Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : NUM473+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n007.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 05:21:06 AM UTC 2025

% Result   : Theorem 0.39s 0.58s
% Output   : Proof 0.39s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM473+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n007.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 01:14:50 EDT 2025
% 0.12/0.34  % CPUTime    : 
% 0.39/0.58  % SZS status Theorem
% 0.39/0.58  % SZS output start Proof
% 0.39/0.58  tff(aNaturalNumber0_type, type, (
% 0.39/0.58     aNaturalNumber0: $i > $o)).
% 0.39/0.58  tff(sdtasdt0_type, type, (
% 0.39/0.58     sdtasdt0: ( $i * $i ) > $i)).
% 0.39/0.58  tff(tptp_fun_W0_3_type, type, (
% 0.39/0.58     tptp_fun_W0_3: $i)).
% 0.39/0.58  tff(xl_type, type, (
% 0.39/0.58     xl: $i)).
% 0.39/0.58  tff(sdtpldt0_type, type, (
% 0.39/0.58     sdtpldt0: ( $i * $i ) > $i)).
% 0.39/0.58  tff(xn_type, type, (
% 0.39/0.58     xn: $i)).
% 0.39/0.58  tff(xm_type, type, (
% 0.39/0.58     xm: $i)).
% 0.39/0.58  tff(doDivides0_type, type, (
% 0.39/0.58     doDivides0: ( $i * $i ) > $o)).
% 0.39/0.58  tff(sdtlseqdt0_type, type, (
% 0.39/0.58     sdtlseqdt0: ( $i * $i ) > $o)).
% 0.39/0.58  tff(tptp_fun_W0_2_type, type, (
% 0.39/0.58     tptp_fun_W0_2: $i)).
% 0.39/0.58  tff(sdtsldt0_type, type, (
% 0.39/0.58     sdtsldt0: ( $i * $i ) > $i)).
% 0.39/0.58  tff(xq_type, type, (
% 0.39/0.58     xq: $i)).
% 0.39/0.58  tff(xp_type, type, (
% 0.39/0.58     xp: $i)).
% 0.39/0.58  tff(sz00_type, type, (
% 0.39/0.58     sz00: $i)).
% 0.39/0.58  tff(1,plain,
% 0.39/0.58      (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, xn) = sdtasdt0(xl, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, xn) = sdtasdt0(xl, W0)))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(2,axiom,(((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, xn) = sdtasdt0(xl, W0)))) & doDivides0(xl, sdtpldt0(xm, xn))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1324_04')).
% 0.39/0.58  tff(3,plain,
% 0.39/0.58      ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, xn) = sdtasdt0(xl, W0)))),
% 0.39/0.58      inference(and_elim,[status(thm)],[2])).
% 0.39/0.58  tff(4,plain,
% 0.39/0.58      (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, xn) = sdtasdt0(xl, W0)))),
% 0.39/0.58      inference(and_elim,[status(thm)],[3])).
% 0.39/0.58  tff(5,plain,
% 0.39/0.58      (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, xn) = sdtasdt0(xl, W0)))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[4, 1])).
% 0.39/0.58  tff(6,plain,(
% 0.39/0.58      aNaturalNumber0(W0!3) & (sdtpldt0(xm, xn) = sdtasdt0(xl, W0!3))),
% 0.39/0.58      inference(skolemize,[status(sab)],[5])).
% 0.39/0.58  tff(7,plain,
% 0.39/0.58      (aNaturalNumber0(W0!3)),
% 0.39/0.58      inference(and_elim,[status(thm)],[6])).
% 0.39/0.58  tff(8,plain,
% 0.39/0.58      (aNaturalNumber0(xl) <=> aNaturalNumber0(xl)),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(9,axiom,((aNaturalNumber0(xl) & aNaturalNumber0(xm)) & aNaturalNumber0(xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1324')).
% 0.39/0.58  tff(10,plain,
% 0.39/0.58      (aNaturalNumber0(xl) & aNaturalNumber0(xm)),
% 0.39/0.58      inference(and_elim,[status(thm)],[9])).
% 0.39/0.58  tff(11,plain,
% 0.39/0.58      (aNaturalNumber0(xl)),
% 0.39/0.58      inference(and_elim,[status(thm)],[10])).
% 0.39/0.58  tff(12,plain,
% 0.39/0.58      (aNaturalNumber0(xl)),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[11, 8])).
% 0.39/0.58  tff(13,plain,
% 0.39/0.58      (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.39/0.58      inference(bind,[status(th)],[])).
% 0.39/0.58  tff(14,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.39/0.58      inference(quant_intro,[status(thm)],[13])).
% 0.39/0.58  tff(15,plain,
% 0.39/0.58      (^[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)))))),
% 0.39/0.58      inference(bind,[status(th)],[])).
% 0.39/0.58  tff(16,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.39/0.58      inference(quant_intro,[status(thm)],[15])).
% 0.39/0.58  tff(17,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(18,plain,
% 0.39/0.58      (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.39/0.58      inference(bind,[status(th)],[])).
% 0.39/0.58  tff(19,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.39/0.58      inference(quant_intro,[status(thm)],[18])).
% 0.39/0.58  tff(20,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 0.39/0.58  tff(21,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[20, 19])).
% 0.39/0.58  tff(22,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[21, 17])).
% 0.39/0.58  tff(23,plain,(
% 0.39/0.58      ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.39/0.58      inference(skolemize,[status(sab)],[22])).
% 0.39/0.58  tff(24,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[23, 16])).
% 0.39/0.58  tff(25,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[24, 14])).
% 0.39/0.58  tff(26,plain,
% 0.39/0.58      (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xl, W0!3)) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(xl)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xl, W0!3)) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(xl)))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(27,plain,
% 0.39/0.58      ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xl, W0!3)) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(xl)))),
% 0.39/0.58      inference(quant_inst,[status(thm)],[])).
