TSTP Solution File: SWB080+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB080+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 08:32:13 EDT 2022
% Result : Theorem 6.39s 6.56s
% Output : Proof 6.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SWB080+1 : TPTP v8.1.0. Released v5.2.0.
% 0.05/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.29 % Computer : n011.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Sat Sep 3 20:17:59 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.29 Usage: tptp [options] [-file:]file
% 0.08/0.29 -h, -? prints this message.
% 0.08/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.29 -m, -model generate model.
% 0.08/0.29 -p, -proof generate proof.
% 0.08/0.29 -c, -core generate unsat core of named formulas.
% 0.08/0.29 -st, -statistics display statistics.
% 0.08/0.29 -t:timeout set timeout (in second).
% 0.08/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.29 -<param>:<value> configuration parameter and value.
% 0.08/0.29 -o:<output-file> file to place output in.
% 6.39/6.56 % SZS status Theorem
% 6.39/6.56 % SZS output start Proof
% 6.39/6.56 tff(iext_type, type, (
% 6.39/6.56 iext: ( $i * $i * $i ) > $o)).
% 6.39/6.56 tff(tptp_fun_Y_62_type, type, (
% 6.39/6.56 tptp_fun_Y_62: ( $i * $i ) > $i)).
% 6.39/6.56 tff(uri_ex_p1_type, type, (
% 6.39/6.56 uri_ex_p1: $i)).
% 6.39/6.56 tff(uri_ex_p2_type, type, (
% 6.39/6.56 uri_ex_p2: $i)).
% 6.39/6.56 tff(tptp_fun_X_63_type, type, (
% 6.39/6.56 tptp_fun_X_63: ( $i * $i ) > $i)).
% 6.39/6.56 tff(uri_ex_u_type, type, (
% 6.39/6.56 uri_ex_u: $i)).
% 6.39/6.56 tff(uri_ex_w_type, type, (
% 6.39/6.56 uri_ex_w: $i)).
% 6.39/6.56 tff(icext_type, type, (
% 6.39/6.56 icext: ( $i * $i ) > $o)).
% 6.39/6.56 tff(tptp_fun_X1_144_type, type, (
% 6.39/6.56 tptp_fun_X1_144: $i)).
% 6.39/6.56 tff(ic_type, type, (
% 6.39/6.56 ic: $i > $o)).
% 6.39/6.56 tff(tptp_fun_X2_146_type, type, (
% 6.39/6.56 tptp_fun_X2_146: $i)).
% 6.39/6.56 tff(uri_owl_oneOf_type, type, (
% 6.39/6.56 uri_owl_oneOf: $i)).
% 6.39/6.56 tff(tptp_fun_X_8_type, type, (
% 6.39/6.56 tptp_fun_X_8: ( $i * $i ) > $i)).
% 6.39/6.56 tff(uri_rdf_nil_type, type, (
% 6.39/6.56 uri_rdf_nil: $i)).
% 6.39/6.56 tff(uri_rdf_rest_type, type, (
% 6.39/6.56 uri_rdf_rest: $i)).
% 6.39/6.56 tff(tptp_fun_X8_148_type, type, (
% 6.39/6.56 tptp_fun_X8_148: $i)).
% 6.39/6.56 tff(uri_rdf_first_type, type, (
% 6.39/6.56 uri_rdf_first: $i)).
% 6.39/6.56 tff(tptp_fun_X4_147_type, type, (
% 6.39/6.56 tptp_fun_X4_147: $i)).
% 6.39/6.56 tff(tptp_fun_X5_145_type, type, (
% 6.39/6.56 tptp_fun_X5_145: $i)).
% 6.39/6.56 tff(tptp_fun_X7_141_type, type, (
% 6.39/6.56 tptp_fun_X7_141: $i)).
% 6.39/6.56 tff(tptp_fun_X6_143_type, type, (
% 6.39/6.56 tptp_fun_X6_143: $i)).
% 6.39/6.56 tff(tptp_fun_X3_142_type, type, (
% 6.39/6.56 tptp_fun_X3_142: $i)).
% 6.39/6.56 tff(tptp_fun_X0_140_type, type, (
% 6.39/6.56 tptp_fun_X0_140: $i)).
% 6.39/6.56 tff(uri_rdfs_range_type, type, (
% 6.39/6.56 uri_rdfs_range: $i)).
% 6.39/6.56 tff(uri_rdfs_domain_type, type, (
% 6.39/6.56 uri_rdfs_domain: $i)).
% 6.39/6.56 tff(ip_type, type, (
% 6.39/6.56 ip: $i > $o)).
% 6.39/6.56 tff(tptp_fun_Y_59_type, type, (
% 6.39/6.56 tptp_fun_Y_59: ( $i * $i ) > $i)).
% 6.39/6.56 tff(tptp_fun_X_60_type, type, (
% 6.39/6.56 tptp_fun_X_60: ( $i * $i ) > $i)).
% 6.39/6.56 tff(uri_rdfs_subPropertyOf_type, type, (
% 6.39/6.56 uri_rdfs_subPropertyOf: $i)).
% 6.39/6.56 tff(tptp_fun_X_58_type, type, (
% 6.39/6.56 tptp_fun_X_58: ( $i * $i ) > $i)).
% 6.39/6.56 tff(tptp_fun_Y_57_type, type, (
% 6.39/6.56 tptp_fun_Y_57: ( $i * $i ) > $i)).
% 6.39/6.56 tff(1,plain,
% 6.39/6.56 (?[X8: $i, X4: $i, X2: $i, X5: $i, X1: $i, X6: $i, X3: $i, X7: $i, X0: $i] : (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_w)) <=> ?[X8: $i, X4: $i, X2: $i, X5: $i, X1: $i, X6: $i, X3: $i, X7: $i, X0: $i] : (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_w))),
% 6.39/6.56 inference(rewrite,[status(thm)],[])).
% 6.39/6.56 tff(2,plain,
% 6.39/6.56 (^[X8: $i, X4: $i, X2: $i, X5: $i, X1: $i, X6: $i, X3: $i, X7: $i, X0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u))), ((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil))), ((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil)))), (((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w))), (((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w)))), ((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil))), ((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil)))), (((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w))), (((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w)))), ((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil))), ((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil)))), (((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5))), (((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5)))), ((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6))), ((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6)))), (((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2))), (((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2)))), ((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u))), ((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u)))), (((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8))), (((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8)))), ((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3))), ((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3)))), (((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7))), (((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7)))), ((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4))), ((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4)))), (((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w))), (((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w)))), ((((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil))), ((((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil)))), (((((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u))), (((((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)))), ((((((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_u)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_u)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_u)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u))), ((((((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_u)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u)))), (((((((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_w)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_w)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_w)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_w))), (((((((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_w)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_w))))),
% 6.43/6.61 inference(bind,[status(th)],[])).
% 6.43/6.61 tff(3,plain,
% 6.43/6.61 (?[X8: $i, X4: $i, X2: $i, X5: $i, X1: $i, X6: $i, X3: $i, X7: $i, X0: $i] : ((((((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_w)) <=> ?[X8: $i, X4: $i, X2: $i, X5: $i, X1: $i, X6: $i, X3: $i, X7: $i, X0: $i] : (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_w))),
% 6.43/6.61 inference(quant_intro,[status(thm)],[2])).
