TSTP Solution File: SWB027+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB027+2 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Tue Sep 20 08:31:58 EDT 2022
% Result : Theorem 0.54s 0.58s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWB027+2 : TPTP v8.1.0. Released v5.2.0.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Sep 3 19:46:20 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 0.54/0.58 % SZS status Theorem
% 0.54/0.58 % SZS output start Proof
% 0.54/0.58 tff(tptp_fun_X2_4_type, type, (
% 0.54/0.58 tptp_fun_X2_4: $i > $i)).
% 0.54/0.58 tff(uri_ex_p_type, type, (
% 0.54/0.58 uri_ex_p: $i)).
% 0.54/0.58 tff(tptp_fun_X1_5_type, type, (
% 0.54/0.58 tptp_fun_X1_5: $i > $i)).
% 0.54/0.58 tff(iext_type, type, (
% 0.54/0.58 iext: ( $i * $i * $i ) > $o)).
% 0.54/0.58 tff(uri_owl_sameAs_type, type, (
% 0.54/0.58 uri_owl_sameAs: $i)).
% 0.54/0.58 tff(tptp_fun_Y_3_type, type, (
% 0.54/0.58 tptp_fun_Y_3: $i > $i)).
% 0.54/0.58 tff(tptp_fun_BNODE_v_8_type, type, (
% 0.54/0.58 tptp_fun_BNODE_v_8: $i)).
% 0.54/0.58 tff(ip_type, type, (
% 0.54/0.58 ip: $i > $o)).
% 0.54/0.58 tff(uri_owl_inverseOf_type, type, (
% 0.54/0.58 uri_owl_inverseOf: $i)).
% 0.54/0.58 tff(tptp_fun_X_7_type, type, (
% 0.54/0.58 tptp_fun_X_7: ( $i * $i ) > $i)).
% 0.54/0.58 tff(tptp_fun_Y_6_type, type, (
% 0.54/0.58 tptp_fun_Y_6: ( $i * $i ) > $i)).
% 0.54/0.58 tff(uri_rdf_nil_type, type, (
% 0.54/0.58 uri_rdf_nil: $i)).
% 0.54/0.58 tff(tptp_fun_BNODE_l2_9_type, type, (
% 0.54/0.58 tptp_fun_BNODE_l2_9: $i)).
% 0.54/0.58 tff(uri_rdf_rest_type, type, (
% 0.54/0.58 uri_rdf_rest: $i)).
% 0.54/0.58 tff(uri_rdf_first_type, type, (
% 0.54/0.58 uri_rdf_first: $i)).
% 0.54/0.58 tff(tptp_fun_BNODE_l1_10_type, type, (
% 0.54/0.58 tptp_fun_BNODE_l1_10: $i)).
% 0.54/0.58 tff(uri_owl_propertyChainAxiom_type, type, (
% 0.54/0.58 uri_owl_propertyChainAxiom: $i)).
% 0.54/0.58 tff(icext_type, type, (
% 0.54/0.58 icext: ( $i * $i ) > $o)).
% 0.54/0.58 tff(uri_owl_InverseFunctionalProperty_type, type, (
% 0.54/0.58 uri_owl_InverseFunctionalProperty: $i)).
% 0.54/0.58 tff(tptp_fun_Y2_0_type, type, (
% 0.54/0.58 tptp_fun_Y2_0: ( $i * $i * $i ) > $i)).
% 0.54/0.58 tff(tptp_fun_Y1_1_type, type, (
% 0.54/0.58 tptp_fun_Y1_1: ( $i * $i * $i ) > $i)).
% 0.54/0.58 tff(tptp_fun_Y0_2_type, type, (
% 0.54/0.58 tptp_fun_Y0_2: ( $i * $i * $i ) > $i)).
% 0.54/0.58 tff(uri_rdf_type_type, type, (
% 0.54/0.58 uri_rdf_type: $i)).
% 0.54/0.58 tff(1,plain,
% 0.54/0.58 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))) <=> (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(2,plain,
% 0.54/0.58 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))) <=> ![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[1])).
% 0.54/0.58 tff(3,plain,
% 0.54/0.58 (^[P1: $i, P2: $i] : refl((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(4,plain,
% 0.54/0.58 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[3])).
% 0.54/0.58 tff(5,plain,
% 0.54/0.58 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(6,plain,
% 0.54/0.58 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[5])).
