%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM529+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:21:17 AM UTC 2025
% Result : Theorem 0.86s 1.06s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM529+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:23:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.86/1.06 % SZS status Theorem
% 0.86/1.06 % SZS output start Proof
% 0.86/1.06 tff(sdtsldt0_type, type, (
% 0.86/1.06 sdtsldt0: ( $i * $i ) > $i)).
% 0.86/1.06 tff(xp_type, type, (
% 0.86/1.06 xp: $i)).
% 0.86/1.06 tff(sdtasdt0_type, type, (
% 0.86/1.06 sdtasdt0: ( $i * $i ) > $i)).
% 0.86/1.06 tff(tptp_fun_W0_7_type, type, (
% 0.86/1.06 tptp_fun_W0_7: $i)).
% 0.86/1.06 tff(sz00_type, type, (
% 0.86/1.06 sz00: $i)).
% 0.86/1.06 tff(xn_type, type, (
% 0.86/1.06 xn: $i)).
% 0.86/1.06 tff(xq_type, type, (
% 0.86/1.06 xq: $i)).
% 0.86/1.06 tff(aNaturalNumber0_type, type, (
% 0.86/1.06 aNaturalNumber0: $i > $o)).
% 0.86/1.06 tff(doDivides0_type, type, (
% 0.86/1.06 doDivides0: ( $i * $i ) > $o)).
% 0.86/1.06 tff(xm_type, type, (
% 0.86/1.06 xm: $i)).
% 0.86/1.06 tff(iLess0_type, type, (
% 0.86/1.06 iLess0: ( $i * $i ) > $o)).
% 0.86/1.06 tff(sdtpldt0_type, type, (
% 0.86/1.06 sdtpldt0: ( $i * $i ) > $i)).
% 0.86/1.06 tff(sdtlseqdt0_type, type, (
% 0.86/1.06 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.86/1.06 tff(tptp_fun_W3_4_type, type, (
% 0.86/1.06 tptp_fun_W3_4: $i > $i)).
% 0.86/1.06 tff(tptp_fun_W4_5_type, type, (
% 0.86/1.06 tptp_fun_W4_5: $i > $i)).
% 0.86/1.06 tff(sz10_type, type, (
% 0.86/1.06 sz10: $i)).
% 0.86/1.06 tff(isPrime0_type, type, (
% 0.86/1.06 isPrime0: $i > $o)).
% 0.86/1.06 tff(1,plain,
% 0.86/1.06 ((sz00 = W0!7) <=> (W0!7 = sz00)),
% 0.86/1.06 inference(commutativity,[status(thm)],[])).
% 0.86/1.06 tff(2,plain,
% 0.86/1.06 ((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) <=> (sdtasdt0(xp, W0!7) = sdtasdt0(xp, sdtsldt0(xn, xp)))),
% 0.86/1.06 inference(commutativity,[status(thm)],[])).
% 0.86/1.06 tff(3,plain,
% 0.86/1.06 ((sdtasdt0(xp, W0!7) = sdtasdt0(xp, sdtsldt0(xn, xp))) <=> (sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2])).
% 0.86/1.06 tff(4,plain,
% 0.86/1.06 ((xq = sdtsldt0(xn, xp)) <=> (xq = sdtsldt0(xn, xp))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(5,axiom,((aNaturalNumber0(xq) & (xn = sdtasdt0(xp, xq))) & (xq = sdtsldt0(xn, xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3059')).
% 0.86/1.06 tff(6,plain,
% 0.86/1.06 (xq = sdtsldt0(xn, xp)),
% 0.86/1.06 inference(and_elim,[status(thm)],[5])).
% 0.86/1.06 tff(7,plain,
% 0.86/1.06 (xq = sdtsldt0(xn, xp)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[6, 4])).
% 0.86/1.06 tff(8,plain,
% 0.86/1.06 (sdtsldt0(xn, xp) = xq),
% 0.86/1.06 inference(symmetry,[status(thm)],[7])).
% 0.86/1.06 tff(9,plain,
% 0.86/1.06 (sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, xq)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[8])).
% 0.86/1.06 tff(10,plain,
% 0.86/1.06 (sdtasdt0(xp, xq) = sdtasdt0(xp, sdtsldt0(xn, xp))),
% 0.86/1.06 inference(symmetry,[status(thm)],[9])).
% 0.86/1.06 tff(11,plain,
% 0.86/1.06 ((xn = sdtasdt0(xp, xq)) <=> (xn = sdtasdt0(xp, xq))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(12,plain,
% 0.86/1.06 (aNaturalNumber0(xq) & (xn = sdtasdt0(xp, xq))),
% 0.86/1.06 inference(and_elim,[status(thm)],[5])).
% 0.86/1.06 tff(13,plain,
% 0.86/1.06 (xn = sdtasdt0(xp, xq)),
% 0.86/1.06 inference(and_elim,[status(thm)],[12])).
% 0.86/1.06 tff(14,plain,
% 0.86/1.06 (xn = sdtasdt0(xp, xq)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[13, 11])).
% 0.86/1.06 tff(15,plain,
% 0.86/1.06 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(16,axiom,(((?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtasdt0(xn, xn))) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))) & doDivides0(xp, xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3046')).
% 0.86/1.06 tff(17,plain,
% 0.86/1.06 ((?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtasdt0(xn, xn))) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.86/1.06 inference(and_elim,[status(thm)],[16])).
% 0.86/1.06 tff(18,plain,
% 0.86/1.06 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.86/1.06 inference(and_elim,[status(thm)],[17])).
