TSTP Solution File: NUM511+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM511+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 13:10:10 EDT 2022
% Result : Theorem 24.98s 16.37s
% Output : Proof 25.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM511+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Sep 2 11:19:46 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 24.98/16.37 % SZS status Theorem
% 24.98/16.37 % SZS output start Proof
% 24.98/16.37 tff(sdtasdt0_type, type, (
% 24.98/16.37 sdtasdt0: ( $i * $i ) > $i)).
% 24.98/16.37 tff(tptp_fun_W0_11_type, type, (
% 24.98/16.37 tptp_fun_W0_11: $i)).
% 24.98/16.37 tff(xp_type, type, (
% 24.98/16.37 xp: $i)).
% 24.98/16.37 tff(xm_type, type, (
% 24.98/16.37 xm: $i)).
% 24.98/16.37 tff(sdtsldt0_type, type, (
% 24.98/16.37 sdtsldt0: ( $i * $i ) > $i)).
% 24.98/16.37 tff(xr_type, type, (
% 24.98/16.37 xr: $i)).
% 24.98/16.37 tff(xn_type, type, (
% 24.98/16.37 xn: $i)).
% 24.98/16.37 tff(tptp_fun_W0_13_type, type, (
% 24.98/16.37 tptp_fun_W0_13: $i)).
% 24.98/16.37 tff(aNaturalNumber0_type, type, (
% 24.98/16.37 aNaturalNumber0: $i > $o)).
% 24.98/16.37 tff(xk_type, type, (
% 24.98/16.37 xk: $i)).
% 24.98/16.37 tff(sdtpldt0_type, type, (
% 24.98/16.37 sdtpldt0: ( $i * $i ) > $i)).
% 24.98/16.37 tff(doDivides0_type, type, (
% 24.98/16.37 doDivides0: ( $i * $i ) > $o)).
% 24.98/16.37 tff(sz00_type, type, (
% 24.98/16.37 sz00: $i)).
% 24.98/16.37 tff(sz10_type, type, (
% 24.98/16.37 sz10: $i)).
% 24.98/16.37 tff(isPrime0_type, type, (
% 24.98/16.37 isPrime0: $i > $o)).
% 24.98/16.37 tff(sdtlseqdt0_type, type, (
% 24.98/16.37 sdtlseqdt0: ( $i * $i ) > $o)).
% 24.98/16.37 tff(1,plain,
% 24.98/16.37 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0)))),
% 24.98/16.37 inference(rewrite,[status(thm)],[])).
% 24.98/16.37 tff(2,axiom,((?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xr, W0) = xk)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0)))) & doDivides0(xr, sdtasdt0(xn, xm))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2362')).
% 24.98/16.37 tff(3,plain,
% 24.98/16.37 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xr, W0) = xk)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0)))),
% 24.98/16.37 inference(and_elim,[status(thm)],[2])).
% 24.98/16.37 tff(4,plain,
% 24.98/16.37 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0)))),
% 24.98/16.37 inference(and_elim,[status(thm)],[3])).
% 24.98/16.37 tff(5,plain,
% 24.98/16.37 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0)))),
% 24.98/16.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 24.98/16.37 tff(6,plain,(
% 24.98/16.37 aNaturalNumber0(W0!13) & (sdtasdt0(xn, xm) = sdtasdt0(xr, W0!13))),
% 24.98/16.37 inference(skolemize,[status(sab)],[5])).
% 24.98/16.37 tff(7,plain,
% 24.98/16.37 (aNaturalNumber0(W0!13)),
% 24.98/16.37 inference(and_elim,[status(thm)],[6])).
% 24.98/16.37 tff(8,plain,
% 24.98/16.37 (aNaturalNumber0(xr) <=> aNaturalNumber0(xr)),
% 24.98/16.37 inference(rewrite,[status(thm)],[])).
% 24.98/16.37 tff(9,axiom,((((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))) & isPrime0(xr)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2342')).
% 24.98/16.37 tff(10,plain,
% 24.98/16.37 (((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))),
% 24.98/16.37 inference(and_elim,[status(thm)],[9])).
% 24.98/16.37 tff(11,plain,
% 24.98/16.37 ((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))),
% 24.98/16.37 inference(and_elim,[status(thm)],[10])).
% 24.98/16.37 tff(12,plain,
% 24.98/16.37 (((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))),
% 24.98/16.37 inference(and_elim,[status(thm)],[11])).
% 24.98/16.37 tff(13,plain,
% 24.98/16.37 ((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)),
% 24.98/16.37 inference(and_elim,[status(thm)],[12])).
% 24.98/16.37 tff(14,plain,
% 24.98/16.37 (aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 24.98/16.37 inference(and_elim,[status(thm)],[13])).
% 24.98/16.37 tff(15,plain,
% 24.98/16.37 (aNaturalNumber0(xr)),
% 24.98/16.37 inference(and_elim,[status(thm)],[14])).