% 0.39/0.58  tff(28,plain,
% 0.39/0.58      ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xl, W0!3)) | (~aNaturalNumber0(W0!3)) | (~aNaturalNumber0(xl))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[27, 26])).
% 0.39/0.58  tff(29,plain,
% 0.39/0.58      (aNaturalNumber0(sdtasdt0(xl, W0!3))),
% 0.39/0.58      inference(unit_resolution,[status(thm)],[28, 25, 12, 7])).
% 0.39/0.58  tff(30,plain,
% 0.39/0.58      (sdtpldt0(xm, xn) = sdtasdt0(xl, W0!3)),
% 0.39/0.58      inference(and_elim,[status(thm)],[6])).
% 0.39/0.58  tff(31,plain,
% 0.39/0.58      ((sdtpldt0(xm, xn) = sdtasdt0(xl, xq)) <=> (sdtpldt0(xm, xn) = sdtasdt0(xl, xq))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(32,axiom,((aNaturalNumber0(xq) & (sdtpldt0(xm, xn) = sdtasdt0(xl, xq))) & (xq = sdtsldt0(sdtpldt0(xm, xn), xl))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1379')).
% 0.39/0.58  tff(33,plain,
% 0.39/0.58      (aNaturalNumber0(xq) & (sdtpldt0(xm, xn) = sdtasdt0(xl, xq))),
% 0.39/0.58      inference(and_elim,[status(thm)],[32])).
% 0.39/0.58  tff(34,plain,
% 0.39/0.58      (sdtpldt0(xm, xn) = sdtasdt0(xl, xq)),
% 0.39/0.58      inference(and_elim,[status(thm)],[33])).
% 0.39/0.58  tff(35,plain,
% 0.39/0.58      (sdtpldt0(xm, xn) = sdtasdt0(xl, xq)),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[34, 31])).
% 0.39/0.58  tff(36,plain,
% 0.39/0.58      (sdtasdt0(xl, xq) = sdtpldt0(xm, xn)),
% 0.39/0.58      inference(symmetry,[status(thm)],[35])).
% 0.39/0.58  tff(37,plain,
% 0.39/0.58      ((xq = sdtsldt0(sdtpldt0(xm, xn), xl)) <=> (xq = sdtsldt0(sdtpldt0(xm, xn), xl))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(38,plain,
% 0.39/0.58      (xq = sdtsldt0(sdtpldt0(xm, xn), xl)),
% 0.39/0.58      inference(and_elim,[status(thm)],[32])).
% 0.39/0.58  tff(39,plain,
% 0.39/0.58      (xq = sdtsldt0(sdtpldt0(xm, xn), xl)),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[38, 37])).
% 0.39/0.58  tff(40,plain,
% 0.39/0.58      (sdtsldt0(sdtpldt0(xm, xn), xl) = xq),
% 0.39/0.58      inference(symmetry,[status(thm)],[39])).
% 0.39/0.58  tff(41,plain,
% 0.39/0.58      (sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, xq)),
% 0.39/0.58      inference(monotonicity,[status(thm)],[40])).
% 0.39/0.58  tff(42,plain,
% 0.39/0.58      (sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, W0!3)),
% 0.39/0.58      inference(transitivity,[status(thm)],[41, 36, 30])).
% 0.39/0.58  tff(43,plain,
% 0.39/0.58      (sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, W0!2)) <=> sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))),
% 0.39/0.58      inference(monotonicity,[status(thm)],[42])).
% 0.39/0.58  tff(44,plain,
% 0.39/0.58      (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(45,plain,
% 0.39/0.58      (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm)),
% 0.39/0.58      inference(and_elim,[status(thm)],[3])).
% 0.39/0.58  tff(46,plain,
% 0.39/0.58      (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 0.39/0.58      inference(and_elim,[status(thm)],[45])).
% 0.39/0.58  tff(47,plain,
% 0.39/0.58      (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[46, 44])).
% 0.39/0.58  tff(48,plain,(
% 0.39/0.58      aNaturalNumber0(W0!2) & (xm = sdtasdt0(xl, W0!2))),
% 0.39/0.58      inference(skolemize,[status(sab)],[47])).
% 0.39/0.58  tff(49,plain,
% 0.39/0.58      (xm = sdtasdt0(xl, W0!2)),
% 0.39/0.58      inference(and_elim,[status(thm)],[48])).
% 0.39/0.58  tff(50,plain,
% 0.39/0.58      ((xm = sdtasdt0(xl, xp)) <=> (xm = sdtasdt0(xl, xp))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(51,axiom,((aNaturalNumber0(xp) & (xm = sdtasdt0(xl, xp))) & (xp = sdtsldt0(xm, xl))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1360')).
% 0.39/0.58  tff(52,plain,
% 0.39/0.58      (aNaturalNumber0(xp) & (xm = sdtasdt0(xl, xp))),
% 0.39/0.58      inference(and_elim,[status(thm)],[51])).
% 0.39/0.58  tff(53,plain,
% 0.39/0.58      (xm = sdtasdt0(xl, xp)),
% 0.39/0.58      inference(and_elim,[status(thm)],[52])).
% 0.39/0.58  tff(54,plain,
% 0.39/0.58      (xm = sdtasdt0(xl, xp)),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[53, 50])).
% 0.39/0.58  tff(55,plain,
% 0.39/0.58      (sdtasdt0(xl, xp) = xm),
% 0.39/0.58      inference(symmetry,[status(thm)],[54])).
