%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB014+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:34 AM UTC 2025
% Result : Theorem 0.48s 0.71s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWB014+1 : TPTP v9.0.0. Released v5.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:47:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.48/0.71 % SZS status Theorem
% 0.48/0.71 % SZS output start Proof
% 0.48/0.71 tff(icext_type, type, (
% 0.48/0.71 icext: ( $i * $i ) > $o)).
% 0.48/0.71 tff(uri_ex_harry_type, type, (
% 0.48/0.71 uri_ex_harry: $i)).
% 0.48/0.71 tff(uri_ex_Eagle_type, type, (
% 0.48/0.71 uri_ex_Eagle: $i)).
% 0.48/0.71 tff(uri_ex_Falcon_type, type, (
% 0.48/0.71 uri_ex_Falcon: $i)).
% 0.48/0.71 tff(tptp_fun_BNODE_u_142_type, type, (
% 0.48/0.71 tptp_fun_BNODE_u_142: $i)).
% 0.48/0.71 tff(ic_type, type, (
% 0.48/0.71 ic: $i > $o)).
% 0.48/0.71 tff(iext_type, type, (
% 0.48/0.71 iext: ( $i * $i * $i ) > $o)).
% 0.48/0.71 tff(tptp_fun_BNODE_l1_141_type, type, (
% 0.48/0.71 tptp_fun_BNODE_l1_141: $i)).
% 0.48/0.71 tff(uri_owl_unionOf_type, type, (
% 0.48/0.71 uri_owl_unionOf: $i)).
% 0.48/0.71 tff(tptp_fun_X_6_type, type, (
% 0.48/0.71 tptp_fun_X_6: ( $i * $i * $i ) > $i)).
% 0.48/0.71 tff(uri_rdf_nil_type, type, (
% 0.48/0.71 uri_rdf_nil: $i)).
% 0.48/0.71 tff(tptp_fun_BNODE_l2_140_type, type, (
% 0.48/0.71 tptp_fun_BNODE_l2_140: $i)).
% 0.48/0.71 tff(uri_rdf_rest_type, type, (
% 0.48/0.71 uri_rdf_rest: $i)).
% 0.48/0.71 tff(uri_rdf_first_type, type, (
% 0.48/0.71 uri_rdf_first: $i)).
% 0.48/0.71 tff(uri_rdf_type_type, type, (
% 0.48/0.71 uri_rdf_type: $i)).
% 0.48/0.71 tff(uri_ex_Species_type, type, (
% 0.48/0.71 uri_ex_Species: $i)).
% 0.48/0.71 tff(1,plain,
% 0.48/0.71 (?[BNODE_u: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> ?[BNODE_u: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(2,plain,
% 0.48/0.71 (^[BNODE_u: $i, BNODE_l1: $i, BNODE_l2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) <=> (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u))), ((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) <=> ((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)))), rewrite(((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) <=> (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1))), ((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) <=> (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)))), (((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) <=> ((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)))), rewrite(((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) <=> (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle))), (((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) <=> (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)))), ((((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> ((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)))), rewrite(((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2))), ((((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)))), (((((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon)) <=> ((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon)))), rewrite(((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon)) <=> (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon))), (((((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon)) <=> (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon)))), ((((((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> ((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))), ((((((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(3,plain,
% 0.48/0.71 (?[BNODE_u: $i, BNODE_l1: $i, BNODE_l2: $i] : (((((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> ?[BNODE_u: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[2])).
% 0.48/0.71 tff(4,axiom,(?[BNODE_u: $i, BNODE_l1: $i, BNODE_l2: $i] : (((((((iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)) & iext(uri_rdf_type, uri_ex_harry, BNODE_u)) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_premise_fullish_014_Harry_belongs_to_some_Species')).
% 0.48/0.71 tff(5,plain,
% 0.48/0.71 (?[BNODE_u: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.48/0.71 tff(6,plain,
% 0.48/0.71 (?[BNODE_u: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u) & iext(uri_owl_unionOf, BNODE_u, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_Falcon) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.48/0.71 tff(7,plain,(
% 0.48/0.71 iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species) & iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species) & iext(uri_rdf_type, uri_ex_harry, BNODE_u!142) & iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) & iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle) & iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140) & iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon) & iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)),
% 0.48/0.71 inference(skolemize,[status(sab)],[6])).