% 6.43/6.61 tff(4,axiom,(?[X8: $i, X4: $i, X2: $i, X5: $i, X1: $i, X6: $i, X3: $i, X7: $i, X0: $i] : ((((((((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1)) & iext(uri_rdf_first, X2, uri_ex_u)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X3, uri_ex_w)) & iext(uri_rdf_rest, X3, uri_rdf_nil)) & iext(uri_rdf_first, X4, uri_ex_w)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_rdfs_domain, uri_ex_p2, X5)) & iext(uri_rdfs_range, uri_ex_p2, X6)) & iext(uri_owl_oneOf, X1, X2)) & iext(uri_rdf_first, X7, uri_ex_u)) & iext(uri_rdf_rest, X7, X8)) & iext(uri_owl_oneOf, X0, X3)) & iext(uri_owl_oneOf, X6, X7)) & iext(uri_owl_oneOf, X5, X4)) & iext(uri_rdf_first, X8, uri_ex_w)) & iext(uri_rdf_rest, X8, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_u)) & iext(uri_ex_p2, uri_ex_w, uri_ex_w))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','premise_rdfbased_sem_rdfsext_subprop_ext')).
% 6.43/6.61 tff(5,plain,
% 6.43/6.61 (?[X8: $i, X4: $i, X2: $i, X5: $i, X1: $i, X6: $i, X3: $i, X7: $i, X0: $i] : (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_w))),
% 6.43/6.61 inference(modus_ponens,[status(thm)],[4, 3])).
% 6.43/6.61 tff(6,plain,
% 6.43/6.61 (?[X8: $i, X4: $i, X2: $i, X5: $i, X1: $i, X6: $i, X3: $i, X7: $i, X0: $i] : (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_rdfs_range, uri_ex_p1, X1) & iext(uri_rdf_first, X2, uri_ex_u) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X3, uri_ex_w) & iext(uri_rdf_rest, X3, uri_rdf_nil) & iext(uri_rdf_first, X4, uri_ex_w) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5) & iext(uri_rdfs_range, uri_ex_p2, X6) & iext(uri_owl_oneOf, X1, X2) & iext(uri_rdf_first, X7, uri_ex_u) & iext(uri_rdf_rest, X7, X8) & iext(uri_owl_oneOf, X0, X3) & iext(uri_owl_oneOf, X6, X7) & iext(uri_owl_oneOf, X5, X4) & iext(uri_rdf_first, X8, uri_ex_w) & iext(uri_rdf_rest, X8, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_w))),
% 6.43/6.61 inference(modus_ponens,[status(thm)],[5, 1])).
% 6.43/6.61 tff(7,plain,(
% 6.43/6.61 iext(uri_rdfs_domain, uri_ex_p1, X0!140) & iext(uri_rdfs_range, uri_ex_p1, X1!144) & iext(uri_rdf_first, X2!146, uri_ex_u) & iext(uri_rdf_rest, X2!146, uri_rdf_nil) & iext(uri_rdf_first, X3!142, uri_ex_w) & iext(uri_rdf_rest, X3!142, uri_rdf_nil) & iext(uri_rdf_first, X4!147, uri_ex_w) & iext(uri_rdf_rest, X4!147, uri_rdf_nil) & iext(uri_rdfs_domain, uri_ex_p2, X5!145) & iext(uri_rdfs_range, uri_ex_p2, X6!143) & iext(uri_owl_oneOf, X1!144, X2!146) & iext(uri_rdf_first, X7!141, uri_ex_u) & iext(uri_rdf_rest, X7!141, X8!148) & iext(uri_owl_oneOf, X0!140, X3!142) & iext(uri_owl_oneOf, X6!143, X7!141) & iext(uri_owl_oneOf, X5!145, X4!147) & iext(uri_rdf_first, X8!148, uri_ex_w) & iext(uri_rdf_rest, X8!148, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_u) & iext(uri_ex_p2, uri_ex_w, uri_ex_w)),
% 6.43/6.61 inference(skolemize,[status(sab)],[6])).
% 6.43/6.61 tff(8,plain,
% 6.43/6.61 (iext(uri_rdf_rest, X2!146, uri_rdf_nil)),
% 6.43/6.61 inference(and_elim,[status(thm)],[7])).
% 6.43/6.61 tff(9,plain,
% 6.43/6.61 (iext(uri_rdf_first, X2!146, uri_ex_u)),
% 6.43/6.61 inference(and_elim,[status(thm)],[7])).
% 6.43/6.61 tff(10,plain,
% 6.43/6.61 (^[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)))))))))))),
% 6.43/6.61 inference(bind,[status(th)],[])).
% 6.43/6.61 tff(11,plain,
% 6.43/6.61 (![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))))))))))),
% 6.43/6.61 inference(quant_intro,[status(thm)],[10])).
% 6.43/6.61 tff(12,plain,
% 6.43/6.61 (^[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))))))))),
% 6.43/6.62 inference(bind,[status(th)],[])).
% 6.43/6.62 tff(13,plain,
% 6.43/6.62 (![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)))))))),
% 6.43/6.62 inference(quant_intro,[status(thm)],[12])).
% 6.43/6.62 tff(14,plain,
% 6.43/6.62 (^[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))))))))),
% 6.43/6.62 inference(bind,[status(th)],[])).
% 6.43/6.62 tff(15,plain,
% 6.43/6.62 (![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)))))))),
% 6.43/6.62 inference(quant_intro,[status(thm)],[14])).
% 6.43/6.62 tff(16,plain,
% 6.43/6.62 (![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)))))))),
% 6.43/6.62 inference(transitivity,[status(thm)],[15, 13])).
% 6.43/6.62 tff(17,plain,
% 6.43/6.62 (^[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)))))))))),
% 6.43/6.62 inference(bind,[status(th)],[])).
% 6.43/6.62 tff(18,plain,
% 6.43/6.62 (![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)))))))),
% 6.43/6.62 inference(quant_intro,[status(thm)],[17])).
% 6.43/6.62 tff(19,plain,
% 6.43/6.62 (^[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))))))),
% 6.43/6.62 inference(bind,[status(th)],[])).
% 6.43/6.62 tff(20,plain,
% 6.43/6.62 (![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)))))),
% 6.43/6.62 inference(quant_intro,[status(thm)],[19])).
% 6.43/6.62 tff(21,plain,
% 6.43/6.62 (![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)))))),
% 6.43/6.62 inference(rewrite,[status(thm)],[])).
% 6.43/6.62 tff(22,plain,
% 6.43/6.62 (^[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)))))))),
% 6.43/6.62 inference(bind,[status(th)],[])).
% 6.43/6.62 tff(23,plain,
% 6.43/6.62 (![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)))))),
% 6.43/6.62 inference(quant_intro,[status(thm)],[22])).
% 6.43/6.62 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')).
% 6.43/6.62 tff(25,plain,
% 6.43/6.62 (![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)))))),
% 6.43/6.62 inference(modus_ponens,[status(thm)],[24, 23])).
% 6.43/6.62 tff(26,plain,
% 6.43/6.62 (![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)))))),
% 6.43/6.62 inference(modus_ponens,[status(thm)],[25, 21])).
