TSTP Solution File: NUM465+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM465+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 13:09:52 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM465+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n002.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 Sep 2 10:59:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(sdtasdt0_type, type, (
% 0.21/0.42 sdtasdt0: ( $i * $i ) > $i)).
% 0.21/0.42 tff(xm_type, type, (
% 0.21/0.42 xm: $i)).
% 0.21/0.42 tff(xn_type, type, (
% 0.21/0.42 xn: $i)).
% 0.21/0.42 tff(sdtpldt0_type, type, (
% 0.21/0.42 sdtpldt0: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_W0_1_type, type, (
% 0.21/0.42 tptp_fun_W0_1: $i)).
% 0.21/0.42 tff(aNaturalNumber0_type, type, (
% 0.21/0.42 aNaturalNumber0: $i > $o)).
% 0.21/0.42 tff(sz10_type, type, (
% 0.21/0.42 sz10: $i)).
% 0.21/0.42 tff(sdtlseqdt0_type, type, (
% 0.21/0.42 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.21/0.42 tff(sz00_type, type, (
% 0.21/0.42 sz00: $i)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(2,axiom,(aNaturalNumber0(xm) & aNaturalNumber0(xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__987')).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (aNaturalNumber0(xn)),
% 0.21/0.42 inference(and_elim,[status(thm)],[2])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (aNaturalNumber0(xn)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (aNaturalNumber0(xm)),
% 0.21/0.42 inference(and_elim,[status(thm)],[2])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (aNaturalNumber0(xm)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (^[W0: $i, W1: $i] : refl(((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.42 tff(15,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulComm')).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.42 tff(18,plain,(
% 0.21/0.42 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[17])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(xm)) | (sdtasdt0(xm, xn) = sdtasdt0(xn, xm)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xm)) | (sdtasdt0(xm, xn) = sdtasdt0(xn, xm)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (((sdtasdt0(xm, xn) = sdtasdt0(xn, xm)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xm))) <=> ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(xm)) | (sdtasdt0(xm, xn) = sdtasdt0(xn, xm)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xm, xn) = sdtasdt0(xn, xm)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xm)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(xm)) | (sdtasdt0(xm, xn) = sdtasdt0(xn, xm))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xm, xn) = sdtasdt0(xn, xm)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xm)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xm)) | (sdtasdt0(xm, xn) = sdtasdt0(xn, xm)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[23, 21])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xm, xn) = sdtasdt0(xn, xm)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xm)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xm)) | (sdtasdt0(xm, xn) = sdtasdt0(xn, xm))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (sdtasdt0(xm, xn) = sdtasdt0(xn, xm)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[26, 20, 7, 4])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (($false | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))) <=> (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 ((?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm)) <=> (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 ((~((~(xm = sz00)) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm))) | sdtlseqdt0(xn, sdtasdt0(xn, xm))))) <=> (~((xm = sz00) | sdtlseqdt0(xn, sdtasdt0(xn, xm)) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(32,axiom,(~((~(xm = sz00)) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm))) | sdtlseqdt0(xn, sdtasdt0(xn, xm))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (~((xm = sz00) | sdtlseqdt0(xn, sdtasdt0(xn, xm)) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (~(xm = sz00)),
% 0.21/0.42 inference(or_elim,[status(thm)],[33])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 ((xm = sz00) <=> $false),
% 0.21/0.42 inference(iff_false,[status(thm)],[34])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (((xm = sz00) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))) <=> ($false | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[35, 30])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (((xm = sz00) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))) <=> (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))),
% 0.21/0.42 inference(transitivity,[status(thm)],[36, 29])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (((xm = sz00) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))) <=> ((xm = sz00) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[30])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (((~(xm = sz00)) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))) <=> ((xm = sz00) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (((~(xm = sz00)) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))) <=> ((~(xm = sz00)) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[30])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (((~(xm = sz00)) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))) <=> ((xm = sz00) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[40, 39])).
% 0.21/0.42 tff(42,axiom,((~(xm = sz00)) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1007')).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 ((xm = sz00) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 ((xm = sz00) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm)) & sdtlseqdt0(sz10, xm)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm))),
% 0.21/0.42 inference(and_elim,[status(thm)],[45])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sz10, W0) = xm))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[46, 28])).
