TSTP Solution File: RNG119+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG119+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 03:18:31 EDT 2022
% Result : Theorem 5.19s 3.47s
% Output : Proof 5.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG119+4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 22:43:09 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.
% 5.19/3.47 % SZS status Theorem
% 5.19/3.47 % SZS output start Proof
% 5.19/3.47 tff(sdtpldt0_type, type, (
% 5.19/3.47 sdtpldt0: ( $i * $i ) > $i)).
% 5.19/3.47 tff(sz00_type, type, (
% 5.19/3.47 sz00: $i)).
% 5.19/3.47 tff(sdtasdt0_type, type, (
% 5.19/3.47 sdtasdt0: ( $i * $i ) > $i)).
% 5.19/3.47 tff(xu_type, type, (
% 5.19/3.47 xu: $i)).
% 5.19/3.47 tff(xq_type, type, (
% 5.19/3.47 xq: $i)).
% 5.19/3.47 tff(aElement0_type, type, (
% 5.19/3.47 aElement0: $i > $o)).
% 5.19/3.47 tff(tptp_fun_W1_38_type, type, (
% 5.19/3.47 tptp_fun_W1_38: $i)).
% 5.19/3.47 tff(tptp_fun_W0_39_type, type, (
% 5.19/3.47 tptp_fun_W0_39: $i)).
% 5.19/3.47 tff(xa_type, type, (
% 5.19/3.47 xa: $i)).
% 5.19/3.47 tff(xb_type, type, (
% 5.19/3.47 xb: $i)).
% 5.19/3.47 tff(xr_type, type, (
% 5.19/3.47 xr: $i)).
% 5.19/3.47 tff(iLess0_type, type, (
% 5.19/3.47 iLess0: ( $i * $i ) > $o)).
% 5.19/3.47 tff(sbrdtbr0_type, type, (
% 5.19/3.47 sbrdtbr0: $i > $i)).
% 5.19/3.47 tff(doDivides0_type, type, (
% 5.19/3.47 doDivides0: ( $i * $i ) > $o)).
% 5.19/3.47 tff(1,plain,
% 5.19/3.47 ((sdtasdt0(xq, xu) = sdtpldt0(sdtasdt0(xq, xu), sz00)) <=> (sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))),
% 5.19/3.47 inference(commutativity,[status(thm)],[])).
% 5.19/3.47 tff(2,plain,
% 5.19/3.47 (^[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(sdtpldt0(sdtasdt0(xq, xu), sz00), W1)))))),
% 5.19/3.47 inference(bind,[status(th)],[])).
% 5.19/3.47 tff(3,plain,
% 5.19/3.47 (?[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(sdtpldt0(sdtasdt0(xq, xu), sz00), W1))))),
% 5.19/3.47 inference(quant_intro,[status(thm)],[2])).
% 5.19/3.47 tff(4,plain,
% 5.19/3.47 (?[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))))),
% 5.19/3.47 inference(rewrite,[status(thm)],[])).
% 5.19/3.47 tff(5,plain,
% 5.19/3.47 (^[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)))))),
% 5.19/3.47 inference(bind,[status(th)],[])).
% 5.19/3.47 tff(6,plain,
% 5.19/3.47 (?[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))))),
% 5.19/3.47 inference(quant_intro,[status(thm)],[5])).
% 5.19/3.47 tff(7,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')).
% 5.19/3.47 tff(8,plain,
% 5.19/3.47 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[7, 6])).
% 5.19/3.47 tff(9,plain,
% 5.19/3.47 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[8, 4])).
% 5.19/3.47 tff(10,plain,
% 5.19/3.47 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1))))),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[9, 3])).
% 5.19/3.47 tff(11,plain,(
% 5.19/3.47 aElement0(W0!39) & aElement0(W1!38) & (xu = sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)))),
% 5.19/3.47 inference(skolemize,[status(sab)],[10])).
% 5.19/3.47 tff(12,plain,
% 5.19/3.47 (xu = sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))),
% 5.19/3.47 inference(and_elim,[status(thm)],[11])).
