%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM496+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:11 AM UTC 2025
% Result : Theorem 0.21s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM496+3 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:18:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(doDivides0_type, type, (
% 0.21/0.49 doDivides0: ( $i * $i ) > $o)).
% 0.21/0.49 tff(xp_type, type, (
% 0.21/0.49 xp: $i)).
% 0.21/0.49 tff(tptp_fun_W1_3_type, type, (
% 0.21/0.49 tptp_fun_W1_3: $i > $i)).
% 0.21/0.49 tff(sz10_type, type, (
% 0.21/0.49 sz10: $i)).
% 0.21/0.49 tff(aNaturalNumber0_type, type, (
% 0.21/0.49 aNaturalNumber0: $i > $o)).
% 0.21/0.49 tff(sz00_type, type, (
% 0.21/0.49 sz00: $i)).
% 0.21/0.49 tff(isPrime0_type, type, (
% 0.21/0.49 isPrime0: $i > $o)).
% 0.21/0.49 tff(tptp_fun_W1_2_type, type, (
% 0.21/0.49 tptp_fun_W1_2: $i > $i)).
% 0.21/0.49 tff(sdtasdt0_type, type, (
% 0.21/0.49 sdtasdt0: ( $i * $i ) > $i)).
% 0.21/0.49 tff(xm_type, type, (
% 0.21/0.49 xm: $i)).
% 0.21/0.49 tff(xn_type, type, (
% 0.21/0.49 xn: $i)).
% 0.21/0.49 tff(sdtpldt0_type, type, (
% 0.21/0.49 sdtpldt0: ( $i * $i ) > $i)).
% 0.21/0.49 tff(sdtmndt0_type, type, (
% 0.21/0.49 sdtmndt0: ( $i * $i ) > $i)).
% 0.21/0.49 tff(xr_type, type, (
% 0.21/0.49 xr: $i)).
% 0.21/0.49 tff(tptp_fun_W0_12_type, type, (
% 0.21/0.49 tptp_fun_W0_12: $i)).
% 0.21/0.49 tff(tptp_fun_W0_13_type, type, (
% 0.21/0.49 tptp_fun_W0_13: $i)).
% 0.21/0.49 tff(1,plain,
% 0.21/0.49 ((~(xp = sz10)) <=> (~(xp = sz10))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(2,axiom,((((((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtasdt0(xn, xm))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1860')).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 (((((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.21/0.49 inference(and_elim,[status(thm)],[2])).
% 0.21/0.49 tff(4,plain,
% 0.21/0.49 ((((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)),
% 0.21/0.49 inference(and_elim,[status(thm)],[3])).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))),
% 0.21/0.49 inference(and_elim,[status(thm)],[4])).
% 0.21/0.49 tff(6,plain,
% 0.21/0.49 ((~(xp = sz00)) & (~(xp = sz10))),
% 0.21/0.49 inference(and_elim,[status(thm)],[5])).
% 0.21/0.49 tff(7,plain,
% 0.21/0.49 (~(xp = sz10)),
% 0.21/0.49 inference(and_elim,[status(thm)],[6])).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 (~(xp = sz10)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 ((~(xp = sz00)) <=> (~(xp = sz00))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 (~(xp = sz00)),
% 0.21/0.49 inference(and_elim,[status(thm)],[6])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (~(xp = sz00)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(13,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1837')).
% 0.21/0.49 tff(14,plain,
% 0.21/0.49 (aNaturalNumber0(xp)),
% 0.21/0.49 inference(and_elim,[status(thm)],[13])).