% 0.86/1.06 tff(19,plain,
% 0.86/1.06 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.86/1.06 tff(20,plain,(
% 0.86/1.06 aNaturalNumber0(W0!7) & (xn = sdtasdt0(xp, W0!7))),
% 0.86/1.06 inference(skolemize,[status(sab)],[19])).
% 0.86/1.06 tff(21,plain,
% 0.86/1.06 (xn = sdtasdt0(xp, W0!7)),
% 0.86/1.06 inference(and_elim,[status(thm)],[20])).
% 0.86/1.06 tff(22,plain,
% 0.86/1.06 (sdtasdt0(xp, W0!7) = xn),
% 0.86/1.06 inference(symmetry,[status(thm)],[21])).
% 0.86/1.06 tff(23,plain,
% 0.86/1.06 (sdtasdt0(xp, W0!7) = sdtasdt0(xp, sdtsldt0(xn, xp))),
% 0.86/1.06 inference(transitivity,[status(thm)],[22, 14, 10])).
% 0.86/1.06 tff(24,plain,
% 0.86/1.06 (sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[23, 3])).
% 0.86/1.06 tff(25,plain,
% 0.86/1.06 (((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))) | (~(sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(26,plain,
% 0.86/1.06 ((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.86/1.06 tff(27,plain,
% 0.86/1.06 ((~(xp = sz00)) <=> (~(xp = sz00))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(28,axiom,(((((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))) & (~(xm = sz00))) & (~(xp = sz00))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2987')).
% 0.86/1.06 tff(29,plain,
% 0.86/1.06 (~(xp = sz00)),
% 0.86/1.06 inference(and_elim,[status(thm)],[28])).
% 0.86/1.06 tff(30,plain,
% 0.86/1.06 (~(xp = sz00)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.86/1.06 tff(31,plain,
% 0.86/1.06 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(32,plain,
% 0.86/1.06 ((((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))) & (~(xm = sz00))),
% 0.86/1.06 inference(and_elim,[status(thm)],[28])).
% 0.86/1.06 tff(33,plain,
% 0.86/1.06 (((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))),
% 0.86/1.06 inference(and_elim,[status(thm)],[32])).
% 0.86/1.06 tff(34,plain,
% 0.86/1.06 ((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)),
% 0.86/1.06 inference(and_elim,[status(thm)],[33])).
% 0.86/1.06 tff(35,plain,
% 0.86/1.06 (aNaturalNumber0(xp)),
% 0.86/1.06 inference(and_elim,[status(thm)],[34])).
% 0.86/1.06 tff(36,plain,
% 0.86/1.06 (aNaturalNumber0(xp)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.86/1.06 tff(37,plain,
% 0.86/1.06 (^[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)))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(38,plain,
% 0.86/1.06 (![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))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[37])).
% 0.86/1.06 tff(39,plain,
% 0.86/1.06 (^[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)))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(40,plain,
% 0.86/1.06 (![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))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[39])).
% 0.86/1.06 tff(41,plain,
% 0.86/1.06 (![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))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[40, 38])).
% 0.86/1.06 tff(42,plain,
% 0.86/1.06 (^[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))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(43,plain,
% 0.86/1.06 (![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))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[42])).
% 0.86/1.06 tff(44,plain,
% 0.86/1.06 (![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))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(45,plain,
% 0.86/1.06 (^[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))))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(46,plain,
% 0.86/1.06 (![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))))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[45])).
% 0.86/1.06 tff(47,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')).
% 0.86/1.06 tff(48,plain,
% 0.86/1.06 (![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))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.86/1.06 tff(49,plain,
% 0.86/1.06 (![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))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.86/1.06 tff(50,plain,(
% 0.86/1.06 ![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))))))),
% 0.86/1.06 inference(skolemize,[status(sab)],[49])).
% 0.86/1.06 tff(51,plain,
% 0.86/1.06 (![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))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.86/1.06 tff(52,plain,
% 0.86/1.06 (![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))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.86/1.06 tff(53,plain,
% 0.86/1.06 (((~![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))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(54,plain,
% 0.86/1.06 (((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))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(55,plain,
% 0.86/1.06 (^[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))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(56,plain,
% 0.86/1.06 (![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)))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[55])).
% 0.86/1.06 tff(57,plain,
% 0.86/1.06 (((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))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[56])).
% 0.86/1.06 tff(58,plain,
% 0.86/1.06 (((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))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[57, 54])).
% 0.86/1.06 tff(59,plain,
% 0.86/1.06 (((~![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)))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[58])).
% 0.86/1.06 tff(60,plain,
% 0.86/1.06 (((~![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))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[59, 53])).
% 0.86/1.06 tff(61,plain,
% 0.86/1.06 ((~![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))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(62,plain,
% 0.86/1.06 ((~![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)))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.86/1.06 tff(63,plain,
% 0.86/1.06 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[62, 52, 36, 30])).
% 0.86/1.06 tff(64,plain,
% 0.86/1.06 (aNaturalNumber0(sdtsldt0(xn, xp)) <=> aNaturalNumber0(xq)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[8])).
% 0.86/1.06 tff(65,plain,
% 0.86/1.06 (aNaturalNumber0(xq) <=> aNaturalNumber0(sdtsldt0(xn, xp))),
% 0.86/1.06 inference(symmetry,[status(thm)],[64])).
% 0.86/1.06 tff(66,plain,
% 0.86/1.06 (aNaturalNumber0(xq) <=> aNaturalNumber0(xq)),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(67,plain,
% 0.86/1.06 (aNaturalNumber0(xq)),
% 0.86/1.06 inference(and_elim,[status(thm)],[12])).
