)) & iext(uri_rdf_first, X2, uri_ex_x)) & iext(uri_rdf_rest, X2, X0)) <=> ((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x)) & iext(uri_rdf_rest, X2, X0)))), rewrite(((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x)) & iext(uri_rdf_rest, X2, X0)) <=> (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x) & iext(uri_rdf_rest, X2, X0))), (((((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_intersectionOf, X1, X2)) & iext(uri_rdf_first, X2, uri_ex_x)) & iext(uri_rdf_rest, X2, X0)) <=> (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x) & iext(uri_rdf_rest, X2, X0)))), ((((((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_intersectionOf, X1, X2)) & iext(uri_rdf_first, X2, uri_ex_x)) & iext(uri_rdf_rest, X2, X0)) & iext(uri_owl_equivalentClass, uri_ex_c, X1)) <=> ((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x) & iext(uri_rdf_rest, X2, X0)) & iext(uri_owl_equivalentClass, uri_ex_c, X1)))), rewrite(((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x) & iext(uri_rdf_rest, X2, X0)) & iext(uri_owl_equivalentClass, uri_ex_c, X1)) <=> (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x) & iext(uri_rdf_rest, X2, X0) & iext(uri_owl_equivalentClass, uri_ex_c, X1))), ((((((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_intersectionOf, X1, X2)) & iext(uri_rdf_first, X2, uri_ex_x)) & iext(uri_rdf_rest, X2, X0)) & iext(uri_owl_equivalentClass, uri_ex_c, X1)) <=> (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x) & iext(uri_rdf_rest, X2, X0) & iext(uri_owl_equivalentClass, uri_ex_c, X1))))),
% 75.20/75.42 inference(bind,[status(th)],[])).
% 75.20/75.42 tff(4,plain,
% 75.20/75.42 (?[X0: $i, X1: $i, X2: $i] : (((((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_intersectionOf, X1, X2)) & iext(uri_rdf_first, X2, uri_ex_x)) & iext(uri_rdf_rest, X2, X0)) & iext(uri_owl_equivalentClass, uri_ex_c, X1)) <=> ?[X0: $i, X1: $i, X2: $i] : (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x) & iext(uri_rdf_rest, X2, X0) & iext(uri_owl_equivalentClass, uri_ex_c, X1))),
% 75.20/75.42 inference(quant_intro,[status(thm)],[3])).
% 75.20/75.42 tff(5,axiom,(?[X0: $i, X1: $i, X2: $i] : (((((iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_intersectionOf, X1, X2)) & iext(uri_rdf_first, X2, uri_ex_x)) & iext(uri_rdf_rest, X2, X0)) & iext(uri_owl_equivalentClass, uri_ex_c, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','premise_rdfbased_sem_bool_intersection_ext')).
% 75.20/75.42 tff(6,plain,
% 75.20/75.42 (?[X0: $i, X1: $i, X2: $i] : (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x) & iext(uri_rdf_rest, X2, X0) & iext(uri_owl_equivalentClass, uri_ex_c, X1))),
% 75.20/75.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 75.20/75.42 tff(7,plain,
% 75.20/75.42 (?[X0: $i, X1: $i, X2: $i] : (iext(uri_rdf_first, X0, uri_ex_y) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1, X2) & iext(uri_rdf_first, X2, uri_ex_x) & iext(uri_rdf_rest, X2, X0) & iext(uri_owl_equivalentClass, uri_ex_c, X1))),
% 75.20/75.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 75.20/75.42 tff(8,plain,(
% 75.20/75.42 iext(uri_rdf_first, X0!142, uri_ex_y) & iext(uri_rdf_rest, X0!142, uri_rdf_nil) & iext(uri_owl_intersectionOf, X1!141, X2!140) & iext(uri_rdf_first, X2!140, uri_ex_x) & iext(uri_rdf_rest, X2!140, X0!142) & iext(uri_owl_equivalentClass, uri_ex_c, X1!141)),
% 75.20/75.42 inference(skolemize,[status(sab)],[7])).
% 75.20/75.42 tff(9,plain,
% 75.20/75.42 (iext(uri_rdf_rest, X2!140, X0!142)),
% 75.20/75.42 inference(and_elim,[status(thm)],[8])).
% 75.20/75.42 tff(10,plain,
% 75.20/75.42 (iext(uri_rdf_first, X2!140, uri_ex_x)),
% 75.20/75.42 inference(and_elim,[status(thm)],[8])).
