TSTP Solution File: SWB046+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB046+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 1.04s 0.97s
% Output : Proof 1.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB046+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 20:03:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.04/0.97 % SZS status Theorem
% 1.04/0.97 % SZS output start Proof
% 1.04/0.97 tff(tptp_fun_X2_115_type, type, (
% 1.04/0.97 tptp_fun_X2_115: $i > $i)).
% 1.04/0.97 tff(uri_ex_p_type, type, (
% 1.04/0.97 uri_ex_p: $i)).
% 1.04/0.97 tff(tptp_fun_X1_116_type, type, (
% 1.04/0.97 tptp_fun_X1_116: $i > $i)).
% 1.04/0.97 tff(uri_ex_x_type, type, (
% 1.04/0.97 uri_ex_x: $i)).
% 1.04/0.97 tff(icext_type, type, (
% 1.04/0.97 icext: ( $i * $i ) > $o)).
% 1.04/0.97 tff(tptp_fun_X1_141_type, type, (
% 1.04/0.97 tptp_fun_X1_141: $i)).
% 1.04/0.97 tff(ic_type, type, (
% 1.04/0.97 ic: $i > $o)).
% 1.04/0.97 tff(iext_type, type, (
% 1.04/0.97 iext: ( $i * $i * $i ) > $o)).
% 1.04/0.97 tff(tptp_fun_X0_140_type, type, (
% 1.04/0.97 tptp_fun_X0_140: $i)).
% 1.04/0.97 tff(uri_owl_oneOf_type, type, (
% 1.04/0.97 uri_owl_oneOf: $i)).
% 1.04/0.97 tff(tptp_fun_X_8_type, type, (
% 1.04/0.97 tptp_fun_X_8: ( $i * $i ) > $i)).
% 1.04/0.97 tff(uri_rdf_nil_type, type, (
% 1.04/0.97 uri_rdf_nil: $i)).
% 1.04/0.97 tff(uri_rdf_rest_type, type, (
% 1.04/0.97 uri_rdf_rest: $i)).
% 1.04/0.97 tff(uri_rdfs_domain_type, type, (
% 1.04/0.97 uri_rdfs_domain: $i)).
% 1.04/0.97 tff(uri_ex_y_type, type, (
% 1.04/0.97 uri_ex_y: $i)).
% 1.04/0.97 tff(uri_rdf_first_type, type, (
% 1.04/0.97 uri_rdf_first: $i)).
% 1.04/0.97 tff(tptp_fun_Y_114_type, type, (
% 1.04/0.97 tptp_fun_Y_114: $i > $i)).
% 1.04/0.97 tff(ip_type, type, (
% 1.04/0.97 ip: $i > $o)).
% 1.04/0.97 tff(uri_owl_InverseFunctionalProperty_type, type, (
% 1.04/0.97 uri_owl_InverseFunctionalProperty: $i)).
% 1.04/0.97 tff(uri_rdf_type_type, type, (
% 1.04/0.97 uri_rdf_type: $i)).
% 1.04/0.97 tff(tptp_fun_X_58_type, type, (
% 1.04/0.97 tptp_fun_X_58: ( $i * $i ) > $i)).
% 1.04/0.97 tff(tptp_fun_Y_57_type, type, (
% 1.04/0.97 tptp_fun_Y_57: ( $i * $i ) > $i)).
% 1.04/0.97 tff(1,plain,
% 1.04/0.97 (?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1)) <=> ?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))),
% 1.04/0.97 inference(rewrite,[status(thm)],[])).
% 1.04/0.97 tff(2,plain,
% 1.04/0.97 (^[X1: $i, X0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) <=> (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0))), ((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) <=> ((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)))), rewrite(((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) <=> (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y))), ((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) <=> (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)))), (((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1)) <=> ((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1)))), rewrite(((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1)) <=> (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))), (((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1)) <=> (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))))),
% 1.04/0.97 inference(bind,[status(th)],[])).