% 0.86/1.06 tff(68,plain,
% 0.86/1.06 (aNaturalNumber0(xq)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.86/1.06 tff(69,plain,
% 0.86/1.06 (aNaturalNumber0(sdtsldt0(xn, xp))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.86/1.06 tff(70,plain,
% 0.86/1.06 (aNaturalNumber0(W0!7)),
% 0.86/1.06 inference(and_elim,[status(thm)],[20])).
% 0.86/1.06 tff(71,plain,
% 0.86/1.06 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, 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!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(72,plain,
% 0.86/1.06 (((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))))) <=> ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(73,plain,
% 0.86/1.06 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, 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!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[72])).
% 0.86/1.06 tff(74,plain,
% 0.86/1.06 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, 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!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[73, 71])).
% 0.86/1.06 tff(75,plain,
% 0.86/1.06 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(76,plain,
% 0.86/1.06 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.86/1.06 tff(77,plain,
% 0.86/1.06 (sdtsldt0(xn, xp) = W0!7),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[76, 70, 69, 63, 26])).
% 0.86/1.06 tff(78,plain,
% 0.86/1.06 (sdtsldt0(sdtasdt0(xp, W0!7), xp) = sdtsldt0(xn, xp)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[22])).
% 0.86/1.06 tff(79,plain,
% 0.86/1.06 (sdtsldt0(sdtasdt0(xp, W0!7), xp) = W0!7),
% 0.86/1.06 inference(transitivity,[status(thm)],[78, 77])).
% 0.86/1.06 tff(80,plain,
% 0.86/1.06 ((sz00 = sdtsldt0(sdtasdt0(xp, W0!7), xp)) <=> (sz00 = W0!7)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[79])).
% 0.86/1.06 tff(81,plain,
% 0.86/1.06 ((sz00 = sdtsldt0(sdtasdt0(xp, W0!7), xp)) <=> (W0!7 = sz00)),
% 0.86/1.06 inference(transitivity,[status(thm)],[80, 1])).
% 0.86/1.06 tff(82,plain,
% 0.86/1.06 ((W0!7 = sz00) <=> (sz00 = sdtsldt0(sdtasdt0(xp, W0!7), xp))),
% 0.86/1.06 inference(symmetry,[status(thm)],[81])).
% 0.86/1.06 tff(83,plain,
% 0.86/1.06 ((sdtsldt0(xn, xp) = sz00) <=> (W0!7 = sz00)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[77])).
% 0.86/1.06 tff(84,plain,
% 0.86/1.06 ((sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq))) <=> (sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(85,axiom,(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3082')).
% 0.86/1.06 tff(86,plain,
% 0.86/1.06 (sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.86/1.06 tff(87,plain,
% 0.86/1.06 (sdtasdt0(xp, sdtasdt0(xq, xq)) = sdtasdt0(xm, xm)),
% 0.86/1.06 inference(symmetry,[status(thm)],[86])).
% 0.86/1.06 tff(88,plain,
% 0.86/1.06 (sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)) = sdtasdt0(xq, xq)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[8, 8])).
% 0.86/1.06 tff(89,plain,
% 0.86/1.06 (sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xp, sdtasdt0(xq, xq))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[88])).
% 0.86/1.06 tff(90,plain,
% 0.86/1.06 (sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm)),
% 0.86/1.06 inference(transitivity,[status(thm)],[89, 87])).
% 0.86/1.06 tff(91,plain,
% 0.86/1.06 (iLess0(xm, sdtasdt0(xp, W0!7)) <=> iLess0(xm, xn)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[22])).
% 0.86/1.06 tff(92,plain,
% 0.86/1.06 (aNaturalNumber0(sdtasdt0(xp, W0!7)) <=> aNaturalNumber0(xn)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[22])).
% 0.86/1.06 tff(93,plain,
% 0.86/1.06 (aNaturalNumber0(xn) <=> aNaturalNumber0(sdtasdt0(xp, W0!7))),
% 0.86/1.06 inference(symmetry,[status(thm)],[92])).
% 0.86/1.06 tff(94,plain,
% 0.86/1.06 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(95,plain,
% 0.86/1.07 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 0.86/1.07 inference(and_elim,[status(thm)],[34])).
% 0.86/1.07 tff(96,plain,
% 0.86/1.07 (aNaturalNumber0(xn)),
% 0.86/1.07 inference(and_elim,[status(thm)],[95])).
% 0.86/1.07 tff(97,plain,
% 0.86/1.07 (aNaturalNumber0(xn)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[96, 94])).
% 0.86/1.07 tff(98,plain,
% 0.86/1.07 (aNaturalNumber0(sdtasdt0(xp, W0!7))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.86/1.07 tff(99,plain,
% 0.86/1.07 ((xm = sdtasdt0(xp, W0!7)) <=> (xm = xn)),
% 0.86/1.07 inference(monotonicity,[status(thm)],[22])).
% 0.86/1.07 tff(100,plain,
% 0.86/1.07 ((xm = xn) <=> (xm = sdtasdt0(xp, W0!7))),
% 0.86/1.07 inference(symmetry,[status(thm)],[99])).
% 0.86/1.07 tff(101,plain,
% 0.86/1.07 ((~(xm = xn)) <=> (~(xm = sdtasdt0(xp, W0!7)))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[100])).
% 0.86/1.07 tff(102,plain,
% 0.86/1.07 ((~(xm = xn)) <=> (~(xm = xn))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(103,axiom,(((~(xm = xn)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn))) & sdtlseqdt0(xm, xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3124')).
% 0.86/1.07 tff(104,plain,
% 0.86/1.07 ((~(xm = xn)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn))),
% 0.86/1.07 inference(and_elim,[status(thm)],[103])).
