%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM501+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:21:11 AM UTC 2025
% Result : Theorem 50.95s 51.24s
% Output : Proof 51.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM501+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 01:18:54 EDT 2025
% 0.11/0.33 % CPUTime :
% 50.95/51.24 % SZS status Theorem
% 50.95/51.24 % SZS output start Proof
% 50.95/51.24 tff(sdtasdt0_type, type, (
% 50.95/51.24 sdtasdt0: ( $i * $i ) > $i)).
% 50.95/51.24 tff(xp_type, type, (
% 50.95/51.24 xp: $i)).
% 50.95/51.24 tff(tptp_fun_W0_11_type, type, (
% 50.95/51.24 tptp_fun_W0_11: $i)).
% 50.95/51.24 tff(xr_type, type, (
% 50.95/51.24 xr: $i)).
% 50.95/51.24 tff(tptp_fun_W0_8_type, type, (
% 50.95/51.24 tptp_fun_W0_8: $i)).
% 50.95/51.24 tff(aNaturalNumber0_type, type, (
% 50.95/51.24 aNaturalNumber0: $i > $o)).
% 50.95/51.24 tff(xk_type, type, (
% 50.95/51.24 xk: $i)).
% 50.95/51.24 tff(doDivides0_type, type, (
% 50.95/51.24 doDivides0: ( $i * $i ) > $o)).
% 50.95/51.24 tff(sz00_type, type, (
% 50.95/51.24 sz00: $i)).
% 50.95/51.24 tff(sz10_type, type, (
% 50.95/51.24 sz10: $i)).
% 50.95/51.24 tff(isPrime0_type, type, (
% 50.95/51.24 isPrime0: $i > $o)).
% 50.95/51.24 tff(xm_type, type, (
% 50.95/51.24 xm: $i)).
% 50.95/51.24 tff(xn_type, type, (
% 50.95/51.24 xn: $i)).
% 50.95/51.24 tff(sdtpldt0_type, type, (
% 50.95/51.24 sdtpldt0: ( $i * $i ) > $i)).
% 50.95/51.24 tff(tptp_fun_W0_10_type, type, (
% 50.95/51.24 tptp_fun_W0_10: $i)).
% 50.95/51.24 tff(sdtlseqdt0_type, type, (
% 50.95/51.24 sdtlseqdt0: ( $i * $i ) > $o)).
% 50.95/51.24 tff(sdtsldt0_type, type, (
% 50.95/51.24 sdtsldt0: ( $i * $i ) > $i)).
% 50.95/51.24 tff(tptp_fun_W2_1_type, type, (
% 50.95/51.24 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 50.95/51.24 tff(1,plain,
% 50.95/51.24 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 50.95/51.24 inference(rewrite,[status(thm)],[])).
% 50.95/51.24 tff(2,axiom,((((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))) & isPrime0(xr)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2342')).
% 50.95/51.24 tff(3,plain,
% 50.95/51.24 (((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))),
% 50.95/51.24 inference(and_elim,[status(thm)],[2])).
% 50.95/51.24 tff(4,plain,
% 50.95/51.24 ((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))),
% 50.95/51.24 inference(and_elim,[status(thm)],[3])).
% 50.95/51.24 tff(5,plain,
% 50.95/51.24 (((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))),
% 50.95/51.24 inference(and_elim,[status(thm)],[4])).
% 50.95/51.24 tff(6,plain,
% 50.95/51.24 ((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)),
% 50.95/51.24 inference(and_elim,[status(thm)],[5])).
% 50.95/51.24 tff(7,plain,
% 50.95/51.24 (aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 50.95/51.24 inference(and_elim,[status(thm)],[6])).
% 50.95/51.24 tff(8,plain,
% 50.95/51.24 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 50.95/51.24 inference(and_elim,[status(thm)],[7])).
% 50.95/51.24 tff(9,plain,
% 50.95/51.24 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 50.95/51.24 inference(modus_ponens,[status(thm)],[8, 1])).
% 50.95/51.24 tff(10,plain,(
% 50.95/51.24 aNaturalNumber0(W0!11) & (xk = sdtasdt0(xr, W0!11))),
% 50.95/51.24 inference(skolemize,[status(sab)],[9])).
% 50.95/51.24 tff(11,plain,
% 50.95/51.24 (aNaturalNumber0(W0!11)),
% 50.95/51.24 inference(and_elim,[status(thm)],[10])).
% 50.95/51.24 tff(12,plain,
% 50.95/51.24 (aNaturalNumber0(xr) <=> aNaturalNumber0(xr)),
% 50.95/51.24 inference(rewrite,[status(thm)],[])).
% 50.95/51.24 tff(13,plain,
% 50.95/51.24 (aNaturalNumber0(xr)),
% 50.95/51.24 inference(and_elim,[status(thm)],[7])).
% 50.95/51.24 tff(14,plain,
% 50.95/51.24 (aNaturalNumber0(xr)),
% 50.95/51.24 inference(modus_ponens,[status(thm)],[13, 12])).
% 50.95/51.24 tff(15,plain,
% 50.95/51.24 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 50.95/51.24 inference(rewrite,[status(thm)],[])).
% 50.95/51.24 tff(16,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1837')).
