TSTP Solution File: NUM504+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM504+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 13:10:07 EDT 2022
% Result : Theorem 0.49s 0.63s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM504+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Sep 2 11:10:01 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.49/0.63 % SZS status Theorem
% 0.49/0.63 % SZS output start Proof
% 0.49/0.63 tff(sdtlseqdt0_type, type, (
% 0.49/0.63 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.49/0.63 tff(sdtasdt0_type, type, (
% 0.49/0.63 sdtasdt0: ( $i * $i ) > $i)).
% 0.49/0.63 tff(tptp_fun_W0_8_type, type, (
% 0.49/0.63 tptp_fun_W0_8: $i)).
% 0.49/0.63 tff(xp_type, type, (
% 0.49/0.63 xp: $i)).
% 0.49/0.63 tff(xm_type, type, (
% 0.49/0.63 xm: $i)).
% 0.49/0.63 tff(xn_type, type, (
% 0.49/0.63 xn: $i)).
% 0.49/0.63 tff(aNaturalNumber0_type, type, (
% 0.49/0.63 aNaturalNumber0: $i > $o)).
% 0.49/0.63 tff(isPrime0_type, type, (
% 0.49/0.63 isPrime0: $i > $o)).
% 0.49/0.63 tff(sz10_type, type, (
% 0.49/0.63 sz10: $i)).
% 0.49/0.63 tff(doDivides0_type, type, (
% 0.49/0.63 doDivides0: ( $i * $i ) > $o)).
% 0.49/0.63 tff(sz00_type, type, (
% 0.49/0.63 sz00: $i)).
% 0.49/0.63 tff(sdtsldt0_type, type, (
% 0.49/0.63 sdtsldt0: ( $i * $i ) > $i)).
% 0.49/0.63 tff(xk_type, type, (
% 0.49/0.63 xk: $i)).
% 0.49/0.63 tff(sdtpldt0_type, type, (
% 0.49/0.63 sdtpldt0: ( $i * $i ) > $i)).
% 0.49/0.63 tff(1,plain,
% 0.49/0.63 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(2,axiom,((((((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtasdt0(xn, xm))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1860')).
% 0.49/0.63 tff(3,plain,
% 0.49/0.63 (((((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.49/0.63 inference(and_elim,[status(thm)],[2])).
% 0.49/0.63 tff(4,plain,
% 0.49/0.63 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.49/0.63 inference(and_elim,[status(thm)],[3])).
% 0.49/0.63 tff(5,plain,
% 0.49/0.63 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.49/0.63 tff(6,plain,(
% 0.49/0.63 aNaturalNumber0(W0!8) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0!8))),
% 0.49/0.63 inference(skolemize,[status(sab)],[5])).
% 0.49/0.63 tff(7,plain,
% 0.49/0.63 (sdtasdt0(xn, xm) = sdtasdt0(xp, W0!8)),
% 0.49/0.63 inference(and_elim,[status(thm)],[6])).
% 0.49/0.63 tff(8,plain,
% 0.49/0.63 (sdtasdt0(xp, W0!8) = sdtasdt0(xn, xm)),
% 0.49/0.63 inference(symmetry,[status(thm)],[7])).
% 0.49/0.63 tff(9,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8)) <=> sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xn, xm))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[8])).
% 0.49/0.63 tff(10,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xn, xm)) <=> sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))),
% 0.49/0.63 inference(symmetry,[status(thm)],[9])).
% 0.49/0.63 tff(11,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))) <=> sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xn, xm))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(12,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk)) <=> sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(13,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk)) <=> sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(14,axiom,((((((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xn, xm), W0) = sdtasdt0(xp, xm)))) & sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) & (~(sdtasdt0(xp, xm) = sdtasdt0(xp, xk)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xp, xm), W0) = sdtasdt0(xp, xk)))) & sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2414')).
% 0.49/0.63 tff(15,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk))),
% 0.49/0.63 inference(and_elim,[status(thm)],[14])).
% 0.49/0.63 tff(16,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.49/0.63 tff(17,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.49/0.63 tff(18,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xn, xm))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.49/0.63 tff(19,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.49/0.63 tff(20,plain,
% 0.49/0.63 ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) <=> (sdtasdt0(xn, xm) = sdtasdt0(xp, xm))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[8])).
