%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM460+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:21:03 AM UTC 2025
% Result : Theorem 0.23s 0.43s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : NUM460+2 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 01:12:10 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.43 % SZS status Theorem
% 0.23/0.43 % SZS output start Proof
% 0.23/0.43 tff(aNaturalNumber0_type, type, (
% 0.23/0.43 aNaturalNumber0: $i > $o)).
% 0.23/0.43 tff(sdtpldt0_type, type, (
% 0.23/0.43 sdtpldt0: ( $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_W0_2_type, type, (
% 0.23/0.43 tptp_fun_W0_2: $i)).
% 0.23/0.43 tff(tptp_fun_W0_1_type, type, (
% 0.23/0.43 tptp_fun_W0_1: $i)).
% 0.23/0.43 tff(xl_type, type, (
% 0.23/0.43 xl: $i)).
% 0.23/0.43 tff(xm_type, type, (
% 0.23/0.43 xm: $i)).
% 0.23/0.43 tff(xn_type, type, (
% 0.23/0.43 xn: $i)).
% 0.23/0.43 tff(sdtlseqdt0_type, type, (
% 0.23/0.43 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_W2_0_type, type, (
% 0.23/0.43 tptp_fun_W2_0: ( $i * $i ) > $i)).
% 0.23/0.43 tff(1,plain,
% 0.23/0.43 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xl)) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xl))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(2,plain,
% 0.23/0.43 ((~((((?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) & sdtlseqdt0(xm, xn)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xl))) & sdtlseqdt0(xn, xl)) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xl)) | sdtlseqdt0(xm, xl)))) <=> (~(sdtlseqdt0(xm, xl) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xl)) | (~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) & sdtlseqdt0(xm, xn) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xl)) & sdtlseqdt0(xn, xl)))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(3,axiom,(~((((?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) & sdtlseqdt0(xm, xn)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xl))) & sdtlseqdt0(xn, xl)) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xl)) | sdtlseqdt0(xm, xl)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.23/0.43 tff(4,plain,
% 0.23/0.43 (~(sdtlseqdt0(xm, xl) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xl)) | (~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) & sdtlseqdt0(xm, xn) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xl)) & sdtlseqdt0(xn, xl))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.23/0.43 tff(5,plain,
% 0.23/0.43 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) & sdtlseqdt0(xm, xn) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xl)) & sdtlseqdt0(xn, xl)),
% 0.23/0.43 inference(or_elim,[status(thm)],[4])).
% 0.23/0.43 tff(6,plain,
% 0.23/0.43 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xl))),
% 0.23/0.43 inference(and_elim,[status(thm)],[5])).
% 0.23/0.43 tff(7,plain,
% 0.23/0.43 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xl))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.23/0.43 tff(8,plain,(
% 0.23/0.43 aNaturalNumber0(W0!2) & (sdtpldt0(xn, W0!2) = xl)),
% 0.23/0.43 inference(skolemize,[status(sab)],[7])).
% 0.23/0.43 tff(9,plain,
% 0.23/0.43 (sdtpldt0(xn, W0!2) = xl),
% 0.23/0.43 inference(and_elim,[status(thm)],[8])).
% 0.23/0.43 tff(10,plain,
% 0.23/0.43 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(11,plain,
% 0.23/0.43 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn))),
% 0.23/0.43 inference(and_elim,[status(thm)],[5])).
% 0.23/0.43 tff(12,plain,
% 0.23/0.43 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.23/0.43 tff(13,plain,(
% 0.23/0.43 aNaturalNumber0(W0!1) & (sdtpldt0(xm, W0!1) = xn)),
% 0.23/0.43 inference(skolemize,[status(sab)],[12])).
% 0.23/0.43 tff(14,plain,
% 0.23/0.43 (sdtpldt0(xm, W0!1) = xn),
% 0.23/0.43 inference(and_elim,[status(thm)],[13])).
% 0.23/0.43 tff(15,plain,
% 0.23/0.43 (sdtpldt0(sdtpldt0(xm, W0!1), W0!2) = sdtpldt0(xn, W0!2)),
% 0.23/0.43 inference(monotonicity,[status(thm)],[14])).