% 6.43/6.62 tff(27,plain,(
% 6.43/6.62 ![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)))))))),
% 6.43/6.62 inference(skolemize,[status(sab)],[26])).
% 6.43/6.62 tff(28,plain,
% 6.43/6.62 (![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)))))),
% 6.43/6.62 inference(modus_ponens,[status(thm)],[27, 20])).
% 6.43/6.62 tff(29,plain,
% 6.43/6.62 (![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)))))))),
% 6.43/6.62 inference(modus_ponens,[status(thm)],[28, 18])).
% 6.43/6.62 tff(30,plain,
% 6.43/6.62 (![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)))))))),
% 6.43/6.62 inference(modus_ponens,[status(thm)],[29, 16])).
% 6.43/6.62 tff(31,plain,
% 6.43/6.62 (![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))))))))))),
% 6.43/6.62 inference(modus_ponens,[status(thm)],[30, 11])).
% 6.43/6.62 tff(32,plain,
% 6.43/6.62 (((~![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, X2!146, uri_ex_u)) | (~iext(uri_rdf_rest, X2!146, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!144, X2!146) | (~ic(X1!144)) | ((~icext(X1!144, tptp_fun_X_8(uri_ex_u, X1!144))) <=> (tptp_fun_X_8(uri_ex_u, X1!144) = uri_ex_u)))) | (~((~iext(uri_owl_oneOf, X1!144, X2!146)) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u))))))))))) <=> ((~![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, X2!146, uri_ex_u)) | (~iext(uri_rdf_rest, X2!146, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!144, X2!146) | (~ic(X1!144)) | ((~icext(X1!144, tptp_fun_X_8(uri_ex_u, X1!144))) <=> (tptp_fun_X_8(uri_ex_u, X1!144) = uri_ex_u)))) | (~((~iext(uri_owl_oneOf, X1!144, X2!146)) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u))))))))))),
% 6.43/6.62 inference(rewrite,[status(thm)],[])).
% 6.43/6.62 tff(33,plain,
% 6.43/6.62 ((~![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, X2!146, uri_ex_u)) | (~iext(uri_rdf_rest, X2!146, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!144, X2!146) | (~ic(X1!144)) | ((~icext(X1!144, tptp_fun_X_8(uri_ex_u, X1!144))) <=> (tptp_fun_X_8(uri_ex_u, X1!144) = uri_ex_u)))) | (~((~iext(uri_owl_oneOf, X1!144, X2!146)) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u))))))))))),
% 6.43/6.63 inference(quant_inst,[status(thm)],[])).
% 6.43/6.63 tff(34,plain,
% 6.43/6.63 ((~![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, X2!146, uri_ex_u)) | (~iext(uri_rdf_rest, X2!146, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!144, X2!146) | (~ic(X1!144)) | ((~icext(X1!144, tptp_fun_X_8(uri_ex_u, X1!144))) <=> (tptp_fun_X_8(uri_ex_u, X1!144) = uri_ex_u)))) | (~((~iext(uri_owl_oneOf, X1!144, X2!146)) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u)))))))))),
% 6.43/6.63 inference(modus_ponens,[status(thm)],[33, 32])).
% 6.43/6.63 tff(35,plain,
% 6.43/6.63 (~((~(iext(uri_owl_oneOf, X1!144, X2!146) | (~ic(X1!144)) | ((~icext(X1!144, tptp_fun_X_8(uri_ex_u, X1!144))) <=> (tptp_fun_X_8(uri_ex_u, X1!144) = uri_ex_u)))) | (~((~iext(uri_owl_oneOf, X1!144, X2!146)) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u))))))))),
% 6.43/6.63 inference(unit_resolution,[status(thm)],[34, 31, 9, 8])).
% 6.43/6.63 tff(36,plain,
% 6.43/6.63 (((~(iext(uri_owl_oneOf, X1!144, X2!146) | (~ic(X1!144)) | ((~icext(X1!144, tptp_fun_X_8(uri_ex_u, X1!144))) <=> (tptp_fun_X_8(uri_ex_u, X1!144) = uri_ex_u)))) | (~((~iext(uri_owl_oneOf, X1!144, X2!146)) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u)))))))) | ((~iext(uri_owl_oneOf, X1!144, X2!146)) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u))))))),
% 6.43/6.63 inference(tautology,[status(thm)],[])).
% 6.43/6.63 tff(37,plain,
% 6.43/6.63 ((~iext(uri_owl_oneOf, X1!144, X2!146)) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u)))))),
% 6.43/6.63 inference(unit_resolution,[status(thm)],[36, 35])).
% 6.43/6.63 tff(38,plain,
% 6.43/6.63 (iext(uri_owl_oneOf, X1!144, X2!146)),
% 6.43/6.63 inference(and_elim,[status(thm)],[7])).
% 6.43/6.63 tff(39,plain,
% 6.43/6.63 ((~((~iext(uri_owl_oneOf, X1!144, X2!146)) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u))))))) | (~iext(uri_owl_oneOf, X1!144, X2!146)) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u)))))),
% 6.43/6.63 inference(tautology,[status(thm)],[])).
% 6.43/6.63 tff(40,plain,
% 6.43/6.63 ((~((~iext(uri_owl_oneOf, X1!144, X2!146)) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u))))))) | (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u)))))),
% 6.43/6.63 inference(unit_resolution,[status(thm)],[39, 38])).
% 6.43/6.63 tff(41,plain,
% 6.43/6.63 (~((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u))))),
% 6.43/6.63 inference(unit_resolution,[status(thm)],[40, 37])).
% 6.43/6.63 tff(42,plain,
% 6.43/6.63 (((~ic(X1!144)) | (~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u)))) | ![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u))),
% 6.43/6.63 inference(tautology,[status(thm)],[])).
% 6.43/6.63 tff(43,plain,
% 6.43/6.63 (![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u))),
% 6.43/6.63 inference(unit_resolution,[status(thm)],[42, 41])).
% 6.43/6.63 tff(44,plain,
% 6.43/6.63 ((~![X: $i] : (icext(X1!144, X) <=> (X = uri_ex_u))) | (icext(X1!144, tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)) <=> (tptp_fun_Y_62(uri_ex_p2, uri_ex_p1) = uri_ex_u))),
% 6.43/6.63 inference(quant_inst,[status(thm)],[])).
% 6.43/6.63 tff(45,plain,
% 6.43/6.63 (icext(X1!144, tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)) <=> (tptp_fun_Y_62(uri_ex_p2, uri_ex_p1) = uri_ex_u)),
% 6.43/6.63 inference(unit_resolution,[status(thm)],[44, 43])).
% 6.43/6.63 tff(46,plain,
% 6.43/6.63 (^[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))))))))))),
% 6.43/6.63 inference(bind,[status(th)],[])).
% 6.43/6.63 tff(47,plain,
% 6.43/6.63 (![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)))))))))),
% 6.43/6.63 inference(quant_intro,[status(thm)],[46])).
% 6.43/6.63 tff(48,plain,
% 6.43/6.63 (^[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)))))))))),
% 6.43/6.63 inference(bind,[status(th)],[])).
% 6.43/6.63 tff(49,plain,
% 6.43/6.63 (![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))))))))),
% 6.43/6.63 inference(quant_intro,[status(thm)],[48])).
