TSTP Solution File: DAT053_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT053_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT053_1 : TPTP v8.1.0. Released v5.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 01:39:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(length_type, type, (
% 0.13/0.40 length: record > $int)).
% 0.13/0.40 tff(next_type, type, (
% 0.13/0.40 next: record > record)).
% 0.13/0.40 tff(split1_type, type, (
% 0.13/0.40 split1: record > record)).
% 0.13/0.40 tff(b_type, type, (
% 0.13/0.40 b: record)).
% 0.13/0.40 tff(isrecord_type, type, (
% 0.13/0.40 isrecord: record > $o)).
% 0.13/0.40 tff(a_type, type, (
% 0.13/0.40 a: record)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (isrecord(b) <=> isrecord(b)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 ((~((((isrecord(b) & isrecord(next(b))) & (next(next(b)) = a)) & (($product(2, length(split1(a))) = $sum(length(a), 1)) | ($product(2, length(split1(a))) = length(a)))) => (($product(2, length(split1(b))) = $sum(length(b), 1)) | ($product(2, length(split1(b))) = length(b))))) <=> (~(($product(2, length(split1(b))) = length(b)) | ($product(2, length(split1(b))) = $sum(1, length(b))) | (~(isrecord(b) & isrecord(next(b)) & (next(next(b)) = a) & (($product(2, length(split1(a))) = length(a)) | ($product(2, length(split1(a))) = $sum(1, length(a))))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(3,axiom,(~((((isrecord(b) & isrecord(next(b))) & (next(next(b)) = a)) & (($product(2, length(split1(a))) = $sum(length(a), 1)) | ($product(2, length(split1(a))) = length(a)))) => (($product(2, length(split1(b))) = $sum(length(b), 1)) | ($product(2, length(split1(b))) = length(b))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (~(($product(2, length(split1(b))) = length(b)) | ($product(2, length(split1(b))) = $sum(1, length(b))) | (~(isrecord(b) & isrecord(next(b)) & (next(next(b)) = a) & (($product(2, length(split1(a))) = length(a)) | ($product(2, length(split1(a))) = $sum(1, length(a)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (isrecord(b) & isrecord(next(b)) & (next(next(b)) = a) & (($product(2, length(split1(a))) = length(a)) | ($product(2, length(split1(a))) = $sum(1, length(a))))),
% 0.13/0.40 inference(or_elim,[status(thm)],[4])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (isrecord(b)),
% 0.13/0.40 inference(and_elim,[status(thm)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (isrecord(b)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (^[U: record] : refl(((~isrecord(U)) | isrecord(split1(U))) <=> ((~isrecord(U)) | isrecord(split1(U))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![U: record] : ((~isrecord(U)) | isrecord(split1(U))) <=> ![U: record] : ((~isrecord(U)) | isrecord(split1(U)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (![U: record] : ((~isrecord(U)) | isrecord(split1(U))) <=> ![U: record] : ((~isrecord(U)) | isrecord(split1(U)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (^[U: record] : rewrite((isrecord(U) => isrecord(split1(U))) <=> ((~isrecord(U)) | isrecord(split1(U))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![U: record] : (isrecord(U) => isrecord(split1(U))) <=> ![U: record] : ((~isrecord(U)) | isrecord(split1(U)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.40 tff(13,axiom,(![U: record] : (isrecord(U) => isrecord(split1(U)))), file('/export/starexec/sandbox/benchmark/Axioms/DAT003=0.ax','ax5')).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (![U: record] : ((~isrecord(U)) | isrecord(split1(U)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![U: record] : ((~isrecord(U)) | isrecord(split1(U)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.13/0.40 tff(16,plain,(
% 0.13/0.40 ![U: record] : ((~isrecord(U)) | isrecord(split1(U)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![U: record] : ((~isrecord(U)) | isrecord(split1(U)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (((~![U: record] : ((~isrecord(U)) | isrecord(split1(U)))) | ((~isrecord(b)) | isrecord(split1(b)))) <=> ((~![U: record] : ((~isrecord(U)) | isrecord(split1(U)))) | (~isrecord(b)) | isrecord(split1(b)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 ((~![U: record] : ((~isrecord(U)) | isrecord(split1(U)))) | ((~isrecord(b)) | isrecord(split1(b)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 ((~![U: record] : ((~isrecord(U)) | isrecord(split1(U)))) | (~isrecord(b)) | isrecord(split1(b))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 (isrecord(split1(b))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[20, 17, 7])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 (^[U: record] : refl(((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1)) <=> ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 (![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1)) <=> ![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (^[U: record] : rewrite(((~isrecord(U)) | (length(U) = $sum(1, length(next(U))))) <=> ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U))))) <=> ![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U))))) <=> ![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (^[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)))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (![U: record] : (isrecord(U) => (length(U) = $sum(length(next(U)), 1))) <=> ![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.41 tff(29,axiom,(![U: record] : (isrecord(U) => (length(U) = $sum(length(next(U)), 1)))), file('/export/starexec/sandbox/benchmark/Axioms/DAT003=0.ax','ax3')).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (![U: record] : ((~isrecord(U)) | (length(U) = $sum(1, length(next(U)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.13/0.41 tff(33,plain,(
% 0.13/0.41 ![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))),
% 0.13/0.41 inference(skolemize,[status(sab)],[32])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 (![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(split1(b))) | ($sum(length(split1(b)), $product(-1, length(next(split1(b))))) = 1))) <=> ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(split1(b))) | ($sum(length(split1(b)), $product(-1, length(next(split1(b))))) = 1))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(split1(b))) | ($sum(length(split1(b)), $product(-1, length(next(split1(b))))) = 1))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(split1(b))) | ($sum(length(split1(b)), $product(-1, length(next(split1(b))))) = 1)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 ($sum(length(split1(b)), $product(-1, length(next(split1(b))))) = 1),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[37, 34, 21])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 ((~($sum(length(split1(b)), $product(-1, length(next(split1(b))))) = 1)) | $lesseq($sum(length(split1(b)), $product(-1, length(next(split1(b))))), 1)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 ($lesseq($sum(length(split1(b)), $product(-1, length(next(split1(b))))), 1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(b)) | ($sum(length(b), $product(-1, length(next(b)))) = 1))) <=> ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(b)) | ($sum(length(b), $product(-1, length(next(b)))) = 1))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(b)) | ($sum(length(b), $product(-1, length(next(b)))) = 1))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(b)) | ($sum(length(b), $product(-1, length(next(b)))) = 1)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 ($sum(length(b), $product(-1, length(next(b)))) = 1),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[43, 34, 7])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 ((~($sum(length(b), $product(-1, length(next(b)))) = 1)) | $greatereq($sum(length(b), $product(-1, length(next(b)))), 1)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 ($greatereq($sum(length(b), $product(-1, length(next(b)))), 1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.13/0.41 tff(47,assumption,(~$greatereq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 1)), introduced(assumption)).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 ((~($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 1)) | $greatereq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 1)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (~($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 ((($product(2, length(split1(next(next(b))))) = length(next(next(b)))) | ($product(2, length(split1(next(next(b))))) = $sum(1, length(next(next(b)))))) <=> (($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 0) | ($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 1))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 ((($product(2, length(split1(a))) = length(a)) | ($product(2, length(split1(a))) = $sum(1, length(a)))) <=> (($product(2, length(split1(next(next(b))))) = length(next(next(b)))) | ($product(2, length(split1(next(next(b))))) = $sum(1, length(next(next(b))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (($product(2, length(split1(a))) = $sum(1, length(a))) <=> ($product(2, length(split1(a))) = $sum(1, length(a)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 ((($product(2, length(split1(a))) = length(a)) | ($product(2, length(split1(a))) = $sum(1, length(a)))) <=> (($product(2, length(split1(a))) = length(a)) | ($product(2, length(split1(a))) = $sum(1, length(a))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[52])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 ((($product(2, length(split1(a))) = length(a)) | ($product(2, length(split1(a))) = $sum(1, length(a)))) <=> (($product(2, length(split1(a))) = length(a)) | ($product(2, length(split1(a))) = $sum(1, length(a))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (($product(2, length(split1(a))) = length(a)) | ($product(2, length(split1(a))) = $sum(1, length(a)))),
