%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM511+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:21:13 AM UTC 2025
% Result : Theorem 3.99s 4.18s
% Output : Proof 4.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM511+3 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:20:09 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.99/4.18 % SZS status Theorem
% 3.99/4.18 % SZS output start Proof
% 3.99/4.18 tff(sdtasdt0_type, type, (
% 3.99/4.18 sdtasdt0: ( $i * $i ) > $i)).
% 3.99/4.18 tff(tptp_fun_W0_11_type, type, (
% 3.99/4.18 tptp_fun_W0_11: $i)).
% 3.99/4.18 tff(xp_type, type, (
% 3.99/4.18 xp: $i)).
% 3.99/4.18 tff(xm_type, type, (
% 3.99/4.18 xm: $i)).
% 3.99/4.18 tff(sdtsldt0_type, type, (
% 3.99/4.18 sdtsldt0: ( $i * $i ) > $i)).
% 3.99/4.18 tff(xr_type, type, (
% 3.99/4.18 xr: $i)).
% 3.99/4.18 tff(xn_type, type, (
% 3.99/4.18 xn: $i)).
% 3.99/4.18 tff(tptp_fun_W0_13_type, type, (
% 3.99/4.18 tptp_fun_W0_13: $i)).
% 3.99/4.18 tff(aNaturalNumber0_type, type, (
% 3.99/4.18 aNaturalNumber0: $i > $o)).
% 3.99/4.18 tff(xk_type, type, (
% 3.99/4.18 xk: $i)).
% 3.99/4.18 tff(sdtpldt0_type, type, (
% 3.99/4.18 sdtpldt0: ( $i * $i ) > $i)).
% 3.99/4.18 tff(doDivides0_type, type, (
% 3.99/4.18 doDivides0: ( $i * $i ) > $o)).
% 3.99/4.18 tff(sz00_type, type, (
% 3.99/4.18 sz00: $i)).
% 3.99/4.18 tff(sz10_type, type, (
% 3.99/4.18 sz10: $i)).
% 3.99/4.18 tff(isPrime0_type, type, (
% 3.99/4.18 isPrime0: $i > $o)).
% 3.99/4.18 tff(sdtlseqdt0_type, type, (
% 3.99/4.18 sdtlseqdt0: ( $i * $i ) > $o)).
% 3.99/4.18 tff(1,plain,
% 3.99/4.18 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0)))),
% 3.99/4.18 inference(rewrite,[status(thm)],[])).
% 3.99/4.18 tff(2,axiom,((?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xr, W0) = xk)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0)))) & doDivides0(xr, sdtasdt0(xn, xm))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2362')).
% 3.99/4.18 tff(3,plain,
% 3.99/4.18 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xr, W0) = xk)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0)))),
% 3.99/4.18 inference(and_elim,[status(thm)],[2])).
% 3.99/4.18 tff(4,plain,
% 3.99/4.18 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0)))),
% 3.99/4.18 inference(and_elim,[status(thm)],[3])).
% 3.99/4.18 tff(5,plain,
% 3.99/4.18 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0)))),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[4, 1])).
% 3.99/4.18 tff(6,plain,(
% 3.99/4.18 aNaturalNumber0(W0!13) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0!13))),
% 3.99/4.18 inference(skolemize,[status(sab)],[5])).
% 3.99/4.18 tff(7,plain,
% 3.99/4.18 (aNaturalNumber0(W0!13)),
% 3.99/4.18 inference(and_elim,[status(thm)],[6])).
% 3.99/4.18 tff(8,plain,
% 3.99/4.18 (aNaturalNumber0(xr) <=> aNaturalNumber0(xr)),
% 3.99/4.18 inference(rewrite,[status(thm)],[])).
% 3.99/4.18 tff(9,axiom,((((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))) & isPrime0(xr)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2342')).
% 3.99/4.18 tff(10,plain,
% 3.99/4.18 (((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))),
% 3.99/4.18 inference(and_elim,[status(thm)],[9])).
% 3.99/4.18 tff(11,plain,
% 3.99/4.18 ((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))),
% 3.99/4.18 inference(and_elim,[status(thm)],[10])).
% 3.99/4.18 tff(12,plain,
% 3.99/4.18 (((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))),
% 3.99/4.18 inference(and_elim,[status(thm)],[11])).
% 3.99/4.18 tff(13,plain,
% 3.99/4.18 ((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)),
% 3.99/4.18 inference(and_elim,[status(thm)],[12])).
