TSTP Solution File: NUM505+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM505+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Sun Sep 18 13:10:08 EDT 2022
% Result : Theorem 0.19s 0.54s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM505+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 11:00:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.54 % SZS status Theorem
% 0.19/0.54 % SZS output start Proof
% 0.19/0.54 tff(sdtlseqdt0_type, type, (
% 0.19/0.54 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.19/0.54 tff(xp_type, type, (
% 0.19/0.54 xp: $i)).
% 0.19/0.54 tff(sdtsldt0_type, type, (
% 0.19/0.54 sdtsldt0: ( $i * $i ) > $i)).
% 0.19/0.54 tff(sdtasdt0_type, type, (
% 0.19/0.54 sdtasdt0: ( $i * $i ) > $i)).
% 0.19/0.54 tff(xm_type, type, (
% 0.19/0.54 xm: $i)).
% 0.19/0.54 tff(xn_type, type, (
% 0.19/0.54 xn: $i)).
% 0.19/0.54 tff(tptp_fun_W0_11_type, type, (
% 0.19/0.54 tptp_fun_W0_11: $i)).
% 0.19/0.54 tff(xr_type, type, (
% 0.19/0.54 xr: $i)).
% 0.19/0.54 tff(aNaturalNumber0_type, type, (
% 0.19/0.54 aNaturalNumber0: $i > $o)).
% 0.19/0.54 tff(xk_type, type, (
% 0.19/0.54 xk: $i)).
% 0.19/0.54 tff(doDivides0_type, type, (
% 0.19/0.54 doDivides0: ( $i * $i ) > $o)).
% 0.19/0.54 tff(sz00_type, type, (
% 0.19/0.54 sz00: $i)).
% 0.19/0.54 tff(sz10_type, type, (
% 0.19/0.54 sz10: $i)).
% 0.19/0.54 tff(isPrime0_type, type, (
% 0.19/0.54 isPrime0: $i > $o)).
% 0.19/0.54 tff(sdtpldt0_type, type, (
% 0.19/0.54 sdtpldt0: ( $i * $i ) > $i)).
% 0.19/0.54 tff(1,plain,
% 0.19/0.54 (^[W0: $i] : rewrite((aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0))) <=> (aNaturalNumber0(W0) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(2,plain,
% 0.19/0.54 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0)))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.54 tff(3,plain,
% 0.19/0.54 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(4,axiom,((((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))) & isPrime0(xr)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2342')).
% 0.19/0.54 tff(5,plain,
% 0.19/0.54 (((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))),
% 0.19/0.54 inference(and_elim,[status(thm)],[4])).
% 0.19/0.54 tff(6,plain,
% 0.19/0.54 ((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))),
% 0.19/0.54 inference(and_elim,[status(thm)],[5])).
% 0.19/0.54 tff(7,plain,
% 0.19/0.54 (((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))),
% 0.19/0.54 inference(and_elim,[status(thm)],[6])).
% 0.19/0.54 tff(8,plain,
% 0.19/0.54 ((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)),
% 0.19/0.54 inference(and_elim,[status(thm)],[7])).
% 0.19/0.54 tff(9,plain,
% 0.19/0.54 (aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 0.19/0.54 inference(and_elim,[status(thm)],[8])).
% 0.19/0.54 tff(10,plain,
% 0.19/0.54 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 0.19/0.54 inference(and_elim,[status(thm)],[9])).
% 0.19/0.54 tff(11,plain,
% 0.19/0.54 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.54 tff(12,plain,
% 0.19/0.54 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.19/0.54 tff(13,plain,(
% 0.19/0.54 aNaturalNumber0(W0!11) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0!11))),
% 0.19/0.54 inference(skolemize,[status(sab)],[12])).
% 0.19/0.54 tff(14,plain,
% 0.19/0.54 (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0!11)),
% 0.19/0.54 inference(and_elim,[status(thm)],[13])).
% 0.19/0.54 tff(15,plain,
% 0.19/0.54 (sdtasdt0(xr, W0!11) = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 0.19/0.54 inference(symmetry,[status(thm)],[14])).