% 0.13/0.41 inference(and_elim,[status(thm)],[5])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (($product(2, length(split1(a))) = length(a)) | ($product(2, length(split1(a))) = $sum(1, length(a)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (($product(2, length(split1(a))) = length(a)) | ($product(2, length(split1(a))) = $sum(1, length(a)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[56, 53])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (($product(2, length(split1(next(next(b))))) = length(next(next(b)))) | ($product(2, length(split1(next(next(b))))) = $sum(1, length(next(next(b)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[57, 51])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 0) | ($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 1)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[58, 50])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 ($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 0),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[59, 49])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 ((~($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 0)) | $greatereq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 ($greatereq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 ((~($sum(length(split1(b)), $product(-1, length(next(split1(b))))) = 1)) | $greatereq($sum(length(split1(b)), $product(-1, length(next(split1(b))))), 1)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 ($greatereq($sum(length(split1(b)), $product(-1, length(next(split1(b))))), 1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[63, 38])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 ((~($sum(length(b), $product(-1, length(next(b)))) = 1)) | $lesseq($sum(length(b), $product(-1, length(next(b)))), 1)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 ($lesseq($sum(length(b), $product(-1, length(next(b)))), 1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[65, 44])).
% 0.13/0.41 tff(67,assumption,(~$greatereq($sum($product(2, length(split1(b))), $product(-1, length(b))), 0)), introduced(assumption)).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (isrecord(next(b)) <=> isrecord(next(b))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (isrecord(next(b))),
% 0.13/0.41 inference(and_elim,[status(thm)],[5])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (isrecord(next(b))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(next(b))) | ($sum(length(next(next(b))), $product(-1, length(next(b)))) = -1))) <=> ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(next(b))) | ($sum(length(next(next(b))), $product(-1, length(next(b)))) = -1))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (((~isrecord(next(b))) | ($sum(length(next(b)), $product(-1, length(next(next(b))))) = 1)) <=> ((~isrecord(next(b))) | ($sum(length(next(next(b))), $product(-1, length(next(b)))) = -1))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(next(b))) | ($sum(length(next(b)), $product(-1, length(next(next(b))))) = 1))) <=> ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(next(b))) | ($sum(length(next(next(b))), $product(-1, length(next(b)))) = -1)))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(next(b))) | ($sum(length(next(b)), $product(-1, length(next(next(b))))) = 1))) <=> ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(next(b))) | ($sum(length(next(next(b))), $product(-1, length(next(b)))) = -1))),
% 0.13/0.41 inference(transitivity,[status(thm)],[73, 71])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | ((~isrecord(next(b))) | ($sum(length(next(b)), $product(-1, length(next(next(b))))) = 1))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 ((~![U: record] : ((~isrecord(U)) | ($sum(length(U), $product(-1, length(next(U)))) = 1))) | (~isrecord(next(b))) | ($sum(length(next(next(b))), $product(-1, length(next(b)))) = -1)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.13/0.41 tff(77,plain,
% 0.13/0.41 ($sum(length(next(next(b))), $product(-1, length(next(b)))) = -1),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[76, 34, 70])).
