TSTP Solution File: NUM513+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM513+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 13:10:11 EDT 2022
% Result : Theorem 1.12s 0.95s
% Output : Proof 1.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM513+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 11:21:09 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 1.12/0.95 % SZS status Theorem
% 1.12/0.95 % SZS output start Proof
% 1.12/0.95 tff(sdtasdt0_type, type, (
% 1.12/0.95 sdtasdt0: ( $i * $i ) > $i)).
% 1.12/0.95 tff(xm_type, type, (
% 1.12/0.95 xm: $i)).
% 1.12/0.95 tff(sdtsldt0_type, type, (
% 1.12/0.95 sdtsldt0: ( $i * $i ) > $i)).
% 1.12/0.95 tff(xr_type, type, (
% 1.12/0.95 xr: $i)).
% 1.12/0.95 tff(xn_type, type, (
% 1.12/0.95 xn: $i)).
% 1.12/0.95 tff(xp_type, type, (
% 1.12/0.95 xp: $i)).
% 1.12/0.95 tff(aNaturalNumber0_type, type, (
% 1.12/0.95 aNaturalNumber0: $i > $o)).
% 1.12/0.95 tff(xk_type, type, (
% 1.12/0.95 xk: $i)).
% 1.12/0.95 tff(doDivides0_type, type, (
% 1.12/0.95 doDivides0: ( $i * $i ) > $o)).
% 1.12/0.95 tff(sz00_type, type, (
% 1.12/0.95 sz00: $i)).
% 1.12/0.95 tff(sz10_type, type, (
% 1.12/0.95 sz10: $i)).
% 1.12/0.95 tff(isPrime0_type, type, (
% 1.12/0.95 isPrime0: $i > $o)).
% 1.12/0.95 tff(sdtpldt0_type, type, (
% 1.12/0.95 sdtpldt0: ( $i * $i ) > $i)).
% 1.12/0.95 tff(tptp_fun_W0_10_type, type, (
% 1.12/0.95 tptp_fun_W0_10: $i)).
% 1.12/0.95 tff(tptp_fun_W0_11_type, type, (
% 1.12/0.95 tptp_fun_W0_11: $i)).
% 1.12/0.95 tff(sdtlseqdt0_type, type, (
% 1.12/0.95 sdtlseqdt0: ( $i * $i ) > $o)).
% 1.12/0.95 tff(1,plain,
% 1.12/0.95 ((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) <=> (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))),
% 1.12/0.95 inference(commutativity,[status(thm)],[])).
% 1.12/0.95 tff(2,plain,
% 1.12/0.95 ((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))) <=> (sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 1.12/0.95 inference(symmetry,[status(thm)],[1])).
% 1.12/0.95 tff(3,plain,
% 1.12/0.95 (aNaturalNumber0(sdtsldt0(xk, xr)) <=> aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(4,plain,
% 1.12/0.95 (aNaturalNumber0(sdtsldt0(xk, xr)) <=> aNaturalNumber0(sdtsldt0(xk, xr))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(5,plain,
% 1.12/0.95 ((~((aNaturalNumber0(sdtsldt0(xk, xr)) & (xk = sdtasdt0(xr, sdtsldt0(xk, xr)))) => ((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))))) <=> (~((sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (~(aNaturalNumber0(sdtsldt0(xk, xr)) & (xk = sdtasdt0(xr, sdtsldt0(xk, xr)))))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(6,axiom,(~((aNaturalNumber0(sdtsldt0(xk, xr)) & (xk = sdtasdt0(xr, sdtsldt0(xk, xr)))) => ((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 1.12/0.95 tff(7,plain,
% 1.12/0.95 (~((sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (~(aNaturalNumber0(sdtsldt0(xk, xr)) & (xk = sdtasdt0(xr, sdtsldt0(xk, xr))))))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.12/0.95 tff(8,plain,
% 1.12/0.95 (aNaturalNumber0(sdtsldt0(xk, xr)) & (xk = sdtasdt0(xr, sdtsldt0(xk, xr)))),
% 1.12/0.95 inference(or_elim,[status(thm)],[7])).
% 1.12/0.95 tff(9,plain,
% 1.12/0.95 (aNaturalNumber0(sdtsldt0(xk, xr))),
% 1.12/0.95 inference(and_elim,[status(thm)],[8])).
