TSTP Solution File: NUM524+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM524+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 13:10:16 EDT 2022
% Result : Theorem 0.18s 0.46s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM524+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n017.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 10:51:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 % SZS output start Proof
% 0.18/0.46 tff(sdtasdt0_type, type, (
% 0.18/0.46 sdtasdt0: ( $i * $i ) > $i)).
% 0.18/0.46 tff(xp_type, type, (
% 0.18/0.46 xp: $i)).
% 0.18/0.46 tff(sdtsldt0_type, type, (
% 0.18/0.46 sdtsldt0: ( $i * $i ) > $i)).
% 0.18/0.46 tff(xn_type, type, (
% 0.18/0.46 xn: $i)).
% 0.18/0.46 tff(xm_type, type, (
% 0.18/0.46 xm: $i)).
% 0.18/0.46 tff(tptp_fun_W0_7_type, type, (
% 0.18/0.46 tptp_fun_W0_7: $i)).
% 0.18/0.46 tff(xq_type, type, (
% 0.18/0.46 xq: $i)).
% 0.18/0.46 tff(aNaturalNumber0_type, type, (
% 0.18/0.46 aNaturalNumber0: $i > $o)).
% 0.18/0.46 tff(doDivides0_type, type, (
% 0.18/0.46 doDivides0: ( $i * $i ) > $o)).
% 0.18/0.46 tff(sz00_type, type, (
% 0.18/0.46 sz00: $i)).
% 0.18/0.46 tff(1,plain,
% 0.18/0.46 ((xn = sdtasdt0(xp, xq)) <=> (xn = sdtasdt0(xp, sdtsldt0(xn, xp)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(2,plain,
% 0.18/0.46 ((xn = sdtasdt0(xp, xq)) <=> (xn = sdtasdt0(xp, xq))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(3,axiom,((aNaturalNumber0(xq) & (xn = sdtasdt0(xp, xq))) & (xq = sdtsldt0(xn, xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3059')).
% 0.18/0.46 tff(4,plain,
% 0.18/0.46 (aNaturalNumber0(xq) & (xn = sdtasdt0(xp, xq))),
% 0.18/0.46 inference(and_elim,[status(thm)],[3])).
% 0.18/0.46 tff(5,plain,
% 0.18/0.46 (xn = sdtasdt0(xp, xq)),
% 0.18/0.46 inference(and_elim,[status(thm)],[4])).
% 0.18/0.46 tff(6,plain,
% 0.18/0.46 (xn = sdtasdt0(xp, xq)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.18/0.46 tff(7,plain,
% 0.18/0.46 (xn = sdtasdt0(xp, sdtsldt0(xn, xp))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.18/0.46 tff(8,plain,
% 0.18/0.46 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(9,axiom,(((?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtasdt0(xn, xn))) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))) & doDivides0(xp, xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3046')).
% 0.18/0.46 tff(10,plain,
% 0.18/0.46 ((?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtasdt0(xn, xn))) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.18/0.46 inference(and_elim,[status(thm)],[9])).
% 0.18/0.46 tff(11,plain,
% 0.18/0.46 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.18/0.46 inference(and_elim,[status(thm)],[10])).
% 0.18/0.46 tff(12,plain,
% 0.18/0.46 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.18/0.46 tff(13,plain,(
% 0.18/0.46 aNaturalNumber0(W0!7) & (xn = sdtasdt0(xp, W0!7))),
% 0.18/0.46 inference(skolemize,[status(sab)],[12])).
% 0.18/0.46 tff(14,plain,
% 0.18/0.46 (xn = sdtasdt0(xp, W0!7)),
% 0.18/0.46 inference(and_elim,[status(thm)],[13])).
% 0.18/0.46 tff(15,plain,
% 0.18/0.46 (sdtasdt0(xp, W0!7) = xn),
% 0.18/0.46 inference(symmetry,[status(thm)],[14])).
% 0.18/0.46 tff(16,plain,
% 0.18/0.46 (sdtasdt0(xp, W0!7) = sdtasdt0(xp, sdtsldt0(xn, xp))),
% 0.18/0.46 inference(transitivity,[status(thm)],[15, 7])).
