TSTP Solution File: RNG125+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG125+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Tue Sep 20 03:18:33 EDT 2022
% Result : Theorem 2.00s 1.51s
% Output : Proof 2.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG125+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 22:56:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 2.00/1.51 % SZS status Theorem
% 2.00/1.51 % SZS output start Proof
% 2.00/1.51 tff(aDivisorOf0_type, type, (
% 2.00/1.51 aDivisorOf0: ( $i * $i ) > $o)).
% 2.00/1.51 tff(xb_type, type, (
% 2.00/1.51 xb: $i)).
% 2.00/1.51 tff(xu_type, type, (
% 2.00/1.51 xu: $i)).
% 2.00/1.51 tff(sdtpldt0_type, type, (
% 2.00/1.51 sdtpldt0: ( $i * $i ) > $i)).
% 2.00/1.51 tff(sdtasdt0_type, type, (
% 2.00/1.51 sdtasdt0: ( $i * $i ) > $i)).
% 2.00/1.51 tff(tptp_fun_W1_21_type, type, (
% 2.00/1.51 tptp_fun_W1_21: $i)).
% 2.00/1.51 tff(tptp_fun_W0_22_type, type, (
% 2.00/1.51 tptp_fun_W0_22: $i)).
% 2.00/1.51 tff(xa_type, type, (
% 2.00/1.51 xa: $i)).
% 2.00/1.51 tff(aElement0_type, type, (
% 2.00/1.51 aElement0: $i > $o)).
% 2.00/1.51 tff(doDivides0_type, type, (
% 2.00/1.51 doDivides0: ( $i * $i ) > $o)).
% 2.00/1.51 tff(1,plain,
% 2.00/1.51 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))) <=> ?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(2,plain,
% 2.00/1.51 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))) <=> (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 2.00/1.51 inference(bind,[status(th)],[])).
% 2.00/1.51 tff(3,plain,
% 2.00/1.51 (?[W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))) <=> ?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 2.00/1.51 inference(quant_intro,[status(thm)],[2])).
% 2.00/1.51 tff(4,axiom,(?[W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2416')).
% 2.00/1.51 tff(5,plain,
% 2.00/1.51 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.00/1.51 tff(6,plain,
% 2.00/1.51 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[5, 1])).
% 2.00/1.51 tff(7,plain,(
% 2.00/1.51 aElement0(W0!22) & aElement0(W1!21) & (xu = sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))),
% 2.00/1.51 inference(skolemize,[status(sab)],[6])).
% 2.00/1.51 tff(8,plain,
% 2.00/1.51 (xu = sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21))),
% 2.00/1.51 inference(and_elim,[status(thm)],[7])).
% 2.00/1.51 tff(9,plain,
% 2.00/1.51 (sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)) = xu),
% 2.00/1.51 inference(symmetry,[status(thm)],[8])).
% 2.00/1.51 tff(10,plain,
% 2.00/1.51 (aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb) <=> aDivisorOf0(xu, xb)),
% 2.00/1.51 inference(monotonicity,[status(thm)],[9])).
% 2.00/1.51 tff(11,plain,
% 2.00/1.51 (aElement0(xb) <=> aElement0(xb)),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(12,axiom,(aElement0(xa) & aElement0(xb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2091')).
% 2.00/1.51 tff(13,plain,
% 2.00/1.51 (aElement0(xb)),
% 2.00/1.51 inference(and_elim,[status(thm)],[12])).
% 2.00/1.51 tff(14,plain,
% 2.00/1.51 (aElement0(xb)),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[13, 11])).
% 2.00/1.51 tff(15,plain,
% 2.00/1.51 (^[W0: $i] : refl(((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0)))))) <=> ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0)))))))),
% 2.00/1.51 inference(bind,[status(th)],[])).
% 2.00/1.51 tff(16,plain,
% 2.00/1.51 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))),
% 2.00/1.51 inference(quant_intro,[status(thm)],[15])).
% 2.00/1.51 tff(17,plain,
% 2.00/1.51 (^[W0: $i] : rewrite(((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0)))))) <=> ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0)))))))),
% 2.00/1.51 inference(bind,[status(th)],[])).
