TSTP Solution File: HEN007-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HEN007-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 22:39:50 EDT 2022
% Result : Unsatisfiable 155.10s 99.91s
% Output : Proof 155.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN007-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n008.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 21:47:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 155.10/99.91 % SZS status Unsatisfiable
% 155.10/99.91 % SZS output start Proof
% 155.10/99.91 tff(less_equal_type, type, (
% 155.10/99.91 less_equal: ( $i * $i ) > $o)).
% 155.10/99.91 tff(zero_type, type, (
% 155.10/99.91 zero: $i)).
% 155.10/99.91 tff(divide_type, type, (
% 155.10/99.91 divide: ( $i * $i ) > $i)).
% 155.10/99.91 tff(a_type, type, (
% 155.10/99.91 a: $i)).
% 155.10/99.91 tff(c_type, type, (
% 155.10/99.91 c: $i)).
% 155.10/99.91 tff(b_type, type, (
% 155.10/99.91 b: $i)).
% 155.10/99.91 tff(1,assumption,(~less_equal(divide(divide(divide(divide(c, b), zero), divide(c, a)), divide(divide(divide(c, a), b), divide(c, a))), divide(divide(divide(divide(c, b), zero), divide(divide(c, a), b)), divide(c, a)))), introduced(assumption)).
% 155.10/99.91 tff(2,plain,
% 155.10/99.91 (^[Z: $i, Y: $i, X: $i] : refl(less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) <=> less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)))),
% 155.10/99.91 inference(bind,[status(th)],[])).
% 155.10/99.91 tff(3,plain,
% 155.10/99.91 (![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) <=> ![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))),
% 155.10/99.91 inference(quant_intro,[status(thm)],[2])).
% 155.10/99.91 tff(4,plain,
% 155.10/99.91 (![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) <=> ![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))),
% 155.10/99.91 inference(rewrite,[status(thm)],[])).
% 155.10/99.91 tff(5,axiom,(![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax','quotient_property')).
% 155.10/99.91 tff(6,plain,
% 155.10/99.91 (![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[5, 4])).
% 155.10/99.91 tff(7,plain,(
% 155.10/99.91 ![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))),
% 155.10/99.91 inference(skolemize,[status(sab)],[6])).
% 155.10/99.91 tff(8,plain,
% 155.10/99.91 (![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[7, 3])).
% 155.10/99.91 tff(9,plain,
% 155.10/99.91 ((~![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))) | less_equal(divide(divide(divide(divide(c, b), zero), divide(c, a)), divide(divide(divide(c, a), b), divide(c, a))), divide(divide(divide(divide(c, b), zero), divide(divide(c, a), b)), divide(c, a)))),
% 155.10/99.91 inference(quant_inst,[status(thm)],[])).
% 155.10/99.91 tff(10,plain,
% 155.10/99.91 ($false),
% 155.10/99.91 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 155.10/99.91 tff(11,plain,(less_equal(divide(divide(divide(divide(c, b), zero), divide(c, a)), divide(divide(divide(c, a), b), divide(c, a))), divide(divide(divide(divide(c, b), zero), divide(divide(c, a), b)), divide(c, a)))), inference(lemma,lemma(discharge,[]))).
% 155.10/99.91 tff(12,plain,
% 155.10/99.91 (^[Y: $i, X: $i] : refl(less_equal(divide(X, Y), X) <=> less_equal(divide(X, Y), X))),
% 155.10/99.91 inference(bind,[status(th)],[])).
% 155.10/99.91 tff(13,plain,
% 155.10/99.91 (![Y: $i, X: $i] : less_equal(divide(X, Y), X) <=> ![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 155.10/99.91 inference(quant_intro,[status(thm)],[12])).
% 155.10/99.91 tff(14,plain,
% 155.10/99.91 (![Y: $i, X: $i] : less_equal(divide(X, Y), X) <=> ![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 155.10/99.91 inference(rewrite,[status(thm)],[])).
% 155.10/99.91 tff(15,axiom,(![Y: $i, X: $i] : less_equal(divide(X, Y), X)), file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax','quotient_smaller_than_numerator')).
% 155.10/99.91 tff(16,plain,
% 155.10/99.91 (![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[15, 14])).
% 155.10/99.91 tff(17,plain,(
% 155.10/99.91 ![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 155.10/99.91 inference(skolemize,[status(sab)],[16])).
% 155.10/99.91 tff(18,plain,
% 155.10/99.91 (![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[17, 13])).
% 155.10/99.91 tff(19,plain,
% 155.10/99.91 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(c, a), c)),
% 155.10/99.91 inference(quant_inst,[status(thm)],[])).
% 155.10/99.91 tff(20,plain,
% 155.10/99.91 (less_equal(divide(c, a), c)),
% 155.10/99.91 inference(unit_resolution,[status(thm)],[19, 18])).
% 155.10/99.91 tff(21,plain,
% 155.10/99.91 (^[Y: $i, X: $i] : refl(((~less_equal(X, Y)) | (divide(X, Y) = zero)) <=> ((~less_equal(X, Y)) | (divide(X, Y) = zero)))),
% 155.10/99.91 inference(bind,[status(th)],[])).
% 155.10/99.91 tff(22,plain,
% 155.10/99.91 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 155.10/99.91 inference(quant_intro,[status(thm)],[21])).
% 155.10/99.91 tff(23,plain,
% 155.10/99.91 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 155.10/99.91 inference(rewrite,[status(thm)],[])).
% 155.10/99.91 tff(24,axiom,(![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax','quotient_less_equal1')).
% 155.10/99.91 tff(25,plain,
% 155.10/99.91 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[24, 23])).
% 155.10/99.91 tff(26,plain,(
% 155.10/99.91 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 155.10/99.91 inference(skolemize,[status(sab)],[25])).
% 155.10/99.91 tff(27,plain,
% 155.10/99.91 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[26, 22])).
% 155.10/99.91 tff(28,plain,
% 155.10/99.91 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(c, a), c)) | (divide(divide(c, a), c) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(c, a), c)) | (divide(divide(c, a), c) = zero))),
% 155.10/99.91 inference(rewrite,[status(thm)],[])).
% 155.10/99.91 tff(29,plain,
% 155.10/99.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(c, a), c)) | (divide(divide(c, a), c) = zero))),
% 155.10/99.91 inference(quant_inst,[status(thm)],[])).
% 155.10/99.91 tff(30,plain,
% 155.10/99.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(c, a), c)) | (divide(divide(c, a), c) = zero)),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[29, 28])).
% 155.10/99.91 tff(31,plain,
% 155.10/99.91 (divide(divide(c, a), c) = zero),
% 155.10/99.91 inference(unit_resolution,[status(thm)],[30, 27, 20])).
% 155.10/99.91 tff(32,plain,
% 155.10/99.91 (zero = divide(divide(c, a), c)),
% 155.10/99.91 inference(symmetry,[status(thm)],[31])).
% 155.10/99.91 tff(33,plain,
% 155.10/99.91 (less_equal(zero, divide(c, a)) <=> less_equal(divide(divide(c, a), c), divide(c, a))),
% 155.10/99.91 inference(monotonicity,[status(thm)],[32])).
% 155.10/99.91 tff(34,plain,
% 155.10/99.91 (less_equal(divide(divide(c, a), c), divide(c, a)) <=> less_equal(zero, divide(c, a))),
% 155.10/99.91 inference(symmetry,[status(thm)],[33])).
% 155.10/99.91 tff(35,plain,
% 155.10/99.91 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(c, a), c), divide(c, a))),
% 155.10/99.91 inference(quant_inst,[status(thm)],[])).
% 155.10/99.91 tff(36,plain,
% 155.10/99.91 (less_equal(divide(divide(c, a), c), divide(c, a))),
% 155.10/99.91 inference(unit_resolution,[status(thm)],[35, 18])).
% 155.10/99.91 tff(37,plain,
% 155.10/99.91 (less_equal(zero, divide(c, a))),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[36, 34])).
% 155.10/99.91 tff(38,plain,
% 155.10/99.91 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(zero, divide(c, a))) | (divide(zero, divide(c, a)) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(zero, divide(c, a))) | (divide(zero, divide(c, a)) = zero))),
% 155.10/99.91 inference(rewrite,[status(thm)],[])).
% 155.10/99.91 tff(39,plain,
% 155.10/99.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(zero, divide(c, a))) | (divide(zero, divide(c, a)) = zero))),
% 155.10/99.91 inference(quant_inst,[status(thm)],[])).
% 155.10/99.91 tff(40,plain,
% 155.10/99.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(zero, divide(c, a))) | (divide(zero, divide(c, a)) = zero)),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[39, 38])).
