TSTP Solution File: SWB079+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB079+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 0.62s 0.70s
% Output : Proof 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWB079+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 20:28:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.62/0.70 % SZS status Theorem
% 0.62/0.70 % SZS output start Proof
% 0.62/0.70 tff(uri_ex_w_type, type, (
% 0.62/0.70 uri_ex_w: $i)).
% 0.62/0.70 tff(tptp_fun_X_61_type, type, (
% 0.62/0.70 tptp_fun_X_61: ( $i * $i ) > $i)).
% 0.62/0.70 tff(uri_ex_c1_type, type, (
% 0.62/0.70 uri_ex_c1: $i)).
% 0.62/0.70 tff(uri_ex_c2_type, type, (
% 0.62/0.70 uri_ex_c2: $i)).
% 0.62/0.70 tff(uri_ex_u_type, type, (
% 0.62/0.70 uri_ex_u: $i)).
% 0.62/0.70 tff(icext_type, type, (
% 0.62/0.70 icext: ( $i * $i ) > $o)).
% 0.62/0.70 tff(ic_type, type, (
% 0.62/0.70 ic: $i > $o)).
% 0.62/0.70 tff(iext_type, type, (
% 0.62/0.70 iext: ( $i * $i * $i ) > $o)).
% 0.62/0.70 tff(tptp_fun_X0_142_type, type, (
% 0.62/0.70 tptp_fun_X0_142: $i)).
% 0.62/0.70 tff(uri_owl_oneOf_type, type, (
% 0.62/0.70 uri_owl_oneOf: $i)).
% 0.62/0.70 tff(tptp_fun_X_9_type, type, (
% 0.62/0.70 tptp_fun_X_9: ( $i * $i * $i ) > $i)).
% 0.62/0.70 tff(uri_rdf_nil_type, type, (
% 0.62/0.70 uri_rdf_nil: $i)).
% 0.62/0.70 tff(tptp_fun_X1_141_type, type, (
% 0.62/0.70 tptp_fun_X1_141: $i)).
% 0.62/0.70 tff(uri_rdf_rest_type, type, (
% 0.62/0.70 uri_rdf_rest: $i)).
% 0.62/0.70 tff(uri_rdf_first_type, type, (
% 0.62/0.70 uri_rdf_first: $i)).
% 0.62/0.70 tff(tptp_fun_X2_140_type, type, (
% 0.62/0.70 tptp_fun_X2_140: $i)).
% 0.62/0.70 tff(uri_rdfs_subClassOf_type, type, (
% 0.62/0.70 uri_rdfs_subClassOf: $i)).
% 0.62/0.70 tff(uri_rdf_List_type, type, (
% 0.62/0.70 uri_rdf_List: $i)).
% 0.62/0.70 tff(tptp_fun_X_8_type, type, (
% 0.62/0.70 tptp_fun_X_8: ( $i * $i ) > $i)).
% 0.62/0.70 tff(1,plain,
% 0.62/0.70 (?[X0: $i, X1: $i, X2: $i] : (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X1, uri_ex_u) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> ?[X0: $i, X1: $i, X2: $i] : (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X1, uri_ex_u) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(2,plain,
% 0.62/0.70 (^[X0: $i, X1: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) <=> (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1))), ((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) <=> ((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) <=> (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2))), ((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) <=> (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2)))), (((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)) <=> ((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)) <=> (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w))), (((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)) <=> (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w)))), ((((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> ((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w)) & iext(uri_rdf_rest, X2, uri_rdf_nil)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil))), ((((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil)))), (((((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X1, uri_ex_u)) <=> ((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X1, uri_ex_u)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X1, uri_ex_u)) <=> (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X1, uri_ex_u))), (((((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X1, uri_ex_u)) <=> (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X1, uri_ex_u)))), ((((((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X1, uri_ex_u)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> ((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X1, uri_ex_u)) & iext(uri_rdf_rest, X1, uri_rdf_nil)))), rewrite(((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X1, uri_ex_u)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X1, uri_ex_u) & iext(uri_rdf_rest, X1, uri_rdf_nil))), ((((((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X1, uri_ex_u)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X1, uri_ex_u) & iext(uri_rdf_rest, X1, uri_rdf_nil))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(3,plain,
% 0.62/0.71 (?[X0: $i, X1: $i, X2: $i] : (((((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X1, uri_ex_u)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> ?[X0: $i, X1: $i, X2: $i] : (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X1, uri_ex_u) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[2])).