% 5.19/3.47 tff(13,plain,
% 5.19/3.47 (sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)) = xu),
% 5.19/3.47 inference(symmetry,[status(thm)],[12])).
% 5.19/3.47 tff(14,plain,
% 5.19/3.47 (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) <=> aElement0(xu)),
% 5.19/3.47 inference(monotonicity,[status(thm)],[13])).
% 5.19/3.47 tff(15,plain,
% 5.19/3.47 (aElement0(W0!39)),
% 5.19/3.47 inference(and_elim,[status(thm)],[11])).
% 5.19/3.47 tff(16,plain,
% 5.19/3.47 (aElement0(xa) <=> aElement0(xa)),
% 5.19/3.47 inference(rewrite,[status(thm)],[])).
% 5.19/3.47 tff(17,axiom,(aElement0(xa) & aElement0(xb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2091')).
% 5.19/3.47 tff(18,plain,
% 5.19/3.47 (aElement0(xa)),
% 5.19/3.47 inference(and_elim,[status(thm)],[17])).
% 5.19/3.47 tff(19,plain,
% 5.19/3.47 (aElement0(xa)),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[18, 16])).
% 5.19/3.47 tff(20,plain,
% 5.19/3.47 (^[W0: $i, W1: $i] : refl((aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 5.19/3.47 inference(bind,[status(th)],[])).
% 5.19/3.47 tff(21,plain,
% 5.19/3.47 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.47 inference(quant_intro,[status(thm)],[20])).
% 5.19/3.47 tff(22,plain,
% 5.19/3.47 (^[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)))))),
% 5.19/3.47 inference(bind,[status(th)],[])).
% 5.19/3.47 tff(23,plain,
% 5.19/3.47 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.47 inference(quant_intro,[status(thm)],[22])).
% 5.19/3.47 tff(24,plain,
% 5.19/3.47 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 5.19/3.47 inference(rewrite,[status(thm)],[])).
% 5.19/3.47 tff(25,plain,
% 5.19/3.47 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 5.19/3.47 inference(bind,[status(th)],[])).
% 5.19/3.47 tff(26,plain,
% 5.19/3.47 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 5.19/3.47 inference(quant_intro,[status(thm)],[25])).
% 5.19/3.47 tff(27,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB_02')).
% 5.19/3.47 tff(28,plain,
% 5.19/3.47 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[27, 26])).
% 5.19/3.47 tff(29,plain,
% 5.19/3.47 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[28, 24])).
% 5.19/3.47 tff(30,plain,(
% 5.19/3.47 ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 5.19/3.47 inference(skolemize,[status(sab)],[29])).
% 5.19/3.47 tff(31,plain,
% 5.19/3.47 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[30, 23])).
% 5.19/3.47 tff(32,plain,
% 5.19/3.47 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[31, 21])).
% 5.19/3.47 tff(33,plain,
% 5.19/3.47 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa)))),
% 5.19/3.47 inference(rewrite,[status(thm)],[])).
% 5.19/3.47 tff(34,plain,
% 5.19/3.47 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa)))),
% 5.19/3.47 inference(quant_inst,[status(thm)],[])).
% 5.19/3.47 tff(35,plain,
% 5.19/3.47 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa))),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[34, 33])).
% 5.19/3.47 tff(36,plain,
% 5.19/3.47 (aElement0(sdtasdt0(xa, W0!39))),
% 5.19/3.47 inference(unit_resolution,[status(thm)],[35, 32, 19, 15])).
% 5.19/3.47 tff(37,plain,
% 5.19/3.47 (aElement0(W1!38)),
% 5.19/3.47 inference(and_elim,[status(thm)],[11])).
% 5.19/3.47 tff(38,plain,
% 5.19/3.47 (aElement0(xb) <=> aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 5.19/3.47 inference(rewrite,[status(thm)],[])).