% 0.19/0.54 tff(16,plain,
% 0.19/0.54 (sdtlseqdt0(sdtasdt0(xr, W0!11), xp) <=> sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)),
% 0.19/0.54 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.54 tff(17,plain,
% 0.19/0.54 (aNaturalNumber0(sdtasdt0(xr, W0!11)) <=> aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.54 tff(18,plain,
% 0.19/0.54 (aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp)) <=> aNaturalNumber0(sdtasdt0(xr, W0!11))),
% 0.19/0.54 inference(symmetry,[status(thm)],[17])).
% 0.45/0.54 tff(19,plain,
% 0.45/0.54 (aNaturalNumber0(xk) <=> aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(20,plain,
% 0.45/0.54 (aNaturalNumber0(xk) <=> aNaturalNumber0(xk)),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(21,axiom,((aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))) & (xk = sdtsldt0(sdtasdt0(xn, xm), xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2306')).
% 0.45/0.54 tff(22,plain,
% 0.45/0.54 (aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 0.45/0.54 inference(and_elim,[status(thm)],[21])).
% 0.45/0.54 tff(23,plain,
% 0.45/0.54 (aNaturalNumber0(xk)),
% 0.45/0.54 inference(and_elim,[status(thm)],[22])).
% 0.45/0.54 tff(24,plain,
% 0.45/0.54 (aNaturalNumber0(xk)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.45/0.54 tff(25,plain,
% 0.45/0.54 (aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.45/0.54 tff(26,plain,
% 0.45/0.54 (aNaturalNumber0(sdtasdt0(xr, W0!11))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.45/0.54 tff(27,plain,
% 0.45/0.54 (sdtlseqdt0(xp, sdtasdt0(xr, W0!11)) <=> sdtlseqdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[15])).
% 0.45/0.54 tff(28,plain,
% 0.45/0.54 (sdtlseqdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) <=> sdtlseqdt0(xp, sdtasdt0(xr, W0!11))),
% 0.45/0.54 inference(symmetry,[status(thm)],[27])).
% 0.45/0.54 tff(29,plain,
% 0.45/0.54 ((~sdtlseqdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))) <=> (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11)))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[28])).
% 0.45/0.54 tff(30,plain,
% 0.45/0.54 ((~sdtlseqdt0(xp, xk)) <=> (~sdtlseqdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(31,plain,
% 0.45/0.54 ((~sdtlseqdt0(xp, xk)) <=> (~sdtlseqdt0(xp, xk))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(32,plain,
% 0.45/0.54 ((~((~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xk)) | sdtlseqdt0(xp, xk))) => ((~(xk = xp)) & (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp)) | sdtlseqdt0(xk, xp))))) <=> (~(sdtlseqdt0(xp, xk) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xk)) | ((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp))))))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(33,axiom,(~((~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xk)) | sdtlseqdt0(xp, xk))) => ((~(xk = xp)) & (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp)) | sdtlseqdt0(xk, xp))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.45/0.54 tff(34,plain,
% 0.45/0.54 (~(sdtlseqdt0(xp, xk) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xk)) | ((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp)))))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.45/0.54 tff(35,plain,
% 0.45/0.54 (~sdtlseqdt0(xp, xk)),
% 0.45/0.54 inference(or_elim,[status(thm)],[34])).
% 0.45/0.54 tff(36,plain,
% 0.45/0.54 (~sdtlseqdt0(xp, xk)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.45/0.54 tff(37,plain,
% 0.45/0.54 (~sdtlseqdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[36, 30])).
% 0.45/0.54 tff(38,plain,
% 0.45/0.54 (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[37, 29])).
% 0.45/0.54 tff(39,plain,
% 0.45/0.54 (((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11)))) | sdtlseqdt0(xp, sdtasdt0(xr, W0!11))),
% 0.45/0.54 inference(tautology,[status(thm)],[])).
% 0.45/0.54 tff(40,plain,
% 0.45/0.54 ((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11)))),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.45/0.54 tff(41,plain,
% 0.45/0.54 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(42,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1837')).