% 0.48/0.71 tff(8,plain,
% 0.48/0.71 (iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)),
% 0.48/0.71 inference(and_elim,[status(thm)],[7])).
% 0.48/0.71 tff(9,plain,
% 0.48/0.71 (iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)),
% 0.48/0.71 inference(and_elim,[status(thm)],[7])).
% 0.48/0.71 tff(10,plain,
% 0.48/0.71 (iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)),
% 0.48/0.71 inference(and_elim,[status(thm)],[7])).
% 0.48/0.71 tff(11,plain,
% 0.48/0.71 (iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)),
% 0.48/0.71 inference(and_elim,[status(thm)],[7])).
% 0.48/0.71 tff(12,plain,
% 0.48/0.71 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))))), rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))))),
% 0.48/0.72 inference(bind,[status(th)],[])).
% 0.48/0.72 tff(13,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 0.48/0.72 inference(quant_intro,[status(thm)],[12])).
% 0.48/0.72 tff(14,plain,
% 0.48/0.72 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : refl(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))))),
% 0.48/0.72 inference(bind,[status(th)],[])).
% 0.48/0.72 tff(15,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.48/0.72 inference(quant_intro,[status(thm)],[14])).
% 0.48/0.72 tff(16,plain,
% 0.48/0.72 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))))),
% 0.48/0.72 inference(bind,[status(th)],[])).
% 0.48/0.72 tff(17,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.48/0.72 inference(quant_intro,[status(thm)],[16])).
% 0.48/0.72 tff(18,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.48/0.72 inference(transitivity,[status(thm)],[17, 15])).
% 0.48/0.72 tff(19,plain,
% 0.48/0.72 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) <=> ((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))) <=> (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))), rewrite((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))), rewrite((((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))) <=> (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))))), rewrite((((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))))),
% 0.48/0.72 inference(bind,[status(th)],[])).
% 0.48/0.72 tff(20,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.48/0.72 inference(quant_intro,[status(thm)],[19])).
% 0.48/0.72 tff(21,plain,
% 0.48/0.72 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 0.48/0.72 inference(bind,[status(th)],[])).
% 0.48/0.72 tff(22,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))),
% 0.48/0.72 inference(quant_intro,[status(thm)],[21])).
% 0.48/0.72 tff(23,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.48/0.72 inference(rewrite,[status(thm)],[])).
% 0.48/0.72 tff(24,plain,
% 0.48/0.72 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X))))) <=> (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))),
% 0.48/0.72 inference(bind,[status(th)],[])).
% 0.48/0.72 tff(25,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.48/0.72 inference(quant_intro,[status(thm)],[24])).
% 0.48/0.72 tff(26,axiom,(![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_unionof_class_002')).
% 0.48/0.72 tff(27,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.48/0.72 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.48/0.72 tff(28,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.48/0.72 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.48/0.72 tff(29,plain,(
% 0.48/0.72 ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 0.48/0.72 inference(skolemize,[status(sab)],[28])).
% 0.48/0.72 tff(30,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))),
% 0.48/0.72 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.48/0.72 tff(31,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.48/0.72 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.48/0.72 tff(32,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.48/0.72 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.48/0.72 tff(33,plain,
% 0.48/0.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 0.48/0.72 inference(modus_ponens,[status(thm)],[32, 13])).
% 0.48/0.72 tff(34,plain,
% 0.48/0.72 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))))))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(35,plain,
% 0.57/0.73 (((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))))))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(36,plain,
% 0.57/0.73 ((~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))))) <=> (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X))))))))))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(37,plain,
% 0.57/0.73 (((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))))))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[36])).
% 0.57/0.73 tff(38,plain,
% 0.57/0.73 (((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))))))),
% 0.57/0.73 inference(transitivity,[status(thm)],[37, 35])).
% 0.57/0.73 tff(39,plain,
% 0.57/0.73 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X))))))))))))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[38])).
% 0.57/0.73 tff(40,plain,
% 0.57/0.73 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))))))),
% 0.57/0.73 inference(transitivity,[status(thm)],[39, 34])).
