TSTP Solution File: NUM521+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM521+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 13:10:14 EDT 2022
% Result : Theorem 0.18s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM521+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 11:22:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.33 Usage: tptp [options] [-file:]file
% 0.18/0.33 -h, -? prints this message.
% 0.18/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.33 -m, -model generate model.
% 0.18/0.33 -p, -proof generate proof.
% 0.18/0.33 -c, -core generate unsat core of named formulas.
% 0.18/0.33 -st, -statistics display statistics.
% 0.18/0.33 -t:timeout set timeout (in second).
% 0.18/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.33 -<param>:<value> configuration parameter and value.
% 0.18/0.33 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(xp_type, type, (
% 0.18/0.40 xp: $i)).
% 0.18/0.40 tff(sdtpldt0_type, type, (
% 0.18/0.40 sdtpldt0: ( $i * $i ) > $i)).
% 0.18/0.40 tff(xm_type, type, (
% 0.18/0.40 xm: $i)).
% 0.18/0.40 tff(aNaturalNumber0_type, type, (
% 0.18/0.40 aNaturalNumber0: $i > $o)).
% 0.18/0.40 tff(sdtlseqdt0_type, type, (
% 0.18/0.40 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.18/0.40 tff(xn_type, type, (
% 0.18/0.40 xn: $i)).
% 0.18/0.40 tff(1,plain,
% 0.18/0.40 ((~sdtlseqdt0(xp, xm)) <=> (~sdtlseqdt0(xp, xm))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(2,axiom,(~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xm)) | sdtlseqdt0(xp, xm))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2075')).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (~sdtlseqdt0(xp, xm)),
% 0.18/0.40 inference(or_elim,[status(thm)],[2])).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (~sdtlseqdt0(xp, xm)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.18/0.40 tff(5,plain,
% 0.18/0.40 (((~sdtlseqdt0(xp, xm)) | (xp = xm)) | sdtlseqdt0(xp, xm)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 ((~sdtlseqdt0(xp, xm)) | (xp = xm)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.18/0.40 tff(7,plain,
% 0.18/0.40 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(8,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1837')).
% 0.18/0.40 tff(9,plain,
% 0.18/0.40 (aNaturalNumber0(xp)),
% 0.18/0.40 inference(and_elim,[status(thm)],[8])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 (aNaturalNumber0(xp)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[9, 7])).
% 0.18/0.40 tff(11,plain,
% 0.18/0.40 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(12,plain,
% 0.18/0.40 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 0.18/0.40 inference(and_elim,[status(thm)],[8])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 (aNaturalNumber0(xm)),
% 0.18/0.40 inference(and_elim,[status(thm)],[12])).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 (aNaturalNumber0(xm)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[13, 11])).
% 0.18/0.40 tff(15,plain,
% 0.18/0.40 (^[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))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.40 tff(17,plain,
% 0.18/0.40 (^[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)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(20,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(21,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.18/0.40 tff(22,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mLETotal')).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.18/0.40 tff(25,plain,(
% 0.18/0.40 ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[24])).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.18/0.40 tff(27,plain,
% 0.18/0.40 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.18/0.40 tff(28,plain,
% 0.18/0.40 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(29,plain,
% 0.18/0.40 ((sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm)))) <=> (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(30,plain,
% 0.18/0.40 ((~((xp = xm) | (~sdtlseqdt0(xp, xm)))) <=> (~((~sdtlseqdt0(xp, xm)) | (xp = xm)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 ((sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xp = xm) | (~sdtlseqdt0(xp, xm))))) <=> (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[30])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 ((sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xp = xm) | (~sdtlseqdt0(xp, xm))))) <=> (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[31, 29])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xp = xm) | (~sdtlseqdt0(xp, xm)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[32])).
% 0.18/0.41 tff(34,plain,
% 0.18/0.41 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xp = xm) | (~sdtlseqdt0(xp, xm)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[33, 28])).
% 0.18/0.41 tff(35,plain,
% 0.18/0.41 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xp = xm) | (~sdtlseqdt0(xp, xm)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(36,plain,
% 0.18/0.41 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.41 tff(37,plain,
% 0.18/0.41 (sdtlseqdt0(xm, xp)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[36, 27, 14, 10, 6])).