% 24.98/16.37 tff(16,plain,
% 24.98/16.37 (aNaturalNumber0(xr)),
% 24.98/16.37 inference(modus_ponens,[status(thm)],[15, 8])).
% 24.98/16.37 tff(17,plain,
% 24.98/16.37 (^[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))))),
% 24.98/16.37 inference(bind,[status(th)],[])).
% 24.98/16.37 tff(18,plain,
% 24.98/16.37 (![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)))),
% 24.98/16.37 inference(quant_intro,[status(thm)],[17])).
% 24.98/16.37 tff(19,plain,
% 24.98/16.37 (^[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)))))),
% 24.98/16.37 inference(bind,[status(th)],[])).
% 24.98/16.37 tff(20,plain,
% 24.98/16.37 (![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)))),
% 24.98/16.37 inference(quant_intro,[status(thm)],[19])).
% 24.98/16.37 tff(21,plain,
% 24.98/16.37 (![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)))),
% 24.98/16.37 inference(rewrite,[status(thm)],[])).
% 24.98/16.37 tff(22,plain,
% 24.98/16.37 (^[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))))),
% 24.98/16.37 inference(bind,[status(th)],[])).
% 24.98/16.37 tff(23,plain,
% 24.98/16.37 (![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)))),
% 24.98/16.37 inference(quant_intro,[status(thm)],[22])).
% 24.98/16.37 tff(24,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulComm')).
% 24.98/16.37 tff(25,plain,
% 24.98/16.37 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 24.98/16.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 24.98/16.37 tff(26,plain,
% 24.98/16.37 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 24.98/16.37 inference(modus_ponens,[status(thm)],[25, 21])).
% 24.98/16.37 tff(27,plain,(
% 24.98/16.37 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 24.98/16.37 inference(skolemize,[status(sab)],[26])).
% 24.98/16.37 tff(28,plain,
% 24.98/16.37 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 24.98/16.37 inference(modus_ponens,[status(thm)],[27, 20])).
% 24.98/16.37 tff(29,plain,
% 24.98/16.37 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 24.98/16.37 inference(modus_ponens,[status(thm)],[28, 18])).
% 24.98/16.37 tff(30,plain,
% 24.98/16.37 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(xr)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(xr)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)))),
% 24.98/16.37 inference(rewrite,[status(thm)],[])).
% 24.98/16.38 tff(31,plain,
% 24.98/16.38 (((sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13))) <=> ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(xr)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)))),
% 24.98/16.38 inference(rewrite,[status(thm)],[])).
% 24.98/16.38 tff(32,plain,
% 24.98/16.38 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(xr)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13))))),
% 24.98/16.38 inference(monotonicity,[status(thm)],[31])).
% 24.98/16.38 tff(33,plain,
% 24.98/16.38 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(xr)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)))),
% 24.98/16.38 inference(transitivity,[status(thm)],[32, 30])).
% 24.98/16.38 tff(34,plain,
% 24.98/16.38 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!13)))),
% 24.98/16.38 inference(quant_inst,[status(thm)],[])).
% 24.98/16.38 tff(35,plain,
% 24.98/16.38 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(xr)) | (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13))),
% 24.98/16.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 24.98/16.38 tff(36,plain,
% 24.98/16.38 (sdtasdt0(W0!13, xr) = sdtasdt0(xr, W0!13)),
% 24.98/16.38 inference(unit_resolution,[status(thm)],[35, 29, 16, 7])).
% 24.98/16.38 tff(37,plain,
% 24.98/16.38 (sdtasdt0(xr, W0!13) = sdtasdt0(W0!13, xr)),
% 24.98/16.38 inference(symmetry,[status(thm)],[36])).
% 24.98/16.38 tff(38,plain,
% 24.98/16.38 (sdtasdt0(xn, xm) = sdtasdt0(xr, W0!13)),
% 24.98/16.38 inference(and_elim,[status(thm)],[6])).
% 24.98/16.38 tff(39,plain,
% 24.98/16.38 ((sdtasdt0(xn, xm) = sdtasdt0(xp, xk)) <=> (sdtasdt0(xn, xm) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 24.98/16.38 inference(rewrite,[status(thm)],[])).
% 24.98/16.38 tff(40,plain,
% 24.98/16.38 ((sdtasdt0(xn, xm) = sdtasdt0(xp, xk)) <=> (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 24.98/16.38 inference(rewrite,[status(thm)],[])).
% 24.98/16.38 tff(41,axiom,((aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))) & (xk = sdtsldt0(sdtasdt0(xn, xm), xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2306')).
% 24.98/16.38 tff(42,plain,
% 24.98/16.38 (aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 24.98/16.38 inference(and_elim,[status(thm)],[41])).
% 24.98/16.38 tff(43,plain,
% 24.98/16.38 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 24.98/16.38 inference(and_elim,[status(thm)],[42])).