% 0.39/0.58  tff(56,plain,
% 0.39/0.58      ((xp = sdtsldt0(xm, xl)) <=> (xp = sdtsldt0(xm, xl))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(57,plain,
% 0.39/0.58      (xp = sdtsldt0(xm, xl)),
% 0.39/0.58      inference(and_elim,[status(thm)],[51])).
% 0.39/0.58  tff(58,plain,
% 0.39/0.58      (xp = sdtsldt0(xm, xl)),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[57, 56])).
% 0.39/0.58  tff(59,plain,
% 0.39/0.58      (sdtsldt0(xm, xl) = xp),
% 0.39/0.58      inference(symmetry,[status(thm)],[58])).
% 0.39/0.58  tff(60,plain,
% 0.39/0.58      (sdtasdt0(xl, sdtsldt0(xm, xl)) = sdtasdt0(xl, xp)),
% 0.39/0.58      inference(monotonicity,[status(thm)],[59])).
% 0.39/0.58  tff(61,plain,
% 0.39/0.58      (sdtasdt0(xl, sdtsldt0(xm, xl)) = sdtasdt0(xl, W0!2)),
% 0.39/0.58      inference(transitivity,[status(thm)],[60, 55, 49])).
% 0.39/0.58  tff(62,plain,
% 0.39/0.58      (sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl))) <=> sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, W0!2))),
% 0.39/0.58      inference(monotonicity,[status(thm)],[61])).
% 0.39/0.58  tff(63,plain,
% 0.39/0.58      (sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl))) <=> sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))),
% 0.39/0.58      inference(transitivity,[status(thm)],[62, 43])).
% 0.39/0.58  tff(64,plain,
% 0.39/0.58      (aNaturalNumber0(sdtsldt0(xm, xl)) <=> aNaturalNumber0(xp)),
% 0.39/0.58      inference(monotonicity,[status(thm)],[59])).
% 0.39/0.58  tff(65,plain,
% 0.39/0.58      (aNaturalNumber0(xp) <=> aNaturalNumber0(sdtsldt0(xm, xl))),
% 0.39/0.58      inference(symmetry,[status(thm)],[64])).
% 0.39/0.58  tff(66,plain,
% 0.39/0.58      (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(67,plain,
% 0.39/0.58      (aNaturalNumber0(xp)),
% 0.39/0.58      inference(and_elim,[status(thm)],[52])).
% 0.39/0.58  tff(68,plain,
% 0.39/0.58      (aNaturalNumber0(xp)),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[67, 66])).
% 0.39/0.58  tff(69,plain,
% 0.39/0.58      (aNaturalNumber0(sdtsldt0(xm, xl))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[68, 65])).
% 0.39/0.58  tff(70,plain,
% 0.39/0.58      (sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) <=> sdtlseqdt0(xp, xq)),
% 0.39/0.58      inference(monotonicity,[status(thm)],[59, 40])).
% 0.39/0.58  tff(71,plain,
% 0.39/0.58      (sdtlseqdt0(xp, xq) <=> sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl))),
% 0.39/0.58      inference(symmetry,[status(thm)],[70])).
% 0.39/0.58  tff(72,plain,
% 0.39/0.58      ((~sdtlseqdt0(xp, xq)) <=> (~sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)))),
% 0.39/0.58      inference(monotonicity,[status(thm)],[71])).
% 0.39/0.58  tff(73,plain,
% 0.39/0.58      ((~sdtlseqdt0(xp, xq)) <=> (~sdtlseqdt0(xp, xq))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(74,axiom,(~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xq)) | sdtlseqdt0(xp, xq))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.39/0.58  tff(75,plain,
% 0.39/0.58      (~sdtlseqdt0(xp, xq)),
% 0.39/0.58      inference(or_elim,[status(thm)],[74])).
% 0.39/0.58  tff(76,plain,
% 0.39/0.58      (~sdtlseqdt0(xp, xq)),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[75, 73])).
% 0.39/0.58  tff(77,plain,
% 0.39/0.58      (~sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[76, 72])).
% 0.39/0.58  tff(78,plain,
% 0.39/0.58      (aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl)) <=> aNaturalNumber0(xq)),
% 0.39/0.58      inference(monotonicity,[status(thm)],[40])).
% 0.39/0.58  tff(79,plain,
% 0.39/0.58      (aNaturalNumber0(xq) <=> aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))),
% 0.39/0.58      inference(symmetry,[status(thm)],[78])).
% 0.39/0.58  tff(80,plain,
% 0.39/0.58      (aNaturalNumber0(xq) <=> aNaturalNumber0(xq)),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(81,plain,
% 0.39/0.58      (aNaturalNumber0(xq)),
% 0.39/0.58      inference(and_elim,[status(thm)],[33])).
% 0.39/0.58  tff(82,plain,
% 0.39/0.58      (aNaturalNumber0(xq)),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[81, 80])).
% 0.39/0.58  tff(83,plain,
% 0.39/0.58      (aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[82, 79])).
% 0.39/0.58  tff(84,plain,
% 0.39/0.58      (^[W0: $i, W1: $i] : refl((sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0))))) <=> (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0))))))),
% 0.39/0.58      inference(bind,[status(th)],[])).
% 0.39/0.58  tff(85,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0))))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.39/0.58      inference(quant_intro,[status(thm)],[84])).
% 0.39/0.58  tff(86,plain,
% 0.39/0.58      (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((~(W1 = W0)) & sdtlseqdt0(W1, W0)) <=> (~((W1 = W0) | (~sdtlseqdt0(W1, W0))))), trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (sdtlseqdt0(W0, W1) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((sdtlseqdt0(W0, W1) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))), ((sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))))),
% 0.39/0.58      inference(bind,[status(th)],[])).
% 0.39/0.58  tff(87,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.39/0.58      inference(quant_intro,[status(thm)],[86])).