% 0.62/0.71 tff(4,axiom,(?[X0: $i, X1: $i, X2: $i] : (((((((iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_owl_oneOf, uri_ex_c1, X2)) & iext(uri_rdf_first, X2, uri_ex_w)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_rdf_first, X1, uri_ex_u)) & iext(uri_rdf_rest, X1, uri_rdf_nil))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','premise_rdfbased_sem_rdfsext_subclass_ext')).
% 0.62/0.71 tff(5,plain,
% 0.62/0.71 (?[X0: $i, X1: $i, X2: $i] : (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X1, uri_ex_u) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.62/0.71 tff(6,plain,
% 0.62/0.71 (?[X0: $i, X1: $i, X2: $i] : (iext(uri_owl_oneOf, uri_ex_c2, X0) & iext(uri_rdf_first, X0, uri_ex_w) & iext(uri_rdf_rest, X0, X1) & iext(uri_owl_oneOf, uri_ex_c1, X2) & iext(uri_rdf_first, X2, uri_ex_w) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_rdf_first, X1, uri_ex_u) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.62/0.71 tff(7,plain,(
% 0.62/0.71 iext(uri_owl_oneOf, uri_ex_c2, X0!142) & iext(uri_rdf_first, X0!142, uri_ex_w) & iext(uri_rdf_rest, X0!142, X1!141) & iext(uri_owl_oneOf, uri_ex_c1, X2!140) & iext(uri_rdf_first, X2!140, uri_ex_w) & iext(uri_rdf_rest, X2!140, uri_rdf_nil) & iext(uri_rdf_first, X1!141, uri_ex_u) & iext(uri_rdf_rest, X1!141, uri_rdf_nil)),
% 0.62/0.71 inference(skolemize,[status(sab)],[6])).
% 0.62/0.71 tff(8,plain,
% 0.62/0.71 (iext(uri_rdf_rest, X1!141, uri_rdf_nil)),
% 0.62/0.71 inference(and_elim,[status(thm)],[7])).
% 0.62/0.71 tff(9,plain,
% 0.62/0.71 (iext(uri_rdf_first, X1!141, uri_ex_u)),
% 0.62/0.71 inference(and_elim,[status(thm)],[7])).
% 0.62/0.71 tff(10,plain,
% 0.62/0.71 (iext(uri_rdf_rest, X0!142, X1!141)),
% 0.62/0.71 inference(and_elim,[status(thm)],[7])).
% 0.62/0.71 tff(11,plain,
% 0.62/0.71 (iext(uri_rdf_first, X0!142, uri_ex_w)),
% 0.62/0.71 inference(and_elim,[status(thm)],[7])).
% 0.62/0.71 tff(12,plain,
% 0.62/0.71 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))) <=> (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))))))), (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))))))))), rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))), (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(13,plain,
% 0.62/0.71 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[12])).
% 0.62/0.71 tff(14,plain,
% 0.62/0.71 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : refl(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(15,plain,
% 0.62/0.71 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[14])).
% 0.62/0.71 tff(16,plain,
% 0.62/0.71 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(17,plain,
% 0.62/0.71 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[16])).
% 0.62/0.71 tff(18,plain,
% 0.62/0.71 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))))),
% 0.62/0.71 inference(transitivity,[status(thm)],[17, 15])).
% 0.62/0.71 tff(19,plain,
% 0.62/0.71 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) <=> ((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) <=> (((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))), rewrite((((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))) <=> (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))))), rewrite((((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(20,plain,
% 0.62/0.71 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[19])).
