TSTP Solution File: DAT051_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT051_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 14:36:32 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT051_1 : TPTP v8.1.0. Released v5.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 01:42:04 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(length_type, type, (
% 0.20/0.40 length: record > $int)).
% 0.20/0.40 tff(next_type, type, (
% 0.20/0.40 next: record > record)).
% 0.20/0.40 tff(tptp_fun_U_1_type, type, (
% 0.20/0.40 tptp_fun_U_1: record)).
% 0.20/0.40 tff(isrecord_type, type, (
% 0.20/0.40 isrecord: record > $o)).
% 0.20/0.40 tff(split2_type, type, (
% 0.20/0.40 split2: record > record)).
% 0.20/0.40 tff(tptp_fun_V_0_type, type, (
% 0.20/0.40 tptp_fun_V_0: record)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 ((~(($sum(length(U!1), $product(-2, length(split2(U!1)))) = 1) | ($sum(length(U!1), $product(-2, length(split2(U!1)))) = 0) | (~(isrecord(U!1) & isrecord(next(U!1)) & (V!0 = next(next(U!1))) & (($sum(length(V!0), $product(-2, length(split2(V!0)))) = 0) | ($sum(length(V!0), $product(-2, length(split2(V!0)))) = 1)))))) <=> (~(($sum(length(U!1), $product(-2, length(split2(U!1)))) = 1) | ($sum(length(U!1), $product(-2, length(split2(U!1)))) = 0) | (~(isrecord(U!1) & isrecord(next(U!1)) & (V!0 = next(next(U!1))) & (($sum(length(V!0), $product(-2, length(split2(V!0)))) = 0) | ($sum(length(V!0), $product(-2, length(split2(V!0)))) = 1))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 ((~![U: record, V: record] : (($sum(length(U), $product(-2, length(split2(U)))) = 1) | ($sum(length(U), $product(-2, length(split2(U)))) = 0) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($sum(length(V), $product(-2, length(split2(V)))) = 0) | ($sum(length(V), $product(-2, length(split2(V)))) = 1)))))) <=> (~![U: record, V: record] : (($sum(length(U), $product(-2, length(split2(U)))) = 1) | ($sum(length(U), $product(-2, length(split2(U)))) = 0) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($sum(length(V), $product(-2, length(split2(V)))) = 0) | ($sum(length(V), $product(-2, length(split2(V)))) = 1))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 ((~![U: record, V: record] : (($sum($product(2, length(split2(U))), $product(-1, length(U))) = 0) | ($sum($product(2, length(split2(U))), $product(-1, length(U))) = -1) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($sum($product(2, length(split2(V))), $product(-1, length(V))) = 0) | ($sum($product(2, length(split2(V))), $product(-1, length(V))) = -1)))))) <=> (~![U: record, V: record] : (($sum(length(U), $product(-2, length(split2(U)))) = 1) | ($sum(length(U), $product(-2, length(split2(U)))) = 0) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($sum(length(V), $product(-2, length(split2(V)))) = 0) | ($sum(length(V), $product(-2, length(split2(V)))) = 1))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 ((~![U: record, V: record] : (($product(2, length(split2(U))) = length(U)) | ($product(2, length(split2(U))) = $sum(-1, length(U))) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($product(2, length(split2(V))) = length(V)) | ($product(2, length(split2(V))) = $sum(-1, length(V)))))))) <=> (~![U: record, V: record] : (($sum($product(2, length(split2(U))), $product(-1, length(U))) = 0) | ($sum($product(2, length(split2(U))), $product(-1, length(U))) = -1) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($sum($product(2, length(split2(V))), $product(-1, length(V))) = 0) | ($sum($product(2, length(split2(V))), $product(-1, length(V))) = -1))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 ((~![U: record, V: record] : (($product(2, length(split2(U))) = length(U)) | ($product(2, length(split2(U))) = $sum(-1, length(U))) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($product(2, length(split2(V))) = length(V)) | ($product(2, length(split2(V))) = $sum(-1, length(V)))))))) <=> (~![U: record, V: record] : (($product(2, length(split2(U))) = length(U)) | ($product(2, length(split2(U))) = $sum(-1, length(U))) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($product(2, length(split2(V))) = length(V)) | ($product(2, length(split2(V))) = $sum(-1, length(V))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 ((~![U: record, V: record] : ((((isrecord(U) & isrecord(next(U))) & (V = next(next(U)))) & (($product(2, length(split2(V))) = $difference(length(V), 1)) | ($product(2, length(split2(V))) = length(V)))) => (($product(2, length(split2(U))) = $difference(length(U), 