TSTP Solution File: DAT062_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT062_1 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Fri Sep 16 14:36:34 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT062_1 : TPTP v8.1.0. Released v5.5.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 02:00:51 EDT 2022
% 0.12/0.34 % 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.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(length_type, type, (
% 0.12/0.39 length: heap > $int)).
% 0.12/0.39 tff(tptp_fun_H0_2_type, type, (
% 0.12/0.39 tptp_fun_H0_2: heap)).
% 0.12/0.39 tff(app_type, type, (
% 0.12/0.39 app: ( heap * $int ) > heap)).
% 0.12/0.39 tff(tptp_fun_N_0_type, type, (
% 0.12/0.39 tptp_fun_N_0: $int)).
% 0.12/0.39 tff(tptp_fun_H_1_type, type, (
% 0.12/0.39 tptp_fun_H_1: heap)).
% 0.12/0.39 tff(lsls_type, type, (
% 0.12/0.39 lsls: ( heap * heap ) > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 ((![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0))) & (~((~lsls(H0!2, app(H!1, N!0))) | (~$greatereq($sum(length(H0!2), $product(-1, length(app(H!1, N!0)))), 0))))) <=> (![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0))) & (~((~lsls(H0!2, app(H!1, N!0))) | (~$lesseq($sum(length(app(H!1, N!0)), $product(-1, length(H0!2))), 0)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 ((~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$greatereq($sum(length(H0), $product(-1, length(H))), 0)))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$greatereq($sum(length(H0), $product(-1, length(app(H, N)))), 0))))) <=> (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$greatereq($sum(length(H0), $product(-1, length(H))), 0)))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$greatereq($sum(length(H0), $product(-1, length(app(H, N)))), 0)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 ((~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$lesseq($sum(length(H), $product(-1, length(H0))), 0)))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$lesseq($sum(length(app(H, N)), $product(-1, length(H0))), 0))))) <=> (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$greatereq($sum(length(H0), $product(-1, length(H))), 0)))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$greatereq($sum(length(H0), $product(-1, length(app(H, N)))), 0)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 ((~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$lesseq(length(H), length(H0))))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$lesseq(length(app(H, N)), length(H0)))))) <=> (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$lesseq($sum(length(H), $product(-1, length(H0))), 0)))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$lesseq($sum(length(app(H, N)), $product(-1, length(H0))), 0)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 ((~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$lesseq(length(H), length(H0))))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$lesseq(length(app(H, N)), length(H0)))))) <=> (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$lesseq(length(H), length(H0))))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$lesseq(length(app(H, N)), length(H0))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 ((~![H: heap, N: $int] : ((~![H0: heap] : (lsls(H0, H) => $less(length(H0), length(H)))) | ![H0: heap] : (lsls(H0, app(H, N)) => $less(length(H0), length(app(H, N)))))) <=> (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$lesseq(length(H), length(H0))))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$lesseq(length(app(H, N)), length(H0))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(7,axiom,(~![H: heap, N: $int] : ((~![H0: heap] : (lsls(H0, H) => $less(length(H0), length(H)))) | ![H0: heap] : (lsls(H0, app(H, N)) => $less(length(H0), length(app(H, N)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','th_lem_1a')).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$lesseq(length(H), length(H0))))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$lesseq(length(app(H, N)), length(H0)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$lesseq(length(H), length(H0))))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$lesseq(length(app(H, N)), length(H0)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$lesseq(length(H), length(H0))))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$lesseq(length(app(H, N)), length(H0)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$lesseq(length(H), length(H0))))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$lesseq(length(app(H, N)), length(H0)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$lesseq($sum(length(H), $product(-1, length(H0))), 0)))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$lesseq($sum(length(app(H, N)), $product(-1, length(H0))), 0))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$greatereq($sum(length(H0), $product(-1, length(H))), 0)))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$greatereq($sum(length(H0), $product(-1, length(app(H, N)))), 