% 24.98/16.38 tff(44,plain,
% 24.98/16.38 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 24.98/16.38 inference(modus_ponens,[status(thm)],[43, 40])).
% 24.98/16.38 tff(45,plain,
% 24.98/16.38 (sdtasdt0(xn, xm) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))),
% 24.98/16.38 inference(modus_ponens,[status(thm)],[44, 39])).
% 24.98/16.38 tff(46,plain,
% 24.98/16.38 (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xn, xm)),
% 24.98/16.38 inference(symmetry,[status(thm)],[45])).
% 24.98/16.38 tff(47,plain,
% 24.98/16.38 (^[W0: $i] : rewrite((aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0))) <=> (aNaturalNumber0(W0) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0))))),
% 24.98/16.38 inference(bind,[status(th)],[])).
% 24.98/16.38 tff(48,plain,
% 24.98/16.38 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0)))),
% 24.98/16.38 inference(quant_intro,[status(thm)],[47])).
% 24.98/16.38 tff(49,plain,
% 24.98/16.38 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 24.98/16.38 inference(rewrite,[status(thm)],[])).
% 24.98/16.38 tff(50,plain,
% 24.98/16.38 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 24.98/16.38 inference(and_elim,[status(thm)],[14])).
% 24.98/16.38 tff(51,plain,
% 24.98/16.38 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 24.98/16.38 inference(modus_ponens,[status(thm)],[50, 49])).
% 24.98/16.38 tff(52,plain,
% 24.98/16.38 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0)))),
% 24.98/16.38 inference(modus_ponens,[status(thm)],[51, 48])).
% 24.98/16.38 tff(53,plain,(
% 24.98/16.38 aNaturalNumber0(W0!11) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0!11))),
% 24.98/16.38 inference(skolemize,[status(sab)],[52])).
% 24.98/16.38 tff(54,plain,
% 24.98/16.38 (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0!11)),
% 24.98/16.38 inference(and_elim,[status(thm)],[53])).
% 24.98/16.38 tff(55,plain,
% 24.98/16.38 (sdtasdt0(xr, W0!11) = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 24.98/16.38 inference(symmetry,[status(thm)],[54])).
% 24.98/16.38 tff(56,plain,
% 24.98/16.38 (aNaturalNumber0(W0!11)),
% 24.98/16.38 inference(and_elim,[status(thm)],[53])).
% 24.98/16.38 tff(57,plain,
% 24.98/16.38 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)))),
% 24.98/16.38 inference(rewrite,[status(thm)],[])).
% 24.98/16.38 tff(58,plain,
% 24.98/16.38 (((sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11))) <=> ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)))),
% 24.98/16.38 inference(rewrite,[status(thm)],[])).
% 24.98/16.38 tff(59,plain,
% 24.98/16.38 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11))))),
% 24.98/16.38 inference(monotonicity,[status(thm)],[58])).
% 24.98/16.38 tff(60,plain,
% 24.98/16.38 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)))),
% 24.98/16.38 inference(transitivity,[status(thm)],[59, 57])).
% 24.98/16.38 tff(61,plain,
% 24.98/16.38 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)))),
% 24.98/16.38 inference(quant_inst,[status(thm)],[])).
% 24.98/16.38 tff(62,plain,
% 24.98/16.38 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11))),
% 24.98/16.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 24.98/16.38 tff(63,plain,
% 24.98/16.38 (sdtasdt0(W0!11, xr) = sdtasdt0(xr, W0!11)),
% 24.98/16.38 inference(unit_resolution,[status(thm)],[62, 29, 16, 56])).
% 24.98/16.38 tff(64,plain,
% 24.98/16.38 (sdtasdt0(W0!11, xr) = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 24.98/16.38 inference(transitivity,[status(thm)],[63, 55])).
% 24.98/16.38 tff(65,plain,
% 24.98/16.38 (sdtasdt0(xp, sdtasdt0(W0!11, xr)) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))),
% 24.98/16.38 inference(monotonicity,[status(thm)],[64])).
% 24.98/16.38 tff(66,plain,
% 24.98/16.38 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 24.98/16.38 inference(rewrite,[status(thm)],[])).
% 24.98/16.38 tff(67,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1837')).
% 24.98/16.38 tff(68,plain,
% 24.98/16.38 (aNaturalNumber0(xp)),
% 24.98/16.38 inference(and_elim,[status(thm)],[67])).
% 24.98/16.38 tff(69,plain,
% 24.98/16.38 (aNaturalNumber0(xp)),
% 24.98/16.38 inference(modus_ponens,[status(thm)],[68, 66])).
% 24.98/16.38 tff(70,plain,
% 24.98/16.38 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 24.98/16.38 inference(bind,[status(th)],[])).
