TSTP Solution File: RNG119+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG119+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 03:18:30 EDT 2022
% Result : Theorem 2.97s 2.17s
% Output : Proof 3.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG119+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 22:41:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 2.97/2.17 % SZS status Theorem
% 2.97/2.17 % SZS output start Proof
% 2.97/2.17 tff(sdtpldt0_type, type, (
% 2.97/2.17 sdtpldt0: ( $i * $i ) > $i)).
% 2.97/2.17 tff(sz00_type, type, (
% 2.97/2.17 sz00: $i)).
% 2.97/2.17 tff(sdtasdt0_type, type, (
% 2.97/2.17 sdtasdt0: ( $i * $i ) > $i)).
% 2.97/2.17 tff(xu_type, type, (
% 2.97/2.17 xu: $i)).
% 2.97/2.17 tff(xq_type, type, (
% 2.97/2.17 xq: $i)).
% 2.97/2.17 tff(tptp_fun_W3_13_type, type, (
% 2.97/2.17 tptp_fun_W3_13: ( $i * $i ) > $i)).
% 2.97/2.17 tff(sz10_type, type, (
% 2.97/2.17 sz10: $i)).
% 2.97/2.17 tff(tptp_fun_W2_14_type, type, (
% 2.97/2.17 tptp_fun_W2_14: ( $i * $i ) > $i)).
% 2.97/2.17 tff(tptp_fun_W1_21_type, type, (
% 2.97/2.17 tptp_fun_W1_21: $i)).
% 2.97/2.17 tff(tptp_fun_W0_22_type, type, (
% 2.97/2.17 tptp_fun_W0_22: $i)).
% 2.97/2.17 tff(xa_type, type, (
% 2.97/2.17 xa: $i)).
% 2.97/2.17 tff(aElement0_type, type, (
% 2.97/2.17 aElement0: $i > $o)).
% 2.97/2.17 tff(xb_type, type, (
% 2.97/2.17 xb: $i)).
% 2.97/2.17 tff(xr_type, type, (
% 2.97/2.17 xr: $i)).
% 2.97/2.17 tff(iLess0_type, type, (
% 2.97/2.17 iLess0: ( $i * $i ) > $o)).
% 2.97/2.17 tff(sbrdtbr0_type, type, (
% 2.97/2.17 sbrdtbr0: $i > $i)).
% 2.97/2.17 tff(doDivides0_type, type, (
% 2.97/2.17 doDivides0: ( $i * $i ) > $o)).
% 2.97/2.17 tff(tptp_fun_W2_15_type, type, (
% 2.97/2.17 tptp_fun_W2_15: ( $i * $i ) > $i)).
% 2.97/2.17 tff(1,plain,
% 2.97/2.17 (^[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)))))),
% 2.97/2.17 inference(bind,[status(th)],[])).
% 2.97/2.17 tff(2,plain,
% 2.97/2.17 (?[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))))),
% 2.97/2.17 inference(quant_intro,[status(thm)],[1])).
% 2.97/2.17 tff(3,plain,
% 2.97/2.17 (?[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))))),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(4,plain,
% 2.97/2.17 (^[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)))))),
% 2.97/2.17 inference(bind,[status(th)],[])).
% 2.97/2.17 tff(5,plain,
% 2.97/2.17 (?[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))))),
% 2.97/2.17 inference(quant_intro,[status(thm)],[4])).
% 2.97/2.17 tff(6,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')).
% 2.97/2.17 tff(7,plain,
% 2.97/2.17 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.97/2.17 tff(8,plain,
% 2.97/2.17 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.97/2.17 tff(9,plain,
% 2.97/2.17 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1))))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[8, 2])).
% 2.97/2.17 tff(10,plain,(
% 2.97/2.17 aElement0(W0!22) & aElement0(W1!21) & (xu = sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))),
% 2.97/2.17 inference(skolemize,[status(sab)],[9])).
% 2.97/2.17 tff(11,plain,
% 2.97/2.17 (xu = sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))),
% 2.97/2.17 inference(and_elim,[status(thm)],[10])).
% 2.97/2.17 tff(12,plain,
% 2.97/2.17 (sdtasdt0(xq, xu) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))),
% 2.97/2.17 inference(monotonicity,[status(thm)],[11])).
% 2.97/2.17 tff(13,plain,
% 2.97/2.17 (aElement0(sdtasdt0(xq, xu)) <=> aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))),
% 2.97/2.17 inference(monotonicity,[status(thm)],[12])).
% 2.97/2.17 tff(14,plain,
% 2.97/2.17 (aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) <=> aElement0(sdtasdt0(xq, xu))),
% 2.97/2.17 inference(symmetry,[status(thm)],[13])).
% 2.97/2.17 tff(15,plain,
% 2.97/2.17 (aElement0(W0!22)),
% 2.97/2.17 inference(and_elim,[status(thm)],[10])).
% 2.97/2.17 tff(16,plain,
% 2.97/2.17 (aElement0(xa) <=> aElement0(xa)),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(17,axiom,(aElement0(xa) & aElement0(xb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2091')).
% 2.97/2.17 tff(18,plain,
% 2.97/2.17 (aElement0(xa)),
% 2.97/2.17 inference(and_elim,[status(thm)],[17])).