% 3.99/4.18 tff(14,plain,
% 3.99/4.18 (aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 3.99/4.18 inference(and_elim,[status(thm)],[13])).
% 3.99/4.18 tff(15,plain,
% 3.99/4.18 (aNaturalNumber0(xr)),
% 3.99/4.18 inference(and_elim,[status(thm)],[14])).
% 3.99/4.18 tff(16,plain,
% 3.99/4.18 (aNaturalNumber0(xr)),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[15, 8])).
% 3.99/4.18 tff(17,plain,
% 3.99/4.18 (^[W0: $i, W1: $i] : refl(((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 3.99/4.18 inference(bind,[status(th)],[])).
% 3.99/4.18 tff(18,plain,
% 3.99/4.18 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.18 inference(quant_intro,[status(thm)],[17])).
% 3.99/4.18 tff(19,plain,
% 3.99/4.18 (^[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(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 3.99/4.18 inference(bind,[status(th)],[])).
% 3.99/4.18 tff(20,plain,
% 3.99/4.18 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.18 inference(quant_intro,[status(thm)],[19])).
% 3.99/4.18 tff(21,plain,
% 3.99/4.18 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 3.99/4.18 inference(rewrite,[status(thm)],[])).
% 3.99/4.18 tff(22,plain,
% 3.99/4.18 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))),
% 3.99/4.18 inference(bind,[status(th)],[])).
% 3.99/4.18 tff(23,plain,
% 3.99/4.18 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 3.99/4.18 inference(quant_intro,[status(thm)],[22])).
% 3.99/4.18 tff(24,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulComm')).
% 3.99/4.18 tff(25,plain,
% 3.99/4.18 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[24, 23])).
% 3.99/4.18 tff(26,plain,
% 3.99/4.18 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[25, 21])).
% 3.99/4.18 tff(27,plain,(
% 3.99/4.18 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 3.99/4.18 inference(skolemize,[status(sab)],[26])).
% 3.99/4.18 tff(28,plain,
% 3.99/4.18 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[27, 20])).
% 3.99/4.18 tff(29,plain,
% 3.99/4.18 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[28, 18])).
% 3.99/4.18 tff(30,plain,
% 3.99/4.18 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)))),
% 3.99/4.18 inference(rewrite,[status(thm)],[])).
% 3.99/4.18 tff(31,plain,
% 3.99/4.18 (((sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13))) <=> ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)))),
% 3.99/4.18 inference(rewrite,[status(thm)],[])).
% 3.99/4.18 tff(32,plain,
% 3.99/4.18 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13))))),
% 3.99/4.18 inference(monotonicity,[status(thm)],[31])).
% 3.99/4.18 tff(33,plain,
% 3.99/4.18 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)))),
% 3.99/4.18 inference(transitivity,[status(thm)],[32, 30])).
% 3.99/4.18 tff(34,plain,
% 3.99/4.18 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)))),
% 3.99/4.18 inference(quant_inst,[status(thm)],[])).
% 3.99/4.18 tff(35,plain,
% 3.99/4.18 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13))),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[34, 33])).
% 3.99/4.18 tff(36,plain,
% 3.99/4.18 (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)),
% 3.99/4.18 inference(unit_resolution,[status(thm)],[35, 29, 16, 7])).
% 3.99/4.18 tff(37,plain,
% 3.99/4.18 (sdtasdt0(xr, W0!13) = sdtasdt0(W0!13, xr)),
% 3.99/4.18 inference(symmetry,[status(thm)],[36])).
% 3.99/4.18 tff(38,plain,
% 3.99/4.18 (sdtasdt0(xn, xm) = sdtasdt0(xr, W0!13)),
% 3.99/4.18 inference(and_elim,[status(thm)],[6])).
% 3.99/4.18 tff(39,plain,
% 3.99/4.18 ((sdtasdt0(xn, xm) = sdtasdt0(xp, xk)) <=> (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 3.99/4.18 inference(rewrite,[status(thm)],[])).
% 3.99/4.18 tff(40,axiom,((aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))) & (xk = sdtsldt0(sdtasdt0(xn, xm), xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2306')).
% 3.99/4.18 tff(41,plain,
% 3.99/4.18 (aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 3.99/4.18 inference(and_elim,[status(thm)],[40])).