% 0.62/0.71 tff(21,plain,
% 0.62/0.71 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : rewrite(((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_9(A2, A1, Z)) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(22,plain,
% 0.62/0.71 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_9(A2, A1, Z)) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))),
% 0.62/0.72 inference(quant_intro,[status(thm)],[21])).
% 0.62/0.72 tff(23,plain,
% 0.62/0.72 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))),
% 0.62/0.72 inference(rewrite,[status(thm)],[])).
% 0.62/0.72 tff(24,plain,
% 0.62/0.72 (^[Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2))), ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A1) | (X = A2))))) <=> (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))), (((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A1) | (X = A2)))))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))), (((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A1) | (X = A2)))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))))),
% 0.62/0.72 inference(bind,[status(th)],[])).
% 0.62/0.72 tff(25,plain,
% 0.62/0.72 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A1) | (X = A2)))))) <=> ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[24])).
% 0.71/0.72 tff(26,axiom,(![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A1) | (X = A2))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_enum_class_002')).
% 0.71/0.72 tff(27,plain,
% 0.71/0.72 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.71/0.72 tff(28,plain,
% 0.71/0.72 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.71/0.72 tff(29,plain,(
% 0.71/0.72 ![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_9(A2, A1, Z)) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))))),
% 0.71/0.72 inference(skolemize,[status(sab)],[28])).
% 0.71/0.72 tff(30,plain,
% 0.71/0.72 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.71/0.72 tff(31,plain,
% 0.71/0.72 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.71/0.72 tff(32,plain,
% 0.71/0.72 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))))))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.71/0.72 tff(33,plain,
% 0.71/0.72 (![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[32, 13])).
% 0.71/0.72 tff(34,plain,
% 0.71/0.72 (((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, X0!142, uri_ex_w)) | (~iext(uri_rdf_rest, X0!142, X1!141)) | (~iext(uri_rdf_first, X1!141, uri_ex_u)) | (~iext(uri_rdf_rest, X1!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, X0!142) | (~ic(uri_ex_c2)) | ((~icext(uri_ex_c2, tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2))) <=> ((tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_u) | (tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w)))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | (~iext(uri_rdf_first, X0!142, uri_ex_w)) | (~iext(uri_rdf_rest, X0!142, X1!141)) | (~iext(uri_rdf_first, X1!141, uri_ex_u)) | (~iext(uri_rdf_rest, X1!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, X0!142) | (~ic(uri_ex_c2)) | ((~icext(uri_ex_c2, tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2))) <=> ((tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_u) | (tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w)))))))))))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(35,plain,
% 0.71/0.72 ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | ((~iext(uri_rdf_first, X0!142, uri_ex_w)) | (~iext(uri_rdf_rest, X0!142, X1!141)) | (~iext(uri_rdf_first, X1!141, uri_ex_u)) | (~iext(uri_rdf_rest, X1!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, X0!142) | (~ic(uri_ex_c2)) | ((~icext(uri_ex_c2, tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2))) <=> ((tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_u) | (tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w)))))))))))),
% 0.71/0.72 inference(quant_inst,[status(thm)],[])).
% 0.71/0.72 tff(36,plain,
% 0.71/0.72 ((~![Z: $i, S1: $i, A1: $i, S2: $i, A2: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_9(A2, A1, Z))) <=> ((tptp_fun_X_9(A2, A1, Z) = A2) | (tptp_fun_X_9(A2, A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> ((X = A2) | (X = A1)))))))))))) | (~iext(uri_rdf_first, X0!142, uri_ex_w)) | (~iext(uri_rdf_rest, X0!142, X1!141)) | (~iext(uri_rdf_first, X1!141, uri_ex_u)) | (~iext(uri_rdf_rest, X1!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c2, X0!142) | (~ic(uri_ex_c2)) | ((~icext(uri_ex_c2, tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2))) <=> ((tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_u) | (tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w))))))))))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.71/0.72 tff(37,plain,
% 0.71/0.72 (~((~(iext(uri_owl_oneOf, uri_ex_c2, X0!142) | (~ic(uri_ex_c2)) | ((~icext(uri_ex_c2, tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2))) <=> ((tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_u) | (tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w)))))))))),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[36, 33, 11, 10, 9, 8])).