% 24.98/16.38 tff(71,plain,
% 24.98/16.38 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 24.98/16.38 inference(quant_intro,[status(thm)],[70])).
% 24.98/16.38 tff(72,plain,
% 24.98/16.38 (^[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))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 24.98/16.38 inference(bind,[status(th)],[])).
% 24.98/16.38 tff(73,plain,
% 24.98/16.38 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 24.98/16.38 inference(quant_intro,[status(thm)],[72])).
% 24.98/16.38 tff(74,plain,
% 24.98/16.38 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 24.98/16.38 inference(rewrite,[status(thm)],[])).
% 24.98/16.38 tff(75,plain,
% 24.98/16.38 (^[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(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))))),
% 24.98/16.38 inference(bind,[status(th)],[])).
% 24.98/16.38 tff(76,plain,
% 24.98/16.38 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 24.98/16.38 inference(quant_intro,[status(thm)],[75])).
% 24.98/16.38 tff(77,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulAsso')).
% 24.98/16.38 tff(78,plain,
% 24.98/16.38 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 24.98/16.38 inference(modus_ponens,[status(thm)],[77, 76])).
% 24.98/16.38 tff(79,plain,
% 24.98/16.38 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 24.98/16.38 inference(modus_ponens,[status(thm)],[78, 74])).
% 24.98/16.38 tff(80,plain,(
% 24.98/16.38 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 24.98/16.38 inference(skolemize,[status(sab)],[79])).
% 24.98/16.38 tff(81,plain,
% 24.98/16.38 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 24.98/16.38 inference(modus_ponens,[status(thm)],[80, 73])).
% 24.98/16.38 tff(82,plain,
% 24.98/16.38 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 24.98/16.38 inference(modus_ponens,[status(thm)],[81, 71])).
% 24.98/16.38 tff(83,plain,
% 24.98/16.38 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))))),
% 24.98/16.38 inference(rewrite,[status(thm)],[])).
% 24.98/16.38 tff(84,plain,
% 24.98/16.38 (((sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))))),
% 24.98/16.38 inference(rewrite,[status(thm)],[])).
% 24.98/16.38 tff(85,plain,
% 24.98/16.38 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr)))))),
% 24.98/16.38 inference(monotonicity,[status(thm)],[84])).
% 24.98/16.38 tff(86,plain,
% 24.98/16.38 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))))),
% 25.07/16.38 inference(transitivity,[status(thm)],[85, 83])).
% 25.07/16.38 tff(87,plain,
% 25.07/16.38 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))),
% 25.07/16.38 inference(quant_inst,[status(thm)],[])).
% 25.07/16.38 tff(88,plain,
% 25.07/16.38 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(W0!11)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr)))),
% 25.07/16.38 inference(modus_ponens,[status(thm)],[87, 86])).
% 25.07/16.38 tff(89,plain,
% 25.07/16.38 (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(xp, sdtasdt0(W0!11, xr))),
% 25.07/16.38 inference(unit_resolution,[status(thm)],[88, 82, 69, 16, 56])).
% 25.07/16.38 tff(90,plain,
% 25.07/16.38 (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)),
% 25.07/16.38 inference(transitivity,[status(thm)],[89, 65, 46, 38, 37])).
% 25.07/16.38 tff(91,plain,
% 25.07/16.38 (((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr))) | (~(sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))),
% 25.07/16.38 inference(tautology,[status(thm)],[])).
% 25.07/16.38 tff(92,plain,
% 25.07/16.38 ((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr))),
% 25.07/16.38 inference(unit_resolution,[status(thm)],[91, 90])).
% 25.07/16.38 tff(93,plain,
% 25.07/16.38 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 25.07/16.38 inference(bind,[status(th)],[])).
% 25.07/16.38 tff(94,plain,
% 25.07/16.38 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 25.07/16.38 inference(quant_intro,[status(thm)],[93])).
% 25.07/16.38 tff(95,plain,
% 25.07/16.38 (^[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)))))),
% 25.07/16.38 inference(bind,[status(th)],[])).
% 25.07/16.38 tff(96,plain,
% 25.07/16.38 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 25.07/16.38 inference(quant_intro,[status(thm)],[95])).
% 25.07/16.38 tff(97,plain,
% 25.07/16.38 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 25.07/16.38 inference(rewrite,[status(thm)],[])).
% 25.07/16.38 tff(98,plain,
% 25.07/16.38 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 25.07/16.38 inference(bind,[status(th)],[])).
% 25.07/16.38 tff(99,plain,
% 25.07/16.38 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 25.07/16.38 inference(quant_intro,[status(thm)],[98])).
% 25.07/16.38 tff(100,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 25.07/16.38 tff(101,plain,
% 25.07/16.38 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 25.07/16.38 inference(modus_ponens,[status(thm)],[100, 99])).
% 25.07/16.38 tff(102,plain,
% 25.07/16.38 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 25.07/16.38 inference(modus_ponens,[status(thm)],[101, 97])).