% 0.86/1.07 tff(105,plain,
% 0.86/1.07 (~(xm = xn)),
% 0.86/1.07 inference(and_elim,[status(thm)],[104])).
% 0.86/1.07 tff(106,plain,
% 0.86/1.07 (~(xm = xn)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[105, 102])).
% 0.86/1.07 tff(107,plain,
% 0.86/1.07 (~(xm = sdtasdt0(xp, W0!7))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[106, 101])).
% 0.86/1.07 tff(108,plain,
% 0.86/1.07 (sdtlseqdt0(xm, sdtasdt0(xp, W0!7)) <=> sdtlseqdt0(xm, xn)),
% 0.86/1.07 inference(monotonicity,[status(thm)],[22])).
% 0.86/1.07 tff(109,plain,
% 0.86/1.07 (sdtlseqdt0(xm, xn) <=> sdtlseqdt0(xm, sdtasdt0(xp, W0!7))),
% 0.86/1.07 inference(symmetry,[status(thm)],[108])).
% 0.86/1.07 tff(110,plain,
% 0.86/1.07 (sdtlseqdt0(xm, xn) <=> sdtlseqdt0(xm, xn)),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(111,plain,
% 0.86/1.07 (sdtlseqdt0(xm, xn)),
% 0.86/1.07 inference(and_elim,[status(thm)],[103])).
% 0.86/1.07 tff(112,plain,
% 0.86/1.07 (sdtlseqdt0(xm, xn)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.86/1.07 tff(113,plain,
% 0.86/1.07 (sdtlseqdt0(xm, sdtasdt0(xp, W0!7))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[112, 109])).
% 0.86/1.07 tff(114,plain,
% 0.86/1.07 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(115,plain,
% 0.86/1.07 (aNaturalNumber0(xm)),
% 0.86/1.07 inference(and_elim,[status(thm)],[95])).
% 0.86/1.07 tff(116,plain,
% 0.86/1.07 (aNaturalNumber0(xm)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.86/1.07 tff(117,plain,
% 0.86/1.07 (^[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))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(118,plain,
% 0.86/1.07 (![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)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[117])).
% 0.86/1.07 tff(119,plain,
% 0.86/1.07 (^[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)))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(120,plain,
% 0.86/1.07 (![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)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[119])).
% 0.86/1.07 tff(121,plain,
% 0.86/1.07 (![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))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(122,plain,
% 0.86/1.07 (^[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))))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(123,plain,
% 0.86/1.07 (![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))))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[122])).
% 0.86/1.07 tff(124,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')).
% 0.86/1.07 tff(125,plain,
% 0.86/1.07 (![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.86/1.07 tff(126,plain,
% 0.86/1.07 (![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.86/1.07 tff(127,plain,(
% 0.86/1.07 ![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 0.86/1.07 inference(skolemize,[status(sab)],[126])).
% 0.86/1.07 tff(128,plain,
% 0.86/1.07 (![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.86/1.07 tff(129,plain,
% 0.86/1.07 (![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[128, 118])).
% 0.86/1.07 tff(130,plain,
% 0.86/1.07 (((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xm)) | (~sdtlseqdt0(xm, sdtasdt0(xp, W0!7))) | (xm = sdtasdt0(xp, W0!7)) | iLess0(xm, sdtasdt0(xp, W0!7)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xm)) | (~sdtlseqdt0(xm, sdtasdt0(xp, W0!7))) | (xm = sdtasdt0(xp, W0!7)) | iLess0(xm, sdtasdt0(xp, W0!7)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(131,plain,
% 0.86/1.07 (((xm = sdtasdt0(xp, W0!7)) | iLess0(xm, sdtasdt0(xp, W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~sdtlseqdt0(xm, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xm))) <=> ((~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xm)) | (~sdtlseqdt0(xm, sdtasdt0(xp, W0!7))) | (xm = sdtasdt0(xp, W0!7)) | iLess0(xm, sdtasdt0(xp, W0!7)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(132,plain,
% 0.86/1.07 (((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((xm = sdtasdt0(xp, W0!7)) | iLess0(xm, sdtasdt0(xp, W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~sdtlseqdt0(xm, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xm)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xm)) | (~sdtlseqdt0(xm, sdtasdt0(xp, W0!7))) | (xm = sdtasdt0(xp, W0!7)) | iLess0(xm, sdtasdt0(xp, W0!7))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[131])).
% 0.86/1.07 tff(133,plain,
% 0.86/1.07 (((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((xm = sdtasdt0(xp, W0!7)) | iLess0(xm, sdtasdt0(xp, W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~sdtlseqdt0(xm, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xm)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xm)) | (~sdtlseqdt0(xm, sdtasdt0(xp, W0!7))) | (xm = sdtasdt0(xp, W0!7)) | iLess0(xm, sdtasdt0(xp, W0!7)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[132, 130])).
% 0.86/1.07 tff(134,plain,
% 0.86/1.07 ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((xm = sdtasdt0(xp, W0!7)) | iLess0(xm, sdtasdt0(xp, W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~sdtlseqdt0(xm, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xm)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(135,plain,
% 0.86/1.07 ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xm)) | (~sdtlseqdt0(xm, sdtasdt0(xp, W0!7))) | (xm = sdtasdt0(xp, W0!7)) | iLess0(xm, sdtasdt0(xp, W0!7))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.86/1.07 tff(136,plain,
% 0.86/1.07 ((~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~sdtlseqdt0(xm, sdtasdt0(xp, W0!7))) | (xm = sdtasdt0(xp, W0!7)) | iLess0(xm, sdtasdt0(xp, W0!7))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[135, 129, 116])).