% 155.10/99.91 tff(41,plain,
% 155.10/99.91 ((~less_equal(zero, divide(c, a))) | (divide(zero, divide(c, a)) = zero)),
% 155.10/99.91 inference(unit_resolution,[status(thm)],[40, 27])).
% 155.10/99.91 tff(42,plain,
% 155.10/99.91 (divide(zero, divide(c, a)) = zero),
% 155.10/99.91 inference(unit_resolution,[status(thm)],[41, 37])).
% 155.10/99.91 tff(43,plain,
% 155.10/99.91 (less_equal(a, b) <=> less_equal(a, b)),
% 155.10/99.91 inference(rewrite,[status(thm)],[])).
% 155.10/99.91 tff(44,axiom,(less_equal(a, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_LE_b')).
% 155.10/99.91 tff(45,plain,
% 155.10/99.91 (less_equal(a, b)),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[44, 43])).
% 155.10/99.91 tff(46,plain,
% 155.10/99.91 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(a, b)) | (divide(a, b) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(a, b)) | (divide(a, b) = zero))),
% 155.10/99.91 inference(rewrite,[status(thm)],[])).
% 155.10/99.91 tff(47,plain,
% 155.10/99.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(a, b)) | (divide(a, b) = zero))),
% 155.10/99.91 inference(quant_inst,[status(thm)],[])).
% 155.10/99.91 tff(48,plain,
% 155.10/99.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(a, b)) | (divide(a, b) = zero)),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[47, 46])).
% 155.10/99.91 tff(49,plain,
% 155.10/99.91 (divide(a, b) = zero),
% 155.10/99.91 inference(unit_resolution,[status(thm)],[48, 27, 45])).
% 155.10/99.91 tff(50,plain,
% 155.10/99.91 (divide(divide(c, b), divide(a, b)) = divide(divide(c, b), zero)),
% 155.10/99.91 inference(monotonicity,[status(thm)],[49])).
% 155.10/99.91 tff(51,plain,
% 155.10/99.91 (divide(divide(c, b), zero) = divide(divide(c, b), divide(a, b))),
% 155.10/99.91 inference(symmetry,[status(thm)],[50])).
% 155.10/99.91 tff(52,plain,
% 155.10/99.91 (less_equal(divide(divide(c, b), zero), divide(divide(c, a), b)) <=> less_equal(divide(divide(c, b), divide(a, b)), divide(divide(c, a), b))),
% 155.10/99.91 inference(monotonicity,[status(thm)],[51])).
% 155.10/99.91 tff(53,plain,
% 155.10/99.91 (less_equal(divide(divide(c, b), divide(a, b)), divide(divide(c, a), b)) <=> less_equal(divide(divide(c, b), zero), divide(divide(c, a), b))),
% 155.10/99.91 inference(symmetry,[status(thm)],[52])).
% 155.10/99.91 tff(54,plain,
% 155.10/99.91 ((~![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))) | less_equal(divide(divide(c, b), divide(a, b)), divide(divide(c, a), b))),
% 155.10/99.91 inference(quant_inst,[status(thm)],[])).
% 155.10/99.91 tff(55,plain,
% 155.10/99.91 (less_equal(divide(divide(c, b), divide(a, b)), divide(divide(c, a), b))),
% 155.10/99.91 inference(unit_resolution,[status(thm)],[54, 8])).
% 155.10/99.91 tff(56,plain,
% 155.10/99.91 (less_equal(divide(divide(c, b), zero), divide(divide(c, a), b))),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[55, 53])).
% 155.10/99.91 tff(57,plain,
% 155.10/99.91 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), zero), divide(divide(c, a), b))) | (divide(divide(divide(c, b), zero), divide(divide(c, a), b)) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), zero), divide(divide(c, a), b))) | (divide(divide(divide(c, b), zero), divide(divide(c, a), b)) = zero))),
% 155.10/99.91 inference(rewrite,[status(thm)],[])).
% 155.10/99.91 tff(58,plain,
% 155.10/99.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), zero), divide(divide(c, a), b))) | (divide(divide(divide(c, b), zero), divide(divide(c, a), b)) = zero))),
% 155.10/99.91 inference(quant_inst,[status(thm)],[])).
% 155.10/99.91 tff(59,plain,
% 155.10/99.91 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), zero), divide(divide(c, a), b))) | (divide(divide(divide(c, b), zero), divide(divide(c, a), b)) = zero)),
% 155.10/99.91 inference(modus_ponens,[status(thm)],[58, 57])).
% 155.10/99.91 tff(60,plain,
% 155.10/99.91 ((~less_equal(divide(divide(c, b), zero), divide(divide(c, a), b))) | (divide(divide(divide(c, b), zero), divide(divide(c, a), b)) = zero)),
% 155.10/99.91 inference(unit_resolution,[status(thm)],[59, 27])).
% 155.10/99.91 tff(61,plain,
% 155.10/99.91 (divide(divide(divide(c, b), zero), divide(divide(c, a), b)) = zero),
% 155.10/99.91 inference(unit_resolution,[status(thm)],[60, 56])).
% 155.10/99.91 tff(62,plain,
% 155.10/99.91 (divide(divide(divide(divide(c, b), zero), divide(divide(c, a), b)), divide(c, a)) = divide(zero, divide(c, a))),
% 155.10/99.91 inference(monotonicity,[status(thm)],[61])).
% 155.10/99.91 tff(63,plain,
% 155.10/99.91 (divide(divide(divide(divide(c, b), zero), divide(divide(c, a), b)), divide(c, a)) = zero),
% 155.10/99.91 inference(transitivity,[status(thm)],[62, 42])).
% 155.10/99.91 tff(64,assumption,(~(divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))) = zero)), introduced(assumption)).
% 155.10/99.91 tff(65,plain,
% 155.10/99.91 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b)))),
% 155.10/99.91 inference(quant_inst,[status(thm)],[])).
% 155.10/99.91 tff(66,plain,
% 155.10/99.91 (less_equal(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b)))),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[65, 18])).
% 155.10/99.92 tff(67,plain,
% 155.10/99.92 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b)))) | (divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b)))) | (divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))) = zero))),
% 155.10/99.92 inference(rewrite,[status(thm)],[])).
% 155.10/99.92 tff(68,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b)))) | (divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))) = zero))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(69,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b)))) | (divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))) = zero)),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[68, 67])).
% 155.10/99.92 tff(70,plain,
% 155.10/99.92 ($false),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[69, 27, 66, 64])).
% 155.10/99.92 tff(71,plain,(divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))) = zero), inference(lemma,lemma(discharge,[]))).
% 155.10/99.92 tff(72,assumption,(divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))) = zero), introduced(assumption)).
% 155.10/99.92 tff(73,plain,
% 155.10/99.92 (zero = divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b)))),
% 155.10/99.92 inference(symmetry,[status(thm)],[72])).
% 155.10/99.92 tff(74,plain,
% 155.10/99.92 (less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero)) <=> less_equal(divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))), divide(divide(divide(c, b), divide(c, b)), zero))),
% 155.10/99.92 inference(monotonicity,[status(thm)],[73])).
% 155.10/99.92 tff(75,plain,
% 155.10/99.92 (less_equal(divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))), divide(divide(divide(c, b), divide(c, b)), zero)) <=> less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero))),
% 155.10/99.92 inference(symmetry,[status(thm)],[74])).
% 155.10/99.92 tff(76,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))), divide(divide(divide(c, b), divide(c, b)), zero))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(77,plain,
% 155.10/99.92 (less_equal(divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))), divide(divide(divide(c, b), divide(c, b)), zero))),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[76, 18])).
% 155.10/99.92 tff(78,plain,
% 155.10/99.92 (less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero))),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[77, 75])).
% 155.10/99.92 tff(79,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(c, b), zero), divide(c, b))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(80,plain,
% 155.10/99.92 (less_equal(divide(divide(c, b), zero), divide(c, b))),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[79, 18])).
% 155.10/99.92 tff(81,plain,
% 155.10/99.92 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), zero), divide(c, b))) | (divide(divide(divide(c, b), zero), divide(c, b)) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), zero), divide(c, b))) | (divide(divide(divide(c, b), zero), divide(c, b)) = zero))),
% 155.10/99.92 inference(rewrite,[status(thm)],[])).
% 155.10/99.92 tff(82,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), zero), divide(c, b))) | (divide(divide(divide(c, b), zero), divide(c, b)) = zero))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(83,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), zero), divide(c, b))) | (divide(divide(divide(c, b), zero), divide(c, b)) = zero)),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[82, 81])).
% 155.10/99.92 tff(84,plain,
% 155.10/99.92 (divide(divide(divide(c, b), zero), divide(c, b)) = zero),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[83, 27, 80])).