% 3.99/4.18 tff(42,plain,
% 3.99/4.18 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 3.99/4.18 inference(and_elim,[status(thm)],[41])).
% 3.99/4.18 tff(43,plain,
% 3.99/4.18 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[42, 39])).
% 3.99/4.18 tff(44,plain,
% 3.99/4.18 (sdtasdt0(xp, xk) = sdtasdt0(xn, xm)),
% 3.99/4.18 inference(symmetry,[status(thm)],[43])).
% 3.99/4.18 tff(45,plain,
% 3.99/4.18 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 3.99/4.18 inference(rewrite,[status(thm)],[])).
% 3.99/4.18 tff(46,plain,
% 3.99/4.18 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 3.99/4.18 inference(and_elim,[status(thm)],[14])).
% 3.99/4.18 tff(47,plain,
% 3.99/4.18 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[46, 45])).
% 3.99/4.18 tff(48,plain,(
% 3.99/4.18 aNaturalNumber0(W0!11) & (xk = sdtasdt0(xr, W0!11))),
% 3.99/4.18 inference(skolemize,[status(sab)],[47])).
% 3.99/4.18 tff(49,plain,
% 3.99/4.18 (xk = sdtasdt0(xr, W0!11)),
% 3.99/4.18 inference(and_elim,[status(thm)],[48])).
% 3.99/4.18 tff(50,plain,
% 3.99/4.18 (sdtasdt0(xr, W0!11) = xk),
% 3.99/4.18 inference(symmetry,[status(thm)],[49])).
% 3.99/4.18 tff(51,plain,
% 3.99/4.18 (aNaturalNumber0(W0!11)),
% 3.99/4.18 inference(and_elim,[status(thm)],[48])).
% 3.99/4.18 tff(52,plain,
% 3.99/4.18 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)))),
% 3.99/4.18 inference(rewrite,[status(thm)],[])).
% 3.99/4.18 tff(53,plain,
% 3.99/4.18 (((sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11))) <=> ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)))),
% 3.99/4.18 inference(rewrite,[status(thm)],[])).
% 3.99/4.18 tff(54,plain,
% 3.99/4.18 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11))))),
% 3.99/4.18 inference(monotonicity,[status(thm)],[53])).
% 3.99/4.18 tff(55,plain,
% 3.99/4.18 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)))),
% 3.99/4.18 inference(transitivity,[status(thm)],[54, 52])).
% 3.99/4.18 tff(56,plain,
% 3.99/4.18 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)))),
% 3.99/4.18 inference(quant_inst,[status(thm)],[])).
% 3.99/4.18 tff(57,plain,
% 3.99/4.18 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11))),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[56, 55])).
% 3.99/4.18 tff(58,plain,
% 3.99/4.18 (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)),
% 3.99/4.18 inference(unit_resolution,[status(thm)],[57, 29, 16, 51])).
% 3.99/4.18 tff(59,plain,
% 3.99/4.18 (sdtasdt0(W0!11, xr) = xk),
% 3.99/4.18 inference(transitivity,[status(thm)],[58, 50])).
% 3.99/4.18 tff(60,plain,
% 3.99/4.18 (sdtasdt0(xp, sdtasdt0(W0!11, xr)) = sdtasdt0(xp, xk)),
% 3.99/4.18 inference(monotonicity,[status(thm)],[59])).
% 3.99/4.18 tff(61,plain,
% 3.99/4.18 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 3.99/4.18 inference(rewrite,[status(thm)],[])).
% 3.99/4.18 tff(62,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1837')).
% 3.99/4.18 tff(63,plain,
% 3.99/4.18 (aNaturalNumber0(xp)),
% 3.99/4.18 inference(and_elim,[status(thm)],[62])).
% 3.99/4.18 tff(64,plain,
% 3.99/4.18 (aNaturalNumber0(xp)),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[63, 61])).
% 3.99/4.18 tff(65,plain,
% 3.99/4.18 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 3.99/4.18 inference(bind,[status(th)],[])).
% 3.99/4.18 tff(66,plain,
% 3.99/4.18 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.18 inference(quant_intro,[status(thm)],[65])).
% 3.99/4.18 tff(67,plain,
% 3.99/4.18 (^[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))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 3.99/4.18 inference(bind,[status(th)],[])).
% 3.99/4.18 tff(68,plain,
% 3.99/4.18 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.18 inference(quant_intro,[status(thm)],[67])).
