TSTP Solution File: SWB056+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB056+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 08:32:08 EDT 2022
% Result : Theorem 0.19s 0.58s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWB056+1 : TPTP v8.1.0. Released v5.2.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 20:07:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.58 % SZS status Theorem
% 0.19/0.58 % SZS output start Proof
% 0.19/0.58 tff(uri_ex_x_type, type, (
% 0.19/0.58 uri_ex_x: $i)).
% 0.19/0.58 tff(uri_ex_z_type, type, (
% 0.19/0.58 uri_ex_z: $i)).
% 0.19/0.58 tff(uri_ex_y_type, type, (
% 0.19/0.58 uri_ex_y: $i)).
% 0.19/0.58 tff(icext_type, type, (
% 0.19/0.58 icext: ( $i * $i ) > $o)).
% 0.19/0.58 tff(uri_ex_e_type, type, (
% 0.19/0.58 uri_ex_e: $i)).
% 0.19/0.58 tff(iext_type, type, (
% 0.19/0.58 iext: ( $i * $i * $i ) > $o)).
% 0.19/0.58 tff(uri_owl_differentFrom_type, type, (
% 0.19/0.58 uri_owl_differentFrom: $i)).
% 0.19/0.58 tff(uri_rdf_nil_type, type, (
% 0.19/0.58 uri_rdf_nil: $i)).
% 0.19/0.58 tff(tptp_fun_X1_140_type, type, (
% 0.19/0.58 tptp_fun_X1_140: $i)).
% 0.19/0.58 tff(uri_rdf_rest_type, type, (
% 0.19/0.58 uri_rdf_rest: $i)).
% 0.19/0.58 tff(uri_rdf_first_type, type, (
% 0.19/0.58 uri_rdf_first: $i)).
% 0.19/0.58 tff(tptp_fun_X0_141_type, type, (
% 0.19/0.58 tptp_fun_X0_141: $i)).
% 0.19/0.58 tff(uri_owl_oneOf_type, type, (
% 0.19/0.58 uri_owl_oneOf: $i)).
% 0.19/0.58 tff(uri_rdf_type_type, type, (
% 0.19/0.58 uri_rdf_type: $i)).
% 0.19/0.58 tff(uri_owl_sameAs_type, type, (
% 0.19/0.58 uri_owl_sameAs: $i)).
% 0.19/0.58 tff(ic_type, type, (
% 0.19/0.58 ic: $i > $o)).
% 0.19/0.58 tff(tptp_fun_X_9_type, type, (
% 0.19/0.58 tptp_fun_X_9: ( $i * $i * $i ) > $i)).
% 0.19/0.58 tff(1,plain,
% 0.19/0.58 (^[X: $i, Y: $i] : refl((iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y))) <=> (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(2,plain,
% 0.19/0.58 (![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y))) <=> ![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.58 tff(3,plain,
% 0.19/0.58 (![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y))) <=> ![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(4,axiom,(![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_eqdis_differentfrom')).
% 0.19/0.58 tff(5,plain,
% 0.19/0.58 (![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.58 tff(6,plain,(
% 0.19/0.58 ![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))),
% 0.19/0.58 inference(skolemize,[status(sab)],[5])).
% 0.19/0.58 tff(7,plain,
% 0.19/0.58 (![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.58 tff(8,plain,
% 0.19/0.58 ((~![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))) | (iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) <=> (~(uri_ex_z = uri_ex_x)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(9,plain,
% 0.19/0.58 (iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) <=> (~(uri_ex_z = uri_ex_x))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.58 tff(10,plain,
% 0.19/0.58 (?[X0: $i, X1: $i] : (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> ?[X0: $i, X1: $i] : (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(11,plain,
% 0.19/0.58 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) & iext(uri_owl_oneOf, uri_ex_e, X0)) <=> (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0))), ((((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)) <=> ((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)))), rewrite(((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)) <=> (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x))), ((((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)) <=> (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x)))), (((((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)) & iext(uri_rdf_rest, X0, X1)) <=> ((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x)) & iext(uri_rdf_rest, X0, X1)))), rewrite(((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x)) & iext(uri_rdf_rest, X0, X1)) <=> (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1))), (((((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)) & iext(uri_rdf_rest, X0, X1)) <=> (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1)))), ((((((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_y)) <=> ((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_y)))), rewrite(((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_y)) <=> (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y))), ((((((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_y)) <=> (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y)))), (((((((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> ((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)))), rewrite(((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil))), (((((((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(12,plain,
% 0.19/0.58 (?[X0: $i, X1: $i] : ((((((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> ?[X0: $i, X1: $i] : (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.58 tff(13,axiom,(?[X0: $i, X1: $i] : ((((((iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) & iext(uri_owl_oneOf, uri_ex_e, X0)) & iext(uri_rdf_first, X0, uri_ex_x)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_y)) & iext(uri_rdf_rest, X1, uri_rdf_nil))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','premise_rdfbased_sem_enum_inst_closed')).