% 25.07/16.38 tff(103,plain,(
% 25.07/16.38 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 25.07/16.38 inference(skolemize,[status(sab)],[102])).
% 25.07/16.38 tff(104,plain,
% 25.07/16.38 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 25.07/16.38 inference(modus_ponens,[status(thm)],[103, 96])).
% 25.07/16.38 tff(105,plain,
% 25.07/16.38 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 25.07/16.38 inference(modus_ponens,[status(thm)],[104, 94])).
% 25.07/16.38 tff(106,plain,
% 25.07/16.38 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, W0!11)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, W0!11)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))),
% 25.07/16.38 inference(rewrite,[status(thm)],[])).
% 25.07/16.38 tff(107,plain,
% 25.07/16.38 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, W0!11)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp)))),
% 25.07/16.38 inference(quant_inst,[status(thm)],[])).
% 25.07/16.38 tff(108,plain,
% 25.07/16.38 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, W0!11)) | (~aNaturalNumber0(W0!11)) | (~aNaturalNumber0(xp))),
% 25.07/16.38 inference(modus_ponens,[status(thm)],[107, 106])).
% 25.07/16.38 tff(109,plain,
% 25.07/16.38 (aNaturalNumber0(sdtasdt0(xp, W0!11))),
% 25.07/16.38 inference(unit_resolution,[status(thm)],[108, 105, 69, 56])).
% 25.07/16.38 tff(110,plain,
% 25.07/16.38 ((~(xr = sz00)) <=> (~(xr = sz00))),
% 25.07/16.38 inference(rewrite,[status(thm)],[])).
% 25.07/16.38 tff(111,plain,
% 25.07/16.38 (~(xr = sz00)),
% 25.07/16.38 inference(and_elim,[status(thm)],[12])).
% 25.07/16.38 tff(112,plain,
% 25.07/16.38 (~(xr = sz00)),
% 25.07/16.38 inference(modus_ponens,[status(thm)],[111, 110])).
% 25.07/16.38 tff(113,plain,
% 25.07/16.38 (^[W0: $i] : refl(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 25.07/16.38 inference(bind,[status(th)],[])).
% 25.07/16.38 tff(114,plain,
% 25.07/16.38 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 25.07/16.38 inference(quant_intro,[status(thm)],[113])).
% 25.07/16.38 tff(115,plain,
% 25.07/16.38 (^[W0: $i] : rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 25.07/16.38 inference(bind,[status(th)],[])).
% 25.07/16.38 tff(116,plain,
% 25.07/16.38 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 25.07/16.38 inference(quant_intro,[status(thm)],[115])).
% 25.07/16.38 tff(117,plain,
% 25.07/16.38 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 25.07/16.38 inference(transitivity,[status(thm)],[116, 114])).
% 25.07/16.38 tff(118,plain,
% 25.07/16.38 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), rewrite((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) <=> (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), rewrite(((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), (![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))))),
% 25.07/16.38 inference(bind,[status(th)],[])).
% 25.07/16.38 tff(119,plain,
% 25.07/16.38 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 25.07/16.38 inference(quant_intro,[status(thm)],[118])).
% 25.07/16.38 tff(120,plain,
% 25.07/16.38 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 25.07/16.38 inference(rewrite,[status(thm)],[])).
% 25.07/16.38 tff(121,plain,
% 25.07/16.38 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))), rewrite((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2)))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))))), rewrite(((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), (![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), rewrite(((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> (aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))), rewrite((aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))),
% 25.07/16.38 inference(bind,[status(th)],[])).
% 25.07/16.38 tff(122,plain,
% 25.07/16.38 (![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 25.07/16.38 inference(quant_intro,[status(thm)],[121])).
% 25.07/16.38 tff(123,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulCanc')).
% 25.07/16.38 tff(124,plain,
% 25.07/16.38 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 25.07/16.38 inference(modus_ponens,[status(thm)],[123, 122])).
% 25.07/16.38 tff(125,plain,
% 25.07/16.38 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 25.07/16.38 inference(modus_ponens,[status(thm)],[124, 120])).
% 25.07/16.38 tff(126,plain,(
% 25.07/16.38 ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 25.07/16.38 inference(skolemize,[status(sab)],[125])).
% 25.07/16.38 tff(127,plain,
% 25.07/16.38 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 25.07/16.38 inference(modus_ponens,[status(thm)],[126, 119])).
% 25.07/16.38 tff(128,plain,
% 25.07/16.38 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 25.07/16.38 inference(modus_ponens,[status(thm)],[127, 117])).
% 25.07/16.38 tff(129,plain,
% 25.07/16.38 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 25.07/16.38 inference(rewrite,[status(thm)],[])).
% 25.07/16.38 tff(130,plain,
% 25.07/16.38 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 25.07/16.38 inference(rewrite,[status(thm)],[])).