% 0.39/0.58  tff(88,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(89,plain,
% 0.39/0.58      (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)))) <=> (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.39/0.58      inference(bind,[status(th)],[])).
% 0.39/0.58  tff(90,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.39/0.58      inference(quant_intro,[status(thm)],[89])).
% 0.39/0.58  tff(91,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mLETotal')).
% 0.39/0.58  tff(92,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[91, 90])).
% 0.39/0.58  tff(93,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[92, 88])).
% 0.39/0.58  tff(94,plain,(
% 0.39/0.58      ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.39/0.58      inference(skolemize,[status(sab)],[93])).
% 0.39/0.58  tff(95,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[94, 87])).
% 0.39/0.58  tff(96,plain,
% 0.39/0.58      (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[95, 85])).
% 0.39/0.58  tff(97,plain,
% 0.39/0.58      (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | ((~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(98,plain,
% 0.39/0.58      ((sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))) <=> ((~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(99,plain,
% 0.39/0.58      ((~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) <=> (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(100,plain,
% 0.39/0.58      ((sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))) <=> (sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))),
% 0.39/0.58      inference(monotonicity,[status(thm)],[99])).
% 0.39/0.58  tff(101,plain,
% 0.39/0.58      ((sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))) <=> ((~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))),
% 0.39/0.58      inference(transitivity,[status(thm)],[100, 98])).
% 0.39/0.58  tff(102,plain,
% 0.39/0.58      (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | ((~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))))),
% 0.39/0.58      inference(monotonicity,[status(thm)],[101])).
% 0.39/0.58  tff(103,plain,
% 0.39/0.58      (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))),
% 0.39/0.58      inference(transitivity,[status(thm)],[102, 97])).
% 0.39/0.58  tff(104,plain,
% 0.39/0.58      ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))),
% 0.39/0.58      inference(quant_inst,[status(thm)],[])).
% 0.39/0.58  tff(105,plain,
% 0.39/0.58      ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[104, 103])).
% 0.39/0.58  tff(106,plain,
% 0.39/0.58      ((~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | sdtlseqdt0(sdtsldt0(xm, xl), sdtsldt0(sdtpldt0(xm, xn), xl)) | (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))),
% 0.39/0.58      inference(unit_resolution,[status(thm)],[105, 96])).
% 0.39/0.58  tff(107,plain,
% 0.39/0.58      (~((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))),
% 0.39/0.58      inference(unit_resolution,[status(thm)],[106, 83, 77, 69])).
% 0.39/0.58  tff(108,plain,
% 0.39/0.58      (((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~(sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)))),
% 0.39/0.58      inference(tautology,[status(thm)],[])).
% 0.39/0.58  tff(109,plain,
% 0.39/0.58      (~(sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl))),
% 0.39/0.58      inference(unit_resolution,[status(thm)],[108, 107])).
% 0.39/0.58  tff(110,plain,
% 0.39/0.58      (((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))),
% 0.39/0.58      inference(tautology,[status(thm)],[])).
% 0.39/0.58  tff(111,plain,
% 0.39/0.58      (sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))),
% 0.39/0.58      inference(unit_resolution,[status(thm)],[110, 107])).
% 0.39/0.58  tff(112,plain,
% 0.39/0.58      ((~(xl = sz00)) <=> (~(xl = sz00))),
% 0.39/0.58      inference(rewrite,[status(thm)],[])).
% 0.39/0.58  tff(113,axiom,(~(xl = sz00)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1347')).
% 0.39/0.58  tff(114,plain,
% 0.39/0.58      (~(xl = sz00)),
% 0.39/0.58      inference(modus_ponens,[status(thm)],[113, 112])).
% 0.39/0.58  tff(115,plain,
% 0.39/0.58      (^[W0: $i, W1: $i, W2: $i] : refl(((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))) <=> ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))),
% 0.39/0.58      inference(bind,[status(th)],[])).
% 0.39/0.58  tff(116,plain,
% 0.39/0.58      (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))),
% 0.39/0.58      inference(quant_intro,[status(thm)],[115])).
% 0.39/0.58  tff(117,plain,
% 0.39/0.58      (^[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))))), rewrite(((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) <=> (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))), trans(monotonicity(rewrite(((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2)) <=> (~((W1 = W2) | (W0 = sz00) | (~sdtlseqdt0(W1, W2))))), ((~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))) <=> (~(~((W1 = W2) | (W0 = sz00) | (~sdtlseqdt0(W1, W2))))))), rewrite((~(~((W1 = W2) | (W0 = sz00) | (~sdtlseqdt0(W1, W2))))) <=> ((W1 = W2) | (W0 = sz00) | (~sdtlseqdt0(W1, W2)))), ((~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))) <=> ((W1 = W2) | (W0 = sz00) | (~sdtlseqdt0(W1, W2))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) | (~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2)))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) | ((W1 = W2) | (W0 = sz00) | (~sdtlseqdt0(W1, W2)))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) | ((W1 = W2) | (W0 = sz00) | (~sdtlseqdt0(W1, W2)))) <=> ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) | (~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2)))) <=> ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))))),
% 0.39/0.59      inference(bind,[status(th)],[])).
% 0.39/0.59  tff(118,plain,
% 0.39/0.59      (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) | (~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))),
% 0.39/0.59      inference(quant_intro,[status(thm)],[117])).
% 0.39/0.59  tff(119,plain,
% 0.39/0.59      (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) | (~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) | (~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))))),
% 0.39/0.59      inference(rewrite,[status(thm)],[])).
