%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM492+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 05:21:10 AM UTC 2025
% Result : Theorem 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM492+3 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % 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 01:17:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(aNaturalNumber0_type, type, (
% 0.21/0.47 aNaturalNumber0: $i > $o)).
% 0.21/0.47 tff(sdtmndt0_type, type, (
% 0.21/0.47 sdtmndt0: ( $i * $i ) > $i)).
% 0.21/0.47 tff(sdtasdt0_type, type, (
% 0.21/0.47 sdtasdt0: ( $i * $i ) > $i)).
% 0.21/0.47 tff(xm_type, type, (
% 0.21/0.47 xm: $i)).
% 0.21/0.47 tff(xp_type, type, (
% 0.21/0.47 xp: $i)).
% 0.21/0.47 tff(xn_type, type, (
% 0.21/0.47 xn: $i)).
% 0.21/0.47 tff(xr_type, type, (
% 0.21/0.47 xr: $i)).
% 0.21/0.47 tff(sdtpldt0_type, type, (
% 0.21/0.47 sdtpldt0: ( $i * $i ) > $i)).
% 0.21/0.47 tff(doDivides0_type, type, (
% 0.21/0.47 doDivides0: ( $i * $i ) > $o)).
% 0.21/0.47 tff(tptp_fun_W0_11_type, type, (
% 0.21/0.47 tptp_fun_W0_11: $i)).
% 0.21/0.47 tff(isPrime0_type, type, (
% 0.21/0.47 isPrime0: $i > $o)).
% 0.21/0.47 tff(sz10_type, type, (
% 0.21/0.47 sz10: $i)).
% 0.21/0.47 tff(sz00_type, type, (
% 0.21/0.47 sz00: $i)).
% 0.21/0.47 tff(1,plain,
% 0.21/0.47 ((sdtasdt0(xr, xm) = sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) <=> (sdtasdt0(xr, xm) = sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(2,axiom,((sdtpldt0(sdtasdt0(xp, xm), sdtasdt0(xr, xm)) = sdtasdt0(xn, xm)) & (sdtasdt0(xr, xm) = sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1978')).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 (sdtasdt0(xr, xm) = sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.21/0.47 inference(and_elim,[status(thm)],[2])).
% 0.21/0.47 tff(4,plain,
% 0.21/0.47 (sdtasdt0(xr, xm) = sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 ((xr = sdtmndt0(xn, xp)) <=> (xr = sdtmndt0(xn, xp))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(6,axiom,((aNaturalNumber0(xr) & (sdtpldt0(xp, xr) = xn)) & (xr = sdtmndt0(xn, xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1883')).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (xr = sdtmndt0(xn, xp)),
% 0.21/0.47 inference(and_elim,[status(thm)],[6])).
% 0.21/0.47 tff(8,plain,
% 0.21/0.47 (xr = sdtmndt0(xn, xp)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[7, 5])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (sdtmndt0(xn, xp) = xr),
% 0.21/0.47 inference(symmetry,[status(thm)],[8])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 (sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xr, xm)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[9])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 (sdtasdt0(sdtmndt0(xn, xp), xm) = sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.21/0.47 inference(transitivity,[status(thm)],[10, 4])).
% 0.21/0.47 tff(12,plain,
% 0.21/0.47 (aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm)) <=> aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[11])).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (aNaturalNumber0(sdtmndt0(xn, xp)) <=> aNaturalNumber0(xr)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[9])).
% 0.21/0.47 tff(14,plain,
% 0.21/0.47 (aNaturalNumber0(xr) <=> aNaturalNumber0(sdtmndt0(xn, xp))),
% 0.21/0.47 inference(symmetry,[status(thm)],[13])).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (aNaturalNumber0(xr) <=> aNaturalNumber0(xr)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (aNaturalNumber0(xr) & (sdtpldt0(xp, xr) = xn)),
% 0.21/0.47 inference(and_elim,[status(thm)],[6])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 (aNaturalNumber0(xr)),
% 0.21/0.47 inference(and_elim,[status(thm)],[16])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 (aNaturalNumber0(xr)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 (aNaturalNumber0(sdtmndt0(xn, xp))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(21,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1837')).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 0.21/0.47 inference(and_elim,[status(thm)],[21])).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 (aNaturalNumber0(xm)),
% 0.21/0.47 inference(and_elim,[status(thm)],[22])).
% 0.21/0.47 tff(24,plain,
% 0.21/0.47 (aNaturalNumber0(xm)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.21/0.47 tff(25,plain,
% 0.21/0.47 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.47 tff(27,plain,
% 0.21/0.47 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.47 tff(29,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.47 tff(32,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.47 tff(35,plain,(
% 0.21/0.47 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[34])).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.21/0.47 tff(37,plain,
% 0.21/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.21/0.47 tff(38,plain,
% 0.21/0.47 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(39,plain,
% 0.21/0.47 ((aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp)))) <=> ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(40,plain,
% 0.21/0.47 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.47 tff(41,plain,
% 0.21/0.47 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[40, 38])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 ((~aNaturalNumber0(sdtmndt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[43, 37, 24])).