% 0.18/0.46 tff(17,plain,
% 0.18/0.46 (sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)) = sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[16])).
% 0.18/0.46 tff(18,plain,
% 0.18/0.46 (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp))),
% 0.18/0.46 inference(symmetry,[status(thm)],[17])).
% 0.18/0.46 tff(19,plain,
% 0.18/0.46 (aNaturalNumber0(xq) <=> aNaturalNumber0(sdtsldt0(xn, xp))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(20,plain,
% 0.18/0.46 (aNaturalNumber0(xq) <=> aNaturalNumber0(xq)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(21,plain,
% 0.18/0.46 (aNaturalNumber0(xq)),
% 0.18/0.46 inference(and_elim,[status(thm)],[4])).
% 0.18/0.46 tff(22,plain,
% 0.18/0.46 (aNaturalNumber0(xq)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.46 tff(23,plain,
% 0.18/0.46 (aNaturalNumber0(sdtsldt0(xn, xp))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.18/0.46 tff(24,plain,
% 0.18/0.46 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(25,axiom,(((((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))) & (~(xm = sz00))) & (~(xp = sz00))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2987')).
% 0.18/0.46 tff(26,plain,
% 0.18/0.46 ((((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))) & (~(xm = sz00))),
% 0.18/0.46 inference(and_elim,[status(thm)],[25])).
% 0.18/0.46 tff(27,plain,
% 0.18/0.46 (((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))),
% 0.18/0.46 inference(and_elim,[status(thm)],[26])).
% 0.18/0.46 tff(28,plain,
% 0.18/0.46 ((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)),
% 0.18/0.46 inference(and_elim,[status(thm)],[27])).
% 0.18/0.46 tff(29,plain,
% 0.18/0.46 (aNaturalNumber0(xp)),
% 0.18/0.46 inference(and_elim,[status(thm)],[28])).
% 0.18/0.46 tff(30,plain,
% 0.18/0.46 (aNaturalNumber0(xp)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.18/0.46 tff(31,plain,
% 0.18/0.46 (^[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))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(32,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[31])).
% 0.18/0.46 tff(33,plain,
% 0.18/0.46 (^[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)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(34,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.46 tff(35,plain,
% 0.18/0.46 (![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))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(36,plain,
% 0.18/0.46 (^[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))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(37,plain,
% 0.18/0.46 (![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))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[36])).
% 0.18/0.46 tff(38,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/sandbox/benchmark/theBenchmark.p','mMulAsso')).
% 0.18/0.46 tff(39,plain,
% 0.18/0.46 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.18/0.46 tff(40,plain,
% 0.18/0.46 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.18/0.46 tff(41,plain,(
% 0.18/0.46 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.18/0.46 inference(skolemize,[status(sab)],[40])).
% 0.18/0.46 tff(42,plain,
% 0.18/0.46 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.18/0.46 tff(43,plain,
% 0.18/0.46 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.18/0.46 tff(44,plain,
% 0.18/0.46 (((~![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(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, 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(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(45,plain,
% 0.18/0.46 (((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(46,plain,
% 0.18/0.46 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(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(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[45])).
% 0.18/0.47 tff(47,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(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(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[46, 44])).
% 0.18/0.47 tff(48,plain,
% 0.18/0.47 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(49,plain,
% 0.18/0.47 ((~![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(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.18/0.47 tff(50,plain,
% 0.18/0.47 (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[49, 43, 30, 23])).
% 0.18/0.47 tff(51,plain,
% 0.18/0.47 (sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp))),
% 0.18/0.47 inference(symmetry,[status(thm)],[50])).
% 0.18/0.47 tff(52,plain,
% 0.18/0.47 (sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp))),
% 0.18/0.47 inference(transitivity,[status(thm)],[51, 18])).
% 0.18/0.47 tff(53,plain,
% 0.18/0.47 (sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp) = sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[52])).
% 0.18/0.47 tff(54,plain,
% 0.18/0.47 (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp)),
% 0.18/0.47 inference(symmetry,[status(thm)],[53])).