% 3.99/4.18 tff(69,plain,
% 3.99/4.18 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 3.99/4.18 inference(rewrite,[status(thm)],[])).
% 3.99/4.18 tff(70,plain,
% 3.99/4.18 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))))),
% 3.99/4.18 inference(bind,[status(th)],[])).
% 3.99/4.18 tff(71,plain,
% 3.99/4.18 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 3.99/4.18 inference(quant_intro,[status(thm)],[70])).
% 3.99/4.18 tff(72,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulAsso')).
% 3.99/4.18 tff(73,plain,
% 3.99/4.18 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 3.99/4.18 inference(modus_ponens,[status(thm)],[72, 71])).
% 3.99/4.18 tff(74,plain,
% 3.99/4.18 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[73, 69])).
% 3.99/4.19 tff(75,plain,(
% 3.99/4.19 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 3.99/4.19 inference(skolemize,[status(sab)],[74])).
% 3.99/4.19 tff(76,plain,
% 3.99/4.19 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[75, 68])).
% 3.99/4.19 tff(77,plain,
% 3.99/4.19 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[76, 66])).
% 3.99/4.19 tff(78,plain,
% 3.99/4.19 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(79,plain,
% 3.99/4.19 (((sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(80,plain,
% 3.99/4.19 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr)))))),
% 3.99/4.19 inference(monotonicity,[status(thm)],[79])).
% 3.99/4.19 tff(81,plain,
% 3.99/4.19 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))))),
% 3.99/4.19 inference(transitivity,[status(thm)],[80, 78])).
% 3.99/4.19 tff(82,plain,
% 3.99/4.19 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))),
% 3.99/4.19 inference(quant_inst,[status(thm)],[])).
% 3.99/4.19 tff(83,plain,
% 3.99/4.19 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr)))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[82, 81])).
% 3.99/4.19 tff(84,plain,
% 3.99/4.19 (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))),
% 3.99/4.19 inference(unit_resolution,[status(thm)],[83, 77, 64, 16, 51])).
% 3.99/4.19 tff(85,plain,
% 3.99/4.19 (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)),
% 3.99/4.19 inference(transitivity,[status(thm)],[84, 60, 44, 38, 37])).
% 3.99/4.19 tff(86,plain,
% 3.99/4.19 (((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr))) | (~(sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))),
% 3.99/4.19 inference(tautology,[status(thm)],[])).
% 3.99/4.19 tff(87,plain,
% 3.99/4.19 ((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr))),
% 3.99/4.19 inference(unit_resolution,[status(thm)],[86, 85])).
% 3.99/4.19 tff(88,plain,
% 3.99/4.19 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 3.99/4.19 inference(bind,[status(th)],[])).
% 3.99/4.19 tff(89,plain,
% 3.99/4.19 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.19 inference(quant_intro,[status(thm)],[88])).
% 3.99/4.19 tff(90,plain,
% 3.99/4.19 (^[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)))))),
% 3.99/4.19 inference(bind,[status(th)],[])).
% 3.99/4.19 tff(91,plain,
% 3.99/4.19 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.19 inference(quant_intro,[status(thm)],[90])).
% 3.99/4.19 tff(92,plain,
% 3.99/4.19 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(93,plain,
% 3.99/4.19 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 3.99/4.19 inference(bind,[status(th)],[])).
% 3.99/4.19 tff(94,plain,
% 3.99/4.19 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 3.99/4.19 inference(quant_intro,[status(thm)],[93])).
% 3.99/4.19 tff(95,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB_02')).
% 3.99/4.19 tff(96,plain,
% 3.99/4.19 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[95, 94])).
% 3.99/4.19 tff(97,plain,
% 3.99/4.19 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[96, 92])).
% 3.99/4.19 tff(98,plain,(
% 3.99/4.19 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 3.99/4.19 inference(skolemize,[status(sab)],[97])).
% 3.99/4.19 tff(99,plain,
% 3.99/4.19 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[98, 91])).
% 3.99/4.19 tff(100,plain,
% 3.99/4.19 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[99, 89])).
% 3.99/4.19 tff(101,plain,
% 3.99/4.19 (((~![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)))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(102,plain,
% 3.99/4.19 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, W0!11)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))),
% 3.99/4.19 inference(quant_inst,[status(thm)],[])).
% 3.99/4.19 tff(103,plain,
% 3.99/4.19 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, W0!11)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[102, 101])).