% 1.04/0.98 tff(3,plain,
% 1.04/0.98 (?[X1: $i, X0: $i] : ((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1)) <=> ?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))),
% 1.04/0.98 inference(quant_intro,[status(thm)],[2])).
% 1.04/0.98 tff(4,axiom,(?[X1: $i, X0: $i] : ((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','premise_rdfbased_sem_char_inversefunc_ext')).
% 1.04/0.98 tff(5,plain,
% 1.04/0.98 (?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))),
% 1.04/0.98 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.04/0.98 tff(6,plain,
% 1.04/0.98 (?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))),
% 1.04/0.98 inference(modus_ponens,[status(thm)],[5, 1])).
% 1.04/0.98 tff(7,plain,(
% 1.04/0.98 iext(uri_rdf_first, X0!140, uri_ex_x) & iext(uri_rdf_rest, X0!140, uri_rdf_nil) & iext(uri_owl_oneOf, X1!141, X0!140) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1!141)),
% 1.04/0.98 inference(skolemize,[status(sab)],[6])).
% 1.04/0.98 tff(8,plain,
% 1.04/0.98 (iext(uri_rdf_rest, X0!140, uri_rdf_nil)),
% 1.04/0.98 inference(and_elim,[status(thm)],[7])).
% 1.04/0.98 tff(9,plain,
% 1.04/0.98 (iext(uri_rdf_first, X0!140, uri_ex_x)),
% 1.04/0.98 inference(and_elim,[status(thm)],[7])).
% 1.04/0.98 tff(10,plain,
% 1.04/0.98 (^[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)))))))))))),
% 1.04/0.98 inference(bind,[status(th)],[])).
% 1.04/0.98 tff(11,plain,
% 1.04/0.98 (![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))))))))))),
% 1.04/0.98 inference(quant_intro,[status(thm)],[10])).
% 1.04/0.98 tff(12,plain,
% 1.04/0.98 (^[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))))))))),
% 1.04/0.98 inference(bind,[status(th)],[])).
% 1.04/0.98 tff(13,plain,
% 1.04/0.98 (![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)))))))),
% 1.04/0.98 inference(quant_intro,[status(thm)],[12])).
% 1.04/0.98 tff(14,plain,
% 1.04/0.98 (^[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))))))))),
% 1.04/0.98 inference(bind,[status(th)],[])).
% 1.04/0.98 tff(15,plain,
% 1.04/0.98 (![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)))))))),
% 1.04/0.98 inference(quant_intro,[status(thm)],[14])).
% 1.04/0.98 tff(16,plain,
% 1.04/0.98 (![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)))))))),
% 1.04/0.98 inference(transitivity,[status(thm)],[15, 13])).
% 1.04/0.98 tff(17,plain,
% 1.04/0.98 (^[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)))))))))),
% 1.04/0.98 inference(bind,[status(th)],[])).
% 1.04/0.98 tff(18,plain,
% 1.04/0.98 (![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)))))))),
% 1.04/0.98 inference(quant_intro,[status(thm)],[17])).
% 1.04/0.98 tff(19,plain,
% 1.04/0.98 (^[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))))))),
% 1.04/0.98 inference(bind,[status(th)],[])).
% 1.04/0.98 tff(20,plain,
% 1.04/0.98 (![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)))))),
% 1.04/0.98 inference(quant_intro,[status(thm)],[19])).
% 1.04/0.98 tff(21,plain,
% 1.04/0.98 (![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)))))),
% 1.04/0.98 inference(rewrite,[status(thm)],[])).
% 1.04/0.98 tff(22,plain,
% 1.04/0.98 (^[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)))))))),
% 1.04/0.98 inference(bind,[status(th)],[])).
% 1.04/0.98 tff(23,plain,
% 1.04/0.98 (![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)))))),
% 1.04/0.98 inference(quant_intro,[status(thm)],[22])).
% 1.04/0.98 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')).
