TSTP Solution File: RNG122+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG122+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 03:18:32 EDT 2022
% Result : Theorem 1.78s 1.36s
% Output : Proof 1.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG122+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.32 % Computer : n001.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Sep 2 23:08:09 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 1.78/1.36 % SZS status Theorem
% 1.78/1.36 % SZS output start Proof
% 1.78/1.36 tff(sdtpldt0_type, type, (
% 1.78/1.36 sdtpldt0: ( $i * $i ) > $i)).
% 1.78/1.36 tff(xr_type, type, (
% 1.78/1.36 xr: $i)).
% 1.78/1.36 tff(sdtasdt0_type, type, (
% 1.78/1.36 sdtasdt0: ( $i * $i ) > $i)).
% 1.78/1.36 tff(xu_type, type, (
% 1.78/1.36 xu: $i)).
% 1.78/1.36 tff(xq_type, type, (
% 1.78/1.36 xq: $i)).
% 1.78/1.36 tff(smndt0_type, type, (
% 1.78/1.36 smndt0: $i > $i)).
% 1.78/1.36 tff(aElement0_type, type, (
% 1.78/1.36 aElement0: $i > $o)).
% 1.78/1.36 tff(tptp_fun_W1_21_type, type, (
% 1.78/1.36 tptp_fun_W1_21: $i)).
% 1.78/1.36 tff(tptp_fun_W0_22_type, type, (
% 1.78/1.36 tptp_fun_W0_22: $i)).
% 1.78/1.36 tff(xa_type, type, (
% 1.78/1.36 xa: $i)).
% 1.78/1.36 tff(xb_type, type, (
% 1.78/1.36 xb: $i)).
% 1.78/1.36 tff(iLess0_type, type, (
% 1.78/1.36 iLess0: ( $i * $i ) > $o)).
% 1.78/1.36 tff(sbrdtbr0_type, type, (
% 1.78/1.36 sbrdtbr0: $i > $i)).
% 1.78/1.36 tff(sz00_type, type, (
% 1.78/1.36 sz00: $i)).
% 1.78/1.36 tff(1,plain,
% 1.78/1.36 (^[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), xr), W1)))))),
% 1.78/1.36 inference(bind,[status(th)],[])).
% 1.78/1.36 tff(2,plain,
% 1.78/1.36 (?[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), xr), W1))))),
% 1.78/1.36 inference(quant_intro,[status(thm)],[1])).
% 1.78/1.36 tff(3,plain,
% 1.78/1.36 (?[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))))),
% 1.78/1.36 inference(rewrite,[status(thm)],[])).
% 1.78/1.36 tff(4,plain,
% 1.78/1.36 (^[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)))))),
% 1.78/1.36 inference(bind,[status(th)],[])).
% 1.78/1.36 tff(5,plain,
% 1.78/1.36 (?[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))))),
% 1.78/1.36 inference(quant_intro,[status(thm)],[4])).
% 1.78/1.36 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')).
% 1.78/1.36 tff(7,plain,
% 1.78/1.36 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 1.78/1.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.78/1.36 tff(8,plain,
% 1.78/1.36 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 1.78/1.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.78/1.36 tff(9,plain,
% 1.78/1.36 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1))))),
% 1.78/1.36 inference(modus_ponens,[status(thm)],[8, 2])).
% 1.78/1.36 tff(10,plain,(
% 1.78/1.36 aElement0(W0!22) & aElement0(W1!21) & (xu = sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))),
% 1.78/1.36 inference(skolemize,[status(sab)],[9])).
% 1.78/1.36 tff(11,plain,
% 1.78/1.36 (xu = sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))),
% 1.78/1.36 inference(and_elim,[status(thm)],[10])).
% 1.78/1.36 tff(12,plain,
% 1.78/1.36 (sdtasdt0(xq, xu) = sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))),
% 1.78/1.36 inference(monotonicity,[status(thm)],[11])).
% 1.78/1.36 tff(13,plain,
% 1.78/1.36 (aElement0(sdtasdt0(xq, xu)) <=> aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))))),
% 1.78/1.36 inference(monotonicity,[status(thm)],[12])).
% 1.78/1.36 tff(14,plain,
% 1.78/1.36 (aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))) <=> aElement0(sdtasdt0(xq, xu))),
% 1.78/1.36 inference(symmetry,[status(thm)],[13])).