% 6.43/6.63 tff(50,plain,
% 6.43/6.63 (^[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)))))))))),
% 6.43/6.63 inference(bind,[status(th)],[])).
% 6.43/6.63 tff(51,plain,
% 6.43/6.63 (![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))))))))),
% 6.43/6.63 inference(quant_intro,[status(thm)],[50])).
% 6.43/6.63 tff(52,plain,
% 6.43/6.63 (![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))))))))),
% 6.43/6.63 inference(transitivity,[status(thm)],[51, 49])).
% 6.43/6.63 tff(53,plain,
% 6.43/6.63 (^[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))))))))))),
% 6.43/6.63 inference(bind,[status(th)],[])).
% 6.43/6.63 tff(54,plain,
% 6.43/6.63 (![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))))))))),
% 6.43/6.63 inference(quant_intro,[status(thm)],[53])).
% 6.43/6.63 tff(55,plain,
% 6.43/6.63 (^[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)))))))),
% 6.43/6.63 inference(bind,[status(th)],[])).
% 6.43/6.63 tff(56,plain,
% 6.43/6.63 (![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))))))),
% 6.43/6.63 inference(quant_intro,[status(thm)],[55])).
% 6.43/6.63 tff(57,plain,
% 6.43/6.63 (![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))))),
% 6.43/6.63 inference(rewrite,[status(thm)],[])).
% 6.43/6.63 tff(58,plain,
% 6.43/6.63 (^[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)))))),
% 6.43/6.63 inference(bind,[status(th)],[])).
% 6.43/6.63 tff(59,plain,
% 6.43/6.63 (![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))))),
% 6.43/6.63 inference(quant_intro,[status(thm)],[58])).
% 6.43/6.63 tff(60,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')).
% 6.43/6.63 tff(61,plain,
% 6.43/6.63 (![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))))),
% 6.43/6.63 inference(modus_ponens,[status(thm)],[60, 59])).
% 6.43/6.63 tff(62,plain,
% 6.43/6.63 (![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))))),
% 6.43/6.63 inference(modus_ponens,[status(thm)],[61, 57])).
% 6.43/6.63 tff(63,plain,(
% 6.43/6.63 ![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)))))))),
% 6.43/6.63 inference(skolemize,[status(sab)],[62])).
% 6.43/6.63 tff(64,plain,
% 6.43/6.63 (![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))))))),
% 6.43/6.63 inference(modus_ponens,[status(thm)],[63, 56])).
% 6.43/6.63 tff(65,plain,
% 6.43/6.63 (![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))))))))),
% 6.43/6.63 inference(modus_ponens,[status(thm)],[64, 54])).
% 6.43/6.63 tff(66,plain,
% 6.43/6.63 (![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))))))))),
% 6.43/6.63 inference(modus_ponens,[status(thm)],[65, 52])).
% 6.43/6.63 tff(67,plain,
% 6.43/6.63 (![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)))))))))),
% 6.43/6.63 inference(modus_ponens,[status(thm)],[66, 47])).
% 6.43/6.63 tff(68,plain,
% 6.43/6.63 (((~![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_p1, X1!144) | (~ip(uri_ex_p1)) | (~ip(X1!144)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y)))))))))) <=> ((~![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_p1, X1!144) | (~ip(uri_ex_p1)) | (~ip(X1!144)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))))))))))),
% 6.47/6.64 inference(rewrite,[status(thm)],[])).
% 6.47/6.64 tff(69,plain,
% 6.47/6.64 ((~((~(iext(uri_rdfs_range, uri_ex_p1, X1!144) | (~ip(X1!144)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))))))))) <=> (~((~(iext(uri_rdfs_range, uri_ex_p1, X1!144) | (~ip(uri_ex_p1)) | (~ip(X1!144)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y)))))))))),
% 6.47/6.64 inference(rewrite,[status(thm)],[])).
% 6.47/6.64 tff(70,plain,
% 6.47/6.64 (((~![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_p1, X1!144) | (~ip(X1!144)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y)))))))))) <=> ((~![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_p1, X1!144) | (~ip(uri_ex_p1)) | (~ip(X1!144)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))))))))))),
% 6.47/6.64 inference(monotonicity,[status(thm)],[69])).
% 6.47/6.64 tff(71,plain,
% 6.47/6.64 (((~![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_p1, X1!144) | (~ip(X1!144)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y)))))))))) <=> ((~![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_p1, X1!144) | (~ip(uri_ex_p1)) | (~ip(X1!144)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))))))))))),
% 6.48/6.64 inference(transitivity,[status(thm)],[70, 68])).
% 6.48/6.64 tff(72,plain,
% 6.48/6.64 ((~![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_p1, X1!144) | (~ip(X1!144)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y)))))))))),
% 6.48/6.64 inference(quant_inst,[status(thm)],[])).
% 6.48/6.64 tff(73,plain,
% 6.48/6.64 ((~![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_p1, X1!144) | (~ip(uri_ex_p1)) | (~ip(X1!144)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y)))))))))),
% 6.48/6.64 inference(modus_ponens,[status(thm)],[72, 71])).
% 6.48/6.64 tff(74,plain,
% 6.48/6.64 (~((~(iext(uri_rdfs_range, uri_ex_p1, X1!144) | (~ip(uri_ex_p1)) | (~ip(X1!144)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))))))))),
% 6.48/6.64 inference(unit_resolution,[status(thm)],[73, 67])).
% 6.48/6.64 tff(75,plain,
% 6.48/6.64 (((~(iext(uri_rdfs_range, uri_ex_p1, X1!144) | (~ip(uri_ex_p1)) | (~ip(X1!144)) | (~((~iext(uri_ex_p1, tptp_fun_X_60(X1!144, uri_ex_p1), tptp_fun_Y_59(X1!144, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_59(X1!144, uri_ex_p1)))))) | (~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y)))))))) | ((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))))))),
% 6.48/6.64 inference(tautology,[status(thm)],[])).
% 6.48/6.64 tff(76,plain,
% 6.48/6.64 ((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y)))))),
% 6.48/6.64 inference(unit_resolution,[status(thm)],[75, 74])).
% 6.48/6.64 tff(77,plain,
% 6.48/6.64 (iext(uri_rdfs_range, uri_ex_p1, X1!144)),
% 6.48/6.64 inference(and_elim,[status(thm)],[7])).
% 6.48/6.64 tff(78,plain,
% 6.48/6.64 ((~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))))))) | (~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y)))))),
% 6.48/6.64 inference(tautology,[status(thm)],[])).
% 6.48/6.64 tff(79,plain,
% 6.48/6.64 ((~((~iext(uri_rdfs_range, uri_ex_p1, X1!144)) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))))))) | (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y)))))),
% 6.48/6.64 inference(unit_resolution,[status(thm)],[78, 77])).
% 6.48/6.64 tff(80,plain,
% 6.48/6.64 (~((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))))),
% 6.48/6.64 inference(unit_resolution,[status(thm)],[79, 76])).
% 6.48/6.64 tff(81,plain,
% 6.48/6.64 (((~ip(X1!144)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y)))) | ![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))),
% 6.48/6.64 inference(tautology,[status(thm)],[])).
% 6.48/6.64 tff(82,plain,
% 6.48/6.64 (![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))),
% 6.48/6.64 inference(unit_resolution,[status(thm)],[81, 80])).