% 0.19/0.58 tff(14,plain,
% 0.19/0.58 (?[X0: $i, X1: $i] : (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.58 tff(15,plain,
% 0.19/0.58 (?[X0: $i, X1: $i] : (iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0) & iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_y) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.58 tff(16,plain,(
% 0.19/0.58 iext(uri_rdf_type, uri_ex_z, uri_ex_e) & iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) & iext(uri_owl_oneOf, uri_ex_e, X0!141) & iext(uri_rdf_first, X0!141, uri_ex_x) & iext(uri_rdf_rest, X0!141, X1!140) & iext(uri_rdf_first, X1!140, uri_ex_y) & iext(uri_rdf_rest, X1!140, uri_rdf_nil)),
% 0.19/0.58 inference(skolemize,[status(sab)],[15])).
% 0.19/0.58 tff(17,plain,
% 0.19/0.58 (iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)),
% 0.19/0.58 inference(and_elim,[status(thm)],[16])).
% 0.19/0.58 tff(18,plain,
% 0.19/0.58 ((~(iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) <=> (~(uri_ex_z = uri_ex_x)))) | (~iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x)) | (~(uri_ex_z = uri_ex_x))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(19,plain,
% 0.19/0.58 ((~(iext(uri_owl_differentFrom, uri_ex_z, uri_ex_x) <=> (~(uri_ex_z = uri_ex_x)))) | (~(uri_ex_z = uri_ex_x))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.58 tff(20,plain,
% 0.19/0.58 (~(uri_ex_z = uri_ex_x)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[19, 9])).
% 0.19/0.58 tff(21,plain,
% 0.19/0.58 (^[X: $i, Y: $i] : refl((iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> (iext(uri_owl_sameAs, X, Y) <=> (X = Y)))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(22,plain,
% 0.19/0.58 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.58 tff(23,plain,
% 0.19/0.58 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(24,axiom,(![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_eqdis_sameas')).
% 0.19/0.58 tff(25,plain,
% 0.19/0.58 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.58 tff(26,plain,(
% 0.19/0.58 ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.58 inference(skolemize,[status(sab)],[25])).
% 0.19/0.58 tff(27,plain,
% 0.19/0.58 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.58 tff(28,plain,
% 0.19/0.58 ((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | (iext(uri_owl_sameAs, uri_ex_z, uri_ex_y) <=> (uri_ex_z = uri_ex_y))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(29,plain,
% 0.19/0.58 (iext(uri_owl_sameAs, uri_ex_z, uri_ex_y) <=> (uri_ex_z = uri_ex_y)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.58 tff(30,plain,
% 0.19/0.58 ((~iext(uri_owl_sameAs, uri_ex_z, uri_ex_y)) <=> (~iext(uri_owl_sameAs, uri_ex_z, uri_ex_y))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(31,axiom,(~iext(uri_owl_sameAs, uri_ex_z, uri_ex_y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conclusion_rdfbased_sem_enum_inst_closed')).
% 0.19/0.58 tff(32,plain,
% 0.19/0.58 (~iext(uri_owl_sameAs, uri_ex_z, uri_ex_y)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.58 tff(33,plain,
% 0.19/0.58 ((~(iext(uri_owl_sameAs, uri_ex_z, uri_ex_y) <=> (uri_ex_z = uri_ex_y))) | iext(uri_owl_sameAs, uri_ex_z, uri_ex_y) | (~(uri_ex_z = uri_ex_y))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(34,plain,
% 0.19/0.58 ((~(iext(uri_owl_sameAs, uri_ex_z, uri_ex_y) <=> (uri_ex_z = uri_ex_y))) | (~(uri_ex_z = uri_ex_y))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.58 tff(35,plain,
% 0.19/0.58 (~(uri_ex_z = uri_ex_y)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[34, 29])).
% 0.19/0.58 tff(36,plain,
% 0.19/0.58 ((~((uri_ex_z = uri_ex_y) | (uri_ex_z = uri_ex_x))) | (uri_ex_z = uri_ex_y) | (uri_ex_z = uri_ex_x)),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(37,plain,
% 0.19/0.58 (~((uri_ex_z = uri_ex_y) | (uri_ex_z = uri_ex_x))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[36, 35, 20])).