% 0.13/0.41 tff(78,plain,
% 0.13/0.41 ((~($sum(length(next(next(b))), $product(-1, length(next(b)))) = -1)) | $greatereq($sum(length(next(next(b))), $product(-1, length(next(b)))), -1)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(79,plain,
% 0.13/0.41 ($greatereq($sum(length(next(next(b))), $product(-1, length(next(b)))), -1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.13/0.41 tff(80,assumption,($greatereq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 0)), introduced(assumption)).
% 0.13/0.41 tff(81,plain,
% 0.13/0.41 (^[U: record] : refl(((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U))))) <=> ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(82,plain,
% 0.13/0.41 (![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U))))) <=> ![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[81])).
% 0.13/0.41 tff(83,plain,
% 0.13/0.41 (^[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(split1(U)) = split1(next(next(U))))) <=> (((~isrecord(U)) | (~isrecord(next(U)))) | (next(split1(U)) = split1(next(next(U))))))), rewrite((((~isrecord(U)) | (~isrecord(next(U)))) | (next(split1(U)) = split1(next(next(U))))) <=> ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U)))))), (((~(isrecord(U) & isrecord(next(U)))) | (next(split1(U)) = split1(next(next(U))))) <=> ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U)))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(84,plain,
% 0.13/0.41 (![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split1(U)) = split1(next(next(U))))) <=> ![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[83])).
% 0.13/0.41 tff(85,plain,
% 0.13/0.41 (![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split1(U)) = split1(next(next(U))))) <=> ![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split1(U)) = split1(next(next(U)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(86,plain,
% 0.13/0.41 (^[U: record] : rewrite(((isrecord(U) & isrecord(next(U))) => (next(split1(U)) = split1(next(next(U))))) <=> ((~(isrecord(U) & isrecord(next(U)))) | (next(split1(U)) = split1(next(next(U))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(87,plain,
% 0.13/0.41 (![U: record] : ((isrecord(U) & isrecord(next(U))) => (next(split1(U)) = split1(next(next(U))))) <=> ![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split1(U)) = split1(next(next(U)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.13/0.41 tff(88,axiom,(![U: record] : ((isrecord(U) & isrecord(next(U))) => (next(split1(U)) = split1(next(next(U)))))), file('/export/starexec/sandbox/benchmark/Axioms/DAT003=0.ax','ax8')).
% 0.13/0.41 tff(89,plain,
% 0.13/0.41 (![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split1(U)) = split1(next(next(U)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.13/0.41 tff(90,plain,
% 0.13/0.41 (![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split1(U)) = split1(next(next(U)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.13/0.42 tff(91,plain,(
% 0.13/0.42 ![U: record] : ((~(isrecord(U) & isrecord(next(U)))) | (next(split1(U)) = split1(next(next(U)))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[90])).
% 0.13/0.42 tff(92,plain,
% 0.13/0.42 (![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.13/0.42 tff(93,plain,
% 0.13/0.42 (![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.13/0.42 tff(94,plain,
% 0.13/0.42 (((~![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U)))))) | ((~isrecord(b)) | (~isrecord(next(b))) | (next(split1(b)) = split1(next(next(b)))))) <=> ((~![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U)))))) | (~isrecord(b)) | (~isrecord(next(b))) | (next(split1(b)) = split1(next(next(b)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(95,plain,
% 0.13/0.42 ((~![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U)))))) | ((~isrecord(b)) | (~isrecord(next(b))) | (next(split1(b)) = split1(next(next(b)))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(96,plain,
% 0.13/0.42 ((~![U: record] : ((~isrecord(U)) | (~isrecord(next(U))) | (next(split1(U)) = split1(next(next(U)))))) | (~isrecord(b)) | (~isrecord(next(b))) | (next(split1(b)) = split1(next(next(b))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.13/0.42 tff(97,plain,
% 0.13/0.42 (next(split1(b)) = split1(next(next(b)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[96, 93, 7, 70])).
% 0.13/0.42 tff(98,plain,
% 0.13/0.42 (length(next(split1(b))) = length(split1(next(next(b))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[97])).