% 2.00/1.51 tff(18,plain,
% 2.00/1.51 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))),
% 2.00/1.51 inference(quant_intro,[status(thm)],[17])).
% 2.00/1.51 tff(19,plain,
% 2.00/1.51 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))),
% 2.00/1.51 inference(transitivity,[status(thm)],[18, 16])).
% 2.00/1.51 tff(20,plain,
% 2.00/1.51 (^[W0: $i] : rewrite(((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0)))) <=> ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0)))))))),
% 2.00/1.51 inference(bind,[status(th)],[])).
% 2.00/1.51 tff(21,plain,
% 2.00/1.51 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))),
% 2.00/1.51 inference(quant_intro,[status(thm)],[20])).
% 2.00/1.51 tff(22,plain,
% 2.00/1.51 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0))))),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(23,plain,
% 2.00/1.51 (^[W0: $i] : rewrite((aElement0(W0) => ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0)))) <=> ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0)))))),
% 2.00/1.51 inference(bind,[status(th)],[])).
% 2.00/1.51 tff(24,plain,
% 2.00/1.51 (![W0: $i] : (aElement0(W0) => ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0))))),
% 2.00/1.51 inference(quant_intro,[status(thm)],[23])).
% 2.00/1.51 tff(25,axiom,(![W0: $i] : (aElement0(W0) => ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefDvs')).
% 2.00/1.51 tff(26,plain,
% 2.00/1.51 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0))))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[25, 24])).
% 2.00/1.51 tff(27,plain,
% 2.00/1.51 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0))))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[26, 22])).
% 2.00/1.51 tff(28,plain,(
% 2.00/1.51 ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (aElement0(W1) & doDivides0(W1, W0))))),
% 2.00/1.51 inference(skolemize,[status(sab)],[27])).
% 2.00/1.51 tff(29,plain,
% 2.00/1.51 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[28, 21])).
% 2.00/1.51 tff(30,plain,
% 2.00/1.51 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[29, 19])).
% 2.00/1.51 tff(31,plain,
% 2.00/1.51 (((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))) | ((~aElement0(xb)) | ![W1: $i] : (aDivisorOf0(W1, xb) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xb))))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))) | (~aElement0(xb)) | ![W1: $i] : (aDivisorOf0(W1, xb) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xb))))))),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(32,plain,
% 2.00/1.51 ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))) | ((~aElement0(xb)) | ![W1: $i] : (aDivisorOf0(W1, xb) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xb))))))),
% 2.00/1.51 inference(quant_inst,[status(thm)],[])).
% 2.00/1.51 tff(33,plain,
% 2.00/1.51 ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))) | (~aElement0(xb)) | ![W1: $i] : (aDivisorOf0(W1, xb) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xb)))))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[32, 31])).
% 2.00/1.51 tff(34,plain,
% 2.00/1.51 (![W1: $i] : (aDivisorOf0(W1, xb) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xb)))))),
% 2.00/1.51 inference(unit_resolution,[status(thm)],[33, 30, 14])).
% 2.00/1.51 tff(35,plain,
% 2.00/1.51 ((~![W1: $i] : (aDivisorOf0(W1, xb) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xb)))))) | (aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb) <=> (~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb)))))),
% 2.00/1.51 inference(quant_inst,[status(thm)],[])).
% 2.00/1.51 tff(36,plain,
% 2.00/1.51 (aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb) <=> (~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb))))),
% 2.00/1.51 inference(unit_resolution,[status(thm)],[35, 34])).
% 2.00/1.51 tff(37,plain,
% 2.00/1.51 (doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb) <=> doDivides0(xu, xb)),
% 2.00/1.51 inference(monotonicity,[status(thm)],[9])).
% 2.00/1.51 tff(38,plain,
% 2.00/1.51 (doDivides0(xu, xb) <=> doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb)),
% 2.00/1.51 inference(symmetry,[status(thm)],[37])).
% 2.00/1.51 tff(39,plain,
% 2.00/1.51 (doDivides0(xu, xb) <=> doDivides0(xu, xb)),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(40,plain,
% 2.00/1.51 ((~(~doDivides0(xu, xb))) <=> doDivides0(xu, xb)),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(41,axiom,(~(~doDivides0(xu, xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2612')).