% 0.18/0.47 tff(55,plain,
% 0.18/0.47 (aNaturalNumber0(sdtasdt0(xp, W0!7)) <=> aNaturalNumber0(xn)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.47 tff(56,plain,
% 0.18/0.47 (aNaturalNumber0(xn) <=> aNaturalNumber0(sdtasdt0(xp, W0!7))),
% 0.18/0.47 inference(symmetry,[status(thm)],[55])).
% 0.18/0.47 tff(57,plain,
% 0.18/0.47 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(58,plain,
% 0.18/0.47 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 0.18/0.47 inference(and_elim,[status(thm)],[28])).
% 0.18/0.47 tff(59,plain,
% 0.18/0.47 (aNaturalNumber0(xn)),
% 0.18/0.47 inference(and_elim,[status(thm)],[58])).
% 0.18/0.47 tff(60,plain,
% 0.18/0.47 (aNaturalNumber0(xn)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[59, 57])).
% 0.18/0.47 tff(61,plain,
% 0.18/0.47 (aNaturalNumber0(sdtasdt0(xp, W0!7))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.18/0.47 tff(62,plain,
% 0.18/0.47 (((~![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(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), 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(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(63,plain,
% 0.18/0.47 (((sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7)))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(64,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))))) <=> ((~![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(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[63])).
% 0.18/0.47 tff(65,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))))) <=> ((~![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(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[64, 62])).
% 0.18/0.47 tff(66,plain,
% 0.18/0.47 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(67,plain,
% 0.18/0.47 ((~![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(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.47 tff(68,plain,
% 0.18/0.47 (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[67, 43, 30, 23, 61])).
% 0.18/0.47 tff(69,plain,
% 0.18/0.47 (sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp)) = sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), sdtsldt0(xn, xp)), xp)),
% 0.18/0.47 inference(symmetry,[status(thm)],[68])).
% 0.18/0.47 tff(70,plain,
% 0.18/0.47 (sdtasdt0(xp, sdtsldt0(xn, xp)) = xn),
% 0.18/0.47 inference(symmetry,[status(thm)],[7])).
% 0.18/0.47 tff(71,plain,
% 0.18/0.47 (^[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))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(72,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[71])).
% 0.18/0.47 tff(73,plain,
% 0.18/0.47 (^[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)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(74,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[73])).
% 0.18/0.47 tff(75,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(76,plain,
% 0.18/0.47 (^[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))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(77,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.47 tff(78,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulComm')).
% 0.18/0.47 tff(79,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.47 tff(80,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.18/0.47 tff(81,plain,(
% 0.18/0.47 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[80])).
% 0.18/0.47 tff(82,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.18/0.47 tff(83,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.18/0.47 tff(84,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(xp, sdtsldt0(xn, xp))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(xp, sdtsldt0(xn, xp))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(85,plain,
% 0.18/0.47 (((sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(xp, sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp)))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(xp, sdtsldt0(xn, xp))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(86,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(xp, sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(xp, sdtsldt0(xn, xp)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[85])).
% 0.18/0.47 tff(87,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(xp, sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(xp, sdtsldt0(xn, xp))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[86, 84])).
% 0.18/0.47 tff(88,plain,
% 0.18/0.47 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(xp, sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(89,plain,
% 0.18/0.47 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(xp, sdtsldt0(xn, xp)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.47 tff(90,plain,
% 0.18/0.47 (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(xp, sdtsldt0(xn, xp))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[89, 83, 30, 23])).
% 0.18/0.47 tff(91,plain,
% 0.18/0.47 (sdtasdt0(sdtsldt0(xn, xp), xp) = xn),
% 0.18/0.47 inference(transitivity,[status(thm)],[90, 70])).
% 0.18/0.47 tff(92,plain,
% 0.18/0.47 (sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp)) = sdtasdt0(xn, xn)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[15, 91])).
% 0.18/0.47 tff(93,plain,
% 0.18/0.47 (sdtasdt0(xn, xn) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(sdtsldt0(xn, xp), xp))),
% 0.18/0.47 inference(symmetry,[status(thm)],[92])).