% 75.20/75.42 tff(11,plain,
% 75.20/75.42 (iext(uri_rdf_rest, X0!142, uri_rdf_nil)),
% 75.20/75.42 inference(and_elim,[status(thm)],[8])).
% 75.20/75.42 tff(12,plain,
% 75.20/75.42 (iext(uri_rdf_first, X0!142, uri_ex_y)),
% 75.20/75.42 inference(and_elim,[status(thm)],[8])).
% 75.20/75.42 tff(13,plain,
% 75.20/75.42 (^[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)))))))))))))),
% 75.20/75.42 inference(bind,[status(th)],[])).
% 75.20/75.42 tff(14,plain,
% 75.20/75.42 (![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)))))))))))),
% 75.20/75.42 inference(quant_intro,[status(thm)],[13])).
% 75.20/75.42 tff(15,plain,
% 75.20/75.42 (^[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)))))))))),
% 75.20/75.42 inference(bind,[status(th)],[])).
% 75.20/75.42 tff(16,plain,
% 75.20/75.42 (![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))))))))),
% 75.20/75.42 inference(quant_intro,[status(thm)],[15])).
% 75.20/75.42 tff(17,plain,
% 75.20/75.42 (^[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)))))))))),
% 75.20/75.42 inference(bind,[status(th)],[])).
% 75.20/75.42 tff(18,plain,
% 75.20/75.42 (![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))))))))),
% 75.20/75.42 inference(quant_intro,[status(thm)],[17])).
% 75.20/75.42 tff(19,plain,
% 75.20/75.42 (![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))))))))),
% 75.20/75.42 inference(transitivity,[status(thm)],[18, 16])).
% 75.20/75.42 tff(20,plain,
% 75.20/75.42 (^[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))))))))))),
% 75.20/75.42 inference(bind,[status(th)],[])).
% 75.20/75.42 tff(21,plain,
% 75.20/75.42 (![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))))))))),
% 75.20/75.42 inference(quant_intro,[status(thm)],[20])).
% 75.20/75.42 tff(22,plain,
% 75.20/75.42 (^[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)))))))))),
% 75.20/75.42 inference(bind,[status(th)],[])).
% 75.20/75.42 tff(23,plain,
% 75.20/75.42 (![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))))))))),
% 75.20/75.42 inference(quant_intro,[status(thm)],[22])).
% 75.20/75.42 tff(24,plain,
% 75.20/75.42 (![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))))))),
% 75.20/75.42 inference(rewrite,[status(thm)],[])).
% 75.20/75.42 tff(25,plain,
% 75.20/75.42 (^[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))))))))),
% 75.20/75.42 inference(bind,[status(th)],[])).
% 75.20/75.42 tff(26,plain,
% 75.20/75.42 (![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))))))),
% 75.20/75.42 inference(quant_intro,[status(thm)],[25])).
% 75.20/75.42 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')).
% 75.20/75.42 tff(28,plain,
% 75.20/75.42 (![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))))))),
% 75.20/75.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 75.20/75.42 tff(29,plain,
% 75.20/75.42 (![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))))))),
% 75.20/75.42 inference(modus_ponens,[status(thm)],[28, 24])).
% 75.20/75.42 tff(30,plain,(
% 75.20/75.42 ![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)))))))))),
% 75.20/75.42 inference(skolemize,[status(sab)],[29])).
% 75.20/75.42 tff(31,plain,
% 75.20/75.42 (![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))))))))),
% 75.20/75.42 inference(modus_ponens,[status(thm)],[30, 23])).
% 75.20/75.42 tff(32,plain,
% 75.20/75.42 (![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))))))))),
% 75.20/75.42 inference(modus_ponens,[status(thm)],[31, 21])).
% 75.20/75.42 tff(33,plain,
% 75.20/75.42 (![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))))))))),
% 75.20/75.42 inference(modus_ponens,[status(thm)],[32, 19])).
% 75.20/75.42 tff(34,plain,
% 75.20/75.42 (![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)))))))))))),
% 75.20/75.42 inference(modus_ponens,[status(thm)],[33, 14])).
% 75.20/75.42 tff(35,plain,
% 75.20/75.42 (((~![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!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, 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, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X)))))))))))),
% 75.20/75.43 inference(rewrite,[status(thm)],[])).
