%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB105+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 : Sat Jun 21 05:29:52 AM UTC 2025
% Result : Theorem 15.47s 15.70s
% Output : Proof 15.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWB105+1 : TPTP v9.0.0. Released v5.2.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 07:58:54 EDT 2025
% 0.14/0.36 % CPUTime :
% 15.47/15.70 % SZS status Theorem
% 15.47/15.70 % SZS output start Proof
% 15.47/15.70 tff(icext_type, type, (
% 15.47/15.70 icext: ( $i * $i ) > $o)).
% 15.47/15.70 tff(tptp_fun_Y_11_type, type, (
% 15.47/15.70 tptp_fun_Y_11: ( $i * $i * $i ) > $i)).
% 15.47/15.70 tff(uri_ex_p_type, type, (
% 15.47/15.70 uri_ex_p: $i)).
% 15.47/15.70 tff(uri_ex_nc_type, type, (
% 15.47/15.70 uri_ex_nc: $i)).
% 15.47/15.70 tff(tptp_fun_X_67_type, type, (
% 15.47/15.70 tptp_fun_X_67: ( $i * $i ) > $i)).
% 15.47/15.70 tff(uri_ex_z1_type, type, (
% 15.47/15.70 uri_ex_z1: $i)).
% 15.47/15.70 tff(uri_ex_nz2_type, type, (
% 15.47/15.70 uri_ex_nz2: $i)).
% 15.47/15.70 tff(uri_ex_c_type, type, (
% 15.47/15.70 uri_ex_c: $i)).
% 15.47/15.70 tff(ic_type, type, (
% 15.47/15.70 ic: $i > $o)).
% 15.47/15.70 tff(iext_type, type, (
% 15.47/15.70 iext: ( $i * $i * $i ) > $o)).
% 15.47/15.70 tff(uri_owl_complementOf_type, type, (
% 15.47/15.70 uri_owl_complementOf: $i)).
% 15.47/15.70 tff(uri_ex_z2_type, type, (
% 15.47/15.70 uri_ex_z2: $i)).
% 15.47/15.70 tff(uri_owl_someValuesFrom_type, type, (
% 15.47/15.70 uri_owl_someValuesFrom: $i)).
% 15.47/15.70 tff(uri_owl_onProperty_type, type, (
% 15.47/15.70 uri_owl_onProperty: $i)).
% 15.47/15.70 tff(uri_owl_allValuesFrom_type, type, (
% 15.47/15.70 uri_owl_allValuesFrom: $i)).
% 15.47/15.70 tff(tptp_fun_Y_42_type, type, (
% 15.47/15.70 tptp_fun_Y_42: ( $i * $i * $i ) > $i)).
% 15.47/15.70 tff(uri_owl_equivalentClass_type, type, (
% 15.47/15.70 uri_owl_equivalentClass: $i)).
% 15.47/15.70 tff(uri_owl_Restriction_type, type, (
% 15.47/15.70 uri_owl_Restriction: $i)).
% 15.47/15.70 tff(1,plain,
% 15.47/15.70 (iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c) <=> iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)),
% 15.47/15.70 inference(rewrite,[status(thm)],[])).
% 15.47/15.70 tff(2,axiom,(((((iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2) & iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)) & iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','premise_rdfbased_sem_restrict_term_sameall')).
% 15.47/15.70 tff(3,plain,
% 15.47/15.70 ((((iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2) & iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)) & iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)),
% 15.47/15.70 inference(and_elim,[status(thm)],[2])).
% 15.47/15.70 tff(4,plain,
% 15.47/15.70 (((iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2) & iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)) & iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)),
% 15.47/15.70 inference(and_elim,[status(thm)],[3])).
% 15.47/15.70 tff(5,plain,
% 15.47/15.70 ((iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2) & iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)) & iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)),
% 15.47/15.70 inference(and_elim,[status(thm)],[4])).
% 15.47/15.70 tff(6,plain,
% 15.47/15.70 (iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2) & iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)),
% 15.47/15.70 inference(and_elim,[status(thm)],[5])).
% 15.47/15.70 tff(7,plain,
% 15.47/15.70 (iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)),
% 15.47/15.70 inference(and_elim,[status(thm)],[6])).
% 15.47/15.70 tff(8,plain,
% 15.47/15.70 (iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)),
% 15.47/15.70 inference(modus_ponens,[status(thm)],[7, 1])).
% 15.47/15.70 tff(9,plain,
% 15.47/15.70 (^[Z: $i, C: $i] : refl(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 15.47/15.70 inference(bind,[status(th)],[])).
% 15.47/15.70 tff(10,plain,
% 15.47/15.70 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 15.47/15.70 inference(quant_intro,[status(thm)],[9])).
% 15.47/15.70 tff(11,plain,
% 15.47/15.70 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 15.47/15.70 inference(bind,[status(th)],[])).
% 15.47/15.70 tff(12,plain,
% 15.47/15.70 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 15.47/15.70 inference(quant_intro,[status(thm)],[11])).
% 15.47/15.70 tff(13,plain,
% 15.47/15.70 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 15.47/15.70 inference(transitivity,[status(thm)],[12, 10])).
% 15.47/15.70 tff(14,plain,
% 15.47/15.70 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 15.47/15.70 inference(bind,[status(th)],[])).
% 15.47/15.70 tff(15,plain,
% 15.47/15.70 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 15.47/15.70 inference(quant_intro,[status(thm)],[14])).
% 15.47/15.70 tff(16,plain,
% 15.47/15.70 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 15.47/15.70 inference(rewrite,[status(thm)],[])).
% 15.47/15.70 tff(17,plain,
% 15.47/15.70 (^[Z: $i, C: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(rewrite((icext(Z, X) <=> (~icext(C, X))) <=> (~(icext(C, X) <=> icext(Z, X)))), rewrite((~(icext(C, X) <=> icext(Z, X))) <=> (~(icext(C, X) <=> icext(Z, X)))), ((icext(Z, X) <=> (~icext(C, X))) <=> (~(icext(C, X) <=> icext(Z, X)))))), (![X: $i] : (icext(Z, X) <=> (~icext(C, X))) <=> ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))), (((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> ((ic(Z) & ic(C)) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), rewrite(((ic(Z) & ic(C)) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) <=> (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))), (((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> (iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))), rewrite((iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 15.47/15.70 inference(bind,[status(th)],[])).
% 15.47/15.70 tff(18,plain,
% 15.47/15.70 (![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 15.47/15.70 inference(quant_intro,[status(thm)],[17])).
% 15.47/15.70 tff(19,axiom,(![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_complementof_class')).