% 0.18/0.47 tff(94,plain,
% 0.18/0.47 ((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn)) <=> (sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(95,axiom,(sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3014')).
% 0.18/0.47 tff(96,plain,
% 0.18/0.47 (sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.47 tff(97,plain,
% 0.18/0.47 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(98,plain,
% 0.18/0.47 (aNaturalNumber0(xm)),
% 0.18/0.47 inference(and_elim,[status(thm)],[58])).
% 0.18/0.47 tff(99,plain,
% 0.18/0.47 (aNaturalNumber0(xm)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.47 tff(100,plain,
% 0.18/0.47 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(101,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[100])).
% 0.18/0.47 tff(102,plain,
% 0.18/0.47 (^[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)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(103,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[102])).
% 0.18/0.47 tff(104,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(105,plain,
% 0.18/0.47 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(106,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[105])).
% 0.18/0.47 tff(107,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 0.18/0.47 tff(108,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.47 tff(109,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.18/0.47 tff(110,plain,(
% 0.18/0.47 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.18/0.47 inference(skolemize,[status(sab)],[109])).
% 0.18/0.47 tff(111,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.18/0.47 tff(112,plain,
% 0.18/0.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[111, 101])).
% 0.18/0.47 tff(113,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(114,plain,
% 0.18/0.47 ((aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xm))) <=> (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(115,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xm)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[114])).
% 0.18/0.47 tff(116,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xm)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[115, 113])).
% 0.18/0.47 tff(117,plain,
% 0.18/0.47 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xm)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(118,plain,
% 0.18/0.47 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.18/0.47 tff(119,plain,
% 0.18/0.47 (aNaturalNumber0(sdtasdt0(xm, xm))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[118, 112, 99])).
% 0.18/0.47 tff(120,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(xp, sdtasdt0(xm, xm))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(xp, sdtasdt0(xm, xm))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(121,plain,
% 0.18/0.47 (((sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(xp, sdtasdt0(xm, xm))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm)))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(xp, sdtasdt0(xm, xm))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(122,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(xp, sdtasdt0(xm, xm))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(xp, sdtasdt0(xm, xm)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[121])).
% 0.18/0.47 tff(123,plain,
% 0.18/0.47 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(xp, sdtasdt0(xm, xm))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(xp, sdtasdt0(xm, xm))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[122, 120])).
% 0.18/0.47 tff(124,plain,
% 0.18/0.47 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(xp, sdtasdt0(xm, xm))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(125,plain,
% 0.18/0.47 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(xp, sdtasdt0(xm, xm)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.47 tff(126,plain,
% 0.18/0.47 (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(xp, sdtasdt0(xm, xm))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[125, 83, 30, 119])).
% 0.18/0.47 tff(127,plain,
% 0.18/0.47 (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp)),
% 0.18/0.47 inference(transitivity,[status(thm)],[126, 96, 93, 69, 54])).
% 0.18/0.47 tff(128,plain,
% 0.18/0.47 ((~(xp = sz00)) <=> (~(xp = sz00))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(129,plain,
% 0.18/0.47 (~(xp = sz00)),
% 0.18/0.47 inference(and_elim,[status(thm)],[25])).
% 0.18/0.47 tff(130,plain,
% 0.18/0.47 (~(xp = sz00)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.18/0.47 tff(131,plain,
% 0.18/0.47 (^[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)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(132,plain,
% 0.18/0.47 (![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))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[131])).
% 0.18/0.47 tff(133,plain,
% 0.18/0.47 (^[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)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(134,plain,
% 0.18/0.47 (![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))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[133])).
% 0.18/0.47 tff(135,plain,
% 0.18/0.47 (![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))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[134, 132])).
% 0.18/0.47 tff(136,plain,
% 0.18/0.47 (^[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))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(137,plain,
% 0.18/0.48 (![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))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[136])).
% 0.18/0.48 tff(138,plain,
% 0.18/0.48 (![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))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(139,plain,
% 0.18/0.48 (^[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))))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(140,plain,
% 0.18/0.48 (![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))))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[139])).