% 2.00/1.51 tff(42,plain,
% 2.00/1.51 (doDivides0(xu, xb)),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[41, 40])).
% 2.00/1.51 tff(43,plain,
% 2.00/1.51 (doDivides0(xu, xb)),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[42, 39])).
% 2.00/1.51 tff(44,plain,
% 2.00/1.51 (doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb)),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[43, 38])).
% 2.00/1.51 tff(45,plain,
% 2.00/1.51 (aElement0(W0!22)),
% 2.00/1.51 inference(and_elim,[status(thm)],[7])).
% 2.00/1.51 tff(46,plain,
% 2.00/1.51 (aElement0(xa) <=> aElement0(xa)),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(47,plain,
% 2.00/1.51 (aElement0(xa)),
% 2.00/1.51 inference(and_elim,[status(thm)],[12])).
% 2.00/1.51 tff(48,plain,
% 2.00/1.51 (aElement0(xa)),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[47, 46])).
% 2.00/1.51 tff(49,plain,
% 2.00/1.51 (^[W0: $i, W1: $i] : refl((aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 2.00/1.51 inference(bind,[status(th)],[])).
% 2.00/1.51 tff(50,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.00/1.51 inference(quant_intro,[status(thm)],[49])).
% 2.00/1.51 tff(51,plain,
% 2.00/1.51 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aElement0(W0))))), ((aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtasdt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))))), rewrite((aElement0(sdtasdt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))), ((aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 2.00/1.51 inference(bind,[status(th)],[])).
% 2.00/1.51 tff(52,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.00/1.51 inference(quant_intro,[status(thm)],[51])).
% 2.00/1.51 tff(53,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(54,plain,
% 2.00/1.51 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 2.00/1.51 inference(bind,[status(th)],[])).
% 2.00/1.51 tff(55,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.00/1.51 inference(quant_intro,[status(thm)],[54])).
% 2.00/1.51 tff(56,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB_02')).
% 2.00/1.51 tff(57,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[56, 55])).
% 2.00/1.51 tff(58,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[57, 53])).
% 2.00/1.51 tff(59,plain,(
% 2.00/1.51 ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.00/1.51 inference(skolemize,[status(sab)],[58])).
% 2.00/1.51 tff(60,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[59, 52])).
% 2.00/1.51 tff(61,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[60, 50])).
% 2.00/1.51 tff(62,plain,
% 2.00/1.51 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!22)) | (~aElement0(W0!22)) | (~aElement0(xa)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!22)) | (~aElement0(W0!22)) | (~aElement0(xa)))),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(63,plain,
% 2.00/1.51 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!22)) | (~aElement0(W0!22)) | (~aElement0(xa)))),
% 2.00/1.51 inference(quant_inst,[status(thm)],[])).
% 2.00/1.51 tff(64,plain,
% 2.00/1.51 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!22)) | (~aElement0(W0!22)) | (~aElement0(xa))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[63, 62])).
% 2.00/1.51 tff(65,plain,
% 2.00/1.51 (aElement0(sdtasdt0(xa, W0!22))),
% 2.00/1.51 inference(unit_resolution,[status(thm)],[64, 61, 48, 45])).
% 2.00/1.51 tff(66,plain,
% 2.00/1.51 (aElement0(W1!21)),
% 2.00/1.51 inference(and_elim,[status(thm)],[7])).
% 2.00/1.51 tff(67,plain,
% 2.00/1.51 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xb, W1!21)) | (~aElement0(W1!21)) | (~aElement0(xb)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xb, W1!21)) | (~aElement0(W1!21)) | (~aElement0(xb)))),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(68,plain,
% 2.00/1.51 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xb, W1!21)) | (~aElement0(W1!21)) | (~aElement0(xb)))),
% 2.00/1.51 inference(quant_inst,[status(thm)],[])).
% 2.00/1.51 tff(69,plain,
% 2.00/1.51 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xb, W1!21)) | (~aElement0(W1!21)) | (~aElement0(xb))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[68, 67])).
% 2.00/1.51 tff(70,plain,
% 2.00/1.51 (aElement0(sdtasdt0(xb, W1!21))),
% 2.00/1.51 inference(unit_resolution,[status(thm)],[69, 61, 14, 66])).