% 0.18/0.41 tff(38,plain,
% 0.18/0.41 ((sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))) | (~sdtlseqdt0(xm, xp))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(39,plain,
% 0.18/0.41 (sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.18/0.41 tff(40,plain,
% 0.18/0.41 ((~sdtlseqdt0(xp, xn)) <=> (~sdtlseqdt0(xp, xn))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(41,axiom,(~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xn)) | sdtlseqdt0(xp, xn))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1870')).
% 0.18/0.41 tff(42,plain,
% 0.18/0.41 (~sdtlseqdt0(xp, xn)),
% 0.18/0.41 inference(or_elim,[status(thm)],[41])).
% 0.18/0.41 tff(43,plain,
% 0.18/0.41 (~sdtlseqdt0(xp, xn)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[42, 40])).
% 0.18/0.41 tff(44,plain,
% 0.18/0.41 (((~sdtlseqdt0(xp, xn)) | (xp = xn)) | sdtlseqdt0(xp, xn)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(45,plain,
% 0.18/0.41 ((~sdtlseqdt0(xp, xn)) | (xp = xn)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.18/0.41 tff(46,plain,
% 0.18/0.41 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(47,plain,
% 0.18/0.41 (aNaturalNumber0(xn)),
% 0.18/0.41 inference(and_elim,[status(thm)],[12])).
% 0.18/0.41 tff(48,plain,
% 0.18/0.41 (aNaturalNumber0(xn)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.41 tff(49,plain,
% 0.18/0.41 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(50,plain,
% 0.18/0.41 ((sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn)))) <=> (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(51,plain,
% 0.18/0.41 ((~((xp = xn) | (~sdtlseqdt0(xp, xn)))) <=> (~((~sdtlseqdt0(xp, xn)) | (xp = xn)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(52,plain,
% 0.18/0.41 ((sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xp = xn) | (~sdtlseqdt0(xp, xn))))) <=> (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[51])).
% 0.18/0.41 tff(53,plain,
% 0.18/0.41 ((sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xp = xn) | (~sdtlseqdt0(xp, xn))))) <=> (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[52, 50])).
% 0.18/0.41 tff(54,plain,
% 0.18/0.41 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xp = xn) | (~sdtlseqdt0(xp, xn)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[53])).
% 0.18/0.41 tff(55,plain,
% 0.18/0.41 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xp = xn) | (~sdtlseqdt0(xp, xn)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[54, 49])).
% 0.18/0.41 tff(56,plain,
% 0.18/0.41 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xp = xn) | (~sdtlseqdt0(xp, xn)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(57,plain,
% 0.18/0.41 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.41 tff(58,plain,
% 0.18/0.41 (sdtlseqdt0(xn, xp)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[57, 27, 48, 10, 45])).
% 0.18/0.41 tff(59,plain,
% 0.18/0.41 ((sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))) | (~sdtlseqdt0(xn, xp))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(60,plain,
% 0.18/0.41 (sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.18/0.41 tff(61,plain,
% 0.18/0.41 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(62,plain,
% 0.18/0.41 ((sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp))))) <=> (sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(63,plain,
% 0.18/0.41 ((~((xn = xp) | (~sdtlseqdt0(xn, xp)))) <=> (~((xn = xp) | (~sdtlseqdt0(xn, xp))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(64,plain,
% 0.18/0.41 ((sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp))))) <=> (sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.18/0.41 tff(65,plain,
% 0.18/0.41 ((sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp))))) <=> (sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[64, 62])).
% 0.18/0.41 tff(66,plain,
% 0.18/0.41 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[65])).
% 0.18/0.41 tff(67,plain,
% 0.18/0.41 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[66, 61])).
% 0.18/0.41 tff(68,plain,
% 0.18/0.41 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(69,plain,
% 0.18/0.41 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.18/0.41 tff(70,plain,
% 0.18/0.41 (~((xn = xp) | (~sdtlseqdt0(xn, xp)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[69, 27, 48, 10, 43])).