% 50.95/51.24 tff(17,plain,
% 50.95/51.24 (aNaturalNumber0(xp)),
% 50.95/51.24 inference(and_elim,[status(thm)],[16])).
% 50.95/51.24 tff(18,plain,
% 50.95/51.24 (aNaturalNumber0(xp)),
% 50.95/51.24 inference(modus_ponens,[status(thm)],[17, 15])).
% 50.95/51.24 tff(19,plain,
% 50.95/51.24 (^[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))))),
% 50.95/51.24 inference(bind,[status(th)],[])).
% 50.95/51.24 tff(20,plain,
% 50.95/51.24 (![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)))),
% 50.95/51.24 inference(quant_intro,[status(thm)],[19])).
% 50.95/51.24 tff(21,plain,
% 50.95/51.24 (^[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)))))),
% 50.95/51.24 inference(bind,[status(th)],[])).
% 50.95/51.24 tff(22,plain,
% 50.95/51.24 (![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)))),
% 50.95/51.24 inference(quant_intro,[status(thm)],[21])).
% 50.95/51.24 tff(23,plain,
% 50.95/51.24 (![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))))),
% 50.95/51.24 inference(rewrite,[status(thm)],[])).
% 50.95/51.24 tff(24,plain,
% 50.95/51.24 (^[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))))))),
% 50.95/51.24 inference(bind,[status(th)],[])).
% 50.95/51.24 tff(25,plain,
% 50.95/51.24 (![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))))),
% 50.95/51.24 inference(quant_intro,[status(thm)],[24])).
% 50.95/51.24 tff(26,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')).
% 50.95/51.24 tff(27,plain,
% 50.95/51.24 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 50.95/51.24 inference(modus_ponens,[status(thm)],[26, 25])).
% 50.95/51.24 tff(28,plain,
% 50.95/51.24 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 50.95/51.24 inference(modus_ponens,[status(thm)],[27, 23])).
% 50.95/51.24 tff(29,plain,(
% 50.95/51.24 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 50.95/51.24 inference(skolemize,[status(sab)],[28])).
% 50.95/51.24 tff(30,plain,
% 50.95/51.24 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 50.95/51.24 inference(modus_ponens,[status(thm)],[29, 22])).
% 50.95/51.24 tff(31,plain,
% 50.95/51.24 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 50.95/51.24 inference(modus_ponens,[status(thm)],[30, 20])).
% 50.95/51.24 tff(32,plain,
% 50.95/51.24 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xr, sdtasdt0(W0!11, xp))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xr, sdtasdt0(W0!11, xp))))),
% 50.95/51.24 inference(rewrite,[status(thm)],[])).
% 50.95/51.24 tff(33,plain,
% 50.95/51.24 (((sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xr, sdtasdt0(W0!11, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xr))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xr, sdtasdt0(W0!11, xp))))),
% 50.95/51.24 inference(rewrite,[status(thm)],[])).
% 50.95/51.24 tff(34,plain,
% 50.95/51.24 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xr, sdtasdt0(W0!11, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xr, sdtasdt0(W0!11, xp)))))),
% 50.95/51.24 inference(monotonicity,[status(thm)],[33])).
% 50.95/51.24 tff(35,plain,
% 50.95/51.24 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xr, sdtasdt0(W0!11, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xr, sdtasdt0(W0!11, xp))))),
% 50.95/51.24 inference(transitivity,[status(thm)],[34, 32])).
% 50.95/51.24 tff(36,plain,
% 50.95/51.24 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xr, sdtasdt0(W0!11, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xr)))),
% 50.95/51.24 inference(quant_inst,[status(thm)],[])).
% 50.95/51.24 tff(37,plain,
% 50.95/51.24 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xr, sdtasdt0(W0!11, xp)))),
% 50.95/51.24 inference(modus_ponens,[status(thm)],[36, 35])).
% 50.95/51.24 tff(38,plain,
% 50.95/51.24 (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xr, sdtasdt0(W0!11, xp))),
% 50.95/51.24 inference(unit_resolution,[status(thm)],[37, 31, 18, 14, 11])).
% 50.95/51.24 tff(39,plain,
% 50.95/51.24 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 50.95/51.24 inference(rewrite,[status(thm)],[])).
% 50.95/51.24 tff(40,axiom,((((((~(xn = xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & sdtlseqdt0(xn, xp)) & (~(xm = xp))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))) & sdtlseqdt0(xm, xp)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2287')).
% 50.95/51.24 tff(41,plain,
% 50.95/51.24 (((((~(xn = xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & sdtlseqdt0(xn, xp)) & (~(xm = xp))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 50.95/51.24 inference(and_elim,[status(thm)],[40])).
% 50.95/51.24 tff(42,plain,
% 50.95/51.24 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 50.95/51.24 inference(and_elim,[status(thm)],[41])).
% 50.95/51.24 tff(43,plain,
% 50.95/51.24 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 50.95/51.24 inference(modus_ponens,[status(thm)],[42, 39])).
% 50.95/51.24 tff(44,plain,(
% 50.95/51.24 aNaturalNumber0(W0!10) & (sdtpldt0(xm, W0!10) = xp)),
% 50.95/51.24 inference(skolemize,[status(sab)],[43])).