% 0.39/0.59  tff(120,plain,
% 0.39/0.59      (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), trans(monotonicity(rewrite((((~(W0 = sz00)) & (~(W1 = W2))) & sdtlseqdt0(W1, W2)) <=> ((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))), trans(monotonicity(rewrite((((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) <=> ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))), (((((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) <=> (((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))), rewrite((((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) <=> ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))), (((((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) <=> ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))), (((((~(W0 = sz00)) & (~(W1 = W2))) & sdtlseqdt0(W1, W2)) => ((((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))) <=> (((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2)) => ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))), rewrite((((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2)) => ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))) <=> ((~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))), (((((~(W0 = sz00)) & (~(W1 = W2))) & sdtlseqdt0(W1, W2)) => ((((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))) <=> ((~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((~(W0 = sz00)) & (~(W1 = W2))) & sdtlseqdt0(W1, W2)) => ((((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) | (~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((~(W0 = sz00)) & (~(W1 = W2))) & sdtlseqdt0(W1, W2)) => ((((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) | (~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))))))),
% 0.39/0.59      inference(bind,[status(th)],[])).
% 0.39/0.59  tff(121,plain,
% 0.39/0.59      (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((~(W0 = sz00)) & (~(W1 = W2))) & sdtlseqdt0(W1, W2)) => ((((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) | (~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))))),
% 0.39/0.59      inference(quant_intro,[status(thm)],[120])).
% 0.39/0.59  tff(122,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((~(W0 = sz00)) & (~(W1 = W2))) & sdtlseqdt0(W1, W2)) => ((((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMonMul')).
% 0.39/0.59  tff(123,plain,
% 0.39/0.59      (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) | (~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))))),
% 0.39/0.59      inference(modus_ponens,[status(thm)],[122, 121])).
% 0.39/0.59  tff(124,plain,
% 0.39/0.59      (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) | (~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))))),
% 0.39/0.59      inference(modus_ponens,[status(thm)],[123, 119])).
% 0.39/0.59  tff(125,plain,(
% 0.39/0.59      ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((~(sdtasdt0(W0, W1) = sdtasdt0(W0, W2))) & sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & (~(sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) & sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))) | (~((~(W0 = sz00)) & (~(W1 = W2)) & sdtlseqdt0(W1, W2))))),
% 0.39/0.59      inference(skolemize,[status(sab)],[124])).
% 0.39/0.59  tff(126,plain,
% 0.39/0.59      (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))),
% 0.39/0.59      inference(modus_ponens,[status(thm)],[125, 118])).
% 0.39/0.59  tff(127,plain,
% 0.39/0.59      (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))),
% 0.39/0.59      inference(modus_ponens,[status(thm)],[126, 116])).
% 0.39/0.59  tff(128,plain,
% 0.39/0.59      (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))) | ((xl = sz00) | (~aNaturalNumber0(xl)) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))) | (xl = sz00) | (~aNaturalNumber0(xl)) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl))))))),
% 0.39/0.59      inference(rewrite,[status(thm)],[])).
% 0.39/0.59  tff(129,plain,
% 0.39/0.59      (((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (xl = sz00) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl)))))) <=> ((xl = sz00) | (~aNaturalNumber0(xl)) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl))))))),
% 0.39/0.59      inference(rewrite,[status(thm)],[])).
% 0.39/0.59  tff(130,plain,
% 0.39/0.59      ((~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl))))) <=> (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl)))))),
% 0.39/0.59      inference(rewrite,[status(thm)],[])).
% 0.39/0.59  tff(131,plain,
% 0.39/0.59      (((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (xl = sz00) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl)))))) <=> ((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (xl = sz00) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl))))))),
% 0.39/0.59      inference(monotonicity,[status(thm)],[130])).
% 0.39/0.59  tff(132,plain,
% 0.39/0.59      (((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (xl = sz00) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl)))))) <=> ((xl = sz00) | (~aNaturalNumber0(xl)) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl))))))),
% 0.39/0.59      inference(transitivity,[status(thm)],[131, 129])).
% 0.39/0.59  tff(133,plain,
% 0.39/0.59      (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))) | ((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (xl = sz00) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))) | ((xl = sz00) | (~aNaturalNumber0(xl)) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl)))))))),
% 0.39/0.59      inference(monotonicity,[status(thm)],[132])).
% 0.39/0.59  tff(134,plain,
% 0.39/0.59      (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))) | ((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (xl = sz00) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))) | (xl = sz00) | (~aNaturalNumber0(xl)) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl))))))),
% 0.39/0.59      inference(transitivity,[status(thm)],[133, 128])).
% 0.39/0.59  tff(135,plain,
% 0.39/0.59      ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))) | ((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (xl = sz00) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~aNaturalNumber0(xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl))))))),
% 0.39/0.59      inference(quant_inst,[status(thm)],[])).
% 0.39/0.59  tff(136,plain,
% 0.39/0.59      ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (W0 = sz00) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)) | (~sdtlseqdt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) | (~sdtlseqdt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))) | (xl = sz00) | (~aNaturalNumber0(xl)) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl)))))),
% 0.39/0.60      inference(modus_ponens,[status(thm)],[135, 134])).
% 0.39/0.60  tff(137,plain,
% 0.39/0.60      ((~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~sdtlseqdt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl)))))),
% 0.39/0.60      inference(unit_resolution,[status(thm)],[136, 127, 12, 114])).
% 0.39/0.60  tff(138,plain,
% 0.39/0.60      (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl))))),
% 0.39/0.60      inference(unit_resolution,[status(thm)],[137, 111, 69, 83, 109])).
% 0.39/0.60  tff(139,plain,
% 0.39/0.60      (((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)) | (~sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))) | (~sdtlseqdt0(sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl), sdtasdt0(sdtsldt0(xm, xl), xl)))) | sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))),
% 0.39/0.60      inference(tautology,[status(thm)],[])).
% 0.39/0.60  tff(140,plain,
% 0.39/0.60      (sdtlseqdt0(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)), sdtasdt0(xl, sdtsldt0(xm, xl)))),
% 0.39/0.60      inference(unit_resolution,[status(thm)],[139, 138])).