% 1.04/0.98 tff(25,plain,
% 1.04/0.98 (![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)))))),
% 1.04/0.98 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.04/0.98 tff(26,plain,
% 1.04/0.98 (![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)))))),
% 1.04/0.98 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.04/0.98 tff(27,plain,(
% 1.04/0.98 ![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)))))))),
% 1.04/0.98 inference(skolemize,[status(sab)],[26])).
% 1.04/0.98 tff(28,plain,
% 1.04/0.98 (![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)))))),
% 1.04/0.99 inference(modus_ponens,[status(thm)],[27, 20])).
% 1.04/0.99 tff(29,plain,
% 1.04/0.99 (![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)))))))),
% 1.04/0.99 inference(modus_ponens,[status(thm)],[28, 18])).
% 1.04/0.99 tff(30,plain,
% 1.04/0.99 (![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)))))))),
% 1.04/0.99 inference(modus_ponens,[status(thm)],[29, 16])).
% 1.04/0.99 tff(31,plain,
% 1.04/0.99 (![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))))))))))),
% 1.04/0.99 inference(modus_ponens,[status(thm)],[30, 11])).
% 1.04/0.99 tff(32,plain,
% 1.04/0.99 (((~![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, X0!140, uri_ex_x)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | ((~icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141))) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x)))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))))))) <=> ((~![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, X0!140, uri_ex_x)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | ((~icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141))) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x)))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))))))),
% 1.04/0.99 inference(rewrite,[status(thm)],[])).
% 1.04/0.99 tff(33,plain,
% 1.04/0.99 ((~![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, X0!140, uri_ex_x)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | ((~icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141))) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x)))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))))))),
% 1.04/0.99 inference(quant_inst,[status(thm)],[])).
% 1.04/0.99 tff(34,plain,
% 1.04/0.99 ((~![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, X0!140, uri_ex_x)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | ((~icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141))) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x)))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))))))))),
% 1.04/0.99 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.04/0.99 tff(35,plain,
% 1.04/0.99 (~((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | ((~icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141))) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x)))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))))),
% 1.04/0.99 inference(unit_resolution,[status(thm)],[34, 31, 9, 8])).
% 1.04/0.99 tff(36,plain,
% 1.04/0.99 (((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | ((~icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141))) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x)))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))))))) | ((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))),
% 1.04/0.99 inference(tautology,[status(thm)],[])).
% 1.04/0.99 tff(37,plain,
% 1.04/0.99 ((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))))),
% 1.04/0.99 inference(unit_resolution,[status(thm)],[36, 35])).
% 1.04/0.99 tff(38,plain,
% 1.04/0.99 (iext(uri_owl_oneOf, X1!141, X0!140)),
% 1.04/0.99 inference(and_elim,[status(thm)],[7])).
% 1.04/0.99 tff(39,plain,
% 1.04/0.99 ((~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))) | (~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))))),
% 1.04/0.99 inference(tautology,[status(thm)],[])).
% 1.04/0.99 tff(40,plain,
% 1.04/0.99 ((~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))))),
% 1.04/0.99 inference(unit_resolution,[status(thm)],[39, 38])).
% 1.04/0.99 tff(41,plain,
% 1.04/0.99 (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))),
% 1.04/0.99 inference(unit_resolution,[status(thm)],[40, 37])).
% 1.04/0.99 tff(42,plain,
% 1.04/0.99 (((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))) | ![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))),
% 1.04/0.99 inference(tautology,[status(thm)],[])).
% 1.04/0.99 tff(43,plain,
% 1.04/0.99 (![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))),
% 1.04/0.99 inference(unit_resolution,[status(thm)],[42, 41])).
% 1.04/0.99 tff(44,plain,
% 1.04/0.99 ((~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))) | (icext(X1!141, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_x))),
% 1.04/0.99 inference(quant_inst,[status(thm)],[])).
% 1.04/0.99 tff(45,plain,
% 1.04/0.99 (icext(X1!141, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_x)),
% 1.04/0.99 inference(unit_resolution,[status(thm)],[44, 43])).