% 155.10/99.92 tff(85,plain,
% 155.10/99.92 (zero = divide(divide(divide(c, b), zero), divide(c, b))),
% 155.10/99.92 inference(symmetry,[status(thm)],[84])).
% 155.10/99.92 tff(86,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(c, b), c)),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(87,plain,
% 155.10/99.92 (less_equal(divide(c, b), c)),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[86, 18])).
% 155.10/99.92 tff(88,plain,
% 155.10/99.92 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(c, b), c)) | (divide(divide(c, b), c) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(c, b), c)) | (divide(divide(c, b), c) = zero))),
% 155.10/99.92 inference(rewrite,[status(thm)],[])).
% 155.10/99.92 tff(89,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(c, b), c)) | (divide(divide(c, b), c) = zero))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(90,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(c, b), c)) | (divide(divide(c, b), c) = zero)),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[89, 88])).
% 155.10/99.92 tff(91,plain,
% 155.10/99.92 (divide(divide(c, b), c) = zero),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[90, 27, 87])).
% 155.10/99.92 tff(92,plain,
% 155.10/99.92 (zero = divide(divide(c, b), c)),
% 155.10/99.92 inference(symmetry,[status(thm)],[91])).
% 155.10/99.92 tff(93,plain,
% 155.10/99.92 (less_equal(zero, divide(c, b)) <=> less_equal(divide(divide(c, b), c), divide(c, b))),
% 155.10/99.92 inference(monotonicity,[status(thm)],[92])).
% 155.10/99.92 tff(94,plain,
% 155.10/99.92 (less_equal(divide(divide(c, b), c), divide(c, b)) <=> less_equal(zero, divide(c, b))),
% 155.10/99.92 inference(symmetry,[status(thm)],[93])).
% 155.10/99.92 tff(95,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(c, b), c), divide(c, b))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(96,plain,
% 155.10/99.92 (less_equal(divide(divide(c, b), c), divide(c, b))),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[95, 18])).
% 155.10/99.92 tff(97,plain,
% 155.10/99.92 (less_equal(zero, divide(c, b))),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[96, 94])).
% 155.10/99.92 tff(98,plain,
% 155.10/99.92 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(zero, divide(c, b))) | (divide(zero, divide(c, b)) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(zero, divide(c, b))) | (divide(zero, divide(c, b)) = zero))),
% 155.10/99.92 inference(rewrite,[status(thm)],[])).
% 155.10/99.92 tff(99,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(zero, divide(c, b))) | (divide(zero, divide(c, b)) = zero))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(100,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(zero, divide(c, b))) | (divide(zero, divide(c, b)) = zero)),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[99, 98])).
% 155.10/99.92 tff(101,plain,
% 155.10/99.92 ((~less_equal(zero, divide(c, b))) | (divide(zero, divide(c, b)) = zero)),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[100, 27])).
% 155.10/99.92 tff(102,plain,
% 155.10/99.92 (divide(zero, divide(c, b)) = zero),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[101, 97])).
% 155.10/99.92 tff(103,plain,
% 155.10/99.92 (divide(divide(divide(c, b), divide(c, b)), divide(zero, divide(c, b))) = divide(divide(divide(c, b), divide(c, b)), zero)),
% 155.10/99.92 inference(monotonicity,[status(thm)],[102])).
% 155.10/99.92 tff(104,plain,
% 155.10/99.92 (divide(divide(divide(c, b), divide(c, b)), zero) = divide(divide(divide(c, b), divide(c, b)), divide(zero, divide(c, b)))),
% 155.10/99.92 inference(symmetry,[status(thm)],[103])).
% 155.10/99.92 tff(105,plain,
% 155.10/99.92 (less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero) <=> less_equal(divide(divide(divide(c, b), divide(c, b)), divide(zero, divide(c, b))), divide(divide(divide(c, b), zero), divide(c, b)))),
% 155.10/99.92 inference(monotonicity,[status(thm)],[104, 85])).
% 155.10/99.92 tff(106,plain,
% 155.10/99.92 (less_equal(divide(divide(divide(c, b), divide(c, b)), divide(zero, divide(c, b))), divide(divide(divide(c, b), zero), divide(c, b))) <=> less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)),
% 155.10/99.92 inference(symmetry,[status(thm)],[105])).
% 155.10/99.92 tff(107,plain,
% 155.10/99.92 ((~![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))) | less_equal(divide(divide(divide(c, b), divide(c, b)), divide(zero, divide(c, b))), divide(divide(divide(c, b), zero), divide(c, b)))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(108,plain,
% 155.10/99.92 (less_equal(divide(divide(divide(c, b), divide(c, b)), divide(zero, divide(c, b))), divide(divide(divide(c, b), zero), divide(c, b)))),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[107, 8])).
% 155.10/99.92 tff(109,plain,
% 155.10/99.92 (less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[108, 106])).
% 155.10/99.92 tff(110,assumption,(~(divide(divide(divide(c, b), divide(c, b)), zero) = zero)), introduced(assumption)).
% 155.10/99.92 tff(111,plain,
% 155.10/99.92 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X))) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 155.10/99.92 inference(rewrite,[status(thm)],[])).
% 155.10/99.92 tff(112,plain,
% 155.10/99.92 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X))) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 155.10/99.92 inference(rewrite,[status(thm)],[])).
% 155.10/99.92 tff(113,plain,
% 155.10/99.92 (^[Y: $i, X: $i] : rewrite((((~less_equal(X, Y)) | (~less_equal(Y, X))) | (X = Y)) <=> ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X))))),
% 155.10/99.92 inference(bind,[status(th)],[])).
% 155.10/99.92 tff(114,plain,
% 155.10/99.92 (![Y: $i, X: $i] : (((~less_equal(X, Y)) | (~less_equal(Y, X))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 155.10/99.92 inference(quant_intro,[status(thm)],[113])).
% 155.10/99.92 tff(115,axiom,(![Y: $i, X: $i] : (((~less_equal(X, Y)) | (~less_equal(Y, X))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax','less_equal_and_equal')).
% 155.10/99.92 tff(116,plain,
% 155.10/99.92 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[115, 114])).
% 155.10/99.92 tff(117,plain,
% 155.10/99.92 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[116, 112])).
% 155.10/99.92 tff(118,plain,(
% 155.10/99.92 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 155.10/99.92 inference(skolemize,[status(sab)],[117])).
% 155.10/99.92 tff(119,plain,
% 155.10/99.92 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[118, 111])).
% 155.10/99.92 tff(120,plain,
% 155.10/99.92 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(divide(c, b), divide(c, b)), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(c, b)), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero))))),
% 155.10/99.92 inference(rewrite,[status(thm)],[])).
% 155.10/99.92 tff(121,plain,
% 155.10/99.92 (((~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)) | (divide(divide(divide(c, b), divide(c, b)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero)))) <=> ((divide(divide(divide(c, b), divide(c, b)), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero))))),
% 155.10/99.92 inference(rewrite,[status(thm)],[])).
% 155.10/99.92 tff(122,plain,
% 155.10/99.92 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)) | (divide(divide(divide(c, b), divide(c, b)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(divide(c, b), divide(c, b)), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero)))))),
% 155.10/99.92 inference(monotonicity,[status(thm)],[121])).
% 155.10/99.92 tff(123,plain,
% 155.10/99.92 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)) | (divide(divide(divide(c, b), divide(c, b)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(c, b)), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero))))),
% 155.10/99.92 inference(transitivity,[status(thm)],[122, 120])).
% 155.10/99.92 tff(124,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)) | (divide(divide(divide(c, b), divide(c, b)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero))))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(125,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(c, b)), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(c, b)), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero)))),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[124, 123])).
% 155.10/99.92 tff(126,plain,
% 155.10/99.92 (~less_equal(zero, divide(divide(divide(c, b), divide(c, b)), zero))),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[125, 119, 110, 109])).
% 155.10/99.92 tff(127,plain,
% 155.10/99.92 ($false),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[126, 78])).
% 155.10/99.92 tff(128,plain,((~(divide(divide(divide(divide(c, b), divide(c, b)), zero), divide(divide(c, b), divide(c, b))) = zero)) | (divide(divide(divide(c, b), divide(c, b)), zero) = zero)), inference(lemma,lemma(discharge,[]))).
% 155.10/99.92 tff(129,plain,
% 155.10/99.92 (divide(divide(divide(c, b), divide(c, b)), zero) = zero),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[128, 71])).
% 155.10/99.92 tff(130,plain,
% 155.10/99.92 (^[Y: $i, X: $i] : refl(((~(divide(X, Y) = zero)) | less_equal(X, Y)) <=> ((~(divide(X, Y) = zero)) | less_equal(X, Y)))),
% 155.10/99.92 inference(bind,[status(th)],[])).