% 3.99/4.19 tff(104,plain,
% 3.99/4.19 (aNaturalNumber0(sdtasdt0(xp, W0!11))),
% 3.99/4.19 inference(unit_resolution,[status(thm)],[103, 100, 64, 51])).
% 3.99/4.19 tff(105,plain,
% 3.99/4.19 ((~(xr = sz00)) <=> (~(xr = sz00))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(106,plain,
% 3.99/4.19 (~(xr = sz00)),
% 3.99/4.19 inference(and_elim,[status(thm)],[12])).
% 3.99/4.19 tff(107,plain,
% 3.99/4.19 (~(xr = sz00)),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[106, 105])).
% 3.99/4.19 tff(108,plain,
% 3.99/4.19 (^[W0: $i] : refl(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 3.99/4.19 inference(bind,[status(th)],[])).
% 3.99/4.19 tff(109,plain,
% 3.99/4.19 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 3.99/4.19 inference(quant_intro,[status(thm)],[108])).
% 3.99/4.19 tff(110,plain,
% 3.99/4.19 (^[W0: $i] : rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 3.99/4.19 inference(bind,[status(th)],[])).
% 3.99/4.19 tff(111,plain,
% 3.99/4.19 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 3.99/4.19 inference(quant_intro,[status(thm)],[110])).
% 3.99/4.19 tff(112,plain,
% 3.99/4.19 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 3.99/4.19 inference(transitivity,[status(thm)],[111, 109])).
% 3.99/4.19 tff(113,plain,
% 3.99/4.19 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), rewrite((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) <=> (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), rewrite(((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), (![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))))),
% 3.99/4.19 inference(bind,[status(th)],[])).
% 3.99/4.19 tff(114,plain,
% 3.99/4.19 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 3.99/4.19 inference(quant_intro,[status(thm)],[113])).
% 3.99/4.19 tff(115,plain,
% 3.99/4.19 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(116,plain,
% 3.99/4.19 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))), rewrite((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2)))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))))), rewrite(((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), (![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), rewrite(((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> (aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))), rewrite((aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))),
% 3.99/4.19 inference(bind,[status(th)],[])).
% 3.99/4.19 tff(117,plain,
% 3.99/4.19 (![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 3.99/4.19 inference(quant_intro,[status(thm)],[116])).
% 3.99/4.19 tff(118,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulCanc')).
% 3.99/4.19 tff(119,plain,
% 3.99/4.19 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[118, 117])).
% 3.99/4.19 tff(120,plain,
% 3.99/4.19 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[119, 115])).
% 3.99/4.19 tff(121,plain,(
% 3.99/4.19 ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 3.99/4.19 inference(skolemize,[status(sab)],[120])).
% 3.99/4.19 tff(122,plain,
% 3.99/4.19 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[121, 114])).
% 3.99/4.19 tff(123,plain,
% 3.99/4.19 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[122, 112])).
% 3.99/4.19 tff(124,plain,
% 3.99/4.19 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(125,plain,
% 3.99/4.19 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(126,plain,
% 3.99/4.19 (^[W1: $i, W2: $i] : rewrite(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 3.99/4.19 inference(bind,[status(th)],[])).
% 3.99/4.19 tff(127,plain,
% 3.99/4.19 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 3.99/4.19 inference(quant_intro,[status(thm)],[126])).
% 3.99/4.19 tff(128,plain,
% 3.99/4.19 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1)))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 3.99/4.19 inference(monotonicity,[status(thm)],[127])).
% 3.99/4.19 tff(129,plain,
% 3.99/4.19 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1)))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 3.99/4.19 inference(transitivity,[status(thm)],[128, 125])).
% 3.99/4.19 tff(130,plain,
% 3.99/4.19 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))))),
% 3.99/4.19 inference(monotonicity,[status(thm)],[129])).
% 3.99/4.19 tff(131,plain,
% 3.99/4.19 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 3.99/4.19 inference(transitivity,[status(thm)],[130, 124])).
% 3.99/4.19 tff(132,plain,
% 3.99/4.19 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))),
% 3.99/4.19 inference(quant_inst,[status(thm)],[])).
% 3.99/4.19 tff(133,plain,
% 3.99/4.19 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[132, 131])).
% 3.99/4.19 tff(134,plain,
% 3.99/4.19 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 3.99/4.19 inference(unit_resolution,[status(thm)],[133, 123, 16, 107])).