% 0.21/0.49 tff(15,plain,
% 0.21/0.49 (aNaturalNumber0(xp)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.21/0.49 tff(16,plain,
% 0.21/0.49 (^[W0: $i] : refl(((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))) <=> ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 (![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10))) <=> (~((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)))), ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) <=> (~(~((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)))))), rewrite((~(~((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)))) <=> ((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10))), ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) <=> ((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)))), rewrite((aNaturalNumber0(tptp_fun_W1_3(W0)) & doDivides0(tptp_fun_W1_3(W0), W0) & isPrime0(tptp_fun_W1_3(W0))) <=> (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))), (((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | (aNaturalNumber0(tptp_fun_W1_3(W0)) & doDivides0(tptp_fun_W1_3(W0), W0) & isPrime0(tptp_fun_W1_3(W0)))) <=> (((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))))), rewrite((((~aNaturalNumber0(W0)) | (W0 = sz00) | (W0 = sz10)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0)))))) <=> ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))), (((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | (aNaturalNumber0(tptp_fun_W1_3(W0)) & doDivides0(tptp_fun_W1_3(W0), W0) & isPrime0(tptp_fun_W1_3(W0)))) <=> ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(19,plain,
% 0.21/0.49 (![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | (aNaturalNumber0(tptp_fun_W1_3(W0)) & doDivides0(tptp_fun_W1_3(W0), W0) & isPrime0(tptp_fun_W1_3(W0)))) <=> ![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 (![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1))) <=> ![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 (^[W0: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & (~(W0 = sz00))) & (~(W0 = sz10))) <=> (aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))), quant_intro(proof_bind(^[W1: $i] : rewrite(((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1)) <=> (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))), (?[W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1)) <=> ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))), ((((aNaturalNumber0(W0) & (~(W0 = sz00))) & (~(W0 = sz10))) => ?[W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1))) <=> ((aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10))) => ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1))))), rewrite(((aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10))) => ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1))) <=> ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))), ((((aNaturalNumber0(W0) & (~(W0 = sz00))) & (~(W0 = sz10))) => ?[W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1))) <=> ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(22,plain,
% 0.21/0.49 (![W0: $i] : (((aNaturalNumber0(W0) & (~(W0 = sz00))) & (~(W0 = sz10))) => ?[W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1))) <=> ![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.49 tff(23,axiom,(![W0: $i] : (((aNaturalNumber0(W0) & (~(W0 = sz00))) & (~(W0 = sz10))) => ?[W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) & isPrime0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mPrimDiv')).
% 0.21/0.49 tff(24,plain,
% 0.21/0.49 (![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.49 tff(25,plain,
% 0.21/0.49 (![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | ?[W1: $i] : (aNaturalNumber0(W1) & doDivides0(W1, W0) & isPrime0(W1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.49 tff(26,plain,(
% 0.21/0.49 ![W0: $i] : ((~(aNaturalNumber0(W0) & (~(W0 = sz00)) & (~(W0 = sz10)))) | (aNaturalNumber0(tptp_fun_W1_3(W0)) & doDivides0(tptp_fun_W1_3(W0), W0) & isPrime0(tptp_fun_W1_3(W0))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[25])).
% 0.21/0.49 tff(27,plain,
% 0.21/0.49 (![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.49 tff(28,plain,
% 0.21/0.49 (![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.21/0.49 tff(29,plain,
% 0.21/0.49 (((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | ((xp = sz00) | (xp = sz10) | (~aNaturalNumber0(xp)) | (~((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (~isPrime0(tptp_fun_W1_3(xp))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | (xp = sz00) | (xp = sz10) | (~aNaturalNumber0(xp)) | (~((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (~isPrime0(tptp_fun_W1_3(xp))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(30,plain,
% 0.21/0.49 ((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | ((xp = sz00) | (xp = sz10) | (~aNaturalNumber0(xp)) | (~((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (~isPrime0(tptp_fun_W1_3(xp))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(31,plain,
% 0.21/0.49 ((~![W0: $i] : ((W0 = sz00) | (W0 = sz10) | (~aNaturalNumber0(W0)) | (~((~aNaturalNumber0(tptp_fun_W1_3(W0))) | (~doDivides0(tptp_fun_W1_3(W0), W0)) | (~isPrime0(tptp_fun_W1_3(W0))))))) | (xp = sz00) | (xp = sz10) | (~aNaturalNumber0(xp)) | (~((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (~isPrime0(tptp_fun_W1_3(xp)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.49 tff(32,plain,
% 0.21/0.49 (~((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (~isPrime0(tptp_fun_W1_3(xp))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[31, 28, 15, 11, 8])).