% 2.97/2.17 tff(19,plain,
% 2.97/2.17 (aElement0(xa)),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[18, 16])).
% 2.97/2.17 tff(20,plain,
% 2.97/2.17 (^[W0: $i, W1: $i] : refl((aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 2.97/2.17 inference(bind,[status(th)],[])).
% 2.97/2.17 tff(21,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(quant_intro,[status(thm)],[20])).
% 2.97/2.17 tff(22,plain,
% 2.97/2.17 (^[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)))))),
% 2.97/2.17 inference(bind,[status(th)],[])).
% 2.97/2.17 tff(23,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(quant_intro,[status(thm)],[22])).
% 2.97/2.17 tff(24,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(25,plain,
% 2.97/2.17 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 2.97/2.17 inference(bind,[status(th)],[])).
% 2.97/2.17 tff(26,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.97/2.17 inference(quant_intro,[status(thm)],[25])).
% 2.97/2.17 tff(27,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB_02')).
% 2.97/2.17 tff(28,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[27, 26])).
% 2.97/2.17 tff(29,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[28, 24])).
% 2.97/2.17 tff(30,plain,(
% 2.97/2.17 ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.97/2.17 inference(skolemize,[status(sab)],[29])).
% 2.97/2.17 tff(31,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[30, 23])).
% 2.97/2.17 tff(32,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[31, 21])).
% 2.97/2.17 tff(33,plain,
% 2.97/2.17 (((~![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)))),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(34,plain,
% 2.97/2.17 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!22)) | (~aElement0(W0!22)) | (~aElement0(xa)))),
% 2.97/2.17 inference(quant_inst,[status(thm)],[])).
% 2.97/2.17 tff(35,plain,
% 2.97/2.17 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!22)) | (~aElement0(W0!22)) | (~aElement0(xa))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[34, 33])).
% 2.97/2.17 tff(36,plain,
% 2.97/2.17 (aElement0(sdtasdt0(xa, W0!22))),
% 2.97/2.17 inference(unit_resolution,[status(thm)],[35, 32, 19, 15])).
% 2.97/2.17 tff(37,plain,
% 2.97/2.17 (aElement0(W1!21)),
% 2.97/2.17 inference(and_elim,[status(thm)],[10])).
% 2.97/2.17 tff(38,plain,
% 2.97/2.17 (aElement0(xb) <=> aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(39,plain,
% 2.97/2.17 (aElement0(xb) <=> aElement0(xb)),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(40,plain,
% 2.97/2.17 (aElement0(xb)),
% 2.97/2.17 inference(and_elim,[status(thm)],[17])).
% 2.97/2.17 tff(41,plain,
% 2.97/2.17 (aElement0(xb)),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[40, 39])).
% 2.97/2.17 tff(42,plain,
% 2.97/2.17 (aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[41, 38])).
% 2.97/2.17 tff(43,plain,
% 2.97/2.17 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)) | (~aElement0(W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)) | (~aElement0(W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(44,plain,
% 2.97/2.17 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)) | (~aElement0(W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 2.97/2.17 inference(quant_inst,[status(thm)],[])).
% 2.97/2.17 tff(45,plain,
% 2.97/2.17 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)) | (~aElement0(W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00)))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[44, 43])).
% 2.97/2.17 tff(46,plain,
% 2.97/2.17 (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))),
% 2.97/2.17 inference(unit_resolution,[status(thm)],[45, 32, 42, 37])).
% 2.97/2.17 tff(47,plain,
% 2.97/2.17 (^[W0: $i, W1: $i] : refl((aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 2.97/2.17 inference(bind,[status(th)],[])).
% 2.97/2.17 tff(48,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(quant_intro,[status(thm)],[47])).
% 2.97/2.17 tff(49,plain,
% 2.97/2.17 (^[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)))))),
% 2.97/2.17 inference(bind,[status(th)],[])).
% 2.97/2.17 tff(50,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(quant_intro,[status(thm)],[49])).
% 2.97/2.17 tff(51,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(52,plain,
% 2.97/2.17 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 2.97/2.17 inference(bind,[status(th)],[])).
% 2.97/2.17 tff(53,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.97/2.17 inference(quant_intro,[status(thm)],[52])).
% 2.97/2.17 tff(54,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB')).
% 2.97/2.17 tff(55,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[54, 53])).
% 2.97/2.17 tff(56,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[55, 51])).
% 2.97/2.17 tff(57,plain,(
% 2.97/2.17 ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 2.97/2.17 inference(skolemize,[status(sab)],[56])).
% 2.97/2.17 tff(58,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[57, 50])).
% 2.97/2.17 tff(59,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[58, 48])).
% 2.97/2.17 tff(60,plain,
% 2.97/2.17 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(61,plain,
% 2.97/2.17 ((aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22)))) <=> ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(62,plain,
% 2.97/2.17 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))),
% 2.97/2.17 inference(monotonicity,[status(thm)],[61])).
% 2.97/2.17 tff(63,plain,
% 2.97/2.17 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))),
% 2.97/2.17 inference(transitivity,[status(thm)],[62, 60])).
% 2.97/2.17 tff(64,plain,
% 2.97/2.17 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))))),
% 2.97/2.17 inference(quant_inst,[status(thm)],[])).