% 50.95/51.24 tff(45,plain,
% 50.95/51.24 (sdtpldt0(xm, W0!10) = xp),
% 50.95/51.24 inference(and_elim,[status(thm)],[44])).
% 50.95/51.24 tff(46,plain,
% 50.95/51.24 (xp = sdtpldt0(xm, W0!10)),
% 50.95/51.24 inference(symmetry,[status(thm)],[45])).
% 50.95/51.24 tff(47,plain,
% 50.95/51.24 ((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) <=> (sdtasdt0(xp, W0!8) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 50.95/51.24 inference(commutativity,[status(thm)],[])).
% 50.95/51.24 tff(48,plain,
% 50.95/51.24 ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))) <=> (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8))),
% 50.95/51.24 inference(symmetry,[status(thm)],[47])).
% 50.95/51.24 tff(49,plain,
% 50.95/51.24 ((xk = sdtsldt0(sdtasdt0(xn, xm), xp)) <=> (xk = sdtsldt0(sdtasdt0(xn, xm), xp))),
% 50.95/51.24 inference(rewrite,[status(thm)],[])).
% 50.95/51.24 tff(50,axiom,((aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))) & (xk = sdtsldt0(sdtasdt0(xn, xm), xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2306')).
% 50.95/51.24 tff(51,plain,
% 50.95/51.24 (xk = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 50.95/51.24 inference(and_elim,[status(thm)],[50])).
% 50.95/51.24 tff(52,plain,
% 50.95/51.24 (xk = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 50.95/51.24 inference(modus_ponens,[status(thm)],[51, 49])).
% 50.95/51.24 tff(53,plain,
% 50.95/51.24 (sdtsldt0(sdtasdt0(xn, xm), xp) = xk),
% 50.95/51.24 inference(symmetry,[status(thm)],[52])).
% 50.95/51.24 tff(54,plain,
% 50.95/51.24 (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, xk)),
% 50.95/51.24 inference(monotonicity,[status(thm)],[53])).
% 50.95/51.24 tff(55,plain,
% 50.95/51.24 (sdtasdt0(xp, xk) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))),
% 50.95/51.24 inference(symmetry,[status(thm)],[54])).
% 50.95/51.24 tff(56,plain,
% 50.95/51.24 ((sdtasdt0(xn, xm) = sdtasdt0(xp, xk)) <=> (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 50.95/51.24 inference(rewrite,[status(thm)],[])).
% 50.95/51.24 tff(57,plain,
% 50.95/51.24 (aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 50.95/51.25 inference(and_elim,[status(thm)],[50])).
% 50.95/51.25 tff(58,plain,
% 50.95/51.25 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 50.95/51.25 inference(and_elim,[status(thm)],[57])).
% 50.95/51.25 tff(59,plain,
% 50.95/51.25 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[58, 56])).
% 50.95/51.25 tff(60,plain,
% 50.95/51.25 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 50.95/51.25 inference(rewrite,[status(thm)],[])).
% 50.95/51.25 tff(61,axiom,((((((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtasdt0(xn, xm))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1860')).
% 50.95/51.25 tff(62,plain,
% 50.95/51.25 (((((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 50.95/51.25 inference(and_elim,[status(thm)],[61])).
% 50.95/51.25 tff(63,plain,
% 50.95/51.25 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 50.95/51.25 inference(and_elim,[status(thm)],[62])).
% 50.95/51.25 tff(64,plain,
% 50.95/51.25 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[63, 60])).
% 50.95/51.25 tff(65,plain,(
% 50.95/51.25 aNaturalNumber0(W0!8) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0!8))),
% 50.95/51.25 inference(skolemize,[status(sab)],[64])).
% 50.95/51.25 tff(66,plain,
% 50.95/51.25 (sdtasdt0(xn, xm) = sdtasdt0(xp, W0!8)),
% 50.95/51.25 inference(and_elim,[status(thm)],[65])).
% 50.95/51.25 tff(67,plain,
% 50.95/51.25 (sdtasdt0(xp, W0!8) = sdtasdt0(xn, xm)),
% 50.95/51.25 inference(symmetry,[status(thm)],[66])).
% 50.95/51.25 tff(68,plain,
% 50.95/51.25 (sdtasdt0(xp, W0!8) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))),
% 50.95/51.25 inference(transitivity,[status(thm)],[67, 59, 55])).
% 50.95/51.25 tff(69,plain,
% 50.95/51.25 (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[68, 48])).
% 50.95/51.25 tff(70,plain,
% 50.95/51.25 (((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp))) | (~(sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)))),
% 50.95/51.25 inference(tautology,[status(thm)],[])).
% 50.95/51.25 tff(71,plain,
% 50.95/51.25 ((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp))),
% 50.95/51.25 inference(unit_resolution,[status(thm)],[70, 69])).
% 50.95/51.25 tff(72,plain,
% 50.95/51.25 ((~(xp = sz00)) <=> (~(xp = sz00))),
% 50.95/51.25 inference(rewrite,[status(thm)],[])).
% 50.95/51.25 tff(73,plain,
% 50.95/51.25 ((((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)),
% 50.95/51.25 inference(and_elim,[status(thm)],[62])).