% 0.45/0.54 tff(43,plain,
% 0.45/0.54 (aNaturalNumber0(xp)),
% 0.45/0.54 inference(and_elim,[status(thm)],[42])).
% 0.45/0.54 tff(44,plain,
% 0.45/0.54 (aNaturalNumber0(xp)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[43, 41])).
% 0.45/0.54 tff(45,plain,
% 0.45/0.54 (^[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))))))),
% 0.45/0.54 inference(bind,[status(th)],[])).
% 0.45/0.54 tff(46,plain,
% 0.45/0.54 (![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)))))),
% 0.45/0.54 inference(quant_intro,[status(thm)],[45])).
% 0.45/0.54 tff(47,plain,
% 0.45/0.54 (^[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)))))))),
% 0.45/0.54 inference(bind,[status(th)],[])).
% 0.45/0.54 tff(48,plain,
% 0.45/0.54 (![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)))))),
% 0.45/0.54 inference(quant_intro,[status(thm)],[47])).
% 0.45/0.54 tff(49,plain,
% 0.45/0.54 (![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))))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(50,plain,
% 0.45/0.54 (^[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)))))),
% 0.45/0.54 inference(bind,[status(th)],[])).
% 0.45/0.54 tff(51,plain,
% 0.45/0.54 (![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))))),
% 0.45/0.54 inference(quant_intro,[status(thm)],[50])).
% 0.45/0.54 tff(52,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mLETotal')).
% 0.45/0.54 tff(53,plain,
% 0.45/0.54 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.45/0.54 tff(54,plain,
% 0.45/0.54 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.45/0.54 tff(55,plain,(
% 0.45/0.54 ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.45/0.54 inference(skolemize,[status(sab)],[54])).
% 0.45/0.54 tff(56,plain,
% 0.45/0.54 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.45/0.55 tff(57,plain,
% 0.45/0.55 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.45/0.55 tff(58,plain,
% 0.45/0.55 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11))))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11))))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(59,plain,
% 0.45/0.55 ((sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11)))))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11))))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(60,plain,
% 0.45/0.55 ((~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11))))) <=> (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11)))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(61,plain,
% 0.45/0.55 ((sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11)))))) <=> (sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11))))))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[60])).
% 0.45/0.55 tff(62,plain,
% 0.45/0.55 ((sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11)))))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11))))))),
% 0.45/0.55 inference(transitivity,[status(thm)],[61, 59])).
% 0.45/0.55 tff(63,plain,
% 0.45/0.55 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11))))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11)))))))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[62])).
% 0.45/0.55 tff(64,plain,
% 0.45/0.55 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11))))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11))))))),
% 0.45/0.55 inference(transitivity,[status(thm)],[63, 58])).
% 0.45/0.55 tff(65,plain,
% 0.45/0.55 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11))))))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(66,plain,
% 0.45/0.55 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11)))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.45/0.55 tff(67,plain,
% 0.45/0.55 ((~aNaturalNumber0(sdtasdt0(xr, W0!11))) | sdtlseqdt0(sdtasdt0(xr, W0!11), xp) | (~((xp = sdtasdt0(xr, W0!11)) | (~sdtlseqdt0(xp, sdtasdt0(xr, W0!11)))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[66, 57, 44])).
% 0.45/0.55 tff(68,plain,
% 0.45/0.55 (sdtlseqdt0(sdtasdt0(xr, W0!11), xp)),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[67, 40, 26])).
% 0.45/0.55 tff(69,plain,
% 0.45/0.55 (sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[68, 16])).
% 0.45/0.55 tff(70,plain,
% 0.45/0.55 ((xp = sdtsldt0(sdtasdt0(xn, xm), xp)) <=> (sdtsldt0(sdtasdt0(xn, xm), xp) = xp)),
% 0.45/0.55 inference(commutativity,[status(thm)],[])).
% 0.45/0.55 tff(71,plain,
% 0.45/0.55 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(72,plain,
% 0.45/0.55 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[71])).
% 0.45/0.55 tff(73,plain,
% 0.45/0.55 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(74,plain,
% 0.45/0.55 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[73])).