% 0.23/0.43 tff(16,plain,
% 0.23/0.43 (aNaturalNumber0(W0!2)),
% 0.23/0.43 inference(and_elim,[status(thm)],[8])).
% 0.23/0.43 tff(17,plain,
% 0.23/0.43 (aNaturalNumber0(W0!1)),
% 0.23/0.43 inference(and_elim,[status(thm)],[13])).
% 0.23/0.43 tff(18,plain,
% 0.23/0.43 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(19,axiom,((aNaturalNumber0(xm) & aNaturalNumber0(xn)) & aNaturalNumber0(xl)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__773')).
% 0.23/0.43 tff(20,plain,
% 0.23/0.43 (aNaturalNumber0(xm) & aNaturalNumber0(xn)),
% 0.23/0.43 inference(and_elim,[status(thm)],[19])).
% 0.23/0.43 tff(21,plain,
% 0.23/0.43 (aNaturalNumber0(xm)),
% 0.23/0.43 inference(and_elim,[status(thm)],[20])).
% 0.23/0.43 tff(22,plain,
% 0.23/0.43 (aNaturalNumber0(xm)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.23/0.43 tff(23,plain,
% 0.23/0.43 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(24,plain,
% 0.23/0.43 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[23])).
% 0.23/0.43 tff(25,plain,
% 0.23/0.43 (^[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))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(26,plain,
% 0.23/0.43 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[25])).
% 0.23/0.43 tff(27,plain,
% 0.23/0.43 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(28,plain,
% 0.23/0.43 (^[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)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(29,plain,
% 0.23/0.43 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[28])).
% 0.23/0.43 tff(30,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddAsso')).
% 0.23/0.43 tff(31,plain,
% 0.23/0.43 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.23/0.43 tff(32,plain,
% 0.23/0.43 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.23/0.43 tff(33,plain,(
% 0.23/0.43 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 0.23/0.43 inference(skolemize,[status(sab)],[32])).
% 0.23/0.43 tff(34,plain,
% 0.23/0.43 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.23/0.43 tff(35,plain,
% 0.23/0.43 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.23/0.43 tff(36,plain,
% 0.23/0.43 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(xm, W0!1), W0!2) = sdtpldt0(xm, sdtpldt0(W0!1, W0!2))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xm)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (sdtpldt0(sdtpldt0(xm, W0!1), W0!2) = sdtpldt0(xm, sdtpldt0(W0!1, W0!2))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xm)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(37,plain,
% 0.23/0.43 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(xm, W0!1), W0!2) = sdtpldt0(xm, sdtpldt0(W0!1, W0!2))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xm)))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(38,plain,
% 0.23/0.43 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (sdtpldt0(sdtpldt0(xm, W0!1), W0!2) = sdtpldt0(xm, sdtpldt0(W0!1, W0!2))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xm))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.23/0.43 tff(39,plain,
% 0.23/0.43 (sdtpldt0(sdtpldt0(xm, W0!1), W0!2) = sdtpldt0(xm, sdtpldt0(W0!1, W0!2))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[38, 35, 22, 17, 16])).
% 0.23/0.43 tff(40,plain,
% 0.23/0.43 (sdtpldt0(xm, sdtpldt0(W0!1, W0!2)) = sdtpldt0(sdtpldt0(xm, W0!1), W0!2)),
% 0.23/0.43 inference(symmetry,[status(thm)],[39])).
% 0.23/0.43 tff(41,plain,
% 0.23/0.43 (sdtpldt0(xm, sdtpldt0(W0!1, W0!2)) = xl),
% 0.23/0.43 inference(transitivity,[status(thm)],[40, 15, 9])).
% 0.23/0.43 tff(42,plain,
% 0.23/0.43 (aNaturalNumber0(xl) <=> aNaturalNumber0(xl)),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(43,plain,
% 0.23/0.43 (aNaturalNumber0(xl)),
% 0.23/0.43 inference(and_elim,[status(thm)],[19])).