% 75.20/75.43 tff(36,plain,
% 75.20/75.43 (((~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X))))))))))) <=> ((~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X)))))))))))),
% 75.20/75.43 inference(rewrite,[status(thm)],[])).
% 75.20/75.43 tff(37,plain,
% 75.20/75.43 ((~((~(iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X)))))))))) <=> (~((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X))))))))))),
% 75.20/75.43 inference(rewrite,[status(thm)],[])).
% 75.20/75.43 tff(38,plain,
% 75.20/75.43 (((~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X))))))))))) <=> ((~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X)))))))))))),
% 75.20/75.43 inference(monotonicity,[status(thm)],[37])).
% 75.20/75.43 tff(39,plain,
% 75.20/75.43 (((~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X))))))))))) <=> ((~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X)))))))))))),
% 75.20/75.43 inference(transitivity,[status(thm)],[38, 36])).
% 75.20/75.43 tff(40,plain,
% 75.20/75.43 (((~![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!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, 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, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X))))))))))))),
% 75.20/75.43 inference(monotonicity,[status(thm)],[39])).
% 75.20/75.43 tff(41,plain,
% 75.20/75.43 (((~![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!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, 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, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X)))))))))))),
% 75.20/75.43 inference(transitivity,[status(thm)],[40, 35])).
% 75.20/75.43 tff(42,plain,
% 75.20/75.43 ((~![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!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X)))))))))))),
% 75.20/75.43 inference(quant_inst,[status(thm)],[])).
% 75.20/75.43 tff(43,plain,
% 75.20/75.43 ((~![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!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X))))))))))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[42, 41])).
% 75.20/75.43 tff(44,plain,
% 75.20/75.43 (~((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X)))))))))),
% 75.20/75.43 inference(unit_resolution,[status(thm)],[43, 34, 12, 11, 10, 9])).
% 75.20/75.43 tff(45,plain,
% 75.20/75.43 (((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)) | (~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~ic(uri_ex_c)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(uri_ex_c, X))))))))) | ((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))),
% 75.20/75.43 inference(tautology,[status(thm)],[])).
% 75.20/75.43 tff(46,plain,
% 75.20/75.43 ((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.43 inference(unit_resolution,[status(thm)],[45, 44])).
% 75.20/75.43 tff(47,plain,
% 75.20/75.43 (iext(uri_owl_equivalentClass, uri_ex_c, X1!141)),
% 75.20/75.43 inference(and_elim,[status(thm)],[8])).
% 75.20/75.43 tff(48,plain,
% 75.20/75.43 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 75.20/75.43 inference(bind,[status(th)],[])).
% 75.20/75.43 tff(49,plain,
% 75.20/75.43 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 75.20/75.43 inference(quant_intro,[status(thm)],[48])).
% 75.20/75.43 tff(50,plain,
% 75.20/75.43 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y))) <=> ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 75.20/75.43 inference(bind,[status(th)],[])).
% 75.20/75.43 tff(51,plain,
% 75.20/75.43 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 75.20/75.43 inference(quant_intro,[status(thm)],[50])).
% 75.20/75.43 tff(52,plain,
% 75.20/75.43 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 75.20/75.43 inference(rewrite,[status(thm)],[])).
% 75.20/75.43 tff(53,plain,
% 75.20/75.43 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_equivalentClass, X, Y) => (ic(X) & ic(Y))) <=> ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y))))),
% 75.20/75.43 inference(bind,[status(th)],[])).
% 75.20/75.43 tff(54,plain,
% 75.20/75.43 (![X: $i, Y: $i] : (iext(uri_owl_equivalentClass, X, Y) => (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 75.20/75.43 inference(quant_intro,[status(thm)],[53])).
% 75.20/75.43 tff(55,axiom,(![X: $i, Y: $i] : (iext(uri_owl_equivalentClass, X, Y) => (ic(X) & ic(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_equivalentclass_ext')).
% 75.20/75.43 tff(56,plain,
% 75.20/75.43 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 75.20/75.43 tff(57,plain,
% 75.20/75.43 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[56, 52])).
% 75.20/75.43 tff(58,plain,(
% 75.20/75.43 ![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 75.20/75.43 inference(skolemize,[status(sab)],[57])).
% 75.20/75.43 tff(59,plain,
% 75.20/75.43 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[58, 51])).
% 75.20/75.43 tff(60,plain,
% 75.20/75.43 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[59, 49])).
% 75.20/75.43 tff(61,plain,
% 75.20/75.43 (((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c)))))),
% 75.20/75.43 inference(rewrite,[status(thm)],[])).