% 0.57/0.73 tff(41,plain,
% 0.57/0.73 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(uri_ex_Falcon)) | (~ic(uri_ex_Eagle)) | (~ic(BNODE_u!142)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))))))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(42,plain,
% 0.57/0.73 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!141, uri_ex_Eagle)) | (~iext(uri_rdf_rest, BNODE_l1!141, BNODE_l2!140)) | (~iext(uri_rdf_first, BNODE_l2!140, uri_ex_Falcon)) | (~iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X))))))))))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.57/0.73 tff(43,plain,
% 0.57/0.73 (~((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[42, 33, 11, 10, 9, 8])).
% 0.57/0.73 tff(44,plain,
% 0.57/0.73 (((~(iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141) | (~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~(icext(BNODE_u!142, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) <=> (icext(uri_ex_Eagle, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142)) | icext(uri_ex_Falcon, tptp_fun_X_6(uri_ex_Falcon, uri_ex_Eagle, BNODE_u!142))))))) | (~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X))))))))) | ((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(45,plain,
% 0.57/0.73 ((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X))))))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.57/0.73 tff(46,plain,
% 0.57/0.73 (iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)),
% 0.57/0.73 inference(and_elim,[status(thm)],[7])).
% 0.57/0.73 tff(47,plain,
% 0.57/0.73 ((~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))) | (~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X))))))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(48,plain,
% 0.57/0.73 ((~((~iext(uri_owl_unionOf, BNODE_u!142, BNODE_l1!141)) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))))) | (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X))))))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.57/0.73 tff(49,plain,
% 0.57/0.73 (~((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.57/0.73 tff(50,plain,
% 0.57/0.73 (((~ic(BNODE_u!142)) | (~ic(uri_ex_Eagle)) | (~ic(uri_ex_Falcon)) | (~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X))))) | ![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(51,plain,
% 0.57/0.73 (![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.57/0.73 tff(52,plain,
% 0.57/0.73 ((~![X: $i] : (icext(BNODE_u!142, X) <=> (icext(uri_ex_Falcon, X) | icext(uri_ex_Eagle, X)))) | (icext(BNODE_u!142, uri_ex_harry) <=> (icext(uri_ex_Falcon, uri_ex_harry) | icext(uri_ex_Eagle, uri_ex_harry)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(53,plain,
% 0.57/0.73 (icext(BNODE_u!142, uri_ex_harry) <=> (icext(uri_ex_Falcon, uri_ex_harry) | icext(uri_ex_Eagle, uri_ex_harry))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.57/0.73 tff(54,plain,
% 0.57/0.73 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.57/0.73 inference(bind,[status(th)],[])).
% 0.57/0.73 tff(55,plain,
% 0.57/0.73 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[54])).
% 0.57/0.73 tff(56,plain,
% 0.57/0.73 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(57,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','rdfs_cext_def')).
% 0.57/0.73 tff(58,plain,
% 0.57/0.73 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.57/0.73 tff(59,plain,(
% 0.57/0.73 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.57/0.73 inference(skolemize,[status(sab)],[58])).
% 0.57/0.73 tff(60,plain,
% 0.57/0.73 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.57/0.73 tff(61,plain,
% 0.57/0.73 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_harry, BNODE_u!142) <=> icext(BNODE_u!142, uri_ex_harry))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(62,plain,
% 0.57/0.73 (iext(uri_rdf_type, uri_ex_harry, BNODE_u!142) <=> icext(BNODE_u!142, uri_ex_harry)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.57/0.73 tff(63,plain,
% 0.57/0.73 (iext(uri_rdf_type, uri_ex_harry, BNODE_u!142)),
% 0.57/0.73 inference(and_elim,[status(thm)],[7])).
% 0.57/0.73 tff(64,plain,
% 0.57/0.73 ((~(iext(uri_rdf_type, uri_ex_harry, BNODE_u!142) <=> icext(BNODE_u!142, uri_ex_harry))) | (~iext(uri_rdf_type, uri_ex_harry, BNODE_u!142)) | icext(BNODE_u!142, uri_ex_harry)),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(65,plain,
% 0.57/0.73 ((~(iext(uri_rdf_type, uri_ex_harry, BNODE_u!142) <=> icext(BNODE_u!142, uri_ex_harry))) | icext(BNODE_u!142, uri_ex_harry)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.57/0.73 tff(66,plain,
% 0.57/0.73 (icext(BNODE_u!142, uri_ex_harry)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[65, 62])).