% 0.23/0.43 tff(44,plain,
% 0.23/0.43 (aNaturalNumber0(xl)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.23/0.43 tff(45,plain,
% 0.23/0.43 (^[W0: $i, W1: $i] : refl(((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1)))))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1)))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(46,plain,
% 0.23/0.43 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.23/0.43 tff(47,plain,
% 0.23/0.43 (^[W0: $i, W1: $i] : rewrite(((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1)))))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1)))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(48,plain,
% 0.23/0.43 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.23/0.43 tff(49,plain,
% 0.23/0.43 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[48, 46])).
% 0.23/0.43 tff(50,plain,
% 0.23/0.43 (^[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))))), trans(monotonicity(rewrite(((~sdtlseqdt0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_0(W1, W0)) & (sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1))) <=> ((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))), rewrite((sdtlseqdt0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))) <=> (sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))), ((((~sdtlseqdt0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_0(W1, W0)) & (sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1))) & (sdtlseqdt0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))) <=> (((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1))))) & (sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))), rewrite((((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1))))) & (sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))) <=> (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1)))))))), ((((~sdtlseqdt0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_0(W1, W0)) & (sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1))) & (sdtlseqdt0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))) <=> (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~sdtlseqdt0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_0(W1, W0)) & (sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1))) & (sdtlseqdt0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1)))))))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1)))))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~sdtlseqdt0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_0(W1, W0)) & (sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1))) & (sdtlseqdt0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(51,plain,
% 0.23/0.43 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~sdtlseqdt0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_0(W1, W0)) & (sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1))) & (sdtlseqdt0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[50])).
% 0.23/0.43 tff(52,plain,
% 0.23/0.43 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(53,plain,
% 0.23/0.43 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) <=> (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(54,plain,
% 0.23/0.43 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[53])).
% 0.23/0.43 tff(55,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefLE')).
% 0.23/0.43 tff(56,plain,
% 0.23/0.43 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.23/0.43 tff(57,plain,
% 0.23/0.43 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtlseqdt0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.23/0.43 tff(58,plain,(
% 0.23/0.43 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~sdtlseqdt0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_0(W1, W0)) & (sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1))) & (sdtlseqdt0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))))),
% 0.23/0.43 inference(skolemize,[status(sab)],[57])).
% 0.23/0.43 tff(59,plain,
% 0.23/0.43 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.23/0.43 tff(60,plain,
% 0.23/0.43 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.23/0.43 tff(61,plain,
% 0.23/0.43 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))) | ((~aNaturalNumber0(xl)) | (~aNaturalNumber0(xm)) | (~((~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))) | (~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl)))))))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))) | (~aNaturalNumber0(xl)) | (~aNaturalNumber0(xm)) | (~((~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))) | (~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl)))))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(62,plain,
% 0.23/0.44 (((~aNaturalNumber0(xl)) | (~aNaturalNumber0(xm)) | (~((~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl)))))) | (~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl)))))))) <=> ((~aNaturalNumber0(xl)) | (~aNaturalNumber0(xm)) | (~((~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))) | (~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl)))))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(63,plain,
% 0.23/0.44 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))) | ((~aNaturalNumber0(xl)) | (~aNaturalNumber0(xm)) | (~((~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl)))))) | (~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))) | ((~aNaturalNumber0(xl)) | (~aNaturalNumber0(xm)) | (~((~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))) | (~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl))))))))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[62])).
% 0.23/0.44 tff(64,plain,
% 0.23/0.44 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))) | ((~aNaturalNumber0(xl)) | (~aNaturalNumber0(xm)) | (~((~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl)))))) | (~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))) | (~aNaturalNumber0(xl)) | (~aNaturalNumber0(xm)) | (~((~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))) | (~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl)))))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[63, 61])).