% 50.95/51.25 tff(74,plain,
% 50.95/51.25 (((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))),
% 50.95/51.25 inference(and_elim,[status(thm)],[73])).
% 50.95/51.25 tff(75,plain,
% 50.95/51.25 ((~(xp = sz00)) & (~(xp = sz10))),
% 50.95/51.25 inference(and_elim,[status(thm)],[74])).
% 50.95/51.25 tff(76,plain,
% 50.95/51.25 (~(xp = sz00)),
% 50.95/51.25 inference(and_elim,[status(thm)],[75])).
% 50.95/51.25 tff(77,plain,
% 50.95/51.25 (~(xp = sz00)),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[76, 72])).
% 50.95/51.25 tff(78,plain,
% 50.95/51.25 (^[W0: $i] : refl(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 50.95/51.25 inference(bind,[status(th)],[])).
% 50.95/51.25 tff(79,plain,
% 50.95/51.25 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 50.95/51.25 inference(quant_intro,[status(thm)],[78])).
% 50.95/51.25 tff(80,plain,
% 50.95/51.25 (^[W0: $i] : rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 50.95/51.25 inference(bind,[status(th)],[])).
% 50.95/51.25 tff(81,plain,
% 50.95/51.25 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 50.95/51.25 inference(quant_intro,[status(thm)],[80])).
% 50.95/51.25 tff(82,plain,
% 50.95/51.25 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 50.95/51.25 inference(transitivity,[status(thm)],[81, 79])).
% 50.95/51.25 tff(83,plain,
% 50.95/51.25 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), rewrite((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) <=> (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), rewrite(((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), (![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))))),
% 50.95/51.25 inference(bind,[status(th)],[])).
% 50.95/51.25 tff(84,plain,
% 50.95/51.25 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 50.95/51.25 inference(quant_intro,[status(thm)],[83])).
% 50.95/51.25 tff(85,plain,
% 50.95/51.25 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 50.95/51.25 inference(rewrite,[status(thm)],[])).
% 50.95/51.25 tff(86,plain,
% 50.95/51.25 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))), rewrite((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2)))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))))), rewrite(((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), (![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), rewrite(((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> (aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))), rewrite((aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))),
% 50.95/51.25 inference(bind,[status(th)],[])).
% 50.95/51.25 tff(87,plain,
% 50.95/51.25 (![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 50.95/51.25 inference(quant_intro,[status(thm)],[86])).
% 50.95/51.25 tff(88,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulCanc')).
% 50.95/51.25 tff(89,plain,
% 50.95/51.25 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[88, 87])).
% 50.95/51.25 tff(90,plain,
% 50.95/51.25 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[89, 85])).
% 50.95/51.25 tff(91,plain,(
% 50.95/51.25 ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 50.95/51.25 inference(skolemize,[status(sab)],[90])).
% 50.95/51.25 tff(92,plain,
% 50.95/51.25 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[91, 84])).
% 50.95/51.25 tff(93,plain,
% 50.95/51.25 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[92, 82])).
% 50.95/51.25 tff(94,plain,
% 50.95/51.25 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 50.95/51.25 inference(rewrite,[status(thm)],[])).
% 50.95/51.25 tff(95,plain,
% 50.95/51.25 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 50.95/51.25 inference(rewrite,[status(thm)],[])).
% 50.95/51.25 tff(96,plain,
% 50.95/51.25 (^[W1: $i, W2: $i] : rewrite(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 50.95/51.25 inference(bind,[status(th)],[])).
% 50.95/51.25 tff(97,plain,
% 50.95/51.25 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 50.95/51.25 inference(quant_intro,[status(thm)],[96])).
% 50.95/51.25 tff(98,plain,
% 50.95/51.25 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1)))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 50.95/51.25 inference(monotonicity,[status(thm)],[97])).
% 50.95/51.25 tff(99,plain,
% 50.95/51.25 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1)))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 50.95/51.25 inference(transitivity,[status(thm)],[98, 95])).
% 50.95/51.25 tff(100,plain,
% 50.95/51.25 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))))),
% 50.95/51.25 inference(monotonicity,[status(thm)],[99])).
% 50.95/51.25 tff(101,plain,
% 50.95/51.25 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 50.95/51.25 inference(transitivity,[status(thm)],[100, 94])).
% 50.95/51.25 tff(102,plain,
% 50.95/51.25 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))))),
% 50.95/51.25 inference(quant_inst,[status(thm)],[])).
% 50.95/51.25 tff(103,plain,
% 50.95/51.25 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[102, 101])).
% 50.95/51.25 tff(104,plain,
% 50.95/51.25 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 50.95/51.25 inference(unit_resolution,[status(thm)],[103, 93, 18, 77])).
% 50.95/51.25 tff(105,plain,
% 50.95/51.25 (aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp)) <=> aNaturalNumber0(xk)),
% 50.95/51.25 inference(monotonicity,[status(thm)],[53])).
% 50.95/51.25 tff(106,plain,
% 50.95/51.25 (aNaturalNumber0(xk) <=> aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 50.95/51.25 inference(symmetry,[status(thm)],[105])).
% 50.95/51.25 tff(107,plain,
% 50.95/51.25 (aNaturalNumber0(xk) <=> aNaturalNumber0(xk)),
% 50.95/51.25 inference(rewrite,[status(thm)],[])).