% 5.19/3.47 tff(39,plain,
% 5.19/3.47 (aElement0(xb) <=> aElement0(xb)),
% 5.19/3.47 inference(rewrite,[status(thm)],[])).
% 5.19/3.47 tff(40,plain,
% 5.19/3.47 (aElement0(xb)),
% 5.19/3.47 inference(and_elim,[status(thm)],[17])).
% 5.19/3.47 tff(41,plain,
% 5.19/3.47 (aElement0(xb)),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[40, 39])).
% 5.19/3.47 tff(42,plain,
% 5.19/3.47 (aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[41, 38])).
% 5.19/3.47 tff(43,plain,
% 5.19/3.47 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)))),
% 5.19/3.47 inference(rewrite,[status(thm)],[])).
% 5.19/3.47 tff(44,plain,
% 5.19/3.47 ((aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)) | (~aElement0(W1!38)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00)))) <=> ((~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)))),
% 5.19/3.47 inference(rewrite,[status(thm)],[])).
% 5.19/3.47 tff(45,plain,
% 5.19/3.47 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)) | (~aElement0(W1!38)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))))),
% 5.19/3.47 inference(monotonicity,[status(thm)],[44])).
% 5.19/3.47 tff(46,plain,
% 5.19/3.47 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)) | (~aElement0(W1!38)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)))),
% 5.19/3.47 inference(transitivity,[status(thm)],[45, 43])).
% 5.19/3.47 tff(47,plain,
% 5.19/3.47 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)) | (~aElement0(W1!38)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 5.19/3.47 inference(quant_inst,[status(thm)],[])).
% 5.19/3.47 tff(48,plain,
% 5.19/3.47 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))),
% 5.19/3.47 inference(modus_ponens,[status(thm)],[47, 46])).
% 5.19/3.47 tff(49,plain,
% 5.19/3.47 (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))),
% 5.19/3.47 inference(unit_resolution,[status(thm)],[48, 32, 42, 37])).
% 5.19/3.47 tff(50,plain,
% 5.19/3.47 (^[W0: $i, W1: $i] : refl((aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 5.19/3.47 inference(bind,[status(th)],[])).
% 5.19/3.47 tff(51,plain,
% 5.19/3.47 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.47 inference(quant_intro,[status(thm)],[50])).
% 5.19/3.47 tff(52,plain,
% 5.19/3.47 (^[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)))))),
% 5.19/3.48 inference(bind,[status(th)],[])).
% 5.19/3.48 tff(53,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.48 inference(quant_intro,[status(thm)],[52])).
% 5.19/3.48 tff(54,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 5.19/3.48 inference(rewrite,[status(thm)],[])).
% 5.19/3.48 tff(55,plain,
% 5.19/3.48 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 5.19/3.48 inference(bind,[status(th)],[])).
% 5.19/3.48 tff(56,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 5.19/3.48 inference(quant_intro,[status(thm)],[55])).
% 5.19/3.48 tff(57,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB')).
% 5.19/3.48 tff(58,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[57, 56])).
% 5.19/3.48 tff(59,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[58, 54])).
% 5.19/3.48 tff(60,plain,(
% 5.19/3.48 ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 5.19/3.48 inference(skolemize,[status(sab)],[59])).
% 5.19/3.48 tff(61,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[60, 53])).
% 5.19/3.48 tff(62,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[61, 51])).
% 5.19/3.48 tff(63,plain,
% 5.19/3.48 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))))),
% 5.19/3.48 inference(rewrite,[status(thm)],[])).
% 5.19/3.48 tff(64,plain,
% 5.19/3.48 ((aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39)))) <=> ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))))),
% 5.19/3.48 inference(rewrite,[status(thm)],[])).
% 5.19/3.48 tff(65,plain,
% 5.19/3.48 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)))))),
% 5.19/3.48 inference(monotonicity,[status(thm)],[64])).
% 5.19/3.48 tff(66,plain,
% 5.19/3.48 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))))),
% 5.19/3.48 inference(transitivity,[status(thm)],[65, 63])).