% 75.20/75.43 tff(62,plain,
% 75.20/75.43 ((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c)))))),
% 75.20/75.43 inference(quant_inst,[status(thm)],[])).
% 75.20/75.43 tff(63,plain,
% 75.20/75.43 ((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c))))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 75.20/75.43 tff(64,plain,
% 75.20/75.43 (~((~ic(X1!141)) | (~ic(uri_ex_c)))),
% 75.20/75.43 inference(unit_resolution,[status(thm)],[63, 60, 47])).
% 75.20/75.43 tff(65,plain,
% 75.20/75.43 (((~ic(X1!141)) | (~ic(uri_ex_c))) | ic(uri_ex_c)),
% 75.20/75.43 inference(tautology,[status(thm)],[])).
% 75.20/75.43 tff(66,plain,
% 75.20/75.43 (ic(uri_ex_c)),
% 75.20/75.43 inference(unit_resolution,[status(thm)],[65, 64])).
% 75.20/75.43 tff(67,plain,
% 75.20/75.43 (^[X1: $i, X0: $i] : refl(((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0))) <=> ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0))))),
% 75.20/75.43 inference(bind,[status(th)],[])).
% 75.20/75.43 tff(68,plain,
% 75.20/75.43 (![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0))) <=> ![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))),
% 75.20/75.43 inference(quant_intro,[status(thm)],[67])).
% 75.20/75.43 tff(69,plain,
% 75.20/75.43 (^[X1: $i, X0: $i] : trans(monotonicity(rewrite((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0)) <=> (~((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0))))), ((~(iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0))) <=> (~(~((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0))))))), rewrite((~(~((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0))))) <=> ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))), ((~(iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0))) <=> ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))))),
% 75.20/75.43 inference(bind,[status(th)],[])).
% 75.20/75.43 tff(70,plain,
% 75.20/75.43 (![X1: $i, X0: $i] : (~(iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0))) <=> ![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))),
% 75.20/75.43 inference(quant_intro,[status(thm)],[69])).
% 75.20/75.43 tff(71,plain,
% 75.20/75.43 ((~?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0))) <=> (~?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0)))),
% 75.20/75.43 inference(rewrite,[status(thm)],[])).
% 75.20/75.43 tff(72,plain,
% 75.20/75.43 ((~?[X1: $i, X0: $i] : ((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_owl_intersectionOf, uri_ex_c, X0))) <=> (~?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0)))),
% 75.20/75.43 inference(rewrite,[status(thm)],[])).
% 75.20/75.43 tff(73,axiom,(~?[X1: $i, X0: $i] : ((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_owl_intersectionOf, uri_ex_c, X0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion_rdfbased_sem_bool_intersection_ext')).
% 75.20/75.43 tff(74,plain,
% 75.20/75.43 (~?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[73, 72])).
% 75.20/75.43 tff(75,plain,
% 75.20/75.43 (~?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[74, 71])).
% 75.20/75.43 tff(76,plain,
% 75.20/75.43 (~?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[75, 71])).
% 75.20/75.43 tff(77,plain,
% 75.20/75.43 (~?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[76, 71])).
% 75.20/75.43 tff(78,plain,
% 75.20/75.43 (^[X1: $i, X0: $i] : refl($oeq((~(iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0))), (~(iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0)))))),
% 75.20/75.43 inference(bind,[status(th)],[])).
% 75.20/75.43 tff(79,plain,(
% 75.20/75.43 ![X1: $i, X0: $i] : (~(iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_intersectionOf, uri_ex_c, X0)))),
% 75.20/75.43 inference(nnf-neg,[status(sab)],[77, 78])).
% 75.20/75.43 tff(80,plain,
% 75.20/75.43 (![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[79, 70])).
% 75.20/75.43 tff(81,plain,
% 75.20/75.43 (![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[80, 68])).
% 75.20/75.43 tff(82,plain,
% 75.20/75.43 (((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))) | ((~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)))) <=> ((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)))),
% 75.20/75.43 inference(rewrite,[status(thm)],[])).
% 75.20/75.43 tff(83,plain,
% 75.20/75.43 (((~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X2!140))) <=> ((~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)))),
% 75.20/75.43 inference(rewrite,[status(thm)],[])).
% 75.20/75.43 tff(84,plain,
% 75.20/75.43 (((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))) | ((~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)))) <=> ((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))) | ((~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X2!140))))),
% 75.20/75.43 inference(monotonicity,[status(thm)],[83])).