% 0.45/0.55 tff(75,plain,
% 0.45/0.55 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(76,plain,
% 0.45/0.55 (^[W0: $i] : rewrite((aNaturalNumber0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(77,plain,
% 0.45/0.55 (![W0: $i] : (aNaturalNumber0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[76])).
% 0.45/0.55 tff(78,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_AddZero')).
% 0.45/0.55 tff(79,plain,
% 0.45/0.55 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.45/0.55 tff(80,plain,
% 0.45/0.55 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.45/0.55 tff(81,plain,(
% 0.45/0.55 ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.45/0.55 inference(skolemize,[status(sab)],[80])).
% 0.45/0.55 tff(82,plain,
% 0.45/0.55 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.45/0.55 tff(83,plain,
% 0.45/0.55 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.45/0.55 tff(84,plain,
% 0.45/0.55 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aNaturalNumber0(xp)) | (~((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aNaturalNumber0(xp)) | (~((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp))))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(85,plain,
% 0.45/0.55 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aNaturalNumber0(xp)) | (~((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp))))))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(86,plain,
% 0.45/0.55 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aNaturalNumber0(xp)) | (~((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp)))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.45/0.55 tff(87,plain,
% 0.45/0.55 (~((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[86, 83, 44])).
% 0.45/0.55 tff(88,plain,
% 0.45/0.55 (((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp)))) | (sdtpldt0(xp, sz00) = xp)),
% 0.45/0.55 inference(tautology,[status(thm)],[])).
% 0.45/0.55 tff(89,plain,
% 0.45/0.55 (sdtpldt0(xp, sz00) = xp),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.45/0.55 tff(90,plain,
% 0.45/0.55 ((sdtpldt0(xp, sz00) = sdtsldt0(sdtasdt0(xn, xm), xp)) <=> (xp = sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[89])).
% 0.45/0.55 tff(91,plain,
% 0.45/0.55 ((sdtpldt0(xp, sz00) = sdtsldt0(sdtasdt0(xn, xm), xp)) <=> (sdtsldt0(sdtasdt0(xn, xm), xp) = xp)),
% 0.45/0.55 inference(transitivity,[status(thm)],[90, 70])).
% 0.45/0.55 tff(92,plain,
% 0.45/0.55 ((~(sdtpldt0(xp, sz00) = sdtsldt0(sdtasdt0(xn, xm), xp))) <=> (~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[91])).
% 0.45/0.55 tff(93,plain,
% 0.45/0.55 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(94,plain,
% 0.45/0.55 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[93])).
% 0.45/0.55 tff(95,plain,
% 0.45/0.55 (^[W0: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))) <=> (~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))) <=> (~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))))))), rewrite((~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(96,plain,
% 0.45/0.55 (![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[95])).
% 0.45/0.55 tff(97,plain,
% 0.45/0.55 ((~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))) <=> (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(98,plain,
% 0.45/0.55 ((~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xk))) <=> (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(99,plain,
% 0.45/0.55 ((~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xk))) <=> (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xk)))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(100,plain,
% 0.45/0.55 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xk))),
% 0.45/0.56 inference(or_elim,[status(thm)],[34])).
% 0.45/0.56 tff(101,plain,
% 0.45/0.56 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xk))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.45/0.56 tff(102,plain,
% 0.45/0.56 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xk))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[101, 99])).
% 0.45/0.56 tff(103,plain,
% 0.45/0.56 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xk))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.45/0.56 tff(104,plain,
% 0.45/0.56 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[103, 98])).
% 0.45/0.56 tff(105,plain,
% 0.45/0.56 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.45/0.56 tff(106,plain,
% 0.45/0.56 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[105, 97])).
% 0.45/0.56 tff(107,plain,
% 0.45/0.56 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[106, 97])).
% 0.45/0.56 tff(108,plain,
% 0.45/0.56 (^[W0: $i] : refl($oeq((~(aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp)))), (~(aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(109,plain,(
% 0.45/0.56 ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))),
% 0.45/0.56 inference(nnf-neg,[status(sab)],[107, 108])).