% 1.12/0.95 tff(10,plain,
% 1.12/0.95 (aNaturalNumber0(sdtsldt0(xk, xr))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[9, 4])).
% 1.12/0.95 tff(11,plain,
% 1.12/0.95 (aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[10, 3])).
% 1.12/0.95 tff(12,plain,
% 1.12/0.95 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(13,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1837')).
% 1.12/0.95 tff(14,plain,
% 1.12/0.95 (aNaturalNumber0(xp)),
% 1.12/0.95 inference(and_elim,[status(thm)],[13])).
% 1.12/0.95 tff(15,plain,
% 1.12/0.95 (aNaturalNumber0(xp)),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[14, 12])).
% 1.12/0.95 tff(16,plain,
% 1.12/0.95 (^[W0: $i, W1: $i] : refl(((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 1.12/0.95 inference(bind,[status(th)],[])).
% 1.12/0.95 tff(17,plain,
% 1.12/0.95 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.95 inference(quant_intro,[status(thm)],[16])).
% 1.12/0.95 tff(18,plain,
% 1.12/0.95 (^[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))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 1.12/0.95 inference(bind,[status(th)],[])).
% 1.12/0.95 tff(19,plain,
% 1.12/0.95 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.95 inference(quant_intro,[status(thm)],[18])).
% 1.12/0.95 tff(20,plain,
% 1.12/0.95 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(21,plain,
% 1.12/0.95 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))),
% 1.12/0.95 inference(bind,[status(th)],[])).
% 1.12/0.95 tff(22,plain,
% 1.12/0.95 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 1.12/0.95 inference(quant_intro,[status(thm)],[21])).
% 1.12/0.95 tff(23,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulComm')).
% 1.12/0.95 tff(24,plain,
% 1.12/0.95 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.12/0.95 tff(25,plain,
% 1.12/0.95 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[24, 20])).
% 1.12/0.95 tff(26,plain,(
% 1.12/0.95 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 1.12/0.95 inference(skolemize,[status(sab)],[25])).
% 1.12/0.95 tff(27,plain,
% 1.12/0.95 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[26, 19])).
% 1.12/0.95 tff(28,plain,
% 1.12/0.95 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[27, 17])).
% 1.12/0.95 tff(29,plain,
% 1.12/0.95 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp) = sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp) = sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(30,plain,
% 1.12/0.95 (((sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp) = sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp) = sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(31,plain,
% 1.12/0.95 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp) = sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp) = sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))))),
% 1.12/0.96 inference(monotonicity,[status(thm)],[30])).
% 1.12/0.96 tff(32,plain,
% 1.12/0.96 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp) = sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp) = sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))),
% 1.12/0.96 inference(transitivity,[status(thm)],[31, 29])).
% 1.12/0.96 tff(33,plain,
% 1.12/0.96 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp) = sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))),
% 1.12/0.96 inference(quant_inst,[status(thm)],[])).
% 1.12/0.96 tff(34,plain,
% 1.12/0.96 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp) = sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.12/0.96 tff(35,plain,
% 1.12/0.96 (sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp) = sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[34, 28, 15, 11])).
% 1.12/0.96 tff(36,plain,
% 1.12/0.96 (sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)) = sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp)),
% 1.12/0.96 inference(symmetry,[status(thm)],[35])).
% 1.12/0.96 tff(37,plain,
% 1.12/0.96 (sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp))),
% 1.12/0.96 inference(monotonicity,[status(thm)],[36])).
% 1.12/0.96 tff(38,plain,
% 1.12/0.96 (sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp)) = sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))),
% 1.12/0.96 inference(symmetry,[status(thm)],[37])).
% 1.12/0.96 tff(39,plain,
% 1.12/0.96 (aNaturalNumber0(xr) <=> aNaturalNumber0(xr)),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(40,axiom,((((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))) & isPrime0(xr)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2342')).
% 1.12/0.96 tff(41,plain,
% 1.12/0.96 (((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))),
% 1.12/0.96 inference(and_elim,[status(thm)],[40])).
% 1.12/0.96 tff(42,plain,
% 1.12/0.96 ((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))),
% 1.12/0.96 inference(and_elim,[status(thm)],[41])).
% 1.12/0.96 tff(43,plain,
% 1.12/0.96 (((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))),
% 1.12/0.96 inference(and_elim,[status(thm)],[42])).
% 1.12/0.96 tff(44,plain,
% 1.12/0.96 ((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)),
% 1.12/0.96 inference(and_elim,[status(thm)],[43])).