% 0.49/0.63 tff(21,plain,
% 0.49/0.63 ((sdtasdt0(xn, xm) = sdtasdt0(xp, xm)) <=> (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm))),
% 0.49/0.63 inference(symmetry,[status(thm)],[20])).
% 0.49/0.63 tff(22,plain,
% 0.49/0.63 ((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) <=> (~(sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[21])).
% 0.49/0.63 tff(23,plain,
% 0.49/0.63 ((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) <=> (~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(24,plain,
% 0.49/0.63 (((((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xn, xm), W0) = sdtasdt0(xp, xm)))) & sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) & (~(sdtasdt0(xp, xm) = sdtasdt0(xp, xk)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xp, xm), W0) = sdtasdt0(xp, xk)))),
% 0.49/0.63 inference(and_elim,[status(thm)],[14])).
% 0.49/0.63 tff(25,plain,
% 0.49/0.63 ((((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xn, xm), W0) = sdtasdt0(xp, xm)))) & sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) & (~(sdtasdt0(xp, xm) = sdtasdt0(xp, xk)))),
% 0.49/0.63 inference(and_elim,[status(thm)],[24])).
% 0.49/0.63 tff(26,plain,
% 0.49/0.63 (((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xn, xm), W0) = sdtasdt0(xp, xm)))) & sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.49/0.63 inference(and_elim,[status(thm)],[25])).
% 0.49/0.63 tff(27,plain,
% 0.49/0.63 ((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xn, xm), W0) = sdtasdt0(xp, xm)))),
% 0.49/0.63 inference(and_elim,[status(thm)],[26])).
% 0.49/0.63 tff(28,plain,
% 0.49/0.63 (~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))),
% 0.49/0.63 inference(and_elim,[status(thm)],[27])).
% 0.49/0.63 tff(29,plain,
% 0.49/0.63 (~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.49/0.63 tff(30,plain,
% 0.49/0.63 (~(sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.49/0.63 tff(31,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm)) <=> sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[8])).
% 0.49/0.63 tff(32,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)) <=> sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))),
% 0.49/0.63 inference(symmetry,[status(thm)],[31])).
% 0.49/0.63 tff(33,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)) <=> sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(34,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.49/0.63 inference(and_elim,[status(thm)],[26])).
% 0.49/0.63 tff(35,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.49/0.63 tff(36,plain,
% 0.49/0.63 (sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.49/0.63 tff(37,plain,
% 0.49/0.63 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(38,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1837')).
% 0.49/0.63 tff(39,plain,
% 0.49/0.63 (aNaturalNumber0(xp)),
% 0.49/0.63 inference(and_elim,[status(thm)],[38])).
% 0.49/0.63 tff(40,plain,
% 0.49/0.63 (aNaturalNumber0(xp)),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[39, 37])).
% 0.49/0.63 tff(41,plain,
% 0.49/0.63 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(42,plain,
% 0.49/0.63 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 0.49/0.63 inference(and_elim,[status(thm)],[38])).
% 0.49/0.63 tff(43,plain,
% 0.49/0.63 (aNaturalNumber0(xm)),
% 0.49/0.63 inference(and_elim,[status(thm)],[42])).
% 0.49/0.63 tff(44,plain,
% 0.49/0.63 (aNaturalNumber0(xm)),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[43, 41])).
% 0.49/0.63 tff(45,plain,
% 0.49/0.63 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.63/0.63 inference(bind,[status(th)],[])).
% 0.63/0.63 tff(46,plain,
% 0.63/0.63 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.63/0.63 inference(quant_intro,[status(thm)],[45])).
% 0.63/0.63 tff(47,plain,
% 0.63/0.63 (^[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)))))),
% 0.63/0.63 inference(bind,[status(th)],[])).
% 0.63/0.63 tff(48,plain,
% 0.63/0.63 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.63/0.63 inference(quant_intro,[status(thm)],[47])).
% 0.63/0.63 tff(49,plain,
% 0.63/0.63 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.63/0.63 inference(rewrite,[status(thm)],[])).
% 0.63/0.63 tff(50,plain,
% 0.63/0.63 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.63/0.63 inference(bind,[status(th)],[])).
% 0.63/0.63 tff(51,plain,
% 0.63/0.63 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.63/0.63 inference(quant_intro,[status(thm)],[50])).