% 0.39/0.60  tff(141,plain,
% 0.39/0.60      (sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))),
% 0.39/0.60      inference(modus_ponens,[status(thm)],[140, 63])).
% 0.39/0.60  tff(142,plain,
% 0.39/0.60      (sdtasdt0(xl, W0!3) = sdtpldt0(xm, xn)),
% 0.39/0.60      inference(symmetry,[status(thm)],[30])).
% 0.39/0.60  tff(143,plain,
% 0.39/0.60      (sdtasdt0(xl, W0!2) = xm),
% 0.39/0.60      inference(symmetry,[status(thm)],[49])).
% 0.39/0.60  tff(144,plain,
% 0.39/0.60      (sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3)) <=> sdtlseqdt0(xm, sdtpldt0(xm, xn))),
% 0.39/0.60      inference(monotonicity,[status(thm)],[143, 142])).
% 0.39/0.60  tff(145,plain,
% 0.39/0.60      (sdtlseqdt0(xm, sdtpldt0(xm, xn)) <=> sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))),
% 0.39/0.60      inference(symmetry,[status(thm)],[144])).
% 0.39/0.60  tff(146,plain,
% 0.39/0.60      (sdtlseqdt0(xm, sdtpldt0(xm, xn)) <=> sdtlseqdt0(xm, sdtpldt0(xm, xn))),
% 0.39/0.60      inference(rewrite,[status(thm)],[])).
% 0.39/0.60  tff(147,axiom,(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = sdtpldt0(xm, xn))) & sdtlseqdt0(xm, sdtpldt0(xm, xn))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1409')).
% 0.39/0.60  tff(148,plain,
% 0.39/0.60      (sdtlseqdt0(xm, sdtpldt0(xm, xn))),
% 0.39/0.60      inference(and_elim,[status(thm)],[147])).
% 0.39/0.60  tff(149,plain,
% 0.39/0.60      (sdtlseqdt0(xm, sdtpldt0(xm, xn))),
% 0.39/0.60      inference(modus_ponens,[status(thm)],[148, 146])).
% 0.39/0.60  tff(150,plain,
% 0.39/0.60      (sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))),
% 0.39/0.60      inference(modus_ponens,[status(thm)],[149, 145])).
% 0.39/0.60  tff(151,plain,
% 0.39/0.60      ((sdtasdt0(xl, W0!2) = sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl))) <=> (sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3))),
% 0.39/0.60      inference(monotonicity,[status(thm)],[42])).
% 0.39/0.60  tff(152,plain,
% 0.39/0.60      ((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, W0!2)) <=> (sdtasdt0(xl, W0!2) = sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)))),
% 0.39/0.60      inference(commutativity,[status(thm)],[])).
% 0.39/0.60  tff(153,plain,
% 0.39/0.60      ((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) <=> (sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, W0!2))),
% 0.39/0.60      inference(monotonicity,[status(thm)],[61])).
% 0.39/0.60  tff(154,plain,
% 0.39/0.60      ((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) <=> (sdtasdt0(xl, W0!2) = sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)))),
% 0.39/0.60      inference(transitivity,[status(thm)],[153, 152])).
% 0.39/0.60  tff(155,plain,
% 0.39/0.60      ((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) <=> (sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3))),
% 0.39/0.60      inference(transitivity,[status(thm)],[154, 151])).
% 0.39/0.60  tff(156,plain,
% 0.39/0.60      ((~(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl)))) <=> (~(sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3)))),
% 0.39/0.60      inference(monotonicity,[status(thm)],[155])).
% 0.39/0.60  tff(157,plain,
% 0.39/0.60      (^[W0: $i] : refl(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 0.39/0.60      inference(bind,[status(th)],[])).
% 0.39/0.60  tff(158,plain,
% 0.39/0.60      (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.39/0.60      inference(quant_intro,[status(thm)],[157])).
% 0.39/0.60  tff(159,plain,
% 0.39/0.60      (^[W0: $i] : rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 0.39/0.60      inference(bind,[status(th)],[])).
% 0.39/0.60  tff(160,plain,
% 0.39/0.60      (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.39/0.60      inference(quant_intro,[status(thm)],[159])).
% 0.39/0.60  tff(161,plain,
% 0.39/0.60      (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.39/0.60      inference(transitivity,[status(thm)],[160, 158])).
% 0.39/0.60  tff(162,plain,
% 0.39/0.60      (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), rewrite((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) <=> (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), rewrite(((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), (![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))))),
% 0.39/0.60      inference(bind,[status(th)],[])).
% 0.39/0.60  tff(163,plain,
% 0.39/0.60      (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.39/0.60      inference(quant_intro,[status(thm)],[162])).
% 0.39/0.60  tff(164,plain,
% 0.39/0.60      (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.39/0.60      inference(rewrite,[status(thm)],[])).
% 0.39/0.60  tff(165,plain,
% 0.39/0.60      (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))), rewrite((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2)))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))))), rewrite(((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), (![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), rewrite(((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> (aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))), rewrite((aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))),
% 0.39/0.60      inference(bind,[status(th)],[])).
% 0.39/0.60  tff(166,plain,
% 0.39/0.60      (![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.39/0.60      inference(quant_intro,[status(thm)],[165])).
% 0.39/0.60  tff(167,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/sandbox/benchmark/theBenchmark.p','mMulCanc')).
% 0.39/0.60  tff(168,plain,
% 0.39/0.60      (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.39/0.60      inference(modus_ponens,[status(thm)],[167, 166])).
% 0.39/0.60  tff(169,plain,
% 0.39/0.60      (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.39/0.60      inference(modus_ponens,[status(thm)],[168, 164])).