% 0.71/0.72 tff(38,plain,
% 0.71/0.72 (((~(iext(uri_owl_oneOf, uri_ex_c2, X0!142) | (~ic(uri_ex_c2)) | ((~icext(uri_ex_c2, tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2))) <=> ((tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_u) | (tptp_fun_X_9(uri_ex_u, uri_ex_w, uri_ex_c2) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w))))))))) | ((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w)))))))),
% 0.71/0.72 inference(tautology,[status(thm)],[])).
% 0.71/0.72 tff(39,plain,
% 0.71/0.72 ((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w))))))),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.71/0.72 tff(40,plain,
% 0.71/0.72 (iext(uri_owl_oneOf, uri_ex_c2, X0!142)),
% 0.71/0.72 inference(and_elim,[status(thm)],[7])).
% 0.71/0.72 tff(41,plain,
% 0.71/0.72 ((~((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w)))))))) | (~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w))))))),
% 0.71/0.72 inference(tautology,[status(thm)],[])).
% 0.71/0.72 tff(42,plain,
% 0.71/0.72 ((~((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w)))))))) | (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w))))))),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.71/0.72 tff(43,plain,
% 0.71/0.72 (~((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w)))))),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.71/0.72 tff(44,plain,
% 0.71/0.72 (((~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w))))) | ![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w)))),
% 0.71/0.72 inference(tautology,[status(thm)],[])).
% 0.71/0.72 tff(45,plain,
% 0.71/0.72 (![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w)))),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.71/0.72 tff(46,plain,
% 0.71/0.72 ((~![X: $i] : (icext(uri_ex_c2, X) <=> ((X = uri_ex_u) | (X = uri_ex_w)))) | (icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)) <=> ((tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_u) | (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w)))),
% 0.71/0.72 inference(quant_inst,[status(thm)],[])).
% 0.71/0.72 tff(47,plain,
% 0.71/0.72 (icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)) <=> ((tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_u) | (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w))),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.71/0.72 tff(48,plain,
% 0.71/0.72 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(49,plain,
% 0.71/0.72 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[48])).
% 0.71/0.72 tff(50,plain,
% 0.71/0.72 (^[C1: $i, C2: $i] : refl((~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(51,plain,
% 0.71/0.72 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[50])).
% 0.71/0.72 tff(52,plain,
% 0.71/0.72 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(53,plain,
% 0.71/0.72 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[52])).
% 0.71/0.72 tff(54,plain,
% 0.71/0.72 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.71/0.72 inference(transitivity,[status(thm)],[53, 51])).
% 0.71/0.72 tff(55,plain,
% 0.71/0.72 (^[C1: $i, C2: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) <=> ((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))), rewrite((iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))) <=> (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))), ((((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) <=> (((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))), rewrite((((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))), ((((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(56,plain,
% 0.71/0.72 (![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[55])).
% 0.71/0.72 tff(57,plain,
% 0.71/0.72 (^[C1: $i, C2: $i] : rewrite((((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))) <=> (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(58,plain,
% 0.71/0.72 (![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))) <=> ![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[57])).
% 0.71/0.72 tff(59,plain,
% 0.71/0.72 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(60,plain,
% 0.71/0.72 (^[C1: $i, C2: $i] : rewrite((iext(uri_rdfs_subClassOf, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) => icext(C2, X)))) <=> (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(61,plain,
% 0.71/0.72 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) => icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[60])).
% 0.71/0.72 tff(62,axiom,(![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) => icext(C2, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_subclassof')).
% 0.71/0.72 tff(63,plain,
% 0.71/0.72 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.71/0.72 tff(64,plain,
% 0.71/0.72 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.71/0.73 tff(65,plain,(
% 0.71/0.73 ![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))),
% 0.71/0.73 inference(skolemize,[status(sab)],[64])).
% 0.71/0.73 tff(66,plain,
% 0.71/0.73 (![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.71/0.73 tff(67,plain,
% 0.71/0.73 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.71/0.73 tff(68,plain,
% 0.71/0.73 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[67, 54])).