% 1.78/1.36 tff(15,plain,
% 1.78/1.36 (aElement0(W0!22)),
% 1.78/1.36 inference(and_elim,[status(thm)],[10])).
% 1.78/1.36 tff(16,plain,
% 1.78/1.36 (aElement0(xa) <=> aElement0(xa)),
% 1.78/1.36 inference(rewrite,[status(thm)],[])).
% 1.78/1.36 tff(17,axiom,(aElement0(xa) & aElement0(xb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2091')).
% 1.78/1.37 tff(18,plain,
% 1.78/1.37 (aElement0(xa)),
% 1.78/1.37 inference(and_elim,[status(thm)],[17])).
% 1.78/1.37 tff(19,plain,
% 1.78/1.37 (aElement0(xa)),
% 1.78/1.37 inference(modus_ponens,[status(thm)],[18, 16])).
% 1.78/1.37 tff(20,plain,
% 1.78/1.37 (^[W0: $i, W1: $i] : refl((aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 1.78/1.37 inference(bind,[status(th)],[])).
% 1.78/1.37 tff(21,plain,
% 1.78/1.37 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.78/1.37 inference(quant_intro,[status(thm)],[20])).
% 1.78/1.37 tff(22,plain,
% 1.78/1.37 (^[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)))))),
% 1.78/1.37 inference(bind,[status(th)],[])).
% 1.78/1.37 tff(23,plain,
% 1.78/1.37 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.78/1.37 inference(quant_intro,[status(thm)],[22])).
% 1.78/1.37 tff(24,plain,
% 1.78/1.37 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.78/1.37 inference(rewrite,[status(thm)],[])).
% 1.78/1.37 tff(25,plain,
% 1.78/1.37 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 1.78/1.37 inference(bind,[status(th)],[])).
% 1.78/1.37 tff(26,plain,
% 1.78/1.37 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.78/1.37 inference(quant_intro,[status(thm)],[25])).
% 1.78/1.37 tff(27,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB_02')).
% 1.78/1.37 tff(28,plain,
% 1.78/1.37 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.78/1.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.78/1.37 tff(29,plain,
% 1.78/1.37 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.78/1.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.78/1.37 tff(30,plain,(
% 1.78/1.37 ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.78/1.37 inference(skolemize,[status(sab)],[29])).
% 1.78/1.37 tff(31,plain,
% 1.78/1.37 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.78/1.37 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.78/1.37 tff(32,plain,
% 1.78/1.37 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.78/1.37 inference(modus_ponens,[status(thm)],[31, 21])).
% 1.78/1.37 tff(33,plain,
% 1.78/1.37 (((~![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)))),
% 1.78/1.37 inference(rewrite,[status(thm)],[])).
% 1.78/1.37 tff(34,plain,
% 1.78/1.37 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!22)) | (~aElement0(W0!22)) | (~aElement0(xa)))),
% 1.78/1.37 inference(quant_inst,[status(thm)],[])).
% 1.81/1.37 tff(35,plain,
% 1.81/1.37 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!22)) | (~aElement0(W0!22)) | (~aElement0(xa))),
% 1.81/1.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 1.81/1.37 tff(36,plain,
% 1.81/1.37 (aElement0(sdtasdt0(xa, W0!22))),
% 1.81/1.37 inference(unit_resolution,[status(thm)],[35, 32, 19, 15])).
% 1.81/1.37 tff(37,plain,
% 1.81/1.37 (aElement0(W1!21)),
% 1.81/1.37 inference(and_elim,[status(thm)],[10])).
% 1.81/1.37 tff(38,plain,
% 1.81/1.37 (aElement0(xb) <=> aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))),
% 1.81/1.37 inference(rewrite,[status(thm)],[])).
% 1.81/1.37 tff(39,plain,
% 1.81/1.37 (aElement0(xb) <=> aElement0(xb)),
% 1.81/1.37 inference(rewrite,[status(thm)],[])).
% 1.81/1.37 tff(40,plain,
% 1.81/1.37 (aElement0(xb)),
% 1.81/1.37 inference(and_elim,[status(thm)],[17])).
% 1.81/1.37 tff(41,plain,
% 1.81/1.37 (aElement0(xb)),
% 1.81/1.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 1.81/1.37 tff(42,plain,
% 1.81/1.37 (aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))),
% 1.81/1.37 inference(modus_ponens,[status(thm)],[41, 38])).