% 0.21/0.49 tff(33,plain,
% 0.21/0.49 (((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (~isPrime0(tptp_fun_W1_3(xp)))) | aNaturalNumber0(tptp_fun_W1_3(xp))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(34,plain,
% 0.21/0.49 (aNaturalNumber0(tptp_fun_W1_3(xp))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.49 tff(35,plain,
% 0.21/0.49 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0))))))))) <=> ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0))))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(36,plain,
% 0.21/0.49 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0))))))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0))))))))) <=> ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(38,plain,
% 0.21/0.49 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0))))))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0))))))))) <=> ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(40,plain,
% 0.21/0.49 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0))))))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.49 tff(41,plain,
% 0.21/0.49 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0))))))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[40, 38])).
% 0.21/0.49 tff(42,plain,
% 0.21/0.49 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | (((~isPrime0(W0)) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))) & ((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~(aNaturalNumber0(tptp_fun_W1_2(W0)) & doDivides0(tptp_fun_W1_2(W0), W0)))))))) <=> ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(43,plain,
% 0.21/0.49 (![W0: $i] : ((~aNaturalNumber0(W0)) | (((~isPrime0(W0)) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))) & ((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~(aNaturalNumber0(tptp_fun_W1_2(W0)) & doDivides0(tptp_fun_W1_2(W0), W0)))))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.49 tff(44,plain,
% 0.21/0.49 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | (((~isPrime0(W0)) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))) & (isPrime0(W0) | ((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~(aNaturalNumber0(tptp_fun_W1_2(W0)) & doDivides0(tptp_fun_W1_2(W0), W0))))))))) <=> ((~aNaturalNumber0(W0)) | (((~isPrime0(W0)) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))) & ((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~(aNaturalNumber0(tptp_fun_W1_2(W0)) & doDivides0(tptp_fun_W1_2(W0), W0)))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(45,plain,
% 0.21/0.49 (![W0: $i] : ((~aNaturalNumber0(W0)) | (((~isPrime0(W0)) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))) & (isPrime0(W0) | ((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~(aNaturalNumber0(tptp_fun_W1_2(W0)) & doDivides0(tptp_fun_W1_2(W0), W0))))))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (((~isPrime0(W0)) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))) & ((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~(aNaturalNumber0(tptp_fun_W1_2(W0)) & doDivides0(tptp_fun_W1_2(W0), W0))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.50 tff(46,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | (isPrime0(W0) <=> ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0))))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (isPrime0(W0) <=> ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(47,plain,
% 0.21/0.50 (^[W0: $i] : trans(monotonicity(rewrite((isPrime0(W0) <=> (((~(W0 = sz00)) & (~(W0 = sz10))) & ![W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) => ((W1 = sz10) | (W1 = W0))))) <=> (isPrime0(W0) <=> ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0))))))), ((aNaturalNumber0(W0) => (isPrime0(W0) <=> (((~(W0 = sz00)) & (~(W0 = sz10))) & ![W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) => ((W1 = sz10) | (W1 = W0)))))) <=> (aNaturalNumber0(W0) => (isPrime0(W0) <=> ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0))))))))), rewrite((aNaturalNumber0(W0) => (isPrime0(W0) <=> ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0))))))) <=> ((~aNaturalNumber0(W0)) | (isPrime0(W0) <=> ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))))), ((aNaturalNumber0(W0) => (isPrime0(W0) <=> (((~(W0 = sz00)) & (~(W0 = sz10))) & ![W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) => ((W1 = sz10) | (W1 = W0)))))) <=> ((~aNaturalNumber0(W0)) | (isPrime0(W0) <=> ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(48,plain,
% 0.21/0.50 (![W0: $i] : (aNaturalNumber0(W0) => (isPrime0(W0) <=> (((~(W0 = sz00)) & (~(W0 = sz10))) & ![W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) => ((W1 = sz10) | (W1 = W0)))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (isPrime0(W0) <=> ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.50 tff(49,axiom,(![W0: $i] : (aNaturalNumber0(W0) => (isPrime0(W0) <=> (((~(W0 = sz00)) & (~(W0 = sz10))) & ![W1: $i] : ((aNaturalNumber0(W1) & doDivides0(W1, W0)) => ((W1 = sz10) | (W1 = W0))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefPrime')).
