%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM500+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:11 AM UTC 2025
% Result : Theorem 0.60s 0.79s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM500+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n010.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 01:19:56 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.60/0.79 % SZS status Theorem
% 0.60/0.79 % SZS output start Proof
% 0.60/0.79 tff(doDivides0_type, type, (
% 0.60/0.79 doDivides0: ( $i * $i ) > $o)).
% 0.60/0.79 tff(xk_type, type, (
% 0.60/0.79 xk: $i)).
% 0.60/0.79 tff(tptp_fun_W1_3_type, type, (
% 0.60/0.79 tptp_fun_W1_3: $i > $i)).
% 0.60/0.79 tff(tptp_fun_W0_8_type, type, (
% 0.60/0.79 tptp_fun_W0_8: $i)).
% 0.60/0.79 tff(sdtsldt0_type, type, (
% 0.60/0.79 sdtsldt0: ( $i * $i ) > $i)).
% 0.60/0.79 tff(xp_type, type, (
% 0.60/0.79 xp: $i)).
% 0.60/0.79 tff(sdtasdt0_type, type, (
% 0.60/0.79 sdtasdt0: ( $i * $i ) > $i)).
% 0.60/0.79 tff(xm_type, type, (
% 0.60/0.79 xm: $i)).
% 0.60/0.79 tff(xn_type, type, (
% 0.60/0.79 xn: $i)).
% 0.60/0.79 tff(aNaturalNumber0_type, type, (
% 0.60/0.79 aNaturalNumber0: $i > $o)).
% 0.60/0.79 tff(isPrime0_type, type, (
% 0.60/0.79 isPrime0: $i > $o)).
% 0.60/0.79 tff(sz10_type, type, (
% 0.60/0.79 sz10: $i)).
% 0.60/0.79 tff(sz00_type, type, (
% 0.60/0.79 sz00: $i)).
% 0.60/0.79 tff(tptp_fun_W1_11_type, type, (
% 0.60/0.79 tptp_fun_W1_11: $i > $i)).
% 0.60/0.79 tff(tptp_fun_W2_12_type, type, (
% 0.60/0.79 tptp_fun_W2_12: $i > $i)).
% 0.60/0.79 tff(1,plain,
% 0.60/0.79 ((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) <=> (sdtasdt0(xp, W0!8) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.60/0.79 inference(commutativity,[status(thm)],[])).
% 0.60/0.79 tff(2,plain,
% 0.60/0.79 ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))) <=> (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8))),
% 0.60/0.79 inference(symmetry,[status(thm)],[1])).
% 0.60/0.79 tff(3,plain,
% 0.60/0.79 ((xk = sdtsldt0(sdtasdt0(xn, xm), xp)) <=> (xk = sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(4,axiom,((aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))) & (xk = sdtsldt0(sdtasdt0(xn, xm), xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2306')).
% 0.60/0.79 tff(5,plain,
% 0.60/0.79 (xk = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 0.60/0.79 inference(and_elim,[status(thm)],[4])).
% 0.60/0.79 tff(6,plain,
% 0.60/0.79 (xk = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[5, 3])).
% 0.60/0.79 tff(7,plain,
% 0.60/0.79 (sdtsldt0(sdtasdt0(xn, xm), xp) = xk),
% 0.60/0.79 inference(symmetry,[status(thm)],[6])).
% 0.60/0.79 tff(8,plain,
% 0.60/0.79 (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, xk)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[7])).
% 0.60/0.79 tff(9,plain,
% 0.60/0.79 (sdtasdt0(xp, xk) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.60/0.79 inference(symmetry,[status(thm)],[8])).
% 0.60/0.79 tff(10,plain,
% 0.60/0.79 ((sdtasdt0(xn, xm) = sdtasdt0(xp, xk)) <=> (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(11,plain,
% 0.60/0.79 (aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 0.60/0.79 inference(and_elim,[status(thm)],[4])).
% 0.60/0.79 tff(12,plain,
% 0.60/0.79 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 0.60/0.79 inference(and_elim,[status(thm)],[11])).
% 0.60/0.79 tff(13,plain,
% 0.60/0.79 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[12, 10])).
% 0.60/0.79 tff(14,plain,
% 0.60/0.79 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(15,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')).
% 0.60/0.79 tff(16,plain,
% 0.60/0.79 (((((~(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)))),
% 0.60/0.79 inference(and_elim,[status(thm)],[15])).