% 15.47/15.70 tff(20,plain,
% 15.47/15.70 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 15.47/15.70 inference(modus_ponens,[status(thm)],[19, 18])).
% 15.47/15.70 tff(21,plain,
% 15.47/15.70 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 15.47/15.70 inference(modus_ponens,[status(thm)],[20, 16])).
% 15.47/15.70 tff(22,plain,(
% 15.47/15.70 ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 15.47/15.70 inference(skolemize,[status(sab)],[21])).
% 15.47/15.70 tff(23,plain,
% 15.47/15.70 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 15.47/15.70 inference(modus_ponens,[status(thm)],[22, 15])).
% 15.47/15.70 tff(24,plain,
% 15.47/15.70 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 15.47/15.70 inference(modus_ponens,[status(thm)],[23, 13])).
% 15.47/15.70 tff(25,plain,
% 15.47/15.70 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)) | (~((~ic(uri_ex_c)) | (~ic(uri_ex_nc)) | (~![X: $i] : (~(icext(uri_ex_c, X) <=> icext(uri_ex_nc, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)) | (~((~ic(uri_ex_c)) | (~ic(uri_ex_nc)) | (~![X: $i] : (~(icext(uri_ex_c, X) <=> icext(uri_ex_nc, X)))))))),
% 15.47/15.70 inference(rewrite,[status(thm)],[])).
% 15.47/15.70 tff(26,plain,
% 15.47/15.70 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)) | (~((~ic(uri_ex_c)) | (~ic(uri_ex_nc)) | (~![X: $i] : (~(icext(uri_ex_c, X) <=> icext(uri_ex_nc, X)))))))),
% 15.47/15.70 inference(quant_inst,[status(thm)],[])).
% 15.47/15.70 tff(27,plain,
% 15.47/15.70 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, uri_ex_nc, uri_ex_c)) | (~((~ic(uri_ex_c)) | (~ic(uri_ex_nc)) | (~![X: $i] : (~(icext(uri_ex_c, X) <=> icext(uri_ex_nc, X))))))),
% 15.47/15.70 inference(modus_ponens,[status(thm)],[26, 25])).
% 15.47/15.70 tff(28,plain,
% 15.47/15.70 (~((~ic(uri_ex_c)) | (~ic(uri_ex_nc)) | (~![X: $i] : (~(icext(uri_ex_c, X) <=> icext(uri_ex_nc, X)))))),
% 15.47/15.70 inference(unit_resolution,[status(thm)],[27, 24, 8])).
% 15.47/15.70 tff(29,plain,
% 15.47/15.70 (((~ic(uri_ex_c)) | (~ic(uri_ex_nc)) | (~![X: $i] : (~(icext(uri_ex_c, X) <=> icext(uri_ex_nc, X))))) | ![X: $i] : (~(icext(uri_ex_c, X) <=> icext(uri_ex_nc, X)))),
% 15.47/15.70 inference(tautology,[status(thm)],[])).
% 15.47/15.70 tff(30,plain,
% 15.47/15.70 (![X: $i] : (~(icext(uri_ex_c, X) <=> icext(uri_ex_nc, X)))),
% 15.47/15.70 inference(unit_resolution,[status(thm)],[29, 28])).
% 15.47/15.70 tff(31,plain,
% 15.47/15.70 ((~![X: $i] : (~(icext(uri_ex_c, X) <=> icext(uri_ex_nc, X)))) | (~(icext(uri_ex_c, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)) <=> icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))))),
% 15.47/15.70 inference(quant_inst,[status(thm)],[])).
% 15.47/15.70 tff(32,plain,
% 15.47/15.70 (~(icext(uri_ex_c, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)) <=> icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)))),
% 15.47/15.70 inference(unit_resolution,[status(thm)],[31, 30])).
% 15.47/15.70 tff(33,plain,
% 15.47/15.70 ((~![X: $i] : (~(icext(uri_ex_c, X) <=> icext(uri_ex_nc, X)))) | (~(icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)) <=> icext(uri_ex_nc, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))))),
% 15.47/15.70 inference(quant_inst,[status(thm)],[])).
% 15.47/15.70 tff(34,plain,
% 15.47/15.70 (~(icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)) <=> icext(uri_ex_nc, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))),
% 15.47/15.70 inference(unit_resolution,[status(thm)],[33, 30])).
% 15.47/15.70 tff(35,assumption,(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))), introduced(assumption)).
% 15.47/15.70 tff(36,plain,
% 15.47/15.70 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))))))),
% 15.47/15.70 inference(bind,[status(th)],[])).
% 15.47/15.70 tff(37,plain,
% 15.47/15.70 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 15.47/15.70 inference(quant_intro,[status(thm)],[36])).
% 15.47/15.70 tff(38,plain,
% 15.47/15.70 (^[C1: $i, C2: $i] : refl((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))))),
% 15.47/15.70 inference(bind,[status(th)],[])).
% 15.47/15.70 tff(39,plain,
% 15.47/15.70 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 15.47/15.70 inference(quant_intro,[status(thm)],[38])).
% 15.47/15.70 tff(40,plain,
% 15.47/15.70 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))))),
% 15.47/15.70 inference(bind,[status(th)],[])).
% 15.47/15.70 tff(41,plain,
% 15.47/15.70 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 15.47/15.70 inference(quant_intro,[status(thm)],[40])).
% 15.47/15.70 tff(42,plain,
% 15.47/15.70 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 15.47/15.70 inference(transitivity,[status(thm)],[41, 39])).
% 15.47/15.70 tff(43,plain,
% 15.47/15.70 (^[C1: $i, C2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))), trans(monotonicity(rewrite((~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))) <=> (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))), rewrite((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))), ((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> (((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))), rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))), ((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))))),
% 15.47/15.70 inference(bind,[status(th)],[])).
% 15.47/15.70 tff(44,plain,
% 15.47/15.70 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 15.47/15.70 inference(quant_intro,[status(thm)],[43])).
% 15.47/15.70 tff(45,plain,
% 15.47/15.70 (^[C1: $i, C2: $i] : rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 15.47/15.71 inference(bind,[status(th)],[])).
% 15.47/15.71 tff(46,plain,
% 15.47/15.71 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> ![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))),
% 15.47/15.71 inference(quant_intro,[status(thm)],[45])).
% 15.47/15.71 tff(47,plain,
% 15.47/15.71 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 15.47/15.71 inference(rewrite,[status(thm)],[])).
% 15.47/15.71 tff(48,plain,
% 15.47/15.71 (^[C1: $i, C2: $i] : rewrite((iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))))),
% 15.47/15.71 inference(bind,[status(th)],[])).