% 0.39/0.60  tff(170,plain,(
% 0.39/0.60      ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.39/0.60      inference(skolemize,[status(sab)],[169])).
% 0.39/0.60  tff(171,plain,
% 0.39/0.60      (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.39/0.60      inference(modus_ponens,[status(thm)],[170, 163])).
% 0.39/0.60  tff(172,plain,
% 0.39/0.60      (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.39/0.60      inference(modus_ponens,[status(thm)],[171, 161])).
% 0.39/0.60  tff(173,plain,
% 0.39/0.60      (((~![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))))) | ((xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl))))))) <=> ((~![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))))) | (xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl))))))),
% 0.39/0.60      inference(rewrite,[status(thm)],[])).
% 0.39/0.60  tff(174,plain,
% 0.39/0.60      (((xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))) <=> ((xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl))))))),
% 0.39/0.60      inference(rewrite,[status(thm)],[])).
% 0.39/0.60  tff(175,plain,
% 0.39/0.60      (^[W1: $i, W2: $i] : rewrite(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))) | (~aNaturalNumber0(W1))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl))))))),
% 0.39/0.60      inference(bind,[status(th)],[])).
% 0.39/0.60  tff(176,plain,
% 0.39/0.60      (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))) | (~aNaturalNumber0(W1))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))),
% 0.39/0.60      inference(quant_intro,[status(thm)],[175])).
% 0.39/0.60  tff(177,plain,
% 0.39/0.60      (((xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))) | (~aNaturalNumber0(W1)))) <=> ((xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl))))))),
% 0.39/0.60      inference(monotonicity,[status(thm)],[176])).
% 0.39/0.60  tff(178,plain,
% 0.39/0.60      (((xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))) | (~aNaturalNumber0(W1)))) <=> ((xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl))))))),
% 0.39/0.60      inference(transitivity,[status(thm)],[177, 174])).
% 0.39/0.60  tff(179,plain,
% 0.39/0.60      (((~![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))))) | ((xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))) | (~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))))) | ((xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))))),
% 0.39/0.60      inference(monotonicity,[status(thm)],[178])).
% 0.39/0.60  tff(180,plain,
% 0.39/0.60      (((~![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))))) | ((xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))) | (~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))))) | (xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl))))))),
% 0.39/0.60      inference(transitivity,[status(thm)],[179, 173])).
% 0.39/0.60  tff(181,plain,
% 0.39/0.60      ((~![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))))) | ((xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))) | (~aNaturalNumber0(W1))))),
% 0.39/0.60      inference(quant_inst,[status(thm)],[])).
% 0.39/0.61  tff(182,plain,
% 0.39/0.61      ((~![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))))) | (xl = sz00) | (~aNaturalNumber0(xl)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))),
% 0.39/0.61      inference(modus_ponens,[status(thm)],[181, 180])).
% 0.39/0.61  tff(183,plain,
% 0.39/0.61      (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))),
% 0.39/0.61      inference(unit_resolution,[status(thm)],[182, 172, 12, 114])).
% 0.39/0.61  tff(184,plain,
% 0.39/0.61      (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))) | ((~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)))))),
% 0.39/0.61      inference(rewrite,[status(thm)],[])).
% 0.39/0.61  tff(185,plain,
% 0.39/0.61      (((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl))))) <=> ((~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)))))),
% 0.39/0.61      inference(rewrite,[status(thm)],[])).
% 0.39/0.61  tff(186,plain,
% 0.39/0.61      (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))) | ((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))) | ((~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl))))))),
% 0.39/0.61      inference(monotonicity,[status(thm)],[185])).
% 0.39/0.61  tff(187,plain,
% 0.39/0.61      (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))) | ((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)))))),
% 0.39/0.61      inference(transitivity,[status(thm)],[186, 184])).
% 0.39/0.61  tff(188,plain,
% 0.39/0.61      ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))) | ((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)))))),
% 0.39/0.61      inference(quant_inst,[status(thm)],[])).
% 0.39/0.61  tff(189,plain,
% 0.39/0.61      ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xl, W1) = sdtasdt0(xl, W2)) | (sdtasdt0(W1, xl) = sdtasdt0(W2, xl)))))) | (~aNaturalNumber0(sdtsldt0(xm, xl))) | (~aNaturalNumber0(sdtsldt0(sdtpldt0(xm, xn), xl))) | (sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl))))),
% 0.39/0.61      inference(modus_ponens,[status(thm)],[188, 187])).
% 0.39/0.61  tff(190,plain,
% 0.39/0.61      ((sdtsldt0(sdtpldt0(xm, xn), xl) = sdtsldt0(xm, xl)) | (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl))))),
% 0.39/0.61      inference(unit_resolution,[status(thm)],[189, 69, 83, 183])).
% 0.39/0.61  tff(191,plain,
% 0.39/0.61      (~((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl)))),
% 0.39/0.61      inference(unit_resolution,[status(thm)],[190, 109])).
% 0.39/0.61  tff(192,plain,
% 0.39/0.61      (((sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))) | (sdtasdt0(sdtsldt0(sdtpldt0(xm, xn), xl), xl) = sdtasdt0(sdtsldt0(xm, xl), xl))) | (~(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl))))),
% 0.39/0.61      inference(tautology,[status(thm)],[])).
% 0.39/0.61  tff(193,plain,
% 0.39/0.61      (~(sdtasdt0(xl, sdtsldt0(sdtpldt0(xm, xn), xl)) = sdtasdt0(xl, sdtsldt0(xm, xl)))),
% 0.39/0.61      inference(unit_resolution,[status(thm)],[192, 191])).
% 0.39/0.61  tff(194,plain,
% 0.39/0.61      (~(sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3))),
% 0.39/0.61      inference(modus_ponens,[status(thm)],[193, 156])).