% 2.97/2.17 tff(65,plain,
% 2.97/2.17 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[64, 63])).
% 2.97/2.17 tff(66,plain,
% 2.97/2.17 ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))),
% 2.97/2.17 inference(unit_resolution,[status(thm)],[65, 59])).
% 2.97/2.17 tff(67,plain,
% 2.97/2.17 (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))),
% 2.97/2.17 inference(unit_resolution,[status(thm)],[66, 46, 36])).
% 2.97/2.17 tff(68,plain,
% 2.97/2.17 (aElement0(xq) <=> aElement0(xq)),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(69,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')).
% 2.97/2.17 tff(70,plain,
% 2.97/2.17 ((aElement0(xq) & aElement0(xr)) & (xb = sdtpldt0(sdtasdt0(xq, xu), xr))),
% 2.97/2.17 inference(and_elim,[status(thm)],[69])).
% 2.97/2.17 tff(71,plain,
% 2.97/2.17 (aElement0(xq) & aElement0(xr)),
% 2.97/2.17 inference(and_elim,[status(thm)],[70])).
% 2.97/2.17 tff(72,plain,
% 2.97/2.17 (aElement0(xq)),
% 2.97/2.17 inference(and_elim,[status(thm)],[71])).
% 2.97/2.17 tff(73,plain,
% 2.97/2.17 (aElement0(xq)),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[72, 68])).
% 2.97/2.17 tff(74,plain,
% 2.97/2.17 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(75,plain,
% 2.97/2.17 ((aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(xq))) <=> ((~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(76,plain,
% 2.97/2.17 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(xq)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))))),
% 2.97/2.17 inference(monotonicity,[status(thm)],[75])).
% 2.97/2.17 tff(77,plain,
% 2.97/2.17 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(xq)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))),
% 2.97/2.17 inference(transitivity,[status(thm)],[76, 74])).
% 2.97/2.17 tff(78,plain,
% 2.97/2.17 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(xq)))),
% 2.97/2.17 inference(quant_inst,[status(thm)],[])).
% 2.97/2.17 tff(79,plain,
% 2.97/2.17 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[78, 77])).
% 2.97/2.17 tff(80,plain,
% 2.97/2.17 ((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))),
% 2.97/2.17 inference(unit_resolution,[status(thm)],[79, 32, 73])).
% 2.97/2.17 tff(81,plain,
% 2.97/2.17 (aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))),
% 2.97/2.17 inference(unit_resolution,[status(thm)],[80, 67])).
% 2.97/2.17 tff(82,plain,
% 2.97/2.17 (aElement0(sdtasdt0(xq, xu))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[81, 14])).
% 2.97/2.17 tff(83,plain,
% 2.97/2.17 (^[W0: $i, W1: $i] : refl(((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 2.97/2.17 inference(bind,[status(th)],[])).
% 2.97/2.17 tff(84,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(quant_intro,[status(thm)],[83])).
% 2.97/2.17 tff(85,plain,
% 2.97/2.17 (^[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))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> (((~aElement0(W1)) | (~aElement0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))), rewrite((((~aElement0(W1)) | (~aElement0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))), (((~(aElement0(W0) & aElement0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 2.97/2.17 inference(bind,[status(th)],[])).
% 2.97/2.17 tff(86,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(quant_intro,[status(thm)],[85])).
% 2.97/2.17 tff(87,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(88,plain,
% 2.97/2.17 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((~(aElement0(W0) & aElement0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))),
% 2.97/2.17 inference(bind,[status(th)],[])).
% 2.97/2.17 tff(89,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 2.97/2.17 inference(quant_intro,[status(thm)],[88])).
% 2.97/2.17 tff(90,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddComm')).
% 2.97/2.17 tff(91,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[90, 89])).
% 2.97/2.17 tff(92,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[91, 87])).
% 2.97/2.17 tff(93,plain,(
% 2.97/2.17 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 2.97/2.17 inference(skolemize,[status(sab)],[92])).
% 2.97/2.17 tff(94,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[93, 86])).
% 2.97/2.17 tff(95,plain,
% 2.97/2.17 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[94, 84])).
% 2.97/2.17 tff(96,plain,
% 2.97/2.17 (aElement0(sz00) <=> aElement0(sz00)),
% 2.97/2.17 inference(rewrite,[status(thm)],[])).
% 2.97/2.17 tff(97,axiom,(aElement0(sz00)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsC')).
% 2.97/2.17 tff(98,plain,
% 2.97/2.17 (aElement0(sz00)),
% 2.97/2.17 inference(modus_ponens,[status(thm)],[97, 96])).
% 2.97/2.17 tff(99,plain,
% 2.97/2.17 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00)) | (~aElement0(sz00)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00)) | (~aElement0(sz00)))),
% 2.97/2.18 inference(rewrite,[status(thm)],[])).
% 2.97/2.18 tff(100,plain,
% 2.97/2.18 (((sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(sz00))) <=> ((~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00)) | (~aElement0(sz00)))),
% 2.97/2.18 inference(rewrite,[status(thm)],[])).
% 2.97/2.18 tff(101,plain,
% 2.97/2.18 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(sz00)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00)) | (~aElement0(sz00))))),
% 2.97/2.18 inference(monotonicity,[status(thm)],[100])).