% 15.47/15.71 tff(49,plain,
% 15.47/15.71 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 15.47/15.71 inference(quant_intro,[status(thm)],[48])).
% 15.47/15.71 tff(50,axiom,(![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_eqdis_equivalentclass')).
% 15.47/15.71 tff(51,plain,
% 15.47/15.71 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[50, 49])).
% 15.47/15.71 tff(52,plain,
% 15.47/15.71 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[51, 47])).
% 15.47/15.71 tff(53,plain,(
% 15.47/15.71 ![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 15.47/15.71 inference(skolemize,[status(sab)],[52])).
% 15.47/15.71 tff(54,plain,
% 15.47/15.71 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[53, 46])).
% 15.47/15.71 tff(55,plain,
% 15.47/15.71 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[54, 44])).
% 15.47/15.71 tff(56,plain,
% 15.47/15.71 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[55, 42])).
% 15.47/15.71 tff(57,plain,
% 15.47/15.71 (![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[56, 37])).
% 15.47/15.71 tff(58,plain,
% 15.47/15.71 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X))))))))))),
% 15.47/15.71 inference(rewrite,[status(thm)],[])).
% 15.47/15.71 tff(59,plain,
% 15.47/15.71 ((~((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X))))))))) <=> (~((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X)))))))))),
% 15.47/15.71 inference(rewrite,[status(thm)],[])).
% 15.47/15.71 tff(60,plain,
% 15.47/15.71 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X))))))))))),
% 15.47/15.71 inference(monotonicity,[status(thm)],[59])).
% 15.47/15.71 tff(61,plain,
% 15.47/15.71 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X))))))))))),
% 15.47/15.71 inference(transitivity,[status(thm)],[60, 58])).
% 15.47/15.71 tff(62,plain,
% 15.47/15.71 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X)))))))))),
% 15.47/15.71 inference(quant_inst,[status(thm)],[])).
% 15.47/15.71 tff(63,plain,
% 15.47/15.71 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X)))))))))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[62, 61])).
% 15.47/15.71 tff(64,plain,
% 15.47/15.71 (~((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X))))))))),
% 15.47/15.71 inference(unit_resolution,[status(thm)],[63, 57])).
% 15.47/15.71 tff(65,plain,
% 15.47/15.71 (((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z1, X) <=> icext(uri_ex_nz2, X)))))))) | (iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))),
% 15.47/15.71 inference(tautology,[status(thm)],[])).
% 15.47/15.71 tff(66,plain,
% 15.47/15.71 (iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))))),
% 15.47/15.71 inference(unit_resolution,[status(thm)],[65, 64])).
% 15.47/15.71 tff(67,plain,
% 15.47/15.71 (iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2) <=> iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)),
% 15.47/15.71 inference(rewrite,[status(thm)],[])).
% 15.47/15.71 tff(68,plain,
% 15.47/15.71 (iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)),
% 15.47/15.71 inference(and_elim,[status(thm)],[6])).
% 15.47/15.71 tff(69,plain,
% 15.47/15.71 (iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[68, 67])).
% 15.47/15.71 tff(70,plain,
% 15.47/15.71 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 15.47/15.71 inference(bind,[status(th)],[])).
% 15.47/15.71 tff(71,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 15.47/15.71 inference(quant_intro,[status(thm)],[70])).
% 15.47/15.71 tff(72,plain,
% 15.47/15.71 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))) <=> ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 15.47/15.71 inference(bind,[status(th)],[])).
% 15.47/15.71 tff(73,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 15.47/15.71 inference(quant_intro,[status(thm)],[72])).
% 15.47/15.71 tff(74,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 15.47/15.71 inference(rewrite,[status(thm)],[])).
% 15.47/15.71 tff(75,plain,
% 15.47/15.71 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_complementOf, X, Y) => (ic(X) & ic(Y))) <=> ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))))),
% 15.47/15.71 inference(bind,[status(th)],[])).
% 15.47/15.71 tff(76,plain,
% 15.47/15.71 (![X: $i, Y: $i] : (iext(uri_owl_complementOf, X, Y) => (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 15.47/15.71 inference(quant_intro,[status(thm)],[75])).
% 15.47/15.71 tff(77,axiom,(![X: $i, Y: $i] : (iext(uri_owl_complementOf, X, Y) => (ic(X) & ic(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_complementof_ext')).
% 15.47/15.71 tff(78,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[77, 76])).
% 15.47/15.71 tff(79,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[78, 74])).
% 15.47/15.71 tff(80,plain,(
% 15.47/15.71 ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 15.47/15.71 inference(skolemize,[status(sab)],[79])).
% 15.47/15.71 tff(81,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[80, 73])).
% 15.47/15.71 tff(82,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[81, 71])).
% 15.47/15.71 tff(83,plain,
% 15.47/15.71 (((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)))))),
% 15.47/15.71 inference(rewrite,[status(thm)],[])).
% 15.47/15.71 tff(84,plain,
% 15.47/15.71 (((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_nz2))))) <=> ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)))))),
% 15.47/15.71 inference(rewrite,[status(thm)],[])).
% 15.47/15.71 tff(85,plain,
% 15.47/15.71 (((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_nz2)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2))))))),
% 15.47/15.71 inference(monotonicity,[status(thm)],[84])).
% 15.47/15.71 tff(86,plain,
% 15.47/15.71 (((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_nz2)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)))))),
% 15.47/15.71 inference(transitivity,[status(thm)],[85, 83])).
% 15.47/15.71 tff(87,plain,
% 15.47/15.71 ((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_nz2)))))),
% 15.47/15.71 inference(quant_inst,[status(thm)],[])).
% 15.47/15.71 tff(88,plain,
% 15.47/15.71 ((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2))))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[87, 86])).
% 15.47/15.71 tff(89,plain,
% 15.47/15.71 (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)))),
% 15.47/15.71 inference(unit_resolution,[status(thm)],[88, 82, 69])).
% 15.47/15.71 tff(90,plain,
% 15.47/15.71 (((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2))) | ic(uri_ex_nz2)),
% 15.47/15.71 inference(tautology,[status(thm)],[])).
% 15.47/15.71 tff(91,plain,
% 15.47/15.71 (ic(uri_ex_nz2)),
% 15.47/15.71 inference(unit_resolution,[status(thm)],[90, 89])).
% 15.47/15.71 tff(92,plain,
% 15.47/15.71 (iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc) <=> iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)),
% 15.47/15.71 inference(rewrite,[status(thm)],[])).
% 15.47/15.71 tff(93,plain,
% 15.47/15.71 (iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)),
% 15.47/15.71 inference(and_elim,[status(thm)],[3])).