% 5.19/3.48 tff(67,plain,
% 5.19/3.48 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))))),
% 5.19/3.48 inference(quant_inst,[status(thm)],[])).
% 5.19/3.48 tff(68,plain,
% 5.19/3.48 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)))),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[67, 66])).
% 5.19/3.48 tff(69,plain,
% 5.19/3.48 ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)))),
% 5.19/3.48 inference(unit_resolution,[status(thm)],[68, 62])).
% 5.19/3.48 tff(70,plain,
% 5.19/3.48 (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!38)))),
% 5.19/3.48 inference(unit_resolution,[status(thm)],[69, 49, 36])).
% 5.19/3.48 tff(71,plain,
% 5.19/3.48 (aElement0(xu)),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[70, 14])).
% 5.19/3.48 tff(72,plain,
% 5.19/3.48 (aElement0(xq) <=> aElement0(xq)),
% 5.19/3.48 inference(rewrite,[status(thm)],[])).
% 5.19/3.48 tff(73,axiom,(((aElement0(xq) & aElement0(xr)) & (xb = sdtpldt0(sdtasdt0(xq, xu), xr))) & ((xr = sz00) | iLess0(sbrdtbr0(xr), sbrdtbr0(xu)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2666')).
% 5.19/3.48 tff(74,plain,
% 5.19/3.48 ((aElement0(xq) & aElement0(xr)) & (xb = sdtpldt0(sdtasdt0(xq, xu), xr))),
% 5.19/3.48 inference(and_elim,[status(thm)],[73])).
% 5.19/3.48 tff(75,plain,
% 5.19/3.48 (aElement0(xq) & aElement0(xr)),
% 5.19/3.48 inference(and_elim,[status(thm)],[74])).
% 5.19/3.48 tff(76,plain,
% 5.19/3.48 (aElement0(xq)),
% 5.19/3.48 inference(and_elim,[status(thm)],[75])).
% 5.19/3.48 tff(77,plain,
% 5.19/3.48 (aElement0(xq)),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[76, 72])).
% 5.19/3.48 tff(78,plain,
% 5.19/3.48 (^[W0: $i, W1: $i] : refl(((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 5.19/3.48 inference(bind,[status(th)],[])).
% 5.19/3.48 tff(79,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.48 inference(quant_intro,[status(thm)],[78])).
% 5.19/3.48 tff(80,plain,
% 5.19/3.48 (^[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(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> (((~aElement0(W1)) | (~aElement0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))), rewrite((((~aElement0(W1)) | (~aElement0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))), (((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 5.19/3.48 inference(bind,[status(th)],[])).
% 5.19/3.48 tff(81,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.48 inference(quant_intro,[status(thm)],[80])).
% 5.19/3.48 tff(82,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 5.19/3.48 inference(rewrite,[status(thm)],[])).
% 5.19/3.48 tff(83,plain,
% 5.19/3.48 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))),
% 5.19/3.48 inference(bind,[status(th)],[])).
% 5.19/3.48 tff(84,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 5.19/3.48 inference(quant_intro,[status(thm)],[83])).
% 5.19/3.48 tff(85,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulComm')).
% 5.19/3.48 tff(86,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[85, 84])).
% 5.19/3.48 tff(87,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[86, 82])).
% 5.19/3.48 tff(88,plain,(
% 5.19/3.48 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 5.19/3.48 inference(skolemize,[status(sab)],[87])).
% 5.19/3.48 tff(89,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[88, 81])).
% 5.19/3.48 tff(90,plain,
% 5.19/3.48 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[89, 79])).
% 5.19/3.48 tff(91,plain,
% 5.19/3.48 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu)))),
% 5.19/3.48 inference(rewrite,[status(thm)],[])).
% 5.19/3.48 tff(92,plain,
% 5.19/3.48 (((sdtasdt0(xu, xq) = sdtasdt0(xq, xu)) | (~aElement0(xq)) | (~aElement0(xu))) <=> ((~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu)))),
% 5.19/3.48 inference(rewrite,[status(thm)],[])).