% 1.81/1.37 tff(43,plain,
% 1.81/1.37 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!21)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!21)))),
% 1.81/1.37 inference(rewrite,[status(thm)],[])).
% 1.81/1.37 tff(44,plain,
% 1.81/1.37 ((aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)) | (~aElement0(W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr)))) <=> (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!21)))),
% 1.81/1.37 inference(rewrite,[status(thm)],[])).
% 1.81/1.37 tff(45,plain,
% 1.81/1.37 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)) | (~aElement0(W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!21))))),
% 1.81/1.37 inference(monotonicity,[status(thm)],[44])).
% 1.81/1.37 tff(46,plain,
% 1.81/1.37 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)) | (~aElement0(W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!21)))),
% 1.81/1.37 inference(transitivity,[status(thm)],[45, 43])).
% 1.81/1.37 tff(47,plain,
% 1.81/1.37 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)) | (~aElement0(W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))))),
% 1.81/1.37 inference(quant_inst,[status(thm)],[])).
% 1.81/1.37 tff(48,plain,
% 1.81/1.37 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!21))),
% 1.81/1.37 inference(modus_ponens,[status(thm)],[47, 46])).
% 1.81/1.37 tff(49,plain,
% 1.81/1.37 (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))),
% 1.81/1.37 inference(unit_resolution,[status(thm)],[48, 32, 42, 37])).
% 1.81/1.37 tff(50,plain,
% 1.81/1.37 (^[W0: $i, W1: $i] : refl((aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 1.81/1.37 inference(bind,[status(th)],[])).
% 1.81/1.37 tff(51,plain,
% 1.81/1.37 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.81/1.37 inference(quant_intro,[status(thm)],[50])).
% 1.81/1.37 tff(52,plain,
% 1.81/1.37 (^[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)))))),
% 1.81/1.37 inference(bind,[status(th)],[])).
% 1.81/1.37 tff(53,plain,
% 1.81/1.37 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.81/1.37 inference(quant_intro,[status(thm)],[52])).
% 1.81/1.37 tff(54,plain,
% 1.81/1.37 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.81/1.37 inference(rewrite,[status(thm)],[])).
% 1.81/1.37 tff(55,plain,
% 1.81/1.37 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 1.81/1.37 inference(bind,[status(th)],[])).
% 1.81/1.37 tff(56,plain,
% 1.81/1.37 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.81/1.37 inference(quant_intro,[status(thm)],[55])).
% 1.81/1.37 tff(57,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB')).
% 1.81/1.37 tff(58,plain,
% 1.81/1.37 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.81/1.37 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.81/1.37 tff(59,plain,
% 1.81/1.37 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.81/1.37 inference(modus_ponens,[status(thm)],[58, 54])).
% 1.81/1.37 tff(60,plain,(
% 1.81/1.37 ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.81/1.37 inference(skolemize,[status(sab)],[59])).
% 1.81/1.37 tff(61,plain,
% 1.81/1.37 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.81/1.37 inference(modus_ponens,[status(thm)],[60, 53])).
% 1.81/1.37 tff(62,plain,
% 1.81/1.37 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.81/1.37 inference(modus_ponens,[status(thm)],[61, 51])).
% 1.81/1.37 tff(63,plain,
% 1.81/1.37 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))))),
% 1.81/1.37 inference(rewrite,[status(thm)],[])).
% 1.81/1.37 tff(64,plain,
% 1.81/1.37 ((aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22)))) <=> ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))))),
% 1.81/1.37 inference(rewrite,[status(thm)],[])).
% 1.81/1.37 tff(65,plain,
% 1.81/1.37 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), 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), xr), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))))),
% 1.81/1.37 inference(monotonicity,[status(thm)],[64])).
% 1.81/1.37 tff(66,plain,
% 1.81/1.37 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), 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), xr), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))))),
% 1.81/1.37 inference(transitivity,[status(thm)],[65, 63])).
% 1.81/1.37 tff(67,plain,
% 1.81/1.37 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))))),
% 1.81/1.37 inference(quant_inst,[status(thm)],[])).
% 1.81/1.37 tff(68,plain,
% 1.81/1.37 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))),
% 1.81/1.37 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.81/1.37 tff(69,plain,
% 1.81/1.37 ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))) | (~aElement0(sdtasdt0(xa, W0!22))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))),
% 1.81/1.37 inference(unit_resolution,[status(thm)],[68, 62])).