% 25.07/16.38 tff(131,plain,
% 25.07/16.38 (^[W1: $i, W2: $i] : rewrite(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 25.07/16.38 inference(bind,[status(th)],[])).
% 25.07/16.38 tff(132,plain,
% 25.07/16.38 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 25.07/16.38 inference(quant_intro,[status(thm)],[131])).
% 25.07/16.38 tff(133,plain,
% 25.07/16.38 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1)))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 25.07/16.38 inference(monotonicity,[status(thm)],[132])).
% 25.07/16.38 tff(134,plain,
% 25.07/16.38 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1)))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 25.07/16.38 inference(transitivity,[status(thm)],[133, 130])).
% 25.07/16.38 tff(135,plain,
% 25.07/16.38 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))))),
% 25.07/16.39 inference(monotonicity,[status(thm)],[134])).
% 25.07/16.39 tff(136,plain,
% 25.07/16.39 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 25.07/16.39 inference(transitivity,[status(thm)],[135, 129])).
% 25.07/16.39 tff(137,plain,
% 25.07/16.39 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))),
% 25.07/16.39 inference(quant_inst,[status(thm)],[])).
% 25.07/16.39 tff(138,plain,
% 25.07/16.39 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 25.07/16.39 inference(modus_ponens,[status(thm)],[137, 136])).
% 25.07/16.39 tff(139,plain,
% 25.07/16.39 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 25.07/16.39 inference(unit_resolution,[status(thm)],[138, 128, 16, 112])).
% 25.07/16.39 tff(140,plain,
% 25.07/16.39 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(141,plain,
% 25.07/16.39 (((sdtasdt0(xp, W0!11) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr))))) <=> ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(142,plain,
% 25.07/16.39 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(xp, W0!11) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr))))))),
% 25.07/16.39 inference(monotonicity,[status(thm)],[141])).
% 25.07/16.39 tff(143,plain,
% 25.07/16.39 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(xp, W0!11) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))),
% 25.07/16.39 inference(transitivity,[status(thm)],[142, 140])).
% 25.07/16.39 tff(144,plain,
% 25.07/16.39 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(xp, W0!11) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr)))))),
% 25.07/16.39 inference(quant_inst,[status(thm)],[])).
% 25.07/16.39 tff(145,plain,
% 25.07/16.39 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(xp, W0!11))) | (sdtasdt0(xp, W0!11) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(xp, W0!11)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(xp, W0!11), xr) = sdtasdt0(W0!13, xr))))),
% 25.07/16.39 inference(modus_ponens,[status(thm)],[144, 143])).
% 25.07/16.39 tff(146,plain,
% 25.07/16.39 (sdtasdt0(xp, W0!11) = W0!13),
% 25.07/16.39 inference(unit_resolution,[status(thm)],[145, 7, 139, 109, 92])).
% 25.07/16.39 tff(147,plain,
% 25.07/16.39 (W0!13 = sdtasdt0(xp, W0!11)),
% 25.07/16.39 inference(symmetry,[status(thm)],[146])).
% 25.07/16.39 tff(148,plain,
% 25.07/16.39 ((xn = sdtasdt0(xr, sdtsldt0(xn, xr))) <=> (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(149,axiom,(((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))) & sdtlseqdt0(sdtsldt0(xn, xr), xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2504')).
% 25.07/16.39 tff(150,plain,
% 25.07/16.39 ((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))),
% 25.07/16.39 inference(and_elim,[status(thm)],[149])).
% 25.07/16.39 tff(151,plain,
% 25.07/16.39 (((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 25.07/16.39 inference(and_elim,[status(thm)],[150])).
% 25.07/16.39 tff(152,plain,
% 25.07/16.39 (xn = sdtasdt0(xr, sdtsldt0(xn, xr))),
% 25.07/16.39 inference(and_elim,[status(thm)],[151])).
% 25.07/16.39 tff(153,plain,
% 25.07/16.39 (xn = sdtasdt0(xr, sdtsldt0(xn, xr))),
% 25.07/16.39 inference(modus_ponens,[status(thm)],[152, 148])).
% 25.07/16.39 tff(154,plain,
% 25.07/16.39 (sdtasdt0(xr, sdtsldt0(xn, xr)) = xn),
% 25.07/16.39 inference(symmetry,[status(thm)],[153])).
% 25.07/16.39 tff(155,plain,
% 25.07/16.39 (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xn, xm)),
% 25.07/16.39 inference(monotonicity,[status(thm)],[154])).
% 25.07/16.39 tff(156,plain,
% 25.07/16.39 (aNaturalNumber0(sdtsldt0(xn, xr)) <=> aNaturalNumber0(sdtsldt0(xn, xr))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(157,plain,
% 25.07/16.39 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) <=> (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn)))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(158,plain,
% 25.07/16.39 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))),
% 25.07/16.39 inference(and_elim,[status(thm)],[151])).
