%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM517+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:21:15 AM UTC 2025
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM517+3 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:25:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(aNaturalNumber0_type, type, (
% 0.20/0.43 aNaturalNumber0: $i > $o)).
% 0.20/0.43 tff(sdtpldt0_type, type, (
% 0.20/0.43 sdtpldt0: ( $i * $i ) > $i)).
% 0.20/0.43 tff(xp_type, type, (
% 0.20/0.43 xp: $i)).
% 0.20/0.43 tff(xm_type, type, (
% 0.20/0.43 xm: $i)).
% 0.20/0.43 tff(xn_type, type, (
% 0.20/0.43 xn: $i)).
% 0.20/0.43 tff(tptp_fun_W0_19_type, type, (
% 0.20/0.43 tptp_fun_W0_19: $i)).
% 0.20/0.43 tff(sdtsldt0_type, type, (
% 0.20/0.43 sdtsldt0: ( $i * $i ) > $i)).
% 0.20/0.43 tff(xr_type, type, (
% 0.20/0.43 xr: $i)).
% 0.20/0.43 tff(sdtasdt0_type, type, (
% 0.20/0.43 sdtasdt0: ( $i * $i ) > $i)).
% 0.20/0.43 tff(sdtlseqdt0_type, type, (
% 0.20/0.43 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.20/0.43 tff(iLess0_type, type, (
% 0.20/0.43 iLess0: ( $i * $i ) > $o)).
% 0.20/0.43 tff(tptp_fun_W3_5_type, type, (
% 0.20/0.43 tptp_fun_W3_5: ( $i * $i ) > $i)).
% 0.20/0.43 tff(doDivides0_type, type, (
% 0.20/0.43 doDivides0: ( $i * $i ) > $o)).
% 0.20/0.43 tff(sz10_type, type, (
% 0.20/0.43 sz10: $i)).
% 0.20/0.43 tff(tptp_fun_W3_6_type, type, (
% 0.20/0.43 tptp_fun_W3_6: $i > $i)).
% 0.20/0.43 tff(tptp_fun_W4_7_type, type, (
% 0.20/0.43 tptp_fun_W4_7: $i > $i)).
% 0.20/0.43 tff(sz00_type, type, (
% 0.20/0.43 sz00: $i)).
% 0.20/0.43 tff(isPrime0_type, type, (
% 0.20/0.43 isPrime0: $i > $o)).
% 0.20/0.43 tff(tptp_fun_W3_4_type, type, (
% 0.20/0.43 tptp_fun_W3_4: ( $i * $i ) > $i)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0) = sdtpldt0(sdtpldt0(xn, xm), xp))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0) = sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(2,axiom,(((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0) = sdtpldt0(sdtpldt0(xn, xm), xp)))) & sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2686')).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 ((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0) = sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 0.20/0.43 inference(and_elim,[status(thm)],[2])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0) = sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 0.20/0.43 inference(and_elim,[status(thm)],[3])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0) = sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.43 tff(6,plain,(
% 0.20/0.43 aNaturalNumber0(W0!19) & (sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19) = sdtpldt0(sdtpldt0(xn, xm), xp))),
% 0.20/0.43 inference(skolemize,[status(sab)],[5])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19) = sdtpldt0(sdtpldt0(xn, xm), xp)),
% 0.20/0.43 inference(and_elim,[status(thm)],[6])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 (sdtpldt0(sdtpldt0(xn, xm), xp) = sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19)),
% 0.20/0.43 inference(symmetry,[status(thm)],[7])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp)) <=> aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[8])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19)) <=> aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))),
% 0.20/0.43 inference(symmetry,[status(thm)],[9])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 (aNaturalNumber0(sdtsldt0(xn, xr)) <=> aNaturalNumber0(sdtsldt0(xn, xr))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) <=> (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(13,axiom,(((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))) & sdtlseqdt0(sdtsldt0(xn, xr), xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2504')).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 ((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))),
% 0.20/0.43 inference(and_elim,[status(thm)],[13])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 0.20/0.43 inference(and_elim,[status(thm)],[14])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))),
% 0.20/0.43 inference(and_elim,[status(thm)],[15])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))),
% 0.20/0.43 inference(and_elim,[status(thm)],[16])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 0.20/0.43 inference(or_elim,[status(thm)],[18])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 0.20/0.43 inference(and_elim,[status(thm)],[19])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(23,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1837')).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 0.20/0.43 inference(and_elim,[status(thm)],[23])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (aNaturalNumber0(xm)),
% 0.20/0.43 inference(and_elim,[status(thm)],[24])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 (aNaturalNumber0(xm)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((aNaturalNumber0(sdtpldt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.43 tff(34,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB')).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.43 tff(37,plain,(
% 0.20/0.43 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[36])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 ((aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr)))) <=> ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[42, 40])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[45, 39, 26, 21])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (aNaturalNumber0(xp)),
% 0.20/0.44 inference(and_elim,[status(thm)],[23])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (aNaturalNumber0(xp)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 ((aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm)))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[52, 50])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(sdtsldt0(xn, xr), xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[55, 39, 49, 46])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (aNaturalNumber0(W0!19)),
% 0.20/0.44 inference(and_elim,[status(thm)],[6])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!19)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!19)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 ((aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19)) | (~aNaturalNumber0(W0!19)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)))) <=> ((~aNaturalNumber0(W0!19)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19)) | (~aNaturalNumber0(W0!19)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!19)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19)) | (~aNaturalNumber0(W0!19)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!19)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[60, 58])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19)) | (~aNaturalNumber0(W0!19)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!19)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (aNaturalNumber0(sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), W0!19))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[63, 39, 57, 56])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[64, 10])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 ((~doDivides0(xp, sdtsldt0(xn, xr))) <=> (~doDivides0(xp, sdtsldt0(xn, xr)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) | doDivides0(xp, sdtsldt0(xn, xr))))) <=> (~(doDivides0(xp, sdtsldt0(xn, xr)) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) | (~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(68,axiom,(~((((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) | doDivides0(xp, sdtsldt0(xn, xr)))) | ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0)))) | doDivides0(xp, xm))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (~(((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) | doDivides0(xp, sdtsldt0(xn, xr)))) | ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))))),
% 0.20/0.44 inference(or_elim,[status(thm)],[68])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) | doDivides0(xp, sdtsldt0(xn, xr))))),
