TSTP Solution File: SWB045+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB045+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 08:32:06 EDT 2022
% Result : Theorem 0.79s 0.80s
% Output : Proof 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWB045+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 20:06:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.79/0.80 % SZS status Theorem
% 0.79/0.80 % SZS output start Proof
% 0.79/0.80 tff(tptp_fun_Y2_111_type, type, (
% 0.79/0.80 tptp_fun_Y2_111: $i > $i)).
% 0.79/0.80 tff(uri_ex_p_type, type, (
% 0.79/0.80 uri_ex_p: $i)).
% 0.79/0.80 tff(tptp_fun_Y1_112_type, type, (
% 0.79/0.80 tptp_fun_Y1_112: $i > $i)).
% 0.79/0.80 tff(uri_ex_y_type, type, (
% 0.79/0.80 uri_ex_y: $i)).
% 0.79/0.80 tff(icext_type, type, (
% 0.79/0.80 icext: ( $i * $i ) > $o)).
% 0.79/0.80 tff(tptp_fun_X0_141_type, type, (
% 0.79/0.80 tptp_fun_X0_141: $i)).
% 0.79/0.80 tff(ic_type, type, (
% 0.79/0.80 ic: $i > $o)).
% 0.79/0.80 tff(iext_type, type, (
% 0.79/0.80 iext: ( $i * $i * $i ) > $o)).
% 0.79/0.80 tff(tptp_fun_X1_140_type, type, (
% 0.79/0.80 tptp_fun_X1_140: $i)).
% 0.79/0.80 tff(uri_owl_oneOf_type, type, (
% 0.79/0.80 uri_owl_oneOf: $i)).
% 0.79/0.80 tff(tptp_fun_X_8_type, type, (
% 0.79/0.80 tptp_fun_X_8: ( $i * $i ) > $i)).
% 0.79/0.80 tff(uri_rdf_nil_type, type, (
% 0.79/0.80 uri_rdf_nil: $i)).
% 0.79/0.80 tff(uri_rdf_rest_type, type, (
% 0.79/0.80 uri_rdf_rest: $i)).
% 0.79/0.80 tff(uri_rdf_first_type, type, (
% 0.79/0.80 uri_rdf_first: $i)).
% 0.79/0.80 tff(uri_ex_x_type, type, (
% 0.79/0.80 uri_ex_x: $i)).
% 0.79/0.80 tff(uri_rdfs_range_type, type, (
% 0.79/0.80 uri_rdfs_range: $i)).
% 0.79/0.80 tff(tptp_fun_X_113_type, type, (
% 0.79/0.80 tptp_fun_X_113: $i > $i)).
% 0.79/0.80 tff(ip_type, type, (
% 0.79/0.80 ip: $i > $o)).
% 0.79/0.80 tff(uri_owl_FunctionalProperty_type, type, (
% 0.79/0.80 uri_owl_FunctionalProperty: $i)).
% 0.79/0.80 tff(uri_rdf_type_type, type, (
% 0.79/0.80 uri_rdf_type: $i)).
% 0.79/0.80 tff(tptp_fun_Y_59_type, type, (
% 0.79/0.80 tptp_fun_Y_59: ( $i * $i ) > $i)).
% 0.79/0.80 tff(tptp_fun_X_60_type, type, (
% 0.79/0.80 tptp_fun_X_60: ( $i * $i ) > $i)).
% 0.79/0.80 tff(1,plain,
% 0.79/0.80 (?[X0: $i, X1: $i] : (iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1)) <=> ?[X0: $i, X1: $i] : (iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(2,plain,
% 0.79/0.80 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_y)) <=> (iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y))), ((((iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> ((iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> (iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil))), ((((iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> (iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil)))), (((((iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) <=> ((iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)))), rewrite(((iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) <=> (iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1))), (((((iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) <=> (iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1))))),
% 0.79/0.80 inference(bind,[status(th)],[])).
% 0.79/0.80 tff(3,plain,
% 0.79/0.80 (?[X0: $i, X1: $i] : ((((iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) <=> ?[X0: $i, X1: $i] : (iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1))),
% 0.79/0.80 inference(quant_intro,[status(thm)],[2])).
% 0.79/0.80 tff(4,axiom,(?[X0: $i, X1: $i] : ((((iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','premise_rdfbased_sem_char_functional_ext')).