% 0.21/0.50 tff(50,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | (isPrime0(W0) <=> ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.50 tff(51,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | (isPrime0(W0) <=> ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.50 tff(52,plain,(
% 0.21/0.50 ![W0: $i] : ((~aNaturalNumber0(W0)) | (((~isPrime0(W0)) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))) & (isPrime0(W0) | ((W0 = sz00) | (W0 = sz10) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~(aNaturalNumber0(tptp_fun_W1_2(W0)) & doDivides0(tptp_fun_W1_2(W0), W0)))))))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[51])).
% 0.21/0.50 tff(53,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | (((~isPrime0(W0)) | ((~(W0 = sz00)) & (~(W0 = sz10)) & ![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~(aNaturalNumber0(W1) & doDivides0(W1, W0)))))) & ((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~(aNaturalNumber0(tptp_fun_W1_2(W0)) & doDivides0(tptp_fun_W1_2(W0), W0))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.50 tff(54,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.21/0.50 tff(55,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))) | (~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[54, 41])).
% 0.21/0.50 tff(56,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[55, 36])).
% 0.21/0.50 tff(57,plain,
% 0.21/0.50 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | ((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~((~(isPrime0(tptp_fun_W1_3(xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~((~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | (~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~((~(isPrime0(tptp_fun_W1_3(xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~((~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(58,plain,
% 0.21/0.50 (((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~((~((tptp_fun_W1_3(xp) = sz00) | (tptp_fun_W1_3(xp) = sz10) | isPrime0(tptp_fun_W1_3(xp)) | (~((tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz00) | (tptp_fun_W1_3(xp) = sz10) | (~![W1: $i] : ((W1 = tptp_fun_W1_3(xp)) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, tptp_fun_W1_3(xp)))))))))))) <=> ((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~((~(isPrime0(tptp_fun_W1_3(xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~((~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(59,plain,
% 0.21/0.50 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | ((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~((~((tptp_fun_W1_3(xp) = sz00) | (tptp_fun_W1_3(xp) = sz10) | isPrime0(tptp_fun_W1_3(xp)) | (~((tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz00) | (tptp_fun_W1_3(xp) = sz10) | (~![W1: $i] : ((W1 = tptp_fun_W1_3(xp)) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | ((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~((~(isPrime0(tptp_fun_W1_3(xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~((~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp)))))))))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.50 tff(60,plain,
% 0.21/0.50 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | ((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~((~((tptp_fun_W1_3(xp) = sz00) | (tptp_fun_W1_3(xp) = sz10) | isPrime0(tptp_fun_W1_3(xp)) | (~((tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz00) | (tptp_fun_W1_3(xp) = sz10) | (~![W1: $i] : ((W1 = tptp_fun_W1_3(xp)) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | (~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~((~(isPrime0(tptp_fun_W1_3(xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~((~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[59, 57])).
% 0.21/0.50 tff(61,plain,
% 0.21/0.50 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | ((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~((~((tptp_fun_W1_3(xp) = sz00) | (tptp_fun_W1_3(xp) = sz10) | isPrime0(tptp_fun_W1_3(xp)) | (~((tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz00) | (tptp_fun_W1_3(xp) = sz10) | (~![W1: $i] : ((W1 = tptp_fun_W1_3(xp)) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(62,plain,
% 0.21/0.50 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | (~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~((~(isPrime0(tptp_fun_W1_3(xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~((~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp)))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.50 tff(63,plain,
% 0.21/0.50 (~((~(isPrime0(tptp_fun_W1_3(xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~((~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[62, 56, 34])).