% 75.20/75.43 tff(85,plain,
% 75.20/75.43 (((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))) | ((~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)))) <=> ((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)))),
% 75.20/75.43 inference(transitivity,[status(thm)],[84, 82])).
% 75.20/75.43 tff(86,plain,
% 75.20/75.43 ((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))) | ((~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)))),
% 75.20/75.43 inference(quant_inst,[status(thm)],[])).
% 75.20/75.43 tff(87,plain,
% 75.20/75.43 ((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_x)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_y)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X0)))) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_owl_intersectionOf, uri_ex_c, X2!140))),
% 75.20/75.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 75.20/75.43 tff(88,plain,
% 75.20/75.43 (~iext(uri_owl_intersectionOf, uri_ex_c, X2!140)),
% 75.20/75.43 inference(unit_resolution,[status(thm)],[87, 81, 12, 11, 10, 9])).
% 75.20/75.43 tff(89,plain,
% 75.20/75.43 (((~![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!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, 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, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))))))))),
% 75.20/75.44 inference(rewrite,[status(thm)],[])).
% 75.20/75.44 tff(90,plain,
% 75.20/75.44 (((~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))))))))) <=> ((~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))))))))),
% 75.20/75.44 inference(rewrite,[status(thm)],[])).
% 75.20/75.44 tff(91,plain,
% 75.20/75.44 ((~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))))))) <=> (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))))))))),
% 75.20/75.44 inference(rewrite,[status(thm)],[])).
% 75.20/75.44 tff(92,plain,
% 75.20/75.44 (((~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))))))))) <=> ((~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))))))))),
% 75.20/75.44 inference(monotonicity,[status(thm)],[91])).
% 75.20/75.44 tff(93,plain,
% 75.20/75.44 (((~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))))))))) <=> ((~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))))))))),
% 75.20/75.44 inference(transitivity,[status(thm)],[92, 90])).
% 75.20/75.44 tff(94,plain,
% 75.20/75.44 (((~![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!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, 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, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))))))))))),
% 75.20/75.44 inference(monotonicity,[status(thm)],[93])).
% 75.20/75.44 tff(95,plain,
% 75.20/75.44 (((~![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!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, 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, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))))))))),
% 75.20/75.44 inference(transitivity,[status(thm)],[94, 89])).
% 75.20/75.44 tff(96,plain,
% 75.20/75.44 ((~![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!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X1!141)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))))))))),
% 75.20/75.44 inference(quant_inst,[status(thm)],[])).
% 75.20/75.44 tff(97,plain,
% 75.20/75.44 ((~![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!142, uri_ex_y)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!140, uri_ex_x)) | (~iext(uri_rdf_rest, X2!140, X0!142)) | (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))))))))),
% 75.20/75.44 inference(modus_ponens,[status(thm)],[96, 95])).
% 75.20/75.44 tff(98,plain,
% 75.20/75.44 (~((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))))))),
% 75.20/75.44 inference(unit_resolution,[status(thm)],[97, 34, 12, 11, 10, 9])).
% 75.20/75.44 tff(99,plain,
% 75.20/75.44 (((~(iext(uri_owl_intersectionOf, X1!141, X2!140) | (~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, X1!141))))) | (~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))))))) | ((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))))),
% 75.20/75.44 inference(tautology,[status(thm)],[])).
% 75.20/75.44 tff(100,plain,
% 75.20/75.44 ((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))))),
% 75.20/75.44 inference(unit_resolution,[status(thm)],[99, 98])).
% 75.20/75.44 tff(101,plain,
% 75.20/75.44 (iext(uri_owl_intersectionOf, X1!141, X2!140)),
% 75.20/75.44 inference(and_elim,[status(thm)],[8])).
% 75.20/75.44 tff(102,plain,
% 75.20/75.44 ((~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))))) | (~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))))),
% 75.20/75.44 inference(tautology,[status(thm)],[])).
% 75.20/75.44 tff(103,plain,
% 75.20/75.44 ((~((~iext(uri_owl_intersectionOf, X1!141, X2!140)) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))))) | (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))))),
% 75.20/75.44 inference(unit_resolution,[status(thm)],[102, 101])).
% 75.20/75.44 tff(104,plain,
% 75.20/75.44 (~((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))))),
% 75.20/75.44 inference(unit_resolution,[status(thm)],[103, 100])).