% 0.13/0.42 tff(99,plain,
% 0.13/0.42 (length(split1(next(next(b)))) = length(next(split1(b)))),
% 0.13/0.42 inference(symmetry,[status(thm)],[98])).
% 0.13/0.42 tff(100,plain,
% 0.13/0.42 ((~(length(split1(next(next(b)))) = length(next(split1(b))))) | $lesseq($sum(length(split1(next(next(b)))), $product(-1, length(next(split1(b))))), 0)),
% 0.13/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.42 tff(101,plain,
% 0.13/0.42 ($lesseq($sum(length(split1(next(next(b)))), $product(-1, length(next(split1(b))))), 0)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.13/0.42 tff(102,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(theory_lemma,[status(thm)],[101, 80, 79, 67, 66, 64])).
% 0.13/0.42 tff(103,plain,($greatereq($sum($product(2, length(split1(b))), $product(-1, length(b))), 0) | (~$greatereq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.42 tff(104,plain,
% 0.13/0.42 ($greatereq($sum($product(2, length(split1(b))), $product(-1, length(b))), 0)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[103, 62])).
% 0.13/0.42 tff(105,plain,
% 0.13/0.42 ((~($product(2, length(split1(b))) = length(b))) <=> (~($sum($product(2, length(split1(b))), $product(-1, length(b))) = 0))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(106,plain,
% 0.13/0.42 ((~($product(2, length(split1(b))) = length(b))) <=> (~($product(2, length(split1(b))) = length(b)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(107,plain,
% 0.13/0.42 (~($product(2, length(split1(b))) = length(b))),
% 0.13/0.42 inference(or_elim,[status(thm)],[4])).
% 0.13/0.42 tff(108,plain,
% 0.13/0.42 (~($product(2, length(split1(b))) = length(b))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.13/0.42 tff(109,plain,
% 0.13/0.42 (~($sum($product(2, length(split1(b))), $product(-1, length(b))) = 0)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[108, 105])).
% 0.13/0.42 tff(110,plain,
% 0.13/0.42 (($sum($product(2, length(split1(b))), $product(-1, length(b))) = 0) | (~$lesseq($sum($product(2, length(split1(b))), $product(-1, length(b))), 0)) | (~$greatereq($sum($product(2, length(split1(b))), $product(-1, length(b))), 0))),
% 0.13/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.42 tff(111,plain,
% 0.13/0.42 ((~$lesseq($sum($product(2, length(split1(b))), $product(-1, length(b))), 0)) | (~$greatereq($sum($product(2, length(split1(b))), $product(-1, length(b))), 0))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.13/0.42 tff(112,plain,
% 0.13/0.42 (~$lesseq($sum($product(2, length(split1(b))), $product(-1, length(b))), 0)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[111, 104])).
% 0.13/0.42 tff(113,plain,
% 0.13/0.42 ($lesseq($sum($product(2, length(split1(b))), $product(-1, length(b))), 0) | $greatereq($sum($product(2, length(split1(b))), $product(-1, length(b))), 1)),
% 0.13/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.42 tff(114,plain,
% 0.13/0.42 ($greatereq($sum($product(2, length(split1(b))), $product(-1, length(b))), 1)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.13/0.42 tff(115,plain,
% 0.13/0.42 ((~($product(2, length(split1(b))) = $sum(1, length(b)))) <=> (~($sum($product(2, length(split1(b))), $product(-1, length(b))) = 1))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(116,plain,
% 0.13/0.42 (($product(2, length(split1(b))) = $sum(1, length(b))) <=> ($product(2, length(split1(b))) = $sum(1, length(b)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(117,plain,
% 0.13/0.42 ((~($product(2, length(split1(b))) = $sum(1, length(b)))) <=> (~($product(2, length(split1(b))) = $sum(1, length(b))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[116])).