% 6.48/6.64 tff(83,plain,
% 6.48/6.64 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))))))),
% 6.48/6.64 inference(bind,[status(th)],[])).
% 6.48/6.64 tff(84,plain,
% 6.48/6.64 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))),
% 6.48/6.64 inference(quant_intro,[status(thm)],[83])).
% 6.48/6.64 tff(85,plain,
% 6.48/6.64 (^[P1: $i, P2: $i] : refl((~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))))),
% 6.48/6.64 inference(bind,[status(th)],[])).
% 6.48/6.64 tff(86,plain,
% 6.48/6.64 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 6.48/6.64 inference(quant_intro,[status(thm)],[85])).
% 6.48/6.64 tff(87,plain,
% 6.48/6.64 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))))),
% 6.48/6.64 inference(bind,[status(th)],[])).
% 6.48/6.64 tff(88,plain,
% 6.48/6.64 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 6.48/6.64 inference(quant_intro,[status(thm)],[87])).
% 6.48/6.64 tff(89,plain,
% 6.48/6.64 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 6.48/6.64 inference(transitivity,[status(thm)],[88, 86])).
% 6.48/6.64 tff(90,plain,
% 6.48/6.64 (^[P1: $i, P2: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) <=> ((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))), rewrite((iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))) <=> (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))), ((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) <=> (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))), rewrite((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))), ((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))))),
% 6.48/6.65 inference(bind,[status(th)],[])).
% 6.48/6.65 tff(91,plain,
% 6.48/6.65 (![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 6.48/6.65 inference(quant_intro,[status(thm)],[90])).
% 6.48/6.65 tff(92,plain,
% 6.48/6.65 (^[P1: $i, P2: $i] : rewrite((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))) <=> (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))),
% 6.48/6.65 inference(bind,[status(th)],[])).
% 6.48/6.65 tff(93,plain,
% 6.48/6.65 (![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))) <=> ![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))),
% 6.48/6.65 inference(quant_intro,[status(thm)],[92])).
% 6.48/6.65 tff(94,plain,
% 6.48/6.65 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) <=> ![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 6.48/6.65 inference(rewrite,[status(thm)],[])).
% 6.48/6.65 tff(95,plain,
% 6.48/6.65 (^[P1: $i, P2: $i] : rewrite((iext(uri_rdfs_subPropertyOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) => iext(P2, X, Y)))) <=> (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))),
% 6.48/6.65 inference(bind,[status(th)],[])).
% 6.48/6.65 tff(96,plain,
% 6.48/6.65 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) => iext(P2, X, Y)))) <=> ![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 6.48/6.65 inference(quant_intro,[status(thm)],[95])).
% 6.48/6.65 tff(97,axiom,(![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) => iext(P2, X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_subpropertyof')).
% 6.48/6.65 tff(98,plain,
% 6.48/6.65 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[97, 96])).
% 6.48/6.65 tff(99,plain,
% 6.48/6.65 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[98, 94])).
% 6.48/6.65 tff(100,plain,(
% 6.48/6.65 ![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))),
% 6.48/6.65 inference(skolemize,[status(sab)],[99])).
% 6.48/6.65 tff(101,plain,
% 6.48/6.65 (![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[100, 93])).
% 6.48/6.65 tff(102,plain,
% 6.48/6.65 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[101, 91])).
% 6.48/6.65 tff(103,plain,
% 6.48/6.65 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[102, 89])).
% 6.48/6.65 tff(104,plain,
% 6.48/6.65 (![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[103, 84])).
% 6.48/6.65 tff(105,plain,
% 6.48/6.65 ((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2)) | (~((~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p2, X, Y)))))))))),
% 6.48/6.65 inference(quant_inst,[status(thm)],[])).
% 6.48/6.65 tff(106,plain,
% 6.48/6.65 (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2)) | (~((~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p2, X, Y))))))))),
% 6.48/6.65 inference(unit_resolution,[status(thm)],[105, 104])).
% 6.48/6.65 tff(107,plain,
% 6.48/6.65 (((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2)) | (~((~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p2, X, Y)))))))) | (iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)))))),
% 6.48/6.65 inference(tautology,[status(thm)],[])).
% 6.48/6.65 tff(108,plain,
% 6.48/6.65 (iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))))),
% 6.48/6.65 inference(unit_resolution,[status(thm)],[107, 106])).
% 6.48/6.65 tff(109,plain,
% 6.48/6.65 (iext(uri_ex_p1, uri_ex_w, uri_ex_u)),
% 6.48/6.65 inference(and_elim,[status(thm)],[7])).
% 6.48/6.65 tff(110,plain,
% 6.48/6.65 (^[S: $i, P: $i, O: $i] : refl((ip(P) | (~iext(P, S, O))) <=> (ip(P) | (~iext(P, S, O))))),
% 6.48/6.65 inference(bind,[status(th)],[])).
% 6.48/6.65 tff(111,plain,
% 6.48/6.65 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O))) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 6.48/6.65 inference(quant_intro,[status(thm)],[110])).
% 6.48/6.65 tff(112,plain,
% 6.48/6.65 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O))) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 6.48/6.65 inference(rewrite,[status(thm)],[])).
% 6.48/6.65 tff(113,plain,
% 6.48/6.65 (^[S: $i, P: $i, O: $i] : rewrite((iext(P, S, O) => ip(P)) <=> (ip(P) | (~iext(P, S, O))))),
% 6.48/6.65 inference(bind,[status(th)],[])).
% 6.48/6.65 tff(114,plain,
% 6.48/6.65 (![S: $i, P: $i, O: $i] : (iext(P, S, O) => ip(P)) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 6.48/6.65 inference(quant_intro,[status(thm)],[113])).
% 6.48/6.65 tff(115,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')).
% 6.48/6.65 tff(116,plain,
% 6.48/6.65 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[115, 114])).
% 6.48/6.65 tff(117,plain,
% 6.48/6.65 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[116, 112])).
% 6.48/6.65 tff(118,plain,(
% 6.48/6.65 ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 6.48/6.65 inference(skolemize,[status(sab)],[117])).
% 6.48/6.65 tff(119,plain,
% 6.48/6.65 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[118, 111])).
% 6.48/6.65 tff(120,plain,
% 6.48/6.65 (((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p1) | (~iext(uri_ex_p1, uri_ex_w, uri_ex_u)))) <=> ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p1) | (~iext(uri_ex_p1, uri_ex_w, uri_ex_u)))),
% 6.48/6.65 inference(rewrite,[status(thm)],[])).
% 6.48/6.65 tff(121,plain,
% 6.48/6.65 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p1) | (~iext(uri_ex_p1, uri_ex_w, uri_ex_u)))),
% 6.48/6.65 inference(quant_inst,[status(thm)],[])).
% 6.48/6.65 tff(122,plain,
% 6.48/6.65 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p1) | (~iext(uri_ex_p1, uri_ex_w, uri_ex_u))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[121, 120])).
% 6.48/6.65 tff(123,plain,
% 6.48/6.65 (ip(uri_ex_p1)),
% 6.48/6.65 inference(unit_resolution,[status(thm)],[122, 119, 109])).
% 6.48/6.65 tff(124,plain,
% 6.48/6.65 (iext(uri_ex_p2, uri_ex_w, uri_ex_u)),
% 6.48/6.65 inference(and_elim,[status(thm)],[7])).