% 0.79/0.80 tff(5,plain,
% 0.79/0.80 (?[X0: $i, X1: $i] : (iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.79/0.80 tff(6,plain,
% 0.79/0.80 (?[X0: $i, X1: $i] : (iext(uri_rdfs_range, uri_ex_p, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.79/0.80 tff(7,plain,(
% 0.79/0.80 iext(uri_rdfs_range, uri_ex_p, X0!141) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdf_first, X1!140, uri_ex_y) & iext(uri_rdf_rest, X1!140, uri_rdf_nil) & iext(uri_owl_oneOf, X0!141, X1!140)),
% 0.79/0.80 inference(skolemize,[status(sab)],[6])).
% 0.79/0.80 tff(8,plain,
% 0.79/0.80 (iext(uri_rdf_rest, X1!140, uri_rdf_nil)),
% 0.79/0.80 inference(and_elim,[status(thm)],[7])).
% 0.79/0.80 tff(9,plain,
% 0.79/0.80 (iext(uri_rdf_first, X1!140, uri_ex_y)),
% 0.79/0.80 inference(and_elim,[status(thm)],[7])).
% 0.79/0.80 tff(10,plain,
% 0.79/0.80 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))))))))),
% 0.79/0.80 inference(bind,[status(th)],[])).
% 0.79/0.80 tff(11,plain,
% 0.79/0.80 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.79/0.80 inference(quant_intro,[status(thm)],[10])).
% 0.79/0.80 tff(12,plain,
% 0.79/0.80 (^[Z: $i, S1: $i, A1: $i] : refl(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.79/0.80 inference(bind,[status(th)],[])).
% 0.79/0.80 tff(13,plain,
% 0.79/0.80 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[12])).
% 0.79/0.81 tff(14,plain,
% 0.79/0.81 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(15,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[14])).
% 0.79/0.81 tff(16,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.79/0.81 inference(transitivity,[status(thm)],[15, 13])).
% 0.79/0.81 tff(17,plain,
% 0.79/0.81 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> ((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))), rewrite((((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))))), rewrite((((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(18,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[17])).
% 0.79/0.81 tff(19,plain,
% 0.79/0.81 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(20,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[19])).
% 0.79/0.81 tff(21,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(22,plain,
% 0.79/0.81 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(monotonicity(rewrite((ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))), ((iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(23,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[22])).
% 0.79/0.81 tff(24,axiom,(![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_enum_class_001')).
% 0.79/0.81 tff(25,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.79/0.81 tff(26,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.79/0.81 tff(27,plain,(
% 0.79/0.81 ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.79/0.81 inference(skolemize,[status(sab)],[26])).
% 0.79/0.81 tff(28,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.79/0.81 tff(29,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.79/0.81 tff(30,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.79/0.81 tff(31,plain,
% 0.79/0.81 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.79/0.81 tff(32,plain,
% 0.79/0.81 (((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, X1!140, uri_ex_y)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!141, X1!140) | (~ic(X0!141)) | ((~icext(X0!141, tptp_fun_X_8(uri_ex_y, X0!141))) <=> (tptp_fun_X_8(uri_ex_y, X0!141) = uri_ex_y)))) | (~((~iext(uri_owl_oneOf, X0!141, X1!140)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, X1!140, uri_ex_y)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!141, X1!140) | (~ic(X0!141)) | ((~icext(X0!141, tptp_fun_X_8(uri_ex_y, X0!141))) <=> (tptp_fun_X_8(uri_ex_y, X0!141) = uri_ex_y)))) | (~((~iext(uri_owl_oneOf, X0!141, X1!140)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))))))))))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(33,plain,
% 0.79/0.81 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, X1!140, uri_ex_y)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!141, X1!140) | (~ic(X0!141)) | ((~icext(X0!141, tptp_fun_X_8(uri_ex_y, X0!141))) <=> (tptp_fun_X_8(uri_ex_y, X0!141) = uri_ex_y)))) | (~((~iext(uri_owl_oneOf, X0!141, X1!140)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))))))))))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(34,plain,
% 0.79/0.81 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, X1!140, uri_ex_y)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!141, X1!140) | (~ic(X0!141)) | ((~icext(X0!141, tptp_fun_X_8(uri_ex_y, X0!141))) <=> (tptp_fun_X_8(uri_ex_y, X0!141) = uri_ex_y)))) | (~((~iext(uri_owl_oneOf, X0!141, X1!140)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y)))))))))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.79/0.81 tff(35,plain,
% 0.79/0.81 (~((~(iext(uri_owl_oneOf, X0!141, X1!140) | (~ic(X0!141)) | ((~icext(X0!141, tptp_fun_X_8(uri_ex_y, X0!141))) <=> (tptp_fun_X_8(uri_ex_y, X0!141) = uri_ex_y)))) | (~((~iext(uri_owl_oneOf, X0!141, X1!140)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))))))))),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[34, 31, 9, 8])).