% 1.81/1.37 tff(70,plain,
% 1.81/1.37 (aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))),
% 1.81/1.37 inference(unit_resolution,[status(thm)],[69, 49, 36])).
% 1.81/1.37 tff(71,plain,
% 1.81/1.37 (aElement0(xq) <=> aElement0(xq)),
% 1.81/1.37 inference(rewrite,[status(thm)],[])).
% 1.81/1.37 tff(72,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')).
% 1.81/1.37 tff(73,plain,
% 1.81/1.37 ((aElement0(xq) & aElement0(xr)) & (xb = sdtpldt0(sdtasdt0(xq, xu), xr))),
% 1.81/1.37 inference(and_elim,[status(thm)],[72])).
% 1.81/1.37 tff(74,plain,
% 1.81/1.37 (aElement0(xq) & aElement0(xr)),
% 1.81/1.37 inference(and_elim,[status(thm)],[73])).
% 1.81/1.37 tff(75,plain,
% 1.81/1.37 (aElement0(xq)),
% 1.81/1.37 inference(and_elim,[status(thm)],[74])).
% 1.81/1.37 tff(76,plain,
% 1.81/1.37 (aElement0(xq)),
% 1.81/1.37 inference(modus_ponens,[status(thm)],[75, 71])).
% 1.81/1.37 tff(77,plain,
% 1.81/1.37 (((~![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), xr), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), 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), xr), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))))),
% 1.81/1.37 inference(rewrite,[status(thm)],[])).
% 1.81/1.37 tff(78,plain,
% 1.81/1.37 ((aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))) | (~aElement0(xq))) <=> ((~aElement0(xq)) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))))),
% 1.81/1.38 inference(rewrite,[status(thm)],[])).
% 1.81/1.38 tff(79,plain,
% 1.81/1.38 (((~![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), xr), W1!21)))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), 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), xr), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))))))),
% 1.81/1.38 inference(monotonicity,[status(thm)],[78])).
% 1.81/1.38 tff(80,plain,
% 1.81/1.38 (((~![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), xr), W1!21)))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), 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), xr), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))))),
% 1.81/1.38 inference(transitivity,[status(thm)],[79, 77])).
% 1.81/1.38 tff(81,plain,
% 1.81/1.38 ((~![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), xr), W1!21)))) | (~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))) | (~aElement0(xq)))),
% 1.81/1.38 inference(quant_inst,[status(thm)],[])).
% 1.81/1.38 tff(82,plain,
% 1.81/1.38 ((~![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), xr), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))))),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.81/1.38 tff(83,plain,
% 1.81/1.38 ((~aElement0(sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21)))) | aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))))),
% 1.81/1.38 inference(unit_resolution,[status(thm)],[82, 32, 76])).
% 1.81/1.38 tff(84,plain,
% 1.81/1.38 (aElement0(sdtasdt0(xq, sdtpldt0(sdtasdt0(xa, W0!22), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!21))))),
% 1.81/1.38 inference(unit_resolution,[status(thm)],[83, 70])).
% 1.81/1.38 tff(85,plain,
% 1.81/1.38 (aElement0(sdtasdt0(xq, xu))),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[84, 14])).
% 1.81/1.38 tff(86,plain,
% 1.81/1.38 (^[W0: $i] : refl((aElement0(smndt0(W0)) | (~aElement0(W0))) <=> (aElement0(smndt0(W0)) | (~aElement0(W0))))),
% 1.81/1.38 inference(bind,[status(th)],[])).
% 1.81/1.38 tff(87,plain,
% 1.81/1.38 (![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0))) <=> ![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 1.81/1.38 inference(quant_intro,[status(thm)],[86])).
% 1.81/1.38 tff(88,plain,
% 1.81/1.38 (![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0))) <=> ![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 1.81/1.38 inference(rewrite,[status(thm)],[])).
% 1.81/1.38 tff(89,plain,
% 1.81/1.38 (^[W0: $i] : rewrite((aElement0(W0) => aElement0(smndt0(W0))) <=> (aElement0(smndt0(W0)) | (~aElement0(W0))))),
% 1.81/1.38 inference(bind,[status(th)],[])).
% 1.81/1.38 tff(90,plain,
% 1.81/1.38 (![W0: $i] : (aElement0(W0) => aElement0(smndt0(W0))) <=> ![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 1.81/1.38 inference(quant_intro,[status(thm)],[89])).