% 5.19/3.48 tff(93,plain,
% 5.19/3.48 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(xu, xq) = sdtasdt0(xq, xu)) | (~aElement0(xq)) | (~aElement0(xu)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu))))),
% 5.19/3.48 inference(monotonicity,[status(thm)],[92])).
% 5.19/3.48 tff(94,plain,
% 5.19/3.48 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(xu, xq) = sdtasdt0(xq, xu)) | (~aElement0(xq)) | (~aElement0(xu)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu)))),
% 5.19/3.48 inference(transitivity,[status(thm)],[93, 91])).
% 5.19/3.48 tff(95,plain,
% 5.19/3.48 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(xu, xq) = sdtasdt0(xq, xu)) | (~aElement0(xq)) | (~aElement0(xu)))),
% 5.19/3.48 inference(quant_inst,[status(thm)],[])).
% 5.19/3.48 tff(96,plain,
% 5.19/3.48 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu))),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[95, 94])).
% 5.19/3.48 tff(97,plain,
% 5.19/3.48 ((~aElement0(xu)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu))),
% 5.19/3.48 inference(unit_resolution,[status(thm)],[96, 90, 77])).
% 5.19/3.48 tff(98,plain,
% 5.19/3.48 (sdtasdt0(xu, xq) = sdtasdt0(xq, xu)),
% 5.19/3.48 inference(unit_resolution,[status(thm)],[97, 71])).
% 5.19/3.48 tff(99,plain,
% 5.19/3.48 ((sdtasdt0(xu, xq) = sdtpldt0(sdtasdt0(xq, xu), sz00)) <=> (sdtasdt0(xq, xu) = sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 5.19/3.48 inference(monotonicity,[status(thm)],[98])).
% 5.19/3.48 tff(100,plain,
% 5.19/3.48 ((sdtasdt0(xu, xq) = sdtpldt0(sdtasdt0(xq, xu), sz00)) <=> (sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))),
% 5.19/3.48 inference(transitivity,[status(thm)],[99, 1])).
% 5.19/3.48 tff(101,plain,
% 5.19/3.48 ((sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu)) <=> (sdtasdt0(xu, xq) = sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 5.19/3.48 inference(symmetry,[status(thm)],[100])).
% 5.19/3.48 tff(102,plain,
% 5.19/3.48 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu)))),
% 5.19/3.48 inference(rewrite,[status(thm)],[])).
% 5.19/3.48 tff(103,plain,
% 5.19/3.48 ((aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq))) <=> ((~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu)))),
% 5.19/3.48 inference(rewrite,[status(thm)],[])).
% 5.19/3.48 tff(104,plain,
% 5.19/3.48 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu))))),
% 5.19/3.48 inference(monotonicity,[status(thm)],[103])).
% 5.19/3.48 tff(105,plain,
% 5.19/3.48 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu)))),
% 5.19/3.48 inference(transitivity,[status(thm)],[104, 102])).
% 5.19/3.48 tff(106,plain,
% 5.19/3.48 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq)))),
% 5.19/3.48 inference(quant_inst,[status(thm)],[])).
% 5.19/3.48 tff(107,plain,
% 5.19/3.48 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu))),
% 5.19/3.48 inference(modus_ponens,[status(thm)],[106, 105])).
% 5.19/3.48 tff(108,plain,
% 5.19/3.48 ((~aElement0(xu)) | aElement0(sdtasdt0(xq, xu))),
% 5.19/3.48 inference(unit_resolution,[status(thm)],[107, 32, 77])).
% 5.19/3.48 tff(109,plain,
% 5.19/3.48 (aElement0(sdtasdt0(xq, xu))),
% 5.19/3.48 inference(unit_resolution,[status(thm)],[108, 71])).
% 5.19/3.48 tff(110,plain,
% 5.19/3.48 (^[W0: $i] : refl(((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 5.19/3.48 inference(bind,[status(th)],[])).