% 0.60/0.79 tff(17,plain,
% 0.60/0.79 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.60/0.79 inference(and_elim,[status(thm)],[16])).
% 0.60/0.79 tff(18,plain,
% 0.60/0.79 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.60/0.79 tff(19,plain,(
% 0.60/0.79 aNaturalNumber0(W0!8) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0!8))),
% 0.60/0.79 inference(skolemize,[status(sab)],[18])).
% 0.60/0.79 tff(20,plain,
% 0.60/0.79 (sdtasdt0(xn, xm) = sdtasdt0(xp, W0!8)),
% 0.60/0.79 inference(and_elim,[status(thm)],[19])).
% 0.60/0.79 tff(21,plain,
% 0.60/0.79 (sdtasdt0(xp, W0!8) = sdtasdt0(xn, xm)),
% 0.60/0.79 inference(symmetry,[status(thm)],[20])).
% 0.60/0.79 tff(22,plain,
% 0.60/0.79 (sdtasdt0(xp, W0!8) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.60/0.79 inference(transitivity,[status(thm)],[21, 13, 9])).
% 0.60/0.79 tff(23,plain,
% 0.60/0.79 (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[22, 2])).
% 0.60/0.79 tff(24,plain,
% 0.60/0.79 (((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp))) | (~(sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)))),
% 0.60/0.79 inference(tautology,[status(thm)],[])).
% 0.60/0.79 tff(25,plain,
% 0.60/0.79 ((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.60/0.79 tff(26,plain,
% 0.60/0.79 ((~(xp = sz00)) <=> (~(xp = sz00))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(27,plain,
% 0.60/0.79 ((((~(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)),
% 0.60/0.79 inference(and_elim,[status(thm)],[16])).
% 0.60/0.79 tff(28,plain,
% 0.60/0.79 (((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))),
% 0.60/0.79 inference(and_elim,[status(thm)],[27])).
% 0.60/0.79 tff(29,plain,
% 0.60/0.79 ((~(xp = sz00)) & (~(xp = sz10))),
% 0.60/0.79 inference(and_elim,[status(thm)],[28])).
% 0.60/0.79 tff(30,plain,
% 0.60/0.79 (~(xp = sz00)),
% 0.60/0.79 inference(and_elim,[status(thm)],[29])).
% 0.60/0.79 tff(31,plain,
% 0.60/0.79 (~(xp = sz00)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.60/0.79 tff(32,plain,
% 0.60/0.79 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(33,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1837')).
% 0.60/0.79 tff(34,plain,
% 0.60/0.79 (aNaturalNumber0(xp)),
% 0.60/0.79 inference(and_elim,[status(thm)],[33])).
% 0.60/0.79 tff(35,plain,
% 0.60/0.79 (aNaturalNumber0(xp)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[34, 32])).
% 0.60/0.79 tff(36,plain,
% 0.60/0.79 (^[W0: $i] : refl(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(37,plain,
% 0.60/0.79 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[36])).
% 0.60/0.79 tff(38,plain,
% 0.60/0.79 (^[W0: $i] : rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(39,plain,
% 0.60/0.79 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[38])).
% 0.60/0.79 tff(40,plain,
% 0.60/0.79 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.60/0.79 inference(transitivity,[status(thm)],[39, 37])).
% 0.60/0.79 tff(41,plain,
% 0.60/0.79 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), rewrite((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) <=> (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), rewrite(((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), (![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(42,plain,
% 0.60/0.79 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[41])).
% 0.60/0.79 tff(43,plain,
% 0.60/0.79 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(44,plain,
% 0.60/0.79 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))), rewrite((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2)))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))))), rewrite(((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), (![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), rewrite(((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> (aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))), rewrite((aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(45,plain,
% 0.60/0.80 (![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[44])).
% 0.60/0.80 tff(46,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulCanc')).
% 0.60/0.80 tff(47,plain,
% 0.60/0.80 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.60/0.80 tff(48,plain,
% 0.60/0.80 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.60/0.80 tff(49,plain,(
% 0.60/0.80 ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.60/0.80 inference(skolemize,[status(sab)],[48])).
% 0.60/0.80 tff(50,plain,
% 0.60/0.80 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.60/0.80 tff(51,plain,
% 0.60/0.80 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.60/0.80 tff(52,plain,
% 0.60/0.80 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(53,plain,
% 0.60/0.80 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(54,plain,
% 0.60/0.80 (^[W1: $i, W2: $i] : rewrite(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(55,plain,
% 0.60/0.80 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[54])).