% 1.12/0.96 tff(45,plain,
% 1.12/0.96 (aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 1.12/0.96 inference(and_elim,[status(thm)],[44])).
% 1.12/0.96 tff(46,plain,
% 1.12/0.96 (aNaturalNumber0(xr)),
% 1.12/0.96 inference(and_elim,[status(thm)],[45])).
% 1.12/0.96 tff(47,plain,
% 1.12/0.96 (aNaturalNumber0(xr)),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[46, 39])).
% 1.12/0.96 tff(48,plain,
% 1.12/0.96 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 1.12/0.96 inference(bind,[status(th)],[])).
% 1.12/0.96 tff(49,plain,
% 1.12/0.96 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.96 inference(quant_intro,[status(thm)],[48])).
% 1.12/0.96 tff(50,plain,
% 1.12/0.96 (^[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))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 1.12/0.96 inference(bind,[status(th)],[])).
% 1.12/0.96 tff(51,plain,
% 1.12/0.96 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.96 inference(quant_intro,[status(thm)],[50])).
% 1.12/0.96 tff(52,plain,
% 1.12/0.96 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(53,plain,
% 1.12/0.96 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))))),
% 1.12/0.96 inference(bind,[status(th)],[])).
% 1.12/0.96 tff(54,plain,
% 1.12/0.96 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 1.12/0.96 inference(quant_intro,[status(thm)],[53])).
% 1.12/0.96 tff(55,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulAsso')).
% 1.12/0.96 tff(56,plain,
% 1.12/0.96 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.12/0.96 tff(57,plain,
% 1.12/0.96 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[56, 52])).
% 1.12/0.96 tff(58,plain,(
% 1.12/0.96 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 1.12/0.96 inference(skolemize,[status(sab)],[57])).
% 1.12/0.96 tff(59,plain,
% 1.12/0.96 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[58, 51])).
% 1.12/0.96 tff(60,plain,
% 1.12/0.96 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[59, 49])).
% 1.12/0.96 tff(61,plain,
% 1.12/0.96 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp))))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(62,plain,
% 1.12/0.96 (((sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xr))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp))))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(63,plain,
% 1.12/0.96 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp)))))),
% 1.12/0.96 inference(monotonicity,[status(thm)],[62])).
% 1.12/0.96 tff(64,plain,
% 1.12/0.96 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp))))),
% 1.12/0.96 inference(transitivity,[status(thm)],[63, 61])).
% 1.12/0.96 tff(65,plain,
% 1.12/0.96 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xr)))),
% 1.12/0.96 inference(quant_inst,[status(thm)],[])).
% 1.12/0.96 tff(66,plain,
% 1.12/0.96 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.12/0.96 tff(67,plain,
% 1.12/0.96 (sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr), xp))),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[66, 60, 15, 47, 11])).
% 1.12/0.96 tff(68,plain,
% 1.12/0.96 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(69,axiom,((((((~(xn = xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & sdtlseqdt0(xn, xp)) & (~(xm = xp))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))) & sdtlseqdt0(xm, xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2287')).
% 1.12/0.96 tff(70,plain,
% 1.12/0.96 (((((~(xn = xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & sdtlseqdt0(xn, xp)) & (~(xm = xp))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 1.12/0.96 inference(and_elim,[status(thm)],[69])).
% 1.12/0.96 tff(71,plain,
% 1.12/0.96 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 1.12/0.96 inference(and_elim,[status(thm)],[70])).
% 1.12/0.96 tff(72,plain,
% 1.12/0.96 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[71, 68])).
% 1.12/0.96 tff(73,plain,(
% 1.12/0.96 aNaturalNumber0(W0!10) & (sdtpldt0(xm, W0!10) = xp)),
% 1.12/0.96 inference(skolemize,[status(sab)],[72])).
% 1.12/0.96 tff(74,plain,
% 1.12/0.96 (sdtpldt0(xm, W0!10) = xp),
% 1.12/0.96 inference(and_elim,[status(thm)],[73])).
% 1.12/0.96 tff(75,plain,
% 1.12/0.96 (xp = sdtpldt0(xm, W0!10)),
% 1.12/0.96 inference(symmetry,[status(thm)],[74])).
