TSTP Solution File: NUM475+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM475+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:09:56 EDT 2022
% Result : Theorem 1.02s 0.95s
% Output : Proof 1.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.16 % Problem : NUM475+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.18 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.38 % Computer : n014.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8042.1875MB
% 0.13/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 2 10:54:46 EDT 2022
% 0.13/0.38 % CPUTime :
% 0.13/0.39 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.39 Usage: tptp [options] [-file:]file
% 0.13/0.39 -h, -? prints this message.
% 0.13/0.39 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.39 -m, -model generate model.
% 0.13/0.39 -p, -proof generate proof.
% 0.13/0.39 -c, -core generate unsat core of named formulas.
% 0.13/0.39 -st, -statistics display statistics.
% 0.13/0.39 -t:timeout set timeout (in second).
% 0.13/0.39 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.39 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.39 -<param>:<value> configuration parameter and value.
% 0.13/0.39 -o:<output-file> file to place output in.
% 1.02/0.95 % SZS status Theorem
% 1.02/0.95 % SZS output start Proof
% 1.02/0.95 tff(sdtpldt0_type, type, (
% 1.02/0.95 sdtpldt0: ( $i * $i ) > $i)).
% 1.02/0.95 tff(xn_type, type, (
% 1.02/0.95 xn: $i)).
% 1.02/0.95 tff(sdtasdt0_type, type, (
% 1.02/0.95 sdtasdt0: ( $i * $i ) > $i)).
% 1.02/0.95 tff(tptp_fun_W0_2_type, type, (
% 1.02/0.95 tptp_fun_W0_2: $i)).
% 1.02/0.95 tff(xl_type, type, (
% 1.02/0.95 xl: $i)).
% 1.02/0.95 tff(sdtmndt0_type, type, (
% 1.02/0.95 sdtmndt0: ( $i * $i ) > $i)).
% 1.02/0.95 tff(sdtsldt0_type, type, (
% 1.02/0.95 sdtsldt0: ( $i * $i ) > $i)).
% 1.02/0.95 tff(xm_type, type, (
% 1.02/0.95 xm: $i)).
% 1.02/0.95 tff(aNaturalNumber0_type, type, (
% 1.02/0.95 aNaturalNumber0: $i > $o)).
% 1.02/0.95 tff(doDivides0_type, type, (
% 1.02/0.95 doDivides0: ( $i * $i ) > $o)).
% 1.02/0.95 tff(xp_type, type, (
% 1.02/0.95 xp: $i)).
% 1.02/0.95 tff(xr_type, type, (
% 1.02/0.95 xr: $i)).
% 1.02/0.95 tff(xq_type, type, (
% 1.02/0.95 xq: $i)).
% 1.02/0.95 tff(1,plain,
% 1.02/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(2,axiom,(((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, xn) = sdtasdt0(xl, W0)))) & doDivides0(xl, sdtpldt0(xm, xn))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1324_04')).
% 1.02/0.95 tff(3,plain,
% 1.02/0.95 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, xn) = sdtasdt0(xl, W0)))),
% 1.02/0.95 inference(and_elim,[status(thm)],[2])).
% 1.02/0.95 tff(4,plain,
% 1.02/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm)),
% 1.02/0.95 inference(and_elim,[status(thm)],[3])).
% 1.02/0.95 tff(5,plain,
% 1.02/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 1.02/0.95 inference(and_elim,[status(thm)],[4])).
% 1.02/0.95 tff(6,plain,
% 1.02/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[5, 1])).
% 1.02/0.95 tff(7,plain,(
% 1.02/0.95 aNaturalNumber0(W0!2) & (xm = sdtasdt0(xl, W0!2))),
% 1.02/0.95 inference(skolemize,[status(sab)],[6])).
% 1.02/0.95 tff(8,plain,
% 1.02/0.95 (xm = sdtasdt0(xl, W0!2)),
% 1.02/0.95 inference(and_elim,[status(thm)],[7])).
% 1.02/0.95 tff(9,plain,
% 1.02/0.95 (sdtasdt0(xl, W0!2) = xm),
% 1.02/0.95 inference(symmetry,[status(thm)],[8])).