% 1.81/1.38 tff(91,axiom,(![W0: $i] : (aElement0(W0) => aElement0(smndt0(W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsU')).
% 1.81/1.38 tff(92,plain,
% 1.81/1.38 (![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.81/1.38 tff(93,plain,
% 1.81/1.38 (![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[92, 88])).
% 1.81/1.38 tff(94,plain,(
% 1.81/1.38 ![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 1.81/1.38 inference(skolemize,[status(sab)],[93])).
% 1.81/1.38 tff(95,plain,
% 1.81/1.38 (![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[94, 87])).
% 1.81/1.38 tff(96,plain,
% 1.81/1.38 (((~![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))) | (aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElement0(sdtasdt0(xq, xu))))) <=> ((~![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))) | aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElement0(sdtasdt0(xq, xu))))),
% 1.81/1.38 inference(rewrite,[status(thm)],[])).
% 1.81/1.38 tff(97,plain,
% 1.81/1.38 ((~![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))) | (aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElement0(sdtasdt0(xq, xu))))),
% 1.81/1.38 inference(quant_inst,[status(thm)],[])).
% 1.81/1.38 tff(98,plain,
% 1.81/1.38 ((~![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))) | aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElement0(sdtasdt0(xq, xu)))),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.81/1.38 tff(99,plain,
% 1.81/1.38 (aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElement0(sdtasdt0(xq, xu)))),
% 1.81/1.38 inference(unit_resolution,[status(thm)],[98, 95])).
% 1.81/1.38 tff(100,plain,
% 1.81/1.38 (aElement0(smndt0(sdtasdt0(xq, xu)))),
% 1.81/1.38 inference(unit_resolution,[status(thm)],[99, 85])).
% 1.81/1.38 tff(101,plain,
% 1.81/1.38 (aElement0(xr) <=> aElement0(xr)),
% 1.81/1.38 inference(rewrite,[status(thm)],[])).
% 1.81/1.38 tff(102,plain,
% 1.81/1.38 (aElement0(xr)),
% 1.81/1.38 inference(and_elim,[status(thm)],[74])).
% 1.81/1.38 tff(103,plain,
% 1.81/1.38 (aElement0(xr)),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.81/1.38 tff(104,plain,
% 1.81/1.38 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 1.81/1.38 inference(bind,[status(th)],[])).
% 1.81/1.38 tff(105,plain,
% 1.81/1.38 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.81/1.38 inference(quant_intro,[status(thm)],[104])).
% 1.81/1.38 tff(106,plain,
% 1.81/1.38 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1) & aElement0(W2)) <=> (~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) <=> (~(~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) <=> ((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))), (((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> (((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite((((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))), (((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 1.81/1.38 inference(bind,[status(th)],[])).
% 1.81/1.38 tff(107,plain,
% 1.81/1.38 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.81/1.38 inference(quant_intro,[status(thm)],[106])).
% 1.81/1.38 tff(108,plain,
% 1.81/1.38 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 1.81/1.38 inference(rewrite,[status(thm)],[])).
% 1.81/1.38 tff(109,plain,
% 1.81/1.38 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aElement0(W0) & aElement0(W1)) & aElement0(W2)) <=> (aElement0(W0) & aElement0(W1) & aElement0(W2))), ((((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((aElement0(W0) & aElement0(W1) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite(((aElement0(W0) & aElement0(W1) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), ((((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))))),
% 1.81/1.38 inference(bind,[status(th)],[])).
% 1.81/1.38 tff(110,plain,
% 1.81/1.38 (![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 1.81/1.38 inference(quant_intro,[status(thm)],[109])).
% 1.81/1.38 tff(111,axiom,(![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddAsso')).
% 1.81/1.38 tff(112,plain,
% 1.81/1.38 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.81/1.38 tff(113,plain,
% 1.81/1.38 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[112, 108])).
% 1.81/1.38 tff(114,plain,(
% 1.81/1.38 ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 1.81/1.38 inference(skolemize,[status(sab)],[113])).
% 1.81/1.38 tff(115,plain,
% 1.81/1.38 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[114, 107])).
% 1.81/1.38 tff(116,plain,
% 1.81/1.38 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[115, 105])).
% 1.81/1.38 tff(117,plain,
% 1.81/1.38 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(xq, xu))) | (~aElement0(xr)) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(xr)) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))),
% 1.81/1.38 inference(rewrite,[status(thm)],[])).