% 1.12/0.96 tff(76,plain,
% 1.12/0.96 (^[W0: $i] : rewrite((aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0))) <=> (aNaturalNumber0(W0) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0))))),
% 1.12/0.96 inference(bind,[status(th)],[])).
% 1.12/0.96 tff(77,plain,
% 1.12/0.96 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0)))),
% 1.12/0.96 inference(quant_intro,[status(thm)],[76])).
% 1.12/0.96 tff(78,plain,
% 1.12/0.96 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(79,plain,
% 1.12/0.96 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 1.12/0.96 inference(and_elim,[status(thm)],[45])).
% 1.12/0.96 tff(80,plain,
% 1.12/0.96 (?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.12/0.96 tff(81,plain,
% 1.12/0.96 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[80, 77])).
% 1.12/0.96 tff(82,plain,(
% 1.12/0.96 aNaturalNumber0(W0!11) & (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0!11))),
% 1.12/0.96 inference(skolemize,[status(sab)],[81])).
% 1.12/0.96 tff(83,plain,
% 1.12/0.96 (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, W0!11)),
% 1.12/0.96 inference(and_elim,[status(thm)],[82])).
% 1.12/0.96 tff(84,plain,
% 1.12/0.96 ((xk = sdtasdt0(xr, sdtsldt0(xk, xr))) <=> (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(85,plain,
% 1.12/0.96 ((xk = sdtasdt0(xr, sdtsldt0(xk, xr))) <=> (xk = sdtasdt0(xr, sdtsldt0(xk, xr)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(86,plain,
% 1.12/0.96 (xk = sdtasdt0(xr, sdtsldt0(xk, xr))),
% 1.12/0.96 inference(and_elim,[status(thm)],[8])).
% 1.12/0.96 tff(87,plain,
% 1.12/0.96 (xk = sdtasdt0(xr, sdtsldt0(xk, xr))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.12/0.96 tff(88,plain,
% 1.12/0.96 (sdtsldt0(sdtasdt0(xn, xm), xp) = sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[87, 84])).
% 1.12/0.96 tff(89,plain,
% 1.12/0.96 (sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)) = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 1.12/0.96 inference(symmetry,[status(thm)],[88])).
% 1.12/0.96 tff(90,plain,
% 1.12/0.96 (sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)) = sdtasdt0(xr, W0!11)),
% 1.12/0.96 inference(transitivity,[status(thm)],[89, 83])).
% 1.12/0.96 tff(91,plain,
% 1.12/0.96 (sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp) = sdtasdt0(sdtasdt0(xr, W0!11), sdtpldt0(xm, W0!10))),
% 1.12/0.96 inference(monotonicity,[status(thm)],[90, 75])).
% 1.12/0.96 tff(92,plain,
% 1.12/0.96 (sdtasdt0(sdtasdt0(xr, W0!11), sdtpldt0(xm, W0!10)) = sdtasdt0(sdtasdt0(xr, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xp)),
% 1.12/0.96 inference(symmetry,[status(thm)],[91])).
% 1.12/0.96 tff(93,plain,
% 1.12/0.96 (sdtasdt0(sdtasdt0(xr, W0!11), sdtpldt0(xm, W0!10)) = sdtasdt0(sdtasdt0(xr, W0!11), xp)),
% 1.12/0.96 inference(monotonicity,[status(thm)],[74])).
% 1.12/0.96 tff(94,plain,
% 1.12/0.96 (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(sdtasdt0(xr, W0!11), sdtpldt0(xm, W0!10))),
% 1.12/0.96 inference(symmetry,[status(thm)],[93])).
% 1.12/0.96 tff(95,plain,
% 1.12/0.96 (sdtasdt0(xr, W0!11) = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 1.12/0.96 inference(symmetry,[status(thm)],[83])).
% 1.12/0.96 tff(96,plain,
% 1.12/0.96 (aNaturalNumber0(sdtasdt0(xr, W0!11)) <=> aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 1.12/0.96 inference(monotonicity,[status(thm)],[95])).
% 1.12/0.96 tff(97,plain,
% 1.12/0.96 (aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp)) <=> aNaturalNumber0(sdtasdt0(xr, W0!11))),
% 1.12/0.96 inference(symmetry,[status(thm)],[96])).
% 1.12/0.96 tff(98,plain,
% 1.12/0.96 (aNaturalNumber0(xk) <=> aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(99,plain,
% 1.12/0.96 (aNaturalNumber0(xk) <=> aNaturalNumber0(xk)),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(100,axiom,((aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))) & (xk = sdtsldt0(sdtasdt0(xn, xm), xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2306')).