% 2.00/1.51 tff(71,plain,
% 2.00/1.51 (^[W0: $i, W1: $i] : refl((aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 2.00/1.51 inference(bind,[status(th)],[])).
% 2.00/1.51 tff(72,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.00/1.51 inference(quant_intro,[status(thm)],[71])).
% 2.00/1.51 tff(73,plain,
% 2.00/1.51 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aElement0(W0))))), ((aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtpldt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))))), rewrite((aElement0(sdtpldt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))), ((aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 2.00/1.51 inference(bind,[status(th)],[])).
% 2.00/1.51 tff(74,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.00/1.51 inference(quant_intro,[status(thm)],[73])).
% 2.00/1.51 tff(75,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(76,plain,
% 2.00/1.51 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 2.00/1.51 inference(bind,[status(th)],[])).
% 2.00/1.51 tff(77,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.00/1.51 inference(quant_intro,[status(thm)],[76])).
% 2.00/1.51 tff(78,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB')).
% 2.00/1.51 tff(79,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[78, 77])).
% 2.00/1.51 tff(80,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[79, 75])).
% 2.00/1.51 tff(81,plain,(
% 2.00/1.51 ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.00/1.51 inference(skolemize,[status(sab)],[80])).
% 2.00/1.51 tff(82,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[81, 74])).
% 2.00/1.51 tff(83,plain,
% 2.00/1.51 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.00/1.51 inference(modus_ponens,[status(thm)],[82, 72])).
% 2.00/1.51 tff(84,plain,
% 2.00/1.51 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(xa, W0!22))) | (~aElement0(sdtasdt0(xb, W1!21))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xa, W0!22))) | (~aElement0(sdtasdt0(xb, W1!21))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21))))),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(85,plain,
% 2.00/1.51 ((aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21))) | (~aElement0(sdtasdt0(xb, W1!21))) | (~aElement0(sdtasdt0(xa, W0!22)))) <=> ((~aElement0(sdtasdt0(xa, W0!22))) | (~aElement0(sdtasdt0(xb, W1!21))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21))))),
% 2.00/1.51 inference(rewrite,[status(thm)],[])).
% 2.00/1.51 tff(86,plain,
% 2.00/1.51 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21))) | (~aElement0(sdtasdt0(xb, W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(xa, W0!22))) | (~aElement0(sdtasdt0(xb, W1!21))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))))),
% 2.00/1.51 inference(monotonicity,[status(thm)],[85])).
% 2.00/1.51 tff(87,plain,
% 2.00/1.51 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21))) | (~aElement0(sdtasdt0(xb, W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xa, W0!22))) | (~aElement0(sdtasdt0(xb, W1!21))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21))))),
% 2.00/1.52 inference(transitivity,[status(thm)],[86, 84])).
% 2.00/1.52 tff(88,plain,
% 2.00/1.52 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21))) | (~aElement0(sdtasdt0(xb, W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))))),
% 2.00/1.52 inference(quant_inst,[status(thm)],[])).
% 2.00/1.52 tff(89,plain,
% 2.00/1.52 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xa, W0!22))) | (~aElement0(sdtasdt0(xb, W1!21))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))),
% 2.00/1.52 inference(modus_ponens,[status(thm)],[88, 87])).
% 2.00/1.52 tff(90,plain,
% 2.00/1.52 ((~aElement0(sdtasdt0(xa, W0!22))) | (~aElement0(sdtasdt0(xb, W1!21))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))),
% 2.00/1.52 inference(unit_resolution,[status(thm)],[89, 83])).
% 2.00/1.52 tff(91,plain,
% 2.00/1.52 (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))),
% 2.00/1.52 inference(unit_resolution,[status(thm)],[90, 70, 65])).
% 2.00/1.52 tff(92,plain,
% 2.00/1.52 ((~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb)))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb))),
% 2.00/1.52 inference(tautology,[status(thm)],[])).
% 2.00/1.52 tff(93,plain,
% 2.00/1.52 (~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb)))),
% 2.00/1.52 inference(unit_resolution,[status(thm)],[92, 91, 44])).