% 15.47/15.71 tff(94,plain,
% 15.47/15.71 (iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[93, 92])).
% 15.47/15.71 tff(95,plain,
% 15.47/15.71 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X))))) <=> ((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X))))))),
% 15.47/15.71 inference(bind,[status(th)],[])).
% 15.47/15.71 tff(96,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X)))))),
% 15.47/15.71 inference(quant_intro,[status(thm)],[95])).
% 15.47/15.71 tff(97,plain,
% 15.47/15.71 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_allValuesFrom, X, Y)) | (icext(uri_owl_Restriction, X) & ic(Y))) <=> ((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X))))))),
% 15.47/15.71 inference(bind,[status(th)],[])).
% 15.47/15.71 tff(98,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (icext(uri_owl_Restriction, X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X)))))),
% 15.47/15.71 inference(quant_intro,[status(thm)],[97])).
% 15.47/15.71 tff(99,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (icext(uri_owl_Restriction, X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (icext(uri_owl_Restriction, X) & ic(Y)))),
% 15.47/15.71 inference(rewrite,[status(thm)],[])).
% 15.47/15.71 tff(100,plain,
% 15.47/15.71 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_allValuesFrom, X, Y) => (icext(uri_owl_Restriction, X) & ic(Y))) <=> ((~iext(uri_owl_allValuesFrom, X, Y)) | (icext(uri_owl_Restriction, X) & ic(Y))))),
% 15.47/15.71 inference(bind,[status(th)],[])).
% 15.47/15.71 tff(101,plain,
% 15.47/15.71 (![X: $i, Y: $i] : (iext(uri_owl_allValuesFrom, X, Y) => (icext(uri_owl_Restriction, X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (icext(uri_owl_Restriction, X) & ic(Y)))),
% 15.47/15.71 inference(quant_intro,[status(thm)],[100])).
% 15.47/15.71 tff(102,axiom,(![X: $i, Y: $i] : (iext(uri_owl_allValuesFrom, X, Y) => (icext(uri_owl_Restriction, X) & ic(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_allvaluesfrom_ext')).
% 15.47/15.71 tff(103,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (icext(uri_owl_Restriction, X) & ic(Y)))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[102, 101])).
% 15.47/15.71 tff(104,plain,
% 15.47/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (icext(uri_owl_Restriction, X) & ic(Y)))),
% 15.47/15.71 inference(modus_ponens,[status(thm)],[103, 99])).
% 15.57/15.71 tff(105,plain,(
% 15.57/15.71 ![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (icext(uri_owl_Restriction, X) & ic(Y)))),
% 15.57/15.71 inference(skolemize,[status(sab)],[104])).
% 15.57/15.71 tff(106,plain,
% 15.57/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X)))))),
% 15.57/15.71 inference(modus_ponens,[status(thm)],[105, 98])).
% 15.57/15.71 tff(107,plain,
% 15.57/15.71 (![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X)))))),
% 15.57/15.71 inference(modus_ponens,[status(thm)],[106, 96])).
% 15.57/15.71 tff(108,plain,
% 15.57/15.71 (((~![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X)))))) | ((~iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)) | (~((~ic(uri_ex_nc)) | (~icext(uri_owl_Restriction, uri_ex_z1)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X)))))) | (~iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)) | (~((~ic(uri_ex_nc)) | (~icext(uri_owl_Restriction, uri_ex_z1)))))),
% 15.57/15.71 inference(rewrite,[status(thm)],[])).
% 15.57/15.71 tff(109,plain,
% 15.57/15.71 ((~![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X)))))) | ((~iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)) | (~((~ic(uri_ex_nc)) | (~icext(uri_owl_Restriction, uri_ex_z1)))))),
% 15.57/15.71 inference(quant_inst,[status(thm)],[])).
% 15.57/15.71 tff(110,plain,
% 15.57/15.71 ((~![X: $i, Y: $i] : ((~iext(uri_owl_allValuesFrom, X, Y)) | (~((~ic(Y)) | (~icext(uri_owl_Restriction, X)))))) | (~iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)) | (~((~ic(uri_ex_nc)) | (~icext(uri_owl_Restriction, uri_ex_z1))))),
% 15.57/15.71 inference(modus_ponens,[status(thm)],[109, 108])).
% 15.57/15.71 tff(111,plain,
% 15.57/15.71 (~((~ic(uri_ex_nc)) | (~icext(uri_owl_Restriction, uri_ex_z1)))),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[110, 107, 94])).
% 15.57/15.71 tff(112,plain,
% 15.57/15.71 (((~ic(uri_ex_nc)) | (~icext(uri_owl_Restriction, uri_ex_z1))) | icext(uri_owl_Restriction, uri_ex_z1)),
% 15.57/15.71 inference(tautology,[status(thm)],[])).
% 15.57/15.71 tff(113,plain,
% 15.57/15.71 (icext(uri_owl_Restriction, uri_ex_z1)),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[112, 111])).
% 15.57/15.71 tff(114,plain,
% 15.57/15.71 (^[X: $i] : refl((ic(X) | (~icext(uri_owl_Restriction, X))) <=> (ic(X) | (~icext(uri_owl_Restriction, X))))),
% 15.57/15.71 inference(bind,[status(th)],[])).
% 15.57/15.71 tff(115,plain,
% 15.57/15.71 (![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X))) <=> ![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X)))),
% 15.57/15.71 inference(quant_intro,[status(thm)],[114])).
% 15.57/15.71 tff(116,plain,
% 15.57/15.71 (![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X))) <=> ![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X)))),
% 15.57/15.71 inference(rewrite,[status(thm)],[])).
% 15.57/15.71 tff(117,plain,
% 15.57/15.71 (^[X: $i] : rewrite((icext(uri_owl_Restriction, X) => ic(X)) <=> (ic(X) | (~icext(uri_owl_Restriction, X))))),
% 15.57/15.71 inference(bind,[status(th)],[])).
% 15.57/15.71 tff(118,plain,
% 15.57/15.71 (![X: $i] : (icext(uri_owl_Restriction, X) => ic(X)) <=> ![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X)))),
% 15.57/15.71 inference(quant_intro,[status(thm)],[117])).
% 15.57/15.71 tff(119,axiom,(![X: $i] : (icext(uri_owl_Restriction, X) => ic(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_class_restriction_ext')).
% 15.57/15.71 tff(120,plain,
% 15.57/15.71 (![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X)))),
% 15.57/15.71 inference(modus_ponens,[status(thm)],[119, 118])).