% 1.04/0.99 tff(46,plain,
% 1.04/0.99 (^[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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))) <=> (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))))))),
% 1.04/0.99 inference(bind,[status(th)],[])).
% 1.04/0.99 tff(47,plain,
% 1.04/0.99 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))) <=> ![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 1.04/0.99 inference(quant_intro,[status(thm)],[46])).
% 1.04/0.99 tff(48,plain,
% 1.04/0.99 (^[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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))))),
% 1.04/0.99 inference(bind,[status(th)],[])).
% 1.04/0.99 tff(49,plain,
% 1.04/0.99 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 1.04/0.99 inference(quant_intro,[status(thm)],[48])).
% 1.04/0.99 tff(50,plain,
% 1.04/0.99 (^[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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))))),
% 1.04/0.99 inference(bind,[status(th)],[])).
% 1.04/0.99 tff(51,plain,
% 1.04/0.99 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 1.04/0.99 inference(quant_intro,[status(thm)],[50])).
% 1.04/0.99 tff(52,plain,
% 1.04/0.99 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 1.04/0.99 inference(transitivity,[status(thm)],[51, 49])).
% 1.04/0.99 tff(53,plain,
% 1.04/0.99 (^[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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))) <=> (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))), rewrite((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))))),
% 1.04/0.99 inference(bind,[status(th)],[])).
% 1.04/0.99 tff(54,plain,
% 1.04/0.99 (![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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 1.04/0.99 inference(quant_intro,[status(thm)],[53])).
% 1.04/0.99 tff(55,plain,
% 1.04/0.99 (^[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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))))))),
% 1.04/0.99 inference(bind,[status(th)],[])).
% 1.04/0.99 tff(56,plain,
% 1.04/0.99 (![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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))))),
% 1.04/0.99 inference(quant_intro,[status(thm)],[55])).
% 1.04/0.99 tff(57,plain,
% 1.04/0.99 (![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))))),
% 1.04/0.99 inference(rewrite,[status(thm)],[])).
% 1.04/0.99 tff(58,plain,
% 1.04/0.99 (^[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)))))),
% 1.04/0.99 inference(bind,[status(th)],[])).
% 1.04/0.99 tff(59,plain,
% 1.04/0.99 (![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))))),
% 1.04/0.99 inference(quant_intro,[status(thm)],[58])).
% 1.04/0.99 tff(60,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/Axioms/SWB001+0.ax','owl_char_inversefunctional')).
% 1.12/0.99 tff(61,plain,
% 1.12/0.99 (![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))))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.12/0.99 tff(62,plain,
% 1.12/0.99 (![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))))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[61, 57])).
% 1.12/0.99 tff(63,plain,(
% 1.12/0.99 ![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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))))))),
% 1.12/0.99 inference(skolemize,[status(sab)],[62])).
% 1.12/0.99 tff(64,plain,
% 1.12/0.99 (![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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[63, 56])).
% 1.12/0.99 tff(65,plain,
% 1.12/0.99 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[64, 54])).
% 1.12/0.99 tff(66,plain,
% 1.12/0.99 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[65, 52])).
% 1.12/0.99 tff(67,plain,
% 1.12/0.99 (![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[66, 47])).
% 1.12/0.99 tff(68,plain,
% 1.12/0.99 ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(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))))))))))),
% 1.12/0.99 inference(quant_inst,[status(thm)],[])).
% 1.12/0.99 tff(69,plain,
% 1.12/0.99 (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(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)))))))))),
% 1.12/0.99 inference(unit_resolution,[status(thm)],[68, 67])).
% 1.12/0.99 tff(70,plain,
% 1.12/0.99 (((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(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_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))))))),
% 1.12/0.99 inference(tautology,[status(thm)],[])).
% 1.12/0.99 tff(71,plain,
% 1.12/0.99 (icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p)))))),
% 1.12/0.99 inference(unit_resolution,[status(thm)],[70, 69])).