% 1.12/0.96 tff(101,plain,
% 1.12/0.96 (aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 1.12/0.96 inference(and_elim,[status(thm)],[100])).
% 1.12/0.96 tff(102,plain,
% 1.12/0.96 (aNaturalNumber0(xk)),
% 1.12/0.96 inference(and_elim,[status(thm)],[101])).
% 1.12/0.96 tff(103,plain,
% 1.12/0.96 (aNaturalNumber0(xk)),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[102, 99])).
% 1.12/0.96 tff(104,plain,
% 1.12/0.96 (aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[103, 98])).
% 1.12/0.96 tff(105,plain,
% 1.12/0.96 (aNaturalNumber0(sdtasdt0(xr, W0!11))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[104, 97])).
% 1.12/0.96 tff(106,plain,
% 1.12/0.96 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11))))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(107,plain,
% 1.12/0.96 (((sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11)))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11))))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(108,plain,
% 1.12/0.96 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11)))))),
% 1.12/0.96 inference(monotonicity,[status(thm)],[107])).
% 1.12/0.96 tff(109,plain,
% 1.12/0.96 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11))))),
% 1.12/0.96 inference(transitivity,[status(thm)],[108, 106])).
% 1.12/0.96 tff(110,plain,
% 1.12/0.96 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))))),
% 1.12/0.96 inference(quant_inst,[status(thm)],[])).
% 1.12/0.96 tff(111,plain,
% 1.12/0.96 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.12/0.96 tff(112,plain,
% 1.12/0.96 ((~aNaturalNumber0(sdtasdt0(xr, W0!11))) | (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11)))),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[111, 28, 15])).
% 1.12/0.96 tff(113,plain,
% 1.12/0.96 (sdtasdt0(sdtasdt0(xr, W0!11), xp) = sdtasdt0(xp, sdtasdt0(xr, W0!11))),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[112, 105])).
% 1.12/0.96 tff(114,plain,
% 1.12/0.96 (sdtasdt0(xp, sdtasdt0(xr, W0!11)) = sdtasdt0(sdtasdt0(xr, W0!11), xp)),
% 1.12/0.96 inference(symmetry,[status(thm)],[113])).
% 1.12/0.96 tff(115,plain,
% 1.12/0.96 (sdtasdt0(xp, sdtasdt0(xr, W0!11)) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))),
% 1.12/0.96 inference(monotonicity,[status(thm)],[95])).
% 1.12/0.96 tff(116,plain,
% 1.12/0.96 (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, sdtasdt0(xr, W0!11))),
% 1.12/0.96 inference(symmetry,[status(thm)],[115])).
% 1.12/0.96 tff(117,plain,
% 1.12/0.96 ((sdtasdt0(xn, xm) = sdtasdt0(xp, xk)) <=> (sdtasdt0(xn, xm) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(118,plain,
% 1.12/0.96 ((sdtasdt0(xn, xm) = sdtasdt0(xp, xk)) <=> (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(119,plain,
% 1.12/0.96 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 1.12/0.96 inference(and_elim,[status(thm)],[101])).
% 1.12/0.96 tff(120,plain,
% 1.12/0.96 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.12/0.96 tff(121,plain,
% 1.12/0.96 (sdtasdt0(xn, xm) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[120, 117])).
% 1.12/0.96 tff(122,plain,
% 1.12/0.96 ((sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm)) <=> (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(123,axiom,(((((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))) & aNaturalNumber0(sdtsldt0(sdtasdt0(xp, xk), xr))) & (sdtasdt0(xp, xk) = sdtasdt0(xr, sdtsldt0(sdtasdt0(xp, xk), xr)))) & (sdtasdt0(xn, xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp, xk), xr), xr))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2576')).
% 1.12/0.96 tff(124,plain,
% 1.12/0.96 ((((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))) & aNaturalNumber0(sdtsldt0(sdtasdt0(xp, xk), xr))) & (sdtasdt0(xp, xk) = sdtasdt0(xr, sdtsldt0(sdtasdt0(xp, xk), xr)))),
% 1.12/0.96 inference(and_elim,[status(thm)],[123])).
% 1.12/0.96 tff(125,plain,
% 1.12/0.96 (((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))) & aNaturalNumber0(sdtsldt0(sdtasdt0(xp, xk), xr))),
% 1.12/0.96 inference(and_elim,[status(thm)],[124])).