% 155.10/99.92 tff(131,plain,
% 155.10/99.92 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 155.10/99.92 inference(quant_intro,[status(thm)],[130])).
% 155.10/99.92 tff(132,plain,
% 155.10/99.92 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 155.10/99.92 inference(rewrite,[status(thm)],[])).
% 155.10/99.92 tff(133,axiom,(![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax','quotient_less_equal2')).
% 155.10/99.92 tff(134,plain,
% 155.10/99.92 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[133, 132])).
% 155.10/99.92 tff(135,plain,(
% 155.10/99.92 ![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 155.10/99.92 inference(skolemize,[status(sab)],[134])).
% 155.10/99.92 tff(136,plain,
% 155.10/99.92 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[135, 131])).
% 155.10/99.92 tff(137,plain,
% 155.10/99.92 (((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(divide(c, b), divide(c, b)), zero) = zero)) | less_equal(divide(divide(c, b), divide(c, b)), zero))) <=> ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(divide(c, b), divide(c, b)), zero) = zero)) | less_equal(divide(divide(c, b), divide(c, b)), zero))),
% 155.10/99.92 inference(rewrite,[status(thm)],[])).
% 155.10/99.92 tff(138,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(divide(c, b), divide(c, b)), zero) = zero)) | less_equal(divide(divide(c, b), divide(c, b)), zero))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(139,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(divide(c, b), divide(c, b)), zero) = zero)) | less_equal(divide(divide(c, b), divide(c, b)), zero)),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[138, 137])).
% 155.10/99.92 tff(140,plain,
% 155.10/99.92 ((~(divide(divide(divide(c, b), divide(c, b)), zero) = zero)) | less_equal(divide(divide(c, b), divide(c, b)), zero)),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[139, 136])).
% 155.10/99.92 tff(141,plain,
% 155.10/99.92 (less_equal(divide(divide(c, b), divide(c, b)), zero)),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[140, 129])).
% 155.10/99.92 tff(142,plain,
% 155.10/99.92 ((~![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))) | less_equal(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(143,plain,
% 155.10/99.92 (less_equal(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b))),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[142, 8])).
% 155.10/99.92 tff(144,plain,
% 155.10/99.92 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b))) | (divide(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b)) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b))) | (divide(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b)) = zero))),
% 155.10/99.92 inference(rewrite,[status(thm)],[])).
% 155.10/99.92 tff(145,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b))) | (divide(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b)) = zero))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(146,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b))) | (divide(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b)) = zero)),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[145, 144])).
% 155.10/99.92 tff(147,plain,
% 155.10/99.92 (divide(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b)) = zero),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[146, 27, 143])).
% 155.10/99.92 tff(148,plain,
% 155.10/99.92 (zero = divide(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b))),
% 155.10/99.92 inference(symmetry,[status(thm)],[147])).
% 155.10/99.92 tff(149,plain,
% 155.10/99.92 (less_equal(zero, divide(divide(c, b), divide(c, b))) <=> less_equal(divide(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b)), divide(divide(c, b), divide(c, b)))),
% 155.10/99.92 inference(monotonicity,[status(thm)],[148])).
% 155.10/99.92 tff(150,plain,
% 155.10/99.92 (less_equal(divide(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b)), divide(divide(c, b), divide(c, b))) <=> less_equal(zero, divide(divide(c, b), divide(c, b)))),
% 155.10/99.92 inference(symmetry,[status(thm)],[149])).
% 155.10/99.92 tff(151,plain,
% 155.10/99.92 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b)), divide(divide(c, b), divide(c, b)))),
% 155.10/99.92 inference(quant_inst,[status(thm)],[])).
% 155.10/99.92 tff(152,plain,
% 155.10/99.92 (less_equal(divide(divide(divide(c, b), divide(c, b)), divide(divide(c, c), b)), divide(divide(c, b), divide(c, b)))),
% 155.10/99.92 inference(unit_resolution,[status(thm)],[151, 18])).
% 155.10/99.92 tff(153,plain,
% 155.10/99.92 (less_equal(zero, divide(divide(c, b), divide(c, b)))),
% 155.10/99.92 inference(modus_ponens,[status(thm)],[152, 150])).
% 155.10/99.92 tff(154,assumption,(~(divide(divide(c, b), divide(c, b)) = zero)), introduced(assumption)).
% 155.10/99.92 tff(155,plain,
% 155.10/99.92 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(c, b), divide(c, b)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, b)))) | (~less_equal(divide(divide(c, b), divide(c, b)), zero)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(c, b), divide(c, b)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, b)))) | (~less_equal(divide(divide(c, b), divide(c, b)), zero)))),
% 155.10/99.93 inference(rewrite,[status(thm)],[])).
% 155.10/99.93 tff(156,plain,
% 155.10/99.93 (((~less_equal(divide(divide(c, b), divide(c, b)), zero)) | (divide(divide(c, b), divide(c, b)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, b))))) <=> ((divide(divide(c, b), divide(c, b)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, b)))) | (~less_equal(divide(divide(c, b), divide(c, b)), zero)))),
% 155.10/99.93 inference(rewrite,[status(thm)],[])).
% 155.10/99.93 tff(157,plain,
% 155.10/99.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(c, b), divide(c, b)), zero)) | (divide(divide(c, b), divide(c, b)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, b)))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(c, b), divide(c, b)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, b)))) | (~less_equal(divide(divide(c, b), divide(c, b)), zero))))),
% 155.10/99.93 inference(monotonicity,[status(thm)],[156])).
% 155.10/99.93 tff(158,plain,
% 155.10/99.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(c, b), divide(c, b)), zero)) | (divide(divide(c, b), divide(c, b)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, b)))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(c, b), divide(c, b)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, b)))) | (~less_equal(divide(divide(c, b), divide(c, b)), zero)))),
% 155.10/99.93 inference(transitivity,[status(thm)],[157, 155])).
% 155.10/99.93 tff(159,plain,
% 155.10/99.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(c, b), divide(c, b)), zero)) | (divide(divide(c, b), divide(c, b)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, b)))))),
% 155.10/99.93 inference(quant_inst,[status(thm)],[])).
% 155.10/99.93 tff(160,plain,
% 155.10/99.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(c, b), divide(c, b)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, b)))) | (~less_equal(divide(divide(c, b), divide(c, b)), zero))),
% 155.10/99.93 inference(modus_ponens,[status(thm)],[159, 158])).
% 155.10/99.93 tff(161,plain,
% 155.10/99.93 ($false),
% 155.10/99.93 inference(unit_resolution,[status(thm)],[160, 119, 154, 153, 141])).
% 155.10/99.93 tff(162,plain,(divide(divide(c, b), divide(c, b)) = zero), inference(lemma,lemma(discharge,[]))).
% 155.10/99.93 tff(163,plain,
% 155.10/99.93 (divide(divide(divide(c, b), divide(c, b)), divide(c, a)) = divide(zero, divide(c, a))),
% 155.10/99.93 inference(monotonicity,[status(thm)],[162])).
% 155.10/99.93 tff(164,plain,
% 155.10/99.93 (divide(divide(divide(c, b), divide(c, b)), divide(c, a)) = zero),
% 155.10/99.93 inference(transitivity,[status(thm)],[163, 42])).
% 155.10/99.93 tff(165,plain,
% 155.10/99.93 (less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a))) <=> less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero)),
% 155.10/99.93 inference(monotonicity,[status(thm)],[164])).
% 155.10/99.93 tff(166,plain,
% 155.10/99.93 ((~![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))) | less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a)))),
% 155.10/99.93 inference(quant_inst,[status(thm)],[])).
% 155.10/99.93 tff(167,plain,
% 155.10/99.93 (less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a)))),
% 155.10/99.93 inference(unit_resolution,[status(thm)],[166, 8])).
% 155.10/99.93 tff(168,plain,
% 155.10/99.93 (less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero)),
% 155.10/99.93 inference(modus_ponens,[status(thm)],[167, 165])).
% 155.10/99.93 tff(169,plain,
% 155.10/99.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a)))) | (divide(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a))) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a)))) | (divide(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a))) = zero))),
% 155.10/99.93 inference(rewrite,[status(thm)],[])).
% 155.10/99.93 tff(170,plain,
% 155.10/99.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a)))) | (divide(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a))) = zero))),
% 155.10/99.93 inference(quant_inst,[status(thm)],[])).
% 155.10/99.93 tff(171,plain,
% 155.10/99.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a)))) | (divide(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a))) = zero)),
% 155.10/99.93 inference(modus_ponens,[status(thm)],[170, 169])).