% 1.12/0.99 tff(72,plain,
% 1.12/0.99 (iext(uri_ex_p, uri_ex_x, uri_ex_y)),
% 1.12/0.99 inference(and_elim,[status(thm)],[7])).
% 1.12/0.99 tff(73,plain,
% 1.12/0.99 (^[S: $i, P: $i, O: $i] : refl((ip(P) | (~iext(P, S, O))) <=> (ip(P) | (~iext(P, S, O))))),
% 1.12/0.99 inference(bind,[status(th)],[])).
% 1.12/0.99 tff(74,plain,
% 1.12/0.99 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O))) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 1.12/0.99 inference(quant_intro,[status(thm)],[73])).
% 1.12/0.99 tff(75,plain,
% 1.12/0.99 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O))) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 1.12/0.99 inference(rewrite,[status(thm)],[])).
% 1.12/0.99 tff(76,plain,
% 1.12/0.99 (^[S: $i, P: $i, O: $i] : rewrite((iext(P, S, O) => ip(P)) <=> (ip(P) | (~iext(P, S, O))))),
% 1.12/0.99 inference(bind,[status(th)],[])).
% 1.12/0.99 tff(77,plain,
% 1.12/0.99 (![S: $i, P: $i, O: $i] : (iext(P, S, O) => ip(P)) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 1.12/0.99 inference(quant_intro,[status(thm)],[76])).
% 1.12/0.99 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')).
% 1.12/0.99 tff(79,plain,
% 1.12/0.99 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.12/0.99 tff(80,plain,
% 1.12/0.99 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[79, 75])).
% 1.12/0.99 tff(81,plain,(
% 1.12/0.99 ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 1.12/0.99 inference(skolemize,[status(sab)],[80])).
% 1.12/0.99 tff(82,plain,
% 1.12/0.99 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[81, 74])).
% 1.12/0.99 tff(83,plain,
% 1.12/0.99 (((~![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)))),
% 1.12/0.99 inference(rewrite,[status(thm)],[])).
% 1.12/0.99 tff(84,plain,
% 1.12/0.99 ((~![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)))),
% 1.12/0.99 inference(quant_inst,[status(thm)],[])).
% 1.12/0.99 tff(85,plain,
% 1.12/0.99 ((~![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))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.12/0.99 tff(86,plain,
% 1.12/0.99 (ip(uri_ex_p)),
% 1.12/0.99 inference(unit_resolution,[status(thm)],[85, 82, 72])).
% 1.12/0.99 tff(87,plain,
% 1.12/0.99 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 1.12/0.99 inference(bind,[status(th)],[])).
% 1.12/0.99 tff(88,plain,
% 1.12/0.99 (![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))),
% 1.12/0.99 inference(quant_intro,[status(thm)],[87])).
% 1.12/0.99 tff(89,plain,
% 1.12/0.99 (![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))),
% 1.12/0.99 inference(rewrite,[status(thm)],[])).
% 1.12/0.99 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')).
% 1.12/0.99 tff(91,plain,
% 1.12/0.99 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.12/0.99 tff(92,plain,(
% 1.12/0.99 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 1.12/0.99 inference(skolemize,[status(sab)],[91])).
% 1.12/0.99 tff(93,plain,
% 1.12/0.99 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[92, 88])).
% 1.12/0.99 tff(94,plain,
% 1.12/0.99 ((~![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))),
% 1.12/0.99 inference(quant_inst,[status(thm)],[])).
% 1.12/0.99 tff(95,plain,
% 1.12/0.99 (iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 1.12/0.99 inference(unit_resolution,[status(thm)],[94, 93])).
% 1.12/0.99 tff(96,plain,
% 1.12/0.99 ((~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)) <=> (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty))),
% 1.12/0.99 inference(rewrite,[status(thm)],[])).
% 1.12/0.99 tff(97,axiom,(~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion_rdfbased_sem_char_inversefunc_ext')).
% 1.12/0.99 tff(98,plain,
% 1.12/0.99 (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)),
% 1.12/0.99 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.12/0.99 tff(99,plain,
% 1.12/0.99 ((~(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))),
% 1.12/0.99 inference(tautology,[status(thm)],[])).