% 0.54/0.58 tff(7,plain,
% 0.54/0.58 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))),
% 0.54/0.58 inference(transitivity,[status(thm)],[6, 4])).
% 0.54/0.58 tff(8,plain,
% 0.54/0.58 (^[P1: $i, P2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))), rewrite((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))), rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(9,plain,
% 0.54/0.58 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[8])).
% 0.54/0.58 tff(10,plain,
% 0.54/0.58 (^[P1: $i, P2: $i] : rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(11,plain,
% 0.54/0.58 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))) <=> ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[10])).
% 0.54/0.58 tff(12,plain,
% 0.54/0.58 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(13,plain,
% 0.54/0.58 (^[P1: $i, P2: $i] : rewrite((iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(14,plain,
% 0.54/0.58 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[13])).
% 0.54/0.58 tff(15,axiom,(![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_inv')).
% 0.57/0.59 tff(16,plain,
% 0.57/0.59 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.57/0.59 tff(17,plain,
% 0.57/0.59 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.57/0.59 tff(18,plain,(
% 0.57/0.59 ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))),
% 0.57/0.59 inference(skolemize,[status(sab)],[17])).
% 0.57/0.59 tff(19,plain,
% 0.57/0.59 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.57/0.59 tff(20,plain,
% 0.57/0.59 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.57/0.59 tff(21,plain,
% 0.57/0.59 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.57/0.59 tff(22,plain,
% 0.57/0.59 (![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.57/0.59 tff(23,plain,
% 0.57/0.59 ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1))) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | ((~iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8))) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))))))),
% 0.57/0.59 inference(quant_inst,[status(thm)],[])).
% 0.57/0.59 tff(24,plain,
% 0.57/0.59 (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | ((~iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8))) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))))),
% 0.57/0.59 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.57/0.59 tff(25,plain,
% 0.57/0.59 (((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | ((~iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8))) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))))) | ((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))),
% 0.57/0.59 inference(tautology,[status(thm)],[])).
% 0.57/0.59 tff(26,plain,
% 0.57/0.59 ((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))),
% 0.57/0.59 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.57/0.59 tff(27,plain,
% 0.57/0.59 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)) <=> ?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))),
% 0.57/0.59 inference(rewrite,[status(thm)],[])).
% 0.57/0.59 tff(28,plain,
% 0.57/0.59 (^[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2))), ((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) <=> ((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v))), ((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v)))), (((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> ((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))), (((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)))), ((((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)) <=> ((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))), ((((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))))),
% 0.57/0.59 inference(bind,[status(th)],[])).
% 0.57/0.59 tff(29,plain,
% 0.57/0.59 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)) <=> ?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))),
% 0.57/0.59 inference(quant_intro,[status(thm)],[28])).
% 0.57/0.59 tff(30,axiom,(?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_premise_fullish_027_Inferred_Property_Characteristics_II')).
% 0.57/0.59 tff(31,plain,
% 0.57/0.59 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.57/0.59 tff(32,plain,
% 0.57/0.59 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.57/0.59 tff(33,plain,(
% 0.57/0.59 iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) & iext(uri_rdf_first, BNODE_l1!10, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9) & iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8) & iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)),
% 0.57/0.59 inference(skolemize,[status(sab)],[32])).
% 0.57/0.59 tff(34,plain,
% 0.57/0.59 (iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)),
% 0.57/0.59 inference(and_elim,[status(thm)],[33])).
% 0.57/0.59 tff(35,plain,
% 0.57/0.59 ((~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))) | (~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))),
% 0.57/0.59 inference(tautology,[status(thm)],[])).
% 0.57/0.59 tff(36,plain,
% 0.57/0.59 ((~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))),
% 0.57/0.59 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.57/0.59 tff(37,plain,
% 0.57/0.59 (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))),
% 0.57/0.59 inference(unit_resolution,[status(thm)],[36, 26])).
% 0.57/0.59 tff(38,plain,
% 0.57/0.59 (((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))) | ![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))),
% 0.57/0.59 inference(tautology,[status(thm)],[])).
% 0.57/0.59 tff(39,plain,
% 0.57/0.59 (![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))),
% 0.57/0.59 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.57/0.59 tff(40,plain,
% 0.57/0.59 ((~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))) | (iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) <=> iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))),
% 0.57/0.59 inference(quant_inst,[status(thm)],[])).