% 155.10/99.93 tff(172,plain,
% 155.10/99.93 (divide(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a))) = zero),
% 155.10/99.93 inference(unit_resolution,[status(thm)],[171, 27, 167])).
% 155.10/99.93 tff(173,plain,
% 155.10/99.93 (zero = divide(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a)))),
% 155.10/99.93 inference(symmetry,[status(thm)],[172])).
% 155.10/99.93 tff(174,plain,
% 155.10/99.93 (less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))) <=> less_equal(divide(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a))), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))),
% 155.10/99.93 inference(monotonicity,[status(thm)],[173])).
% 155.10/99.93 tff(175,plain,
% 155.10/99.93 (less_equal(divide(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a))), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))) <=> less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))),
% 155.10/99.93 inference(symmetry,[status(thm)],[174])).
% 155.10/99.93 tff(176,plain,
% 155.10/99.93 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a))), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))),
% 155.10/99.93 inference(quant_inst,[status(thm)],[])).
% 155.10/99.93 tff(177,plain,
% 155.10/99.93 (less_equal(divide(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, b)), divide(c, a))), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))),
% 155.10/99.93 inference(unit_resolution,[status(thm)],[176, 18])).
% 155.10/99.93 tff(178,plain,
% 155.10/99.93 (less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))),
% 155.10/99.93 inference(modus_ponens,[status(thm)],[177, 175])).
% 155.10/99.93 tff(179,assumption,(~(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero)), introduced(assumption)).
% 155.10/99.93 tff(180,plain,
% 155.10/99.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero)))),
% 155.18/99.93 inference(rewrite,[status(thm)],[])).
% 155.18/99.93 tff(181,plain,
% 155.18/99.93 (((~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero)) | (divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))) <=> ((divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero)))),
% 155.18/99.93 inference(rewrite,[status(thm)],[])).
% 155.18/99.93 tff(182,plain,
% 155.18/99.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero)) | (divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero))))),
% 155.18/99.93 inference(monotonicity,[status(thm)],[181])).
% 155.18/99.93 tff(183,plain,
% 155.18/99.93 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero)) | (divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero)))),
% 155.18/99.93 inference(transitivity,[status(thm)],[182, 180])).
% 155.18/99.93 tff(184,plain,
% 155.18/99.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero)) | (divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))),
% 155.18/99.93 inference(quant_inst,[status(thm)],[])).
% 155.18/99.93 tff(185,plain,
% 155.18/99.93 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))), zero))),
% 155.18/99.93 inference(modus_ponens,[status(thm)],[184, 183])).
% 155.18/99.93 tff(186,plain,
% 155.18/99.93 ($false),
% 155.18/99.93 inference(unit_resolution,[status(thm)],[185, 119, 179, 178, 168])).
% 155.18/99.93 tff(187,plain,(divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))) = zero), inference(lemma,lemma(discharge,[]))).
% 155.18/99.93 tff(188,plain,
% 155.18/99.93 (divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))) = divide(divide(c, b), zero)),
% 155.18/99.93 inference(monotonicity,[status(thm)],[187])).
% 155.18/99.93 tff(189,plain,
% 155.18/99.93 (divide(divide(c, b), zero) = divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))),
% 155.18/99.93 inference(symmetry,[status(thm)],[188])).
% 155.18/99.93 tff(190,plain,
% 155.18/99.93 (less_equal(divide(c, b), divide(divide(c, b), zero)) <=> less_equal(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.93 inference(monotonicity,[status(thm)],[189])).
% 155.18/99.93 tff(191,plain,
% 155.18/99.93 (less_equal(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) <=> less_equal(divide(c, b), divide(divide(c, b), zero))),
% 155.18/99.93 inference(symmetry,[status(thm)],[190])).
% 155.18/99.93 tff(192,assumption,(~less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero)), introduced(assumption)).
% 155.18/99.93 tff(193,assumption,(~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))), divide(divide(divide(c, b), zero), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))), introduced(assumption)).
% 155.18/99.93 tff(194,plain,
% 155.18/99.93 ((~![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))) | less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))), divide(divide(divide(c, b), zero), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))),
% 155.18/99.93 inference(quant_inst,[status(thm)],[])).
% 155.18/99.93 tff(195,plain,
% 155.18/99.93 ($false),
% 155.18/99.93 inference(unit_resolution,[status(thm)],[194, 8, 193])).
% 155.18/99.93 tff(196,plain,(less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))), divide(divide(divide(c, b), zero), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))), inference(lemma,lemma(discharge,[]))).
% 155.18/99.93 tff(197,assumption,(~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))), introduced(assumption)).
% 155.18/99.93 tff(198,plain,
% 155.18/99.93 (^[X: $i] : refl(less_equal(zero, X) <=> less_equal(zero, X))),
% 155.18/99.93 inference(bind,[status(th)],[])).
% 155.18/99.93 tff(199,plain,
% 155.18/99.93 (![X: $i] : less_equal(zero, X) <=> ![X: $i] : less_equal(zero, X)),
% 155.18/99.93 inference(quant_intro,[status(thm)],[198])).
% 155.18/99.93 tff(200,plain,
% 155.18/99.93 (![X: $i] : less_equal(zero, X) <=> ![X: $i] : less_equal(zero, X)),
% 155.18/99.93 inference(rewrite,[status(thm)],[])).
% 155.18/99.93 tff(201,axiom,(![X: $i] : less_equal(zero, X)), file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax','zero_is_smallest')).
% 155.18/99.93 tff(202,plain,
% 155.18/99.93 (![X: $i] : less_equal(zero, X)),
% 155.18/99.93 inference(modus_ponens,[status(thm)],[201, 200])).
% 155.18/99.93 tff(203,plain,(
% 155.18/99.93 ![X: $i] : less_equal(zero, X)),
% 155.18/99.93 inference(skolemize,[status(sab)],[202])).
% 155.18/99.93 tff(204,plain,
% 155.18/99.93 (![X: $i] : less_equal(zero, X)),
% 155.18/99.93 inference(modus_ponens,[status(thm)],[203, 199])).
% 155.18/99.93 tff(205,plain,
% 155.18/99.93 ((~![X: $i] : less_equal(zero, X)) | less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))),
% 155.18/99.93 inference(quant_inst,[status(thm)],[])).
% 155.18/99.93 tff(206,plain,
% 155.18/99.93 ($false),
% 155.18/99.93 inference(unit_resolution,[status(thm)],[205, 204, 197])).
% 155.18/99.93 tff(207,plain,(less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))), inference(lemma,lemma(discharge,[]))).
% 155.18/99.93 tff(208,plain,
% 155.18/99.93 (divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = divide(divide(divide(c, b), zero), divide(divide(c, b), zero))),
% 155.18/99.93 inference(monotonicity,[status(thm)],[188, 188])).
% 155.18/99.94 tff(209,plain,
% 155.18/99.94 (divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.94 inference(symmetry,[status(thm)],[208])).
% 155.18/99.94 tff(210,plain,
% 155.18/99.94 ((divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) <=> (divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)),
% 155.18/99.94 inference(monotonicity,[status(thm)],[209])).
% 155.18/99.94 tff(211,plain,
% 155.18/99.94 ((divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero) <=> (divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero)),
% 155.18/99.94 inference(symmetry,[status(thm)],[210])).
% 155.18/99.94 tff(212,plain,
% 155.18/99.94 ((~(divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)) <=> (~(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero))),
% 155.18/99.94 inference(monotonicity,[status(thm)],[211])).
% 155.18/99.94 tff(213,assumption,(~(divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)), introduced(assumption)).
% 155.18/99.94 tff(214,plain,
% 155.18/99.94 (~(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero)),
% 155.18/99.94 inference(modus_ponens,[status(thm)],[213, 212])).
% 155.18/99.94 tff(215,plain,
% 155.18/99.94 (divide(divide(divide(c, b), divide(c, b)), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))) = divide(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))),
% 155.18/99.94 inference(monotonicity,[status(thm)],[162])).
% 155.18/99.94 tff(216,plain,
% 155.18/99.94 (divide(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))) = divide(divide(divide(c, b), divide(c, b)), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))),
% 155.18/99.94 inference(symmetry,[status(thm)],[215])).
% 155.18/99.94 tff(217,plain,
% 155.18/99.94 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) | (divide(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) | (divide(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))) = zero))),
% 155.18/99.94 inference(rewrite,[status(thm)],[])).
% 155.18/99.94 tff(218,plain,
% 155.18/99.94 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) | (divide(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))) = zero))),
% 155.18/99.94 inference(quant_inst,[status(thm)],[])).