% 0.60/0.80 tff(56,plain,
% 0.60/0.80 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1)))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[55])).
% 0.60/0.80 tff(57,plain,
% 0.60/0.80 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1)))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[56, 53])).
% 0.60/0.80 tff(58,plain,
% 0.60/0.80 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[57])).
% 0.60/0.80 tff(59,plain,
% 0.60/0.80 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[58, 52])).
% 0.60/0.80 tff(60,plain,
% 0.60/0.80 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(61,plain,
% 0.60/0.80 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.60/0.80 tff(62,plain,
% 0.60/0.80 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[61, 51, 35, 31])).
% 0.60/0.80 tff(63,plain,
% 0.60/0.80 (aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp)) <=> aNaturalNumber0(xk)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[7])).
% 0.60/0.80 tff(64,plain,
% 0.60/0.80 (aNaturalNumber0(xk) <=> aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.60/0.80 inference(symmetry,[status(thm)],[63])).
% 0.60/0.80 tff(65,plain,
% 0.60/0.80 (aNaturalNumber0(xk) <=> aNaturalNumber0(xk)),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(66,plain,
% 0.60/0.80 (aNaturalNumber0(xk)),
% 0.60/0.80 inference(and_elim,[status(thm)],[11])).
% 0.60/0.80 tff(67,plain,
% 0.60/0.80 (aNaturalNumber0(xk)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.60/0.80 tff(68,plain,
% 0.60/0.80 (aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.60/0.80 tff(69,plain,
% 0.60/0.80 (aNaturalNumber0(W0!8)),
% 0.60/0.80 inference(and_elim,[status(thm)],[19])).
% 0.60/0.80 tff(70,plain,
% 0.60/0.80 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(71,plain,
% 0.60/0.80 (((sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp))))) <=> ((~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(72,plain,
% 0.60/0.80 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp))))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[71])).
% 0.60/0.80 tff(73,plain,
% 0.60/0.80 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[72, 70])).
% 0.60/0.80 tff(74,plain,
% 0.60/0.80 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp)))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(75,plain,
% 0.60/0.80 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8) | (~((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, W0!8)) | (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(W0!8, xp))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.60/0.80 tff(76,plain,
% 0.60/0.80 (sdtsldt0(sdtasdt0(xn, xm), xp) = W0!8),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[75, 69, 68, 62, 25])).
% 0.60/0.80 tff(77,plain,
% 0.60/0.80 (xk = W0!8),
% 0.60/0.80 inference(transitivity,[status(thm)],[6, 76])).
% 0.60/0.80 tff(78,plain,
% 0.60/0.80 (doDivides0(tptp_fun_W1_3(W0!8), xk) <=> doDivides0(tptp_fun_W1_3(W0!8), W0!8)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[77])).
% 0.60/0.80 tff(79,plain,
% 0.60/0.80 (doDivides0(tptp_fun_W1_3(W0!8), W0!8) <=> doDivides0(tptp_fun_W1_3(W0!8), xk)),
% 0.60/0.80 inference(symmetry,[status(thm)],[78])).
% 0.60/0.80 tff(80,plain,
% 0.60/0.80 (tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)) = tptp_fun_W1_3(W0!8)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[76])).
% 0.60/0.80 tff(81,plain,
% 0.60/0.80 (doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp)) <=> doDivides0(tptp_fun_W1_3(W0!8), W0!8)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[80, 76])).
% 0.60/0.80 tff(82,plain,
% 0.60/0.80 ((sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) <=> (xk = sz10)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[7])).
% 0.60/0.80 tff(83,plain,
% 0.60/0.80 ((xk = sz10) <=> (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10)),
% 0.60/0.80 inference(symmetry,[status(thm)],[82])).
% 0.60/0.80 tff(84,plain,
% 0.60/0.80 ((~(xk = sz10)) <=> (~(sdtsldt0(sdtasdt0(xn, xm), xp) = sz10))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[83])).
% 0.60/0.80 tff(85,plain,
% 0.60/0.80 ((~(xk = sz10)) <=> (~(xk = sz10))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(86,axiom,(~((xk = sz00) | (xk = sz10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2315')).
% 0.60/0.80 tff(87,plain,
% 0.60/0.80 (~(xk = sz10)),
% 0.60/0.80 inference(or_elim,[status(thm)],[86])).