% 0.39/0.61  tff(195,plain,
% 0.39/0.61      (aNaturalNumber0(sdtasdt0(xl, W0!2)) <=> aNaturalNumber0(xm)),
% 0.39/0.61      inference(monotonicity,[status(thm)],[143])).
% 0.39/0.61  tff(196,plain,
% 0.39/0.61      (aNaturalNumber0(xm) <=> aNaturalNumber0(sdtasdt0(xl, W0!2))),
% 0.39/0.61      inference(symmetry,[status(thm)],[195])).
% 0.39/0.61  tff(197,plain,
% 0.39/0.61      (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.39/0.61      inference(rewrite,[status(thm)],[])).
% 0.39/0.61  tff(198,plain,
% 0.39/0.61      (aNaturalNumber0(xm)),
% 0.39/0.61      inference(and_elim,[status(thm)],[10])).
% 0.39/0.61  tff(199,plain,
% 0.39/0.61      (aNaturalNumber0(xm)),
% 0.39/0.61      inference(modus_ponens,[status(thm)],[198, 197])).
% 0.39/0.61  tff(200,plain,
% 0.39/0.61      (aNaturalNumber0(sdtasdt0(xl, W0!2))),
% 0.39/0.61      inference(modus_ponens,[status(thm)],[199, 196])).
% 0.39/0.61  tff(201,plain,
% 0.39/0.61      (^[W0: $i, W1: $i] : refl(((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0))) <=> ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0))))),
% 0.39/0.61      inference(bind,[status(th)],[])).
% 0.39/0.61  tff(202,plain,
% 0.39/0.61      (![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.39/0.61      inference(quant_intro,[status(thm)],[201])).
% 0.39/0.61  tff(203,plain,
% 0.39/0.61      (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), trans(monotonicity(rewrite((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) <=> (~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> (~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))))), rewrite((~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), (((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))))), rewrite(((W0 = W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))), (((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))))),
% 0.39/0.61      inference(bind,[status(th)],[])).
% 0.39/0.61  tff(204,plain,
% 0.39/0.61      (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.39/0.61      inference(quant_intro,[status(thm)],[203])).
% 0.39/0.61  tff(205,plain,
% 0.39/0.61      (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.39/0.61      inference(rewrite,[status(thm)],[])).
% 0.39/0.61  tff(206,plain,
% 0.39/0.61      (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)) <=> ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))) <=> ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))))),
% 0.39/0.61      inference(bind,[status(th)],[])).
% 0.39/0.61  tff(207,plain,
% 0.39/0.61      (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.39/0.61      inference(quant_intro,[status(thm)],[206])).
% 0.39/0.61  tff(208,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mLEAsym')).
% 0.39/0.61  tff(209,plain,
% 0.39/0.61      (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.39/0.61      inference(modus_ponens,[status(thm)],[208, 207])).
% 0.39/0.61  tff(210,plain,
% 0.39/0.61      (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.39/0.61      inference(modus_ponens,[status(thm)],[209, 205])).
% 0.39/0.61  tff(211,plain,(
% 0.39/0.61      ![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.39/0.61      inference(skolemize,[status(sab)],[210])).
% 0.39/0.61  tff(212,plain,
% 0.39/0.61      (![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.39/0.61      inference(modus_ponens,[status(thm)],[211, 204])).
% 0.39/0.61  tff(213,plain,
% 0.39/0.61      (![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.39/0.61      inference(modus_ponens,[status(thm)],[212, 202])).
% 0.39/0.61  tff(214,plain,
% 0.39/0.61      (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3)) | (~sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))) | (~sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, W0!3))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3)) | (~sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))) | (~sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, W0!3))))),
% 0.39/0.61      inference(rewrite,[status(thm)],[])).
% 0.39/0.61  tff(215,plain,
% 0.39/0.61      (((sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3)) | (~aNaturalNumber0(sdtasdt0(xl, W0!3))) | (~sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2)))) <=> ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3)) | (~sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))) | (~sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, W0!3))))),
% 0.39/0.61      inference(rewrite,[status(thm)],[])).
% 0.39/0.61  tff(216,plain,
% 0.39/0.61      (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3)) | (~aNaturalNumber0(sdtasdt0(xl, W0!3))) | (~sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3)) | (~sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))) | (~sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, W0!3)))))),
% 0.39/0.61      inference(monotonicity,[status(thm)],[215])).
% 0.39/0.61  tff(217,plain,
% 0.39/0.61      (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3)) | (~aNaturalNumber0(sdtasdt0(xl, W0!3))) | (~sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3)) | (~sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))) | (~sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, W0!3))))),
% 0.39/0.61      inference(transitivity,[status(thm)],[216, 214])).
% 0.39/0.61  tff(218,plain,
% 0.39/0.61      ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3)) | (~aNaturalNumber0(sdtasdt0(xl, W0!3))) | (~sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))))),
% 0.39/0.61      inference(quant_inst,[status(thm)],[])).
% 0.39/0.61  tff(219,plain,
% 0.39/0.61      ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtasdt0(xl, W0!2) = sdtasdt0(xl, W0!3)) | (~sdtlseqdt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, W0!3))) | (~sdtlseqdt0(sdtasdt0(xl, W0!3), sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, W0!3)))),
% 0.39/0.61      inference(modus_ponens,[status(thm)],[218, 217])).
% 0.39/0.61  tff(220,plain,
% 0.39/0.61      ($false),
% 0.39/0.61      inference(unit_resolution,[status(thm)],[219, 213, 200, 194, 150, 141, 29])).
% 0.39/0.61  % SZS output end Proof
% 0.39/0.62  % E exiting
%------------------------------------------------------------------------------