% 0.23/0.44 tff(65,plain,
% 0.23/0.44 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))) | ((~aNaturalNumber0(xl)) | (~aNaturalNumber0(xm)) | (~((~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl)))))) | (~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(66,plain,
% 0.23/0.44 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~sdtlseqdt0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_0(W1, W0))) | (~(sdtpldt0(W0, tptp_fun_W2_0(W1, W0)) = W1)))))) | (~(sdtlseqdt0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))))) | (~aNaturalNumber0(xl)) | (~aNaturalNumber0(xm)) | (~((~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))) | (~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl))))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.23/0.44 tff(67,plain,
% 0.23/0.44 (~((~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))) | (~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl)))))))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[66, 60, 22, 44])).
% 0.23/0.44 tff(68,plain,
% 0.23/0.44 (((~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))) | (~((~sdtlseqdt0(xm, xl)) | (~((~aNaturalNumber0(tptp_fun_W2_0(xl, xm))) | (~(sdtpldt0(xm, tptp_fun_W2_0(xl, xm)) = xl))))))) | (sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(69,plain,
% 0.23/0.44 (sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.23/0.44 tff(70,plain,
% 0.23/0.44 ((~sdtlseqdt0(xm, xl)) <=> (~sdtlseqdt0(xm, xl))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(71,plain,
% 0.23/0.44 (~sdtlseqdt0(xm, xl)),
% 0.23/0.44 inference(or_elim,[status(thm)],[4])).
% 0.23/0.44 tff(72,plain,
% 0.23/0.44 (~sdtlseqdt0(xm, xl)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.23/0.44 tff(73,plain,
% 0.23/0.44 ((~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))) | sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl)))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(74,plain,
% 0.23/0.44 ((~(sdtlseqdt0(xm, xl) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl))))) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.23/0.44 tff(75,plain,
% 0.23/0.44 (![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[74, 69])).
% 0.23/0.44 tff(76,plain,
% 0.23/0.44 (((~![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl)))) | ((~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (~(sdtpldt0(xm, sdtpldt0(W0!1, W0!2)) = xl)))) <=> ((~![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl)))) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (~(sdtpldt0(xm, sdtpldt0(W0!1, W0!2)) = xl)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(77,plain,
% 0.23/0.44 ((~![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl)))) | ((~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (~(sdtpldt0(xm, sdtpldt0(W0!1, W0!2)) = xl)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(78,plain,
% 0.23/0.44 ((~![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xl)))) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (~(sdtpldt0(xm, sdtpldt0(W0!1, W0!2)) = xl))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.23/0.44 tff(79,plain,
% 0.23/0.44 (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[78, 75, 41])).
% 0.23/0.44 tff(80,plain,
% 0.23/0.44 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(81,plain,
% 0.23/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[80])).
% 0.23/0.44 tff(82,plain,
% 0.23/0.44 (^[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(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((aNaturalNumber0(sdtpldt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(83,plain,
% 0.23/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[82])).
% 0.23/0.44 tff(84,plain,
% 0.23/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(85,plain,
% 0.23/0.44 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(86,plain,
% 0.23/0.44 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[85])).
% 0.23/0.44 tff(87,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB')).
% 0.23/0.44 tff(88,plain,
% 0.23/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.23/0.44 tff(89,plain,
% 0.23/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.23/0.44 tff(90,plain,(
% 0.23/0.44 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.23/0.44 inference(skolemize,[status(sab)],[89])).
% 0.23/0.44 tff(91,plain,
% 0.23/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.23/0.44 tff(92,plain,
% 0.23/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[91, 81])).
% 0.23/0.44 tff(93,plain,
% 0.23/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(94,plain,
% 0.23/0.44 ((aNaturalNumber0(sdtpldt0(W0!1, W0!2)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1))) <=> ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(95,plain,
% 0.23/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(W0!1, W0!2)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[94])).
% 0.23/0.44 tff(96,plain,
% 0.23/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(W0!1, W0!2)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2)))),
% 0.23/0.44 inference(transitivity,[status(thm)],[95, 93])).
% 0.23/0.44 tff(97,plain,
% 0.23/0.44 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(W0!1, W0!2)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(98,plain,
% 0.23/0.44 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.23/0.44 tff(99,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[98, 92, 17, 16, 79])).
% 0.23/0.44 % SZS output end Proof
% 0.23/0.45 % E exiting
%------------------------------------------------------------------------------