% 0.60/0.80 tff(88,plain,
% 0.60/0.80 (~(xk = sz10)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[87, 85])).
% 0.60/0.80 tff(89,plain,
% 0.60/0.80 (~(sdtsldt0(sdtasdt0(xn, xm), xp) = sz10)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.60/0.80 tff(90,plain,
% 0.60/0.80 ((sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) <=> (xk = sz00)),
% 0.60/0.80 inference(monotonicity,[status(thm)],[7])).
% 0.60/0.80 tff(91,plain,
% 0.60/0.80 ((xk = sz00) <=> (sdtsldt0(sdtasdt0(xn, xm), xp) = sz00)),
% 0.60/0.80 inference(symmetry,[status(thm)],[90])).
% 0.60/0.80 tff(92,plain,
% 0.60/0.80 ((~(xk = sz00)) <=> (~(sdtsldt0(sdtasdt0(xn, xm), xp) = sz00))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[91])).
% 0.60/0.80 tff(93,plain,
% 0.60/0.80 ((~(xk = sz00)) <=> (~(xk = sz00))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(94,plain,
% 0.60/0.80 (~(xk = sz00)),
% 0.60/0.80 inference(or_elim,[status(thm)],[86])).
% 0.60/0.80 tff(95,plain,
% 0.60/0.80 (~(xk = sz00)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.60/0.80 tff(96,plain,
% 0.60/0.80 (~(sdtsldt0(sdtasdt0(xn, xm), xp) = sz00)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[95, 92])).
% 0.60/0.80 tff(97,plain,
% 0.60/0.80 (^[W0: $i] : refl(((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))) <=> ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(98,plain,
% 0.60/0.80 (![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[97])).
% 0.60/0.80 tff(99,plain,
% 0.60/0.80 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10))) <=> (~((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)))), ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) <=> (~(~((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)))))), rewrite((~(~((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)))) <=> ((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10))), ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) <=> ((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)))), rewrite((aNaturalNumber0(tptp_fun_W1_3(W0)) & doDivides0(tptp_fun_W1_3(W0), W0) & isPrime0(tptp_fun_W1_3(W0))) <=> (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))), (((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | (aNaturalNumber0(tptp_fun_W1_3(W0)) & doDivides0(tptp_fun_W1_3(W0), W0) & isPrime0(tptp_fun_W1_3(W0)))) <=> (((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))))), rewrite((((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))) <=> ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))), (((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | (aNaturalNumber0(tptp_fun_W1_3(W0)) & doDivides0(tptp_fun_W1_3(W0), W0) & isPrime0(tptp_fun_W1_3(W0)))) <=> ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(100,plain,
% 0.60/0.80 (![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | (aNaturalNumber0(tptp_fun_W1_3(W0)) & doDivides0(tptp_fun_W1_3(W0), W0) & isPrime0(tptp_fun_W1_3(W0)))) <=> ![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[99])).
% 0.60/0.80 tff(101,plain,
% 0.60/0.80 (![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1))) <=> ![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(102,plain,
% 0.60/0.80 (^[W0: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & (~(W0 = sz00))) & (~(W0 = sz10))) <=> (aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))), quant_intro(proof_bind(^[W1: $i] : rewrite(((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1)) <=> (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))), (?[W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1)) <=> ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))), ((((aNaturalNumber0(W0) & (~(W0 = sz00))) & (~(W0 = sz10))) => ?[W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1))) <=> ((aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10))) => ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1))))), rewrite(((aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10))) => ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1))) <=> ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))), ((((aNaturalNumber0(W0) & (~(W0 = sz00))) & (~(W0 = sz10))) => ?[W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1))) <=> ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(103,plain,
% 0.60/0.80 (![W0: $i] : (((aNaturalNumber0(W0) & (~(W0 = sz00))) & (~(W0 = sz10))) => ?[W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1))) <=> ![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[102])).
% 0.60/0.80 tff(104,axiom,(![W0: $i] : (((aNaturalNumber0(W0) & (~(W0 = sz00))) & (~(W0 = sz10))) => ?[W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mPrimDiv')).
% 0.60/0.80 tff(105,plain,
% 0.60/0.80 (![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.60/0.80 tff(106,plain,
% 0.60/0.80 (![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.60/0.80 tff(107,plain,(
% 0.60/0.80 ![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | (aNaturalNumber0(tptp_fun_W1_3(W0)) & doDivides0(tptp_fun_W1_3(W0), W0) & isPrime0(tptp_fun_W1_3(W0))))),
% 0.60/0.80 inference(skolemize,[status(sab)],[106])).