% 50.95/51.25 tff(108,plain,
% 50.95/51.25 (aNaturalNumber0(xk)),
% 50.95/51.25 inference(and_elim,[status(thm)],[57])).
% 50.95/51.25 tff(109,plain,
% 50.95/51.25 (aNaturalNumber0(xk)),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[108, 107])).
% 50.95/51.25 tff(110,plain,
% 50.95/51.25 (aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[109, 106])).
% 50.95/51.25 tff(111,plain,
% 50.95/51.25 (aNaturalNumber0(W0!8)),
% 50.95/51.25 inference(and_elim,[status(thm)],[65])).
% 50.95/51.25 tff(112,plain,
% 50.95/51.25 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))),
% 50.95/51.25 inference(rewrite,[status(thm)],[])).
% 50.95/51.25 tff(113,plain,
% 50.95/51.25 (((sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp))))) <=> ((~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))),
% 50.95/51.25 inference(rewrite,[status(thm)],[])).
% 50.95/51.25 tff(114,plain,
% 50.95/51.25 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp))))))),
% 50.95/51.25 inference(monotonicity,[status(thm)],[113])).
% 50.95/51.25 tff(115,plain,
% 50.95/51.25 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))),
% 50.95/51.25 inference(transitivity,[status(thm)],[114, 112])).
% 50.95/51.25 tff(116,plain,
% 50.95/51.25 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))),
% 50.95/51.25 inference(quant_inst,[status(thm)],[])).
% 50.95/51.25 tff(117,plain,
% 50.95/51.25 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp))))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[116, 115])).
% 50.95/51.25 tff(118,plain,
% 50.95/51.25 (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8),
% 50.95/51.25 inference(unit_resolution,[status(thm)],[117, 111, 110, 104, 71])).
% 50.95/51.25 tff(119,plain,
% 50.95/51.25 (xk = sdtasdt0(xr, W0!11)),
% 50.95/51.25 inference(and_elim,[status(thm)],[10])).
% 50.95/51.25 tff(120,plain,
% 50.95/51.25 (sdtasdt0(xr, W0!11) = xk),
% 50.95/51.25 inference(symmetry,[status(thm)],[119])).
% 50.95/51.25 tff(121,plain,
% 50.95/51.25 (sdtasdt0(xr, W0!11) = W0!8),
% 50.95/51.25 inference(transitivity,[status(thm)],[120, 52, 118])).
% 50.95/51.25 tff(122,plain,
% 50.95/51.25 (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(W0!8, sdtpldt0(xm, W0!10))),
% 50.95/51.25 inference(monotonicity,[status(thm)],[121, 46])).
% 50.95/51.25 tff(123,plain,
% 50.95/51.25 (sdtasdt0(W0!8, sdtpldt0(xm, W0!10)) = sdtasdt0(sdtasdt0(xr, W0!11), xp)),
% 50.95/51.25 inference(symmetry,[status(thm)],[122])).
% 50.95/51.25 tff(124,plain,
% 50.95/51.25 (sdtasdt0(W0!8, sdtpldt0(xm, W0!10)) = sdtasdt0(W0!8, xp)),
% 50.95/51.25 inference(monotonicity,[status(thm)],[45])).
% 50.95/51.25 tff(125,plain,
% 50.95/51.25 (sdtasdt0(W0!8, xp) = sdtasdt0(W0!8, sdtpldt0(xm, W0!10))),
% 50.95/51.25 inference(symmetry,[status(thm)],[124])).
% 50.95/51.25 tff(126,plain,
% 50.95/51.25 (^[W0: $i, W1: $i] : refl(((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 50.95/51.25 inference(bind,[status(th)],[])).
% 50.95/51.25 tff(127,plain,
% 50.95/51.25 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 50.95/51.25 inference(quant_intro,[status(thm)],[126])).
% 50.95/51.25 tff(128,plain,
% 50.95/51.25 (^[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(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 50.95/51.25 inference(bind,[status(th)],[])).
% 50.95/51.25 tff(129,plain,
% 50.95/51.25 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 50.95/51.25 inference(quant_intro,[status(thm)],[128])).
% 50.95/51.25 tff(130,plain,
% 50.95/51.25 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 50.95/51.25 inference(rewrite,[status(thm)],[])).
% 50.95/51.25 tff(131,plain,
% 50.95/51.25 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))),
% 50.95/51.25 inference(bind,[status(th)],[])).
% 50.95/51.25 tff(132,plain,
% 50.95/51.25 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 50.95/51.25 inference(quant_intro,[status(thm)],[131])).
% 50.95/51.25 tff(133,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulComm')).
% 50.95/51.25 tff(134,plain,
% 50.95/51.25 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[133, 132])).
% 50.95/51.25 tff(135,plain,
% 50.95/51.25 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[134, 130])).
% 50.95/51.25 tff(136,plain,(
% 50.95/51.25 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 50.95/51.25 inference(skolemize,[status(sab)],[135])).
% 50.95/51.25 tff(137,plain,
% 50.95/51.25 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[136, 129])).
% 50.95/51.25 tff(138,plain,
% 50.95/51.25 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[137, 127])).