% 0.86/1.07 tff(137,plain,
% 0.86/1.07 (iLess0(xm, sdtasdt0(xp, W0!7))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[136, 113, 107, 98])).
% 0.86/1.07 tff(138,plain,
% 0.86/1.07 (iLess0(xm, xn)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[137, 91])).
% 0.86/1.07 tff(139,plain,
% 0.86/1.07 (isPrime0(xp) <=> isPrime0(xp)),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(140,axiom,(((~(xp = sz10)) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3025')).
% 0.86/1.07 tff(141,plain,
% 0.86/1.07 (isPrime0(xp)),
% 0.86/1.07 inference(and_elim,[status(thm)],[140])).
% 0.86/1.07 tff(142,plain,
% 0.86/1.07 (isPrime0(xp)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[141, 139])).
% 0.86/1.07 tff(143,plain,
% 0.86/1.07 ((isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp))))))) | (~isPrime0(xp))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(144,plain,
% 0.86/1.07 (isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.86/1.07 tff(145,plain,
% 0.86/1.07 (^[W0: $i, W1: $i, W2: $i] : refl(((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2))))))))) <=> ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2))))))))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(146,plain,
% 0.86/1.07 (![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[145])).
% 0.86/1.07 tff(147,plain,
% 0.86/1.07 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00))) <=> (~((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))) <=> (~(~((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))) <=> ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), trans(monotonicity(trans(monotonicity(rewrite(((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2)) <=> (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2))))), (((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2))) <=> ((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2))))))), rewrite(((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2))))) <=> ((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))), (((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2))) <=> ((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2))))))), (((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2)))) <=> ((~isPrime0(W2)) & ((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))), rewrite(((~isPrime0(W2)) & ((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))) <=> (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2))))))))), (((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2)))) <=> (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))), (((~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2))))) <=> ((~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2))))))))))), rewrite(((~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2))))))))) <=> ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))), (((~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2))))) <=> ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(148,plain,
% 0.86/1.07 (![W0: $i, W1: $i, W2: $i] : ((~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[147])).
% 0.86/1.07 tff(149,plain,
% 0.86/1.07 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_4(W2)) & (aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) & doDivides0(tptp_fun_W3_4(W2), W2))))) <=> ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2))))), (((~iLess0(W0, xn)) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_4(W2)) & (aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) & doDivides0(tptp_fun_W3_4(W2), W2))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00))))) <=> ((~iLess0(W0, xn)) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2)))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00))))))), rewrite(((~iLess0(W0, xn)) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2)))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00))))) <=> ((~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2)))))), (((~iLess0(W0, xn)) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_4(W2)) & (aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) & doDivides0(tptp_fun_W3_4(W2), W2))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00))))) <=> ((~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2)))))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(150,plain,
% 0.86/1.07 (![W0: $i, W1: $i, W2: $i] : ((~iLess0(W0, xn)) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_4(W2)) & (aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) & doDivides0(tptp_fun_W3_4(W2), W2))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2)))))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[149])).
% 0.86/1.07 tff(151,plain,
% 0.86/1.07 (![W0: $i, W1: $i, W2: $i] : ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(152,plain,
% 0.86/1.07 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) & (~(W0 = sz00))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) & (~(W0 = sz00))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) & (~(W0 = sz00))) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) & (~(W0 = sz00))) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00))))), (((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) & (~(W0 = sz00))) & (~(W1 = sz00))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00))) & (~(W1 = sz00))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00))) & (~(W1 = sz00))) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)))), (((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) & (~(W0 = sz00))) & (~(W1 = sz00))) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00))))), ((((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) & (~(W0 = sz00))) & (~(W1 = sz00))) & (~(W2 = sz00))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00))) & (~(W2 = sz00))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00))) & (~(W2 = sz00))) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))), ((((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) & (~(W0 = sz00))) & (~(W1 = sz00))) & (~(W2 = sz00))) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00))))), trans(monotonicity(trans(monotonicity(rewrite((~(((~(W2 = sz10)) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2))) <=> (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))))), ((iLess0(W0, xn) => (~(((~(W2 = sz10)) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)))) <=> (iLess0(W0, xn) => (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))))))), rewrite((iLess0(W0, xn) => (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))))) <=> ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))))), ((iLess0(W0, xn) => (~(((~(W2 = sz10)) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)))) <=> ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))))))), (((sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0)) => (iLess0(W0, xn) => (~(((~(W2 = sz10)) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2))))) <=> ((sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0)) => ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))))))), rewrite(((sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0)) => ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))))) <=> ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))))), (((sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0)) => (iLess0(W0, xn) => (~(((~(W2 = sz10)) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2))))) <=> ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0)))))), (((((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) & (~(W0 = sz00))) & (~(W1 = sz00))) & (~(W2 = sz00))) => ((sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0)) => (iLess0(W0, xn) => (~(((~(W2 = sz10)) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)))))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00))) => ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00))) => ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))))) <=> ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))))), (((((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) & (~(W0 = sz00))) & (~(W1 = sz00))) & (~(W2 = sz00))) => ((sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0)) => (iLess0(W0, xn) => (~(((~(W2 = sz10)) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)))))) <=> ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(153,plain,
% 0.86/1.07 (![W0: $i, W1: $i, W2: $i] : ((((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) & (~(W0 = sz00))) & (~(W1 = sz00))) & (~(W2 = sz00))) => ((sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0)) => (iLess0(W0, xn) => (~(((~(W2 = sz10)) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[152])).
% 0.86/1.07 tff(154,axiom,(![W0: $i, W1: $i, W2: $i] : ((((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) & (~(W0 = sz00))) & (~(W1 = sz00))) & (~(W2 = sz00))) => ((sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0)) => (iLess0(W0, xn) => (~(((~(W2 = sz10)) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2963')).