% 0.71/0.73 tff(69,plain,
% 0.71/0.73 (![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[68, 49])).
% 0.71/0.73 tff(70,plain,
% 0.71/0.73 ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | icext(uri_ex_c2, X)))))))))),
% 0.71/0.73 inference(quant_inst,[status(thm)],[])).
% 0.71/0.73 tff(71,plain,
% 0.71/0.73 (~((~(iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | icext(uri_ex_c2, X))))))))),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.71/0.73 tff(72,plain,
% 0.71/0.73 (((~(iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | icext(uri_ex_c2, X)))))))) | (iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)))))),
% 0.71/0.73 inference(tautology,[status(thm)],[])).
% 0.71/0.73 tff(73,plain,
% 0.71/0.73 (iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))))),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.71/0.73 tff(74,plain,
% 0.71/0.73 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(75,plain,
% 0.71/0.73 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[74])).
% 0.71/0.73 tff(76,plain,
% 0.71/0.73 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(77,plain,
% 0.71/0.73 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[76])).
% 0.71/0.73 tff(78,plain,
% 0.71/0.73 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(79,plain,
% 0.71/0.73 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_oneOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(80,plain,
% 0.71/0.73 (![X: $i, Y: $i] : (iext(uri_owl_oneOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[79])).
% 0.71/0.73 tff(81,axiom,(![X: $i, Y: $i] : (iext(uri_owl_oneOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_oneof_ext')).
% 0.71/0.73 tff(82,plain,
% 0.71/0.73 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.71/0.73 tff(83,plain,
% 0.71/0.73 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.71/0.73 tff(84,plain,(
% 0.71/0.73 ![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.71/0.73 inference(skolemize,[status(sab)],[83])).
% 0.71/0.73 tff(85,plain,
% 0.71/0.73 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.71/0.73 tff(86,plain,
% 0.71/0.73 (![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.71/0.73 tff(87,plain,
% 0.71/0.73 (((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!142)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!142)))))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(88,plain,
% 0.71/0.73 ((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!142)))))),
% 0.71/0.73 inference(quant_inst,[status(thm)],[])).
% 0.71/0.73 tff(89,plain,
% 0.71/0.73 ((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_oneOf, uri_ex_c2, X0!142)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!142))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.71/0.73 tff(90,plain,
% 0.71/0.73 (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!142)))),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[89, 86, 40])).
% 0.71/0.73 tff(91,plain,
% 0.71/0.73 (((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!142))) | ic(uri_ex_c2)),
% 0.71/0.73 inference(tautology,[status(thm)],[])).
% 0.71/0.73 tff(92,plain,
% 0.71/0.73 (ic(uri_ex_c2)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.71/0.73 tff(93,plain,
% 0.71/0.73 (iext(uri_owl_oneOf, uri_ex_c1, X2!140)),
% 0.71/0.73 inference(and_elim,[status(thm)],[7])).
% 0.71/0.73 tff(94,plain,
% 0.71/0.73 (((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~icext(uri_rdf_List, X2!140)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~icext(uri_rdf_List, X2!140)))))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(95,plain,
% 0.71/0.73 ((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~icext(uri_rdf_List, X2!140)))))),
% 0.71/0.73 inference(quant_inst,[status(thm)],[])).
% 0.71/0.73 tff(96,plain,
% 0.71/0.73 ((~![X: $i, Y: $i] : ((~iext(uri_owl_oneOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~icext(uri_rdf_List, X2!140))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.71/0.73 tff(97,plain,
% 0.71/0.73 (~((~ic(uri_ex_c1)) | (~icext(uri_rdf_List, X2!140)))),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[96, 86, 93])).
% 0.71/0.73 tff(98,plain,
% 0.71/0.73 (((~ic(uri_ex_c1)) | (~icext(uri_rdf_List, X2!140))) | ic(uri_ex_c1)),
% 0.71/0.73 inference(tautology,[status(thm)],[])).