% 50.95/51.25 tff(139,plain,
% 50.95/51.25 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!8)) | (sdtasdt0(W0!8, xp) = sdtasdt0(xp, W0!8)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!8)) | (sdtasdt0(W0!8, xp) = sdtasdt0(xp, W0!8)))),
% 50.95/51.25 inference(rewrite,[status(thm)],[])).
% 50.95/51.25 tff(140,plain,
% 50.95/51.25 (((sdtasdt0(W0!8, xp) = sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!8))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!8)) | (sdtasdt0(W0!8, xp) = sdtasdt0(xp, W0!8)))),
% 50.95/51.25 inference(rewrite,[status(thm)],[])).
% 50.95/51.25 tff(141,plain,
% 50.95/51.25 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!8, xp) = sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!8)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!8)) | (sdtasdt0(W0!8, xp) = sdtasdt0(xp, W0!8))))),
% 50.95/51.25 inference(monotonicity,[status(thm)],[140])).
% 50.95/51.25 tff(142,plain,
% 50.95/51.25 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!8, xp) = sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!8)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!8)) | (sdtasdt0(W0!8, xp) = sdtasdt0(xp, W0!8)))),
% 50.95/51.25 inference(transitivity,[status(thm)],[141, 139])).
% 50.95/51.25 tff(143,plain,
% 50.95/51.25 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!8, xp) = sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!8)))),
% 50.95/51.25 inference(quant_inst,[status(thm)],[])).
% 50.95/51.25 tff(144,plain,
% 50.95/51.25 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!8)) | (sdtasdt0(W0!8, xp) = sdtasdt0(xp, W0!8))),
% 50.95/51.25 inference(modus_ponens,[status(thm)],[143, 142])).
% 50.95/51.25 tff(145,plain,
% 50.95/51.25 (sdtasdt0(W0!8, xp) = sdtasdt0(xp, W0!8)),
% 50.95/51.25 inference(unit_resolution,[status(thm)],[144, 138, 18, 111])).
% 50.95/51.25 tff(146,plain,
% 50.95/51.25 (sdtasdt0(xp, W0!8) = sdtasdt0(W0!8, xp)),
% 50.95/51.25 inference(symmetry,[status(thm)],[145])).
% 50.95/51.25 tff(147,plain,
% 50.95/51.25 (sdtasdt0(xp, W0!8) = sdtasdt0(xr, sdtasdt0(W0!11, xp))),
% 50.95/51.25 inference(transitivity,[status(thm)],[146, 125, 123, 38])).
% 50.95/51.25 tff(148,plain,
% 50.95/51.25 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 50.95/51.25 inference(bind,[status(th)],[])).
% 50.95/51.25 tff(149,plain,
% 50.95/51.25 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 50.95/51.26 inference(quant_intro,[status(thm)],[148])).
% 50.95/51.26 tff(150,plain,
% 50.95/51.26 (^[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)))))),
% 50.95/51.26 inference(bind,[status(th)],[])).
% 50.95/51.26 tff(151,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 50.95/51.26 inference(quant_intro,[status(thm)],[150])).
% 50.95/51.26 tff(152,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(153,plain,
% 50.95/51.26 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 50.95/51.26 inference(bind,[status(th)],[])).
% 50.95/51.26 tff(154,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 50.95/51.26 inference(quant_intro,[status(thm)],[153])).
% 50.95/51.26 tff(155,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 50.95/51.26 tff(156,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[155, 154])).
% 50.95/51.26 tff(157,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[156, 152])).
% 50.95/51.26 tff(158,plain,(
% 50.95/51.26 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 50.95/51.26 inference(skolemize,[status(sab)],[157])).
% 50.95/51.26 tff(159,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[158, 151])).
% 50.95/51.26 tff(160,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[159, 149])).
% 50.95/51.26 tff(161,plain,
% 50.95/51.26 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)) | aNaturalNumber0(sdtasdt0(W0!11, xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)) | aNaturalNumber0(sdtasdt0(W0!11, xp)))),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(162,plain,
% 50.95/51.26 ((aNaturalNumber0(sdtasdt0(W0!11, xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)) | aNaturalNumber0(sdtasdt0(W0!11, xp)))),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(163,plain,
% 50.95/51.26 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!11, xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)) | aNaturalNumber0(sdtasdt0(W0!11, xp))))),
% 50.95/51.26 inference(monotonicity,[status(thm)],[162])).
% 50.95/51.26 tff(164,plain,
% 50.95/51.26 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!11, xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)) | aNaturalNumber0(sdtasdt0(W0!11, xp)))),
% 50.95/51.26 inference(transitivity,[status(thm)],[163, 161])).
% 50.95/51.26 tff(165,plain,
% 50.95/51.26 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!11, xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)))),
% 50.95/51.26 inference(quant_inst,[status(thm)],[])).
% 50.95/51.26 tff(166,plain,
% 50.95/51.26 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!11)) | aNaturalNumber0(sdtasdt0(W0!11, xp))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[165, 164])).
% 50.95/51.26 tff(167,plain,
% 50.95/51.26 (aNaturalNumber0(sdtasdt0(W0!11, xp))),
% 50.95/51.26 inference(unit_resolution,[status(thm)],[166, 160, 18, 11])).