% 0.21/0.50 tff(64,plain,
% 0.21/0.50 (((~(isPrime0(tptp_fun_W1_3(xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~((~doDivides0(tptp_fun_W1_2(tptp_fun_W1_3(xp)), tptp_fun_W1_3(xp))) | (~aNaturalNumber0(tptp_fun_W1_2(tptp_fun_W1_3(xp)))) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = sz10) | (tptp_fun_W1_2(tptp_fun_W1_3(xp)) = tptp_fun_W1_3(xp)))))) | (~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp)))))))))) | ((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(65,plain,
% 0.21/0.50 ((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp)))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.21/0.50 tff(66,plain,
% 0.21/0.50 (((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (~isPrime0(tptp_fun_W1_3(xp)))) | isPrime0(tptp_fun_W1_3(xp))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(67,plain,
% 0.21/0.50 (isPrime0(tptp_fun_W1_3(xp))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[66, 32])).
% 0.21/0.50 tff(68,plain,
% 0.21/0.50 ((~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))))) | (~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp)))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(69,plain,
% 0.21/0.50 ((~((~isPrime0(tptp_fun_W1_3(xp))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))))) | (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp)))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.21/0.50 tff(70,plain,
% 0.21/0.50 (~((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[69, 65])).
% 0.21/0.50 tff(71,plain,
% 0.21/0.50 (((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = sz00) | (~![W1: $i] : ((W1 = sz10) | (~aNaturalNumber0(W1)) | (W1 = tptp_fun_W1_3(xp)) | (~doDivides0(W1, tptp_fun_W1_3(xp)))))) | (~(tptp_fun_W1_3(xp) = sz10))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(72,plain,
% 0.21/0.50 (~(tptp_fun_W1_3(xp) = sz10)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | ((~aNaturalNumber0(xp)) | (~((~(isPrime0(xp) | (xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W1_2(xp), xp)) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (tptp_fun_W1_2(xp) = sz10) | (tptp_fun_W1_2(xp) = xp))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | (~aNaturalNumber0(xp)) | (~((~(isPrime0(xp) | (xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W1_2(xp), xp)) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (tptp_fun_W1_2(xp) = sz10) | (tptp_fun_W1_2(xp) = xp))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 (((~aNaturalNumber0(xp)) | (~((~((xp = sz00) | (xp = sz10) | isPrime0(xp) | (~((tptp_fun_W1_2(xp) = xp) | (tptp_fun_W1_2(xp) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (~doDivides0(tptp_fun_W1_2(xp), xp)))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = xp) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp))))))))))) <=> ((~aNaturalNumber0(xp)) | (~((~(isPrime0(xp) | (xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W1_2(xp), xp)) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (tptp_fun_W1_2(xp) = sz10) | (tptp_fun_W1_2(xp) = xp))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | ((~aNaturalNumber0(xp)) | (~((~((xp = sz00) | (xp = sz10) | isPrime0(xp) | (~((tptp_fun_W1_2(xp) = xp) | (tptp_fun_W1_2(xp) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (~doDivides0(tptp_fun_W1_2(xp), xp)))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = xp) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | ((~aNaturalNumber0(xp)) | (~((~(isPrime0(xp) | (xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W1_2(xp), xp)) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (tptp_fun_W1_2(xp) = sz10) | (tptp_fun_W1_2(xp) = xp))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp))))))))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | ((~aNaturalNumber0(xp)) | (~((~((xp = sz00) | (xp = sz10) | isPrime0(xp) | (~((tptp_fun_W1_2(xp) = xp) | (tptp_fun_W1_2(xp) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (~doDivides0(tptp_fun_W1_2(xp), xp)))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = xp) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | (~aNaturalNumber0(xp)) | (~((~(isPrime0(xp) | (xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W1_2(xp), xp)) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (tptp_fun_W1_2(xp) = sz10) | (tptp_fun_W1_2(xp) = xp))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[75, 73])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | ((~aNaturalNumber0(xp)) | (~((~((xp = sz00) | (xp = sz10) | isPrime0(xp) | (~((tptp_fun_W1_2(xp) = xp) | (tptp_fun_W1_2(xp) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (~doDivides0(tptp_fun_W1_2(xp), xp)))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = xp) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(78,plain,
% 0.21/0.51 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~((W0 = sz00) | (W0 = sz10) | isPrime0(W0) | (~((tptp_fun_W1_2(W0) = W0) | (tptp_fun_W1_2(W0) = sz10) | (~aNaturalNumber0(tptp_fun_W1_2(W0))) | (~doDivides0(tptp_fun_W1_2(W0), W0)))))) | (~((~isPrime0(W0)) | (~((W0 = sz00) | (W0 = sz10) | (~![W1: $i] : ((W1 = W0) | (W1 = sz10) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, W0)))))))))))) | (~aNaturalNumber0(xp)) | (~((~(isPrime0(xp) | (xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W1_2(xp), xp)) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (tptp_fun_W1_2(xp) = sz10) | (tptp_fun_W1_2(xp) = xp))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp))))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.51 tff(79,plain,
% 0.21/0.51 (~((~(isPrime0(xp) | (xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W1_2(xp), xp)) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (tptp_fun_W1_2(xp) = sz10) | (tptp_fun_W1_2(xp) = xp))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[78, 56, 15])).