% 0.71/0.73 tff(99,plain,
% 0.71/0.73 (ic(uri_ex_c1)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.71/0.73 tff(100,plain,
% 0.71/0.73 ((~iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2)) <=> (~iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(101,axiom,(~iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion_rdfbased_sem_rdfsext_subclass_ext')).
% 0.71/0.73 tff(102,plain,
% 0.71/0.73 (~iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.71/0.73 tff(103,plain,
% 0.71/0.73 ((~(iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)))))) | iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))))),
% 0.71/0.73 inference(tautology,[status(thm)],[])).
% 0.71/0.73 tff(104,plain,
% 0.71/0.73 ((~(iext(uri_rdfs_subClassOf, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)))))) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))))),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.71/0.73 tff(105,plain,
% 0.71/0.73 (~((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)))),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[104, 99, 92, 73])).
% 0.71/0.73 tff(106,plain,
% 0.71/0.73 (((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)))),
% 0.71/0.73 inference(tautology,[status(thm)],[])).
% 0.71/0.73 tff(107,plain,
% 0.71/0.73 (~icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.71/0.73 tff(108,plain,
% 0.71/0.73 ((~(icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)) <=> ((tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_u) | (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w)))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)) | (~((tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_u) | (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w)))),
% 0.71/0.73 inference(tautology,[status(thm)],[])).
% 0.71/0.73 tff(109,plain,
% 0.71/0.73 ((~(icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)) <=> ((tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_u) | (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w)))) | (~((tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_u) | (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w)))),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.71/0.73 tff(110,plain,
% 0.71/0.73 (~((tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_u) | (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w))),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[109, 47])).
% 0.71/0.73 tff(111,plain,
% 0.71/0.73 (iext(uri_rdf_rest, X2!140, uri_rdf_nil)),
% 0.71/0.73 inference(and_elim,[status(thm)],[7])).
% 0.71/0.73 tff(112,plain,
% 0.71/0.73 (iext(uri_rdf_first, X2!140, uri_ex_w)),
% 0.71/0.73 inference(and_elim,[status(thm)],[7])).
% 0.71/0.73 tff(113,plain,
% 0.71/0.73 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))))))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(114,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[113])).
% 0.71/0.73 tff(115,plain,
% 0.71/0.73 (^[Z: $i, S1: $i, A1: $i] : refl(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(116,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[115])).
% 0.71/0.73 tff(117,plain,
% 0.71/0.73 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(118,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[117])).
% 0.71/0.73 tff(119,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.71/0.73 inference(transitivity,[status(thm)],[118, 116])).
% 0.71/0.73 tff(120,plain,
% 0.71/0.73 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> ((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))), rewrite((((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))))), rewrite((((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(121,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[120])).
% 0.71/0.73 tff(122,plain,
% 0.71/0.73 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(123,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[122])).
% 0.71/0.73 tff(124,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(125,plain,
% 0.71/0.73 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(monotonicity(rewrite((ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))), ((iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(126,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[125])).
% 0.71/0.73 tff(127,axiom,(![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_enum_class_001')).
% 0.71/0.73 tff(128,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.71/0.73 tff(129,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.71/0.73 tff(130,plain,(
% 0.71/0.73 ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.71/0.73 inference(skolemize,[status(sab)],[129])).
% 0.71/0.73 tff(131,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.71/0.73 tff(132,plain,
% 0.71/0.73 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[131, 121])).
% 0.71/0.74 tff(133,plain,
% 0.71/0.74 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[132, 119])).
% 0.71/0.74 tff(134,plain,
% 0.71/0.74 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[133, 114])).