% 6.48/6.65 tff(125,plain,
% 6.48/6.65 (((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p2) | (~iext(uri_ex_p2, uri_ex_w, uri_ex_u)))) <=> ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p2) | (~iext(uri_ex_p2, uri_ex_w, uri_ex_u)))),
% 6.48/6.65 inference(rewrite,[status(thm)],[])).
% 6.48/6.65 tff(126,plain,
% 6.48/6.65 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p2) | (~iext(uri_ex_p2, uri_ex_w, uri_ex_u)))),
% 6.48/6.65 inference(quant_inst,[status(thm)],[])).
% 6.48/6.65 tff(127,plain,
% 6.48/6.65 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p2) | (~iext(uri_ex_p2, uri_ex_w, uri_ex_u))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[126, 125])).
% 6.48/6.65 tff(128,plain,
% 6.48/6.65 (ip(uri_ex_p2)),
% 6.48/6.65 inference(unit_resolution,[status(thm)],[127, 119, 124])).
% 6.48/6.65 tff(129,plain,
% 6.48/6.65 ((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2)) <=> (~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2))),
% 6.48/6.65 inference(rewrite,[status(thm)],[])).
% 6.48/6.65 tff(130,axiom,(~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion_rdfbased_sem_rdfsext_subprop_ext')).
% 6.48/6.65 tff(131,plain,
% 6.48/6.65 (~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2)),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[130, 129])).
% 6.48/6.65 tff(132,plain,
% 6.48/6.65 ((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)))))) | iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))))),
% 6.48/6.65 inference(tautology,[status(thm)],[])).
% 6.48/6.65 tff(133,plain,
% 6.48/6.65 ((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p2) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)))))) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))))),
% 6.48/6.65 inference(unit_resolution,[status(thm)],[132, 131])).
% 6.48/6.65 tff(134,plain,
% 6.48/6.65 (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)))),
% 6.48/6.65 inference(unit_resolution,[status(thm)],[133, 128, 123, 108])).
% 6.48/6.65 tff(135,plain,
% 6.48/6.65 (((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))),
% 6.48/6.65 inference(tautology,[status(thm)],[])).
% 6.48/6.65 tff(136,plain,
% 6.48/6.65 (iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))),
% 6.48/6.65 inference(unit_resolution,[status(thm)],[135, 134])).
% 6.48/6.65 tff(137,plain,
% 6.48/6.65 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))) | ((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))) | (~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)))),
% 6.48/6.65 inference(rewrite,[status(thm)],[])).
% 6.48/6.65 tff(138,plain,
% 6.48/6.65 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))) | ((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)))),
% 6.48/6.65 inference(quant_inst,[status(thm)],[])).
% 6.48/6.65 tff(139,plain,
% 6.48/6.65 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X1!144, Y))) | (~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | icext(X1!144, tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))),
% 6.48/6.65 inference(modus_ponens,[status(thm)],[138, 137])).
% 6.48/6.65 tff(140,plain,
% 6.48/6.65 (icext(X1!144, tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))),
% 6.48/6.65 inference(unit_resolution,[status(thm)],[139, 136, 82])).
% 6.48/6.65 tff(141,plain,
% 6.48/6.65 ((~(icext(X1!144, tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)) <=> (tptp_fun_Y_62(uri_ex_p2, uri_ex_p1) = uri_ex_u))) | (~icext(X1!144, tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | (tptp_fun_Y_62(uri_ex_p2, uri_ex_p1) = uri_ex_u)),
% 6.48/6.65 inference(tautology,[status(thm)],[])).
% 6.48/6.65 tff(142,plain,
% 6.48/6.65 ((~(icext(X1!144, tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)) <=> (tptp_fun_Y_62(uri_ex_p2, uri_ex_p1) = uri_ex_u))) | (tptp_fun_Y_62(uri_ex_p2, uri_ex_p1) = uri_ex_u)),
% 6.48/6.65 inference(unit_resolution,[status(thm)],[141, 140])).
% 6.48/6.65 tff(143,plain,
% 6.48/6.65 (tptp_fun_Y_62(uri_ex_p2, uri_ex_p1) = uri_ex_u),
% 6.48/6.65 inference(unit_resolution,[status(thm)],[142, 45])).
% 6.48/6.65 tff(144,plain,
% 6.48/6.65 (iext(uri_rdf_rest, X3!142, uri_rdf_nil)),
% 6.48/6.65 inference(and_elim,[status(thm)],[7])).
% 6.48/6.65 tff(145,plain,
% 6.48/6.65 (iext(uri_rdf_first, X3!142, uri_ex_w)),
% 6.48/6.66 inference(and_elim,[status(thm)],[7])).
% 6.48/6.66 tff(146,plain,
% 6.48/6.66 (((~![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, X3!142, uri_ex_w)) | (~iext(uri_rdf_rest, X3!142, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!140, X3!142) | (~ic(X0!140)) | ((~icext(X0!140, tptp_fun_X_8(uri_ex_w, X0!140))) <=> (tptp_fun_X_8(uri_ex_w, X0!140) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, X0!140, X3!142)) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w))))))))))) <=> ((~![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, X3!142, uri_ex_w)) | (~iext(uri_rdf_rest, X3!142, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!140, X3!142) | (~ic(X0!140)) | ((~icext(X0!140, tptp_fun_X_8(uri_ex_w, X0!140))) <=> (tptp_fun_X_8(uri_ex_w, X0!140) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, X0!140, X3!142)) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w))))))))))),
% 6.48/6.66 inference(rewrite,[status(thm)],[])).
% 6.48/6.66 tff(147,plain,
% 6.48/6.66 ((~![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, X3!142, uri_ex_w)) | (~iext(uri_rdf_rest, X3!142, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!140, X3!142) | (~ic(X0!140)) | ((~icext(X0!140, tptp_fun_X_8(uri_ex_w, X0!140))) <=> (tptp_fun_X_8(uri_ex_w, X0!140) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, X0!140, X3!142)) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w))))))))))),
% 6.48/6.66 inference(quant_inst,[status(thm)],[])).
% 6.48/6.66 tff(148,plain,
% 6.48/6.66 ((~![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, X3!142, uri_ex_w)) | (~iext(uri_rdf_rest, X3!142, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!140, X3!142) | (~ic(X0!140)) | ((~icext(X0!140, tptp_fun_X_8(uri_ex_w, X0!140))) <=> (tptp_fun_X_8(uri_ex_w, X0!140) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, X0!140, X3!142)) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w)))))))))),
% 6.48/6.66 inference(modus_ponens,[status(thm)],[147, 146])).
% 6.48/6.66 tff(149,plain,
% 6.48/6.66 (~((~(iext(uri_owl_oneOf, X0!140, X3!142) | (~ic(X0!140)) | ((~icext(X0!140, tptp_fun_X_8(uri_ex_w, X0!140))) <=> (tptp_fun_X_8(uri_ex_w, X0!140) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, X0!140, X3!142)) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w))))))))),
% 6.48/6.66 inference(unit_resolution,[status(thm)],[148, 31, 145, 144])).