% 0.18/0.41 tff(71,plain,
% 0.18/0.41 (((xn = xp) | (~sdtlseqdt0(xn, xp))) | (~(xn = xp))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(72,plain,
% 0.18/0.41 (~(xn = xp)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.18/0.41 tff(73,plain,
% 0.18/0.41 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(74,plain,
% 0.18/0.41 ((sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp))))) <=> (sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(75,plain,
% 0.18/0.41 ((~((xm = xp) | (~sdtlseqdt0(xm, xp)))) <=> (~((xm = xp) | (~sdtlseqdt0(xm, xp))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 ((sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp))))) <=> (sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.18/0.41 tff(77,plain,
% 0.18/0.41 ((sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp))))) <=> (sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[76, 74])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp))))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[77])).
% 0.18/0.42 tff(79,plain,
% 0.18/0.42 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[78, 73])).
% 0.18/0.42 tff(80,plain,
% 0.18/0.42 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(81,plain,
% 0.18/0.42 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.42 tff(82,plain,
% 0.18/0.42 (~((xm = xp) | (~sdtlseqdt0(xm, xp)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[81, 27, 14, 10, 4])).
% 0.18/0.42 tff(83,plain,
% 0.18/0.42 (((xm = xp) | (~sdtlseqdt0(xm, xp))) | (~(xm = xp))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(84,plain,
% 0.18/0.42 (~(xm = xp)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.18/0.42 tff(85,plain,
% 0.18/0.42 (((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))))) <=> ((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(86,plain,
% 0.18/0.42 (((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))))) <=> ((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(87,plain,
% 0.18/0.42 (((~sdtlseqdt0(xm, xp)) & ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))) <=> (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(88,plain,
% 0.18/0.42 (^[W0: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)) <=> (~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))) <=> (~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))))), rewrite((~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(89,plain,
% 0.18/0.42 (![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[88])).
% 0.18/0.42 tff(90,plain,
% 0.18/0.42 (((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))) <=> ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[89])).
% 0.18/0.42 tff(91,plain,
% 0.18/0.42 (((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))) <=> (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[90, 87])).
% 0.18/0.42 tff(92,plain,
% 0.18/0.42 (((~sdtlseqdt0(xn, xp)) & ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))) <=> (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(93,plain,
% 0.18/0.42 (^[W0: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)) <=> (~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) <=> (~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))))), rewrite((~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(94,plain,
% 0.18/0.42 (![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[93])).
% 0.18/0.42 tff(95,plain,
% 0.18/0.42 (((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) <=> ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[94])).
% 0.18/0.42 tff(96,plain,
% 0.18/0.42 (((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) <=> (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[95, 92])).
% 0.18/0.42 tff(97,plain,
% 0.18/0.42 (((xn = xp) | (xm = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> ((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[96, 91])).
% 0.18/0.42 tff(98,plain,
% 0.18/0.42 (((xn = xp) | (xm = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> ((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[97, 86])).
% 0.18/0.42 tff(99,plain,
% 0.18/0.42 (((xn = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | (xm = xp) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> ((xn = xp) | (xm = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(100,plain,
% 0.18/0.42 (((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))) <=> ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(101,plain,
% 0.18/0.42 ((~(~(xm = xp))) <=> (xm = xp)),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(102,plain,
% 0.18/0.42 (((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) <=> ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(103,plain,
% 0.18/0.42 ((~(~(xn = xp))) <=> (xn = xp)),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(104,plain,
% 0.18/0.42 (((~(~(xn = xp))) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | (~(~(xm = xp))) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> ((xn = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | (xm = xp) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[103, 102, 101, 100])).
% 0.18/0.42 tff(105,plain,
% 0.18/0.42 (((~(~(xn = xp))) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | (~(~(xm = xp))) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> ((xn = xp) | (xm = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[104, 99])).
% 0.18/0.42 tff(106,plain,
% 0.18/0.42 ((sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))) <=> (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(107,plain,
% 0.18/0.42 ((sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) <=> (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(108,plain,
% 0.18/0.42 (((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))) <=> ((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[107, 106])).
% 0.18/0.42 tff(109,plain,
% 0.18/0.42 ((~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[108])).
% 0.18/0.42 tff(110,plain,
% 0.18/0.42 ((~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(111,plain,
% 0.18/0.42 ((~((((~(xn = xp)) & (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)) | sdtlseqdt0(xn, xp))) & (~(xm = xp))) & (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)) | sdtlseqdt0(xm, xp)))) <=> (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(112,axiom,(~((((~(xn = xp)) & (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)) | sdtlseqdt0(xn, xp))) & (~(xm = xp))) & (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)) | sdtlseqdt0(xm, xp)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2287')).