% 25.07/16.39 tff(159,plain,
% 25.07/16.39 (~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))),
% 25.07/16.39 inference(and_elim,[status(thm)],[158])).
% 25.07/16.39 tff(160,plain,
% 25.07/16.39 (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn))),
% 25.07/16.39 inference(modus_ponens,[status(thm)],[159, 157])).
% 25.07/16.39 tff(161,plain,
% 25.07/16.39 (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 25.07/16.39 inference(or_elim,[status(thm)],[160])).
% 25.07/16.39 tff(162,plain,
% 25.07/16.39 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 25.07/16.39 inference(and_elim,[status(thm)],[161])).
% 25.07/16.39 tff(163,plain,
% 25.07/16.39 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 25.07/16.39 inference(modus_ponens,[status(thm)],[162, 156])).
% 25.07/16.39 tff(164,plain,
% 25.07/16.39 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(165,plain,
% 25.07/16.39 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 25.07/16.39 inference(and_elim,[status(thm)],[67])).
% 25.07/16.39 tff(166,plain,
% 25.07/16.39 (aNaturalNumber0(xm)),
% 25.07/16.39 inference(and_elim,[status(thm)],[165])).
% 25.07/16.39 tff(167,plain,
% 25.07/16.39 (aNaturalNumber0(xm)),
% 25.07/16.39 inference(modus_ponens,[status(thm)],[166, 164])).
% 25.07/16.39 tff(168,plain,
% 25.07/16.39 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(169,plain,
% 25.07/16.39 (((sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~aNaturalNumber0(xr))) <=> ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(170,plain,
% 25.07/16.39 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)))))),
% 25.07/16.39 inference(monotonicity,[status(thm)],[169])).
% 25.07/16.39 tff(171,plain,
% 25.07/16.39 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))))),
% 25.07/16.39 inference(transitivity,[status(thm)],[170, 168])).
% 25.07/16.39 tff(172,plain,
% 25.07/16.39 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (~aNaturalNumber0(xr)))),
% 25.07/16.39 inference(quant_inst,[status(thm)],[])).
% 25.07/16.39 tff(173,plain,
% 25.07/16.39 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 25.07/16.39 inference(modus_ponens,[status(thm)],[172, 171])).
% 25.07/16.39 tff(174,plain,
% 25.07/16.39 (sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))),
% 25.07/16.39 inference(unit_resolution,[status(thm)],[173, 82, 167, 16, 163])).
% 25.07/16.39 tff(175,plain,
% 25.07/16.39 (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(xr, sdtsldt0(xn, xr)), xm)),
% 25.07/16.39 inference(symmetry,[status(thm)],[174])).
% 25.07/16.39 tff(176,plain,
% 25.07/16.39 (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)),
% 25.07/16.39 inference(transitivity,[status(thm)],[175, 155, 38])).
% 25.07/16.39 tff(177,plain,
% 25.07/16.39 (((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr))) | (~(sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)))),
% 25.07/16.39 inference(tautology,[status(thm)],[])).
% 25.07/16.39 tff(178,plain,
% 25.07/16.39 ((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr))),
% 25.07/16.39 inference(unit_resolution,[status(thm)],[177, 176])).
% 25.07/16.39 tff(179,plain,
% 25.07/16.39 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(180,plain,
% 25.07/16.39 ((aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr)))) <=> ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(181,plain,
% 25.07/16.39 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))))),
% 25.07/16.39 inference(monotonicity,[status(thm)],[180])).
% 25.07/16.39 tff(182,plain,
% 25.07/16.39 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 25.07/16.39 inference(transitivity,[status(thm)],[181, 179])).
% 25.07/16.39 tff(183,plain,
% 25.07/16.39 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))),
% 25.07/16.39 inference(quant_inst,[status(thm)],[])).
% 25.07/16.39 tff(184,plain,
% 25.07/16.39 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))),
% 25.07/16.39 inference(modus_ponens,[status(thm)],[183, 182])).
% 25.07/16.39 tff(185,plain,
% 25.07/16.39 (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))),
% 25.07/16.39 inference(unit_resolution,[status(thm)],[184, 105, 167, 163])).
% 25.07/16.39 tff(186,plain,
% 25.07/16.39 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(187,plain,
% 25.07/16.39 (((sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr))))) <=> ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(188,plain,
% 25.07/16.39 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr))))))),
% 25.07/16.39 inference(monotonicity,[status(thm)],[187])).
% 25.07/16.39 tff(189,plain,
% 25.07/16.39 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))),
% 25.07/16.39 inference(transitivity,[status(thm)],[188, 186])).
% 25.07/16.39 tff(190,plain,
% 25.07/16.39 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr)))))),
% 25.07/16.39 inference(quant_inst,[status(thm)],[])).