% 0.60/0.80 tff(108,plain,
% 0.60/0.80 (![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.60/0.80 tff(109,plain,
% 0.60/0.80 (![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[108, 98])).
% 0.60/0.80 tff(110,plain,
% 0.60/0.80 (((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | ((~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(111,plain,
% 0.60/0.80 (((sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))))))) <=> ((~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(112,plain,
% 0.60/0.80 ((~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))))) <=> (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(113,plain,
% 0.60/0.80 (((sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))))))) <=> ((sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[112])).
% 0.60/0.80 tff(114,plain,
% 0.60/0.80 (((sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))))))) <=> ((~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[113, 111])).
% 0.60/0.80 tff(115,plain,
% 0.60/0.80 (((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | ((sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | ((~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))))))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[114])).
% 0.60/0.80 tff(116,plain,
% 0.60/0.80 (((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | ((sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[115, 110])).
% 0.60/0.80 tff(117,plain,
% 0.60/0.80 ((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | ((sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(118,plain,
% 0.60/0.80 ((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.60/0.80 tff(119,plain,
% 0.60/0.80 ((~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz00) | (sdtsldt0(sdtasdt0(xn, xm), xp) = sz10) | (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[118, 109])).
% 0.60/0.80 tff(120,plain,
% 0.60/0.80 (~((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[119, 96, 89, 68])).
% 0.60/0.81 tff(121,plain,
% 0.60/0.81 (((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))))) | doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(122,plain,
% 0.60/0.81 (doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.60/0.81 tff(123,plain,
% 0.60/0.81 (doDivides0(tptp_fun_W1_3(W0!8), W0!8)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[122, 81])).
% 0.60/0.81 tff(124,plain,
% 0.60/0.81 (doDivides0(tptp_fun_W1_3(W0!8), xk)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[123, 79])).
% 0.60/0.81 tff(125,plain,
% 0.60/0.81 (isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))) <=> isPrime0(tptp_fun_W1_3(W0!8))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[80])).
% 0.60/0.81 tff(126,plain,
% 0.60/0.81 (((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))))) | isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(127,plain,
% 0.60/0.81 (isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[126, 120])).
% 0.60/0.81 tff(128,plain,
% 0.60/0.81 (isPrime0(tptp_fun_W1_3(W0!8))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[127, 125])).
% 0.60/0.81 tff(129,plain,
% 0.60/0.81 ((isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz10) | (tptp_fun_W1_3(W0!8) = sz00) | (~((~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10)))))) | (~isPrime0(tptp_fun_W1_3(W0!8)))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(130,plain,
% 0.60/0.81 (isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz10) | (tptp_fun_W1_3(W0!8) = sz00) | (~((~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10)))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.60/0.81 tff(131,plain,
% 0.60/0.81 (aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))) <=> aNaturalNumber0(tptp_fun_W1_3(W0!8))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[80])).
% 0.60/0.81 tff(132,plain,
% 0.60/0.81 (((~aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))) | (~doDivides0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)), sdtsldt0(sdtasdt0(xn, xm), xp))) | (~isPrime0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp))))) | aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(133,plain,
% 0.60/0.81 (aNaturalNumber0(tptp_fun_W1_3(sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[132, 120])).
% 0.60/0.81 tff(134,plain,
% 0.60/0.81 (aNaturalNumber0(tptp_fun_W1_3(W0!8))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[133, 131])).
% 0.60/0.81 tff(135,plain,
% 0.60/0.81 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0))))))))) <=> ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0))))))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(136,plain,
% 0.60/0.81 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0))))))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[135])).
% 0.60/0.81 tff(137,plain,
% 0.60/0.81 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0))))))))) <=> ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0))))))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(138,plain,
% 0.60/0.81 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0))))))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[137])).
% 0.60/0.81 tff(139,plain,
% 0.60/0.81 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0))))))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))),
% 0.60/0.81 inference(transitivity,[status(thm)],[138, 136])).
% 0.60/0.81 tff(140,plain,
% 0.60/0.81 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & aNaturalNumber0(tptp_fun_W1_11(W0)) & aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0))) & doDivides0(tptp_fun_W1_11(W0), W0))))) <=> ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0))))))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(141,plain,
% 0.60/0.81 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & aNaturalNumber0(tptp_fun_W1_11(W0)) & aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0))) & doDivides0(tptp_fun_W1_11(W0), W0))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[140])).
