%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM466+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:21:04 AM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM466+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:13:41 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(aNaturalNumber0_type, type, (
% 0.19/0.40 aNaturalNumber0: $i > $o)).
% 0.19/0.40 tff(sdtasdt0_type, type, (
% 0.19/0.40 sdtasdt0: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_W0_3_type, type, (
% 0.19/0.40 tptp_fun_W0_3: $i)).
% 0.19/0.40 tff(tptp_fun_W0_2_type, type, (
% 0.19/0.40 tptp_fun_W0_2: $i)).
% 0.19/0.40 tff(xl_type, type, (
% 0.19/0.40 xl: $i)).
% 0.19/0.40 tff(xn_type, type, (
% 0.19/0.40 xn: $i)).
% 0.19/0.40 tff(xm_type, type, (
% 0.19/0.40 xm: $i)).
% 0.19/0.40 tff(doDivides0_type, type, (
% 0.19/0.40 doDivides0: ( $i * $i ) > $o)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~((((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm)) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0)))) & doDivides0(xm, xn)) => (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0))) | doDivides0(xl, xn)))) <=> (~(doDivides0(xl, xn) | ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0))) | (~(?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0))) & doDivides0(xm, xn)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,axiom,(~((((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm)) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0)))) & doDivides0(xm, xn)) => (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0))) | doDivides0(xl, xn)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (~(doDivides0(xl, xn) | ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0))) | (~(?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0))) & doDivides0(xm, xn))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0))) & doDivides0(xm, xn)),
% 0.19/0.40 inference(or_elim,[status(thm)],[4])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0)))),
% 0.19/0.40 inference(and_elim,[status(thm)],[5])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.40 tff(8,plain,(
% 0.19/0.40 aNaturalNumber0(W0!3) & (xn = sdtasdt0(xm, W0!3))),
% 0.19/0.40 inference(skolemize,[status(sab)],[7])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (aNaturalNumber0(W0!3)),
% 0.19/0.40 inference(and_elim,[status(thm)],[8])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 0.19/0.40 inference(and_elim,[status(thm)],[5])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.40 tff(13,plain,(
% 0.19/0.40 aNaturalNumber0(W0!2) & (xm = sdtasdt0(xl, W0!2))),
% 0.19/0.40 inference(skolemize,[status(sab)],[12])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (aNaturalNumber0(W0!2)),
% 0.19/0.40 inference(and_elim,[status(thm)],[13])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (aNaturalNumber0(xl) <=> aNaturalNumber0(xl)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,axiom,((aNaturalNumber0(xl) & aNaturalNumber0(xm)) & aNaturalNumber0(xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1218')).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (aNaturalNumber0(xl) & aNaturalNumber0(xm)),
% 0.19/0.40 inference(and_elim,[status(thm)],[16])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (aNaturalNumber0(xl)),
% 0.19/0.40 inference(and_elim,[status(thm)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (aNaturalNumber0(xl)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.41 tff(27,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulAsso')).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.41 tff(30,plain,(
% 0.19/0.41 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xl, W0!2), W0!3) = sdtasdt0(xl, sdtasdt0(W0!2, W0!3))) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(xl)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (sdtasdt0(sdtasdt0(xl, W0!2), W0!3) = sdtasdt0(xl, sdtasdt0(W0!2, W0!3))) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(xl)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xl, W0!2), W0!3) = sdtasdt0(xl, sdtasdt0(W0!2, W0!3))) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(xl)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (sdtasdt0(sdtasdt0(xl, W0!2), W0!3) = sdtasdt0(xl, sdtasdt0(W0!2, W0!3))) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(xl))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (sdtasdt0(sdtasdt0(xl, W0!2), W0!3) = sdtasdt0(xl, sdtasdt0(W0!2, W0!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[35, 32, 19, 14, 9])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (xm = sdtasdt0(xl, W0!2)),
% 0.19/0.41 inference(and_elim,[status(thm)],[13])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (sdtasdt0(xl, W0!2) = xm),
% 0.19/0.41 inference(symmetry,[status(thm)],[37])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (sdtasdt0(sdtasdt0(xl, W0!2), W0!3) = sdtasdt0(xm, W0!3)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (sdtasdt0(xm, W0!3) = sdtasdt0(sdtasdt0(xl, W0!2), W0!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[39])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (xn = sdtasdt0(xm, W0!3)),
% 0.19/0.41 inference(and_elim,[status(thm)],[8])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (xn = sdtasdt0(xl, sdtasdt0(W0!2, W0!3))),
% 0.19/0.41 inference(transitivity,[status(thm)],[41, 40, 36])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0)))) <=> ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (^[W0: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0))) <=> (~((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0)))))), ((~(aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0)))) <=> (~(~((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0)))))))), rewrite((~(~((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0)))))) <=> ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0))))), ((~(aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0)))) <=> ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![W0: $i] : (~(aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 ((~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0)))) <=> (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0)))),
% 0.19/0.41 inference(or_elim,[status(thm)],[4])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[49, 47])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (^[W0: $i] : refl($oeq((~(aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0)))), (~(aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(53,plain,(
% 0.19/0.41 ![W0: $i] : (~(aNaturalNumber0(W0) & (xn = sdtasdt0(xl, W0))))),
% 0.19/0.41 inference(nnf-neg,[status(sab)],[51, 52])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0))))) | ((~aNaturalNumber0(sdtasdt0(W0!2, W0!3))) | (~(xn = sdtasdt0(xl, sdtasdt0(W0!2, W0!3)))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0))))) | (~aNaturalNumber0(sdtasdt0(W0!2, W0!3))) | (~(xn = sdtasdt0(xl, sdtasdt0(W0!2, W0!3)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0))))) | ((~aNaturalNumber0(sdtasdt0(W0!2, W0!3))) | (~(xn = sdtasdt0(xl, sdtasdt0(W0!2, W0!3)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xl, W0))))) | (~aNaturalNumber0(sdtasdt0(W0!2, W0!3))) | (~(xn = sdtasdt0(xl, sdtasdt0(W0!2, W0!3))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (~aNaturalNumber0(sdtasdt0(W0!2, W0!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[58, 55, 42])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.41 tff(67,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.41 tff(70,plain,(
% 0.19/0.41 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[69])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)) | aNaturalNumber0(sdtasdt0(W0!2, W0!3)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)) | aNaturalNumber0(sdtasdt0(W0!2, W0!3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 ((aNaturalNumber0(sdtasdt0(W0!2, W0!3)) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2))) <=> ((~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)) | aNaturalNumber0(sdtasdt0(W0!2, W0!3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!2, W0!3)) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)) | aNaturalNumber0(sdtasdt0(W0!2, W0!3))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[74])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!2, W0!3)) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)) | aNaturalNumber0(sdtasdt0(W0!2, W0!3)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[75, 73])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!2, W0!3)) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(W0!2)) | aNaturalNumber0(sdtasdt0(W0!2, W0!3))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[78, 72, 14, 9, 59])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------