% 75.20/75.44 tff(105,plain,
% 75.20/75.44 (((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))) | ic(uri_ex_y)),
% 75.20/75.44 inference(tautology,[status(thm)],[])).
% 75.20/75.44 tff(106,plain,
% 75.20/75.44 (ic(uri_ex_y)),
% 75.20/75.44 inference(unit_resolution,[status(thm)],[105, 104])).
% 75.20/75.44 tff(107,plain,
% 75.20/75.44 (((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))) | ic(uri_ex_x)),
% 75.20/75.44 inference(tautology,[status(thm)],[])).
% 75.20/75.44 tff(108,plain,
% 75.20/75.44 (ic(uri_ex_x)),
% 75.20/75.44 inference(unit_resolution,[status(thm)],[107, 104])).
% 75.20/75.44 tff(109,plain,
% 75.20/75.44 ((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.44 inference(tautology,[status(thm)],[])).
% 75.20/75.44 tff(110,plain,
% 75.20/75.44 ((~((~ic(uri_ex_x)) | (~ic(uri_ex_y)) | iext(uri_owl_intersectionOf, uri_ex_c, X2!140) | (~ic(uri_ex_c)) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.44 inference(unit_resolution,[status(thm)],[109, 108, 106, 88, 66])).
% 75.20/75.44 tff(111,plain,
% 75.20/75.44 (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.44 inference(unit_resolution,[status(thm)],[110, 46])).
% 75.20/75.44 tff(112,plain,
% 75.20/75.44 ((~(((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | (~((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.44 inference(tautology,[status(thm)],[])).
% 75.20/75.44 tff(113,plain,
% 75.20/75.44 ((~((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.44 inference(unit_resolution,[status(thm)],[112, 111])).
% 75.20/75.44 tff(114,plain,
% 75.20/75.44 (~((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))),
% 75.20/75.44 inference(unit_resolution,[status(thm)],[113, 1])).
% 75.20/75.44 tff(115,plain,
% 75.20/75.44 (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.44 inference(tautology,[status(thm)],[])).
% 75.20/75.44 tff(116,plain,
% 75.20/75.44 (icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.44 inference(unit_resolution,[status(thm)],[115, 114])).
% 75.20/75.44 tff(117,plain,
% 75.20/75.44 (^[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))))))))))),
% 75.20/75.44 inference(bind,[status(th)],[])).
% 75.20/75.44 tff(118,plain,
% 75.20/75.44 (![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)))))))))),
% 75.20/75.44 inference(quant_intro,[status(thm)],[117])).
% 75.20/75.44 tff(119,plain,
% 75.20/75.44 (^[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)))))))))),
% 75.20/75.44 inference(bind,[status(th)],[])).
% 75.20/75.44 tff(120,plain,
% 75.20/75.44 (![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))))))))),
% 75.20/75.44 inference(quant_intro,[status(thm)],[119])).
% 75.20/75.44 tff(121,plain,
% 75.20/75.44 (^[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)))))))))),
% 75.20/75.44 inference(bind,[status(th)],[])).
% 75.20/75.44 tff(122,plain,
% 75.20/75.44 (![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))))))))),
% 75.20/75.44 inference(quant_intro,[status(thm)],[121])).
% 75.20/75.44 tff(123,plain,
% 75.20/75.44 (![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))))))))),
% 75.20/75.44 inference(transitivity,[status(thm)],[122, 120])).
% 75.20/75.44 tff(124,plain,
% 75.20/75.44 (^[C1: $i, C2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(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))))))))))),
% 75.20/75.44 inference(bind,[status(th)],[])).
% 75.20/75.44 tff(125,plain,
% 75.20/75.44 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(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))))))))),
% 75.20/75.44 inference(quant_intro,[status(thm)],[124])).
% 75.20/75.44 tff(126,plain,
% 75.20/75.44 (^[C1: $i, C2: $i] : rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_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)))))))),
% 75.20/75.44 inference(bind,[status(th)],[])).
% 75.20/75.44 tff(127,plain,
% 75.20/75.44 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_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))))))),
% 75.20/75.44 inference(quant_intro,[status(thm)],[126])).
% 75.20/75.44 tff(128,plain,
% 75.20/75.44 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 75.20/75.44 inference(rewrite,[status(thm)],[])).
% 75.20/75.44 tff(129,plain,
% 75.20/75.44 (^[C1: $i, C2: $i] : rewrite((iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))))),
% 75.20/75.44 inference(bind,[status(th)],[])).