% 0.79/0.81 tff(36,plain,
% 0.79/0.81 (((~(iext(uri_owl_oneOf, X0!141, X1!140) | (~ic(X0!141)) | ((~icext(X0!141, tptp_fun_X_8(uri_ex_y, X0!141))) <=> (tptp_fun_X_8(uri_ex_y, X0!141) = uri_ex_y)))) | (~((~iext(uri_owl_oneOf, X0!141, X1!140)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y)))))))) | ((~iext(uri_owl_oneOf, X0!141, X1!140)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))))))),
% 0.79/0.81 inference(tautology,[status(thm)],[])).
% 0.79/0.81 tff(37,plain,
% 0.79/0.81 ((~iext(uri_owl_oneOf, X0!141, X1!140)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y)))))),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.79/0.81 tff(38,plain,
% 0.79/0.81 (iext(uri_owl_oneOf, X0!141, X1!140)),
% 0.79/0.81 inference(and_elim,[status(thm)],[7])).
% 0.79/0.81 tff(39,plain,
% 0.79/0.81 ((~((~iext(uri_owl_oneOf, X0!141, X1!140)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))))))) | (~iext(uri_owl_oneOf, X0!141, X1!140)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y)))))),
% 0.79/0.81 inference(tautology,[status(thm)],[])).
% 0.79/0.81 tff(40,plain,
% 0.79/0.81 ((~((~iext(uri_owl_oneOf, X0!141, X1!140)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))))))) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y)))))),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.79/0.81 tff(41,plain,
% 0.79/0.81 (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))))),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.79/0.81 tff(42,plain,
% 0.79/0.81 (((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y)))) | ![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))),
% 0.79/0.81 inference(tautology,[status(thm)],[])).
% 0.79/0.81 tff(43,plain,
% 0.79/0.81 (![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.79/0.81 tff(44,plain,
% 0.79/0.81 ((~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))) | (icext(X0!141, tptp_fun_Y2_111(uri_ex_p)) <=> (tptp_fun_Y2_111(uri_ex_p) = uri_ex_y))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(45,plain,
% 0.79/0.81 (icext(X0!141, tptp_fun_Y2_111(uri_ex_p)) <=> (tptp_fun_Y2_111(uri_ex_p) = uri_ex_y)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.79/0.81 tff(46,plain,
% 0.79/0.81 (^[P: $i] : rewrite((~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(47,plain,
% 0.79/0.81 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> ![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[46])).
% 0.79/0.81 tff(48,plain,
% 0.79/0.81 (^[P: $i] : refl((~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(49,plain,
% 0.79/0.81 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[48])).
% 0.79/0.81 tff(50,plain,
% 0.79/0.81 (^[P: $i] : rewrite((~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(51,plain,
% 0.79/0.81 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[50])).
% 0.79/0.81 tff(52,plain,
% 0.79/0.81 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.79/0.81 inference(transitivity,[status(thm)],[51, 49])).
% 0.79/0.81 tff(53,plain,
% 0.79/0.81 (^[P: $i] : trans(monotonicity(rewrite(((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) <=> ((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))), trans(monotonicity(rewrite((~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))) <=> (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))), ((icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))) <=> (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))), rewrite((icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))) <=> (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))), ((icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))) <=> (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))), ((((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))))) <=> (((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))), rewrite((((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) <=> (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))), ((((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))))) <=> (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(54,plain,
% 0.79/0.81 (![P: $i] : (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))))) <=> ![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[53])).
% 0.79/0.81 tff(55,plain,
% 0.79/0.81 (^[P: $i] : rewrite((((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))))) <=> (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(56,plain,
% 0.79/0.81 (![P: $i] : (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))))) <=> ![P: $i] : (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[55])).
% 0.79/0.81 tff(57,plain,
% 0.79/0.81 (![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) <=> ![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2))))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(58,plain,
% 0.79/0.81 (^[P: $i] : rewrite((icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((iext(P, X, Y1) & iext(P, X, Y2)) => (Y1 = Y2)))) <=> (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(59,plain,
% 0.79/0.81 (![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((iext(P, X, Y1) & iext(P, X, Y2)) => (Y1 = Y2)))) <=> ![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2))))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[58])).