% 2.00/1.52 tff(94,plain,
% 2.00/1.52 ((~(aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb) <=> (~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb)))))) | aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb) | ((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb)))),
% 2.00/1.52 inference(tautology,[status(thm)],[])).
% 2.00/1.52 tff(95,plain,
% 2.00/1.52 ((~(aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb) <=> (~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb)))))) | aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb)),
% 2.00/1.52 inference(unit_resolution,[status(thm)],[94, 93])).
% 2.00/1.52 tff(96,plain,
% 2.00/1.52 (aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xb)),
% 2.00/1.52 inference(unit_resolution,[status(thm)],[95, 36])).
% 2.00/1.52 tff(97,plain,
% 2.00/1.52 (aDivisorOf0(xu, xb)),
% 2.00/1.52 inference(modus_ponens,[status(thm)],[96, 10])).
% 2.00/1.52 tff(98,plain,
% 2.00/1.52 (aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa) <=> aDivisorOf0(xu, xa)),
% 2.00/1.52 inference(monotonicity,[status(thm)],[9])).
% 2.00/1.52 tff(99,plain,
% 2.00/1.52 (((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))) | ((~aElement0(xa)) | ![W1: $i] : (aDivisorOf0(W1, xa) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xa))))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))) | (~aElement0(xa)) | ![W1: $i] : (aDivisorOf0(W1, xa) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xa))))))),
% 2.00/1.52 inference(rewrite,[status(thm)],[])).
% 2.00/1.52 tff(100,plain,
% 2.00/1.52 ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))) | ((~aElement0(xa)) | ![W1: $i] : (aDivisorOf0(W1, xa) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xa))))))),
% 2.00/1.52 inference(quant_inst,[status(thm)],[])).
% 2.00/1.52 tff(101,plain,
% 2.00/1.52 ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (aDivisorOf0(W1, W0) <=> (~((~aElement0(W1)) | (~doDivides0(W1, W0))))))) | (~aElement0(xa)) | ![W1: $i] : (aDivisorOf0(W1, xa) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xa)))))),
% 2.00/1.52 inference(modus_ponens,[status(thm)],[100, 99])).
% 2.00/1.52 tff(102,plain,
% 2.00/1.52 (![W1: $i] : (aDivisorOf0(W1, xa) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xa)))))),
% 2.00/1.52 inference(unit_resolution,[status(thm)],[101, 30, 48])).
% 2.00/1.52 tff(103,plain,
% 2.00/1.52 ((~![W1: $i] : (aDivisorOf0(W1, xa) <=> (~((~aElement0(W1)) | (~doDivides0(W1, xa)))))) | (aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa) <=> (~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa)))))),
% 2.00/1.52 inference(quant_inst,[status(thm)],[])).
% 2.00/1.52 tff(104,plain,
% 2.00/1.52 (aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa) <=> (~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa))))),
% 2.00/1.52 inference(unit_resolution,[status(thm)],[103, 102])).
% 2.00/1.52 tff(105,plain,
% 2.00/1.52 (doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa) <=> doDivides0(xu, xa)),
% 2.00/1.52 inference(monotonicity,[status(thm)],[9])).
% 2.00/1.52 tff(106,plain,
% 2.00/1.52 (doDivides0(xu, xa) <=> doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa)),
% 2.00/1.52 inference(symmetry,[status(thm)],[105])).
% 2.00/1.52 tff(107,plain,
% 2.00/1.52 (doDivides0(xu, xa) <=> doDivides0(xu, xa)),
% 2.00/1.52 inference(rewrite,[status(thm)],[])).
% 2.00/1.52 tff(108,plain,
% 2.00/1.52 ((~(~doDivides0(xu, xa))) <=> doDivides0(xu, xa)),
% 2.00/1.52 inference(rewrite,[status(thm)],[])).
% 2.00/1.52 tff(109,axiom,(~(~doDivides0(xu, xa))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2479')).
% 2.00/1.52 tff(110,plain,
% 2.00/1.52 (doDivides0(xu, xa)),
% 2.00/1.52 inference(modus_ponens,[status(thm)],[109, 108])).
% 2.00/1.52 tff(111,plain,
% 2.00/1.52 (doDivides0(xu, xa)),
% 2.00/1.52 inference(modus_ponens,[status(thm)],[110, 107])).