% 0.86/1.07 tff(155,plain,
% 0.86/1.07 (![W0: $i, W1: $i, W2: $i] : ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.86/1.07 tff(156,plain,
% 0.86/1.07 (![W0: $i, W1: $i, W2: $i] : ((~iLess0(W0, xn)) | (~(isPrime0(W2) | ((~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2))))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.86/1.07 tff(157,plain,(
% 0.86/1.07 ![W0: $i, W1: $i, W2: $i] : ((~iLess0(W0, xn)) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_4(W2)) & (aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) & doDivides0(tptp_fun_W3_4(W2), W2))))) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))))),
% 0.86/1.07 inference(skolemize,[status(sab)],[156])).
% 0.86/1.07 tff(158,plain,
% 0.86/1.07 (![W0: $i, W1: $i, W2: $i] : ((~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2) & (~(W0 = sz00)) & (~(W1 = sz00)) & (~(W2 = sz00)))) | ((~isPrime0(W2)) & ((W2 = sz10) | ((~(tptp_fun_W3_4(W2) = W2)) & (~(tptp_fun_W3_4(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_4(W2)) & aNaturalNumber0(tptp_fun_W4_5(W2)) & (W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2))) & doDivides0(tptp_fun_W3_4(W2), W2)))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.86/1.07 tff(159,plain,
% 0.86/1.07 (![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[158, 148])).
% 0.86/1.07 tff(160,plain,
% 0.86/1.07 (![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[159, 146])).
% 0.86/1.08 tff(161,plain,
% 0.86/1.08 ((~(xm = sz00)) <=> (~(xm = sz00))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(162,plain,
% 0.86/1.08 (~(xm = sz00)),
% 0.86/1.08 inference(and_elim,[status(thm)],[32])).
% 0.86/1.08 tff(163,plain,
% 0.86/1.08 (~(xm = sz00)),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.86/1.08 tff(164,plain,
% 0.86/1.08 (((~![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))) | ((xm = sz00) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))) | (~iLess0(xm, xn)) | (sdtsldt0(xn, xp) = sz00) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))) | (xm = sz00) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))) | (~iLess0(xm, xn)) | (sdtsldt0(xn, xp) = sz00) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(165,plain,
% 0.86/1.08 (((xp = sz00) | (sdtsldt0(xn, xp) = sz00) | (xm = sz00) | (~aNaturalNumber0(xp)) | (~iLess0(xm, xn)) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp))))))))) <=> ((xm = sz00) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))) | (~iLess0(xm, xn)) | (sdtsldt0(xn, xp) = sz00) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(166,plain,
% 0.86/1.08 ((~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))) <=> (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(167,plain,
% 0.86/1.08 ((isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp))))))) <=> (isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[166])).
% 0.86/1.08 tff(168,plain,
% 0.86/1.08 ((~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))) <=> (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp))))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[167])).
% 0.86/1.08 tff(169,plain,
% 0.86/1.08 (((xp = sz00) | (sdtsldt0(xn, xp) = sz00) | (xm = sz00) | (~aNaturalNumber0(xp)) | (~iLess0(xm, xn)) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp))))))))) <=> ((xp = sz00) | (sdtsldt0(xn, xp) = sz00) | (xm = sz00) | (~aNaturalNumber0(xp)) | (~iLess0(xm, xn)) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[168])).
% 0.86/1.08 tff(170,plain,
% 0.86/1.08 (((xp = sz00) | (sdtsldt0(xn, xp) = sz00) | (xm = sz00) | (~aNaturalNumber0(xp)) | (~iLess0(xm, xn)) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp))))))))) <=> ((xm = sz00) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))) | (~iLess0(xm, xn)) | (sdtsldt0(xn, xp) = sz00) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[169, 165])).
% 0.86/1.08 tff(171,plain,
% 0.92/1.08 (((~![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))) | ((xp = sz00) | (sdtsldt0(xn, xp) = sz00) | (xm = sz00) | (~aNaturalNumber0(xp)) | (~iLess0(xm, xn)) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))) | ((xm = sz00) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))) | (~iLess0(xm, xn)) | (sdtsldt0(xn, xp) = sz00) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm)))))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[170])).
% 0.92/1.08 tff(172,plain,
% 0.92/1.08 (((~![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))) | ((xp = sz00) | (sdtsldt0(xn, xp) = sz00) | (xm = sz00) | (~aNaturalNumber0(xp)) | (~iLess0(xm, xn)) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))) | (xm = sz00) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))) | (~iLess0(xm, xn)) | (sdtsldt0(xn, xp) = sz00) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))))),
% 0.92/1.08 inference(transitivity,[status(thm)],[171, 164])).
% 0.92/1.08 tff(173,plain,
% 0.92/1.08 ((~![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))) | ((xp = sz00) | (sdtsldt0(xn, xp) = sz00) | (xm = sz00) | (~aNaturalNumber0(xp)) | (~iLess0(xm, xn)) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(174,plain,
% 0.92/1.08 ((~![W0: $i, W1: $i, W2: $i] : ((W2 = sz00) | (W1 = sz00) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~iLess0(W0, xn)) | (~(sdtasdt0(W2, sdtasdt0(W1, W1)) = sdtasdt0(W0, W0))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(isPrime0(W2) | (~((W2 = sz10) | (~((tptp_fun_W3_4(W2) = sz10) | (tptp_fun_W3_4(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_4(W2))) | (~aNaturalNumber0(tptp_fun_W4_5(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_4(W2), tptp_fun_W4_5(W2)))) | (~doDivides0(tptp_fun_W3_4(W2), W2)))))))))) | (xm = sz00) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xm)) | (~(isPrime0(xp) | (~((xp = sz10) | (~((tptp_fun_W3_4(xp) = sz10) | (tptp_fun_W3_4(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_4(xp))) | (~aNaturalNumber0(tptp_fun_W4_5(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_4(xp), tptp_fun_W4_5(xp)))) | (~doDivides0(tptp_fun_W3_4(xp), xp)))))))) | (~iLess0(xm, xn)) | (sdtsldt0(xn, xp) = sz00) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.92/1.08 tff(175,plain,
% 0.92/1.08 ((~aNaturalNumber0(sdtsldt0(xn, xp))) | (~iLess0(xm, xn)) | (sdtsldt0(xn, xp) = sz00) | (~(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xm, xm)))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[174, 116, 36, 163, 30, 160, 144])).