% 0.19/0.58 tff(38,plain,
% 0.19/0.58 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(39,plain,
% 0.19/0.58 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.58 tff(40,plain,
% 0.19/0.58 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(41,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','rdfs_cext_def')).
% 0.19/0.58 tff(42,plain,
% 0.19/0.58 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.58 tff(43,plain,(
% 0.19/0.58 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.58 inference(skolemize,[status(sab)],[42])).
% 0.19/0.58 tff(44,plain,
% 0.19/0.58 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.58 tff(45,plain,
% 0.19/0.58 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_z, uri_ex_e) <=> icext(uri_ex_e, uri_ex_z))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(46,plain,
% 0.19/0.58 (iext(uri_rdf_type, uri_ex_z, uri_ex_e) <=> icext(uri_ex_e, uri_ex_z)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.58 tff(47,plain,
% 0.19/0.58 (iext(uri_rdf_type, uri_ex_z, uri_ex_e)),
% 0.19/0.58 inference(and_elim,[status(thm)],[16])).
% 0.19/0.58 tff(48,plain,
% 0.19/0.58 ((~(iext(uri_rdf_type, uri_ex_z, uri_ex_e) <=> icext(uri_ex_e, uri_ex_z))) | (~iext(uri_rdf_type, uri_ex_z, uri_ex_e)) | icext(uri_ex_e, uri_ex_z)),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(49,plain,
% 0.19/0.58 ((~(iext(uri_rdf_type, uri_ex_z, uri_ex_e) <=> icext(uri_ex_e, uri_ex_z))) | icext(uri_ex_e, uri_ex_z)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.58 tff(50,plain,
% 0.19/0.58 (icext(uri_ex_e, uri_ex_z)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.19/0.58 tff(51,plain,
% 0.19/0.58 ((~(icext(uri_ex_e, uri_ex_z) <=> ((uri_ex_z = uri_ex_y) | (uri_ex_z = uri_ex_x)))) | (~icext(uri_ex_e, uri_ex_z)) | ((uri_ex_z = uri_ex_y) | (uri_ex_z = uri_ex_x))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(52,plain,
% 0.19/0.58 (~(icext(uri_ex_e, uri_ex_z) <=> ((uri_ex_z = uri_ex_y) | (uri_ex_z = uri_ex_x)))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[51, 50, 37])).
% 0.19/0.58 tff(53,plain,
% 0.19/0.58 (iext(uri_rdf_rest, X1!140, uri_rdf_nil)),
% 0.19/0.58 inference(and_elim,[status(thm)],[16])).
% 0.19/0.58 tff(54,plain,
% 0.19/0.58 (iext(uri_rdf_first, X1!140, uri_ex_y)),
% 0.19/0.58 inference(and_elim,[status(thm)],[16])).
% 0.19/0.58 tff(55,plain,
% 0.19/0.58 (iext(uri_rdf_rest, X0!141, X1!140)),
% 0.19/0.58 inference(and_elim,[status(thm)],[16])).
% 0.19/0.58 tff(56,plain,
% 0.19/0.58 (iext(uri_rdf_first, X0!141, uri_ex_x)),
% 0.19/0.58 inference(and_elim,[status(thm)],[16])).
% 0.19/0.58 tff(57,plain,
% 0.19/0.58 (^[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)))))))))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(58,plain,
% 0.19/0.58 (![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)))))))))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.58 tff(59,plain,
% 0.19/0.58 (^[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)))))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(60,plain,
% 0.19/0.58 (![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))))))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.58 tff(61,plain,
% 0.19/0.58 (^[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)))))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(62,plain,
% 0.19/0.58 (![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))))))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.58 tff(63,plain,
% 0.19/0.58 (![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))))))))),
% 0.19/0.58 inference(transitivity,[status(thm)],[62, 60])).
% 0.19/0.58 tff(64,plain,
% 0.19/0.58 (^[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))))))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(65,plain,
% 0.19/0.58 (![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))))))))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.59 tff(66,plain,
% 0.19/0.59 (^[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)))))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(67,plain,
% 0.19/0.59 (![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))))))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.59 tff(68,plain,
% 0.19/0.59 (![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))))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(69,plain,
% 0.19/0.59 (^[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))))))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(70,plain,
% 0.19/0.59 (![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))))))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.59 tff(71,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/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_enum_class_002')).
% 0.19/0.59 tff(72,plain,
% 0.19/0.59 (![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))))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.59 tff(73,plain,
% 0.19/0.59 (![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))))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.19/0.59 tff(74,plain,(
% 0.19/0.59 ![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))))))))),
% 0.19/0.59 inference(skolemize,[status(sab)],[73])).