% 0.57/0.73 tff(67,plain,
% 0.57/0.73 ((~(icext(BNODE_u!142, uri_ex_harry) <=> (icext(uri_ex_Falcon, uri_ex_harry) | icext(uri_ex_Eagle, uri_ex_harry)))) | (~icext(BNODE_u!142, uri_ex_harry)) | (icext(uri_ex_Falcon, uri_ex_harry) | icext(uri_ex_Eagle, uri_ex_harry))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(68,plain,
% 0.57/0.73 ((~(icext(BNODE_u!142, uri_ex_harry) <=> (icext(uri_ex_Falcon, uri_ex_harry) | icext(uri_ex_Eagle, uri_ex_harry)))) | (icext(uri_ex_Falcon, uri_ex_harry) | icext(uri_ex_Eagle, uri_ex_harry))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.57/0.73 tff(69,plain,
% 0.57/0.73 (icext(uri_ex_Falcon, uri_ex_harry) | icext(uri_ex_Eagle, uri_ex_harry)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[68, 53])).
% 0.57/0.73 tff(70,plain,
% 0.57/0.73 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_harry, uri_ex_Eagle) <=> icext(uri_ex_Eagle, uri_ex_harry))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(71,plain,
% 0.57/0.73 (iext(uri_rdf_type, uri_ex_harry, uri_ex_Eagle) <=> icext(uri_ex_Eagle, uri_ex_harry)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[70, 60])).
% 0.57/0.73 tff(72,plain,
% 0.57/0.73 (iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species)),
% 0.57/0.73 inference(and_elim,[status(thm)],[7])).
% 0.57/0.73 tff(73,plain,
% 0.57/0.73 (^[BNODE_x: $i] : refl(((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species))) <=> ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species))))),
% 0.57/0.73 inference(bind,[status(th)],[])).
% 0.57/0.73 tff(74,plain,
% 0.57/0.73 (![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species))) <=> ![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[73])).
% 0.57/0.73 tff(75,plain,
% 0.57/0.73 (^[BNODE_x: $i] : trans(monotonicity(rewrite((iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species)) <=> (~((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species))))), ((~(iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species))) <=> (~(~((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species))))))), rewrite((~(~((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species))))) <=> ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))), ((~(iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species))) <=> ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(76,plain,
% 0.57/0.74 (![BNODE_x: $i] : (~(iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species))) <=> ![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[75])).
% 0.57/0.74 tff(77,plain,
% 0.57/0.74 ((~?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species))) <=> (~?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(78,axiom,(~?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_conclusion_fullish_014_Harry_belongs_to_some_Species')).
% 0.57/0.74 tff(79,plain,
% 0.57/0.74 (~?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.57/0.74 tff(80,plain,
% 0.57/0.74 (~?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[79, 77])).
% 0.57/0.74 tff(81,plain,
% 0.57/0.74 (~?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[80, 77])).
% 0.57/0.74 tff(82,plain,
% 0.57/0.74 (~?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.57/0.74 tff(83,plain,
% 0.57/0.74 (^[BNODE_x: $i] : refl($oeq((~(iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species))), (~(iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species)))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(84,plain,(
% 0.57/0.74 ![BNODE_x: $i] : (~(iext(uri_rdf_type, uri_ex_harry, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_ex_Species)))),
% 0.57/0.74 inference(nnf-neg,[status(sab)],[82, 83])).
% 0.57/0.74 tff(85,plain,
% 0.57/0.74 (![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[84, 76])).
% 0.57/0.74 tff(86,plain,
% 0.57/0.74 (![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[85, 74])).
% 0.57/0.74 tff(87,plain,
% 0.57/0.74 (((~![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))) | ((~iext(uri_rdf_type, uri_ex_harry, uri_ex_Eagle)) | (~iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species)))) <=> ((~![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))) | (~iext(uri_rdf_type, uri_ex_harry, uri_ex_Eagle)) | (~iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(88,plain,
% 0.57/0.74 ((~![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))) | ((~iext(uri_rdf_type, uri_ex_harry, uri_ex_Eagle)) | (~iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(89,plain,
% 0.57/0.74 ((~![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))) | (~iext(uri_rdf_type, uri_ex_harry, uri_ex_Eagle)) | (~iext(uri_rdf_type, uri_ex_Eagle, uri_ex_Species))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.57/0.74 tff(90,plain,
% 0.57/0.76 (~iext(uri_rdf_type, uri_ex_harry, uri_ex_Eagle)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[89, 86, 72])).