% 1.12/0.96 tff(126,plain,
% 1.12/0.96 ((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))),
% 1.12/0.96 inference(and_elim,[status(thm)],[125])).
% 1.12/0.96 tff(127,plain,
% 1.12/0.96 (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm)),
% 1.12/0.96 inference(and_elim,[status(thm)],[126])).
% 1.12/0.96 tff(128,plain,
% 1.12/0.96 (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm)),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[127, 122])).
% 1.12/0.96 tff(129,plain,
% 1.12/0.96 (aNaturalNumber0(sdtsldt0(xn, xr)) <=> aNaturalNumber0(sdtsldt0(xn, xr))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(130,plain,
% 1.12/0.96 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) <=> (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(131,axiom,(((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))) & sdtlseqdt0(sdtsldt0(xn, xr), xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2504')).
% 1.12/0.96 tff(132,plain,
% 1.12/0.96 ((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))),
% 1.12/0.96 inference(and_elim,[status(thm)],[131])).
% 1.12/0.96 tff(133,plain,
% 1.12/0.96 (((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 1.12/0.96 inference(and_elim,[status(thm)],[132])).
% 1.12/0.96 tff(134,plain,
% 1.12/0.96 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))),
% 1.12/0.96 inference(and_elim,[status(thm)],[133])).
% 1.12/0.96 tff(135,plain,
% 1.12/0.96 (~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))),
% 1.12/0.96 inference(and_elim,[status(thm)],[134])).
% 1.12/0.96 tff(136,plain,
% 1.12/0.96 (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[135, 130])).
% 1.12/0.96 tff(137,plain,
% 1.12/0.96 (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 1.12/0.96 inference(or_elim,[status(thm)],[136])).
% 1.12/0.96 tff(138,plain,
% 1.12/0.96 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 1.12/0.96 inference(and_elim,[status(thm)],[137])).
% 1.12/0.96 tff(139,plain,
% 1.12/0.96 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[138, 129])).
% 1.12/0.96 tff(140,plain,
% 1.12/0.96 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(141,plain,
% 1.12/0.96 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 1.12/0.96 inference(and_elim,[status(thm)],[13])).
% 1.12/0.96 tff(142,plain,
% 1.12/0.96 (aNaturalNumber0(xm)),
% 1.12/0.96 inference(and_elim,[status(thm)],[141])).
% 1.12/0.96 tff(143,plain,
% 1.12/0.96 (aNaturalNumber0(xm)),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[142, 140])).
% 1.12/0.96 tff(144,plain,
% 1.12/0.96 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 1.12/0.96 inference(bind,[status(th)],[])).
% 1.12/0.96 tff(145,plain,
% 1.12/0.96 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.96 inference(quant_intro,[status(thm)],[144])).
% 1.12/0.96 tff(146,plain,
% 1.12/0.96 (^[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)))))),
% 1.12/0.96 inference(bind,[status(th)],[])).
% 1.12/0.96 tff(147,plain,
% 1.12/0.96 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.97 inference(quant_intro,[status(thm)],[146])).
% 1.12/0.97 tff(148,plain,
% 1.12/0.97 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(149,plain,
% 1.12/0.97 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 1.12/0.97 inference(bind,[status(th)],[])).
% 1.12/0.97 tff(150,plain,
% 1.12/0.97 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.12/0.97 inference(quant_intro,[status(thm)],[149])).
% 1.12/0.97 tff(151,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB_02')).
% 1.12/0.97 tff(152,plain,
% 1.12/0.97 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[151, 150])).
% 1.12/0.97 tff(153,plain,
% 1.12/0.97 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[152, 148])).
% 1.12/0.97 tff(154,plain,(
% 1.12/0.97 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.12/0.97 inference(skolemize,[status(sab)],[153])).
% 1.12/0.97 tff(155,plain,
% 1.12/0.97 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[154, 147])).
% 1.12/0.97 tff(156,plain,
% 1.12/0.97 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[155, 145])).
% 1.12/0.97 tff(157,plain,
% 1.12/0.97 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(158,plain,
% 1.12/0.97 ((aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr)))) <=> ((~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(159,plain,
% 1.12/0.97 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr)))))),
% 1.12/0.97 inference(monotonicity,[status(thm)],[158])).