% 0.21/0.47 tff(45,plain,
% 0.21/0.47 (aNaturalNumber0(sdtasdt0(sdtmndt0(xn, xp), xm))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[44, 19])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[45, 12])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 ((sdtasdt0(xn, xm) = sdtpldt0(sdtasdt0(xp, xm), sdtasdt0(xr, xm))) <=> (sdtasdt0(xn, xm) = sdtpldt0(sdtasdt0(xp, xm), sdtasdt0(xr, xm)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(48,axiom,(sdtasdt0(xn, xm) = sdtpldt0(sdtasdt0(xp, xm), sdtasdt0(xr, xm))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1951')).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 (sdtasdt0(xn, xm) = sdtpldt0(sdtasdt0(xp, xm), sdtasdt0(xr, xm))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (sdtpldt0(sdtasdt0(xp, xm), sdtasdt0(xr, xm)) = sdtasdt0(xn, xm)),
% 0.21/0.47 inference(symmetry,[status(thm)],[49])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 (sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)) = sdtasdt0(xr, xm)),
% 0.21/0.47 inference(symmetry,[status(thm)],[4])).
% 0.21/0.47 tff(52,plain,
% 0.21/0.47 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xp, xm) = sdtasdt0(xp, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xp, xm) = sdtasdt0(xp, W0)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(53,axiom,((?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xp, xm) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtasdt0(xp, xm))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2001')).
% 0.21/0.47 tff(54,plain,
% 0.21/0.47 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xp, xm) = sdtasdt0(xp, W0)))),
% 0.21/0.47 inference(and_elim,[status(thm)],[53])).
% 0.21/0.47 tff(55,plain,
% 0.21/0.47 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xp, xm) = sdtasdt0(xp, W0)))),
% 0.21/0.47 inference(and_elim,[status(thm)],[54])).
% 0.21/0.47 tff(56,plain,
% 0.21/0.47 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xp, xm) = sdtasdt0(xp, W0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.21/0.47 tff(57,plain,(
% 0.21/0.47 aNaturalNumber0(W0!11) & (sdtasdt0(xp, xm) = sdtasdt0(xp, W0!11))),
% 0.21/0.47 inference(skolemize,[status(sab)],[56])).
% 0.21/0.47 tff(58,plain,
% 0.21/0.47 (sdtasdt0(xp, xm) = sdtasdt0(xp, W0!11)),
% 0.21/0.47 inference(and_elim,[status(thm)],[57])).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 (sdtasdt0(xp, W0!11) = sdtasdt0(xp, xm)),
% 0.21/0.47 inference(symmetry,[status(thm)],[58])).
% 0.21/0.47 tff(60,plain,
% 0.21/0.47 (sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) = sdtpldt0(sdtasdt0(xp, xm), sdtasdt0(xr, xm))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[59, 51])).
% 0.21/0.47 tff(61,plain,
% 0.21/0.47 (sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) = sdtasdt0(xn, xm)),
% 0.21/0.47 inference(transitivity,[status(thm)],[60, 50])).
% 0.21/0.47 tff(62,plain,
% 0.21/0.47 (doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) <=> doDivides0(xp, sdtasdt0(xn, xm))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.47 tff(63,plain,
% 0.21/0.47 (doDivides0(xp, sdtasdt0(xn, xm)) <=> doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))))),
% 0.21/0.47 inference(symmetry,[status(thm)],[62])).
% 0.21/0.47 tff(64,plain,
% 0.21/0.47 (doDivides0(xp, sdtasdt0(xn, xm)) <=> doDivides0(xp, sdtasdt0(xn, xm))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(65,axiom,((((((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtasdt0(xn, xm))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1860')).
% 0.21/0.47 tff(66,plain,
% 0.21/0.47 (doDivides0(xp, sdtasdt0(xn, xm))),
% 0.21/0.47 inference(and_elim,[status(thm)],[65])).
% 0.21/0.47 tff(67,plain,
% 0.21/0.47 (doDivides0(xp, sdtasdt0(xn, xm))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[66, 64])).
% 0.21/0.47 tff(68,plain,
% 0.21/0.47 (doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.21/0.47 tff(69,plain,
% 0.21/0.47 (aNaturalNumber0(W0!11)),
% 0.21/0.47 inference(and_elim,[status(thm)],[57])).
% 0.21/0.47 tff(70,plain,
% 0.21/0.47 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(71,plain,
% 0.21/0.47 (aNaturalNumber0(xp)),
% 0.21/0.47 inference(and_elim,[status(thm)],[21])).
% 0.21/0.47 tff(72,plain,
% 0.21/0.47 (aNaturalNumber0(xp)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.47 tff(73,plain,
% 0.21/0.47 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, W0!11)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, W0!11)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(74,plain,
% 0.21/0.47 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, W0!11)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(75,plain,
% 0.21/0.47 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, W0!11)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.47 tff(76,plain,
% 0.21/0.47 (aNaturalNumber0(sdtasdt0(xp, W0!11))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[75, 37, 72, 69])).
% 0.21/0.47 tff(77,plain,
% 0.21/0.47 (doDivides0(xp, sdtasdt0(xp, W0!11)) <=> doDivides0(xp, sdtasdt0(xp, xm))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[59])).