% 15.57/15.71 tff(121,plain,
% 15.57/15.71 (![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X)))),
% 15.57/15.71 inference(modus_ponens,[status(thm)],[120, 116])).
% 15.57/15.71 tff(122,plain,(
% 15.57/15.71 ![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X)))),
% 15.57/15.71 inference(skolemize,[status(sab)],[121])).
% 15.57/15.71 tff(123,plain,
% 15.57/15.71 (![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X)))),
% 15.57/15.71 inference(modus_ponens,[status(thm)],[122, 115])).
% 15.57/15.71 tff(124,plain,
% 15.57/15.71 (((~![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X)))) | (ic(uri_ex_z1) | (~icext(uri_owl_Restriction, uri_ex_z1)))) <=> ((~![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X)))) | ic(uri_ex_z1) | (~icext(uri_owl_Restriction, uri_ex_z1)))),
% 15.57/15.71 inference(rewrite,[status(thm)],[])).
% 15.57/15.71 tff(125,plain,
% 15.57/15.71 ((~![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X)))) | (ic(uri_ex_z1) | (~icext(uri_owl_Restriction, uri_ex_z1)))),
% 15.57/15.71 inference(quant_inst,[status(thm)],[])).
% 15.57/15.71 tff(126,plain,
% 15.57/15.71 ((~![X: $i] : (ic(X) | (~icext(uri_owl_Restriction, X)))) | ic(uri_ex_z1) | (~icext(uri_owl_Restriction, uri_ex_z1))),
% 15.57/15.71 inference(modus_ponens,[status(thm)],[125, 124])).
% 15.57/15.71 tff(127,plain,
% 15.57/15.71 (ic(uri_ex_z1)),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[126, 123, 113])).
% 15.57/15.71 tff(128,plain,
% 15.57/15.71 ((~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)) <=> (~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2))),
% 15.57/15.71 inference(rewrite,[status(thm)],[])).
% 15.57/15.71 tff(129,axiom,(~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion_rdfbased_sem_restrict_term_sameall')).
% 15.57/15.71 tff(130,plain,
% 15.57/15.71 (~iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2)),
% 15.57/15.71 inference(modus_ponens,[status(thm)],[129, 128])).
% 15.57/15.71 tff(131,plain,
% 15.57/15.71 ((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))))),
% 15.57/15.71 inference(tautology,[status(thm)],[])).
% 15.57/15.71 tff(132,plain,
% 15.57/15.71 ((~(iext(uri_owl_equivalentClass, uri_ex_z1, uri_ex_nz2) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))))) | (~ic(uri_ex_z1)) | (~ic(uri_ex_nz2)) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))))),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[131, 130])).
% 15.57/15.71 tff(133,plain,
% 15.57/15.71 (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[132, 127, 91, 66])).
% 15.57/15.71 tff(134,plain,
% 15.57/15.71 ((icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))),
% 15.57/15.71 inference(tautology,[status(thm)],[])).
% 15.57/15.71 tff(135,plain,
% 15.57/15.71 ((~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[134, 133])).
% 15.57/15.71 tff(136,plain,
% 15.57/15.71 (~icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[135, 35])).
% 15.57/15.71 tff(137,plain,
% 15.57/15.71 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X)))))))),
% 15.57/15.71 inference(rewrite,[status(thm)],[])).
% 15.57/15.71 tff(138,plain,
% 15.57/15.71 (((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_nz2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X))))))) <=> ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X)))))))),
% 15.57/15.71 inference(rewrite,[status(thm)],[])).
% 15.57/15.71 tff(139,plain,
% 15.57/15.71 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_nz2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X))))))))),
% 15.57/15.71 inference(monotonicity,[status(thm)],[138])).
% 15.57/15.71 tff(140,plain,
% 15.57/15.71 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_nz2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X)))))))),
% 15.57/15.71 inference(transitivity,[status(thm)],[139, 137])).
% 15.57/15.71 tff(141,plain,
% 15.57/15.71 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_nz2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X)))))))),
% 15.57/15.71 inference(quant_inst,[status(thm)],[])).
% 15.57/15.71 tff(142,plain,
% 15.57/15.71 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, uri_ex_nz2, uri_ex_z2)) | (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X))))))),
% 15.57/15.71 inference(modus_ponens,[status(thm)],[141, 140])).
% 15.57/15.71 tff(143,plain,
% 15.57/15.71 (~((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X)))))),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[142, 24, 69])).
% 15.57/15.71 tff(144,plain,
% 15.57/15.71 (((~ic(uri_ex_nz2)) | (~ic(uri_ex_z2)) | (~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X))))) | ![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X)))),
% 15.57/15.71 inference(tautology,[status(thm)],[])).
% 15.57/15.71 tff(145,plain,
% 15.57/15.71 (![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X)))),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[144, 143])).
% 15.57/15.71 tff(146,plain,
% 15.57/15.71 ((~![X: $i] : (~(icext(uri_ex_z2, X) <=> icext(uri_ex_nz2, X)))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))))),
% 15.57/15.71 inference(quant_inst,[status(thm)],[])).
% 15.57/15.71 tff(147,plain,
% 15.57/15.71 (~(icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[146, 145])).
% 15.57/15.71 tff(148,plain,
% 15.57/15.71 ((icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))),
% 15.57/15.71 inference(tautology,[status(thm)],[])).
% 15.57/15.71 tff(149,plain,
% 15.57/15.71 (icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[148, 147])).
% 15.57/15.71 tff(150,plain,
% 15.57/15.71 (icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))),
% 15.57/15.71 inference(unit_resolution,[status(thm)],[149, 136])).
% 15.57/15.71 tff(151,plain,
% 15.57/15.71 (iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) <=> iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)),
% 15.57/15.71 inference(rewrite,[status(thm)],[])).
% 15.57/15.71 tff(152,plain,
% 15.57/15.71 (iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)),
% 15.57/15.71 inference(and_elim,[status(thm)],[4])).
% 15.57/15.71 tff(153,plain,
% 15.57/15.71 (iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)),
% 15.57/15.71 inference(modus_ponens,[status(thm)],[152, 151])).
% 15.57/15.71 tff(154,plain,
% 15.57/15.71 (iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c) <=> iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)),
% 15.57/15.71 inference(rewrite,[status(thm)],[])).
% 15.57/15.71 tff(155,plain,
% 15.57/15.71 (iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)),
% 15.57/15.71 inference(and_elim,[status(thm)],[5])).
% 15.57/15.71 tff(156,plain,
% 15.57/15.71 (iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)),
% 15.57/15.71 inference(modus_ponens,[status(thm)],[155, 154])).