% 6.48/6.66 tff(150,plain,
% 6.48/6.66 (((~(iext(uri_owl_oneOf, X0!140, X3!142) | (~ic(X0!140)) | ((~icext(X0!140, tptp_fun_X_8(uri_ex_w, X0!140))) <=> (tptp_fun_X_8(uri_ex_w, X0!140) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, X0!140, X3!142)) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w)))))))) | ((~iext(uri_owl_oneOf, X0!140, X3!142)) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w))))))),
% 6.48/6.66 inference(tautology,[status(thm)],[])).
% 6.48/6.66 tff(151,plain,
% 6.48/6.66 ((~iext(uri_owl_oneOf, X0!140, X3!142)) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w)))))),
% 6.48/6.66 inference(unit_resolution,[status(thm)],[150, 149])).
% 6.48/6.66 tff(152,plain,
% 6.48/6.66 (iext(uri_owl_oneOf, X0!140, X3!142)),
% 6.48/6.66 inference(and_elim,[status(thm)],[7])).
% 6.48/6.66 tff(153,plain,
% 6.48/6.66 ((~((~iext(uri_owl_oneOf, X0!140, X3!142)) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w))))))) | (~iext(uri_owl_oneOf, X0!140, X3!142)) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w)))))),
% 6.48/6.66 inference(tautology,[status(thm)],[])).
% 6.48/6.66 tff(154,plain,
% 6.48/6.66 ((~((~iext(uri_owl_oneOf, X0!140, X3!142)) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w))))))) | (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w)))))),
% 6.48/6.66 inference(unit_resolution,[status(thm)],[153, 152])).
% 6.48/6.66 tff(155,plain,
% 6.48/6.66 (~((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w))))),
% 6.48/6.66 inference(unit_resolution,[status(thm)],[154, 151])).
% 6.48/6.66 tff(156,plain,
% 6.48/6.66 (((~ic(X0!140)) | (~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w)))) | ![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w))),
% 6.48/6.66 inference(tautology,[status(thm)],[])).
% 6.48/6.66 tff(157,plain,
% 6.48/6.66 (![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w))),
% 6.48/6.66 inference(unit_resolution,[status(thm)],[156, 155])).
% 6.48/6.66 tff(158,plain,
% 6.48/6.66 ((~![X: $i] : (icext(X0!140, X) <=> (X = uri_ex_w))) | (icext(X0!140, tptp_fun_X_63(uri_ex_p2, uri_ex_p1)) <=> (tptp_fun_X_63(uri_ex_p2, uri_ex_p1) = uri_ex_w))),
% 6.48/6.66 inference(quant_inst,[status(thm)],[])).
% 6.48/6.66 tff(159,plain,
% 6.48/6.66 (icext(X0!140, tptp_fun_X_63(uri_ex_p2, uri_ex_p1)) <=> (tptp_fun_X_63(uri_ex_p2, uri_ex_p1) = uri_ex_w)),
% 6.48/6.66 inference(unit_resolution,[status(thm)],[158, 157])).
% 6.48/6.66 tff(160,plain,
% 6.48/6.66 (^[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))))))))))),
% 6.48/6.66 inference(bind,[status(th)],[])).
% 6.48/6.66 tff(161,plain,
% 6.48/6.66 (![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)))))))))),
% 6.48/6.66 inference(quant_intro,[status(thm)],[160])).
% 6.48/6.66 tff(162,plain,
% 6.48/6.66 (^[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)))))))))),
% 6.48/6.66 inference(bind,[status(th)],[])).
% 6.48/6.66 tff(163,plain,
% 6.48/6.66 (![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))))))))),
% 6.48/6.66 inference(quant_intro,[status(thm)],[162])).
% 6.48/6.66 tff(164,plain,
% 6.48/6.66 (^[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)))))))))),
% 6.48/6.66 inference(bind,[status(th)],[])).
% 6.48/6.66 tff(165,plain,
% 6.48/6.66 (![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))))))))),
% 6.48/6.66 inference(quant_intro,[status(thm)],[164])).
% 6.48/6.66 tff(166,plain,
% 6.48/6.66 (![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))))))))),
% 6.48/6.66 inference(transitivity,[status(thm)],[165, 163])).
% 6.48/6.66 tff(167,plain,
% 6.48/6.66 (^[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))))))))))),
% 6.48/6.66 inference(bind,[status(th)],[])).
% 6.48/6.66 tff(168,plain,
% 6.48/6.66 (![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))))))))),
% 6.48/6.66 inference(quant_intro,[status(thm)],[167])).
% 6.48/6.66 tff(169,plain,
% 6.48/6.66 (^[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)))))))),
% 6.48/6.66 inference(bind,[status(th)],[])).
% 6.48/6.66 tff(170,plain,
% 6.48/6.66 (![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))))))),
% 6.48/6.66 inference(quant_intro,[status(thm)],[169])).
% 6.48/6.66 tff(171,plain,
% 6.48/6.66 (![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))))),
% 6.48/6.66 inference(rewrite,[status(thm)],[])).
% 6.48/6.66 tff(172,plain,
% 6.48/6.66 (^[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)))))),
% 6.48/6.66 inference(bind,[status(th)],[])).
% 6.48/6.66 tff(173,plain,
% 6.48/6.66 (![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))))),
% 6.48/6.66 inference(quant_intro,[status(thm)],[172])).
% 6.48/6.66 tff(174,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')).
% 6.48/6.66 tff(175,plain,
% 6.48/6.66 (![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))))),
% 6.48/6.66 inference(modus_ponens,[status(thm)],[174, 173])).
% 6.48/6.66 tff(176,plain,
% 6.48/6.66 (![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))))),
% 6.48/6.66 inference(modus_ponens,[status(thm)],[175, 171])).
% 6.48/6.66 tff(177,plain,(
% 6.48/6.66 ![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)))))))),
% 6.48/6.66 inference(skolemize,[status(sab)],[176])).
% 6.48/6.66 tff(178,plain,
% 6.48/6.66 (![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))))))),
% 6.48/6.67 inference(modus_ponens,[status(thm)],[177, 170])).
% 6.48/6.67 tff(179,plain,
% 6.48/6.67 (![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))))))))),
% 6.48/6.67 inference(modus_ponens,[status(thm)],[178, 168])).
% 6.48/6.67 tff(180,plain,
% 6.48/6.67 (![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))))))))),
% 6.48/6.67 inference(modus_ponens,[status(thm)],[179, 166])).
% 6.48/6.67 tff(181,plain,
% 6.48/6.67 (![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)))))))))),
% 6.48/6.67 inference(modus_ponens,[status(thm)],[180, 161])).
% 6.48/6.67 tff(182,plain,
% 6.48/6.67 (((~![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_p1, X0!140) | (~ip(uri_ex_p1)) | (~ic(X0!140)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X)))))))))) <=> ((~![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_p1, X0!140) | (~ip(uri_ex_p1)) | (~ic(X0!140)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))))))))))),
% 6.48/6.67 inference(rewrite,[status(thm)],[])).
% 6.48/6.67 tff(183,plain,
% 6.48/6.67 ((~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!140) | (~ic(X0!140)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))))))))) <=> (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!140) | (~ip(uri_ex_p1)) | (~ic(X0!140)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X)))))))))),
% 6.48/6.67 inference(rewrite,[status(thm)],[])).