% 0.60/0.81 tff(142,plain,
% 0.60/0.81 (^[W0: $i] : trans(monotonicity(rewrite(((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) <=> ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))))), rewrite(((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0))))) <=> ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & aNaturalNumber0(tptp_fun_W1_11(W0)) & aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0))) & doDivides0(tptp_fun_W1_11(W0), W0))))), (((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0)))))) <=> ((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & aNaturalNumber0(tptp_fun_W1_11(W0)) & aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0))) & doDivides0(tptp_fun_W1_11(W0), W0))))))), rewrite(((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & aNaturalNumber0(tptp_fun_W1_11(W0)) & aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0))) & doDivides0(tptp_fun_W1_11(W0), W0))))) <=> ((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & aNaturalNumber0(tptp_fun_W1_11(W0)) & aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0))) & doDivides0(tptp_fun_W1_11(W0), W0)))))), (((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0)))))) <=> ((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & aNaturalNumber0(tptp_fun_W1_11(W0)) & aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0))) & doDivides0(tptp_fun_W1_11(W0), W0)))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(143,plain,
% 0.60/0.81 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0)))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & aNaturalNumber0(tptp_fun_W1_11(W0)) & aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0))) & doDivides0(tptp_fun_W1_11(W0), W0)))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[142])).
% 0.60/0.81 tff(144,plain,
% 0.60/0.81 ((~?[W0: $i] : (aNaturalNumber0(W0) & (doDivides0(W0, xk) | ?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))) & (isPrime0(W0) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0)))))))) <=> (~?[W0: $i] : (aNaturalNumber0(W0) & (doDivides0(W0, xk) | ?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))) & (isPrime0(W0) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0))))))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(145,plain,
% 0.60/0.81 ((~?[W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))) | doDivides0(W0, xk))) & ((((~(W0 = sz00)) & (~(W0 = sz10))) & ![W1: $i] : (((aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2)))) & doDivides0(W1, W0)) => ((W1 = sz10) | (W1 = W0)))) | isPrime0(W0)))) <=> (~?[W0: $i] : (aNaturalNumber0(W0) & (doDivides0(W0, xk) | ?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))) & (isPrime0(W0) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0))))))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(146,axiom,(~?[W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))) | doDivides0(W0, xk))) & ((((~(W0 = sz00)) & (~(W0 = sz10))) & ![W1: $i] : (((aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2)))) & doDivides0(W1, W0)) => ((W1 = sz10) | (W1 = W0)))) | isPrime0(W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.60/0.81 tff(147,plain,
% 0.60/0.81 (~?[W0: $i] : (aNaturalNumber0(W0) & (doDivides0(W0, xk) | ?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))) & (isPrime0(W0) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0)))))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.60/0.81 tff(148,plain,
% 0.60/0.81 (~?[W0: $i] : (aNaturalNumber0(W0) & (doDivides0(W0, xk) | ?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))) & (isPrime0(W0) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0)))))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[147, 144])).
% 0.60/0.81 tff(149,plain,
% 0.60/0.81 (~?[W0: $i] : (aNaturalNumber0(W0) & (doDivides0(W0, xk) | ?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))) & (isPrime0(W0) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0)))))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.60/0.81 tff(150,plain,
% 0.60/0.81 (~?[W0: $i] : (aNaturalNumber0(W0) & (doDivides0(W0, xk) | ?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))) & (isPrime0(W0) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0)))))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[149, 144])).