% 1.12/0.97 tff(160,plain,
% 1.12/0.97 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))),
% 1.12/0.97 inference(transitivity,[status(thm)],[159, 157])).
% 1.12/0.97 tff(161,plain,
% 1.12/0.97 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))),
% 1.12/0.97 inference(quant_inst,[status(thm)],[])).
% 1.12/0.97 tff(162,plain,
% 1.12/0.97 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr)))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.12/0.97 tff(163,plain,
% 1.12/0.97 (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))),
% 1.12/0.97 inference(unit_resolution,[status(thm)],[162, 156, 143, 139])).
% 1.12/0.97 tff(164,plain,
% 1.12/0.97 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(165,plain,
% 1.12/0.97 (((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xr))) <=> ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(166,plain,
% 1.12/0.97 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr))))),
% 1.12/0.97 inference(monotonicity,[status(thm)],[165])).
% 1.12/0.97 tff(167,plain,
% 1.12/0.97 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))),
% 1.12/0.97 inference(transitivity,[status(thm)],[166, 164])).
% 1.12/0.97 tff(168,plain,
% 1.12/0.97 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xr)))),
% 1.12/0.97 inference(quant_inst,[status(thm)],[])).
% 1.12/0.97 tff(169,plain,
% 1.12/0.97 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.12/0.97 tff(170,plain,
% 1.12/0.97 (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)),
% 1.12/0.97 inference(unit_resolution,[status(thm)],[169, 28, 47, 163])).
% 1.12/0.97 tff(171,plain,
% 1.12/0.97 (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))),
% 1.12/0.97 inference(transitivity,[status(thm)],[170, 128, 121, 116, 114, 94, 92, 67, 38])).
% 1.12/0.97 tff(172,plain,
% 1.12/0.97 (sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[171, 2])).
% 1.12/0.97 tff(173,plain,
% 1.12/0.97 ((~(xr = sz00)) <=> (~(xr = sz00))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(174,plain,
% 1.12/0.97 (~(xr = sz00)),
% 1.12/0.97 inference(and_elim,[status(thm)],[43])).
% 1.12/0.97 tff(175,plain,
% 1.12/0.97 (~(xr = sz00)),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[174, 173])).
% 1.12/0.97 tff(176,plain,
% 1.12/0.97 (^[W0: $i] : refl(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 1.12/0.97 inference(bind,[status(th)],[])).
% 1.12/0.97 tff(177,plain,
% 1.12/0.97 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 1.12/0.97 inference(quant_intro,[status(thm)],[176])).
% 1.12/0.97 tff(178,plain,
% 1.12/0.97 (^[W0: $i] : rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 1.12/0.97 inference(bind,[status(th)],[])).
% 1.12/0.97 tff(179,plain,
% 1.12/0.97 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 1.12/0.97 inference(quant_intro,[status(thm)],[178])).
% 1.12/0.97 tff(180,plain,
% 1.12/0.97 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 1.12/0.97 inference(transitivity,[status(thm)],[179, 177])).
% 1.12/0.97 tff(181,plain,
% 1.12/0.97 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), rewrite((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) <=> (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), rewrite(((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), (![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))))),
% 1.12/0.97 inference(bind,[status(th)],[])).
% 1.12/0.97 tff(182,plain,
% 1.12/0.97 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 1.12/0.97 inference(quant_intro,[status(thm)],[181])).
% 1.12/0.97 tff(183,plain,
% 1.12/0.97 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(184,plain,
% 1.12/0.97 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))), rewrite((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2)))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))))), rewrite(((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), (![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), rewrite(((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> (aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))), rewrite((aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))),
% 1.12/0.97 inference(bind,[status(th)],[])).
% 1.12/0.97 tff(185,plain,
% 1.12/0.97 (![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 1.12/0.97 inference(quant_intro,[status(thm)],[184])).
% 1.12/0.97 tff(186,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulCanc')).
% 1.12/0.97 tff(187,plain,
% 1.12/0.97 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[186, 185])).
% 1.12/0.97 tff(188,plain,
% 1.12/0.97 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[187, 183])).
% 1.12/0.97 tff(189,plain,(
% 1.12/0.97 ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 1.12/0.97 inference(skolemize,[status(sab)],[188])).
% 1.12/0.97 tff(190,plain,
% 1.12/0.97 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[189, 182])).
% 1.12/0.97 tff(191,plain,
% 1.12/0.97 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[190, 180])).