% 0.57/0.76 tff(91,plain,
% 0.57/0.76 ((~(iext(uri_rdf_type, uri_ex_harry, uri_ex_Eagle) <=> icext(uri_ex_Eagle, uri_ex_harry))) | iext(uri_rdf_type, uri_ex_harry, uri_ex_Eagle) | (~icext(uri_ex_Eagle, uri_ex_harry))),
% 0.57/0.76 inference(tautology,[status(thm)],[])).
% 0.57/0.76 tff(92,plain,
% 0.57/0.76 ((~(iext(uri_rdf_type, uri_ex_harry, uri_ex_Eagle) <=> icext(uri_ex_Eagle, uri_ex_harry))) | (~icext(uri_ex_Eagle, uri_ex_harry))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.57/0.76 tff(93,plain,
% 0.57/0.76 (~icext(uri_ex_Eagle, uri_ex_harry)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[92, 71])).
% 0.57/0.76 tff(94,plain,
% 0.57/0.76 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_harry, uri_ex_Falcon) <=> icext(uri_ex_Falcon, uri_ex_harry))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(95,plain,
% 0.57/0.76 (iext(uri_rdf_type, uri_ex_harry, uri_ex_Falcon) <=> icext(uri_ex_Falcon, uri_ex_harry)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[94, 60])).
% 0.57/0.76 tff(96,plain,
% 0.57/0.76 (iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)),
% 0.57/0.76 inference(and_elim,[status(thm)],[7])).
% 0.57/0.76 tff(97,plain,
% 0.57/0.76 (((~![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))) | ((~iext(uri_rdf_type, uri_ex_harry, uri_ex_Falcon)) | (~iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)))) <=> ((~![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))) | (~iext(uri_rdf_type, uri_ex_harry, uri_ex_Falcon)) | (~iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(98,plain,
% 0.57/0.76 ((~![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))) | ((~iext(uri_rdf_type, uri_ex_harry, uri_ex_Falcon)) | (~iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(99,plain,
% 0.57/0.76 ((~![BNODE_x: $i] : ((~iext(uri_rdf_type, uri_ex_harry, BNODE_x)) | (~iext(uri_rdf_type, BNODE_x, uri_ex_Species)))) | (~iext(uri_rdf_type, uri_ex_harry, uri_ex_Falcon)) | (~iext(uri_rdf_type, uri_ex_Falcon, uri_ex_Species))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.57/0.76 tff(100,plain,
% 0.57/0.76 (~iext(uri_rdf_type, uri_ex_harry, uri_ex_Falcon)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[99, 86, 96])).
% 0.57/0.76 tff(101,plain,
% 0.57/0.76 ((~(iext(uri_rdf_type, uri_ex_harry, uri_ex_Falcon) <=> icext(uri_ex_Falcon, uri_ex_harry))) | iext(uri_rdf_type, uri_ex_harry, uri_ex_Falcon) | (~icext(uri_ex_Falcon, uri_ex_harry))),
% 0.57/0.76 inference(tautology,[status(thm)],[])).
% 0.57/0.76 tff(102,plain,
% 0.57/0.76 ((~(iext(uri_rdf_type, uri_ex_harry, uri_ex_Falcon) <=> icext(uri_ex_Falcon, uri_ex_harry))) | (~icext(uri_ex_Falcon, uri_ex_harry))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.57/0.76 tff(103,plain,
% 0.57/0.76 (~icext(uri_ex_Falcon, uri_ex_harry)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[102, 95])).
% 0.57/0.76 tff(104,plain,
% 0.57/0.76 ((~(icext(uri_ex_Falcon, uri_ex_harry) | icext(uri_ex_Eagle, uri_ex_harry))) | icext(uri_ex_Falcon, uri_ex_harry) | icext(uri_ex_Eagle, uri_ex_harry)),
% 0.57/0.76 inference(tautology,[status(thm)],[])).
% 0.57/0.76 tff(105,plain,
% 0.57/0.76 ($false),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[104, 103, 93, 69])).
% 0.57/0.76 % SZS output end Proof
% 0.57/0.76 % E exiting
%------------------------------------------------------------------------------