1)) | ($product(2, length(split2(U))) = length(U))))) <=> (~![U: record, V: record] : (($product(2, length(split2(U))) = length(U)) | ($product(2, length(split2(U))) = $sum(-1, length(U))) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($product(2, length(split2(V))) = length(V)) | ($product(2, length(split2(V))) = $sum(-1, length(V))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(7,axiom,(~![U: record, V: record] : ((((isrecord(U) & isrecord(next(U))) & (V = next(next(U)))) & (($product(2, length(split2(V))) = $difference(length(V), 1)) | ($product(2, length(split2(V))) = length(V)))) => (($product(2, length(split2(U))) = $difference(length(U), 1)) | ($product(2, length(split2(U))) = length(U))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (~![U: record, V: record] : (($product(2, length(split2(U))) = length(U)) | ($product(2, length(split2(U))) = $sum(-1, length(U))) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($product(2, length(split2(V))) = length(V)) | ($product(2, length(split2(V))) = $sum(-1, length(V)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (~![U: record, V: record] : (($product(2, length(split2(U))) = length(U)) | ($product(2, length(split2(U))) = $sum(-1, length(U))) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($product(2, length(split2(V))) = length(V)) | ($product(2, length(split2(V))) = $sum(-1, length(V)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (~![U: record, V: record] : (($product(2, length(split2(U))) = length(U)) | ($product(2, length(split2(U))) = $sum(-1, length(U))) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($product(2, length(split2(V))) = length(V)) | ($product(2, length(split2(V))) = $sum(-1, length(V)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (~![U: record, V: record] : (($product(2, length(split2(U))) = length(U)) | ($product(2, length(split2(U))) = $sum(-1, length(U))) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($product(2, length(split2(V))) = length(V)) | ($product(2, length(split2(V))) = $sum(-1, length(V)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (~![U: record, V: record] : (($sum($product(2, length(split2(U))), $product(-1, length(U))) = 0) | ($sum($product(2, length(split2(U))), $product(-1, length(U))) = -1) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($sum($product(2, length(split2(V))), $product(-1, length(V))) = 0) | ($sum($product(2, length(split2(V))), $product(-1, length(V))) = -1)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (~![U: record, V: record] : (($sum(length(U), $product(-2, length(split2(U)))) = 1) | ($sum(length(U), $product(-2, length(split2(U)))) = 0) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($sum(length(V), $product(-2, length(split2(V)))) = 0) | ($sum(length(V), $product(-2, length(split2(V)))) = 1)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (~![U: record, V: record] : (($sum(length(U), $product(-2, length(split2(U)))) = 1) | ($sum(length(U), $product(-2, length(split2(U)))) = 0) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($sum(length(V), $product(-2, length(split2(V)))) = 0) | ($sum(length(V), $product(-2, length(split2(V)))) = 1)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (~![U: record, V: record] : (($sum(length(U), $product(-2, length(split2(U)))) = 1) | ($sum(length(U), $product(-2, length(split2(U)))) = 0) | (~(isrecord(U) & isrecord(next(U)) & (V = next(next(U))) & (($sum(length(V), $product(-2, length(split2(V)))) = 0) | ($sum(length(V), $product(-2, length(split2(V)))) = 1)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.20/0.40 tff(16,plain,(
% 0.20/0.40 ~(($sum(length(U!1), $product(-2, length(split2(U!1)))) = 1) | ($sum(length(U!1), $product(-2, length(split2(U!1)))) = 0) | (~(isrecord(U!1) & isrecord(next(U!1)) & (V!0 = next(next(U!1))) & (($sum(length(V!0), $product(-2, length(split2(V!0)))) = 0) | ($sum(length(V!0), $product(-2, length(split2(V!0)))) = 1)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (~(($sum(length(U!1), $product(-2, length(split2(U!1)))) = 1) | ($sum(length(U!1), $product(-2, length(split2(U!1)))) = 0) | (~(isrecord(U!1) & isrecord(next(U!1)) & (V!0 = next(next(U!1))) & (($sum(length(V!0), $product(-2, length(split2(V!0)))) = 0) | ($sum(length(V!0), $product(-2, length(split2(V!0)))) = 1)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 1])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (isrecord(U!1) & isrecord(next(U!1)) & (V!0 = next(next(U!1))) & (($sum(length(V!0), $product(-2, length(split2(V!0)))) = 0) | ($sum(length(V!0), $product(-2, length(split2(V!0)))) = 1))),