% 0.60/0.81 tff(151,plain,
% 0.60/0.81 (^[W0: $i] : nnf_neg(refl($oeq((~aNaturalNumber0(W0)), (~aNaturalNumber0(W0)))), nnf_neg(refl($oeq((~doDivides0(W0, xk)), (~doDivides0(W0, xk)))), nnf_neg(proof_bind(^[W1: $i] : refl($oeq((~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))), (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))))), $oeq((~?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))), ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))))), $oeq((~(doDivides0(W0, xk) | ?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))), ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))))), nnf_neg(refl($oeq((~isPrime0(W0)), (~isPrime0(W0)))), nnf_neg(refl($oeq((W0 = sz00), (W0 = sz00))), refl($oeq((W0 = sz10), (W0 = sz10))), trans(sk($oeq((~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0))))), (~((tptp_fun_W1_11(W0) = W0) | (tptp_fun_W1_11(W0) = sz10) | (~(aNaturalNumber0(tptp_fun_W1_11(W0)) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), W2))) & doDivides0(tptp_fun_W1_11(W0), W0))))))), nnf_neg(refl($oeq((~(tptp_fun_W1_11(W0) = W0)), (~(tptp_fun_W1_11(W0) = W0)))), refl($oeq((~(tptp_fun_W1_11(W0) = sz10)), (~(tptp_fun_W1_11(W0) = sz10)))), nnf_neg(monotonicity(refl($oeq(aNaturalNumber0(tptp_fun_W1_11(W0)), aNaturalNumber0(tptp_fun_W1_11(W0)))), sk($oeq(?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), W2))), (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))))), refl($oeq(doDivides0(tptp_fun_W1_11(W0), W0), doDivides0(tptp_fun_W1_11(W0), W0))), $oeq((aNaturalNumber0(tptp_fun_W1_11(W0)) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), W2))) & doDivides0(tptp_fun_W1_11(W0), W0)), (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0)))), $oeq((~(~(aNaturalNumber0(tptp_fun_W1_11(W0)) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), W2))) & doDivides0(tptp_fun_W1_11(W0), W0)))), (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0)))), $oeq((~((tptp_fun_W1_11(W0) = W0) | (tptp_fun_W1_11(W0) = sz10) | (~(aNaturalNumber0(tptp_fun_W1_11(W0)) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), W2))) & doDivides0(tptp_fun_W1_11(W0), W0))))), ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0))))), $oeq((~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0))))), ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0))))), $oeq((~((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0)))))), ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0)))))), $oeq((~(isPrime0(W0) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0))))))), ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0))))))), $oeq((~(aNaturalNumber0(W0) & (doDivides0(W0, xk) | ?[W1: $i] : (aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1)))) & (isPrime0(W0) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & ?[W2: $i] : (aNaturalNumber0(W2) & (W0 = sdtasdt0(W1, W2))) & doDivides0(W1, W0)))))))), ((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0))))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(152,plain,(
% 0.60/0.81 ![W0: $i] : ((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & (aNaturalNumber0(tptp_fun_W1_11(W0)) & (aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) & doDivides0(tptp_fun_W1_11(W0), W0))))))),
% 0.60/0.81 inference(nnf-neg,[status(sab)],[150, 151])).
% 0.60/0.81 tff(153,plain,
% 0.60/0.81 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((~doDivides0(W0, xk)) & ![W1: $i] : (~(aNaturalNumber0(W1) & (xk = sdtasdt0(W0, W1))))) | ((~isPrime0(W0)) & ((W0 = sz00) | (W0 = sz10) | ((~(tptp_fun_W1_11(W0) = W0)) & (~(tptp_fun_W1_11(W0) = sz10)) & aNaturalNumber0(tptp_fun_W1_11(W0)) & aNaturalNumber0(tptp_fun_W2_12(W0)) & (W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0))) & doDivides0(tptp_fun_W1_11(W0), W0)))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[152, 143])).
% 0.60/0.81 tff(154,plain,
% 0.60/0.81 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[153, 141])).
% 0.60/0.81 tff(155,plain,
% 0.60/0.81 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[154, 139])).
% 0.60/0.81 tff(156,plain,
% 0.60/0.81 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))) | ((~aNaturalNumber0(tptp_fun_W1_3(W0!8))) | (~((~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))) | doDivides0(tptp_fun_W1_3(W0!8), xk))) | (~(isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz10) | (tptp_fun_W1_3(W0!8) = sz00) | (~((~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10))))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))) | (~aNaturalNumber0(tptp_fun_W1_3(W0!8))) | (~((~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))) | doDivides0(tptp_fun_W1_3(W0!8), xk))) | (~(isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz10) | (tptp_fun_W1_3(W0!8) = sz00) | (~((~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10))))))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(157,plain,
% 0.60/0.81 (((~aNaturalNumber0(tptp_fun_W1_3(W0!8))) | (~(doDivides0(tptp_fun_W1_3(W0!8), xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))))) | (~(isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz00) | (tptp_fun_W1_3(W0!8) = sz10) | (~((tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8)))))))))) <=> ((~aNaturalNumber0(tptp_fun_W1_3(W0!8))) | (~((~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))) | doDivides0(tptp_fun_W1_3(W0!8), xk))) | (~(isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz10) | (tptp_fun_W1_3(W0!8) = sz00) | (~((~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10))))))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(158,plain,
% 0.60/0.81 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))) | ((~aNaturalNumber0(tptp_fun_W1_3(W0!8))) | (~(doDivides0(tptp_fun_W1_3(W0!8), xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))))) | (~(isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz00) | (tptp_fun_W1_3(W0!8) = sz10) | (~((tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8))))))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))) | ((~aNaturalNumber0(tptp_fun_W1_3(W0!8))) | (~((~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))) | doDivides0(tptp_fun_W1_3(W0!8), xk))) | (~(isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz10) | (tptp_fun_W1_3(W0!8) = sz00) | (~((~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10)))))))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[157])).