% 0.21/0.42 tff(48,plain,(
% 0.21/0.42 aNaturalNumber0(W0!1) & (sdtpldt0(sz10, W0!1) = xm)),
% 0.21/0.42 inference(skolemize,[status(sab)],[47])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (sdtpldt0(sz10, W0!1) = xm),
% 0.21/0.42 inference(and_elim,[status(thm)],[48])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (sdtasdt0(sdtpldt0(sz10, W0!1), xn) = sdtasdt0(xm, xn)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[49])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (aNaturalNumber0(W0!1)),
% 0.21/0.42 inference(and_elim,[status(thm)],[48])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (^[W0: $i, W1: $i, W2: $i] : refl(((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (^[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, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))) <=> (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.43 tff(59,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAMDistr')).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.21/0.43 tff(62,plain,(
% 0.21/0.43 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[61])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (aNaturalNumber0(sz10) <=> aNaturalNumber0(sz10)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(66,axiom,(aNaturalNumber0(sz10) & (~(sz10 = sz00))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsC_01')).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (aNaturalNumber0(sz10)),
% 0.21/0.43 inference(and_elim,[status(thm)],[66])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (aNaturalNumber0(sz10)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))) | ((~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(sz10)) | (~aNaturalNumber0(xn)) | (~((~(sdtasdt0(xn, sdtpldt0(sz10, W0!1)) = sdtpldt0(sdtasdt0(xn, sz10), sdtasdt0(xn, W0!1)))) | (~(sdtasdt0(sdtpldt0(sz10, W0!1), xn) = sdtpldt0(sdtasdt0(sz10, xn), sdtasdt0(W0!1, xn)))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(sz10)) | (~aNaturalNumber0(xn)) | (~((~(sdtasdt0(xn, sdtpldt0(sz10, W0!1)) = sdtpldt0(sdtasdt0(xn, sz10), sdtasdt0(xn, W0!1)))) | (~(sdtasdt0(sdtpldt0(sz10, W0!1), xn) = sdtpldt0(sdtasdt0(sz10, xn), sdtasdt0(W0!1, xn)))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))) | ((~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(sz10)) | (~aNaturalNumber0(xn)) | (~((~(sdtasdt0(xn, sdtpldt0(sz10, W0!1)) = sdtpldt0(sdtasdt0(xn, sz10), sdtasdt0(xn, W0!1)))) | (~(sdtasdt0(sdtpldt0(sz10, W0!1), xn) = sdtpldt0(sdtasdt0(sz10, xn), sdtasdt0(W0!1, xn)))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W1, W2), W0) = sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0)))))))) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(sz10)) | (~aNaturalNumber0(xn)) | (~((~(sdtasdt0(xn, sdtpldt0(sz10, W0!1)) = sdtpldt0(sdtasdt0(xn, sz10), sdtasdt0(xn, W0!1)))) | (~(sdtasdt0(sdtpldt0(sz10, W0!1), xn) = sdtpldt0(sdtasdt0(sz10, xn), sdtasdt0(W0!1, xn))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (~((~(sdtasdt0(xn, sdtpldt0(sz10, W0!1)) = sdtpldt0(sdtasdt0(xn, sz10), sdtasdt0(xn, W0!1)))) | (~(sdtasdt0(sdtpldt0(sz10, W0!1), xn) = sdtpldt0(sdtasdt0(sz10, xn), sdtasdt0(W0!1, xn)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[71, 68, 64, 4, 51])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (((~(sdtasdt0(xn, sdtpldt0(sz10, W0!1)) = sdtpldt0(sdtasdt0(xn, sz10), sdtasdt0(xn, W0!1)))) | (~(sdtasdt0(sdtpldt0(sz10, W0!1), xn) = sdtpldt0(sdtasdt0(sz10, xn), sdtasdt0(W0!1, xn))))) | (sdtasdt0(sdtpldt0(sz10, W0!1), xn) = sdtpldt0(sdtasdt0(sz10, xn), sdtasdt0(W0!1, xn)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (sdtasdt0(sdtpldt0(sz10, W0!1), xn) = sdtpldt0(sdtasdt0(sz10, xn), sdtasdt0(W0!1, xn))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (sdtpldt0(sdtasdt0(sz10, xn), sdtasdt0(W0!1, xn)) = sdtasdt0(sdtpldt0(sz10, W0!1), xn)),
% 0.21/0.43 inference(symmetry,[status(thm)],[74])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0)))))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0)))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (^[W0: $i] : rewrite((aNaturalNumber0(W0) => ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))) <=> ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (![W0: $i] : (aNaturalNumber0(W0) => ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.43 tff(83,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_MulUnit')).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.21/0.43 tff(86,plain,(
% 0.21/0.43 ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[85])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | ((~aNaturalNumber0(xn)) | (~((~(xn = sdtasdt0(sz10, xn))) | (~(sdtasdt0(xn, sz10) = xn)))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | (~aNaturalNumber0(xn)) | (~((~(xn = sdtasdt0(sz10, xn))) | (~(sdtasdt0(xn, sz10) = xn)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (((~aNaturalNumber0(xn)) | (~((~(sdtasdt0(xn, sz10) = xn)) | (~(xn = sdtasdt0(sz10, xn)))))) <=> ((~aNaturalNumber0(xn)) | (~((~(xn = sdtasdt0(sz10, xn))) | (~(sdtasdt0(xn, sz10) = xn)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | ((~aNaturalNumber0(xn)) | (~((~(sdtasdt0(xn, sz10) = xn)) | (~(xn = sdtasdt0(sz10, xn))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | ((~aNaturalNumber0(xn)) | (~((~(xn = sdtasdt0(sz10, xn))) | (~(sdtasdt0(xn, sz10) = xn))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | ((~aNaturalNumber0(xn)) | (~((~(sdtasdt0(xn, sz10) = xn)) | (~(xn = sdtasdt0(sz10, xn))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | (~aNaturalNumber0(xn)) | (~((~(xn = sdtasdt0(sz10, xn))) | (~(sdtasdt0(xn, sz10) = xn)))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[91, 89])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | ((~aNaturalNumber0(xn)) | (~((~(sdtasdt0(xn, sz10) = xn)) | (~(xn = sdtasdt0(sz10, xn))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | (~aNaturalNumber0(xn)) | (~((~(xn = sdtasdt0(sz10, xn))) | (~(sdtasdt0(xn, sz10) = xn))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (~((~(xn = sdtasdt0(sz10, xn))) | (~(sdtasdt0(xn, sz10) = xn)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[94, 88, 4])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (((~(xn = sdtasdt0(sz10, xn))) | (~(sdtasdt0(xn, sz10) = xn))) | (xn = sdtasdt0(sz10, xn))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (xn = sdtasdt0(sz10, xn)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (sdtpldt0(xn, sdtasdt0(W0!1, xn)) = sdtpldt0(sdtasdt0(sz10, xn), sdtasdt0(W0!1, xn))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (sdtpldt0(xn, sdtasdt0(W0!1, xn)) = sdtasdt0(xn, xm)),
% 0.21/0.43 inference(transitivity,[status(thm)],[98, 75, 50, 27])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[100])).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.44 tff(107,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB_02')).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.21/0.44 tff(110,plain,(
% 0.21/0.44 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[109])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[111, 101])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | aNaturalNumber0(sdtasdt0(W0!1, xn)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | aNaturalNumber0(sdtasdt0(W0!1, xn)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 ((aNaturalNumber0(sdtasdt0(W0!1, xn)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!1))) <=> ((~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | aNaturalNumber0(sdtasdt0(W0!1, xn)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!1, xn)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!1)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | aNaturalNumber0(sdtasdt0(W0!1, xn))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[114])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!1, xn)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!1)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | aNaturalNumber0(sdtasdt0(W0!1, xn)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[115, 113])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!1, xn)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!1)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | aNaturalNumber0(sdtasdt0(W0!1, xn))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (aNaturalNumber0(sdtasdt0(W0!1, xn))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[118, 112, 4, 51])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (^[W0: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm))) <=> (~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))) <=> (~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))))))), rewrite((~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 ((~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))) <=> (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))),
% 0.21/0.44 inference(or_elim,[status(thm)],[33])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[126, 124])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[127, 124])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[129, 124])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[130, 124])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (^[W0: $i] : refl($oeq((~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm)))), (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(134,plain,(
% 0.21/0.44 ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))),
% 0.21/0.44 inference(nnf-neg,[status(sab)],[132, 133])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[134, 123])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[135, 121])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))) | ((~aNaturalNumber0(sdtasdt0(W0!1, xn))) | (~(sdtpldt0(xn, sdtasdt0(W0!1, xn)) = sdtasdt0(xn, xm))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))) | (~aNaturalNumber0(sdtasdt0(W0!1, xn))) | (~(sdtpldt0(xn, sdtasdt0(W0!1, xn)) = sdtasdt0(xn, xm))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(138,plain,
% 0.21/0.45 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))) | ((~aNaturalNumber0(sdtasdt0(W0!1, xn))) | (~(sdtpldt0(xn, sdtasdt0(W0!1, xn)) = sdtasdt0(xn, xm))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(139,plain,
% 0.21/0.45 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = sdtasdt0(xn, xm))))) | (~aNaturalNumber0(sdtasdt0(W0!1, xn))) | (~(sdtpldt0(xn, sdtasdt0(W0!1, xn)) = sdtasdt0(xn, xm)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.45 tff(140,plain,
% 0.21/0.45 ((~aNaturalNumber0(sdtasdt0(W0!1, xn))) | (~(sdtpldt0(xn, sdtasdt0(W0!1, xn)) = sdtasdt0(xn, xm)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[139, 136])).
% 0.21/0.45 tff(141,plain,
% 0.21/0.45 (~(sdtpldt0(xn, sdtasdt0(W0!1, xn)) = sdtasdt0(xn, xm))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[140, 119])).
% 0.21/0.45 tff(142,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[141, 99])).
% 0.21/0.45 % SZS output end Proof
%------------------------------------------------------------------------------