0))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$greatereq($sum(length(H0), $product(-1, length(H))), 0)))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$greatereq($sum(length(H0), $product(-1, length(app(H, N)))), 0))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (~![H: heap, N: $int] : ((~![H0: heap] : ((~lsls(H0, H)) | (~$greatereq($sum(length(H0), $product(-1, length(H))), 0)))) | ![H0: heap] : ((~lsls(H0, app(H, N))) | (~$greatereq($sum(length(H0), $product(-1, length(app(H, N)))), 0))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0))) & (~((~lsls(H0!2, app(H!1, N!0))) | (~$lesseq($sum(length(app(H!1, N!0)), $product(-1, length(H0!2))), 0))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 1])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (~((~lsls(H0!2, app(H!1, N!0))) | (~$lesseq($sum(length(app(H!1, N!0)), $product(-1, length(H0!2))), 0)))),
% 0.12/0.39 inference(and_elim,[status(thm)],[16])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 ($lesseq($sum(length(app(H!1, N!0)), $product(-1, length(H0!2))), 0)),
% 0.12/0.39 inference(or_elim,[status(thm)],[17])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (^[N: $int, H: heap] : refl(($sum(length(H), $product(-1, length(app(H, N)))) = -1) <=> ($sum(length(H), $product(-1, length(app(H, N)))) = -1))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![N: $int, H: heap] : ($sum(length(H), $product(-1, length(app(H, N)))) = -1) <=> ![N: $int, H: heap] : ($sum(length(H), $product(-1, length(app(H, N)))) = -1)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (^[N: $int, H: heap] : trans(monotonicity(rewrite($sum(length(app(H, N)), $product(-1, length(H))) = $sum($product(-1, length(H)), length(app(H, N)))), (($sum(length(app(H, N)), $product(-1, length(H))) = 1) <=> ($sum($product(-1, length(H)), length(app(H, N))) = 1))), rewrite(($sum($product(-1, length(H)), length(app(H, N))) = 1) <=> ($sum(length(H), $product(-1, length(app(H, N)))) = -1)), (($sum(length(app(H, N)), $product(-1, length(H))) = 1) <=> ($sum(length(H), $product(-1, length(app(H, N)))) = -1)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![N: $int, H: heap] : ($sum(length(app(H, N)), $product(-1, length(H))) = 1) <=> ![N: $int, H: heap] : ($sum(length(H), $product(-1, length(app(H, N)))) = -1)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (^[N: $int, H: heap] : rewrite((length(app(H, N)) = $sum(1, length(H))) <=> ($sum(length(app(H, N)), $product(-1, length(H))) = 1))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![N: $int, H: heap] : (length(app(H, N)) = $sum(1, length(H))) <=> ![N: $int, H: heap] : ($sum(length(app(H, N)), $product(-1, length(H))) = 1)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![N: $int, H: heap] : (length(app(H, N)) = $sum(1, length(H))) <=> ![N: $int, H: heap] : (length(app(H, N)) = $sum(1, length(H)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(26,axiom,(![N: $int, H: heap] : (length(app(H, N)) = $sum(1, length(H)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT005=0.ax','ax_23')).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (![N: $int, H: heap] : (length(app(H, N)) = $sum(1, length(H)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (![N: $int, H: heap] : ($sum(length(app(H, N)), $product(-1, length(H))) = 1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (![N: $int, H: heap] : ($sum(length(H), $product(-1, length(app(H, N)))) = -1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.12/0.40 tff(30,plain,(
% 0.12/0.40 ![N: $int, H: heap] : ($sum(length(H), $product(-1, length(app(H, N)))) = -1)),
% 0.12/0.40 inference(skolemize,[status(sab)],[29])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (![N: $int, H: heap] : ($sum(length(H), $product(-1, length(app(H, N)))) = -1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 ((~![N: $int, H: heap] : ($sum(length(H), $product(-1, length(app(H, N)))) = -1)) | ($sum(length(H!1), $product(-1, length(app(H!1, N!0)))) = -1)),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 ($sum(length(H!1), $product(-1, length(app(H!1, N!0)))) = -1),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 ((~($sum(length(H!1), $product(-1, length(app(H!1, N!0)))) = -1)) | $lesseq($sum(length(H!1), $product(-1, length(app(H!1, N!0)))), -1)),
% 0.12/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 ($lesseq($sum(length(H!1), $product(-1, length(app(H!1, N!0)))), -1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 ($lesseq($sum(length(H!1), $product(-1, length(app(H!1, N!0)))), 0) | (~$lesseq($sum(length(H!1), $product(-1, length(app(H!1, N!0)))), -1))),
% 0.12/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 ($lesseq($sum(length(H!1), $product(-1, length(app(H!1, N!0)))), 0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.12/0.40 tff(38,assumption,(~$lesseq($sum(length(H!1), $product(-1, length(H0!2))), 0)), introduced(assumption)).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(theory_lemma,[status(thm)],[38, 37, 18])).