% 0.92/1.08 tff(176,plain,
% 0.92/1.08 (sdtsldt0(xn, xp) = sz00),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[175, 138, 69, 90])).
% 0.92/1.08 tff(177,plain,
% 0.92/1.08 (W0!7 = sz00),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[176, 83])).
% 0.92/1.08 tff(178,plain,
% 0.92/1.08 (sz00 = sdtsldt0(sdtasdt0(xp, W0!7), xp)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[177, 82])).
% 0.92/1.08 tff(179,plain,
% 0.92/1.08 (doDivides0(xp, sdtasdt0(xp, W0!7)) <=> doDivides0(xp, xn)),
% 0.92/1.08 inference(monotonicity,[status(thm)],[22])).
% 0.92/1.08 tff(180,plain,
% 0.92/1.08 (doDivides0(xp, xn) <=> doDivides0(xp, sdtasdt0(xp, W0!7))),
% 0.92/1.08 inference(symmetry,[status(thm)],[179])).
% 0.92/1.08 tff(181,plain,
% 0.92/1.08 (doDivides0(xp, xn) <=> doDivides0(xp, xn)),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(182,plain,
% 0.92/1.08 (doDivides0(xp, xn)),
% 0.92/1.08 inference(and_elim,[status(thm)],[16])).
% 0.92/1.08 tff(183,plain,
% 0.92/1.08 (doDivides0(xp, xn)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.92/1.08 tff(184,plain,
% 0.92/1.08 (doDivides0(xp, sdtasdt0(xp, W0!7))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[183, 180])).
% 0.92/1.08 tff(185,plain,
% 0.92/1.08 (^[W0: $i, W1: $i] : refl(((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(186,plain,
% 0.92/1.08 (![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[185])).
% 0.92/1.08 tff(187,plain,
% 0.92/1.08 (^[W0: $i, W1: $i] : rewrite(((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(188,plain,
% 0.92/1.08 (![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[187])).
% 0.92/1.08 tff(189,plain,
% 0.92/1.08 (![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.92/1.08 inference(transitivity,[status(thm)],[188, 186])).
% 0.92/1.08 tff(190,plain,
% 0.92/1.08 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(trans(monotonicity(rewrite((aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))) <=> (~((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))), (((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) <=> ((W2 = sdtsldt0(W1, W0)) <=> (~((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))), rewrite(((W2 = sdtsldt0(W1, W0)) <=> (~((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))) <=> (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))), (((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) <=> (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))), rewrite((~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))) <=> (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))), (((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) <=> (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))))), (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) <=> ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))), 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 = sz00)) & doDivides0(W0, W1)) <=> (~((W0 = sz00) | (~doDivides0(W0, W1))))), ((~((~(W0 = sz00)) & doDivides0(W0, W1))) <=> (~(~((W0 = sz00) | (~doDivides0(W0, W1))))))), rewrite((~(~((W0 = sz00) | (~doDivides0(W0, W1))))) <=> ((W0 = sz00) | (~doDivides0(W0, W1)))), ((~((~(W0 = sz00)) & doDivides0(W0, W1))) <=> ((W0 = sz00) | (~doDivides0(W0, W1))))), ((![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1)))) <=> (![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((W0 = sz00) | (~doDivides0(W0, W1)))))), rewrite((![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((W0 = sz00) | (~doDivides0(W0, W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))), ((![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(191,plain,
% 0.92/1.08 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1)))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[190])).
% 0.92/1.08 tff(192,plain,
% 0.92/1.08 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1)))) <=> ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(193,plain,
% 0.92/1.08 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((((~(W0 = sz00)) & doDivides0(W0, W1)) => ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ((~((~(W0 = sz00)) & doDivides0(W0, W1))) | ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = sz00)) & doDivides0(W0, W1)) => ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~((~(W0 = sz00)) & doDivides0(W0, W1))) | ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~((~(W0 = sz00)) & doDivides0(W0, W1))) | ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = sz00)) & doDivides0(W0, W1)) => ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(194,plain,
% 0.92/1.08 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = sz00)) & doDivides0(W0, W1)) => ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[193])).
% 0.92/1.08 tff(195,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = sz00)) & doDivides0(W0, W1)) => ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefQuot')).
% 0.92/1.08 tff(196,plain,
% 0.92/1.08 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.92/1.08 tff(197,plain,
% 0.92/1.08 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.92/1.08 tff(198,plain,(
% 0.92/1.08 ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))),
% 0.92/1.08 inference(skolemize,[status(sab)],[197])).
% 0.92/1.08 tff(199,plain,
% 0.92/1.08 (![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.92/1.08 tff(200,plain,
% 0.92/1.08 (![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[199, 189])).