% 0.45/0.56 tff(110,plain,
% 0.45/0.56 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[109, 96])).
% 0.45/0.56 tff(111,plain,
% 0.45/0.56 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[110, 94])).
% 0.45/0.56 tff(112,plain,
% 0.45/0.56 (aNaturalNumber0(sz00) <=> aNaturalNumber0(sz00)),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(113,axiom,(aNaturalNumber0(sz00)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsC')).
% 0.45/0.56 tff(114,plain,
% 0.45/0.56 (aNaturalNumber0(sz00)),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.45/0.56 tff(115,plain,
% 0.45/0.56 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))) | ((~aNaturalNumber0(sz00)) | (~(sdtpldt0(xp, sz00) = sdtsldt0(sdtasdt0(xn, xm), xp))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))) | (~aNaturalNumber0(sz00)) | (~(sdtpldt0(xp, sz00) = sdtsldt0(sdtasdt0(xn, xm), xp))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(116,plain,
% 0.45/0.56 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))) | ((~aNaturalNumber0(sz00)) | (~(sdtpldt0(xp, sz00) = sdtsldt0(sdtasdt0(xn, xm), xp))))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(117,plain,
% 0.45/0.56 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xp, W0) = sdtsldt0(sdtasdt0(xn, xm), xp))))) | (~aNaturalNumber0(sz00)) | (~(sdtpldt0(xp, sz00) = sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.45/0.56 tff(118,plain,
% 0.45/0.56 (~(sdtpldt0(xp, sz00) = sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[117, 114, 111])).
% 0.45/0.56 tff(119,plain,
% 0.45/0.56 (~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp)),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[118, 92])).
% 0.45/0.56 tff(120,plain,
% 0.45/0.56 (((sdtsldt0(sdtasdt0(xn, xm), xp) = xp) | (~(sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))))) <=> ((sdtsldt0(sdtasdt0(xn, xm), xp) = xp) | (~(sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(121,plain,
% 0.45/0.56 (((sdtsldt0(sdtasdt0(xn, xm), xp) = xp) | (~(sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))))) <=> ((sdtsldt0(sdtasdt0(xn, xm), xp) = xp) | (~(sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(122,plain,
% 0.45/0.56 (((~sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) & ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))) <=> (~(sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(123,plain,
% 0.45/0.56 (^[W0: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)) <=> (~((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))), ((~(aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))) <=> (~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))))), rewrite((~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))), ((~(aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(124,plain,
% 0.45/0.56 (![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))),
% 0.45/0.56 inference(quant_intro,[status(thm)],[123])).
% 0.45/0.56 tff(125,plain,
% 0.45/0.56 (((~sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))) <=> ((~sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) & ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[124])).
% 0.45/0.56 tff(126,plain,
% 0.45/0.56 (((~sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))) <=> (~(sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))))),
% 0.45/0.56 inference(transitivity,[status(thm)],[125, 122])).
% 0.45/0.56 tff(127,plain,
% 0.45/0.56 (((sdtsldt0(sdtasdt0(xn, xm), xp) = xp) | ((~sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))) <=> ((sdtsldt0(sdtasdt0(xn, xm), xp) = xp) | (~(sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))))))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[126])).
% 0.45/0.56 tff(128,plain,
% 0.45/0.56 (((sdtsldt0(sdtasdt0(xn, xm), xp) = xp) | ((~sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))) <=> ((sdtsldt0(sdtasdt0(xn, xm), xp) = xp) | (~(sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))))))),
% 0.45/0.56 inference(transitivity,[status(thm)],[127, 121])).
% 0.45/0.56 tff(129,plain,
% 0.45/0.56 (((~(~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp))) | ((~sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))) <=> ((sdtsldt0(sdtasdt0(xn, xm), xp) = xp) | ((~sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(130,plain,
% 0.45/0.56 ((sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))) <=> (sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(131,plain,
% 0.48/0.57 (((~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp)) & (sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))) <=> ((~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp)) & (sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[130])).