% 155.18/99.94 tff(219,plain,
% 155.18/99.94 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) | (divide(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))) = zero)),
% 155.18/99.94 inference(modus_ponens,[status(thm)],[218, 217])).
% 155.18/99.94 tff(220,plain,
% 155.18/99.94 ((~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) | (divide(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))) = zero)),
% 155.18/99.94 inference(unit_resolution,[status(thm)],[219, 27])).
% 155.18/99.94 tff(221,plain,
% 155.18/99.94 (divide(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))) = zero),
% 155.18/99.94 inference(unit_resolution,[status(thm)],[220, 178])).
% 155.18/99.94 tff(222,plain,
% 155.18/99.94 (zero = divide(zero, divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))),
% 155.18/99.94 inference(symmetry,[status(thm)],[221])).
% 155.18/99.94 tff(223,plain,
% 155.18/99.94 (zero = divide(divide(divide(c, b), divide(c, b)), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))),
% 155.18/99.94 inference(transitivity,[status(thm)],[222, 216])).
% 155.18/99.94 tff(224,plain,
% 155.18/99.94 (less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero) <=> less_equal(divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(divide(divide(c, b), divide(c, b)), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.94 inference(monotonicity,[status(thm)],[209, 223])).
% 155.18/99.94 tff(225,plain,
% 155.18/99.94 (less_equal(divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(divide(divide(c, b), divide(c, b)), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) <=> less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero)),
% 155.18/99.94 inference(symmetry,[status(thm)],[224])).
% 155.18/99.94 tff(226,plain,
% 155.18/99.94 ((~![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))) | less_equal(divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(divide(divide(c, b), divide(c, b)), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.94 inference(quant_inst,[status(thm)],[])).
% 155.18/99.94 tff(227,plain,
% 155.18/99.94 (less_equal(divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(divide(divide(c, b), divide(c, b)), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.94 inference(unit_resolution,[status(thm)],[226, 8])).
% 155.18/99.94 tff(228,plain,
% 155.18/99.94 (less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero)),
% 155.18/99.94 inference(modus_ponens,[status(thm)],[227, 225])).
% 155.18/99.94 tff(229,assumption,(less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))), introduced(assumption)).
% 155.18/99.94 tff(230,plain,
% 155.18/99.94 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) | (~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))) | (~less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) | (~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))) | (~less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero)))),
% 155.18/99.94 inference(rewrite,[status(thm)],[])).
% 155.18/99.94 tff(231,plain,
% 155.18/99.94 (((~less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero)) | (divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) | (~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero))))) <=> ((divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) | (~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))) | (~less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero)))),
% 155.18/99.94 inference(rewrite,[status(thm)],[])).
% 155.18/99.94 tff(232,plain,
% 155.18/99.94 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero)) | (divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) | (~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) | (~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))) | (~less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero))))),
% 155.18/99.94 inference(monotonicity,[status(thm)],[231])).
% 155.18/99.94 tff(233,plain,
% 155.18/99.94 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero)) | (divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) | (~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) | (~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))) | (~less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero)))),
% 155.18/99.94 inference(transitivity,[status(thm)],[232, 230])).
% 155.18/99.94 tff(234,plain,
% 155.18/99.94 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero)) | (divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) | (~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))))),
% 155.18/99.94 inference(quant_inst,[status(thm)],[])).
% 155.18/99.94 tff(235,plain,
% 155.18/99.94 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) | (~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))) | (~less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero))),
% 155.18/99.94 inference(modus_ponens,[status(thm)],[234, 233])).
% 155.18/99.94 tff(236,plain,
% 155.18/99.94 ((divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = zero) | (~less_equal(divide(divide(divide(c, b), zero), divide(divide(c, b), zero)), zero))),
% 155.18/99.94 inference(unit_resolution,[status(thm)],[235, 119, 229])).
% 155.18/99.94 tff(237,plain,
% 155.18/99.94 ($false),
% 155.18/99.94 inference(unit_resolution,[status(thm)],[236, 228, 214])).
% 155.18/99.94 tff(238,plain,((~less_equal(zero, divide(divide(divide(c, b), zero), divide(divide(c, b), zero)))) | (divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)), inference(lemma,lemma(discharge,[]))).
% 155.18/99.94 tff(239,plain,
% 155.18/99.94 (divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero),
% 155.18/99.94 inference(unit_resolution,[status(thm)],[238, 207])).
% 155.18/99.94 tff(240,plain,
% 155.18/99.94 (divide(divide(divide(c, b), zero), divide(divide(c, b), zero)) = divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.94 inference(monotonicity,[status(thm)],[189, 189])).
% 155.18/99.94 tff(241,plain,
% 155.18/99.94 (divide(divide(divide(c, b), zero), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = divide(divide(divide(c, b), zero), divide(divide(c, b), zero))),
% 155.18/99.94 inference(monotonicity,[status(thm)],[188])).
% 155.18/99.94 tff(242,plain,
% 155.18/99.94 (divide(divide(divide(c, b), zero), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero),
% 155.18/99.94 inference(transitivity,[status(thm)],[241, 240, 239])).
% 155.18/99.94 tff(243,plain,
% 155.18/99.94 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b))),
% 155.18/99.94 inference(quant_inst,[status(thm)],[])).
% 155.18/99.94 tff(244,plain,
% 155.18/99.94 (less_equal(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b))),
% 155.18/99.94 inference(unit_resolution,[status(thm)],[243, 18])).
% 155.18/99.94 tff(245,plain,
% 155.18/99.94 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b))) | (divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b)) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b))) | (divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b)) = zero))),
% 155.18/99.94 inference(rewrite,[status(thm)],[])).
% 155.18/99.94 tff(246,plain,
% 155.18/99.94 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b))) | (divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b)) = zero))),
% 155.18/99.94 inference(quant_inst,[status(thm)],[])).
% 155.18/99.94 tff(247,plain,
% 155.18/99.94 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b))) | (divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b)) = zero)),
% 155.18/99.94 inference(modus_ponens,[status(thm)],[246, 245])).
% 155.18/99.94 tff(248,plain,
% 155.18/99.94 ((~less_equal(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b))) | (divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b)) = zero)),
% 155.18/99.94 inference(unit_resolution,[status(thm)],[247, 27])).
% 155.18/99.94 tff(249,plain,
% 155.18/99.94 (divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b)) = zero),
% 155.18/99.94 inference(unit_resolution,[status(thm)],[248, 244])).
% 155.18/99.94 tff(250,plain,
% 155.18/99.94 (zero = divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b))),
% 155.18/99.94 inference(symmetry,[status(thm)],[249])).
% 155.18/99.94 tff(251,plain,
% 155.18/99.94 (less_equal(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) <=> less_equal(divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b)), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.94 inference(monotonicity,[status(thm)],[250])).
% 155.18/99.94 tff(252,plain,
% 155.18/99.94 (less_equal(divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b)), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) <=> less_equal(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.94 inference(symmetry,[status(thm)],[251])).
% 155.18/99.94 tff(253,plain,
% 155.18/99.94 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b)), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.94 inference(quant_inst,[status(thm)],[])).
% 155.18/99.94 tff(254,plain,
% 155.18/99.94 (less_equal(divide(divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))), divide(c, b)), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.95 inference(unit_resolution,[status(thm)],[253, 18])).
% 155.18/99.95 tff(255,plain,
% 155.18/99.95 (less_equal(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.95 inference(modus_ponens,[status(thm)],[254, 252])).
% 155.18/99.95 tff(256,plain,
% 155.18/99.95 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))) | (divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))) | (divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero))),
% 155.18/99.95 inference(rewrite,[status(thm)],[])).
% 155.18/99.95 tff(257,plain,
% 155.18/99.95 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))) | (divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero))),
% 155.18/99.95 inference(quant_inst,[status(thm)],[])).
% 155.18/99.95 tff(258,plain,
% 155.18/99.95 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))) | (divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)),
% 155.18/99.95 inference(modus_ponens,[status(thm)],[257, 256])).
% 155.18/99.95 tff(259,plain,
% 155.18/99.95 ((~less_equal(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))) | (divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)),
% 155.18/99.95 inference(unit_resolution,[status(thm)],[258, 27])).
% 155.18/99.95 tff(260,plain,
% 155.18/99.95 (divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero),
% 155.18/99.95 inference(unit_resolution,[status(thm)],[259, 255])).
% 155.18/99.95 tff(261,plain,
% 155.18/99.95 (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))) = divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero)),
% 155.18/99.95 inference(monotonicity,[status(thm)],[260])).
% 155.18/99.95 tff(262,plain,
% 155.18/99.95 (less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))), divide(divide(divide(c, b), zero), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))) <=> less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)),
% 155.18/99.95 inference(monotonicity,[status(thm)],[261, 242])).