% 3.99/4.19 tff(135,plain,
% 3.99/4.19 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(136,plain,
% 3.99/4.19 (((sdtasdt0(xp, W0!11) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr))))) <=> ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(137,plain,
% 3.99/4.19 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(xp, W0!11) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr))))))),
% 3.99/4.19 inference(monotonicity,[status(thm)],[136])).
% 3.99/4.19 tff(138,plain,
% 3.99/4.19 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(xp, W0!11) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))),
% 3.99/4.19 inference(transitivity,[status(thm)],[137, 135])).
% 3.99/4.19 tff(139,plain,
% 3.99/4.19 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(xp, W0!11) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))),
% 3.99/4.19 inference(quant_inst,[status(thm)],[])).
% 3.99/4.19 tff(140,plain,
% 3.99/4.19 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr))))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[139, 138])).
% 3.99/4.19 tff(141,plain,
% 3.99/4.19 (sdtasdt0(xp, W0!11) = W0!13),
% 3.99/4.19 inference(unit_resolution,[status(thm)],[140, 7, 134, 104, 87])).
% 3.99/4.19 tff(142,plain,
% 3.99/4.19 (W0!13 = sdtasdt0(xp, W0!11)),
% 3.99/4.19 inference(symmetry,[status(thm)],[141])).
% 3.99/4.19 tff(143,plain,
% 3.99/4.19 ((xn = sdtasdt0(xr, sdtsldt0(xn, xr))) <=> (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(144,axiom,(((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))) & sdtlseqdt0(sdtsldt0(xn, xr), xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2504')).
% 3.99/4.19 tff(145,plain,
% 3.99/4.19 ((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))),
% 3.99/4.19 inference(and_elim,[status(thm)],[144])).
% 3.99/4.19 tff(146,plain,
% 3.99/4.19 (((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 3.99/4.19 inference(and_elim,[status(thm)],[145])).
% 3.99/4.19 tff(147,plain,
% 3.99/4.19 (xn = sdtasdt0(xr, sdtsldt0(xn, xr))),
% 3.99/4.19 inference(and_elim,[status(thm)],[146])).
% 3.99/4.19 tff(148,plain,
% 3.99/4.19 (xn = sdtasdt0(xr, sdtsldt0(xn, xr))),
% 3.99/4.19 inference(modus_ponens,[status(thm)],[147, 143])).
% 3.99/4.19 tff(149,plain,
% 3.99/4.19 (sdtasdt0(xr, sdtsldt0(xn, xr)) = xn),
% 3.99/4.19 inference(symmetry,[status(thm)],[148])).
% 3.99/4.19 tff(150,plain,
% 3.99/4.19 (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xn, xm)),
% 3.99/4.19 inference(monotonicity,[status(thm)],[149])).
% 3.99/4.19 tff(151,plain,
% 3.99/4.19 (aNaturalNumber0(sdtsldt0(xn, xr)) <=> aNaturalNumber0(sdtsldt0(xn, xr))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(152,plain,
% 3.99/4.19 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) <=> (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn)))),
% 3.99/4.19 inference(rewrite,[status(thm)],[])).
% 3.99/4.19 tff(153,plain,
% 3.99/4.19 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))),
% 3.99/4.20 inference(and_elim,[status(thm)],[146])).
% 3.99/4.20 tff(154,plain,
% 3.99/4.20 (~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))),
% 3.99/4.20 inference(and_elim,[status(thm)],[153])).
% 3.99/4.20 tff(155,plain,
% 3.99/4.20 (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn))),
% 3.99/4.20 inference(modus_ponens,[status(thm)],[154, 152])).
% 3.99/4.20 tff(156,plain,
% 3.99/4.20 (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 3.99/4.20 inference(or_elim,[status(thm)],[155])).
% 3.99/4.20 tff(157,plain,
% 3.99/4.20 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 3.99/4.20 inference(and_elim,[status(thm)],[156])).
% 3.99/4.20 tff(158,plain,
% 3.99/4.20 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 3.99/4.20 inference(modus_ponens,[status(thm)],[157, 151])).
% 3.99/4.20 tff(159,plain,
% 3.99/4.20 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 3.99/4.20 inference(rewrite,[status(thm)],[])).
% 3.99/4.20 tff(160,plain,
% 3.99/4.20 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 3.99/4.20 inference(and_elim,[status(thm)],[62])).