% 5.19/3.48 tff(111,plain,
% 5.19/3.48 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 5.19/3.48 inference(quant_intro,[status(thm)],[110])).
% 5.19/3.48 tff(112,plain,
% 5.19/3.48 (^[W0: $i] : rewrite(((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 5.19/3.49 inference(bind,[status(th)],[])).
% 5.19/3.49 tff(113,plain,
% 5.19/3.49 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 5.19/3.49 inference(quant_intro,[status(thm)],[112])).
% 5.19/3.49 tff(114,plain,
% 5.19/3.49 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 5.19/3.49 inference(rewrite,[status(thm)],[])).
% 5.19/3.49 tff(115,plain,
% 5.19/3.49 (^[W0: $i] : rewrite((aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))))),
% 5.19/3.49 inference(bind,[status(th)],[])).
% 5.19/3.49 tff(116,plain,
% 5.19/3.49 (![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 5.19/3.49 inference(quant_intro,[status(thm)],[115])).
% 5.19/3.49 tff(117,axiom,(![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddZero')).
% 5.19/3.49 tff(118,plain,
% 5.19/3.49 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[117, 116])).
% 5.19/3.49 tff(119,plain,
% 5.19/3.49 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[118, 114])).
% 5.19/3.49 tff(120,plain,(
% 5.19/3.49 ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 5.19/3.49 inference(skolemize,[status(sab)],[119])).
% 5.19/3.49 tff(121,plain,
% 5.19/3.49 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[120, 113])).
% 5.19/3.49 tff(122,plain,
% 5.19/3.49 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[121, 111])).
% 5.19/3.49 tff(123,plain,
% 5.19/3.49 (((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu)))))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu)))))))),
% 5.19/3.49 inference(rewrite,[status(thm)],[])).
% 5.19/3.49 tff(124,plain,
% 5.19/3.49 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu)))))))),
% 5.19/3.49 inference(quant_inst,[status(thm)],[])).
% 5.19/3.49 tff(125,plain,
% 5.19/3.49 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu))))))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[124, 123])).
% 5.19/3.49 tff(126,plain,
% 5.19/3.49 ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu))))))),
% 5.19/3.49 inference(unit_resolution,[status(thm)],[125, 122])).
% 5.19/3.49 tff(127,plain,
% 5.19/3.49 (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu)))))),
% 5.19/3.49 inference(unit_resolution,[status(thm)],[126, 109])).
% 5.19/3.49 tff(128,plain,
% 5.19/3.49 (((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu))))) | (sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))),
% 5.19/3.49 inference(tautology,[status(thm)],[])).
% 5.19/3.49 tff(129,plain,
% 5.19/3.49 (sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu)),
% 5.19/3.49 inference(unit_resolution,[status(thm)],[128, 127])).
% 5.19/3.49 tff(130,plain,
% 5.19/3.49 (sdtasdt0(xu, xq) = sdtpldt0(sdtasdt0(xq, xu), sz00)),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[129, 101])).
% 5.19/3.49 tff(131,plain,
% 5.19/3.49 (^[W0: $i] : refl(((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))) <=> ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))))),
% 5.19/3.49 inference(bind,[status(th)],[])).
% 5.19/3.49 tff(132,plain,
% 5.19/3.49 (![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))) <=> ![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 5.19/3.49 inference(quant_intro,[status(thm)],[131])).
% 5.19/3.49 tff(133,plain,
% 5.19/3.49 (^[W0: $i] : trans(monotonicity(rewrite((aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))) <=> (~((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))))), ((~(aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))) <=> (~(~((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))))))), rewrite((~(~((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))))) <=> ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))), ((~(aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))) <=> ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))),
% 5.19/3.49 inference(bind,[status(th)],[])).
% 5.19/3.49 tff(134,plain,
% 5.19/3.49 (![W0: $i] : (~(aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))) <=> ![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 5.19/3.49 inference(quant_intro,[status(thm)],[133])).