% 50.95/51.26 tff(168,plain,
% 50.95/51.26 (doDivides0(xr, sdtasdt0(xp, W0!8)) <=> doDivides0(xr, sdtasdt0(xn, xm))),
% 50.95/51.26 inference(monotonicity,[status(thm)],[67])).
% 50.95/51.26 tff(169,plain,
% 50.95/51.26 (doDivides0(xr, sdtasdt0(xn, xm)) <=> doDivides0(xr, sdtasdt0(xp, W0!8))),
% 50.95/51.26 inference(symmetry,[status(thm)],[168])).
% 50.95/51.26 tff(170,plain,
% 50.95/51.26 ((~doDivides0(xr, sdtasdt0(xn, xm))) <=> (~doDivides0(xr, sdtasdt0(xp, W0!8)))),
% 50.95/51.26 inference(monotonicity,[status(thm)],[169])).
% 50.95/51.26 tff(171,plain,
% 50.95/51.26 ((~doDivides0(xr, sdtasdt0(xn, xm))) <=> (~doDivides0(xr, sdtasdt0(xn, xm)))),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(172,axiom,(~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0))) | doDivides0(xr, sdtasdt0(xn, xm)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 50.95/51.26 tff(173,plain,
% 50.95/51.26 (~doDivides0(xr, sdtasdt0(xn, xm))),
% 50.95/51.26 inference(or_elim,[status(thm)],[172])).
% 50.95/51.26 tff(174,plain,
% 50.95/51.26 (~doDivides0(xr, sdtasdt0(xn, xm))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[173, 171])).
% 50.95/51.26 tff(175,plain,
% 50.95/51.26 (~doDivides0(xr, sdtasdt0(xp, W0!8))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[174, 170])).
% 50.95/51.26 tff(176,plain,
% 50.95/51.26 (aNaturalNumber0(sdtasdt0(xp, W0!8)) <=> aNaturalNumber0(sdtasdt0(xn, xm))),
% 50.95/51.26 inference(monotonicity,[status(thm)],[67])).
% 50.95/51.26 tff(177,plain,
% 50.95/51.26 (aNaturalNumber0(sdtasdt0(xn, xm)) <=> aNaturalNumber0(sdtasdt0(xp, W0!8))),
% 50.95/51.26 inference(symmetry,[status(thm)],[176])).
% 50.95/51.26 tff(178,plain,
% 50.95/51.26 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(179,plain,
% 50.95/51.26 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 50.95/51.26 inference(and_elim,[status(thm)],[16])).
% 50.95/51.26 tff(180,plain,
% 50.95/51.26 (aNaturalNumber0(xm)),
% 50.95/51.26 inference(and_elim,[status(thm)],[179])).
% 50.95/51.26 tff(181,plain,
% 50.95/51.26 (aNaturalNumber0(xm)),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[180, 178])).
% 50.95/51.26 tff(182,plain,
% 50.95/51.26 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(183,plain,
% 50.95/51.26 (aNaturalNumber0(xn)),
% 50.95/51.26 inference(and_elim,[status(thm)],[179])).
% 50.95/51.26 tff(184,plain,
% 50.95/51.26 (aNaturalNumber0(xn)),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[183, 182])).
% 50.95/51.26 tff(185,plain,
% 50.95/51.26 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xn, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xn, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)))),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(186,plain,
% 50.95/51.26 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xn, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)))),
% 50.95/51.26 inference(quant_inst,[status(thm)],[])).
% 50.95/51.26 tff(187,plain,
% 50.95/51.26 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xn, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[186, 185])).
% 50.95/51.26 tff(188,plain,
% 50.95/51.26 (aNaturalNumber0(sdtasdt0(xn, xm))),
% 50.95/51.26 inference(unit_resolution,[status(thm)],[187, 160, 184, 181])).
% 50.95/51.26 tff(189,plain,
% 50.95/51.26 (aNaturalNumber0(sdtasdt0(xp, W0!8))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[188, 177])).
% 50.95/51.26 tff(190,plain,
% 50.95/51.26 (^[W0: $i, W1: $i] : refl(((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))))),
% 50.95/51.26 inference(bind,[status(th)],[])).
% 50.95/51.26 tff(191,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 50.95/51.26 inference(quant_intro,[status(thm)],[190])).
% 50.95/51.26 tff(192,plain,
% 50.95/51.26 (^[W0: $i, W1: $i] : rewrite(((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))))),
% 50.95/51.26 inference(bind,[status(th)],[])).
% 50.95/51.26 tff(193,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 50.95/51.26 inference(quant_intro,[status(thm)],[192])).
% 50.95/51.26 tff(194,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 50.95/51.26 inference(transitivity,[status(thm)],[193, 191])).
% 50.95/51.26 tff(195,plain,
% 50.95/51.26 (^[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(((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) <=> ((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))), rewrite((doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> (doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))), ((((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> (((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))))) & (doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))), rewrite((((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))))) & (doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))) <=> (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))), ((((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))))),
% 50.95/51.26 inference(bind,[status(th)],[])).
% 50.95/51.26 tff(196,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 50.95/51.26 inference(quant_intro,[status(thm)],[195])).