% 0.20/0.44 inference(or_elim,[status(thm)],[69])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (~(doDivides0(xp, sdtsldt0(xn, xr)) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) | (~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (~doDivides0(xp, sdtsldt0(xn, xr))),
% 0.20/0.44 inference(or_elim,[status(thm)],[71])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (~doDivides0(xp, sdtsldt0(xn, xr))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[72, 66])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | doDivides0(xp, sdtsldt0(xn, xr))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 ((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) <=> doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(77,axiom,(((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2529')).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm))),
% 0.20/0.44 inference(and_elim,[status(thm)],[77])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[78, 76])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 ((doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3)))))) | (~doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (isPrime0(xp) <=> isPrime0(xp)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(83,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/sandbox2/benchmark/theBenchmark.p','m__1860')).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (((((~(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)))),
% 0.20/0.44 inference(and_elim,[status(thm)],[83])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 ((((~(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)),
% 0.20/0.44 inference(and_elim,[status(thm)],[84])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (isPrime0(xp)),
% 0.20/0.44 inference(and_elim,[status(thm)],[85])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (isPrime0(xp)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 ((isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10)))))) | (~isPrime0(xp))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 ((~doDivides0(xp, xm)) <=> (~doDivides0(xp, xm))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 (~doDivides0(xp, xm)),
% 0.20/0.45 inference(or_elim,[status(thm)],[68])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 (~doDivides0(xp, xm)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm))))) | doDivides0(xp, xm)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 ((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite((~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))), rewrite((~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) <=> (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0))))), monotonicity(monotonicity(rewrite((~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))) <=> (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))), ((isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))) <=> (isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))), ((~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) <=> (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))), (((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))))), rewrite(((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))), (((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 (^[W0: $i, W1: $i, W2: $i] : refl(((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (^[W0: $i, W1: $i, W2: $i] : rewrite(((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[100, 98])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (^[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))))), trans(monotonicity(quant_intro(proof_bind(^[W3: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) <=> (~((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))), ((~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))) <=> (~(~((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))), rewrite((~(~((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))) <=> ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))), ((~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))) <=> ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))), (![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))) <=> ![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))), (((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) <=> ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))), rewrite(((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) <=> (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))), (((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) <=> (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))), rewrite((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) <=> (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))))))), rewrite((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) <=> (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0))))), trans(monotonicity(trans(monotonicity(rewrite(((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)) <=> (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))), (((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2))) <=> ((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))), rewrite(((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))) <=> ((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))), (((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2))) <=> ((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))), (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))) <=> ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))), rewrite(((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))) <=> (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))), (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))) <=> (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2))))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))) & doDivides0(W2, W1)) <=> (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1))), rewrite(((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) & doDivides0(W2, W0)) <=> (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0))), rewrite((((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_6(W2)) & (aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) & doDivides0(tptp_fun_W3_6(W2), W2))))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))) <=> (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))), ((((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))) & doDivides0(W2, W1)) | ((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_6(W2)) & (aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) & doDivides0(tptp_fun_W3_6(W2), W2))))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> ((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))), rewrite(((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))))), ((((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))) & doDivides0(W2, W1)) | ((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_6(W2)) & (aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) & doDivides0(tptp_fun_W3_6(W2), W2))))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))) & doDivides0(W2, W1)) | ((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_6(W2)) & (aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) & doDivides0(tptp_fun_W3_6(W2), W2))))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 (![W0: $i, W1: $i, W2: $i] : ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), trans(monotonicity(rewrite((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) <=> ((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))), trans(monotonicity(trans(monotonicity(rewrite((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) <=> (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0))), rewrite((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) <=> (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))), (((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))))), rewrite(((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)))), (((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0))))), ((iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)))) <=> (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)))))), rewrite((iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))))), ((iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)))))), (((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))))) <=> (((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))))))), rewrite((((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))), (((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)))))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)))))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)))))) <=> ![W0: $i, W1: $i, W2: $i] : ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.47 tff(109,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1799')).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (![W0: $i, W1: $i, W2: $i] : ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (![W0: $i, W1: $i, W2: $i] : ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.20/0.47 tff(112,plain,(