% 0.12/0.40 tff(40,plain,($lesseq($sum(length(H!1), $product(-1, length(H0!2))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (^[H0: heap] : refl(((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0))) <=> ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0))) <=> ![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0)))),
% 0.12/0.40 inference(and_elim,[status(thm)],[16])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (((~![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0)))) | ((~lsls(H0!2, H!1)) | (~$lesseq($sum(length(H!1), $product(-1, length(H0!2))), 0)))) <=> ((~![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0)))) | (~lsls(H0!2, H!1)) | (~$lesseq($sum(length(H!1), $product(-1, length(H0!2))), 0)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (((~lsls(H0!2, H!1)) | (~$greatereq($sum(length(H0!2), $product(-1, length(H!1))), 0))) <=> ((~lsls(H0!2, H!1)) | (~$lesseq($sum(length(H!1), $product(-1, length(H0!2))), 0)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (((~![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0)))) | ((~lsls(H0!2, H!1)) | (~$greatereq($sum(length(H0!2), $product(-1, length(H!1))), 0)))) <=> ((~![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0)))) | ((~lsls(H0!2, H!1)) | (~$lesseq($sum(length(H!1), $product(-1, length(H0!2))), 0))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[46])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (((~![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0)))) | ((~lsls(H0!2, H!1)) | (~$greatereq($sum(length(H0!2), $product(-1, length(H!1))), 0)))) <=> ((~![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0)))) | (~lsls(H0!2, H!1)) | (~$lesseq($sum(length(H!1), $product(-1, length(H0!2))), 0)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[47, 45])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 ((~![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0)))) | ((~lsls(H0!2, H!1)) | (~$greatereq($sum(length(H0!2), $product(-1, length(H!1))), 0)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 ((~![H0: heap] : ((~lsls(H0, H!1)) | (~$greatereq($sum(length(H0), $product(-1, length(H!1))), 0)))) | (~lsls(H0!2, H!1)) | (~$lesseq($sum(length(H!1), $product(-1, length(H0!2))), 0))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 ((~lsls(H0!2, H!1)) | (~$lesseq($sum(length(H!1), $product(-1, length(H0!2))), 0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[50, 44])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (~lsls(H0!2, H!1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[51, 40])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (^[N: $int, H0: heap, H: heap] : refl((lsls(H0, app(H, N)) <=> ((H0 = H) | lsls(H0, H))) <=> (lsls(H0, app(H, N)) <=> ((H0 = H) | lsls(H0, H))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (![N: $int, H0: heap, H: heap] : (lsls(H0, app(H, N)) <=> ((H0 = H) | lsls(H0, H))) <=> ![N: $int, H0: heap, H: heap] : (lsls(H0, app(H, N)) <=> ((H0 = H) | lsls(H0, H)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![N: $int, H0: heap, H: heap] : (lsls(H0, app(H, N)) <=> ((H0 = H) | lsls(H0, H))) <=> ![N: $int, H0: heap, H: heap] : (lsls(H0, app(H, N)) <=> ((H0 = H) | lsls(H0, H)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(56,axiom,(![N: $int, H0: heap, H: heap] : (lsls(H0, app(H, N)) <=> ((H0 = H) | lsls(H0, H)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT005=0.ax','ax_27')).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (![N: $int, H0: heap, H: heap] : (lsls(H0, app(H, N)) <=> ((H0 = H) | lsls(H0, H)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.40 tff(58,plain,(
% 0.12/0.40 ![N: $int, H0: heap, H: heap] : (lsls(H0, app(H, N)) <=> ((H0 = H) | lsls(H0, H)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[57])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (![N: $int, H0: heap, H: heap] : (lsls(H0, app(H, N)) <=> ((H0 = H) | lsls(H0, H)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 ((~![N: $int, H0: heap, H: heap] : (lsls(H0, app(H, N)) <=> ((H0 = H) | lsls(H0, H)))) | (lsls(H0!2, app(H!1, N!0)) <=> ((H0!2 = H!1) | lsls(H0!2, H!1)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (lsls(H0!2, app(H!1, N!0)) <=> ((H0!2 = H!1) | lsls(H0!2, H!1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (lsls(H0!2, app(H!1, N!0))),
% 0.12/0.40 inference(or_elim,[status(thm)],[17])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 ((~(lsls(H0!2, app(H!1, N!0)) <=> ((H0!2 = H!1) | lsls(H0!2, H!1)))) | (~lsls(H0!2, app(H!1, N!0))) | ((H0!2 = H!1) | lsls(H0!2, H!1))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 ((~(lsls(H0!2, app(H!1, N!0)) <=> ((H0!2 = H!1) | lsls(H0!2, H!1)))) | ((H0!2 = H!1) | lsls(H0!2, H!1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 ((H0!2 = H!1) | lsls(H0!2, H!1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[64, 61])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 ((~((H0!2 = H!1) | lsls(H0!2, H!1))) | (H0!2 = H!1) | lsls(H0!2, H!1)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 ((H0!2 = H!1) | lsls(H0!2, H!1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (H0!2 = H!1),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[67, 52])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (length(H0!2) = length(H!1)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[68])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (length(H!1) = length(H0!2)),
% 0.12/0.40 inference(symmetry,[status(thm)],[69])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 ((~(length(H!1) = length(H0!2))) | $greatereq($sum(length(H!1), $product(-1, length(H0!2))), 0)),
% 0.12/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 ($greatereq($sum(length(H!1), $product(-1, length(H0!2))), 0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(theory_lemma,[status(thm)],[72, 35, 18])).
% 0.12/0.40 % SZS output end Proof
%------------------------------------------------------------------------------