% 0.48/0.57 tff(132,plain,
% 0.48/0.57 ((~((~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp)) & (sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))) <=> (~((~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp)) & (sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[131])).
% 0.48/0.57 tff(133,plain,
% 0.48/0.57 ((~((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp))))) <=> (~((~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp)) & (sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp)))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(134,plain,
% 0.48/0.57 ((sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp))) <=> (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp)))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(135,plain,
% 0.48/0.57 (((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp)))) <=> ((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[134])).
% 0.48/0.57 tff(136,plain,
% 0.48/0.57 ((~((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp))))) <=> (~((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp)))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[135])).
% 0.48/0.57 tff(137,plain,
% 0.48/0.57 ((~((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp))))) <=> (~((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp)))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(138,plain,
% 0.48/0.57 (~((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp))))),
% 0.48/0.57 inference(or_elim,[status(thm)],[34])).
% 0.48/0.57 tff(139,plain,
% 0.48/0.57 (~((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp))))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[138, 136])).
% 0.48/0.57 tff(140,plain,
% 0.48/0.57 (~((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp))))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[139, 137])).
% 0.48/0.57 tff(141,plain,
% 0.48/0.57 (~((~(xk = xp)) & (sdtlseqdt0(xk, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xk, W0) = xp))))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.48/0.57 tff(142,plain,
% 0.48/0.57 (~((~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp)) & (sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[141, 133])).
% 0.48/0.57 tff(143,plain,
% 0.48/0.57 (~((~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp)) & (sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.48/0.57 tff(144,plain,
% 0.48/0.57 (~((~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp)) & (sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[143, 132])).
% 0.48/0.57 tff(145,plain,
% 0.48/0.57 (~((~(sdtsldt0(sdtasdt0(xn, xm), xp) = xp)) & (sdtlseqdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(sdtasdt0(xn, xm), xp), W0) = xp))))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[144, 132])).
% 0.48/0.57 unexpected number of arguments: (let ((a!1 (not (= (sdtsldt0 (sdtasdt0 xn xm) xp) xp)))
% 0.48/0.57 (a!2 (not (sdtlseqdt0 (sdtsldt0 (sdtasdt0 xn xm) xp) xp)))
% 0.48/0.57 (a!3 (exists ((W0 $i))
% 0.48/0.57 (let ((a!1 (= (sdtpldt0 (sdtsldt0 (sdtasdt0 xn xm) xp) W0) xp)))
% 0.48/0.57 (and (aNaturalNumber0 W0) a!1))))
% 0.48/0.57 (a!4 (forall ((W0 $i))
% 0.48/0.57 (let ((a!1 (= (sdtpldt0 (sdtsldt0 (sdtasdt0 xn xm) xp) W0) xp)))
% 0.48/0.57 (not (and (aNaturalNumber0 W0) a!1))))))
% 0.48/0.57 (let ((a!5 (nnf-neg (proof-bind (lambda ((W0 $i))
% 0.48/0.57 (let ((a!1 (= (sdtpldt0 (sdtsldt0 (sdtasdt0 xn
% 0.48/0.57 xm)
% 0.48/0.57 xp)
% 0.48/0.57 W0)
% 0.48/0.57 xp)))
% 0.48/0.57 (let ((a!2 (~ (not (and (aNaturalNumber0 W0)
% 0.48/0.57 a!1))
% 0.48/0.57 (not (and (aNaturalNumber0 W0)
% 0.48/0.57 a!1)))))
% 0.48/0.57 (refl a!2)))))
% 0.48/0.57 (~ (not a!3) a!4)))
% 0.48/0.57 (a!6 (or (sdtlseqdt0 (sdtsldt0 (sdtasdt0 xn xm) xp) xp) a!3)))
% 0.48/0.57 (nnf-neg (refl (~ (not a!1) (not a!1)))
% 0.48/0.57 (nnf-neg (refl (~ a!2 a!2)) a!5 (~ (not a!6) (and a!2 a!4)))
% 0.48/0.57 (~ (not (and a!1 a!6)) (or (not a!1) (and a!2 a!4))))))
% 0.48/0.57 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------