% 0.60/0.81 tff(159,plain,
% 0.60/0.81 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))) | ((~aNaturalNumber0(tptp_fun_W1_3(W0!8))) | (~(doDivides0(tptp_fun_W1_3(W0!8), xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))))) | (~(isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz00) | (tptp_fun_W1_3(W0!8) = sz10) | (~((tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8))))))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))) | (~aNaturalNumber0(tptp_fun_W1_3(W0!8))) | (~((~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))) | doDivides0(tptp_fun_W1_3(W0!8), xk))) | (~(isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz10) | (tptp_fun_W1_3(W0!8) = sz00) | (~((~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10))))))))),
% 0.60/0.82 inference(transitivity,[status(thm)],[158, 156])).
% 0.60/0.82 tff(160,plain,
% 0.60/0.82 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))) | ((~aNaturalNumber0(tptp_fun_W1_3(W0!8))) | (~(doDivides0(tptp_fun_W1_3(W0!8), xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))))) | (~(isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz00) | (tptp_fun_W1_3(W0!8) = sz10) | (~((tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8))))))))))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(161,plain,
% 0.60/0.82 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(doDivides0(W0, xk) | (~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(W0, W1))))))) | (~(isPrime0(W0) | (~((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_11(W0) = sz10) | (tptp_fun_W1_11(W0) = W0) | (~aNaturalNumber0(tptp_fun_W1_11(W0))) | (~aNaturalNumber0(tptp_fun_W2_12(W0))) | (~(W0 = sdtasdt0(tptp_fun_W1_11(W0), tptp_fun_W2_12(W0)))) | (~doDivides0(tptp_fun_W1_11(W0), W0)))))))))) | (~aNaturalNumber0(tptp_fun_W1_3(W0!8))) | (~((~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))) | doDivides0(tptp_fun_W1_3(W0!8), xk))) | (~(isPrime0(tptp_fun_W1_3(W0!8)) | (~((tptp_fun_W1_3(W0!8) = sz10) | (tptp_fun_W1_3(W0!8) = sz00) | (~((~doDivides0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W1_3(W0!8))) | (~(tptp_fun_W1_3(W0!8) = sdtasdt0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)), tptp_fun_W2_12(tptp_fun_W1_3(W0!8))))) | (~aNaturalNumber0(tptp_fun_W2_12(tptp_fun_W1_3(W0!8)))) | (~aNaturalNumber0(tptp_fun_W1_11(tptp_fun_W1_3(W0!8)))) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = tptp_fun_W1_3(W0!8)) | (tptp_fun_W1_11(tptp_fun_W1_3(W0!8)) = sz10)))))))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.60/0.82 tff(162,plain,
% 0.60/0.82 (~((~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))) | doDivides0(tptp_fun_W1_3(W0!8), xk))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[161, 155, 134, 130])).
% 0.60/0.82 tff(163,plain,
% 0.60/0.82 (((~![W1: $i] : ((~aNaturalNumber0(W1)) | (~(xk = sdtasdt0(tptp_fun_W1_3(W0!8), W1))))) | doDivides0(tptp_fun_W1_3(W0!8), xk)) | (~doDivides0(tptp_fun_W1_3(W0!8), xk))),
% 0.60/0.82 inference(tautology,[status(thm)],[])).
% 0.60/0.82 tff(164,plain,
% 0.60/0.82 (~doDivides0(tptp_fun_W1_3(W0!8), xk)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.60/0.82 tff(165,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[164, 124])).
% 0.60/0.82 % SZS output end Proof
% 0.60/0.82 % E exiting
%------------------------------------------------------------------------------