% 15.57/15.71 tff(157,plain,
% 15.57/15.71 (^[Z: $i, P: $i, C: $i] : rewrite(((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))),
% 15.57/15.71 inference(bind,[status(th)],[])).
% 15.57/15.71 tff(158,plain,
% 15.57/15.71 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 15.57/15.71 inference(quant_intro,[status(thm)],[157])).
% 15.57/15.71 tff(159,plain,
% 15.57/15.71 (^[Z: $i, P: $i, C: $i] : refl(((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))))),
% 15.57/15.71 inference(bind,[status(th)],[])).
% 15.57/15.71 tff(160,plain,
% 15.57/15.71 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 15.57/15.71 inference(quant_intro,[status(thm)],[159])).
% 15.57/15.71 tff(161,plain,
% 15.57/15.71 (^[Z: $i, P: $i, C: $i] : rewrite(((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))))),
% 15.57/15.71 inference(bind,[status(th)],[])).
% 15.57/15.71 tff(162,plain,
% 15.57/15.71 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 15.57/15.71 inference(quant_intro,[status(thm)],[161])).
% 15.57/15.71 tff(163,plain,
% 15.57/15.71 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 15.57/15.72 inference(transitivity,[status(thm)],[162, 160])).
% 15.57/15.72 tff(164,plain,
% 15.57/15.72 (^[Z: $i, P: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) <=> (~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))), ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) <=> (~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))))), rewrite((~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)))), ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))), quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite(((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) <=> ((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))), rewrite((icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))) <=> (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))), ((((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> (((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P)))))) & (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))), rewrite((((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P)))))) & (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))) <=> (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))), ((((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))), (![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))), (((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> (((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))), rewrite((((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))), (((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))))),
% 15.57/15.72 inference(bind,[status(th)],[])).
% 15.57/15.72 tff(165,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 15.57/15.72 inference(quant_intro,[status(thm)],[164])).
% 15.57/15.72 tff(166,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 15.57/15.72 inference(rewrite,[status(thm)],[])).
% 15.57/15.72 tff(167,plain,
% 15.57/15.72 (^[Z: $i, P: $i, C: $i] : rewrite(((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))))),
% 15.57/15.72 inference(bind,[status(th)],[])).
% 15.57/15.72 tff(168,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 15.57/15.72 inference(quant_intro,[status(thm)],[167])).
% 15.57/15.72 tff(169,axiom,(![Z: $i, P: $i, C: $i] : ((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_restrict_somevaluesfrom')).
% 15.57/15.72 tff(170,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 15.57/15.72 inference(modus_ponens,[status(thm)],[169, 168])).
% 15.57/15.72 tff(171,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 15.57/15.72 inference(modus_ponens,[status(thm)],[170, 166])).
% 15.57/15.72 tff(172,plain,(
% 15.57/15.72 ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))))),
% 15.57/15.72 inference(skolemize,[status(sab)],[171])).
% 15.57/15.72 tff(173,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 15.57/15.72 inference(modus_ponens,[status(thm)],[172, 165])).
% 15.57/15.72 tff(174,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 15.57/15.72 inference(modus_ponens,[status(thm)],[173, 163])).
% 15.57/15.72 tff(175,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 15.57/15.72 inference(modus_ponens,[status(thm)],[174, 158])).
% 15.57/15.72 tff(176,plain,
% 15.57/15.72 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) | ![X: $i] : (~((~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z2, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) | ![X: $i] : (~((~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z2, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))))))),
% 15.57/15.72 inference(rewrite,[status(thm)],[])).
% 15.57/15.72 tff(177,plain,
% 15.57/15.72 (((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | (~((~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))) | (~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y)))))))) <=> ((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) | ![X: $i] : (~((~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z2, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))))))),
% 15.57/15.72 inference(rewrite,[status(thm)],[])).
% 15.57/15.72 tff(178,plain,
% 15.57/15.72 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | (~((~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))) | (~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) | ![X: $i] : (~((~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z2, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p)))))))))))),
% 15.57/15.72 inference(monotonicity,[status(thm)],[177])).
% 15.57/15.72 tff(179,plain,
% 15.57/15.72 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | (~((~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))) | (~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) | ![X: $i] : (~((~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z2, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))))))),
% 15.57/15.72 inference(transitivity,[status(thm)],[178, 176])).
% 15.57/15.72 tff(180,plain,
% 15.57/15.72 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | (~((~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))) | (~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))))))),
% 15.57/15.72 inference(quant_inst,[status(thm)],[])).
% 15.57/15.72 tff(181,plain,
% 15.57/15.72 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_someValuesFrom, uri_ex_z2, uri_ex_c)) | ![X: $i] : (~((~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z2, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p)))))))))),
% 15.57/15.72 inference(modus_ponens,[status(thm)],[180, 179])).
% 15.57/15.72 tff(182,plain,
% 15.57/15.72 (![X: $i] : (~((~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z2, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p)))))))))),
% 15.57/15.72 inference(unit_resolution,[status(thm)],[181, 175, 156, 153])).
% 15.57/15.72 tff(183,plain,
% 15.57/15.72 ((~![X: $i] : (~((~(icext(uri_ex_z2, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z2, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p)))))))))) | (~((~(icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y))))) | (~((~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))))))))),
% 15.57/15.72 inference(quant_inst,[status(thm)],[])).
% 15.57/15.72 tff(184,plain,
% 15.57/15.72 (~((~(icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y))))) | (~((~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))))))))),
% 15.57/15.72 inference(unit_resolution,[status(thm)],[183, 182])).
% 15.57/15.72 tff(185,plain,
% 15.57/15.72 (((~(icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y))))) | (~((~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))))))) | ((~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))))))),
% 15.57/15.72 inference(tautology,[status(thm)],[])).
% 15.57/15.72 tff(186,plain,
% 15.57/15.72 ((~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))))),
% 15.57/15.72 inference(unit_resolution,[status(thm)],[185, 184])).
% 15.57/15.72 tff(187,plain,
% 15.57/15.72 ((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))))))) | (~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))))),
% 15.57/15.72 inference(tautology,[status(thm)],[])).
% 15.57/15.72 tff(188,plain,
% 15.57/15.72 ((~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))))),
% 15.57/15.72 inference(unit_resolution,[status(thm)],[187, 186])).
% 15.57/15.72 tff(189,plain,
% 15.57/15.72 (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))))),
% 15.57/15.72 inference(unit_resolution,[status(thm)],[188, 150])).
% 15.57/15.72 tff(190,plain,
% 15.57/15.72 (((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))) | iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))),
% 15.57/15.72 inference(tautology,[status(thm)],[])).