% 1.81/1.38 tff(118,plain,
% 1.81/1.38 (((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu))))) <=> ((~aElement0(sdtasdt0(xq, xu))) | (~aElement0(xr)) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))),
% 1.81/1.38 inference(rewrite,[status(thm)],[])).
% 1.81/1.38 tff(119,plain,
% 1.81/1.38 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(xq, xu))) | (~aElement0(xr)) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu))))))),
% 1.81/1.38 inference(monotonicity,[status(thm)],[118])).
% 1.81/1.38 tff(120,plain,
% 1.81/1.38 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(xr)) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))),
% 1.81/1.38 inference(transitivity,[status(thm)],[119, 117])).
% 1.81/1.38 tff(121,plain,
% 1.81/1.38 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))),
% 1.81/1.38 inference(quant_inst,[status(thm)],[])).
% 1.81/1.38 tff(122,plain,
% 1.81/1.38 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(xr)) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu))))),
% 1.81/1.38 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.81/1.38 tff(123,plain,
% 1.81/1.38 ((~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu))))),
% 1.81/1.38 inference(unit_resolution,[status(thm)],[122, 116, 103])).
% 1.81/1.38 tff(124,plain,
% 1.81/1.38 (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))),
% 1.81/1.38 inference(unit_resolution,[status(thm)],[123, 100, 85])).
% 1.81/1.38 tff(125,plain,
% 1.81/1.38 (^[W0: $i] : refl(((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))))),
% 1.81/1.38 inference(bind,[status(th)],[])).
% 1.81/1.38 tff(126,plain,
% 1.81/1.38 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 1.81/1.38 inference(quant_intro,[status(thm)],[125])).
% 1.81/1.38 tff(127,plain,
% 1.81/1.38 (^[W0: $i] : rewrite(((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))))),
% 1.81/1.39 inference(bind,[status(th)],[])).
% 1.81/1.39 tff(128,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 1.81/1.39 inference(quant_intro,[status(thm)],[127])).
% 1.81/1.39 tff(129,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 1.81/1.39 inference(rewrite,[status(thm)],[])).
% 1.81/1.39 tff(130,plain,
% 1.81/1.39 (^[W0: $i] : rewrite((aElement0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))))),
% 1.81/1.39 inference(bind,[status(th)],[])).
% 1.81/1.39 tff(131,plain,
% 1.81/1.39 (![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 1.81/1.39 inference(quant_intro,[status(thm)],[130])).
% 1.81/1.39 tff(132,axiom,(![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddInvr')).
% 1.81/1.39 tff(133,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 1.81/1.39 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.81/1.39 tff(134,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 1.81/1.39 inference(modus_ponens,[status(thm)],[133, 129])).
% 1.81/1.39 tff(135,plain,(
% 1.81/1.39 ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 1.81/1.39 inference(skolemize,[status(sab)],[134])).
% 1.81/1.39 tff(136,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 1.81/1.39 inference(modus_ponens,[status(thm)],[135, 128])).
% 1.81/1.39 tff(137,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 1.81/1.39 inference(modus_ponens,[status(thm)],[136, 126])).
% 1.81/1.39 tff(138,plain,
% 1.81/1.39 (((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))))),
% 1.81/1.39 inference(rewrite,[status(thm)],[])).
% 1.81/1.39 tff(139,plain,
% 1.81/1.39 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))))),
% 1.81/1.39 inference(quant_inst,[status(thm)],[])).
% 1.81/1.39 tff(140,plain,
% 1.81/1.39 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))))))),
% 1.81/1.39 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.81/1.39 tff(141,plain,
% 1.81/1.39 ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))))))),
% 1.81/1.39 inference(unit_resolution,[status(thm)],[140, 137])).
% 1.81/1.39 tff(142,plain,
% 1.81/1.39 (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))),
% 1.81/1.39 inference(unit_resolution,[status(thm)],[141, 85])).
% 1.81/1.39 tff(143,plain,
% 1.81/1.39 (((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))))) | (sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))),
% 1.81/1.39 inference(tautology,[status(thm)],[])).
% 1.81/1.39 tff(144,plain,
% 1.81/1.39 (sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))),
% 1.81/1.39 inference(unit_resolution,[status(thm)],[143, 142])).
% 1.81/1.39 tff(145,plain,
% 1.81/1.39 (sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)) = sz00),
% 1.81/1.39 inference(symmetry,[status(thm)],[144])).