% 0.21/0.47 tff(78,plain,
% 0.21/0.47 (doDivides0(xp, sdtasdt0(xp, xm)) <=> doDivides0(xp, sdtasdt0(xp, W0!11))),
% 0.21/0.47 inference(symmetry,[status(thm)],[77])).
% 0.21/0.47 tff(79,plain,
% 0.21/0.47 (doDivides0(xp, sdtasdt0(xp, xm)) <=> doDivides0(xp, sdtasdt0(xp, xm))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(80,plain,
% 0.21/0.47 (doDivides0(xp, sdtasdt0(xp, xm))),
% 0.21/0.47 inference(and_elim,[status(thm)],[53])).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 (doDivides0(xp, sdtasdt0(xp, xm))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.47 tff(82,plain,
% 0.21/0.47 (doDivides0(xp, sdtasdt0(xp, W0!11))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.21/0.47 tff(83,plain,
% 0.21/0.48 (doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) <=> doDivides0(xp, sdtasdt0(xr, xm))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[51])).
% 0.21/0.48 tff(84,plain,
% 0.21/0.48 (doDivides0(xp, sdtasdt0(xr, xm)) <=> doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))),
% 0.21/0.48 inference(symmetry,[status(thm)],[83])).
% 0.21/0.48 tff(85,plain,
% 0.21/0.48 ((~doDivides0(xp, sdtasdt0(xr, xm))) <=> (~doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.48 tff(86,plain,
% 0.21/0.48 ((~doDivides0(xp, sdtasdt0(xr, xm))) <=> (~doDivides0(xp, sdtasdt0(xr, xm)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(87,axiom,(~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xr, xm) = sdtasdt0(xp, W0))) | doDivides0(xp, sdtasdt0(xr, xm)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 (~doDivides0(xp, sdtasdt0(xr, xm))),
% 0.21/0.48 inference(or_elim,[status(thm)],[87])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.48 (~doDivides0(xp, sdtasdt0(xr, xm))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[88, 86])).
% 0.21/0.48 tff(90,plain,
% 0.21/0.48 (~doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.21/0.48 tff(91,plain,
% 0.21/0.48 (^[W0: $i, W1: $i, W2: $i] : refl((doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2)))) <=> (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(92,plain,
% 0.21/0.48 (![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.48 tff(93,plain,
% 0.21/0.48 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), trans(monotonicity(rewrite((doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2))) <=> (~((~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2)))))), ((~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))) <=> (~(~((~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2)))))))), rewrite((~(~((~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2)))))) <=> ((~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))), ((~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))) <=> ((~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2)))))), ((doDivides0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2))))) <=> (doDivides0(W0, W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))))), rewrite((doDivides0(W0, W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))) <=> (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))), ((doDivides0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2))))) <=> (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 (![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 (![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(96,plain,
% 0.21/0.48 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), rewrite(((doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2))) => doDivides0(W0, W2)) <=> ((~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))) | doDivides0(W0, W2))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2))) => doDivides0(W0, W2))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))) | doDivides0(W0, W2))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))) | doDivides0(W0, W2))) <=> (doDivides0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2))) => doDivides0(W0, W2))) <=> (doDivides0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2))) => doDivides0(W0, W2))) <=> ![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.48 tff(98,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2))) => doDivides0(W0, W2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDivMin')).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 (![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 (![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.21/0.48 tff(101,plain,(
% 0.21/0.48 ![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(doDivides0(W0, W1) & doDivides0(W0, sdtpldt0(W1, W2)))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[100])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 (![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.21/0.48 tff(103,plain,
% 0.21/0.48 (![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[102, 92])).
% 0.21/0.48 tff(104,plain,
% 0.21/0.48 (((~![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))) | ((~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!11))) | doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!11))) | doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(105,plain,
% 0.21/0.48 ((doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!11))) | (~doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))))) <=> ((~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!11))) | doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(106,plain,
% 0.21/0.48 (((~![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))) | (doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!11))) | (~doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))) | ((~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!11))) | doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[105])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 (((~![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))) | (doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!11))) | (~doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!11))) | doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[106, 104])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 ((~![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))) | (doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!11))) | (~doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(109,plain,
% 0.21/0.48 ((~![W0: $i, W1: $i, W2: $i] : (doDivides0(W0, W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~doDivides0(W0, W1)) | (~doDivides0(W0, sdtpldt0(W1, W2))))) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xp, W0!11))) | doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.48 tff(110,plain,
% 0.21/0.48 ((~doDivides0(xp, sdtasdt0(xp, W0!11))) | doDivides0(xp, sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~doDivides0(xp, sdtpldt0(sdtasdt0(xp, W0!11), sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[109, 103, 72])).
% 0.21/0.48 tff(111,plain,
% 0.21/0.48 (~aNaturalNumber0(sdtmndt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[110, 90, 82, 76, 68])).
% 0.21/0.48 tff(112,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[111, 46])).
% 0.21/0.48 % SZS output end Proof
% 0.21/0.49 % E exiting
%------------------------------------------------------------------------------