% 0.79/0.81 tff(60,axiom,(![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((iext(P, X, Y1) & iext(P, X, Y2)) => (Y1 = Y2))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_char_functional')).
% 0.79/0.81 tff(61,plain,
% 0.79/0.81 (![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2))))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.79/0.81 tff(62,plain,
% 0.79/0.81 (![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2))))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.79/0.82 tff(63,plain,(
% 0.79/0.82 ![P: $i] : (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))))))),
% 0.79/0.82 inference(skolemize,[status(sab)],[62])).
% 0.79/0.82 tff(64,plain,
% 0.79/0.82 (![P: $i] : (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.79/0.82 tff(65,plain,
% 0.79/0.82 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.79/0.82 tff(66,plain,
% 0.79/0.82 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[65, 52])).
% 0.79/0.82 tff(67,plain,
% 0.79/0.82 (![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[66, 47])).
% 0.79/0.82 tff(68,plain,
% 0.79/0.82 ((~![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))) | (~((~(icext(uri_owl_FunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))))))) | (~((~icext(uri_owl_FunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))))))))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(69,plain,
% 0.79/0.82 (~((~(icext(uri_owl_FunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))))))) | (~((~icext(uri_owl_FunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2)))))))))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.79/0.82 tff(70,plain,
% 0.79/0.82 (((~(icext(uri_owl_FunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))))))) | (~((~icext(uri_owl_FunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))))))) | (icext(uri_owl_FunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))))))),
% 0.79/0.82 inference(tautology,[status(thm)],[])).
% 0.79/0.82 tff(71,plain,
% 0.79/0.82 (icext(uri_owl_FunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p)))))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.79/0.82 tff(72,plain,
% 0.79/0.82 (iext(uri_ex_p, uri_ex_x, uri_ex_y)),
% 0.79/0.82 inference(and_elim,[status(thm)],[7])).
% 0.79/0.82 tff(73,plain,
% 0.79/0.82 (^[S: $i, P: $i, O: $i] : refl((ip(P) | (~iext(P, S, O))) <=> (ip(P) | (~iext(P, S, O))))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(74,plain,
% 0.79/0.82 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O))) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[73])).
% 0.79/0.82 tff(75,plain,
% 0.79/0.82 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O))) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(76,plain,
% 0.79/0.82 (^[S: $i, P: $i, O: $i] : rewrite((iext(P, S, O) => ip(P)) <=> (ip(P) | (~iext(P, S, O))))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(77,plain,
% 0.79/0.82 (![S: $i, P: $i, O: $i] : (iext(P, S, O) => ip(P)) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[76])).
% 0.79/0.82 tff(78,axiom,(![S: $i, P: $i, O: $i] : (iext(P, S, O) => ip(P))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','simple_iext_property')).
% 0.79/0.82 tff(79,plain,
% 0.79/0.82 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.79/0.82 tff(80,plain,
% 0.79/0.82 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.79/0.82 tff(81,plain,(
% 0.79/0.82 ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.79/0.82 inference(skolemize,[status(sab)],[80])).
% 0.79/0.82 tff(82,plain,
% 0.79/0.82 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.79/0.82 tff(83,plain,
% 0.79/0.82 (((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p) | (~iext(uri_ex_p, uri_ex_x, uri_ex_y)))) <=> ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p) | (~iext(uri_ex_p, uri_ex_x, uri_ex_y)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(84,plain,
% 0.79/0.82 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p) | (~iext(uri_ex_p, uri_ex_x, uri_ex_y)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(85,plain,
% 0.79/0.82 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p) | (~iext(uri_ex_p, uri_ex_x, uri_ex_y))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.79/0.82 tff(86,plain,
% 0.79/0.82 (ip(uri_ex_p)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[85, 82, 72])).
% 0.79/0.82 tff(87,plain,
% 0.79/0.82 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(88,plain,
% 0.79/0.82 (![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))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[87])).
% 0.79/0.82 tff(89,plain,
% 0.79/0.82 (![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))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(90,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','rdfs_cext_def')).
% 0.79/0.82 tff(91,plain,
% 0.79/0.82 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.79/0.82 tff(92,plain,(
% 0.79/0.82 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.79/0.82 inference(skolemize,[status(sab)],[91])).