% 1.12/0.99 tff(100,plain,
% 1.12/0.99 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))) | (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 1.12/0.99 inference(unit_resolution,[status(thm)],[99, 98])).
% 1.12/0.99 tff(101,plain,
% 1.12/0.99 (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 1.12/0.99 inference(unit_resolution,[status(thm)],[100, 95])).
% 1.12/0.99 tff(102,plain,
% 1.12/0.99 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))))))) | icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p)))))),
% 1.12/0.99 inference(tautology,[status(thm)],[])).
% 1.12/0.99 tff(103,plain,
% 1.12/0.99 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))))))) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p)))))),
% 1.12/0.99 inference(unit_resolution,[status(thm)],[102, 101, 86])).
% 1.12/0.99 tff(104,plain,
% 1.12/0.99 (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))))),
% 1.12/0.99 inference(unit_resolution,[status(thm)],[103, 71])).
% 1.12/0.99 tff(105,plain,
% 1.12/0.99 (((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p)))) | iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 1.12/1.00 inference(tautology,[status(thm)],[])).
% 1.12/1.00 tff(106,plain,
% 1.12/1.00 (iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[105, 104])).
% 1.12/1.00 tff(107,plain,
% 1.12/1.00 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))))))),
% 1.12/1.00 inference(bind,[status(th)],[])).
% 1.12/1.00 tff(108,plain,
% 1.12/1.00 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))),
% 1.12/1.00 inference(quant_intro,[status(thm)],[107])).
% 1.12/1.00 tff(109,plain,
% 1.12/1.00 (^[P: $i, C: $i] : refl((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))))),
% 1.12/1.00 inference(bind,[status(th)],[])).
% 1.12/1.00 tff(110,plain,
% 1.12/1.00 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 1.12/1.00 inference(quant_intro,[status(thm)],[109])).
% 1.12/1.00 tff(111,plain,
% 1.12/1.00 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))))),
% 1.12/1.00 inference(bind,[status(th)],[])).
% 1.12/1.00 tff(112,plain,
% 1.12/1.00 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 1.12/1.00 inference(quant_intro,[status(thm)],[111])).
% 1.12/1.00 tff(113,plain,
% 1.12/1.00 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 1.12/1.00 inference(transitivity,[status(thm)],[112, 110])).
% 1.12/1.00 tff(114,plain,
% 1.12/1.00 (^[P: $i, C: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))), rewrite((iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))) <=> (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))), ((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))), rewrite((((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))), ((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))))),
% 1.12/1.00 inference(bind,[status(th)],[])).
% 1.12/1.00 tff(115,plain,
% 1.12/1.00 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 1.12/1.00 inference(quant_intro,[status(thm)],[114])).
% 1.12/1.00 tff(116,plain,
% 1.12/1.00 (^[P: $i, C: $i] : rewrite((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))) <=> (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))),
% 1.12/1.00 inference(bind,[status(th)],[])).
% 1.12/1.00 tff(117,plain,
% 1.12/1.00 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))) <=> ![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))),
% 1.12/1.00 inference(quant_intro,[status(thm)],[116])).
% 1.12/1.00 tff(118,plain,
% 1.12/1.00 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 1.12/1.00 inference(rewrite,[status(thm)],[])).
% 1.12/1.00 tff(119,plain,
% 1.12/1.00 (^[P: $i, C: $i] : rewrite((iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X)))) <=> (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))),
% 1.12/1.00 inference(bind,[status(th)],[])).
% 1.12/1.00 tff(120,plain,
% 1.12/1.00 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 1.12/1.00 inference(quant_intro,[status(thm)],[119])).
% 1.12/1.00 tff(121,axiom,(![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_domain')).
% 1.12/1.00 tff(122,plain,
% 1.12/1.00 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 1.12/1.00 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.12/1.00 tff(123,plain,
% 1.12/1.00 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 1.12/1.00 inference(modus_ponens,[status(thm)],[122, 118])).