% 1.02/0.95 tff(10,plain,
% 1.02/0.95 (aNaturalNumber0(sdtasdt0(xl, W0!2)) <=> aNaturalNumber0(xm)),
% 1.02/0.95 inference(monotonicity,[status(thm)],[9])).
% 1.02/0.95 tff(11,plain,
% 1.02/0.95 (aNaturalNumber0(xm) <=> aNaturalNumber0(sdtasdt0(xl, W0!2))),
% 1.02/0.95 inference(symmetry,[status(thm)],[10])).
% 1.02/0.95 tff(12,plain,
% 1.02/0.95 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(13,axiom,((aNaturalNumber0(xl) & aNaturalNumber0(xm)) & aNaturalNumber0(xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1324')).
% 1.02/0.95 tff(14,plain,
% 1.02/0.95 (aNaturalNumber0(xl) & aNaturalNumber0(xm)),
% 1.02/0.95 inference(and_elim,[status(thm)],[13])).
% 1.02/0.95 tff(15,plain,
% 1.02/0.95 (aNaturalNumber0(xm)),
% 1.02/0.95 inference(and_elim,[status(thm)],[14])).
% 1.02/0.95 tff(16,plain,
% 1.02/0.95 (aNaturalNumber0(xm)),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[15, 12])).
% 1.02/0.95 tff(17,plain,
% 1.02/0.95 (aNaturalNumber0(sdtasdt0(xl, W0!2))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[16, 11])).
% 1.02/0.95 tff(18,plain,
% 1.02/0.95 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(19,plain,
% 1.02/0.95 (aNaturalNumber0(xn)),
% 1.02/0.95 inference(and_elim,[status(thm)],[13])).
% 1.02/0.95 tff(20,plain,
% 1.02/0.95 (aNaturalNumber0(xn)),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.02/0.95 tff(21,plain,
% 1.02/0.95 (^[W0: $i, W1: $i] : refl(((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 1.02/0.95 inference(bind,[status(th)],[])).
% 1.02/0.95 tff(22,plain,
% 1.02/0.95 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.95 inference(quant_intro,[status(thm)],[21])).
% 1.02/0.95 tff(23,plain,
% 1.02/0.95 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 1.02/0.95 inference(bind,[status(th)],[])).
% 1.02/0.95 tff(24,plain,
% 1.02/0.95 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.95 inference(quant_intro,[status(thm)],[23])).
% 1.02/0.95 tff(25,plain,
% 1.02/0.95 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(26,plain,
% 1.02/0.95 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))),
% 1.02/0.95 inference(bind,[status(th)],[])).
% 1.02/0.95 tff(27,plain,
% 1.02/0.95 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 1.02/0.95 inference(quant_intro,[status(thm)],[26])).
% 1.02/0.95 tff(28,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddComm')).
% 1.02/0.95 tff(29,plain,
% 1.02/0.95 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.02/0.95 tff(30,plain,
% 1.02/0.95 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.02/0.95 tff(31,plain,(
% 1.02/0.95 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 1.02/0.95 inference(skolemize,[status(sab)],[30])).
% 1.02/0.95 tff(32,plain,
% 1.02/0.95 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[31, 24])).
% 1.02/0.95 tff(33,plain,
% 1.02/0.95 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[32, 22])).
% 1.02/0.95 tff(34,plain,
% 1.02/0.95 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(35,plain,
% 1.02/0.95 (((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(xn))) <=> ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(36,plain,
% 1.02/0.95 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(xn)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn))))),
% 1.02/0.95 inference(monotonicity,[status(thm)],[35])).
% 1.02/0.95 tff(37,plain,
% 1.02/0.95 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(xn)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))),
% 1.02/0.95 inference(transitivity,[status(thm)],[36, 34])).
% 1.02/0.95 tff(38,plain,
% 1.02/0.95 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(xn)))),
% 1.02/0.95 inference(quant_inst,[status(thm)],[])).
% 1.02/0.95 tff(39,plain,
% 1.02/0.95 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn))),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.02/0.95 tff(40,plain,
% 1.02/0.95 ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn))),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[39, 33, 20])).
% 1.02/0.95 tff(41,plain,
% 1.02/0.95 (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)),
% 1.02/0.95 inference(unit_resolution,[status(thm)],[40, 17])).