% 2.97/2.18 tff(102,plain,
% 2.97/2.18 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(sz00)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00)) | (~aElement0(sz00)))),
% 2.97/2.18 inference(transitivity,[status(thm)],[101, 99])).
% 2.97/2.18 tff(103,plain,
% 2.97/2.18 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(sz00)))),
% 2.97/2.18 inference(quant_inst,[status(thm)],[])).
% 2.97/2.18 tff(104,plain,
% 2.97/2.18 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00)) | (~aElement0(sz00))),
% 2.97/2.18 inference(modus_ponens,[status(thm)],[103, 102])).
% 2.97/2.18 tff(105,plain,
% 3.06/2.18 ((~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 3.06/2.18 inference(unit_resolution,[status(thm)],[104, 98, 95])).
% 3.06/2.18 tff(106,plain,
% 3.06/2.18 (sdtpldt0(sz00, sdtasdt0(xq, xu)) = sdtpldt0(sdtasdt0(xq, xu), sz00)),
% 3.06/2.18 inference(unit_resolution,[status(thm)],[105, 82])).
% 3.06/2.18 tff(107,plain,
% 3.06/2.18 (^[W0: $i] : refl(((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 3.06/2.18 inference(bind,[status(th)],[])).
% 3.06/2.18 tff(108,plain,
% 3.06/2.18 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 3.06/2.18 inference(quant_intro,[status(thm)],[107])).
% 3.06/2.18 tff(109,plain,
% 3.06/2.18 (^[W0: $i] : rewrite(((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 3.06/2.18 inference(bind,[status(th)],[])).
% 3.06/2.18 tff(110,plain,
% 3.06/2.18 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 3.06/2.18 inference(quant_intro,[status(thm)],[109])).
% 3.06/2.18 tff(111,plain,
% 3.06/2.18 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 3.06/2.18 inference(rewrite,[status(thm)],[])).
% 3.06/2.18 tff(112,plain,
% 3.06/2.18 (^[W0: $i] : rewrite((aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))))),
% 3.06/2.18 inference(bind,[status(th)],[])).
% 3.06/2.18 tff(113,plain,
% 3.06/2.18 (![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 3.06/2.18 inference(quant_intro,[status(thm)],[112])).
% 3.06/2.18 tff(114,axiom,(![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddZero')).
% 3.06/2.18 tff(115,plain,
% 3.06/2.18 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[114, 113])).
% 3.06/2.18 tff(116,plain,
% 3.06/2.18 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[115, 111])).
% 3.06/2.18 tff(117,plain,(
% 3.06/2.18 ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 3.06/2.18 inference(skolemize,[status(sab)],[116])).
% 3.06/2.18 tff(118,plain,
% 3.06/2.18 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[117, 110])).
% 3.06/2.18 tff(119,plain,
% 3.06/2.18 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[118, 108])).
% 3.06/2.18 tff(120,plain,
% 3.06/2.18 (((~![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)))))))),
% 3.06/2.18 inference(rewrite,[status(thm)],[])).
% 3.06/2.18 tff(121,plain,
% 3.06/2.18 ((~![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)))))))),
% 3.06/2.18 inference(quant_inst,[status(thm)],[])).
% 3.06/2.18 tff(122,plain,
% 3.06/2.18 ((~![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))))))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[121, 120])).
% 3.06/2.18 tff(123,plain,
% 3.06/2.18 ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu))))))),
% 3.06/2.18 inference(unit_resolution,[status(thm)],[122, 119])).
% 3.06/2.18 tff(124,plain,
% 3.06/2.18 (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu)))))),
% 3.06/2.18 inference(unit_resolution,[status(thm)],[123, 82])).
% 3.06/2.18 tff(125,plain,
% 3.06/2.18 (((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu))))) | (sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu)))),
% 3.06/2.18 inference(tautology,[status(thm)],[])).
% 3.06/2.18 tff(126,plain,
% 3.06/2.18 (sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu))),
% 3.06/2.18 inference(unit_resolution,[status(thm)],[125, 124])).
% 3.06/2.18 tff(127,plain,
% 3.06/2.18 (sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))) = sdtasdt0(xq, xu)),
% 3.06/2.18 inference(symmetry,[status(thm)],[12])).
% 3.06/2.18 tff(128,plain,
% 3.06/2.18 (^[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))))),
% 3.06/2.18 inference(bind,[status(th)],[])).
% 3.06/2.18 tff(129,plain,
% 3.06/2.18 (![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)))),
% 3.06/2.18 inference(quant_intro,[status(thm)],[128])).
% 3.06/2.18 tff(130,plain,
% 3.06/2.18 (^[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)))))),
% 3.06/2.18 inference(bind,[status(th)],[])).
% 3.06/2.18 tff(131,plain,
% 3.06/2.18 (![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)))),
% 3.06/2.18 inference(quant_intro,[status(thm)],[130])).
% 3.06/2.18 tff(132,plain,
% 3.06/2.18 (![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)))),
% 3.06/2.18 inference(rewrite,[status(thm)],[])).
% 3.06/2.18 tff(133,plain,
% 3.06/2.18 (^[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))))),
% 3.06/2.18 inference(bind,[status(th)],[])).
% 3.06/2.18 tff(134,plain,
% 3.06/2.18 (![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)))),
% 3.06/2.18 inference(quant_intro,[status(thm)],[133])).