% 6.48/6.67 tff(184,plain,
% 6.48/6.67 (((~![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_p1, X0!140) | (~ic(X0!140)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X)))))))))) <=> ((~![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_p1, X0!140) | (~ip(uri_ex_p1)) | (~ic(X0!140)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))))))))))),
% 6.48/6.67 inference(monotonicity,[status(thm)],[183])).
% 6.48/6.67 tff(185,plain,
% 6.48/6.67 (((~![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_p1, X0!140) | (~ic(X0!140)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X)))))))))) <=> ((~![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_p1, X0!140) | (~ip(uri_ex_p1)) | (~ic(X0!140)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))))))))))),
% 6.48/6.67 inference(transitivity,[status(thm)],[184, 182])).
% 6.48/6.67 tff(186,plain,
% 6.48/6.67 ((~![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_p1, X0!140) | (~ic(X0!140)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X)))))))))),
% 6.48/6.67 inference(quant_inst,[status(thm)],[])).
% 6.48/6.67 tff(187,plain,
% 6.48/6.67 ((~![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_p1, X0!140) | (~ip(uri_ex_p1)) | (~ic(X0!140)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X)))))))))),
% 6.48/6.67 inference(modus_ponens,[status(thm)],[186, 185])).
% 6.48/6.67 tff(188,plain,
% 6.48/6.67 (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!140) | (~ip(uri_ex_p1)) | (~ic(X0!140)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))))))))),
% 6.48/6.67 inference(unit_resolution,[status(thm)],[187, 181])).
% 6.48/6.67 tff(189,plain,
% 6.48/6.67 (((~(iext(uri_rdfs_domain, uri_ex_p1, X0!140) | (~ip(uri_ex_p1)) | (~ic(X0!140)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!140, uri_ex_p1), tptp_fun_Y_57(X0!140, uri_ex_p1))) | icext(X0!140, tptp_fun_X_58(X0!140, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X)))))))) | ((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))))))),
% 6.48/6.67 inference(tautology,[status(thm)],[])).
% 6.48/6.67 tff(190,plain,
% 6.48/6.67 ((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X)))))),
% 6.48/6.67 inference(unit_resolution,[status(thm)],[189, 188])).
% 6.48/6.67 tff(191,plain,
% 6.48/6.67 (iext(uri_rdfs_domain, uri_ex_p1, X0!140)),
% 6.48/6.67 inference(and_elim,[status(thm)],[7])).
% 6.48/6.67 tff(192,plain,
% 6.48/6.67 ((~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))))))) | (~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X)))))),
% 6.48/6.67 inference(tautology,[status(thm)],[])).
% 6.48/6.67 tff(193,plain,
% 6.48/6.67 ((~((~iext(uri_rdfs_domain, uri_ex_p1, X0!140)) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))))))) | (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X)))))),
% 6.48/6.67 inference(unit_resolution,[status(thm)],[192, 191])).
% 6.48/6.67 tff(194,plain,
% 6.48/6.67 (~((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))))),
% 6.48/6.67 inference(unit_resolution,[status(thm)],[193, 190])).
% 6.48/6.67 tff(195,plain,
% 6.48/6.67 (((~ic(X0!140)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X)))) | ![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))),
% 6.48/6.67 inference(tautology,[status(thm)],[])).
% 6.48/6.67 tff(196,plain,
% 6.48/6.67 (![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))),
% 6.48/6.67 inference(unit_resolution,[status(thm)],[195, 194])).
% 6.48/6.67 tff(197,plain,
% 6.48/6.67 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))) | ((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | icext(X0!140, tptp_fun_X_63(uri_ex_p2, uri_ex_p1)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))) | (~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | icext(X0!140, tptp_fun_X_63(uri_ex_p2, uri_ex_p1)))),
% 6.48/6.67 inference(rewrite,[status(thm)],[])).
% 6.48/6.67 tff(198,plain,
% 6.48/6.67 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))) | ((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | icext(X0!140, tptp_fun_X_63(uri_ex_p2, uri_ex_p1)))),
% 6.48/6.67 inference(quant_inst,[status(thm)],[])).
% 6.48/6.67 tff(199,plain,
% 6.48/6.67 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!140, X))) | (~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | icext(X0!140, tptp_fun_X_63(uri_ex_p2, uri_ex_p1))),
% 6.48/6.67 inference(modus_ponens,[status(thm)],[198, 197])).
% 6.48/6.67 tff(200,plain,
% 6.48/6.67 (icext(X0!140, tptp_fun_X_63(uri_ex_p2, uri_ex_p1))),
% 6.48/6.67 inference(unit_resolution,[status(thm)],[199, 136, 196])).
% 6.48/6.67 tff(201,plain,
% 6.48/6.67 ((~(icext(X0!140, tptp_fun_X_63(uri_ex_p2, uri_ex_p1)) <=> (tptp_fun_X_63(uri_ex_p2, uri_ex_p1) = uri_ex_w))) | (~icext(X0!140, tptp_fun_X_63(uri_ex_p2, uri_ex_p1))) | (tptp_fun_X_63(uri_ex_p2, uri_ex_p1) = uri_ex_w)),
% 6.48/6.67 inference(tautology,[status(thm)],[])).
% 6.48/6.67 tff(202,plain,
% 6.48/6.67 ((~(icext(X0!140, tptp_fun_X_63(uri_ex_p2, uri_ex_p1)) <=> (tptp_fun_X_63(uri_ex_p2, uri_ex_p1) = uri_ex_w))) | (tptp_fun_X_63(uri_ex_p2, uri_ex_p1) = uri_ex_w)),
% 6.53/6.71 inference(unit_resolution,[status(thm)],[201, 200])).
% 6.53/6.71 tff(203,plain,
% 6.53/6.71 (tptp_fun_X_63(uri_ex_p2, uri_ex_p1) = uri_ex_w),
% 6.53/6.71 inference(unit_resolution,[status(thm)],[202, 159])).
% 6.53/6.71 tff(204,plain,
% 6.53/6.71 (iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)) <=> iext(uri_ex_p2, uri_ex_w, uri_ex_u)),
% 6.53/6.71 inference(monotonicity,[status(thm)],[203, 143])).
% 6.53/6.71 tff(205,plain,
% 6.53/6.71 (iext(uri_ex_p2, uri_ex_w, uri_ex_u) <=> iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))),
% 6.53/6.71 inference(symmetry,[status(thm)],[204])).
% 6.53/6.71 tff(206,plain,
% 6.53/6.71 (iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))),
% 6.53/6.71 inference(modus_ponens,[status(thm)],[124, 205])).
% 6.53/6.71 tff(207,plain,
% 6.53/6.71 (((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))) | (~iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1)))),
% 6.53/6.71 inference(tautology,[status(thm)],[])).
% 6.53/6.71 tff(208,plain,
% 6.53/6.71 (~iext(uri_ex_p2, tptp_fun_X_63(uri_ex_p2, uri_ex_p1), tptp_fun_Y_62(uri_ex_p2, uri_ex_p1))),
% 6.53/6.71 inference(unit_resolution,[status(thm)],[207, 134])).
% 6.53/6.71 tff(209,plain,
% 6.53/6.71 ($false),
% 6.53/6.71 inference(unit_resolution,[status(thm)],[208, 206])).
% 6.53/6.71 % SZS output end Proof
%------------------------------------------------------------------------------