% 0.57/0.59 tff(41,plain,
% 0.57/0.59 (iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) <=> iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))),
% 0.57/0.59 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.57/0.59 tff(42,plain,
% 0.57/0.59 (^[P: $i] : rewrite((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))))))),
% 0.57/0.59 inference(bind,[status(th)],[])).
% 0.57/0.59 tff(43,plain,
% 0.57/0.59 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> ![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 0.57/0.59 inference(quant_intro,[status(thm)],[42])).
% 0.57/0.59 tff(44,plain,
% 0.57/0.59 (^[P: $i] : refl((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(45,plain,
% 0.57/0.60 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[44])).
% 0.57/0.60 tff(46,plain,
% 0.57/0.60 (^[P: $i] : rewrite((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(47,plain,
% 0.57/0.60 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[46])).
% 0.57/0.60 tff(48,plain,
% 0.57/0.60 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.57/0.60 inference(transitivity,[status(thm)],[47, 45])).
% 0.57/0.60 tff(49,plain,
% 0.57/0.60 (^[P: $i] : trans(monotonicity(rewrite(((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) <=> ((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))), trans(monotonicity(rewrite((~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))) <=> (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))), rewrite((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))), ((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))))) <=> (((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))), rewrite((((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))), ((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(50,plain,
% 0.57/0.60 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[49])).
% 0.57/0.60 tff(51,plain,
% 0.57/0.60 (^[P: $i] : rewrite((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))))) <=> (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(52,plain,
% 0.57/0.60 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))))) <=> ![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[51])).
% 0.57/0.60 tff(53,plain,
% 0.57/0.60 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) <=> ![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(54,plain,
% 0.57/0.60 (^[P: $i] : rewrite((icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2)))) <=> (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(55,plain,
% 0.57/0.60 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2)))) <=> ![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[54])).
% 0.57/0.60 tff(56,axiom,(![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_char_inversefunctional')).
% 0.57/0.60 tff(57,plain,
% 0.57/0.60 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.57/0.60 tff(58,plain,
% 0.57/0.60 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.57/0.60 tff(59,plain,(
% 0.57/0.60 ![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))))))),
% 0.57/0.60 inference(skolemize,[status(sab)],[58])).
% 0.57/0.60 tff(60,plain,
% 0.57/0.60 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.57/0.60 tff(61,plain,
% 0.57/0.60 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.57/0.60 tff(62,plain,
% 0.57/0.60 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[61, 48])).
% 0.57/0.60 tff(63,plain,
% 0.57/0.60 (![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[62, 43])).
% 0.57/0.60 tff(64,plain,
% 0.57/0.60 ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))),
% 0.57/0.60 inference(quant_inst,[status(thm)],[])).
% 0.57/0.60 tff(65,plain,
% 0.57/0.60 (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.57/0.60 tff(66,plain,
% 0.57/0.60 (((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))) | (icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))))))),
% 0.57/0.60 inference(tautology,[status(thm)],[])).
% 0.57/0.60 tff(67,plain,
% 0.57/0.60 (icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))))),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.57/0.60 tff(68,plain,
% 0.57/0.60 (iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)),
% 0.57/0.60 inference(and_elim,[status(thm)],[33])).
% 0.57/0.60 tff(69,plain,
% 0.57/0.60 (iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)),
% 0.57/0.60 inference(and_elim,[status(thm)],[33])).
% 0.57/0.60 tff(70,plain,
% 0.57/0.60 (iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)),
% 0.57/0.60 inference(and_elim,[status(thm)],[33])).
% 0.57/0.60 tff(71,plain,
% 0.57/0.60 (iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)),
% 0.57/0.60 inference(and_elim,[status(thm)],[33])).
% 0.57/0.60 tff(72,plain,
% 0.57/0.60 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))))))), (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))))))))), rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))), (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))))),
% 0.57/0.61 inference(bind,[status(th)],[])).
% 0.57/0.61 tff(73,plain,
% 0.57/0.61 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))),
% 0.57/0.61 inference(quant_intro,[status(thm)],[72])).
% 0.57/0.61 tff(74,plain,
% 0.57/0.61 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : refl(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))))),
% 0.57/0.61 inference(bind,[status(th)],[])).
% 0.57/0.61 tff(75,plain,
% 0.57/0.61 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.57/0.61 inference(quant_intro,[status(thm)],[74])).