% 0.92/1.08 tff(201,plain,
% 0.92/1.08 (((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp)))))) <=> ((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp)))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(202,plain,
% 0.92/1.08 (((xp = sz00) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~doDivides0(xp, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp))))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp)))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(203,plain,
% 0.92/1.08 (((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | ((xp = sz00) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~doDivides0(xp, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp)))))) <=> ((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp))))))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[202])).
% 0.92/1.08 tff(204,plain,
% 0.92/1.08 (((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | ((xp = sz00) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~doDivides0(xp, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp)))))) <=> ((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp)))))),
% 0.92/1.08 inference(transitivity,[status(thm)],[203, 201])).
% 0.92/1.08 tff(205,plain,
% 0.92/1.08 ((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | ((xp = sz00) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~doDivides0(xp, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp)))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(206,plain,
% 0.92/1.08 ((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.92/1.08 tff(207,plain,
% 0.92/1.08 ((~doDivides0(xp, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp))))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[206, 200, 36, 30])).
% 0.92/1.08 tff(208,plain,
% 0.92/1.08 (![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp))))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[207, 98, 184])).
% 0.92/1.08 tff(209,plain,
% 0.92/1.08 ((~![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xp, W0!7), xp))))) | (~(((~aNaturalNumber0(sz00)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00)))) <=> (sz00 = sdtsldt0(sdtasdt0(xp, W0!7), xp))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(210,plain,
% 0.92/1.08 (~(((~aNaturalNumber0(sz00)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00)))) <=> (sz00 = sdtsldt0(sdtasdt0(xp, W0!7), xp)))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.92/1.08 tff(211,plain,
% 0.92/1.08 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(212,plain,
% 0.92/1.08 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[211])).
% 0.92/1.08 tff(213,plain,
% 0.92/1.08 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(214,plain,
% 0.92/1.09 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[213])).
% 0.92/1.09 tff(215,plain,
% 0.92/1.09 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(216,plain,
% 0.92/1.09 (^[W0: $i] : rewrite((aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(217,plain,
% 0.92/1.09 (![W0: $i] : (aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[216])).
% 0.92/1.09 tff(218,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_MulZero')).
% 0.92/1.09 tff(219,plain,
% 0.92/1.09 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.92/1.09 tff(220,plain,
% 0.92/1.09 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.92/1.09 tff(221,plain,(
% 0.92/1.09 ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.92/1.09 inference(skolemize,[status(sab)],[220])).
% 0.92/1.09 tff(222,plain,
% 0.92/1.09 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.92/1.09 tff(223,plain,
% 0.92/1.09 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[222, 212])).
% 0.92/1.09 tff(224,plain,
% 0.92/1.09 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | ((~aNaturalNumber0(xp)) | (~((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | (~aNaturalNumber0(xp)) | (~((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp))))))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(225,plain,
% 0.92/1.09 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | ((~aNaturalNumber0(xp)) | (~((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp))))))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(226,plain,
% 0.92/1.09 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | (~aNaturalNumber0(xp)) | (~((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp)))))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.92/1.09 tff(227,plain,
% 0.92/1.09 (~((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp))))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[226, 223, 36])).
% 0.92/1.09 tff(228,plain,
% 0.92/1.09 (((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp)))) | (sdtasdt0(xp, sz00) = sz00)),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(229,plain,
% 0.92/1.09 (sdtasdt0(xp, sz00) = sz00),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.92/1.09 tff(230,plain,
% 0.92/1.09 ((sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00)) <=> (xn = sz00)),
% 0.92/1.09 inference(monotonicity,[status(thm)],[22, 229])).
% 0.92/1.09 tff(231,plain,
% 0.92/1.09 ((xn = sz00) <=> (sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00))),
% 0.92/1.09 inference(symmetry,[status(thm)],[230])).
% 0.92/1.09 tff(232,plain,
% 0.92/1.09 ((~(xn = sz00)) <=> (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00)))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[231])).
% 0.92/1.09 tff(233,plain,
% 0.92/1.09 ((~(xn = sz00)) <=> (~(xn = sz00))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(234,plain,
% 0.92/1.09 (~(xn = sz00)),
% 0.92/1.09 inference(and_elim,[status(thm)],[33])).
% 0.92/1.09 tff(235,plain,
% 0.92/1.09 (~(xn = sz00)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.92/1.09 tff(236,plain,
% 0.92/1.09 (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[235, 232])).
% 0.92/1.09 tff(237,plain,
% 0.92/1.09 (((~aNaturalNumber0(sz00)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00)))) | (sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(238,plain,
% 0.92/1.09 ((~aNaturalNumber0(sz00)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.92/1.09 tff(239,plain,
% 0.92/1.09 ((((~aNaturalNumber0(sz00)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00)))) <=> (sz00 = sdtsldt0(sdtasdt0(xp, W0!7), xp))) | (~((~aNaturalNumber0(sz00)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00))))) | (~(sz00 = sdtsldt0(sdtasdt0(xp, W0!7), xp)))),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(240,plain,
% 0.92/1.09 ((((~aNaturalNumber0(sz00)) | (~(sdtasdt0(xp, W0!7) = sdtasdt0(xp, sz00)))) <=> (sz00 = sdtsldt0(sdtasdt0(xp, W0!7), xp))) | (~(sz00 = sdtsldt0(sdtasdt0(xp, W0!7), xp)))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.92/1.09 tff(241,plain,
% 0.92/1.09 (~(sz00 = sdtsldt0(sdtasdt0(xp, W0!7), xp))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[240, 210])).
% 0.92/1.09 tff(242,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[241, 178])).
% 0.92/1.09 % SZS output end Proof
% 0.92/1.09 % E exiting
%------------------------------------------------------------------------------