% 1.12/1.00 tff(124,plain,(
% 1.12/1.00 ![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))),
% 1.12/1.00 inference(skolemize,[status(sab)],[123])).
% 1.12/1.00 tff(125,plain,
% 1.12/1.00 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))),
% 1.12/1.00 inference(modus_ponens,[status(thm)],[124, 117])).
% 1.12/1.00 tff(126,plain,
% 1.12/1.00 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 1.12/1.00 inference(modus_ponens,[status(thm)],[125, 115])).
% 1.12/1.00 tff(127,plain,
% 1.12/1.00 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 1.12/1.00 inference(modus_ponens,[status(thm)],[126, 113])).
% 1.12/1.00 tff(128,plain,
% 1.12/1.00 (![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))),
% 1.12/1.00 inference(modus_ponens,[status(thm)],[127, 108])).
% 1.12/1.00 tff(129,plain,
% 1.12/1.00 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p, X1!141) | (~ic(X1!141)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_58(X1!141, uri_ex_p), tptp_fun_Y_57(X1!141, uri_ex_p))) | icext(X1!141, tptp_fun_X_58(X1!141, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))))))))),
% 1.12/1.00 inference(quant_inst,[status(thm)],[])).
% 1.12/1.00 tff(130,plain,
% 1.12/1.00 (~((~(iext(uri_rdfs_domain, uri_ex_p, X1!141) | (~ic(X1!141)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_58(X1!141, uri_ex_p), tptp_fun_Y_57(X1!141, uri_ex_p))) | icext(X1!141, tptp_fun_X_58(X1!141, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))))))))),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[129, 128])).
% 1.12/1.00 tff(131,plain,
% 1.12/1.00 (((~(iext(uri_rdfs_domain, uri_ex_p, X1!141) | (~ic(X1!141)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_58(X1!141, uri_ex_p), tptp_fun_Y_57(X1!141, uri_ex_p))) | icext(X1!141, tptp_fun_X_58(X1!141, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))))))) | ((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))))))),
% 1.12/1.00 inference(tautology,[status(thm)],[])).
% 1.12/1.00 tff(132,plain,
% 1.12/1.00 ((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))))),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[131, 130])).
% 1.12/1.00 tff(133,plain,
% 1.12/1.00 (iext(uri_rdfs_domain, uri_ex_p, X1!141)),
% 1.12/1.00 inference(and_elim,[status(thm)],[7])).
% 1.12/1.00 tff(134,plain,
% 1.12/1.00 ((~((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))))))) | (~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))))),
% 1.12/1.00 inference(tautology,[status(thm)],[])).
% 1.12/1.00 tff(135,plain,
% 1.12/1.00 ((~((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))))))) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))))),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[134, 133])).
% 1.12/1.00 tff(136,plain,
% 1.12/1.00 (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))))),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[135, 132])).
% 1.12/1.00 tff(137,plain,
% 1.12/1.00 (((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))) | ![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))),
% 1.12/1.00 inference(tautology,[status(thm)],[])).
% 1.12/1.00 tff(138,plain,
% 1.12/1.00 (![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[137, 136])).
% 1.12/1.00 tff(139,plain,
% 1.12/1.00 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | ((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X2_115(uri_ex_p)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X2_115(uri_ex_p)))),
% 1.12/1.00 inference(rewrite,[status(thm)],[])).
% 1.12/1.00 tff(140,plain,
% 1.12/1.00 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | ((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X2_115(uri_ex_p)))),
% 1.12/1.00 inference(quant_inst,[status(thm)],[])).
% 1.12/1.00 tff(141,plain,
% 1.12/1.00 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X2_115(uri_ex_p))),
% 1.12/1.00 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.12/1.00 tff(142,plain,
% 1.12/1.00 (icext(X1!141, tptp_fun_X2_115(uri_ex_p))),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[141, 138, 106])).