% 0.20/0.40 inference(or_elim,[status(thm)],[17])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (isrecord(next(U!1))),
% 0.20/0.40 inference(and_elim,[status(thm)],[18])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (^[U: record] : refl(((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1)) <=> ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1)) <=> ![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (^[U: record] : rewrite(((~isrecord(U)) | (length(U) = $sum(1, length(next(U))))) <=> ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U))))) <=> ![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U))))) <=> ![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (^[U: record] : trans(monotonicity(rewrite((length(U) = $sum(length(next(U)), 1)) <=> (length(U) = $sum(1, length(next(U))))), ((isrecord(U) => (length(U) = $sum(length(next(U)), 1))) <=> (isrecord(U) => (length(U) = $sum(1, length(next(U))))))), rewrite((isrecord(U) => (length(U) = $sum(1, length(next(U))))) <=> ((~isrecord(U)) | (length(U) = $sum(1, length(next(U)))))), ((isrecord(U) => (length(U) = $sum(length(next(U)), 1))) <=> ((~isrecord(U)) | (length(U) = $sum(1, length(next(U)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (![U: record] : (isrecord(U) => (length(U) = $sum(length(next(U)), 1))) <=> ![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.40 tff(27,axiom,(![U: record] : (isrecord(U) => (length(U) = $sum(length(next(U)), 1)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT003=0.ax','ax3')).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.20/0.40 tff(31,plain,(
% 0.20/0.40 ![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))),
% 0.20/0.40 inference(skolemize,[status(sab)],[30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(next(U!1))) | ($sum(length(next(U!1)), $product(-1, length(next(next(U!1))))) = 1))) <=> ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(next(U!1))) | ($sum(length(next(U!1)), $product(-1, length(next(next(U!1))))) = 1))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(next(U!1))) | ($sum(length(next(U!1)), $product(-1, length(next(next(U!1))))) = 1))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(next(U!1))) | ($sum(length(next(U!1)), $product(-1, length(next(next(U!1))))) = 1)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 ($sum(length(next(U!1)), $product(-1, length(next(next(U!1))))) = 1),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[35, 32, 19])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ((~($sum(length(next(U!1)), $product(-1, length(next(next(U!1))))) = 1)) | $lesseq($sum(length(next(U!1)), $product(-1, length(next(next(U!1))))), 1)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ($lesseq($sum(length(next(U!1)), $product(-1, length(next(next(U!1))))), 1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (isrecord(U!1)),
% 0.20/0.40 inference(and_elim,[status(thm)],[18])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(U!1)) | ($sum(length(U!1), $product(-1, length(next(U!1)))) = 1))) <=> ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(U!1)) | ($sum(length(U!1), $product(-1, length(next(U!1)))) = 1))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(U!1)) | ($sum(length(U!1), $product(-1, length(next(U!1)))) = 1))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(U!1)) | ($sum(length(U!1), $product(-1, length(next(U!1)))) = 1)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ($sum(length(U!1), $product(-1, length(next(U!1)))) = 1),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[42, 32, 39])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 ((~($sum(length(U!1), $product(-1, length(next(U!1)))) = 1)) | $lesseq($sum(length(U!1), $product(-1, length(next(U!1)))), 1)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 ($lesseq($sum(length(U!1), $product(-1, length(next(U!1)))), 1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.40 tff(46,assumption,(~$greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 1)), introduced(assumption)).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ((~($sum(length(V!0), $product(-2, length(split2(V!0)))) = 1)) | $greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 1)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (~($sum(length(V!0), $product(-2, length(split2(V!0)))) = 1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (($sum(length(V!0), $product(-2, length(split2(V!0)))) = 0) | ($sum(length(V!0), $product(-2, length(split2(V!0)))) = 1)),