% 0.13/0.42 tff(118,plain,
% 0.13/0.42 ((~($product(2, length(split1(b))) = $sum(1, length(b)))) <=> (~($product(2, length(split1(b))) = $sum(1, length(b))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(119,plain,
% 0.13/0.42 (~($product(2, length(split1(b))) = $sum(1, length(b)))),
% 0.13/0.42 inference(or_elim,[status(thm)],[4])).
% 0.13/0.42 tff(120,plain,
% 0.13/0.42 (~($product(2, length(split1(b))) = $sum(1, length(b)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.13/0.42 tff(121,plain,
% 0.13/0.42 (~($product(2, length(split1(b))) = $sum(1, length(b)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[120, 117])).
% 0.13/0.42 tff(122,plain,
% 0.13/0.42 (~($sum($product(2, length(split1(b))), $product(-1, length(b))) = 1)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[121, 115])).
% 0.13/0.42 tff(123,plain,
% 0.13/0.42 (($sum($product(2, length(split1(b))), $product(-1, length(b))) = 1) | (~$lesseq($sum($product(2, length(split1(b))), $product(-1, length(b))), 1)) | (~$greatereq($sum($product(2, length(split1(b))), $product(-1, length(b))), 1))),
% 0.13/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.42 tff(124,plain,
% 0.13/0.42 ((~$lesseq($sum($product(2, length(split1(b))), $product(-1, length(b))), 1)) | (~$greatereq($sum($product(2, length(split1(b))), $product(-1, length(b))), 1))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.13/0.42 tff(125,plain,
% 0.13/0.42 (~$lesseq($sum($product(2, length(split1(b))), $product(-1, length(b))), 1)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[124, 114])).
% 0.13/0.42 tff(126,plain,
% 0.13/0.42 ((~($sum(length(next(next(b))), $product(-1, length(next(b)))) = -1)) | $lesseq($sum(length(next(next(b))), $product(-1, length(next(b)))), -1)),
% 0.13/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.42 tff(127,plain,
% 0.13/0.42 ($lesseq($sum(length(next(next(b))), $product(-1, length(next(b)))), -1)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[126, 77])).
% 0.13/0.42 tff(128,plain,
% 0.13/0.42 ((~(length(split1(next(next(b)))) = length(next(split1(b))))) | $greatereq($sum(length(split1(next(next(b)))), $product(-1, length(next(split1(b))))), 0)),
% 0.13/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.42 tff(129,plain,
% 0.13/0.42 ($greatereq($sum(length(split1(next(next(b)))), $product(-1, length(next(split1(b))))), 0)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[128, 99])).
% 0.13/0.42 tff(130,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(theory_lemma,[status(thm)],[129, 47, 127, 125, 46, 40])).
% 0.13/0.42 tff(131,plain,($greatereq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.42 tff(132,plain,
% 0.13/0.42 ($greatereq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 0) | (~$greatereq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 1))),
% 0.13/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.42 tff(133,plain,
% 0.13/0.42 ($greatereq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 0)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.13/0.42 tff(134,plain,
% 0.13/0.42 ($greatereq($sum($product(2, length(split1(b))), $product(-1, length(b))), 0)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[103, 133])).
% 0.13/0.42 tff(135,plain,
% 0.13/0.42 (~$lesseq($sum($product(2, length(split1(b))), $product(-1, length(b))), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[111, 134])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ($greatereq($sum($product(2, length(split1(b))), $product(-1, length(b))), 1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[113, 135])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 (~$lesseq($sum($product(2, length(split1(b))), $product(-1, length(b))), 1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[124, 136])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 ((~$lesseq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 0)) | (~$greatereq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 1))),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (~$lesseq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[138, 131])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 ((~($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 0)) | $lesseq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 0)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 (~($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 ($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 1),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[59, 141])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 ((~($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))) = 1)) | $lesseq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 1)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 ($lesseq($sum($product(2, length(split1(next(next(b))))), $product(-1, length(next(next(b))))), 1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[129, 144, 127, 137, 46, 40])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------