% 0.79/0.82 tff(93,plain,
% 0.79/0.82 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.79/0.82 tff(94,plain,
% 0.79/0.82 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_p, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_p))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(95,plain,
% 0.79/0.82 (iext(uri_rdf_type, uri_ex_p, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_p)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.79/0.82 tff(96,plain,
% 0.79/0.82 ((~iext(uri_rdf_type, uri_ex_p, uri_owl_FunctionalProperty)) <=> (~iext(uri_rdf_type, uri_ex_p, uri_owl_FunctionalProperty))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(97,axiom,(~iext(uri_rdf_type, uri_ex_p, uri_owl_FunctionalProperty)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion_rdfbased_sem_char_functional_ext')).
% 0.79/0.82 tff(98,plain,
% 0.79/0.82 (~iext(uri_rdf_type, uri_ex_p, uri_owl_FunctionalProperty)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.79/0.82 tff(99,plain,
% 0.79/0.82 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_p))) | iext(uri_rdf_type, uri_ex_p, uri_owl_FunctionalProperty) | (~icext(uri_owl_FunctionalProperty, uri_ex_p))),
% 0.79/0.82 inference(tautology,[status(thm)],[])).
% 0.79/0.82 tff(100,plain,
% 0.79/0.82 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_FunctionalProperty) <=> icext(uri_owl_FunctionalProperty, uri_ex_p))) | (~icext(uri_owl_FunctionalProperty, uri_ex_p))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.79/0.82 tff(101,plain,
% 0.79/0.82 (~icext(uri_owl_FunctionalProperty, uri_ex_p)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[100, 95])).
% 0.79/0.82 tff(102,plain,
% 0.79/0.82 ((~(icext(uri_owl_FunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))))))) | icext(uri_owl_FunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p)))))),
% 0.79/0.82 inference(tautology,[status(thm)],[])).
% 0.79/0.82 tff(103,plain,
% 0.79/0.82 ((~(icext(uri_owl_FunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))))))) | (~((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p)))))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[102, 101, 86])).
% 0.79/0.82 tff(104,plain,
% 0.79/0.82 (~((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[103, 71])).
% 0.79/0.82 tff(105,plain,
% 0.79/0.82 (((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p)))) | iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))),
% 0.79/0.82 inference(tautology,[status(thm)],[])).
% 0.79/0.82 tff(106,plain,
% 0.79/0.82 (iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.79/0.82 tff(107,plain,
% 0.79/0.82 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))))))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(108,plain,
% 0.79/0.82 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[107])).
% 0.79/0.82 tff(109,plain,
% 0.79/0.82 (^[P: $i, C: $i] : refl((~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(110,plain,
% 0.79/0.82 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[109])).
% 0.79/0.82 tff(111,plain,
% 0.79/0.82 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(112,plain,
% 0.79/0.82 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[111])).
% 0.79/0.82 tff(113,plain,
% 0.79/0.82 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.79/0.82 inference(transitivity,[status(thm)],[112, 110])).
% 0.79/0.82 tff(114,plain,
% 0.79/0.82 (^[P: $i, C: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) <=> ((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))), rewrite((iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))) <=> (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))), ((((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> (((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))), rewrite((((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))), ((((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(115,plain,
% 0.79/0.82 (![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[114])).
% 0.79/0.82 tff(116,plain,
% 0.79/0.82 (^[P: $i, C: $i] : rewrite((((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | ((~ip(P)) | (~ip(C)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))) <=> (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(117,plain,
% 0.79/0.82 (![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | ((~ip(P)) | (~ip(C)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))) <=> ![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[116])).
% 0.79/0.82 tff(118,plain,
% 0.79/0.82 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(119,plain,
% 0.79/0.82 (^[P: $i, C: $i] : rewrite((iext(uri_rdfs_range, P, C) <=> ((ip(P) & ip(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(120,plain,
% 0.79/0.82 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> ((ip(P) & ip(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[119])).
% 0.79/0.82 tff(121,axiom,(![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> ((ip(P) & ip(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_range')).
% 0.79/0.82 tff(122,plain,
% 0.79/0.82 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.79/0.82 tff(123,plain,
% 0.79/0.82 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.79/0.82 tff(124,plain,(
% 0.79/0.82 ![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | ((~ip(P)) | (~ip(C)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))),
% 0.79/0.82 inference(skolemize,[status(sab)],[123])).