% 1.12/0.97 tff(192,plain,
% 1.12/0.97 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(193,plain,
% 1.12/0.97 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(194,plain,
% 1.12/0.97 (^[W1: $i, W2: $i] : rewrite(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 1.12/0.97 inference(bind,[status(th)],[])).
% 1.12/0.97 tff(195,plain,
% 1.12/0.97 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 1.12/0.97 inference(quant_intro,[status(thm)],[194])).
% 1.12/0.97 tff(196,plain,
% 1.12/0.97 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1)))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 1.12/0.97 inference(monotonicity,[status(thm)],[195])).
% 1.12/0.97 tff(197,plain,
% 1.12/0.97 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1)))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 1.12/0.97 inference(transitivity,[status(thm)],[196, 193])).
% 1.12/0.97 tff(198,plain,
% 1.12/0.97 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))))),
% 1.12/0.97 inference(monotonicity,[status(thm)],[197])).
% 1.12/0.97 tff(199,plain,
% 1.12/0.97 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 1.12/0.97 inference(transitivity,[status(thm)],[198, 192])).
% 1.12/0.97 tff(200,plain,
% 1.12/0.97 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))),
% 1.12/0.97 inference(quant_inst,[status(thm)],[])).
% 1.12/0.97 tff(201,plain,
% 1.12/0.97 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.12/0.97 tff(202,plain,
% 1.12/0.97 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 1.12/0.97 inference(unit_resolution,[status(thm)],[201, 191, 47, 175])).
% 1.12/0.97 tff(203,plain,
% 1.12/0.97 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(204,plain,
% 1.12/0.97 ((aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(205,plain,
% 1.12/0.97 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))))),
% 1.12/0.97 inference(monotonicity,[status(thm)],[204])).
% 1.12/0.97 tff(206,plain,
% 1.12/0.97 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))))),
% 1.12/0.97 inference(transitivity,[status(thm)],[205, 203])).
% 1.12/0.97 tff(207,plain,
% 1.12/0.97 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | (~aNaturalNumber0(xp)))),
% 1.12/0.97 inference(quant_inst,[status(thm)],[])).
% 1.12/0.97 tff(208,plain,
% 1.12/0.97 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.12/0.97 tff(209,plain,
% 1.12/0.97 (aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))),
% 1.12/0.97 inference(unit_resolution,[status(thm)],[208, 156, 15, 11])).
% 1.12/0.97 tff(210,plain,
% 1.12/0.97 ((~(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))) <=> (~(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(211,plain,
% 1.12/0.97 ((~(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))) <=> (~(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(212,plain,
% 1.12/0.97 (~(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))),
% 1.12/0.97 inference(or_elim,[status(thm)],[7])).
% 1.12/0.97 tff(213,plain,
% 1.12/0.97 (~(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.12/0.97 tff(214,plain,
% 1.12/0.97 (~(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[213, 210])).
% 1.12/0.97 tff(215,plain,
% 1.12/0.97 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))) | (~((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))) | (~((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))))),
% 1.12/0.97 inference(rewrite,[status(thm)],[])).
% 1.12/0.97 tff(216,plain,
% 1.12/0.97 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))) | (~((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))))),
% 1.12/0.97 inference(quant_inst,[status(thm)],[])).
% 1.12/0.97 tff(217,plain,
% 1.12/0.97 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)))) | (~((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr))))),
% 1.12/0.97 inference(modus_ponens,[status(thm)],[216, 215])).
% 1.12/0.97 tff(218,plain,
% 1.12/0.97 (~((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))),
% 1.12/0.97 inference(unit_resolution,[status(thm)],[217, 214, 163, 209, 202])).
% 1.12/0.97 tff(219,plain,
% 1.12/0.97 (((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr))) | (~(sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))))),
% 1.12/0.97 inference(tautology,[status(thm)],[])).
% 1.12/0.97 tff(220,plain,
% 1.12/0.97 (~(sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(sdtsldt0(sdtasdt0(xn, xm), xp), xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 1.12/0.97 inference(unit_resolution,[status(thm)],[219, 218])).
% 1.12/0.97 tff(221,plain,
% 1.12/0.97 ($false),
% 1.12/0.97 inference(unit_resolution,[status(thm)],[220, 172])).
% 1.12/0.98 % SZS output end Proof
%------------------------------------------------------------------------------