% 0.57/0.61 tff(76,plain,
% 0.57/0.61 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))))),
% 0.57/0.61 inference(bind,[status(th)],[])).
% 0.57/0.61 tff(77,plain,
% 0.57/0.61 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.57/0.61 inference(quant_intro,[status(thm)],[76])).
% 0.57/0.61 tff(78,plain,
% 0.57/0.61 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.57/0.61 inference(transitivity,[status(thm)],[77, 75])).
% 0.57/0.61 tff(79,plain,
% 0.57/0.61 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) <=> ((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))), trans(monotonicity(rewrite((~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) <=> (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))), rewrite((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) <=> (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))))), rewrite((((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))))),
% 0.57/0.61 inference(bind,[status(th)],[])).
% 0.57/0.61 tff(80,plain,
% 0.57/0.61 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[79])).
% 0.57/0.62 tff(81,plain,
% 0.57/0.62 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : rewrite(((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(82,plain,
% 0.57/0.62 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[81])).
% 0.57/0.62 tff(83,plain,
% 0.57/0.62 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(84,plain,
% 0.57/0.62 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2))), ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2)))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))), (((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))), (((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(85,plain,
% 0.57/0.62 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[84])).
% 0.57/0.62 tff(86,axiom,(![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_chain_002')).
% 0.57/0.62 tff(87,plain,
% 0.57/0.62 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.57/0.62 tff(88,plain,
% 0.57/0.62 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.57/0.62 tff(89,plain,(
% 0.57/0.62 ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))),
% 0.57/0.62 inference(skolemize,[status(sab)],[88])).
% 0.57/0.62 tff(90,plain,
% 0.57/0.62 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.57/0.62 tff(91,plain,
% 0.57/0.62 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.57/0.62 tff(92,plain,
% 0.57/0.62 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[91, 78])).
% 0.57/0.62 tff(93,plain,
% 0.57/0.62 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[92, 73])).
% 0.57/0.62 tff(94,plain,
% 0.57/0.62 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))))))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(95,plain,
% 0.57/0.62 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))))))))),
% 0.61/0.63 inference(quant_inst,[status(thm)],[])).
% 0.61/0.63 tff(96,plain,
% 0.61/0.63 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2))))))))))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.61/0.63 tff(97,plain,
% 0.61/0.63 (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))))))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[96, 93, 71, 70, 69, 68])).
% 0.61/0.63 tff(98,plain,
% 0.61/0.63 (((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2))))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))))),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(99,plain,
% 0.61/0.63 ((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2))))))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.61/0.63 tff(100,plain,
% 0.61/0.63 (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)),
% 0.61/0.63 inference(and_elim,[status(thm)],[33])).
% 0.61/0.63 tff(101,plain,
% 0.61/0.63 ((~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))))) | (~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2))))))),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(102,plain,
% 0.61/0.63 ((~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))))) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2))))))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.61/0.63 tff(103,plain,
% 0.61/0.63 (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.61/0.63 tff(104,plain,
% 0.61/0.63 (((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2))))) | ip(uri_ex_p)),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(105,plain,
% 0.61/0.63 (ip(uri_ex_p)),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.61/0.63 tff(106,plain,
% 0.61/0.63 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.61/0.63 inference(bind,[status(th)],[])).
% 0.61/0.63 tff(107,plain,
% 0.61/0.63 (![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))),
% 0.61/0.63 inference(quant_intro,[status(thm)],[106])).
% 0.61/0.63 tff(108,plain,
% 0.61/0.63 (![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))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(109,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdfs_cext_def')).
% 0.61/0.63 tff(110,plain,
% 0.61/0.63 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.61/0.63 tff(111,plain,(
% 0.61/0.63 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.61/0.63 inference(skolemize,[status(sab)],[110])).
% 0.61/0.63 tff(112,plain,
% 0.61/0.63 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.61/0.63 tff(113,plain,
% 0.61/0.63 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.61/0.63 inference(quant_inst,[status(thm)],[])).
% 0.61/0.63 tff(114,plain,
% 0.61/0.63 (iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.61/0.63 tff(115,plain,
% 0.61/0.63 ((~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)) <=> (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(116,axiom,(~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_conclusion_fullish_027_Inferred_Property_Characteristics_II')).