% 1.12/1.00 tff(143,plain,
% 1.12/1.00 ((~(icext(X1!141, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_x))) | (~icext(X1!141, tptp_fun_X2_115(uri_ex_p))) | (tptp_fun_X2_115(uri_ex_p) = uri_ex_x)),
% 1.12/1.00 inference(tautology,[status(thm)],[])).
% 1.12/1.00 tff(144,plain,
% 1.12/1.00 ((~(icext(X1!141, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_x))) | (tptp_fun_X2_115(uri_ex_p) = uri_ex_x)),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[143, 142])).
% 1.12/1.00 tff(145,plain,
% 1.12/1.00 (tptp_fun_X2_115(uri_ex_p) = uri_ex_x),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[144, 45])).
% 1.12/1.00 tff(146,plain,
% 1.12/1.00 ((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_x)),
% 1.12/1.00 inference(monotonicity,[status(thm)],[145])).
% 1.12/1.00 tff(147,plain,
% 1.12/1.00 ((tptp_fun_X1_116(uri_ex_p) = uri_ex_x) <=> (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))),
% 1.12/1.00 inference(symmetry,[status(thm)],[146])).
% 1.12/1.00 tff(148,plain,
% 1.12/1.00 ((~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))) | (icext(X1!141, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_x))),
% 1.12/1.00 inference(quant_inst,[status(thm)],[])).
% 1.12/1.00 tff(149,plain,
% 1.12/1.00 (icext(X1!141, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_x)),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[148, 43])).
% 1.12/1.00 tff(150,plain,
% 1.12/1.00 (((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p)))) | iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 1.12/1.00 inference(tautology,[status(thm)],[])).
% 1.12/1.00 tff(151,plain,
% 1.12/1.00 (iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[150, 104])).
% 1.12/1.00 tff(152,plain,
% 1.12/1.00 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | ((~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X1_116(uri_ex_p)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X1_116(uri_ex_p)))),
% 1.12/1.00 inference(rewrite,[status(thm)],[])).
% 1.12/1.00 tff(153,plain,
% 1.12/1.00 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | ((~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X1_116(uri_ex_p)))),
% 1.12/1.00 inference(quant_inst,[status(thm)],[])).
% 1.12/1.00 tff(154,plain,
% 1.12/1.00 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X1_116(uri_ex_p))),
% 1.12/1.00 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.12/1.00 tff(155,plain,
% 1.12/1.00 (icext(X1!141, tptp_fun_X1_116(uri_ex_p))),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[154, 138, 151])).
% 1.12/1.00 tff(156,plain,
% 1.12/1.00 ((~(icext(X1!141, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_x))) | (~icext(X1!141, tptp_fun_X1_116(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = uri_ex_x)),
% 1.12/1.00 inference(tautology,[status(thm)],[])).
% 1.12/1.00 tff(157,plain,
% 1.12/1.00 ((~(icext(X1!141, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_x))) | (tptp_fun_X1_116(uri_ex_p) = uri_ex_x)),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[156, 155])).
% 1.12/1.00 tff(158,plain,
% 1.12/1.00 (tptp_fun_X1_116(uri_ex_p) = uri_ex_x),
% 1.12/1.00 inference(unit_resolution,[status(thm)],[157, 149])).
% 1.12/1.00 tff(159,plain,
% 1.12/1.00 (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)),
% 1.12/1.00 inference(modus_ponens,[status(thm)],[158, 147])).
% 1.12/1.00 tff(160,plain,
% 1.12/1.00 (((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p)))) | (~(tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))),
% 1.12/1.03 inference(tautology,[status(thm)],[])).
% 1.12/1.03 tff(161,plain,
% 1.12/1.03 (~(tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))),
% 1.12/1.03 inference(unit_resolution,[status(thm)],[160, 104])).
% 1.12/1.03 tff(162,plain,
% 1.12/1.03 ($false),
% 1.12/1.03 inference(unit_resolution,[status(thm)],[161, 159])).
% 1.12/1.03 % SZS output end Proof
%------------------------------------------------------------------------------