% 3.06/2.18 tff(135,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulComm')).
% 3.06/2.18 tff(136,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[135, 134])).
% 3.06/2.18 tff(137,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[136, 132])).
% 3.06/2.18 tff(138,plain,(
% 3.06/2.18 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 3.06/2.18 inference(skolemize,[status(sab)],[137])).
% 3.06/2.18 tff(139,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[138, 131])).
% 3.06/2.18 tff(140,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[139, 129])).
% 3.06/2.18 tff(141,plain,
% 3.06/2.18 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))),
% 3.06/2.18 inference(rewrite,[status(thm)],[])).
% 3.06/2.18 tff(142,plain,
% 3.06/2.18 (((sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))) <=> ((~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))),
% 3.06/2.18 inference(rewrite,[status(thm)],[])).
% 3.06/2.18 tff(143,plain,
% 3.06/2.18 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))))),
% 3.06/2.18 inference(monotonicity,[status(thm)],[142])).
% 3.06/2.18 tff(144,plain,
% 3.06/2.18 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))),
% 3.06/2.18 inference(transitivity,[status(thm)],[143, 141])).
% 3.06/2.18 tff(145,plain,
% 3.06/2.18 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))))),
% 3.06/2.18 inference(quant_inst,[status(thm)],[])).
% 3.06/2.18 tff(146,plain,
% 3.06/2.18 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[145, 144])).
% 3.06/2.18 tff(147,plain,
% 3.06/2.18 ((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))),
% 3.06/2.18 inference(unit_resolution,[status(thm)],[146, 140, 73])).
% 3.06/2.18 tff(148,plain,
% 3.06/2.18 (sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))),
% 3.06/2.18 inference(unit_resolution,[status(thm)],[147, 67])).
% 3.06/2.18 tff(149,plain,
% 3.06/2.18 (^[W0: $i, W1: $i] : refl(((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))) <=> ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))))),
% 3.06/2.18 inference(bind,[status(th)],[])).
% 3.06/2.18 tff(150,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))) <=> ![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))),
% 3.06/2.18 inference(quant_intro,[status(thm)],[149])).
% 3.06/2.18 tff(151,plain,
% 3.06/2.18 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1) & (~(W1 = sz00))) <=> (~((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) <=> (~(~((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))))) <=> ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) <=> ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))))), rewrite((aElement0(tptp_fun_W2_14(W1, W0)) & aElement0(tptp_fun_W3_13(W1, W0)) & (W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0))) & ((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))) <=> (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))), (((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | (aElement0(tptp_fun_W2_14(W1, W0)) & aElement0(tptp_fun_W3_13(W1, W0)) & (W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0))) & ((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))) <=> (((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))))), rewrite((((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))) <=> ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))), (((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | (aElement0(tptp_fun_W2_14(W1, W0)) & aElement0(tptp_fun_W3_13(W1, W0)) & (W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0))) & ((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))) <=> ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))))),
% 3.06/2.18 inference(bind,[status(th)],[])).
% 3.06/2.18 tff(152,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | (aElement0(tptp_fun_W2_14(W1, W0)) & aElement0(tptp_fun_W3_13(W1, W0)) & (W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0))) & ((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))) <=> ![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))),
% 3.06/2.18 inference(quant_intro,[status(thm)],[151])).
% 3.06/2.18 tff(153,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))),
% 3.06/2.18 inference(rewrite,[status(thm)],[])).
% 3.06/2.18 tff(154,plain,
% 3.06/2.18 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((aElement0(W0) & aElement0(W1)) & (~(W1 = sz00))) <=> (aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))), quant_intro(proof_bind(^[W2: $i, W3: $i] : trans(monotonicity(rewrite(((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) <=> (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)))), rewrite(((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1))) <=> ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))), ((((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))) <=> ((aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))), rewrite(((aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))) <=> (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))), ((((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))) <=> (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))))), (?[W2: $i, W3: $i] : (((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))) <=> ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))), ((((aElement0(W0) & aElement0(W1)) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))) <=> ((aElement0(W0) & aElement0(W1) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))))), rewrite(((aElement0(W0) & aElement0(W1) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))) <=> ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))), ((((aElement0(W0) & aElement0(W1)) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))) <=> ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))))),
% 3.06/2.18 inference(bind,[status(th)],[])).
% 3.06/2.18 tff(155,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : (((aElement0(W0) & aElement0(W1)) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))),
% 3.06/2.18 inference(quant_intro,[status(thm)],[154])).
% 3.06/2.18 tff(156,axiom,(![W0: $i, W1: $i] : (((aElement0(W0) & aElement0(W1)) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDivision')).
% 3.06/2.18 tff(157,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[156, 155])).
% 3.06/2.18 tff(158,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[157, 153])).
% 3.06/2.18 tff(159,plain,(
% 3.06/2.18 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | (aElement0(tptp_fun_W2_14(W1, W0)) & aElement0(tptp_fun_W3_13(W1, W0)) & (W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0))) & ((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))),
% 3.06/2.18 inference(skolemize,[status(sab)],[158])).
% 3.06/2.18 tff(160,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[159, 152])).
% 3.06/2.18 tff(161,plain,
% 3.06/2.18 (![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[160, 150])).