% 0.21/0.51 tff(80,plain,
% 0.21/0.51 (((~(isPrime0(xp) | (xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W1_2(xp), xp)) | (~aNaturalNumber0(tptp_fun_W1_2(xp))) | (tptp_fun_W1_2(xp) = sz10) | (tptp_fun_W1_2(xp) = xp))))) | (~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp))))))))) | ((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(81,plain,
% 0.21/0.51 ((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.21/0.51 tff(82,plain,
% 0.21/0.51 (isPrime0(xp) <=> isPrime0(xp)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(83,plain,
% 0.21/0.51 (isPrime0(xp)),
% 0.21/0.51 inference(and_elim,[status(thm)],[4])).
% 0.21/0.51 tff(84,plain,
% 0.21/0.51 (isPrime0(xp)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.51 tff(85,plain,
% 0.21/0.51 ((~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))))) | (~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp))))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(86,plain,
% 0.21/0.51 ((~((~isPrime0(xp)) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))))) | (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.51 tff(87,plain,
% 0.21/0.51 (~((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[86, 81])).
% 0.21/0.51 tff(88,plain,
% 0.21/0.51 (((xp = sz00) | (xp = sz10) | (~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp))))) | ![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(89,plain,
% 0.21/0.51 (![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.51 tff(90,plain,
% 0.21/0.51 (((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (~isPrime0(tptp_fun_W1_3(xp)))) | doDivides0(tptp_fun_W1_3(xp), xp)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(91,plain,
% 0.21/0.51 (doDivides0(tptp_fun_W1_3(xp), xp)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[90, 32])).
% 0.21/0.51 tff(92,plain,
% 0.21/0.51 (((~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))) | ((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = xp))) <=> ((~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))) | (~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = xp))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(93,plain,
% 0.21/0.51 (((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = xp) | (~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp))) <=> ((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = xp))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(94,plain,
% 0.21/0.51 (((~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))) | ((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = xp) | (~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)))) <=> ((~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))) | ((~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = xp)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.51 tff(95,plain,
% 0.21/0.51 (((~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))) | ((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = xp) | (~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)))) <=> ((~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))) | (~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = xp))),
% 0.21/0.51 inference(transitivity,[status(thm)],[94, 92])).
% 0.21/0.51 tff(96,plain,
% 0.21/0.51 ((~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))) | ((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = xp) | (~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(97,plain,
% 0.21/0.51 ((~![W1: $i] : ((W1 = sz10) | (W1 = xp) | (~aNaturalNumber0(W1)) | (~doDivides0(W1, xp)))) | (~aNaturalNumber0(tptp_fun_W1_3(xp))) | (~doDivides0(tptp_fun_W1_3(xp), xp)) | (tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = xp)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.51 tff(98,plain,
% 0.21/0.51 ((tptp_fun_W1_3(xp) = sz10) | (tptp_fun_W1_3(xp) = xp)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[97, 34, 91, 89])).
% 0.21/0.51 tff(99,plain,
% 0.21/0.51 (tptp_fun_W1_3(xp) = xp),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[98, 72])).