% 0.20/0.40 inference(and_elim,[status(thm)],[18])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 ($sum(length(V!0), $product(-2, length(split2(V!0)))) = 0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 ((~($sum(length(V!0), $product(-2, length(split2(V!0)))) = 0)) | $greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 ($greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 ((~($sum(length(next(U!1)), $product(-1, length(next(next(U!1))))) = 1)) | $greatereq($sum(length(next(U!1)), $product(-1, length(next(next(U!1))))), 1)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 ($greatereq($sum(length(next(U!1)), $product(-1, length(next(next(U!1))))), 1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[53, 36])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 ((~($sum(length(U!1), $product(-1, length(next(U!1)))) = 1)) | $greatereq($sum(length(U!1), $product(-1, length(next(U!1)))), 1)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ($greatereq($sum(length(U!1), $product(-1, length(next(U!1)))), 1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[55, 43])).
% 0.20/0.40 tff(57,assumption,(~$greatereq($sum(length(U!1), $product(-2, length(split2(U!1)))), 0)), introduced(assumption)).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (^[U: record] : refl(((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U)))) <=> ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U)))) <=> ![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (^[U: record] : trans(monotonicity(trans(monotonicity(rewrite((isrecord(U) & isrecord(next(U))) <=> (~((~isrecord(U)) | (~isrecord(next(U)))))), ((~(isrecord(U) & isrecord(next(U)))) <=> (~(~((~isrecord(U)) | (~isrecord(next(U)))))))), rewrite((~(~((~isrecord(U)) | (~isrecord(next(U)))))) <=> ((~isrecord(U)) | (~isrecord(next(U))))), ((~(isrecord(U) & isrecord(next(U)))) <=> ((~isrecord(U)) | (~isrecord(next(U)))))), ((isrecord(split2(U)) | (~(isrecord(U) & isrecord(next(U))))) <=> (isrecord(split2(U)) | ((~isrecord(U)) | (~isrecord(next(U))))))), rewrite((isrecord(split2(U)) | ((~isrecord(U)) | (~isrecord(next(U))))) <=> ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))), ((isrecord(split2(U)) | (~(isrecord(U) & isrecord(next(U))))) <=> ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![U: record] : (isrecord(split2(U)) | (~(isrecord(U) & isrecord(next(U))))) <=> ![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![U: record] : (isrecord(split2(U)) | (~(isrecord(U) & isrecord(next(U))))) <=> ![U: record] : (isrecord(split2(U)) | (~(isrecord(U) & isrecord(next(U)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (^[U: record] : rewrite(((isrecord(U) & isrecord(next(U))) => isrecord(split2(U))) <=> (isrecord(split2(U)) | (~(isrecord(U) & isrecord(next(U))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![U: record] : ((isrecord(U) & isrecord(next(U))) => isrecord(split2(U))) <=> ![U: record] : (isrecord(split2(U)) | (~(isrecord(U) & isrecord(next(U)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.40 tff(65,axiom,(![U: record] : ((isrecord(U) & isrecord(next(U))) => isrecord(split2(U)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT003=0.ax','ax11')).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (![U: record] : (isrecord(split2(U)) | (~(isrecord(U) & isrecord(next(U)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (![U: record] : (isrecord(split2(U)) | (~(isrecord(U) & isrecord(next(U)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.40 tff(68,plain,(
% 0.20/0.40 ![U: record] : (isrecord(split2(U)) | (~(isrecord(U) & isrecord(next(U)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[67])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (((~![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))) | ((~isrecord(U!1)) | (~isrecord(next(U!1))) | isrecord(split2(U!1)))) <=> ((~![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))) | (~isrecord(U!1)) | (~isrecord(next(U!1))) | isrecord(split2(U!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (((~isrecord(U!1)) | isrecord(split2(U!1)) | (~isrecord(next(U!1)))) <=> ((~isrecord(U!1)) | (~isrecord(next(U!1))) | isrecord(split2(U!