% 15.57/15.72 tff(191,plain,
% 15.57/15.72 (iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))),
% 15.57/15.72 inference(unit_resolution,[status(thm)],[190, 189])).
% 15.57/15.72 tff(192,plain,
% 15.57/15.72 (iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) <=> iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)),
% 15.57/15.72 inference(rewrite,[status(thm)],[])).
% 15.57/15.72 tff(193,plain,
% 15.57/15.72 (iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)),
% 15.57/15.72 inference(and_elim,[status(thm)],[2])).
% 15.57/15.72 tff(194,plain,
% 15.57/15.72 (iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)),
% 15.57/15.72 inference(modus_ponens,[status(thm)],[193, 192])).
% 15.57/15.72 tff(195,plain,
% 15.57/15.72 (^[Z: $i, P: $i, C: $i] : refl(((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))))),
% 15.57/15.72 inference(bind,[status(th)],[])).
% 15.57/15.72 tff(196,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 15.57/15.72 inference(quant_intro,[status(thm)],[195])).
% 15.57/15.72 tff(197,plain,
% 15.57/15.72 (^[Z: $i, P: $i, C: $i] : rewrite(((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))))),
% 15.57/15.72 inference(bind,[status(th)],[])).
% 15.57/15.72 tff(198,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 15.57/15.72 inference(quant_intro,[status(thm)],[197])).
% 15.57/15.72 tff(199,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 15.57/15.72 inference(transitivity,[status(thm)],[198, 196])).
% 15.57/15.72 tff(200,plain,
% 15.57/15.72 (^[Z: $i, P: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) <=> (~((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))))), ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) <=> (~(~((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))))))), rewrite((~(~((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)))), ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))))), quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite(((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) <=> ((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))), rewrite((icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))) <=> (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))), ((((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))) <=> (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))), rewrite((((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))) <=> (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))), ((((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))) <=> (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))))), (![X: $i] : (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))) <=> ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))), (((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))) <=> (((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))))), rewrite((((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))), (((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))))),
% 15.57/15.72 inference(bind,[status(th)],[])).
% 15.57/15.72 tff(201,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 15.57/15.72 inference(quant_intro,[status(thm)],[200])).
% 15.57/15.72 tff(202,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 15.57/15.72 inference(rewrite,[status(thm)],[])).
% 15.57/15.72 tff(203,plain,
% 15.57/15.72 (^[Z: $i, P: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite((icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y))) <=> (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))), (![X: $i] : (icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y))) <=> ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))), (((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> ((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))), rewrite(((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) <=> ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))), (((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))),
% 15.57/15.72 inference(bind,[status(th)],[])).
% 15.57/15.72 tff(204,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 15.57/15.72 inference(quant_intro,[status(thm)],[203])).
% 15.57/15.72 tff(205,axiom,(![Z: $i, P: $i, C: $i] : ((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_restrict_allvaluesfrom')).
% 15.57/15.72 tff(206,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 15.57/15.72 inference(modus_ponens,[status(thm)],[205, 204])).
% 15.57/15.72 tff(207,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 15.57/15.72 inference(modus_ponens,[status(thm)],[206, 202])).
% 15.57/15.72 tff(208,plain,(
% 15.57/15.72 ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))),
% 15.57/15.72 inference(skolemize,[status(sab)],[207])).
% 15.57/15.72 tff(209,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 15.57/15.72 inference(modus_ponens,[status(thm)],[208, 201])).
% 15.57/15.72 tff(210,plain,
% 15.57/15.72 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 15.57/15.72 inference(modus_ponens,[status(thm)],[209, 199])).
% 15.57/15.72 tff(211,plain,
% 15.57/15.72 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))) | ((~iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)) | (~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | ![X: $i] : (~((~((~icext(uri_ex_z1, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(uri_ex_nc, Y)))) | (~(icext(uri_ex_z1, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p)))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))) | (~iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)) | (~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | ![X: $i] : (~((~((~icext(uri_ex_z1, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(uri_ex_nc, Y)))) | (~(icext(uri_ex_z1, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p)))))))))),
% 15.57/15.73 inference(rewrite,[status(thm)],[])).
% 15.57/15.73 tff(212,plain,
% 15.57/15.73 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))) | ((~iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)) | (~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | ![X: $i] : (~((~((~icext(uri_ex_z1, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(uri_ex_nc, Y)))) | (~(icext(uri_ex_z1, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p)))))))))),
% 15.57/15.73 inference(quant_inst,[status(thm)],[])).
% 15.57/15.73 tff(213,plain,
% 15.57/15.73 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))) | (~iext(uri_owl_allValuesFrom, uri_ex_z1, uri_ex_nc)) | (~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | ![X: $i] : (~((~((~icext(uri_ex_z1, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(uri_ex_nc, Y)))) | (~(icext(uri_ex_z1, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p))))))))),
% 15.57/15.73 inference(modus_ponens,[status(thm)],[212, 211])).
% 15.57/15.73 tff(214,plain,
% 15.57/15.73 (![X: $i] : (~((~((~icext(uri_ex_z1, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(uri_ex_nc, Y)))) | (~(icext(uri_ex_z1, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p))))))))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[213, 210, 94, 194])).
% 15.57/15.73 tff(215,plain,
% 15.57/15.73 ((~![X: $i] : (~((~((~icext(uri_ex_z1, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(uri_ex_nc, Y)))) | (~(icext(uri_ex_z1, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(X, uri_ex_nc, uri_ex_p))))))))) | (~((~((~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | ![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y)))) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | (~((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))))))))),
% 15.57/15.73 inference(quant_inst,[status(thm)],[])).
% 15.57/15.73 tff(216,plain,
% 15.57/15.73 (~((~((~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | ![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y)))) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | (~((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)))))))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[215, 214])).
% 15.57/15.73 tff(217,plain,
% 15.57/15.73 (((~((~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | ![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y)))) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | (~((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))))))) | ((~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | ![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y)))),
% 15.57/15.73 inference(tautology,[status(thm)],[])).
% 15.57/15.73 tff(218,plain,
% 15.57/15.73 ((~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | ![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[217, 216])).
% 15.57/15.73 tff(219,plain,
% 15.57/15.73 ((~((~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | ![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y)))) | (~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | ![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y))),
% 15.57/15.73 inference(tautology,[status(thm)],[])).
% 15.57/15.73 tff(220,plain,
% 15.57/15.73 ((~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | ![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[219, 218])).
% 15.57/15.73 tff(221,plain,
% 15.57/15.73 (![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[220, 35])).