% 0.21/0.51 tff(100,plain,
% 0.21/0.51 (xp = tptp_fun_W1_3(xp)),
% 0.21/0.51 inference(symmetry,[status(thm)],[99])).
% 0.21/0.51 tff(101,plain,
% 0.21/0.51 (doDivides0(xp, xp) <=> doDivides0(tptp_fun_W1_3(xp), xp)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[100])).
% 0.21/0.51 tff(102,plain,
% 0.21/0.51 (doDivides0(tptp_fun_W1_3(xp), xp) <=> doDivides0(xp, xp)),
% 0.21/0.51 inference(symmetry,[status(thm)],[101])).
% 0.21/0.51 tff(103,plain,
% 0.21/0.51 (doDivides0(xp, xp)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[91, 102])).
% 0.21/0.51 tff(104,plain,
% 0.21/0.51 ((sdtpldt0(xp, xr) = xn) <=> (sdtpldt0(xp, xr) = xn)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(105,axiom,((aNaturalNumber0(xr) & (sdtpldt0(xp, xr) = xn)) & (xr = sdtmndt0(xn, xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1883')).
% 0.21/0.51 tff(106,plain,
% 0.21/0.51 (aNaturalNumber0(xr) & (sdtpldt0(xp, xr) = xn)),
% 0.21/0.51 inference(and_elim,[status(thm)],[105])).
% 0.21/0.51 tff(107,plain,
% 0.21/0.51 (sdtpldt0(xp, xr) = xn),
% 0.21/0.51 inference(and_elim,[status(thm)],[106])).
% 0.21/0.51 tff(108,plain,
% 0.21/0.51 (sdtpldt0(xp, xr) = xn),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[107, 104])).
% 0.21/0.51 tff(109,plain,
% 0.21/0.51 ((xr = sdtmndt0(xn, xp)) <=> (xr = sdtmndt0(xn, xp))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(110,plain,
% 0.21/0.51 (xr = sdtmndt0(xn, xp)),
% 0.21/0.51 inference(and_elim,[status(thm)],[105])).
% 0.21/0.51 tff(111,plain,
% 0.21/0.51 (xr = sdtmndt0(xn, xp)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.51 tff(112,plain,
% 0.21/0.51 (sdtmndt0(xn, xp) = xr),
% 0.21/0.51 inference(symmetry,[status(thm)],[111])).
% 0.21/0.51 tff(113,plain,
% 0.21/0.51 (sdtpldt0(xp, sdtmndt0(xn, xp)) = sdtpldt0(xp, xr)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[112])).
% 0.21/0.51 tff(114,plain,
% 0.21/0.51 (sdtpldt0(xp, sdtmndt0(xn, xp)) = xn),
% 0.21/0.51 inference(transitivity,[status(thm)],[113, 108])).
% 0.21/0.51 tff(115,plain,
% 0.21/0.51 (doDivides0(xp, sdtpldt0(xp, sdtmndt0(xn, xp))) <=> doDivides0(xp, xn)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[114])).
% 0.21/0.51 tff(116,plain,
% 0.21/0.51 (doDivides0(xp, xn) <=> doDivides0(xp, sdtpldt0(xp, sdtmndt0(xn, xp)))),
% 0.21/0.51 inference(symmetry,[status(thm)],[115])).
% 0.21/0.51 tff(117,plain,
% 0.21/0.51 ((~doDivides0(xp, xn)) <=> (~doDivides0(xp, sdtpldt0(xp, sdtmndt0(xn, xp))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[116])).
% 0.21/0.51 tff(118,plain,
% 0.21/0.51 ((~doDivides0(xp, xn)) <=> (~doDivides0(xp, xn))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(119,axiom,(~(((?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))) | doDivides0(xp, xn)) | ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0)))) | doDivides0(xp, xm))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.21/0.51 tff(120,plain,
% 0.21/0.51 (~((?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))) | doDivides0(xp, xn)) | ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))))),
% 0.21/0.51 inference(or_elim,[status(thm)],[119])).