% 1.81/1.39 tff(146,plain,
% 1.81/1.39 (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(sz00, xr)),
% 1.81/1.39 inference(monotonicity,[status(thm)],[145])).
% 1.81/1.39 tff(147,plain,
% 1.81/1.39 (sdtpldt0(sz00, xr) = sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr)),
% 1.81/1.39 inference(symmetry,[status(thm)],[146])).
% 1.81/1.39 tff(148,plain,
% 1.81/1.39 (^[W0: $i] : refl(((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 1.81/1.39 inference(bind,[status(th)],[])).
% 1.81/1.39 tff(149,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 1.81/1.39 inference(quant_intro,[status(thm)],[148])).
% 1.81/1.39 tff(150,plain,
% 1.81/1.39 (^[W0: $i] : rewrite(((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 1.81/1.39 inference(bind,[status(th)],[])).
% 1.81/1.39 tff(151,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 1.81/1.39 inference(quant_intro,[status(thm)],[150])).
% 1.81/1.39 tff(152,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 1.81/1.39 inference(rewrite,[status(thm)],[])).
% 1.81/1.39 tff(153,plain,
% 1.81/1.39 (^[W0: $i] : rewrite((aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))))),
% 1.81/1.39 inference(bind,[status(th)],[])).
% 1.81/1.39 tff(154,plain,
% 1.81/1.39 (![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 1.81/1.39 inference(quant_intro,[status(thm)],[153])).
% 1.81/1.39 tff(155,axiom,(![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddZero')).
% 1.81/1.39 tff(156,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 1.81/1.39 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.81/1.39 tff(157,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 1.81/1.39 inference(modus_ponens,[status(thm)],[156, 152])).
% 1.81/1.39 tff(158,plain,(
% 1.81/1.39 ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 1.81/1.39 inference(skolemize,[status(sab)],[157])).
% 1.81/1.39 tff(159,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 1.81/1.39 inference(modus_ponens,[status(thm)],[158, 151])).
% 1.81/1.39 tff(160,plain,
% 1.81/1.39 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 1.81/1.39 inference(modus_ponens,[status(thm)],[159, 149])).
% 1.81/1.39 tff(161,plain,
% 1.81/1.39 (((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))))),
% 1.81/1.40 inference(rewrite,[status(thm)],[])).
% 1.81/1.40 tff(162,plain,
% 1.81/1.40 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))))),
% 1.81/1.40 inference(quant_inst,[status(thm)],[])).
% 1.81/1.40 tff(163,plain,
% 1.81/1.40 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr)))))),
% 1.81/1.40 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.81/1.40 tff(164,plain,
% 1.81/1.40 (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))),
% 1.81/1.40 inference(unit_resolution,[status(thm)],[163, 160, 103])).
% 1.81/1.40 tff(165,plain,
% 1.81/1.40 (((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr)))) | (xr = sdtpldt0(sz00, xr))),
% 1.81/1.40 inference(tautology,[status(thm)],[])).
% 1.81/1.40 tff(166,plain,
% 1.81/1.40 (xr = sdtpldt0(sz00, xr)),
% 1.81/1.40 inference(unit_resolution,[status(thm)],[165, 164])).
% 1.81/1.40 tff(167,plain,
% 1.81/1.40 (xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))),
% 1.81/1.40 inference(transitivity,[status(thm)],[166, 147, 124])).
% 1.81/1.40 tff(168,plain,
% 1.81/1.40 ((~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))) <=> (~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))))),
% 1.81/1.40 inference(rewrite,[status(thm)],[])).
% 1.81/1.40 tff(169,plain,
% 1.81/1.40 ((~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))) <=> (~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb)))),
% 1.81/1.40 inference(rewrite,[status(thm)],[])).
% 1.81/1.40 tff(170,axiom,(~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 1.81/1.40 tff(171,plain,
% 1.81/1.40 (~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))),
% 1.81/1.40 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.81/1.40 tff(172,plain,
% 1.81/1.40 (~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr)))),
% 1.81/1.40 inference(modus_ponens,[status(thm)],[171, 168])).
% 1.81/1.40 tff(173,plain,
% 1.81/1.40 ($false),
% 1.81/1.40 inference(unit_resolution,[status(thm)],[172, 167])).
% 1.81/1.40 % SZS output end Proof
%------------------------------------------------------------------------------