% 0.61/0.63 tff(117,plain,
% 0.61/0.63 (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.61/0.63 tff(118,plain,
% 0.61/0.63 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))) | iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) | (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(119,plain,
% 0.61/0.63 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))) | (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.61/0.63 tff(120,plain,
% 0.61/0.63 (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[119, 114])).
% 0.61/0.63 tff(121,plain,
% 0.61/0.63 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))))))) | icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))))),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(122,plain,
% 0.61/0.63 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))))))) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[121, 120, 105])).
% 0.61/0.63 tff(123,plain,
% 0.61/0.63 (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[122, 67])).
% 0.61/0.63 tff(124,plain,
% 0.61/0.63 (((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))) | iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(125,plain,
% 0.61/0.63 (iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.61/0.63 tff(126,plain,
% 0.61/0.63 ((~(iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) <=> iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))) | iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))),
% 0.61/0.64 inference(tautology,[status(thm)],[])).
% 0.61/0.64 tff(127,plain,
% 0.61/0.64 ((~(iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) <=> iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))) | iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.61/0.64 tff(128,plain,
% 0.61/0.64 (iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[127, 41])).
% 0.61/0.64 tff(129,plain,
% 0.61/0.64 (((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))) | iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))),
% 0.61/0.64 inference(tautology,[status(thm)],[])).
% 0.61/0.64 tff(130,plain,
% 0.61/0.64 (iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[129, 123])).
% 0.61/0.64 tff(131,plain,
% 0.61/0.64 (((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2))))) | ![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))),
% 0.61/0.64 inference(tautology,[status(thm)],[])).
% 0.61/0.64 tff(132,plain,
% 0.61/0.64 (![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[131, 103])).
% 0.61/0.64 tff(133,plain,
% 0.61/0.64 (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | ((~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(134,plain,
% 0.61/0.64 ((iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p)))) <=> ((~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(135,plain,
% 0.61/0.64 (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p))))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | ((~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p))))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[134])).
% 0.61/0.64 tff(136,plain,
% 0.61/0.64 (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p))))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p)))),
% 0.62/0.64 inference(transitivity,[status(thm)],[135, 133])).
% 0.62/0.64 tff(137,plain,
% 0.62/0.64 ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p))))),
% 0.62/0.64 inference(quant_inst,[status(thm)],[])).
% 0.62/0.64 tff(138,plain,
% 0.62/0.64 ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X2_4(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.62/0.64 tff(139,plain,
% 0.62/0.64 (iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[138, 132, 130, 128])).
% 0.62/0.64 tff(140,plain,
% 0.62/0.64 (((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))) | (~(tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))),
% 0.62/0.64 inference(tautology,[status(thm)],[])).
% 0.62/0.64 tff(141,plain,
% 0.62/0.64 (~(tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[140, 123])).
% 0.62/0.64 tff(142,plain,
% 0.62/0.64 ((~(iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) <=> (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))) | (~iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p))),
% 0.62/0.64 inference(tautology,[status(thm)],[])).
% 0.62/0.64 tff(143,plain,
% 0.62/0.64 (~(iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) <=> (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[142, 141, 139])).
% 0.62/0.64 tff(144,plain,
% 0.62/0.64 (^[X: $i, Y: $i] : refl((iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> (iext(uri_owl_sameAs, X, Y) <=> (X = Y)))),
% 0.62/0.64 inference(bind,[status(th)],[])).
% 0.62/0.64 tff(145,plain,
% 0.62/0.64 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.62/0.64 inference(quant_intro,[status(thm)],[144])).
% 0.62/0.64 tff(146,plain,
% 0.62/0.64 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(147,axiom,(![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_eqdis_sameas')).
% 0.62/0.64 tff(148,plain,
% 0.62/0.64 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.62/0.64 tff(149,plain,(
% 0.62/0.64 ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.62/0.64 inference(skolemize,[status(sab)],[148])).
% 0.62/0.64 tff(150,plain,
% 0.62/0.64 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.62/0.64 tff(151,plain,
% 0.62/0.64 ((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | (iext(uri_owl_sameAs, tptp_fun_X1_5(uri_ex_p), tptp_fun_X2_4(uri_ex_p)) <=> (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))),
% 0.62/0.64 inference(quant_inst,[status(thm)],[])).
% 0.62/0.64 tff(152,plain,
% 0.62/0.64 ($false),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[151, 150, 143])).
% 0.62/0.64 % SZS output end Proof
%------------------------------------------------------------------------------