% 3.06/2.18 tff(162,plain,
% 3.06/2.18 ((~(sz10 = sz00)) <=> (~(sz10 = sz00))),
% 3.06/2.18 inference(rewrite,[status(thm)],[])).
% 3.06/2.18 tff(163,axiom,(~(sz10 = sz00)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mUnNeZr')).
% 3.06/2.18 tff(164,plain,
% 3.06/2.18 (~(sz10 = sz00)),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[163, 162])).
% 3.06/2.18 tff(165,plain,
% 3.06/2.18 (aElement0(sz10) <=> aElement0(sz10)),
% 3.06/2.18 inference(rewrite,[status(thm)],[])).
% 3.06/2.18 tff(166,axiom,(aElement0(sz10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsC_01')).
% 3.06/2.18 tff(167,plain,
% 3.06/2.18 (aElement0(sz10)),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[166, 165])).
% 3.06/2.18 tff(168,plain,
% 3.06/2.18 (((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | ((sz10 = sz00) | (~aElement0(xq)) | (~aElement0(sz10)) | (~((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10)))))))) <=> ((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | (sz10 = sz00) | (~aElement0(xq)) | (~aElement0(sz10)) | (~((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10)))))))),
% 3.06/2.18 inference(rewrite,[status(thm)],[])).
% 3.06/2.18 tff(169,plain,
% 3.06/2.18 (((sz10 = sz00) | (~aElement0(sz10)) | (~aElement0(xq)) | (~((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10))))))) <=> ((sz10 = sz00) | (~aElement0(xq)) | (~aElement0(sz10)) | (~((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10)))))))),
% 3.06/2.18 inference(rewrite,[status(thm)],[])).
% 3.06/2.18 tff(170,plain,
% 3.06/2.18 (((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | ((sz10 = sz00) | (~aElement0(sz10)) | (~aElement0(xq)) | (~((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10)))))))) <=> ((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | ((sz10 = sz00) | (~aElement0(xq)) | (~aElement0(sz10)) | (~((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10))))))))),
% 3.06/2.18 inference(monotonicity,[status(thm)],[169])).
% 3.06/2.18 tff(171,plain,
% 3.06/2.18 (((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | ((sz10 = sz00) | (~aElement0(sz10)) | (~aElement0(xq)) | (~((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10)))))))) <=> ((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | (sz10 = sz00) | (~aElement0(xq)) | (~aElement0(sz10)) | (~((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10)))))))),
% 3.06/2.18 inference(transitivity,[status(thm)],[170, 168])).
% 3.06/2.18 tff(172,plain,
% 3.06/2.18 ((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | ((sz10 = sz00) | (~aElement0(sz10)) | (~aElement0(xq)) | (~((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10)))))))),
% 3.06/2.18 inference(quant_inst,[status(thm)],[])).
% 3.06/2.18 tff(173,plain,
% 3.06/2.18 ((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | (sz10 = sz00) | (~aElement0(xq)) | (~aElement0(sz10)) | (~((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10))))))),
% 3.06/2.18 inference(modus_ponens,[status(thm)],[172, 171])).
% 3.06/2.18 tff(174,plain,
% 3.06/2.18 (~((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10)))))),
% 3.06/2.18 inference(unit_resolution,[status(thm)],[173, 167, 164, 161, 73])).
% 3.06/2.18 tff(175,plain,
% 3.06/2.18 (((~aElement0(tptp_fun_W2_14(sz10, xq))) | (~aElement0(tptp_fun_W3_13(sz10, xq))) | (~(xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~((tptp_fun_W3_13(sz10, xq) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(sz10, xq)), sbrdtbr0(sz10))))) | (xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))),
% 3.06/2.19 inference(tautology,[status(thm)],[])).
% 3.06/2.19 tff(176,plain,
% 3.06/2.19 (xq = sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq))),
% 3.06/2.19 inference(unit_resolution,[status(thm)],[175, 174])).
% 3.06/2.19 tff(177,plain,
% 3.06/2.19 (sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)) = xq),
% 3.06/2.19 inference(symmetry,[status(thm)],[176])).
% 3.06/2.19 tff(178,plain,
% 3.06/2.19 (sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq))) = sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), xq)),
% 3.06/2.19 inference(monotonicity,[status(thm)],[177])).
% 3.06/2.19 tff(179,plain,
% 3.06/2.19 (sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq))) = sdtpldt0(sdtasdt0(xq, xu), sz00)),
% 3.06/2.19 inference(transitivity,[status(thm)],[178, 148, 127, 126, 106])).
% 3.06/2.19 tff(180,plain,
% 3.06/2.19 (aElement0(sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq))) <=> aElement0(xq)),
% 3.06/2.19 inference(monotonicity,[status(thm)],[177])).
% 3.06/2.19 tff(181,plain,
% 3.06/2.19 (aElement0(xq) <=> aElement0(sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))),
% 3.06/2.19 inference(symmetry,[status(thm)],[180])).
% 3.06/2.19 tff(182,plain,
% 3.06/2.19 (aElement0(sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))),
% 3.06/2.19 inference(modus_ponens,[status(thm)],[73, 181])).