% 75.20/75.44 tff(130,plain,
% 75.20/75.44 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 75.20/75.44 inference(quant_intro,[status(thm)],[129])).
% 75.20/75.44 tff(131,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')).
% 75.20/75.44 tff(132,plain,
% 75.20/75.44 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 75.20/75.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 75.20/75.44 tff(133,plain,
% 75.20/75.44 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 75.20/75.44 inference(modus_ponens,[status(thm)],[132, 128])).
% 75.20/75.45 tff(134,plain,(
% 75.20/75.45 ![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 75.20/75.45 inference(skolemize,[status(sab)],[133])).
% 75.20/75.45 tff(135,plain,
% 75.20/75.45 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))),
% 75.20/75.45 inference(modus_ponens,[status(thm)],[134, 127])).
% 75.20/75.45 tff(136,plain,
% 75.20/75.45 (![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))))))))),
% 75.20/75.45 inference(modus_ponens,[status(thm)],[135, 125])).
% 75.20/75.45 tff(137,plain,
% 75.20/75.45 (![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))))))))),
% 75.20/75.45 inference(modus_ponens,[status(thm)],[136, 123])).
% 75.20/75.45 tff(138,plain,
% 75.20/75.45 (![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)))))))))),
% 75.20/75.45 inference(modus_ponens,[status(thm)],[137, 118])).
% 75.20/75.45 tff(139,plain,
% 75.20/75.45 ((~![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_c, X1!141) | (~ic(X1!141)) | (~ic(uri_ex_c)) | (~(icext(uri_ex_c, tptp_fun_X_67(X1!141, uri_ex_c)) <=> icext(X1!141, tptp_fun_X_67(X1!141, uri_ex_c)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X)))))))))),
% 75.20/75.45 inference(quant_inst,[status(thm)],[])).
% 75.20/75.45 tff(140,plain,
% 75.20/75.45 (~((~(iext(uri_owl_equivalentClass, uri_ex_c, X1!141) | (~ic(X1!141)) | (~ic(uri_ex_c)) | (~(icext(uri_ex_c, tptp_fun_X_67(X1!141, uri_ex_c)) <=> icext(X1!141, tptp_fun_X_67(X1!141, uri_ex_c)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X))))))))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[139, 138])).
% 75.20/75.45 tff(141,plain,
% 75.20/75.45 (((~(iext(uri_owl_equivalentClass, uri_ex_c, X1!141) | (~ic(X1!141)) | (~ic(uri_ex_c)) | (~(icext(uri_ex_c, tptp_fun_X_67(X1!141, uri_ex_c)) <=> icext(X1!141, tptp_fun_X_67(X1!141, uri_ex_c)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X)))))))) | ((~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X))))))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(142,plain,
% 75.20/75.45 ((~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X)))))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[141, 140])).
% 75.20/75.45 tff(143,plain,
% 75.20/75.45 ((~((~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X))))))) | (~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X)))))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(144,plain,
% 75.20/75.45 ((~((~iext(uri_owl_equivalentClass, uri_ex_c, X1!141)) | (~((~ic(X1!141)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X))))))) | (~((~ic(X1!141)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X)))))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[143, 47])).
% 75.20/75.45 tff(145,plain,
% 75.20/75.45 (~((~ic(X1!141)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X))))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[144, 142])).
% 75.20/75.45 tff(146,plain,
% 75.20/75.45 (((~ic(X1!141)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X)))) | ![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(147,plain,
% 75.20/75.45 (![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[146, 145])).
% 75.20/75.45 tff(148,plain,
% 75.20/75.45 ((~![X: $i] : (icext(uri_ex_c, X) <=> icext(X1!141, X))) | (icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(quant_inst,[status(thm)],[])).
% 75.20/75.45 tff(149,plain,
% 75.20/75.45 (icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[148, 147])).
% 75.20/75.45 tff(150,plain,
% 75.20/75.45 ((~(icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)) | (~icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(151,plain,
% 75.20/75.45 (icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)) | (~icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[150, 149])).
% 75.20/75.45 tff(152,plain,
% 75.20/75.45 (~icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[151, 1])).
% 75.20/75.45 tff(153,plain,
% 75.20/75.45 (((~ic(X1!141)) | (~ic(uri_ex_x)) | (~ic(uri_ex_y)) | (~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X))))) | ![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(154,plain,
% 75.20/75.45 (![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[153, 104])).