% 0.20/0.47 ![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))) & doDivides0(W2, W1)) | ((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_6(W2)) & (aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) & doDivides0(tptp_fun_W3_6(W2), W2))))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[111])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[114, 101])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[115, 96])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | ((~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3)))))))) <=> ((~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 ((~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))) <=> (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 ((~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) <=> (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 ((~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~doDivides0(xp, sdtsldt0(xn, xr))))) <=> (~((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~doDivides0(xp, sdtsldt0(xn, xr))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3)))))))) <=> ((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[121, 120, 119])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.48 (((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~doDivides0(xp, sdtsldt0(xn, xr))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3)))))))) <=> ((~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[122, 118])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | ((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~doDivides0(xp, sdtsldt0(xn, xr))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | ((~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[123])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 (((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | ((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~doDivides0(xp, sdtsldt0(xn, xr))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[124, 117])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | ((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr)))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~doDivides0(xp, sdtsldt0(xn, xr))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W3))))))) | (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtsldt0(xn, xr))) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtsldt0(xn, xr))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (~iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[127, 26, 49, 116, 21, 94, 89, 81, 75])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 ((~(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp))) <=> (~(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)))) <=> (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 0.20/0.48 inference(and_elim,[status(thm)],[3])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)))) & aNaturalNumber0(sdtsldt0(xn, xr))),
% 0.20/0.48 inference(and_elim,[status(thm)],[131])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 0.20/0.48 inference(and_elim,[status(thm)],[132])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[133, 130])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (~(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp))),
% 0.20/0.48 inference(or_elim,[status(thm)],[134])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (~(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[135, 129])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) <=> sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))),
% 0.20/0.48 inference(and_elim,[status(thm)],[2])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 (sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 (^[W0: $i, W1: $i] : refl(((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0))) <=> ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 (![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.48 tff(142,plain,
% 0.20/0.48 (^[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(((~(W0 = W1)) & sdtlseqdt0(W0, W1)) <=> (~((W0 = W1) | (~sdtlseqdt0(W0, W1))))), ((~((~(W0 = W1)) & sdtlseqdt0(W0, W1))) <=> (~(~((W0 = W1) | (~sdtlseqdt0(W0, W1))))))), rewrite((~(~((W0 = W1) | (~sdtlseqdt0(W0, W1))))) <=> ((W0 = W1) | (~sdtlseqdt0(W0, W1)))), ((~((~(W0 = W1)) & sdtlseqdt0(W0, W1))) <=> ((W0 = W1) | (~sdtlseqdt0(W0, W1))))), ((iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1)))) <=> (iLess0(W0, W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((W0 = W1) | (~sdtlseqdt0(W0, W1)))))), rewrite((iLess0(W0, W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((W0 = W1) | (~sdtlseqdt0(W0, W1)))) <=> ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))), ((iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1)))) <=> ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 (![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[142])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1)))) <=> ![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(145,plain,
% 0.20/0.48 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((((~(W0 = W1)) & sdtlseqdt0(W0, W1)) => iLess0(W0, W1)) <=> ((~((~(W0 = W1)) & sdtlseqdt0(W0, W1))) | iLess0(W0, W1))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = W1)) & sdtlseqdt0(W0, W1)) => iLess0(W0, W1))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~((~(W0 = W1)) & sdtlseqdt0(W0, W1))) | iLess0(W0, W1))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~((~(W0 = W1)) & sdtlseqdt0(W0, W1))) | iLess0(W0, W1))) <=> (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = W1)) & sdtlseqdt0(W0, W1)) => iLess0(W0, W1))) <=> (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = W1)) & sdtlseqdt0(W0, W1)) => iLess0(W0, W1))) <=> ![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[145])).
% 0.20/0.48 tff(147,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = W1)) & sdtlseqdt0(W0, W1)) => iLess0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mIH_03')).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 (![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 (![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.20/0.48 tff(150,plain,(
% 0.20/0.48 ![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[149])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 (![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 (![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[151, 141])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | (sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (((sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp)))) <=> ((sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 (((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 (((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | (sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[155, 153])).
% 0.20/0.49 tff(157,plain,
% 0.20/0.49 ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(158,plain,
% 0.20/0.49 ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | (sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn, xr), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.49 tff(159,plain,
% 0.20/0.49 (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[158, 152, 139, 136, 128, 56])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[159, 65])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------