% 0.79/0.82 tff(125,plain,
% 0.79/0.82 (![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.79/0.82 tff(126,plain,
% 0.79/0.82 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[125, 115])).
% 0.79/0.82 tff(127,plain,
% 0.79/0.82 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[126, 113])).
% 0.79/0.82 tff(128,plain,
% 0.79/0.82 (![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[127, 108])).
% 0.79/0.82 tff(129,plain,
% 0.79/0.82 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_ex_p, X0!141) | (~ip(X0!141)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_60(X0!141, uri_ex_p), tptp_fun_Y_59(X0!141, uri_ex_p))) | icext(X0!141, tptp_fun_Y_59(X0!141, uri_ex_p)))))) | (~((~iext(uri_rdfs_range, uri_ex_p, X0!141)) | (~((~ip(X0!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y)))))))))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(130,plain,
% 0.79/0.82 (~((~(iext(uri_rdfs_range, uri_ex_p, X0!141) | (~ip(X0!141)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_60(X0!141, uri_ex_p), tptp_fun_Y_59(X0!141, uri_ex_p))) | icext(X0!141, tptp_fun_Y_59(X0!141, uri_ex_p)))))) | (~((~iext(uri_rdfs_range, uri_ex_p, X0!141)) | (~((~ip(X0!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))))))))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.79/0.82 tff(131,plain,
% 0.79/0.82 (((~(iext(uri_rdfs_range, uri_ex_p, X0!141) | (~ip(X0!141)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_60(X0!141, uri_ex_p), tptp_fun_Y_59(X0!141, uri_ex_p))) | icext(X0!141, tptp_fun_Y_59(X0!141, uri_ex_p)))))) | (~((~iext(uri_rdfs_range, uri_ex_p, X0!141)) | (~((~ip(X0!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y)))))))) | ((~iext(uri_rdfs_range, uri_ex_p, X0!141)) | (~((~ip(X0!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))))))),
% 0.79/0.82 inference(tautology,[status(thm)],[])).
% 0.79/0.82 tff(132,plain,
% 0.79/0.82 ((~iext(uri_rdfs_range, uri_ex_p, X0!141)) | (~((~ip(X0!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y)))))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.79/0.82 tff(133,plain,
% 0.79/0.82 (iext(uri_rdfs_range, uri_ex_p, X0!141)),
% 0.79/0.82 inference(and_elim,[status(thm)],[7])).
% 0.79/0.82 tff(134,plain,
% 0.79/0.82 ((~((~iext(uri_rdfs_range, uri_ex_p, X0!141)) | (~((~ip(X0!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))))))) | (~iext(uri_rdfs_range, uri_ex_p, X0!141)) | (~((~ip(X0!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y)))))),
% 0.79/0.82 inference(tautology,[status(thm)],[])).
% 0.79/0.82 tff(135,plain,
% 0.79/0.82 ((~((~iext(uri_rdfs_range, uri_ex_p, X0!141)) | (~((~ip(X0!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))))))) | (~((~ip(X0!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y)))))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.79/0.82 tff(136,plain,
% 0.79/0.82 (~((~ip(X0!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.79/0.82 tff(137,plain,
% 0.79/0.82 (((~ip(X0!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y)))) | ![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))),
% 0.79/0.82 inference(tautology,[status(thm)],[])).
% 0.79/0.82 tff(138,plain,
% 0.79/0.82 (![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.79/0.82 tff(139,plain,
% 0.79/0.82 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))) | ((~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))) | icext(X0!141, tptp_fun_Y2_111(uri_ex_p)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))) | icext(X0!141, tptp_fun_Y2_111(uri_ex_p)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(140,plain,
% 0.79/0.82 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))) | ((~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))) | icext(X0!141, tptp_fun_Y2_111(uri_ex_p)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(141,plain,
% 0.79/0.82 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p))) | icext(X0!141, tptp_fun_Y2_111(uri_ex_p))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.79/0.82 tff(142,plain,
% 0.79/0.82 (icext(X0!141, tptp_fun_Y2_111(uri_ex_p))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[141, 138, 106])).
% 0.79/0.82 tff(143,plain,
% 0.79/0.82 ((~(icext(X0!141, tptp_fun_Y2_111(uri_ex_p)) <=> (tptp_fun_Y2_111(uri_ex_p) = uri_ex_y))) | (~icext(X0!141, tptp_fun_Y2_111(uri_ex_p))) | (tptp_fun_Y2_111(uri_ex_p) = uri_ex_y)),
% 0.79/0.82 inference(tautology,[status(thm)],[])).