% 25.07/16.39 tff(191,plain,
% 25.07/16.39 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (~aNaturalNumber0(W0!13)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13) | (~((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, W0!13)) | (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(W0!13, xr))))),
% 25.07/16.39 inference(modus_ponens,[status(thm)],[190, 189])).
% 25.07/16.39 tff(192,plain,
% 25.07/16.39 (sdtasdt0(sdtsldt0(xn, xr), xm) = W0!13),
% 25.07/16.39 inference(unit_resolution,[status(thm)],[191, 7, 185, 139, 178])).
% 25.07/16.39 tff(193,plain,
% 25.07/16.39 (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11)),
% 25.07/16.39 inference(transitivity,[status(thm)],[192, 147])).
% 25.07/16.39 tff(194,plain,
% 25.07/16.39 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))))),
% 25.07/16.39 inference(bind,[status(th)],[])).
% 25.07/16.39 tff(195,plain,
% 25.07/16.39 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 25.07/16.39 inference(quant_intro,[status(thm)],[194])).
% 25.07/16.39 tff(196,plain,
% 25.07/16.39 (^[W0: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))) <=> (~((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))))), ((~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> (~(~((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))))))), rewrite((~(~((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))))) <=> ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))), ((~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))))),
% 25.07/16.39 inference(bind,[status(th)],[])).
% 25.07/16.39 tff(197,plain,
% 25.07/16.39 (![W0: $i] : (~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 25.07/16.39 inference(quant_intro,[status(thm)],[196])).
% 25.07/16.39 tff(198,plain,
% 25.07/16.39 ((~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))) <=> (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 25.07/16.39 inference(rewrite,[status(thm)],[])).
% 25.07/16.39 tff(199,plain,
% 25.07/16.39 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))) | doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm))))) <=> (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))) | (~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))))))),
% 25.07/16.40 inference(rewrite,[status(thm)],[])).
% 25.07/16.40 tff(200,axiom,(~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))) | doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 25.07/16.40 tff(201,plain,
% 25.07/16.40 (~(doDivides0(xp, sdtasdt0(sdtsldt0(xn, xr), xm)) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))) | (~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[200, 199])).
% 25.07/16.40 tff(202,plain,
% 25.07/16.40 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 25.07/16.40 inference(or_elim,[status(thm)],[201])).
% 25.07/16.40 tff(203,plain,
% 25.07/16.40 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[202, 198])).
% 25.07/16.40 tff(204,plain,
% 25.07/16.40 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[203, 198])).
% 25.07/16.40 tff(205,plain,
% 25.07/16.40 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[204, 198])).
% 25.07/16.40 tff(206,plain,
% 25.07/16.40 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[205, 198])).
% 25.07/16.40 tff(207,plain,
% 25.07/16.40 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[206, 198])).
% 25.07/16.40 tff(208,plain,
% 25.07/16.40 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[207, 198])).
% 25.07/16.40 tff(209,plain,
% 25.07/16.40 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[208, 198])).
% 25.07/16.40 tff(210,plain,
% 25.07/16.40 (~?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[209, 198])).
% 25.07/16.40 tff(211,plain,
% 25.07/16.40 (^[W0: $i] : refl($oeq((~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0)))), (~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))))),
% 25.07/16.40 inference(bind,[status(th)],[])).
% 25.07/16.40 tff(212,plain,(
% 25.07/16.40 ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 25.07/16.40 inference(nnf-neg,[status(sab)],[210, 211])).
% 25.07/16.40 tff(213,plain,
% 25.07/16.40 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[212, 197])).
% 25.07/16.40 tff(214,plain,
% 25.07/16.40 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[213, 195])).
% 25.07/16.40 tff(215,plain,
% 25.07/16.40 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))) | ((~aNaturalNumber0(W0!11)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))) | (~aNaturalNumber0(W0!11)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11))))),
% 25.07/16.40 inference(rewrite,[status(thm)],[])).
% 25.07/16.40 tff(216,plain,
% 25.07/16.40 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))) | ((~aNaturalNumber0(W0!11)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11))))),
% 25.07/16.40 inference(quant_inst,[status(thm)],[])).
% 25.07/16.40 tff(217,plain,
% 25.07/16.40 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0))))) | (~aNaturalNumber0(W0!11)) | (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11)))),
% 25.07/16.40 inference(modus_ponens,[status(thm)],[216, 215])).
% 25.07/16.45 tff(218,plain,
% 25.07/16.45 (~(sdtasdt0(sdtsldt0(xn, xr), xm) = sdtasdt0(xp, W0!11))),
% 25.07/16.45 inference(unit_resolution,[status(thm)],[217, 56, 214])).
% 25.07/16.45 tff(219,plain,
% 25.07/16.45 ($false),
% 25.07/16.45 inference(unit_resolution,[status(thm)],[218, 193])).
% 25.07/16.45 % SZS output end Proof
%------------------------------------------------------------------------------