% 3.06/2.19 tff(183,plain,
% 3.06/2.19 (^[W0: $i, W1: $i] : refl(((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1)))))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1)))))))))),
% 3.06/2.19 inference(bind,[status(th)],[])).
% 3.06/2.19 tff(184,plain,
% 3.06/2.19 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))),
% 3.06/2.19 inference(quant_intro,[status(thm)],[183])).
% 3.06/2.19 tff(185,plain,
% 3.06/2.19 (^[W0: $i, W1: $i] : rewrite(((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1)))))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1)))))))))),
% 3.06/2.19 inference(bind,[status(th)],[])).
% 3.06/2.19 tff(186,plain,
% 3.06/2.19 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))),
% 3.06/2.19 inference(quant_intro,[status(thm)],[185])).
% 3.06/2.19 tff(187,plain,
% 3.06/2.19 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))),
% 3.06/2.19 inference(transitivity,[status(thm)],[186, 184])).
% 3.06/2.19 tff(188,plain,
% 3.06/2.19 (^[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))))), trans(monotonicity(rewrite(((~doDivides0(W0, W1)) | (aElement0(tptp_fun_W2_15(W1, W0)) & (sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1))) <=> ((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))), rewrite((doDivides0(W0, W1) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(W0, W2) = W1)))) <=> (doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))), ((((~doDivides0(W0, W1)) | (aElement0(tptp_fun_W2_15(W1, W0)) & (sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(W0, W2) = W1))))) <=> (((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1))))) & (doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))), rewrite((((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1))))) & (doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))) <=> (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1)))))))), ((((~doDivides0(W0, W1)) | (aElement0(tptp_fun_W2_15(W1, W0)) & (sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(W0, W2) = W1))))) <=> (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))), (((~(aElement0(W0) & aElement0(W1))) | (((~doDivides0(W0, W1)) | (aElement0(tptp_fun_W2_15(W1, W0)) & (sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(W0, W2) = W1)))))) <=> (((~aElement0(W1)) | (~aElement0(W0))) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1)))))))))), rewrite((((~aElement0(W1)) | (~aElement0(W0))) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1)))))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))), (((~(aElement0(W0) & aElement0(W1))) | (((~doDivides0(W0, W1)) | (aElement0(tptp_fun_W2_15(W1, W0)) & (sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(W0, W2) = W1)))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))))),
% 3.06/2.19 inference(bind,[status(th)],[])).
% 3.06/2.19 tff(189,plain,
% 3.06/2.19 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (((~doDivides0(W0, W1)) | (aElement0(tptp_fun_W2_15(W1, W0)) & (sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(W0, W2) = W1)))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))),
% 3.06/2.19 inference(quant_intro,[status(thm)],[188])).
% 3.06/2.19 tff(190,plain,
% 3.06/2.19 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1)))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1))))),
% 3.06/2.19 inference(rewrite,[status(thm)],[])).
% 3.06/2.19 tff(191,plain,
% 3.06/2.19 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1))) <=> (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1)))), (((aElement0(W0) & aElement0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1)))) <=> ((aElement0(W0) & aElement0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1)))))), rewrite(((aElement0(W0) & aElement0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1)))) <=> ((~(aElement0(W0) & aElement0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1))))), (((aElement0(W0) & aElement0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1)))) <=> ((~(aElement0(W0) & aElement0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1))))))),
% 3.06/2.19 inference(bind,[status(th)],[])).
% 3.06/2.19 tff(192,plain,
% 3.06/2.19 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1)))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1))))),
% 3.06/2.19 inference(quant_intro,[status(thm)],[191])).
% 3.06/2.19 tff(193,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefDiv')).
% 3.06/2.19 tff(194,plain,
% 3.06/2.19 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1))))),
% 3.06/2.19 inference(modus_ponens,[status(thm)],[193, 192])).
% 3.06/2.19 tff(195,plain,
% 3.06/2.19 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(W0, W2) = W1))))),
% 3.06/2.19 inference(modus_ponens,[status(thm)],[194, 190])).
% 3.06/2.19 tff(196,plain,(
% 3.06/2.19 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (((~doDivides0(W0, W1)) | (aElement0(tptp_fun_W2_15(W1, W0)) & (sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(W0, W2) = W1))))))),
% 3.06/2.19 inference(skolemize,[status(sab)],[195])).
% 3.06/2.19 tff(197,plain,
% 3.06/2.19 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))),
% 3.06/2.19 inference(modus_ponens,[status(thm)],[196, 189])).
% 3.06/2.19 tff(198,plain,
% 3.06/2.19 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))),
% 3.06/2.19 inference(modus_ponens,[status(thm)],[197, 187])).
% 3.06/2.19 tff(199,plain,
% 3.06/2.19 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))) | ((~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~((~((~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~((~aElement0(tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))) | (~(doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00)))))))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~((~((~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~((~aElement0(tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))) | (~(doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00)))))))))),
% 3.06/2.19 inference(rewrite,[status(thm)],[])).
% 3.06/2.19 tff(200,plain,
% 3.06/2.19 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))) | ((~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~((~((~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~((~aElement0(tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))) | (~(doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00)))))))))),
% 3.06/2.19 inference(quant_inst,[status(thm)],[])).