% 0.79/0.82 tff(144,plain,
% 0.79/0.82 ((~(icext(X0!141, tptp_fun_Y2_111(uri_ex_p)) <=> (tptp_fun_Y2_111(uri_ex_p) = uri_ex_y))) | (tptp_fun_Y2_111(uri_ex_p) = uri_ex_y)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.79/0.84 tff(145,plain,
% 0.79/0.84 (tptp_fun_Y2_111(uri_ex_p) = uri_ex_y),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[144, 45])).
% 0.79/0.84 tff(146,plain,
% 0.79/0.84 ((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) <=> (tptp_fun_Y1_112(uri_ex_p) = uri_ex_y)),
% 0.79/0.84 inference(monotonicity,[status(thm)],[145])).
% 0.79/0.84 tff(147,plain,
% 0.79/0.84 ((tptp_fun_Y1_112(uri_ex_p) = uri_ex_y) <=> (tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p))),
% 0.79/0.84 inference(symmetry,[status(thm)],[146])).
% 0.79/0.84 tff(148,plain,
% 0.79/0.84 ((~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_y))) | (icext(X0!141, tptp_fun_Y1_112(uri_ex_p)) <=> (tptp_fun_Y1_112(uri_ex_p) = uri_ex_y))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(149,plain,
% 0.79/0.84 (icext(X0!141, tptp_fun_Y1_112(uri_ex_p)) <=> (tptp_fun_Y1_112(uri_ex_p) = uri_ex_y)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[148, 43])).
% 0.79/0.84 tff(150,plain,
% 0.79/0.84 (((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p)))) | iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))),
% 0.79/0.84 inference(tautology,[status(thm)],[])).
% 0.79/0.84 tff(151,plain,
% 0.79/0.84 (iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[150, 104])).
% 0.79/0.84 tff(152,plain,
% 0.79/0.84 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))) | ((~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | icext(X0!141, tptp_fun_Y1_112(uri_ex_p)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | icext(X0!141, tptp_fun_Y1_112(uri_ex_p)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(153,plain,
% 0.79/0.84 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))) | ((~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | icext(X0!141, tptp_fun_Y1_112(uri_ex_p)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(154,plain,
% 0.79/0.84 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X0!141, Y))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | icext(X0!141, tptp_fun_Y1_112(uri_ex_p))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.79/0.84 tff(155,plain,
% 0.79/0.84 (icext(X0!141, tptp_fun_Y1_112(uri_ex_p))),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[154, 138, 151])).
% 0.79/0.84 tff(156,plain,
% 0.79/0.84 ((~(icext(X0!141, tptp_fun_Y1_112(uri_ex_p)) <=> (tptp_fun_Y1_112(uri_ex_p) = uri_ex_y))) | (~icext(X0!141, tptp_fun_Y1_112(uri_ex_p))) | (tptp_fun_Y1_112(uri_ex_p) = uri_ex_y)),
% 0.79/0.84 inference(tautology,[status(thm)],[])).
% 0.79/0.84 tff(157,plain,
% 0.79/0.84 ((~(icext(X0!141, tptp_fun_Y1_112(uri_ex_p)) <=> (tptp_fun_Y1_112(uri_ex_p) = uri_ex_y))) | (tptp_fun_Y1_112(uri_ex_p) = uri_ex_y)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.79/0.84 tff(158,plain,
% 0.79/0.84 (tptp_fun_Y1_112(uri_ex_p) = uri_ex_y),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[157, 149])).
% 0.79/0.84 tff(159,plain,
% 0.79/0.84 (tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[158, 147])).
% 0.79/0.84 tff(160,plain,
% 0.79/0.84 (((tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y1_112(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_113(uri_ex_p), tptp_fun_Y2_111(uri_ex_p)))) | (~(tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p)))),
% 0.79/0.84 inference(tautology,[status(thm)],[])).
% 0.79/0.84 tff(161,plain,
% 0.79/0.84 (~(tptp_fun_Y1_112(uri_ex_p) = tptp_fun_Y2_111(uri_ex_p))),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[160, 104])).
% 0.79/0.84 tff(162,plain,
% 0.79/0.84 ($false),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[161, 159])).
% 0.79/0.84 % SZS output end Proof
%------------------------------------------------------------------------------