% 0.71/0.74 tff(135,plain,
% 0.71/0.74 (((~![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!140, uri_ex_w)) | (~iext(uri_rdf_rest, X2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, X2!140) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_8(uri_ex_w, uri_ex_c1))) <=> (tptp_fun_X_8(uri_ex_w, uri_ex_c1) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, 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, X2!140, uri_ex_w)) | (~iext(uri_rdf_rest, X2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, X2!140) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_8(uri_ex_w, uri_ex_c1))) <=> (tptp_fun_X_8(uri_ex_w, uri_ex_c1) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w))))))))))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(136,plain,
% 0.71/0.74 ((~![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!140, uri_ex_w)) | (~iext(uri_rdf_rest, X2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, X2!140) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_8(uri_ex_w, uri_ex_c1))) <=> (tptp_fun_X_8(uri_ex_w, uri_ex_c1) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w))))))))))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(137,plain,
% 0.71/0.74 ((~![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!140, uri_ex_w)) | (~iext(uri_rdf_rest, X2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_c1, X2!140) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_8(uri_ex_w, uri_ex_c1))) <=> (tptp_fun_X_8(uri_ex_w, uri_ex_c1) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w)))))))))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.71/0.74 tff(138,plain,
% 0.71/0.74 (~((~(iext(uri_owl_oneOf, uri_ex_c1, X2!140) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_8(uri_ex_w, uri_ex_c1))) <=> (tptp_fun_X_8(uri_ex_w, uri_ex_c1) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w))))))))),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[137, 134, 112, 111])).
% 0.74/0.76 tff(139,plain,
% 0.74/0.76 (((~(iext(uri_owl_oneOf, uri_ex_c1, X2!140) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_8(uri_ex_w, uri_ex_c1))) <=> (tptp_fun_X_8(uri_ex_w, uri_ex_c1) = uri_ex_w)))) | (~((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w)))))))) | ((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w))))))),
% 0.74/0.76 inference(tautology,[status(thm)],[])).
% 0.74/0.76 tff(140,plain,
% 0.74/0.76 ((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w)))))),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.74/0.76 tff(141,plain,
% 0.74/0.76 ((~((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w))))))) | (~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w)))))),
% 0.74/0.76 inference(tautology,[status(thm)],[])).
% 0.74/0.76 tff(142,plain,
% 0.74/0.76 ((~((~iext(uri_owl_oneOf, uri_ex_c1, X2!140)) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w))))))) | (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w)))))),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[141, 93])).
% 0.74/0.76 tff(143,plain,
% 0.74/0.76 (~((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w))))),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[142, 140])).
% 0.74/0.76 tff(144,plain,
% 0.74/0.76 (((~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w)))) | ![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w))),
% 0.74/0.76 inference(tautology,[status(thm)],[])).
% 0.74/0.76 tff(145,plain,
% 0.74/0.76 (![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w))),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.74/0.76 tff(146,plain,
% 0.74/0.76 ((~![X: $i] : (icext(uri_ex_c1, X) <=> (X = uri_ex_w))) | (icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)) <=> (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w))),
% 0.74/0.76 inference(quant_inst,[status(thm)],[])).
% 0.74/0.76 tff(147,plain,
% 0.74/0.76 (icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)) <=> (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w)),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.74/0.76 tff(148,plain,
% 0.74/0.76 (((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))),
% 0.74/0.76 inference(tautology,[status(thm)],[])).
% 0.74/0.76 tff(149,plain,
% 0.74/0.76 (icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[148, 105])).
% 0.74/0.76 tff(150,plain,
% 0.74/0.76 ((~(icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)) <=> (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w))) | (~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1))) | (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w)),
% 0.74/0.76 inference(tautology,[status(thm)],[])).
% 0.74/0.76 tff(151,plain,
% 0.74/0.76 ((~(icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c2, uri_ex_c1)) <=> (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w))) | (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w)),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.74/0.76 tff(152,plain,
% 0.74/0.76 (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[151, 147])).
% 0.74/0.76 tff(153,plain,
% 0.74/0.76 (((tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_u) | (tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w)) | (~(tptp_fun_X_61(uri_ex_c2, uri_ex_c1) = uri_ex_w))),
% 0.74/0.76 inference(tautology,[status(thm)],[])).
% 0.74/0.76 tff(154,plain,
% 0.74/0.76 ($false),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[153, 152, 110])).
% 0.74/0.76 % SZS output end Proof
%------------------------------------------------------------------------------