% 1.02/0.95 tff(42,plain,
% 1.02/0.95 (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(xn, sdtasdt0(xl, W0!2))),
% 1.02/0.95 inference(symmetry,[status(thm)],[41])).
% 1.02/0.95 tff(43,plain,
% 1.02/0.95 (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(xm, xn)),
% 1.02/0.95 inference(monotonicity,[status(thm)],[9])).
% 1.02/0.95 tff(44,plain,
% 1.02/0.95 (sdtpldt0(xm, xn) = sdtpldt0(sdtasdt0(xl, W0!2), xn)),
% 1.02/0.95 inference(symmetry,[status(thm)],[43])).
% 1.02/0.95 tff(45,plain,
% 1.02/0.95 ((sdtpldt0(sdtasdt0(xl, sdtsldt0(xm, xl)), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, sdtsldt0(xm, xl)), xn)) <=> (sdtpldt0(xm, sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(xm, xn))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(46,plain,
% 1.02/0.95 ((sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, xp), xn)) <=> (sdtpldt0(sdtasdt0(xl, sdtsldt0(xm, xl)), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, sdtsldt0(xm, xl)), xn))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(47,plain,
% 1.02/0.95 ((sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, xp), xn)) <=> (sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, xp), xn))),
% 1.02/0.95 inference(rewrite,[status(thm)],[])).
% 1.02/0.95 tff(48,axiom,(sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, xp), xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1459')).
% 1.02/0.95 tff(49,plain,
% 1.02/0.95 (sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, xp), xn)),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.02/0.95 tff(50,plain,
% 1.02/0.95 (sdtpldt0(sdtasdt0(xl, sdtsldt0(xm, xl)), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, sdtsldt0(xm, xl)), xn)),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[49, 46])).
% 1.02/0.95 tff(51,plain,
% 1.02/0.95 (sdtpldt0(xm, sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(xm, xn)),
% 1.02/0.95 inference(modus_ponens,[status(thm)],[50, 45])).
% 1.02/0.95 tff(52,plain,
% 1.02/0.95 (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(xm, sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))),
% 1.02/0.96 inference(monotonicity,[status(thm)],[9])).
% 1.02/0.96 tff(53,plain,
% 1.02/0.96 (aNaturalNumber0(xr) <=> aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(54,plain,
% 1.02/0.96 (aNaturalNumber0(xr) <=> aNaturalNumber0(xr)),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(55,axiom,((aNaturalNumber0(xr) & (sdtpldt0(xp, xr) = xq)) & (xr = sdtmndt0(xq, xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1422')).
% 1.02/0.96 tff(56,plain,
% 1.02/0.96 (aNaturalNumber0(xr) & (sdtpldt0(xp, xr) = xq)),
% 1.02/0.96 inference(and_elim,[status(thm)],[55])).
% 1.02/0.96 tff(57,plain,
% 1.02/0.96 (aNaturalNumber0(xr)),
% 1.02/0.96 inference(and_elim,[status(thm)],[56])).
% 1.02/0.96 tff(58,plain,
% 1.02/0.96 (aNaturalNumber0(xr)),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[57, 54])).
% 1.02/0.96 tff(59,plain,
% 1.02/0.96 (aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[58, 53])).
% 1.02/0.96 tff(60,plain,
% 1.02/0.96 (aNaturalNumber0(xl) <=> aNaturalNumber0(xl)),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(61,plain,
% 1.02/0.96 (aNaturalNumber0(xl)),
% 1.02/0.96 inference(and_elim,[status(thm)],[14])).
% 1.02/0.96 tff(62,plain,
% 1.02/0.96 (aNaturalNumber0(xl)),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.02/0.96 tff(63,plain,
% 1.02/0.96 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 1.02/0.96 inference(bind,[status(th)],[])).
% 1.02/0.96 tff(64,plain,
% 1.02/0.96 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.96 inference(quant_intro,[status(thm)],[63])).
% 1.02/0.96 tff(65,plain,
% 1.02/0.96 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 1.02/0.96 inference(bind,[status(th)],[])).
% 1.02/0.96 tff(66,plain,
% 1.02/0.96 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.96 inference(quant_intro,[status(thm)],[65])).
% 1.02/0.96 tff(67,plain,
% 1.02/0.96 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(68,plain,
% 1.02/0.96 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 1.02/0.96 inference(bind,[status(th)],[])).