% 75.20/75.45 tff(155,plain,
% 75.20/75.45 ((~![X: $i] : (~(((~icext(uri_ex_y, X)) | (~icext(uri_ex_x, X))) <=> icext(X1!141, X)))) | (~(((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))),
% 75.20/75.45 inference(quant_inst,[status(thm)],[])).
% 75.20/75.45 tff(156,plain,
% 75.20/75.45 (~(((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[155, 154])).
% 75.20/75.45 tff(157,plain,
% 75.20/75.45 ((((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | ((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(158,plain,
% 75.20/75.45 (((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[157, 156])).
% 75.20/75.45 tff(159,plain,
% 75.20/75.45 ((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[158, 152])).
% 75.20/75.45 tff(160,assumption,(~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))), introduced(assumption)).
% 75.20/75.45 tff(161,plain,
% 75.20/75.45 (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(162,plain,
% 75.20/75.45 ((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[161, 160])).
% 75.20/75.45 tff(163,plain,
% 75.20/75.45 (icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[113, 162])).
% 75.20/75.45 tff(164,plain,
% 75.20/75.45 (((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(165,plain,
% 75.20/75.45 ((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[164, 160])).
% 75.20/75.45 tff(166,plain,
% 75.20/75.45 ((((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(167,plain,
% 75.20/75.45 ((~((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[166, 156])).
% 75.20/75.45 tff(168,plain,
% 75.20/75.45 (~icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[167, 165])).
% 75.20/75.45 tff(169,plain,
% 75.20/75.45 ((~(icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)) <=> icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | (~icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(170,plain,
% 75.20/75.45 ((~icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[169, 149])).
% 75.20/75.45 tff(171,plain,
% 75.20/75.45 ($false),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[170, 168, 163])).
% 75.20/75.45 tff(172,plain,(icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))), inference(lemma,lemma(discharge,[]))).
% 75.20/75.45 tff(173,plain,
% 75.20/75.45 ((~((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(174,plain,
% 75.20/75.45 ((~((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[173, 172])).
% 75.20/75.45 tff(175,plain,
% 75.20/75.45 ($false),
% 75.20/75.45 inference(unit_resolution,[status(thm)],[174, 159, 116])).
% 75.20/75.45 tff(176,plain,(icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))), inference(lemma,lemma(discharge,[]))).
% 75.20/75.45 tff(177,plain,
% 75.20/75.45 ((~(((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) <=> icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | ((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | (~icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.45 inference(tautology,[status(thm)],[])).
% 75.20/75.45 tff(178,plain,
% 75.20/75.45 (((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | (~icext(uri_ex_c, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.47 inference(unit_resolution,[status(thm)],[177, 111])).
% 75.20/75.47 tff(179,plain,
% 75.20/75.47 ((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.47 inference(unit_resolution,[status(thm)],[178, 176])).
% 75.20/75.47 tff(180,plain,
% 75.20/75.47 ((~((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.47 inference(tautology,[status(thm)],[])).
% 75.20/75.47 tff(181,plain,
% 75.20/75.47 ((~((~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))),
% 75.20/75.47 inference(unit_resolution,[status(thm)],[180, 172])).
% 75.20/75.47 tff(182,plain,
% 75.20/75.47 (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.47 inference(unit_resolution,[status(thm)],[181, 179])).
% 75.20/75.47 tff(183,plain,
% 75.20/75.47 (icext(X1!141, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.47 inference(unit_resolution,[status(thm)],[170, 176])).
% 75.20/75.47 tff(184,plain,
% 75.20/75.47 (~((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))))),
% 75.20/75.47 inference(unit_resolution,[status(thm)],[167, 183])).
% 75.20/75.47 tff(185,plain,
% 75.20/75.47 (((~icext(uri_ex_y, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))) | (~icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c)))) | icext(uri_ex_x, tptp_fun_X_3(uri_ex_y, uri_ex_x, uri_ex_c))),
% 75.20/75.47 inference(tautology,[status(thm)],[])).
% 75.20/75.47 tff(186,plain,
% 75.20/75.47 ($false),
% 75.20/75.47 inference(unit_resolution,[status(thm)],[185, 184, 182])).
% 75.20/75.47 % SZS output end Proof
% 75.20/75.48 % E exiting
%------------------------------------------------------------------------------