% 15.57/15.73 tff(222,plain,
% 15.57/15.73 (((~![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y))) | ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))) <=> ((~![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))),
% 15.57/15.73 inference(rewrite,[status(thm)],[])).
% 15.57/15.73 tff(223,plain,
% 15.57/15.73 ((~![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y))) | ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))),
% 15.57/15.73 inference(quant_inst,[status(thm)],[])).
% 15.57/15.73 tff(224,plain,
% 15.57/15.73 ((~![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))),
% 15.57/15.73 inference(modus_ponens,[status(thm)],[223, 222])).
% 15.57/15.73 tff(225,plain,
% 15.57/15.73 (icext(uri_ex_nc, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[224, 221, 191])).
% 15.57/15.73 tff(226,plain,
% 15.57/15.73 (((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))) | icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))),
% 15.57/15.73 inference(tautology,[status(thm)],[])).
% 15.57/15.73 tff(227,plain,
% 15.57/15.73 (icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[226, 189])).
% 15.57/15.73 tff(228,plain,
% 15.57/15.73 ((icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)) <=> icext(uri_ex_nc, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_nc, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))),
% 15.57/15.73 inference(tautology,[status(thm)],[])).
% 15.57/15.73 tff(229,plain,
% 15.57/15.73 ((icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)) <=> icext(uri_ex_nc, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_nc, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[228, 227])).
% 15.57/15.73 tff(230,plain,
% 15.57/15.73 ($false),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[229, 225, 34])).
% 15.57/15.73 tff(231,plain,(~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))), inference(lemma,lemma(discharge,[]))).
% 15.57/15.73 tff(232,plain,
% 15.57/15.73 ((icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))),
% 15.57/15.73 inference(tautology,[status(thm)],[])).
% 15.57/15.73 tff(233,plain,
% 15.57/15.73 (icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[232, 133])).
% 15.57/15.73 tff(234,plain,
% 15.57/15.73 (icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[233, 231])).
% 15.57/15.73 tff(235,plain,
% 15.57/15.73 ((icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) <=> icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))),
% 15.57/15.73 inference(tautology,[status(thm)],[])).
% 15.57/15.73 tff(236,plain,
% 15.57/15.73 ((~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~icext(uri_ex_nz2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[235, 147])).
% 15.57/15.73 tff(237,plain,
% 15.57/15.73 (~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[236, 234])).
% 15.57/15.73 tff(238,plain,
% 15.57/15.73 (((~(icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y))))) | (~((~icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_42(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_c, uri_ex_p)))))))) | (icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y))))),
% 15.57/15.73 inference(tautology,[status(thm)],[])).
% 15.57/15.73 tff(239,plain,
% 15.57/15.73 (icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[238, 184])).
% 15.57/15.73 tff(240,plain,
% 15.57/15.73 ((~(icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y))))) | icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)))),
% 15.57/15.73 inference(tautology,[status(thm)],[])).
% 15.57/15.73 tff(241,plain,
% 15.57/15.73 (icext(uri_ex_z2, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[240, 239])).
% 15.57/15.73 tff(242,plain,
% 15.57/15.73 (![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[241, 237])).
% 15.57/15.73 tff(243,plain,
% 15.57/15.73 (((~((~icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1))) | ![Y: $i] : ((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)) | icext(uri_ex_nc, Y)))) | (~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | (~((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))))))) | (icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | (~((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)))))),
% 15.57/15.73 inference(tautology,[status(thm)],[])).
% 15.57/15.73 tff(244,plain,
% 15.57/15.73 (icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | (~((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[243, 216])).
% 15.57/15.73 tff(245,plain,
% 15.57/15.73 ((~(icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | (~((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)))))) | icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | (~((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))))),
% 15.57/15.73 inference(tautology,[status(thm)],[])).
% 15.57/15.73 tff(246,plain,
% 15.57/15.73 (icext(uri_ex_z1, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1)) | (~((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[245, 244])).
% 15.57/15.73 tff(247,plain,
% 15.57/15.73 (~((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[246, 231])).
% 15.57/15.73 tff(248,plain,
% 15.57/15.73 (((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))),
% 15.57/15.73 inference(tautology,[status(thm)],[])).
% 15.57/15.73 tff(249,plain,
% 15.57/15.73 (iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))),
% 15.57/15.73 inference(unit_resolution,[status(thm)],[248, 247])).
% 15.57/15.73 tff(250,plain,
% 15.57/15.73 (((~![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)))) | ((~icext(uri_ex_c, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))))) <=> ((~![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)))) | (~icext(uri_ex_c, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))))),
% 15.57/15.73 inference(rewrite,[status(thm)],[])).
% 15.57/15.73 tff(251,plain,
% 15.57/15.73 ((~![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)))) | ((~icext(uri_ex_c, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))))),
% 15.57/15.73 inference(quant_inst,[status(thm)],[])).
% 15.57/15.73 tff(252,plain,
% 15.57/15.73 ((~![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), Y)))) | (~icext(uri_ex_c, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)))),
% 15.57/15.76 inference(modus_ponens,[status(thm)],[251, 250])).
% 15.57/15.76 tff(253,plain,
% 15.57/15.76 (~icext(uri_ex_c, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))),
% 15.57/15.76 inference(unit_resolution,[status(thm)],[252, 249, 242])).
% 15.57/15.76 tff(254,plain,
% 15.57/15.76 (((~iext(uri_ex_p, tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | (~icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)))),
% 15.57/15.76 inference(tautology,[status(thm)],[])).
% 15.57/15.76 tff(255,plain,
% 15.57/15.76 (~icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))),
% 15.57/15.76 inference(unit_resolution,[status(thm)],[254, 247])).
% 15.57/15.76 tff(256,plain,
% 15.57/15.76 ((icext(uri_ex_c, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)) <=> icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_c, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)) | icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))),
% 15.57/15.76 inference(tautology,[status(thm)],[])).
% 15.57/15.76 tff(257,plain,
% 15.57/15.76 ((icext(uri_ex_c, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p)) <=> icext(uri_ex_nc, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))) | icext(uri_ex_c, tptp_fun_Y_11(tptp_fun_X_67(uri_ex_nz2, uri_ex_z1), uri_ex_nc, uri_ex_p))),
% 15.57/15.76 inference(unit_resolution,[status(thm)],[256, 255])).
% 15.57/15.76 tff(258,plain,
% 15.57/15.76 ($false),
% 15.57/15.76 inference(unit_resolution,[status(thm)],[257, 253, 32])).
% 15.57/15.76 % SZS output end Proof
% 15.57/15.77 % E exiting
%------------------------------------------------------------------------------