% 0.21/0.51 tff(121,plain,
% 0.21/0.51 (~(?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))) | doDivides0(xp, xn))),
% 0.21/0.51 inference(or_elim,[status(thm)],[120])).
% 0.21/0.51 tff(122,plain,
% 0.21/0.51 (~doDivides0(xp, xn)),
% 0.21/0.51 inference(or_elim,[status(thm)],[121])).
% 0.21/0.51 tff(123,plain,
% 0.21/0.51 (~doDivides0(xp, xn)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.21/0.51 tff(124,plain,
% 0.21/0.51 (~doDivides0(xp, sdtpldt0(xp, sdtmndt0(xn, xp)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[123, 117])).
% 0.21/0.51 tff(125,plain,
% 0.21/0.51 (doDivides0(xp, sdtmndt0(xn, xp)) <=> doDivides0(xp, xr)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[112])).
% 0.21/0.51 tff(126,plain,
% 0.21/0.51 (doDivides0(xp, xr) <=> doDivides0(xp, sdtmndt0(xn, xp))),
% 0.21/0.51 inference(symmetry,[status(thm)],[125])).
% 0.21/0.51 tff(127,plain,
% 0.21/0.51 ((~doDivides0(xp, xm)) <=> (~doDivides0(xp, xm))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(128,plain,
% 0.21/0.51 (~doDivides0(xp, xm)),
% 0.21/0.51 inference(or_elim,[status(thm)],[119])).
% 0.21/0.51 tff(129,plain,
% 0.21/0.51 (~doDivides0(xp, xm)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.21/0.51 tff(130,plain,
% 0.21/0.51 (((~doDivides0(xp, xm)) | (~aNaturalNumber0(W0!13)) | (~(xm = sdtasdt0(xp, W0!13)))) | doDivides0(xp, xm)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(131,plain,
% 0.21/0.51 ((~doDivides0(xp, xm)) | (~aNaturalNumber0(W0!13)) | (~(xm = sdtasdt0(xp, W0!13)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.21/0.51 tff(132,plain,
% 0.21/0.51 (((aNaturalNumber0(W0!12) & (xr = sdtasdt0(xp, W0!12)) & doDivides0(xp, xr)) | (aNaturalNumber0(W0!13) & (xm = sdtasdt0(xp, W0!13)) & doDivides0(xp, xm))) <=> ((~((~aNaturalNumber0(W0!12)) | (~(xr = sdtasdt0(xp, W0!12))) | (~doDivides0(xp, xr)))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(W0!13)) | (~(xm = sdtasdt0(xp, W0!13))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(133,plain,
% 0.21/0.51 ((((aNaturalNumber0(W0!12) & (xr = sdtasdt0(xp, W0!12))) & doDivides0(xp, xr)) | ((aNaturalNumber0(W0!13) & (xm = sdtasdt0(xp, W0!13))) & doDivides0(xp, xm))) <=> ((aNaturalNumber0(W0!12) & (xr = sdtasdt0(xp, W0!12)) & doDivides0(xp, xr)) | (aNaturalNumber0(W0!13) & (xm = sdtasdt0(xp, W0!13)) & doDivides0(xp, xm)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(134,plain,
% 0.21/0.51 (((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))) <=> ((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(135,plain,
% 0.21/0.51 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) <=> (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(136,plain,
% 0.21/0.51 ((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) <=> (?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(137,plain,
% 0.21/0.51 (((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))) <=> ((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[136, 135])).
% 0.21/0.51 tff(138,plain,
% 0.21/0.51 (((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))) <=> ((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[137, 134])).
% 0.21/0.51 tff(139,axiom,((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2027')).
% 0.21/0.51 tff(140,plain,
% 0.21/0.51 ((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.51 tff(141,plain,
% 0.21/0.51 ((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[140, 138])).
% 0.21/0.51 tff(142,plain,
% 0.21/0.51 ((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.21/0.51 tff(143,plain,
% 0.21/0.51 ((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) & doDivides0(xp, xr)) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.21/0.51 Proof display could not be completed: monotonicity rule is not handled
% 0.21/0.52 % E exiting
%------------------------------------------------------------------------------