% 0.19/0.59 tff(75,plain,
% 0.19/0.59 (![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))))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.19/0.59 tff(76,plain,
% 0.19/0.59 (![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))))))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.19/0.59 tff(77,plain,
% 0.19/0.59 (![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))))))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[76, 63])).
% 0.19/0.59 tff(78,plain,
% 0.19/0.59 (![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)))))))))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[77, 58])).
% 0.19/0.59 tff(79,plain,
% 0.19/0.59 (((~![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!141, uri_ex_x)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_y)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_e, X0!141) | (~ic(uri_ex_e)) | ((~icext(uri_ex_e, tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e))) <=> ((tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_y) | (tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, uri_ex_e, X0!141)) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x)))))))))))) <=> ((~![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!141, uri_ex_x)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_y)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_e, X0!141) | (~ic(uri_ex_e)) | ((~icext(uri_ex_e, tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e))) <=> ((tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_y) | (tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, uri_ex_e, X0!141)) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x)))))))))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(80,plain,
% 0.19/0.59 ((~![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!141, uri_ex_x)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_y)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_e, X0!141) | (~ic(uri_ex_e)) | ((~icext(uri_ex_e, tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e))) <=> ((tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_y) | (tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, uri_ex_e, X0!141)) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x)))))))))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(81,plain,
% 0.19/0.59 ((~![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!141, uri_ex_x)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_y)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, uri_ex_e, X0!141) | (~ic(uri_ex_e)) | ((~icext(uri_ex_e, tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e))) <=> ((tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_y) | (tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, uri_ex_e, X0!141)) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x))))))))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.59 tff(82,plain,
% 0.19/0.59 (~((~(iext(uri_owl_oneOf, uri_ex_e, X0!141) | (~ic(uri_ex_e)) | ((~icext(uri_ex_e, tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e))) <=> ((tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_y) | (tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, uri_ex_e, X0!141)) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x)))))))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[81, 78, 56, 55, 54, 53])).
% 0.19/0.59 tff(83,plain,
% 0.19/0.59 (((~(iext(uri_owl_oneOf, uri_ex_e, X0!141) | (~ic(uri_ex_e)) | ((~icext(uri_ex_e, tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e))) <=> ((tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_y) | (tptp_fun_X_9(uri_ex_y, uri_ex_x, uri_ex_e) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, uri_ex_e, X0!141)) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x))))))))) | ((~iext(uri_owl_oneOf, uri_ex_e, X0!141)) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x)))))))),
% 0.19/0.59 inference(tautology,[status(thm)],[])).
% 0.19/0.59 tff(84,plain,
% 0.19/0.59 ((~iext(uri_owl_oneOf, uri_ex_e, X0!141)) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x))))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.59 tff(85,plain,
% 0.19/0.59 (iext(uri_owl_oneOf, uri_ex_e, X0!141)),
% 0.19/0.59 inference(and_elim,[status(thm)],[16])).
% 0.19/0.59 tff(86,plain,
% 0.19/0.59 ((~((~iext(uri_owl_oneOf, uri_ex_e, X0!141)) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x)))))))) | (~iext(uri_owl_oneOf, uri_ex_e, X0!141)) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x))))))),
% 0.19/0.59 inference(tautology,[status(thm)],[])).
% 0.19/0.59 tff(87,plain,
% 0.19/0.59 ((~((~iext(uri_owl_oneOf, uri_ex_e, X0!141)) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x)))))))) | (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x))))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.59 tff(88,plain,
% 0.19/0.59 (~((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x)))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.19/0.59 tff(89,plain,
% 0.19/0.59 (((~ic(uri_ex_e)) | (~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x))))) | ![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x)))),
% 0.19/0.59 inference(tautology,[status(thm)],[])).
% 0.19/0.59 tff(90,plain,
% 0.19/0.59 (![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x)))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.57/0.61 tff(91,plain,
% 0.57/0.61 ((~![X: $i] : (icext(uri_ex_e, X) <=> ((X = uri_ex_y) | (X = uri_ex_x)))) | (icext(uri_ex_e, uri_ex_z) <=> ((uri_ex_z = uri_ex_y) | (uri_ex_z = uri_ex_x)))),
% 0.57/0.61 inference(quant_inst,[status(thm)],[])).
% 0.57/0.61 tff(92,plain,
% 0.57/0.61 ($false),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[91, 90, 52])).
% 0.57/0.61 % SZS output end Proof
%------------------------------------------------------------------------------