% 3.99/4.20 tff(161,plain,
% 3.99/4.20 (aNaturalNumber0(xm)),
% 3.99/4.20 inference(and_elim,[status(thm)],[160])).
% 3.99/4.20 tff(162,plain,
% 3.99/4.20 (aNaturalNumber0(xm)),
% 3.99/4.20 inference(modus_ponens,[status(thm)],[161, 159])).
% 3.99/4.20 tff(163,plain,
% 3.99/4.20 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))))),
% 3.99/4.20 inference(rewrite,[status(thm)],[])).
% 3.99/4.20 tff(164,plain,
% 3.99/4.20 (((sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~aNaturalNumber0(xr))) <=> ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))))),
% 3.99/4.20 inference(rewrite,[status(thm)],[])).
% 3.99/4.20 tff(165,plain,
% 3.99/4.20 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)))))),
% 3.99/4.20 inference(monotonicity,[status(thm)],[164])).
% 3.99/4.20 tff(166,plain,
% 3.99/4.20 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))))),
% 3.99/4.20 inference(transitivity,[status(thm)],[165, 163])).
% 3.99/4.20 tff(167,plain,
% 3.99/4.20 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~aNaturalNumber0(xr)))),
% 3.99/4.20 inference(quant_inst,[status(thm)],[])).
% 3.99/4.20 tff(168,plain,
% 3.99/4.20 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 3.99/4.20 inference(modus_ponens,[status(thm)],[167, 166])).
% 3.99/4.20 tff(169,plain,
% 3.99/4.20 (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))),
% 3.99/4.20 inference(unit_resolution,[status(thm)],[168, 77, 162, 16, 158])).
% 3.99/4.20 tff(170,plain,
% 3.99/4.20 (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm)),
% 3.99/4.20 inference(symmetry,[status(thm)],[169])).
% 3.99/4.20 tff(171,plain,
% 3.99/4.20 (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)),
% 3.99/4.20 inference(transitivity,[status(thm)],[170, 150, 38])).
% 3.99/4.20 tff(172,plain,
% 3.99/4.20 (((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr))) | (~(sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)))),
% 3.99/4.20 inference(tautology,[status(thm)],[])).
% 3.99/4.20 tff(173,plain,
% 3.99/4.20 ((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr))),
% 3.99/4.20 inference(unit_resolution,[status(thm)],[172, 171])).
% 3.99/4.20 tff(174,plain,
% 3.99/4.20 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 3.99/4.20 inference(rewrite,[status(thm)],[])).
% 3.99/4.20 tff(175,plain,
% 3.99/4.20 ((aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr)))) <=> ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 3.99/4.20 inference(rewrite,[status(thm)],[])).
% 3.99/4.20 tff(176,plain,
% 3.99/4.20 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))))),
% 3.99/4.20 inference(monotonicity,[status(thm)],[175])).
% 3.99/4.20 tff(177,plain,
% 3.99/4.20 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 3.99/4.20 inference(transitivity,[status(thm)],[176, 174])).
% 3.99/4.20 tff(178,plain,
% 3.99/4.20 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))),
% 3.99/4.20 inference(quant_inst,[status(thm)],[])).
% 3.99/4.20 tff(179,plain,
% 3.99/4.20 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))),
% 3.99/4.20 inference(modus_ponens,[status(thm)],[178, 177])).
% 3.99/4.20 tff(180,plain,
% 3.99/4.20 (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))),
% 3.99/4.20 inference(unit_resolution,[status(thm)],[179, 100, 162, 158])).
% 3.99/4.20 tff(181,plain,
% 3.99/4.20 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))),
% 3.99/4.20 inference(rewrite,[status(thm)],[])).
% 3.99/4.20 tff(182,plain,
% 3.99/4.20 (((sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr))))) <=> ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))),
% 3.99/4.20 inference(rewrite,[status(thm)],[])).
% 3.99/4.20 tff(183,plain,
% 3.99/4.20 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr))))))),
% 3.99/4.20 inference(monotonicity,[status(thm)],[182])).
% 3.99/4.20 tff(184,plain,
% 3.99/4.20 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))),
% 3.99/4.20 inference(transitivity,[status(thm)],[183, 181])).
% 3.99/4.20 tff(185,plain,
% 3.99/4.20 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))),
% 3.99/4.20 inference(quant_inst,[status(thm)],[])).