% 5.19/3.49 tff(135,plain,
% 5.19/3.49 ((~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))) <=> (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 5.19/3.49 inference(rewrite,[status(thm)],[])).
% 5.19/3.49 tff(136,plain,
% 5.19/3.49 ((~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb))) <=> (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 5.19/3.49 inference(rewrite,[status(thm)],[])).
% 5.19/3.49 tff(137,plain,
% 5.19/3.49 ((~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb))) <=> (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb)))),
% 5.19/3.49 inference(rewrite,[status(thm)],[])).
% 5.19/3.49 tff(138,axiom,(~(?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb)) | doDivides0(xu, xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2612')).
% 5.19/3.49 tff(139,plain,
% 5.19/3.49 (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb))),
% 5.19/3.49 inference(or_elim,[status(thm)],[138])).
% 5.19/3.49 tff(140,plain,
% 5.19/3.49 (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[139, 137])).
% 5.19/3.49 tff(141,plain,
% 5.19/3.49 (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[140, 137])).
% 5.19/3.49 tff(142,plain,
% 5.19/3.49 (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[141, 137])).
% 5.19/3.49 tff(143,plain,
% 5.19/3.49 (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[142, 137])).
% 5.19/3.49 tff(144,plain,
% 5.19/3.49 (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[143, 136])).
% 5.19/3.49 tff(145,plain,
% 5.19/3.49 (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[144, 135])).
% 5.19/3.49 tff(146,plain,
% 5.19/3.49 (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[145, 135])).
% 5.19/3.49 tff(147,plain,
% 5.19/3.49 (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))),
% 5.19/3.49 inference(modus_ponens,[status(thm)],[146, 135])).
% 5.19/3.49 tff(148,plain,
% 5.19/3.49 (^[W0: $i] : refl($oeq((~(aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00)))), (~(aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))),
% 5.19/3.49 inference(bind,[status(th)],[])).
% 5.19/3.49 tff(149,plain,(
% 5.19/3.49 ![W0: $i] : (~(aElement0(W0) & (sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 5.19/3.50 inference(nnf-neg,[status(sab)],[147, 148])).
% 5.19/3.50 tff(150,plain,
% 5.19/3.50 (![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 5.19/3.50 inference(modus_ponens,[status(thm)],[149, 134])).
% 5.19/3.50 tff(151,plain,
% 5.19/3.50 (![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 5.19/3.50 inference(modus_ponens,[status(thm)],[150, 132])).
% 5.19/3.50 tff(152,plain,
% 5.19/3.50 (((~![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))) | ((~aElement0(xq)) | (~(sdtasdt0(xu, xq) = sdtpldt0(sdtasdt0(xq, xu), sz00))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))) | (~aElement0(xq)) | (~(sdtasdt0(xu, xq) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 5.19/3.50 inference(rewrite,[status(thm)],[])).
% 5.19/3.50 tff(153,plain,
% 5.19/3.50 ((~![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))) | ((~aElement0(xq)) | (~(sdtasdt0(xu, xq) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 5.19/3.50 inference(quant_inst,[status(thm)],[])).
% 5.19/3.50 tff(154,plain,
% 5.19/3.50 ((~![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = sdtpldt0(sdtasdt0(xq, xu), sz00))))) | (~aElement0(xq)) | (~(sdtasdt0(xu, xq) = sdtpldt0(sdtasdt0(xq, xu), sz00)))),
% 5.19/3.50 inference(modus_ponens,[status(thm)],[153, 152])).
% 5.19/3.50 tff(155,plain,
% 5.19/3.50 (~(sdtasdt0(xu, xq) = sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 5.19/3.50 inference(unit_resolution,[status(thm)],[154, 151, 77])).
% 5.19/3.50 tff(156,plain,
% 5.19/3.50 ($false),
% 5.19/3.50 inference(unit_resolution,[status(thm)],[155, 130])).
% 5.19/3.50 % SZS output end Proof
%------------------------------------------------------------------------------