% 50.95/51.26 tff(197,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(198,plain,
% 50.95/51.26 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) <=> (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))))),
% 50.95/51.26 inference(bind,[status(th)],[])).
% 50.95/51.26 tff(199,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))),
% 50.95/51.26 inference(quant_intro,[status(thm)],[198])).
% 50.95/51.26 tff(200,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefDiv')).
% 50.95/51.26 tff(201,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[200, 199])).
% 50.95/51.26 tff(202,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[201, 197])).
% 50.95/51.26 tff(203,plain,(
% 50.95/51.26 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))))),
% 50.95/51.26 inference(skolemize,[status(sab)],[202])).
% 50.95/51.26 tff(204,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[203, 196])).
% 50.95/51.26 tff(205,plain,
% 50.95/51.26 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[204, 194])).
% 50.95/51.26 tff(206,plain,
% 50.95/51.26 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))))))),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(207,plain,
% 50.95/51.26 (((~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(xr)) | (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))))))))))) <=> ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))))))),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(208,plain,
% 50.95/51.26 ((~((~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))) | (~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))))) <=> (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))))))))))),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(209,plain,
% 50.95/51.26 (((~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(xr)) | (~((~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))) | (~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2))))))))) <=> ((~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(xr)) | (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))))))),
% 50.95/51.26 inference(monotonicity,[status(thm)],[208])).
% 50.95/51.26 tff(210,plain,
% 50.95/51.26 (((~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(xr)) | (~((~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))) | (~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2))))))))) <=> ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))))))),
% 50.95/51.26 inference(transitivity,[status(thm)],[209, 207])).
% 50.95/51.26 tff(211,plain,
% 50.95/51.26 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | ((~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(xr)) | (~((~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))) | (~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))))))))))))),
% 50.95/51.26 inference(monotonicity,[status(thm)],[210])).
% 50.95/51.26 tff(212,plain,
% 50.95/51.26 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | ((~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(xr)) | (~((~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))) | (~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))))))),
% 50.95/51.26 inference(transitivity,[status(thm)],[211, 206])).
% 50.95/51.26 tff(213,plain,
% 50.95/51.26 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | ((~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(xr)) | (~((~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))) | (~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))))))),
% 50.95/51.26 inference(quant_inst,[status(thm)],[])).
% 50.95/51.26 tff(214,plain,
% 50.95/51.26 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))))))))))),
% 50.95/51.26 inference(modus_ponens,[status(thm)],[213, 212])).
% 50.95/51.26 tff(215,plain,
% 50.95/51.26 ((~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))))))))))),
% 50.95/51.26 inference(unit_resolution,[status(thm)],[214, 205, 14])).
% 50.95/51.26 tff(216,plain,
% 50.95/51.26 (~((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr)))))))))),
% 50.95/51.26 inference(unit_resolution,[status(thm)],[215, 189])).
% 50.95/51.26 tff(217,plain,
% 50.95/51.26 (((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | (~((~doDivides0(xr, sdtasdt0(xp, W0!8))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, tptp_fun_W2_1(sdtasdt0(xp, W0!8), xr))))))))) | (doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))),
% 50.95/51.26 inference(tautology,[status(thm)],[])).
% 50.95/51.26 tff(218,plain,
% 50.95/51.26 (doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2))))),
% 50.95/51.26 inference(unit_resolution,[status(thm)],[217, 216])).
% 50.95/51.26 tff(219,plain,
% 50.95/51.26 ((~(doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2)))))) | doDivides0(xr, sdtasdt0(xp, W0!8)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2))))),
% 50.95/51.26 inference(tautology,[status(thm)],[])).
% 50.95/51.26 tff(220,plain,
% 50.95/51.26 (![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2))))),
% 50.95/51.26 inference(unit_resolution,[status(thm)],[219, 218, 175])).
% 50.95/51.26 tff(221,plain,
% 50.95/51.26 (((~![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2))))) | ((~aNaturalNumber0(sdtasdt0(W0!11, xp))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, sdtasdt0(W0!11, xp)))))) <=> ((~![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2))))) | (~aNaturalNumber0(sdtasdt0(W0!11, xp))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, sdtasdt0(W0!11, xp)))))),
% 50.95/51.26 inference(rewrite,[status(thm)],[])).
% 50.95/51.26 tff(222,plain,
% 50.95/51.26 ((~![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2))))) | ((~aNaturalNumber0(sdtasdt0(W0!11, xp))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, sdtasdt0(W0!11, xp)))))),
% 50.95/51.26 inference(quant_inst,[status(thm)],[])).
% 50.95/51.26 tff(223,plain,
% 50.95/51.26 ((~![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, W2))))) | (~aNaturalNumber0(sdtasdt0(W0!11, xp))) | (~(sdtasdt0(xp, W0!8) = sdtasdt0(xr, sdtasdt0(W0!11, xp))))),
% 51.27/51.50 inference(modus_ponens,[status(thm)],[222, 221])).
% 51.27/51.50 tff(224,plain,
% 51.27/51.50 ($false),
% 51.27/51.50 inference(unit_resolution,[status(thm)],[223, 220, 167, 147])).
% 51.27/51.50 % SZS output end Proof
% 51.27/51.50 % E exiting
%------------------------------------------------------------------------------