% 155.18/99.95 tff(263,plain,
% 155.18/99.95 (less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero) <=> less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))), divide(divide(divide(c, b), zero), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))),
% 155.18/99.95 inference(symmetry,[status(thm)],[262])).
% 155.18/99.95 tff(264,plain,
% 155.18/99.95 ((~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)) <=> (~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))), divide(divide(divide(c, b), zero), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))))),
% 155.18/99.95 inference(monotonicity,[status(thm)],[263])).
% 155.18/99.95 tff(265,assumption,(~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)), introduced(assumption)).
% 155.18/99.95 tff(266,plain,
% 155.18/99.95 (~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))), divide(divide(divide(c, b), zero), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))),
% 155.18/99.95 inference(modus_ponens,[status(thm)],[265, 264])).
% 155.18/99.95 tff(267,assumption,(less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))), divide(divide(divide(c, b), zero), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))), introduced(assumption)).
% 155.18/99.95 tff(268,plain,
% 155.18/99.95 ($false),
% 155.18/99.95 inference(unit_resolution,[status(thm)],[267, 266])).
% 155.18/99.95 tff(269,plain,((~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(zero, divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))), divide(divide(divide(c, b), zero), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))) | less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)), inference(lemma,lemma(discharge,[]))).
% 155.18/99.95 tff(270,plain,
% 155.18/99.95 (less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)),
% 155.18/99.95 inference(unit_resolution,[status(thm)],[269, 196])).
% 155.18/99.95 tff(271,assumption,(~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))), introduced(assumption)).
% 155.18/99.95 tff(272,plain,
% 155.18/99.95 ((~![X: $i] : less_equal(zero, X)) | less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))),
% 155.18/99.95 inference(quant_inst,[status(thm)],[])).
% 155.18/99.95 tff(273,plain,
% 155.18/99.95 ($false),
% 155.18/99.95 inference(unit_resolution,[status(thm)],[272, 204, 271])).
% 155.18/99.95 tff(274,plain,(less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))), inference(lemma,lemma(discharge,[]))).
% 155.18/99.95 tff(275,assumption,(less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))), introduced(assumption)).
% 155.18/99.95 tff(276,assumption,(less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)), introduced(assumption)).
% 155.18/99.95 tff(277,assumption,(~(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero)), introduced(assumption)).
% 155.18/99.95 tff(278,plain,
% 155.18/99.95 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))))),
% 155.18/99.95 inference(rewrite,[status(thm)],[])).
% 155.18/99.95 tff(279,plain,
% 155.18/99.95 (((~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero)))) <=> ((divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))))),
% 155.18/99.95 inference(rewrite,[status(thm)],[])).
% 155.18/99.95 tff(280,plain,
% 155.18/99.95 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero)))))),
% 155.18/99.95 inference(monotonicity,[status(thm)],[279])).
% 155.18/99.95 tff(281,plain,
% 155.18/99.95 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))))),
% 155.18/99.95 inference(transitivity,[status(thm)],[280, 278])).
% 155.18/99.95 tff(282,plain,
% 155.18/99.95 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))))),
% 155.18/99.95 inference(quant_inst,[status(thm)],[])).
% 155.18/99.95 tff(283,plain,
% 155.18/99.95 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero)) | (~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero)))),
% 155.18/99.95 inference(modus_ponens,[status(thm)],[282, 281])).
% 155.18/99.95 tff(284,plain,
% 155.18/99.95 ($false),
% 155.18/99.95 inference(unit_resolution,[status(thm)],[283, 119, 277, 276, 275])).
% 155.18/99.95 tff(285,plain,((~less_equal(zero, divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero))), inference(lemma,lemma(discharge,[]))).
% 155.18/99.95 tff(286,plain,
% 155.18/99.95 ((divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero) | (~less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero), zero))),
% 155.18/99.95 inference(unit_resolution,[status(thm)],[285, 274])).
% 155.18/99.95 tff(287,plain,
% 155.18/99.95 (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero),
% 155.18/99.95 inference(unit_resolution,[status(thm)],[286, 270])).
% 155.18/99.95 tff(288,plain,
% 155.18/99.95 (((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero)) | less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))) <=> ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero)) | less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))),
% 155.18/99.95 inference(rewrite,[status(thm)],[])).
% 155.18/99.95 tff(289,plain,
% 155.18/99.95 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero)) | less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero))),
% 155.18/99.95 inference(quant_inst,[status(thm)],[])).
% 155.18/99.95 tff(290,plain,
% 155.18/99.95 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) = zero)) | less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero)),
% 155.18/99.96 inference(modus_ponens,[status(thm)],[289, 288])).
% 155.18/99.96 tff(291,plain,
% 155.18/99.96 ($false),
% 155.18/99.96 inference(unit_resolution,[status(thm)],[290, 136, 287, 192])).
% 155.18/99.96 tff(292,plain,(less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero)), inference(lemma,lemma(discharge,[]))).
% 155.18/99.96 tff(293,plain,
% 155.18/99.96 (divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = divide(divide(c, b), divide(divide(c, b), zero))),
% 155.18/99.96 inference(monotonicity,[status(thm)],[188])).
% 155.18/99.96 tff(294,plain,
% 155.18/99.96 (divide(divide(c, b), divide(divide(c, b), zero)) = divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.18/99.96 inference(symmetry,[status(thm)],[293])).
% 155.18/99.96 tff(295,plain,
% 155.18/99.96 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b))),
% 155.18/99.96 inference(quant_inst,[status(thm)],[])).
% 155.18/99.96 tff(296,plain,
% 155.18/99.96 (less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b))),
% 155.18/99.96 inference(unit_resolution,[status(thm)],[295, 18])).
% 155.18/99.96 tff(297,plain,
% 155.18/99.96 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b))) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b)) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b))) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b)) = zero))),
% 155.18/99.96 inference(rewrite,[status(thm)],[])).
% 155.18/99.96 tff(298,plain,
% 155.18/99.96 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b))) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b)) = zero))),
% 155.18/99.96 inference(quant_inst,[status(thm)],[])).
% 155.18/99.96 tff(299,plain,
% 155.18/99.96 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b))) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b)) = zero)),
% 155.18/99.96 inference(modus_ponens,[status(thm)],[298, 297])).
% 155.18/99.96 tff(300,plain,
% 155.18/99.96 ((~less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b))) | (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b)) = zero)),
% 155.18/99.96 inference(unit_resolution,[status(thm)],[299, 27])).
% 155.18/99.96 tff(301,plain,
% 155.18/99.96 (divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b)) = zero),
% 155.18/99.96 inference(unit_resolution,[status(thm)],[300, 296])).
% 155.18/99.96 tff(302,plain,
% 155.18/99.96 (zero = divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b))),
% 155.21/99.96 inference(symmetry,[status(thm)],[301])).
% 155.21/99.96 tff(303,plain,
% 155.21/99.96 (less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero))) <=> less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b)), divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))),
% 155.21/99.96 inference(monotonicity,[status(thm)],[302, 294])).
% 155.21/99.96 tff(304,plain,
% 155.21/99.96 (less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b)), divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))) <=> less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero)))),
% 155.21/99.96 inference(symmetry,[status(thm)],[303])).
% 155.21/99.96 tff(305,plain,
% 155.21/99.96 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b)), divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))),
% 155.21/99.96 inference(quant_inst,[status(thm)],[])).
% 155.21/99.96 tff(306,plain,
% 155.21/99.96 (less_equal(divide(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), divide(c, b)), divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))),
% 155.21/99.96 inference(unit_resolution,[status(thm)],[305, 18])).
% 155.21/99.96 tff(307,plain,
% 155.21/99.96 (less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero)))),
% 155.21/99.96 inference(modus_ponens,[status(thm)],[306, 304])).
% 155.21/99.96 tff(308,plain,
% 155.21/99.96 ((zero = divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))) <=> (divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)),
% 155.21/99.96 inference(commutativity,[status(thm)],[])).
% 155.21/99.96 tff(309,plain,
% 155.21/99.96 ((zero = divide(divide(c, b), divide(divide(c, b), zero))) <=> (zero = divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))),
% 155.21/99.96 inference(monotonicity,[status(thm)],[294])).
% 155.21/99.96 tff(310,plain,
% 155.21/99.96 ((zero = divide(divide(c, b), divide(divide(c, b), zero))) <=> (divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)),
% 155.21/99.96 inference(transitivity,[status(thm)],[309, 308])).
% 155.21/99.96 tff(311,plain,
% 155.21/99.96 ((divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero) <=> (zero = divide(divide(c, b), divide(divide(c, b), zero)))),
% 155.21/99.96 inference(symmetry,[status(thm)],[310])).