% 0.18/0.42 tff(113,plain,
% 0.18/0.42 (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.18/0.42 tff(114,plain,
% 0.18/0.42 (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.18/0.43 tff(115,plain,
% 0.18/0.43 (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.18/0.43 tff(116,plain,
% 0.18/0.43 (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[115, 109])).
% 0.18/0.43 tff(117,plain,
% 0.18/0.43 (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.18/0.43 tff(118,plain,
% 0.18/0.43 (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[117, 109])).
% 0.18/0.43 tff(119,plain,
% 0.18/0.43 (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[118, 109])).
% 0.18/0.43 unexpected number of arguments: (let ((a!1 (~ (not (not (= xn xp))) (not (not (= xn xp)))))
% 0.18/0.43 (a!2 (refl (~ (not (sdtlseqdt0 xn xp)) (not (sdtlseqdt0 xn xp)))))
% 0.18/0.43 (a!3 (proof-bind (lambda ((W0 $i))
% 0.18/0.43 (let ((a!1 (not (and (aNaturalNumber0 W0)
% 0.18/0.43 (= (sdtpldt0 xn W0) xp)))))
% 0.18/0.43 (refl (~ a!1 a!1))))))
% 0.18/0.43 (a!4 (exists ((W0 $i)) (and (aNaturalNumber0 W0) (= (sdtpldt0 xn W0) xp))))
% 0.18/0.43 (a!5 (forall ((W0 $i))
% 0.18/0.43 (not (and (aNaturalNumber0 W0) (= (sdtpldt0 xn W0) xp)))))
% 0.18/0.43 (a!8 (~ (not (not (= xm xp))) (not (not (= xm xp)))))
% 0.18/0.43 (a!9 (refl (~ (not (sdtlseqdt0 xm xp)) (not (sdtlseqdt0 xm xp)))))
% 0.18/0.43 (a!10 (proof-bind (lambda ((W0 $i))
% 0.18/0.43 (let ((a!1 (not (and (aNaturalNumber0 W0)
% 0.18/0.43 (= (sdtpldt0 xm W0) xp)))))
% 0.18/0.43 (refl (~ a!1 a!1))))))
% 0.18/0.43 (a!11 (exists ((W0 $i))
% 0.18/0.43 (and (aNaturalNumber0 W0) (= (sdtpldt0 xm W0) xp))))
% 0.18/0.43 (a!12 (forall ((W0 $i))
% 0.18/0.43 (not (and (aNaturalNumber0 W0) (= (sdtpldt0 xm W0) xp))))))
% 0.18/0.43 (let ((a!6 (~ (not (or (sdtlseqdt0 xn xp) a!4))
% 0.18/0.43 (and (not (sdtlseqdt0 xn xp)) a!5)))
% 0.18/0.43 (a!13 (~ (not (or (sdtlseqdt0 xm xp) a!11))
% 0.18/0.43 (and (not (sdtlseqdt0 xm xp)) a!12)))
% 0.18/0.43 (a!15 (not (and (not (= xn xp))
% 0.18/0.43 (or (sdtlseqdt0 xn xp) a!4)
% 0.18/0.43 (not (= xm xp))
% 0.18/0.43 (or (sdtlseqdt0 xm xp) a!11))))
% 0.18/0.43 (a!16 (or (not (not (= xn xp)))
% 0.18/0.43 (and (not (sdtlseqdt0 xn xp)) a!5)
% 0.18/0.43 (not (not (= xm xp)))
% 0.18/0.43 (and (not (sdtlseqdt0 xm xp)) a!12))))
% 0.18/0.43 (let ((a!7 (nnf-neg a!2 (nnf-neg a!3 (~ (not a!4) a!5)) a!6))
% 0.18/0.43 (a!14 (nnf-neg a!9 (nnf-neg a!10 (~ (not a!11) a!12)) a!13)))
% 0.18/0.43 (nnf-neg (refl a!1) a!7 (refl a!8) a!14 (~ a!15 a!16)))))
% 0.18/0.43 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------