% 3.06/2.19 tff(201,plain,
% 3.06/2.19 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aElement0(tptp_fun_W2_15(W1, W0))) | (~(sdtasdt0(W0, tptp_fun_W2_15(W1, W0)) = W1)))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(W0, W2) = W1))))))))) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~((~((~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~((~aElement0(tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))) | (~(doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))))),
% 3.06/2.19 inference(modus_ponens,[status(thm)],[200, 199])).
% 3.06/2.19 tff(202,plain,
% 3.06/2.19 ((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) | (~((~((~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~((~aElement0(tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))) | (~(doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))))),
% 3.06/2.19 inference(unit_resolution,[status(thm)],[201, 198, 42])).
% 3.06/2.19 tff(203,plain,
% 3.06/2.19 (~((~((~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~((~aElement0(tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))) | (~(doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00)))))))),
% 3.06/2.19 inference(unit_resolution,[status(thm)],[202, 67])).
% 3.06/2.19 tff(204,plain,
% 3.06/2.19 (((~((~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00))) | (~((~aElement0(tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21))))) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), tptp_fun_W2_15(sdtpldt0(sdtasdt0(xq, xu), sz00), sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)))) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))) | (~(doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00))))))) | (doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00)))))),
% 3.06/2.19 inference(tautology,[status(thm)],[])).
% 3.06/2.19 tff(205,plain,
% 3.06/2.19 (doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 3.06/2.19 inference(unit_resolution,[status(thm)],[204, 203])).
% 3.06/2.19 tff(206,plain,
% 3.06/2.19 (sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)) = xu),
% 3.06/2.19 inference(symmetry,[status(thm)],[11])).
% 3.06/2.19 tff(207,plain,
% 3.06/2.19 (doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) <=> doDivides0(xu, sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 3.06/2.19 inference(monotonicity,[status(thm)],[206])).
% 3.06/2.19 tff(208,plain,
% 3.06/2.19 (doDivides0(xu, sdtpldt0(sdtasdt0(xq, xu), sz00)) <=> doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 3.06/2.19 inference(symmetry,[status(thm)],[207])).
% 3.06/2.19 tff(209,plain,
% 3.06/2.19 ((~doDivides0(xu, sdtpldt0(sdtasdt0(xq, xu), sz00))) <=> (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)))),
% 3.06/2.19 inference(monotonicity,[status(thm)],[208])).
% 3.06/2.19 tff(210,plain,
% 3.06/2.19 ((~doDivides0(xu, xb)) <=> (~doDivides0(xu, sdtpldt0(sdtasdt0(xq, xu), sz00)))),
% 3.06/2.19 inference(rewrite,[status(thm)],[])).
% 3.06/2.19 tff(211,plain,
% 3.06/2.19 ((~doDivides0(xu, xb)) <=> (~doDivides0(xu, xb))),
% 3.06/2.19 inference(rewrite,[status(thm)],[])).
% 3.06/2.19 tff(212,axiom,(~doDivides0(xu, xb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2612')).
% 3.06/2.19 tff(213,plain,
% 3.06/2.19 (~doDivides0(xu, xb)),
% 3.06/2.19 inference(modus_ponens,[status(thm)],[212, 211])).
% 3.06/2.19 tff(214,plain,
% 3.06/2.19 (~doDivides0(xu, sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 3.06/2.19 inference(modus_ponens,[status(thm)],[213, 210])).
% 3.06/2.19 tff(215,plain,
% 3.06/2.19 (~doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 3.06/2.19 inference(modus_ponens,[status(thm)],[214, 209])).
% 3.06/2.19 tff(216,plain,
% 3.06/2.19 ((~(doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00)))))) | doDivides0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(xq, xu), sz00)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 3.06/2.19 inference(tautology,[status(thm)],[])).
% 3.06/2.19 tff(217,plain,
% 3.06/2.19 (![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 3.06/2.19 inference(unit_resolution,[status(thm)],[216, 215, 205])).
% 3.06/2.19 tff(218,plain,
% 3.06/2.19 (((~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00))))) | ((~aElement0(sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq))) = sdtpldt0(sdtasdt0(xq, xu), sz00))))) <=> ((~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00))))) | (~aElement0(sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq))) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 3.06/2.20 inference(rewrite,[status(thm)],[])).
% 3.06/2.20 tff(219,plain,
% 3.06/2.20 ((~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00))))) | ((~aElement0(sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq))) = sdtpldt0(sdtasdt0(xq, xu), sz00))))),
% 3.06/2.20 inference(quant_inst,[status(thm)],[])).
% 3.06/2.20 tff(220,plain,
% 3.06/2.20 ((~![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), W2) = sdtpldt0(sdtasdt0(xq, xu), sz00))))) | (~aElement0(sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq)))) | (~(sdtasdt0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), sz00), W1!21)), sdtpldt0(sdtasdt0(tptp_fun_W2_14(sz10, xq), sz10), tptp_fun_W3_13(sz10, xq))) = sdtpldt0(sdtasdt0(xq, xu), sz00)))),
% 3.06/2.20 inference(modus_ponens,[status(thm)],[219, 218])).
% 3.06/2.20 tff(221,plain,
% 3.06/2.20 ($false),
% 3.06/2.20 inference(unit_resolution,[status(thm)],[220, 217, 182, 179])).
% 3.06/2.20 % SZS output end Proof
%------------------------------------------------------------------------------