% 1.02/0.96 tff(69,plain,
% 1.02/0.96 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.02/0.96 inference(quant_intro,[status(thm)],[68])).
% 1.02/0.96 tff(70,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB_02')).
% 1.02/0.96 tff(71,plain,
% 1.02/0.96 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.02/0.96 tff(72,plain,
% 1.02/0.96 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[71, 67])).
% 1.02/0.96 tff(73,plain,(
% 1.02/0.96 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.02/0.96 inference(skolemize,[status(sab)],[72])).
% 1.02/0.96 tff(74,plain,
% 1.02/0.96 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[73, 66])).
% 1.02/0.96 tff(75,plain,
% 1.02/0.96 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[74, 64])).
% 1.02/0.96 tff(76,plain,
% 1.02/0.96 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(77,plain,
% 1.02/0.96 ((aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(xl))) <=> ((~aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(78,plain,
% 1.02/0.96 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(xl)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))),
% 1.02/0.96 inference(monotonicity,[status(thm)],[77])).
% 1.02/0.96 tff(79,plain,
% 1.02/0.96 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(xl)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))),
% 1.02/0.96 inference(transitivity,[status(thm)],[78, 76])).
% 1.02/0.96 tff(80,plain,
% 1.02/0.96 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(xl)))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(81,plain,
% 1.02/0.96 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.02/0.96 tff(82,plain,
% 1.02/0.96 (aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[81, 75, 62, 59])).
% 1.02/0.96 tff(83,plain,
% 1.02/0.96 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(84,plain,
% 1.02/0.96 (((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))) <=> ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(85,plain,
% 1.02/0.96 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))))),
% 1.02/0.96 inference(monotonicity,[status(thm)],[84])).
% 1.02/0.96 tff(86,plain,
% 1.02/0.96 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))),
% 1.02/0.96 inference(transitivity,[status(thm)],[85, 83])).
% 1.02/0.96 tff(87,plain,
% 1.02/0.96 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))))),
% 1.02/0.96 inference(quant_inst,[status(thm)],[])).
% 1.02/0.96 tff(88,plain,
% 1.02/0.96 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.02/0.96 tff(89,plain,
% 1.02/0.96 ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[88, 33])).
% 1.02/0.96 tff(90,plain,
% 1.02/0.96 (sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[89, 17, 82])).
% 1.02/0.96 tff(91,plain,
% 1.02/0.96 (sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))),
% 1.02/0.96 inference(transitivity,[status(thm)],[90, 52, 51, 44, 42])).
% 1.02/0.96 tff(92,plain,
% 1.02/0.96 (((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn))) | (~(sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))))),
% 1.02/0.96 inference(tautology,[status(thm)],[])).
% 1.02/0.96 tff(93,plain,
% 1.02/0.96 ((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn))),
% 1.02/0.96 inference(unit_resolution,[status(thm)],[92, 91])).
% 1.02/0.96 tff(94,plain,
% 1.02/0.96 ((sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) <=> (xn = sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))),
% 1.02/0.96 inference(commutativity,[status(thm)],[])).
% 1.02/0.96 tff(95,plain,
% 1.02/0.96 ((xn = sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) <=> (sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn)),
% 1.02/0.96 inference(symmetry,[status(thm)],[94])).
% 1.02/0.96 tff(96,plain,
% 1.02/0.96 ((~(xn = sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) <=> (~(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn))),
% 1.02/0.96 inference(monotonicity,[status(thm)],[95])).
% 1.02/0.96 tff(97,plain,
% 1.02/0.96 ((~(xn = sdtasdt0(xl, xr))) <=> (~(xn = sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(98,plain,
% 1.02/0.96 ((~(xn = sdtasdt0(xl, xr))) <=> (~(xn = sdtasdt0(xl, xr)))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(99,axiom,(~(xn = sdtasdt0(xl, xr))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 1.02/0.96 tff(100,plain,
% 1.02/0.96 (~(xn = sdtasdt0(xl, xr))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.02/0.96 tff(101,plain,
% 1.02/0.96 (~(xn = sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[100, 97])).
% 1.02/0.96 tff(102,plain,
% 1.02/0.96 (~(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn)),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[101, 96])).