% 2.00/1.52 tff(112,plain,
% 2.00/1.52 (doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa)),
% 2.00/1.52 inference(modus_ponens,[status(thm)],[111, 106])).
% 2.00/1.52 tff(113,plain,
% 2.00/1.52 ((~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa)))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa))),
% 2.00/1.52 inference(tautology,[status(thm)],[])).
% 2.00/1.52 tff(114,plain,
% 2.00/1.52 (~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa)))),
% 2.00/1.52 inference(unit_resolution,[status(thm)],[113, 91, 112])).
% 2.00/1.52 tff(115,plain,
% 2.00/1.52 ((~(aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa) <=> (~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa)))))) | aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa) | ((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa)))),
% 2.00/1.52 inference(tautology,[status(thm)],[])).
% 2.00/1.52 tff(116,plain,
% 2.00/1.52 ((~(aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa) <=> (~((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)))) | (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa)))))) | aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa)),
% 2.00/1.52 inference(unit_resolution,[status(thm)],[115, 114])).
% 2.00/1.52 tff(117,plain,
% 2.00/1.52 (aDivisorOf0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(xb, W1!21)), xa)),
% 2.00/1.52 inference(unit_resolution,[status(thm)],[116, 104])).
% 2.00/1.52 tff(118,plain,
% 2.00/1.52 (aDivisorOf0(xu, xa)),
% 2.00/1.52 inference(modus_ponens,[status(thm)],[117, 98])).
% 2.00/1.52 tff(119,plain,
% 2.00/1.52 ((~(~((~aDivisorOf0(xu, xa)) | (~aDivisorOf0(xu, xb))))) <=> ((~aDivisorOf0(xu, xa)) | (~aDivisorOf0(xu, xb)))),
% 2.00/1.52 inference(rewrite,[status(thm)],[])).
% 2.00/1.52 tff(120,plain,
% 2.00/1.52 ((aDivisorOf0(xu, xa) & aDivisorOf0(xu, xb)) <=> (~((~aDivisorOf0(xu, xa)) | (~aDivisorOf0(xu, xb))))),
% 2.00/1.52 inference(rewrite,[status(thm)],[])).
% 2.00/1.52 tff(121,plain,
% 2.00/1.52 ((~(aDivisorOf0(xu, xa) & aDivisorOf0(xu, xb))) <=> (~(~((~aDivisorOf0(xu, xa)) | (~aDivisorOf0(xu, xb)))))),
% 2.00/1.52 inference(monotonicity,[status(thm)],[120])).
% 2.00/1.52 tff(122,plain,
% 2.00/1.52 ((~(aDivisorOf0(xu, xa) & aDivisorOf0(xu, xb))) <=> ((~aDivisorOf0(xu, xa)) | (~aDivisorOf0(xu, xb)))),
% 2.00/1.52 inference(transitivity,[status(thm)],[121, 119])).
% 2.00/1.52 tff(123,plain,
% 2.00/1.52 ((~(aDivisorOf0(xu, xa) & aDivisorOf0(xu, xb))) <=> (~(aDivisorOf0(xu, xa) & aDivisorOf0(xu, xb)))),
% 2.00/1.52 inference(rewrite,[status(thm)],[])).
% 2.00/1.52 tff(124,axiom,(~(aDivisorOf0(xu, xa) & aDivisorOf0(xu, xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2383')).
% 2.00/1.52 tff(125,plain,
% 2.00/1.52 (~(aDivisorOf0(xu, xa) & aDivisorOf0(xu, xb))),
% 2.00/1.52 inference(modus_ponens,[status(thm)],[124, 123])).
% 2.00/1.52 tff(126,plain,
% 2.00/1.52 ((~aDivisorOf0(xu, xa)) | (~aDivisorOf0(xu, xb))),
% 2.00/1.52 inference(modus_ponens,[status(thm)],[125, 122])).
% 2.00/1.52 tff(127,plain,
% 2.00/1.52 ($false),
% 2.00/1.52 inference(unit_resolution,[status(thm)],[126, 118, 97])).
% 2.00/1.52 % SZS output end Proof
%------------------------------------------------------------------------------