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (((~![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))) | ((~isrecord(U!1)) | isrecord(split2(U!1)) | (~isrecord(next(U!1))))) <=> ((~![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))) | ((~isrecord(U!1)) | (~isrecord(next(U!1))) | isrecord(split2(U!1))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (((~![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))) | ((~isrecord(U!1)) | isrecord(split2(U!1)) | (~isrecord(next(U!1))))) <=> ((~![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))) | (~isrecord(U!1)) | (~isrecord(next(U!1))) | isrecord(split2(U!1)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[73, 71])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 ((~![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))) | ((~isrecord(U!1)) | isrecord(split2(U!1)) | (~isrecord(next(U!1))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 ((~![U: record] : ((~isrecord(U)) | isrecord(split2(U)) | (~isrecord(next(U))))) | (~isrecord(U!1)) | (~isrecord(next(U!1))) | isrecord(split2(U!1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (isrecord(split2(U!1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[76, 70, 39, 19])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(split2(U!1))) | ($sum(length(split2(U!1)), $product(-1, length(next(split2(U!1))))) = 1))) <=> ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(split2(U!1))) | ($sum(length(split2(U!1)), $product(-1, length(next(split2(U!1))))) = 1))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(split2(U!1))) | ($sum(length(split2(U!1)), $product(-1, length(next(split2(U!1))))) = 1))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(split2(U!1))) | ($sum(length(split2(U!1)), $product(-1, length(next(split2(U!1))))) = 1)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 ($sum(length(split2(U!1)), $product(-1, length(next(split2(U!1))))) = 1),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[80, 32, 77])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 ((~($sum(length(split2(U!1)), $product(-1, length(next(split2(U!1))))) = 1)) | $lesseq($sum(length(split2(U!1)), $product(-1, length(next(split2(U!1))))), 1)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 ($lesseq($sum(length(split2(U!1)), $product(-1, length(next(split2(U!1))))), 1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (V!0 = next(next(U!1))),
% 0.20/0.40 inference(and_elim,[status(thm)],[18])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (split2(V!0) = split2(next(next(U!1)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (split2(next(next(U!1))) = split2(V!0)),
% 0.20/0.40 inference(symmetry,[status(thm)],[85])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (^[U: record] : refl(((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U))))) <=> ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U))))) <=> ![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (^[U: record] : trans(monotonicity(trans(monotonicity(rewrite((isrecord(U) & isrecord(next(U))) <=> (~((~isrecord(U)) | (~isrecord(next(U)))))), ((~(isrecord(U) & isrecord(next(U)))) <=> (~(~((~isrecord(U)) | (~isrecord(next(U)))))))), rewrite((~(~((~isrecord(U)) | (~isrecord(next(U)))))) <=> ((~isrecord(U)) | (~isrecord(next(U))))), ((~(isrecord(U) & isrecord(next(U)))) <=> ((~isrecord(U)) | (~isrecord(next(U)))))), (((~(isrecord(U) & isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U))))) <=> (((~isrecord(U)) | (~isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U))))))), rewrite((((~isrecord(U)) | (~isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U))))) <=> ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U)))))), (((~(isrecord(U) & isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U))))) <=> ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U))))) <=> ![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U))))) <=> ![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (^[U: record] : rewrite(((isrecord(U) & isrecord(next(U))) => (next(split2(U)) = split2(next(next(U))))) <=> ((~(isrecord(U) & isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (![U: record] : ((isrecord(U) & isrecord(next(U))) => (next(split2(U)) = split2(next(next(U))))) <=> ![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.41 tff(94,axiom,(![U: record] : ((isrecord(U) & isrecord(next(U))) => (next(split2(U)) = split2(next(next(U)))))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT003=0.ax','ax13')).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.41 tff(97,plain,(