% 1.02/0.96 tff(103,plain,
% 1.02/0.96 (^[W0: $i, W1: $i, W2: $i] : refl(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 1.02/0.96 inference(bind,[status(th)],[])).
% 1.02/0.96 tff(104,plain,
% 1.02/0.96 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.96 inference(quant_intro,[status(thm)],[103])).
% 1.02/0.96 tff(105,plain,
% 1.02/0.96 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), (((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))))), rewrite(((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 1.02/0.96 inference(bind,[status(th)],[])).
% 1.02/0.96 tff(106,plain,
% 1.02/0.96 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.96 inference(quant_intro,[status(thm)],[105])).
% 1.02/0.96 tff(107,plain,
% 1.02/0.96 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 1.02/0.96 inference(rewrite,[status(thm)],[])).
% 1.02/0.96 tff(108,plain,
% 1.02/0.96 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), trans(monotonicity(rewrite(((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) <=> ((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))), ((((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2)) <=> (((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))) => (W1 = W2)))), rewrite((((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))) => (W1 = W2)) <=> ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2))), ((((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2)))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))))),
% 1.02/0.96 inference(bind,[status(th)],[])).
% 1.02/0.96 tff(109,plain,
% 1.02/0.96 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 1.02/0.96 inference(quant_intro,[status(thm)],[108])).
% 1.02/0.96 tff(110,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddCanc')).
% 1.02/0.96 tff(111,plain,
% 1.02/0.96 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.02/0.96 tff(112,plain,
% 1.02/0.96 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[111, 107])).
% 1.02/0.96 tff(113,plain,(
% 1.02/0.96 ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 1.02/0.96 inference(skolemize,[status(sab)],[112])).
% 1.02/0.96 tff(114,plain,
% 1.02/0.96 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.96 inference(modus_ponens,[status(thm)],[113, 106])).
% 1.02/0.96 tff(115,plain,
% 1.02/0.96 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.02/0.97 inference(modus_ponens,[status(thm)],[114, 104])).
% 1.02/0.97 tff(116,plain,
% 1.02/0.97 (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(117,plain,
% 1.02/0.97 (((sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~aNaturalNumber0(xn)) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2)))) <=> ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(118,plain,
% 1.02/0.97 ((~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))) <=> (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn))))),
% 1.02/0.97 inference(rewrite,[status(thm)],[])).
% 1.02/0.97 tff(119,plain,
% 1.02/0.97 (((sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~aNaturalNumber0(xn)) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2)))) <=> ((sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~aNaturalNumber0(xn)) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))))),
% 1.02/0.97 inference(monotonicity,[status(thm)],[118])).
% 1.02/0.97 tff(120,plain,
% 1.02/0.97 (((sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~aNaturalNumber0(xn)) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2)))) <=> ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))))),
% 1.02/0.97 inference(transitivity,[status(thm)],[119, 117])).
% 1.02/0.97 tff(121,plain,
% 1.02/0.97 (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~aNaturalNumber0(xn)) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn))))))),
% 1.02/0.97 inference(monotonicity,[status(thm)],[120])).
% 1.02/0.97 tff(122,plain,
% 1.02/0.97 (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~aNaturalNumber0(xn)) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))))),
% 1.02/0.98 inference(transitivity,[status(thm)],[121, 116])).
% 1.02/0.98 tff(123,plain,
% 1.02/0.98 ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~aNaturalNumber0(xn)) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))))),
% 1.02/0.98 inference(quant_inst,[status(thm)],[])).
% 1.02/0.98 tff(124,plain,
% 1.02/0.98 ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))))) | (sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))) = xn) | (~((sdtpldt0(sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl))), sdtasdt0(xl, W0!2)) = sdtpldt0(xn, sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, sdtmndt0(sdtsldt0(sdtpldt0(xm, xn), xl), sdtsldt0(xm, xl)))) = sdtpldt0(sdtasdt0(xl, W0!2), xn))))),
% 1.02/0.98 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.02/0.98 tff(125,plain,
% 1.02/0.98 ($false),
% 1.02/0.98 inference(unit_resolution,[status(thm)],[124, 115, 20, 17, 82, 102, 93])).
% 1.02/0.98 % SZS output end Proof
%------------------------------------------------------------------------------