% 0.18/0.48 tff(141,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/sandbox/benchmark/theBenchmark.p','mMulCanc')).
% 0.18/0.48 tff(142,plain,
% 0.18/0.48 (![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))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.18/0.48 tff(143,plain,
% 0.18/0.48 (![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))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.18/0.48 tff(144,plain,(
% 0.18/0.48 ![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))))))),
% 0.18/0.48 inference(skolemize,[status(sab)],[143])).
% 0.18/0.48 tff(145,plain,
% 0.18/0.48 (![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))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.18/0.48 tff(146,plain,
% 0.18/0.48 (![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))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[145, 135])).
% 0.18/0.48 tff(147,plain,
% 0.18/0.48 (((~![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))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))) <=> ((~![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))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(148,plain,
% 0.18/0.48 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(149,plain,
% 0.18/0.48 (^[W1: $i, W2: $i] : rewrite(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(150,plain,
% 0.18/0.48 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[149])).
% 0.18/0.48 tff(151,plain,
% 0.18/0.48 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1)))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[150])).
% 0.18/0.48 tff(152,plain,
% 0.18/0.48 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1)))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[151, 148])).
% 0.18/0.48 tff(153,plain,
% 0.18/0.48 (((~![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))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~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))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[152])).
% 0.18/0.48 tff(154,plain,
% 0.18/0.48 (((~![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))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~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))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[153, 147])).
% 0.18/0.48 tff(155,plain,
% 0.18/0.48 ((~![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))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(156,plain,
% 0.18/0.48 ((~![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))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.18/0.48 tff(157,plain,
% 0.18/0.48 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[156, 146, 30, 130])).
% 0.18/0.48 tff(158,plain,
% 0.18/0.48 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(159,plain,
% 0.18/0.48 ((aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp)))) <=> ((~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(160,plain,
% 0.18/0.48 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[159])).
% 0.18/0.48 tff(161,plain,
% 0.18/0.48 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[160, 158])).
% 0.18/0.48 tff(162,plain,
% 0.18/0.48 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(163,plain,
% 0.18/0.48 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.18/0.48 tff(164,plain,
% 0.18/0.48 (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[163, 112, 23])).
% 0.18/0.48 tff(165,plain,
% 0.18/0.48 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(166,plain,
% 0.18/0.48 ((aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(167,plain,
% 0.18/0.48 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[166])).
% 0.18/0.48 tff(168,plain,
% 0.18/0.48 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[167, 165])).
% 0.18/0.48 tff(169,plain,
% 0.18/0.48 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(xp)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(170,plain,
% 0.18/0.48 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.18/0.48 tff(171,plain,
% 0.18/0.48 (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[170, 112, 30, 164])).
% 0.18/0.48 tff(172,plain,
% 0.18/0.48 ((~(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq)))) <=> (~(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(173,plain,
% 0.18/0.48 ((~(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq)))) <=> (~(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(174,axiom,(~(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.18/0.48 tff(175,plain,
% 0.18/0.48 (~(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.18/0.48 tff(176,plain,
% 0.18/0.48 (~(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[175, 172])).
% 0.18/0.48 tff(177,plain,
% 0.18/0.48 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(178,plain,
% 0.18/0.49 (((sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp))))) <=> ((sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(179,plain,
% 0.18/0.49 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp))))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[178])).
% 0.18/0.49 tff(180,plain,
% 0.18/0.49 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp)))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[179, 177])).
% 0.18/0.49 tff(181,plain,
% 0.18/0.49 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp)))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(182,plain,
% 0.18/0.49 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.18/0.49 tff(183,plain,
% 0.18/0.49 (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[182, 176, 119, 171, 157])).
% 0.18/0.49 tff(184,plain,
% 0.18/0.49 (((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp))) | (~(sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(185,plain,
% 0.18/0.49 (~(sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))), xp))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.18/0.49 tff(186,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[185, 127])).
% 0.18/0.49 % SZS output end Proof
%------------------------------------------------------------------------------