% 0.20/0.41 ![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split2(U)) = split2(next(next(U)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[96])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (((~![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U)))))) | ((~isrecord(U!1)) | (~isrecord(next(U!1))) | (next(split2(U!1)) = split2(next(next(U!1)))))) <=> ((~![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U)))))) | (~isrecord(U!1)) | (~isrecord(next(U!1))) | (next(split2(U!1)) = split2(next(next(U!1)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ((~![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U)))))) | ((~isrecord(U!1)) | (~isrecord(next(U!1))) | (next(split2(U!1)) = split2(next(next(U!1)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 ((~![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split2(U)) = split2(next(next(U)))))) | (~isrecord(U!1)) | (~isrecord(next(U!1))) | (next(split2(U!1)) = split2(next(next(U!1))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (next(split2(U!1)) = split2(next(next(U!1)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[102, 99, 39, 19])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (next(split2(U!1)) = split2(V!0)),
% 0.20/0.41 inference(transitivity,[status(thm)],[103, 86])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (length(next(split2(U!1))) = length(split2(V!0))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (length(split2(V!0)) = length(next(split2(U!1)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[105])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 ((~(length(split2(V!0)) = length(next(split2(U!1))))) | $greatereq($sum(length(split2(V!0)), $product(-1, length(next(split2(U!1))))), 0)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 ($greatereq($sum(length(split2(V!0)), $product(-1, length(next(split2(U!1))))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.41 tff(109,assumption,($greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 0)), introduced(assumption)).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (next(next(U!1)) = V!0),
% 0.20/0.41 inference(symmetry,[status(thm)],[84])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (length(next(next(U!1))) = length(V!0)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (length(V!0) = length(next(next(U!1)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[111])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 ((~(length(V!0) = length(next(next(U!1))))) | $lesseq($sum(length(V!0), $product(-1, length(next(next(U!1))))), 0)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 ($lesseq($sum(length(V!0), $product(-1, length(next(next(U!1))))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[114, 109, 108, 83, 57, 56, 54])).
% 0.20/0.41 tff(116,plain,($greatereq($sum(length(U!1), $product(-2, length(split2(U!1)))), 0) | (~$greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 ($greatereq($sum(length(U!1), $product(-2, length(split2(U!1)))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[116, 52])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 (~($sum(length(U!1), $product(-2, length(split2(U!1)))) = 0)),
% 0.20/0.41 inference(or_elim,[status(thm)],[17])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (($sum(length(U!1), $product(-2, length(split2(U!1)))) = 0) | (~$lesseq($sum(length(U!1), $product(-2, length(split2(U!1)))), 0)) | (~$greatereq($sum(length(U!1), $product(-2, length(split2(U!1)))), 0))),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 ((~$lesseq($sum(length(U!1), $product(-2, length(split2(U!1)))), 0)) | (~$greatereq($sum(length(U!1), $product(-2, length(split2(U!1)))), 0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (~$lesseq($sum(length(U!1), $product(-2, length(split2(U!1)))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 ($lesseq($sum(length(U!1), $product(-2, length(split2(U!1)))), 0) | $greatereq($sum(length(U!1), $product(-2, length(split2(U!1)))), 1)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 ($greatereq($sum(length(U!1), $product(-2, length(split2(U!1)))), 1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (~($sum(length(U!1), $product(-2, length(split2(U!1)))) = 1)),