% 0.63/0.63 tff(52,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB_02')).
% 0.63/0.63 tff(53,plain,
% 0.63/0.63 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.63/0.63 tff(54,plain,
% 0.63/0.63 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.63/0.63 tff(55,plain,(
% 0.63/0.63 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.63/0.63 inference(skolemize,[status(sab)],[54])).
% 0.63/0.63 tff(56,plain,
% 0.63/0.63 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.63/0.63 tff(57,plain,
% 0.63/0.63 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.63/0.63 tff(58,plain,
% 0.63/0.63 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)))),
% 0.63/0.63 inference(rewrite,[status(thm)],[])).
% 0.63/0.63 tff(59,plain,
% 0.63/0.63 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)))),
% 0.63/0.63 inference(quant_inst,[status(thm)],[])).
% 0.63/0.63 tff(60,plain,
% 0.63/0.63 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.63/0.63 tff(61,plain,
% 0.63/0.63 (aNaturalNumber0(sdtasdt0(xp, xm))),
% 0.63/0.63 inference(unit_resolution,[status(thm)],[60, 57, 44, 40])).
% 0.63/0.63 tff(62,plain,
% 0.63/0.63 (aNaturalNumber0(W0!8)),
% 0.63/0.63 inference(and_elim,[status(thm)],[6])).
% 0.63/0.63 tff(63,plain,
% 0.63/0.63 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(xp)))),
% 0.63/0.63 inference(rewrite,[status(thm)],[])).
% 0.63/0.63 tff(64,plain,
% 0.63/0.63 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(xp)))),
% 0.63/0.63 inference(quant_inst,[status(thm)],[])).
% 0.63/0.63 tff(65,plain,
% 0.63/0.63 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(xp))),
% 0.63/0.63 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.63/0.63 tff(66,plain,
% 0.63/0.63 (aNaturalNumber0(sdtasdt0(xp, W0!8))),
% 0.63/0.63 inference(unit_resolution,[status(thm)],[65, 57, 40, 62])).
% 0.63/0.63 tff(67,plain,
% 0.63/0.63 (^[W0: $i, W1: $i] : refl(((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0))) <=> ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0))))),
% 0.63/0.63 inference(bind,[status(th)],[])).
% 0.63/0.63 tff(68,plain,
% 0.63/0.63 (![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.63/0.63 inference(quant_intro,[status(thm)],[67])).
% 0.63/0.63 tff(69,plain,
% 0.63/0.63 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), trans(monotonicity(rewrite((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) <=> (~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> (~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))))), rewrite((~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), (((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))))), rewrite(((W0 = W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))), (((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(70,plain,
% 0.63/0.64 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[69])).
% 0.63/0.64 tff(71,plain,
% 0.63/0.64 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(72,plain,
% 0.63/0.64 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)) <=> ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))) <=> ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(73,plain,
% 0.63/0.64 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[72])).
% 0.63/0.64 tff(74,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mLEAsym')).
% 0.63/0.64 tff(75,plain,
% 0.63/0.64 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.63/0.64 tff(76,plain,
% 0.63/0.64 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.63/0.64 tff(77,plain,(
% 0.63/0.64 ![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.63/0.64 inference(skolemize,[status(sab)],[76])).
% 0.63/0.64 tff(78,plain,
% 0.63/0.64 (![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.63/0.64 tff(79,plain,
% 0.63/0.64 (![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.63/0.64 tff(80,plain,
% 0.63/0.64 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(81,plain,
% 0.63/0.64 (((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8)))) <=> ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(82,plain,
% 0.63/0.65 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm)))))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[81])).
% 0.63/0.65 tff(83,plain,
% 0.63/0.65 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm))))),
% 0.63/0.65 inference(transitivity,[status(thm)],[82, 80])).
% 0.63/0.65 tff(84,plain,
% 0.63/0.65 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(85,plain,
% 0.63/0.65 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.63/0.65 tff(86,plain,
% 0.63/0.65 ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8)))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[85, 79, 66, 61])).
% 0.63/0.65 tff(87,plain,
% 0.63/0.65 ($false),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[86, 36, 30, 19])).
% 0.63/0.65 % SZS output end Proof
%------------------------------------------------------------------------------