% 3.99/4.20 tff(186,plain,
% 3.99/4.20 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr))))),
% 3.99/4.20 inference(modus_ponens,[status(thm)],[185, 184])).
% 3.99/4.20 tff(187,plain,
% 3.99/4.20 (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13),
% 3.99/4.20 inference(unit_resolution,[status(thm)],[186, 7, 180, 134, 173])).
% 3.99/4.20 tff(188,plain,
% 3.99/4.20 (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11)),
% 3.99/4.20 inference(transitivity,[status(thm)],[187, 142])).
% 3.99/4.20 tff(189,plain,
% 3.99/4.20 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))))),
% 3.99/4.20 inference(bind,[status(th)],[])).
% 3.99/4.20 tff(190,plain,
% 3.99/4.20 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 3.99/4.20 inference(quant_intro,[status(thm)],[189])).
% 3.99/4.20 tff(191,plain,
% 3.99/4.20 (^[W0: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))) <=> (~((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))))), ((~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> (~(~((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))))))), rewrite((~(~((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))))) <=> ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))), ((~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))))),
% 3.99/4.20 inference(bind,[status(th)],[])).
% 3.99/4.20 tff(192,plain,
% 3.99/4.20 (![W0: $i] : (~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 3.99/4.20 inference(quant_intro,[status(thm)],[191])).
% 3.99/4.20 tff(193,plain,
% 3.99/4.20 ((~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 3.99/4.20 inference(rewrite,[status(thm)],[])).
% 3.99/4.20 tff(194,plain,
% 3.99/4.20 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))) | doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm))))) <=> (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))) | (~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))))))),
% 3.99/4.20 inference(rewrite,[status(thm)],[])).
% 3.99/4.20 tff(195,axiom,(~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))) | doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 3.99/4.20 tff(196,plain,
% 3.99/4.20 (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))) | (~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))))),
% 3.99/4.20 inference(modus_ponens,[status(thm)],[195, 194])).
% 3.99/4.20 tff(197,plain,
% 3.99/4.20 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 3.99/4.20 inference(or_elim,[status(thm)],[196])).
% 3.99/4.20 tff(198,plain,
% 4.09/4.23 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 4.09/4.23 inference(modus_ponens,[status(thm)],[197, 193])).
% 4.09/4.23 tff(199,plain,
% 4.09/4.23 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 4.09/4.23 inference(modus_ponens,[status(thm)],[198, 193])).
% 4.09/4.23 tff(200,plain,
% 4.09/4.23 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 4.09/4.23 inference(modus_ponens,[status(thm)],[199, 193])).
% 4.09/4.23 tff(201,plain,
% 4.09/4.23 (^[W0: $i] : refl($oeq((~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))), (~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))))),
% 4.09/4.23 inference(bind,[status(th)],[])).
% 4.09/4.23 tff(202,plain,(
% 4.09/4.23 ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 4.09/4.23 inference(nnf-neg,[status(sab)],[200, 201])).
% 4.09/4.23 tff(203,plain,
% 4.09/4.23 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 4.09/4.23 inference(modus_ponens,[status(thm)],[202, 192])).
% 4.09/4.23 tff(204,plain,
% 4.09/4.23 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 4.09/4.23 inference(modus_ponens,[status(thm)],[203, 190])).
% 4.09/4.23 tff(205,plain,
% 4.09/4.23 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))) | ((~aNaturalNumber0(W0!11)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))) | (~aNaturalNumber0(W0!11)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11))))),
% 4.09/4.23 inference(rewrite,[status(thm)],[])).
% 4.09/4.23 tff(206,plain,
% 4.09/4.23 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))) | ((~aNaturalNumber0(W0!11)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11))))),
% 4.09/4.23 inference(quant_inst,[status(thm)],[])).
% 4.09/4.23 tff(207,plain,
% 4.09/4.23 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))) | (~aNaturalNumber0(W0!11)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11)))),
% 4.09/4.23 inference(modus_ponens,[status(thm)],[206, 205])).
% 4.09/4.23 tff(208,plain,
% 4.09/4.23 (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11))),
% 4.09/4.23 inference(unit_resolution,[status(thm)],[207, 51, 204])).
% 4.09/4.23 tff(209,plain,
% 4.09/4.23 ($false),
% 4.09/4.23 inference(unit_resolution,[status(thm)],[208, 188])).
% 4.09/4.23 % SZS output end Proof
% 4.09/4.24 % E exiting
%------------------------------------------------------------------------------