% 0.20/0.41 inference(or_elim,[status(thm)],[17])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (($sum(length(U!1), $product(-2, length(split2(U!1)))) = 1) | (~$lesseq($sum(length(U!1), $product(-2, length(split2(U!1)))), 1)) | (~$greatereq($sum(length(U!1), $product(-2, length(split2(U!1)))), 1))),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 ((~$lesseq($sum(length(U!1), $product(-2, length(split2(U!1)))), 1)) | (~$greatereq($sum(length(U!1), $product(-2, length(split2(U!1)))), 1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (~$lesseq($sum(length(U!1), $product(-2, length(split2(U!1)))), 1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[126, 123])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 ((~($sum(length(split2(U!1)), $product(-1, length(next(split2(U!1))))) = 1)) | $greatereq($sum(length(split2(U!1)), $product(-1, length(next(split2(U!1))))), 1)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 ($greatereq($sum(length(split2(U!1)), $product(-1, length(next(split2(U!1))))), 1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[128, 81])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 ((~(length(split2(V!0)) = length(next(split2(U!1))))) | $lesseq($sum(length(split2(V!0)), $product(-1, length(next(split2(U!1))))), 0)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 ($lesseq($sum(length(split2(V!0)), $product(-1, length(next(split2(U!1))))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[130, 106])).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 ($greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 1) | $lesseq($sum(length(V!0), $product(-2, length(split2(V!0)))), 1)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(133,plain,
% 0.20/0.41 ($lesseq($sum(length(V!0), $product(-2, length(split2(V!0)))), 1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[132, 46])).
% 0.20/0.41 tff(134,plain,
% 0.20/0.41 ((~(length(V!0) = length(next(next(U!1))))) | $greatereq($sum(length(V!0), $product(-1, length(next(next(U!1))))), 0)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 ($greatereq($sum(length(V!0), $product(-1, length(next(next(U!1))))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[134, 112])).
% 0.20/0.41 tff(136,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[135, 133, 131, 129, 127, 45, 38])).
% 0.20/0.41 tff(137,plain,($greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(138,plain,
% 0.20/0.41 ($greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 0) | (~$greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 1))),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(139,plain,
% 0.20/0.41 ($greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.20/0.41 tff(140,plain,
% 0.20/0.41 ($greatereq($sum(length(U!1), $product(-2, length(split2(U!1)))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[116, 139])).
% 0.20/0.41 tff(141,plain,
% 0.20/0.41 (~$lesseq($sum(length(U!1), $product(-2, length(split2(U!1)))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[120, 140])).
% 0.20/0.41 tff(142,plain,
% 0.20/0.41 ($greatereq($sum(length(U!1), $product(-2, length(split2(U!1)))), 1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[122, 141])).
% 0.20/0.41 tff(143,plain,
% 0.20/0.41 (~$lesseq($sum(length(U!1), $product(-2, length(split2(U!1)))), 1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[126, 142])).
% 0.20/0.41 tff(144,plain,
% 0.20/0.41 ((~$lesseq($sum(length(V!0), $product(-2, length(split2(V!0)))), 0)) | (~$greatereq($sum(length(V!0), $product(-2, length(split2(V!0)))), 1))),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(145,plain,
% 0.20/0.41 (~$lesseq($sum(length(V!0), $product(-2, length(split2(V!0)))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[144, 137])).
% 0.20/0.41 tff(146,plain,
% 0.20/0.41 ((~($sum(length(V!0), $product(-2, length(split2(V!0)))) = 0)) | $lesseq($sum(length(V!0), $product(-2, length(split2(V!0)))), 0)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(147,plain,
% 0.20/0.41 (~($sum(length(V!0), $product(-2, length(split2(V!0)))) = 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.41 tff(148,plain,
% 0.20/0.41 ($sum(length(V!0), $product(-2, length(split2(V!0)))) = 1),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[49, 147])).
% 0.20/0.41 tff(149,plain,
% 0.20/0.41 ((~($sum(length(V!0), $product(-2, length(split2(V!0)))) = 1)) | $lesseq($sum(length(V!0), $product(-2, length(split2(V!0)))), 1)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(150,plain,
% 0.20/0.41 ($lesseq($sum(length(V!0), $product(-2, length(split2(V!0)))), 1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.41 tff(151,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[135, 150, 131, 129, 143, 45, 38])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------