% 155.21/99.96 tff(312,plain,
% 155.21/99.96 ((~(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)) <=> (~(zero = divide(divide(c, b), divide(divide(c, b), zero))))),
% 155.21/99.96 inference(monotonicity,[status(thm)],[311])).
% 155.21/99.96 tff(313,assumption,(~(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)), introduced(assumption)).
% 155.21/99.96 tff(314,plain,
% 155.21/99.96 (~(zero = divide(divide(c, b), divide(divide(c, b), zero)))),
% 155.21/99.96 inference(modus_ponens,[status(thm)],[313, 312])).
% 155.21/99.96 tff(315,plain,
% 155.21/99.96 (less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero) <=> less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero)),
% 155.21/99.96 inference(monotonicity,[status(thm)],[294])).
% 155.21/99.96 tff(316,plain,
% 155.21/99.96 (less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero) <=> less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)),
% 155.21/99.96 inference(symmetry,[status(thm)],[315])).
% 155.21/99.96 tff(317,assumption,(less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero)), introduced(assumption)).
% 155.21/99.96 tff(318,plain,
% 155.21/99.96 (less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)),
% 155.21/99.96 inference(modus_ponens,[status(thm)],[317, 316])).
% 155.21/99.96 tff(319,plain,
% 155.21/99.96 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((zero = divide(divide(c, b), divide(divide(c, b), zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)) | (~less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero)))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (zero = divide(divide(c, b), divide(divide(c, b), zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)) | (~less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero)))))),
% 155.21/99.96 inference(rewrite,[status(thm)],[])).
% 155.21/99.96 tff(320,plain,
% 155.21/99.96 (((~less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero)))) | (zero = divide(divide(c, b), divide(divide(c, b), zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero))) <=> ((zero = divide(divide(c, b), divide(divide(c, b), zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)) | (~less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero)))))),
% 155.21/99.96 inference(rewrite,[status(thm)],[])).
% 155.21/99.96 tff(321,plain,
% 155.21/99.96 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero)))) | (zero = divide(divide(c, b), divide(divide(c, b), zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((zero = divide(divide(c, b), divide(divide(c, b), zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)) | (~less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero))))))),
% 155.21/99.96 inference(monotonicity,[status(thm)],[320])).
% 155.21/99.96 tff(322,plain,
% 155.21/99.96 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero)))) | (zero = divide(divide(c, b), divide(divide(c, b), zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (zero = divide(divide(c, b), divide(divide(c, b), zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)) | (~less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero)))))),
% 155.21/99.96 inference(transitivity,[status(thm)],[321, 319])).
% 155.21/99.96 tff(323,plain,
% 155.21/99.96 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero)))) | (zero = divide(divide(c, b), divide(divide(c, b), zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)))),
% 155.21/99.96 inference(quant_inst,[status(thm)],[])).
% 155.21/99.96 tff(324,plain,
% 155.21/99.96 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (zero = divide(divide(c, b), divide(divide(c, b), zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)) | (~less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero))))),
% 155.21/99.96 inference(modus_ponens,[status(thm)],[323, 322])).
% 155.21/99.96 tff(325,plain,
% 155.21/99.96 ((zero = divide(divide(c, b), divide(divide(c, b), zero))) | (~less_equal(divide(divide(c, b), divide(divide(c, b), zero)), zero)) | (~less_equal(zero, divide(divide(c, b), divide(divide(c, b), zero))))),
% 155.21/99.96 inference(unit_resolution,[status(thm)],[324, 119])).
% 155.21/99.96 tff(326,plain,
% 155.21/99.96 ($false),
% 155.21/99.96 inference(unit_resolution,[status(thm)],[325, 318, 314, 307])).
% 155.21/99.96 tff(327,plain,((~less_equal(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))), zero)) | (divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)), inference(lemma,lemma(discharge,[]))).
% 155.21/99.96 tff(328,plain,
% 155.21/99.96 (divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero),
% 155.21/99.96 inference(unit_resolution,[status(thm)],[327, 292])).
% 155.21/99.96 tff(329,plain,
% 155.21/99.96 (((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)) | less_equal(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))) <=> ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)) | less_equal(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))),
% 155.21/99.96 inference(rewrite,[status(thm)],[])).
% 155.21/99.96 tff(330,plain,
% 155.21/99.96 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)) | less_equal(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))))),
% 155.21/99.96 inference(quant_inst,[status(thm)],[])).
% 155.21/99.96 tff(331,plain,
% 155.21/99.96 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)) | less_equal(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.21/99.96 inference(modus_ponens,[status(thm)],[330, 329])).
% 155.21/99.96 tff(332,plain,
% 155.21/99.96 ((~(divide(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a))))) = zero)) | less_equal(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.21/99.96 inference(unit_resolution,[status(thm)],[331, 136])).
% 155.21/99.96 tff(333,plain,
% 155.21/99.96 (less_equal(divide(c, b), divide(divide(c, b), divide(divide(divide(c, b), divide(c, a)), divide(divide(c, b), divide(c, a)))))),
% 155.21/99.96 inference(unit_resolution,[status(thm)],[332, 328])).
% 155.21/99.96 tff(334,plain,
% 155.21/99.96 (less_equal(divide(c, b), divide(divide(c, b), zero))),
% 155.21/99.96 inference(modus_ponens,[status(thm)],[333, 191])).
% 155.21/99.96 tff(335,assumption,(~less_equal(divide(c, b), divide(divide(c, b), zero))), introduced(assumption)).
% 155.21/99.96 tff(336,plain,
% 155.21/99.96 ($false),
% 155.21/99.96 inference(unit_resolution,[status(thm)],[335, 334])).
% 155.21/99.96 tff(337,plain,(less_equal(divide(c, b), divide(divide(c, b), zero))), inference(lemma,lemma(discharge,[]))).
% 155.21/99.96 tff(338,assumption,(~(divide(divide(c, b), zero) = divide(c, b))), introduced(assumption)).
% 155.21/99.96 tff(339,plain,
% 155.21/99.96 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(c, b), zero), divide(c, b))) | (~less_equal(divide(c, b), divide(divide(c, b), zero))) | (divide(divide(c, b), zero) = divide(c, b)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (~less_equal(divide(divide(c, b), zero), divide(c, b))) | (~less_equal(divide(c, b), divide(divide(c, b), zero))) | (divide(divide(c, b), zero) = divide(c, b)))),
% 155.21/99.96 inference(rewrite,[status(thm)],[])).
% 155.21/99.96 tff(340,plain,
% 155.21/99.96 (((~less_equal(divide(divide(c, b), zero), divide(c, b))) | (divide(divide(c, b), zero) = divide(c, b)) | (~less_equal(divide(c, b), divide(divide(c, b), zero)))) <=> ((~less_equal(divide(divide(c, b), zero), divide(c, b))) | (~less_equal(divide(c, b), divide(divide(c, b), zero))) | (divide(divide(c, b), zero) = divide(c, b)))),
% 155.21/99.96 inference(rewrite,[status(thm)],[])).
% 155.21/99.96 tff(341,plain,
% 155.21/99.96 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(c, b), zero), divide(c, b))) | (divide(divide(c, b), zero) = divide(c, b)) | (~less_equal(divide(c, b), divide(divide(c, b), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(c, b), zero), divide(c, b))) | (~less_equal(divide(c, b), divide(divide(c, b), zero))) | (divide(divide(c, b), zero) = divide(c, b))))),
% 155.21/99.97 inference(monotonicity,[status(thm)],[340])).
% 155.21/99.97 tff(342,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(c, b), zero), divide(c, b))) | (divide(divide(c, b), zero) = divide(c, b)) | (~less_equal(divide(c, b), divide(divide(c, b), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (~less_equal(divide(divide(c, b), zero), divide(c, b))) | (~less_equal(divide(c, b), divide(divide(c, b), zero))) | (divide(divide(c, b), zero) = divide(c, b)))),
% 155.21/99.97 inference(transitivity,[status(thm)],[341, 339])).
% 155.21/99.97 tff(343,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(c, b), zero), divide(c, b))) | (divide(divide(c, b), zero) = divide(c, b)) | (~less_equal(divide(c, b), divide(divide(c, b), zero))))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(344,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (~less_equal(divide(divide(c, b), zero), divide(c, b))) | (~less_equal(divide(c, b), divide(divide(c, b), zero))) | (divide(divide(c, b), zero) = divide(c, b))),
% 155.21/99.97 inference(modus_ponens,[status(thm)],[343, 342])).
% 155.21/99.97 tff(345,plain,
% 155.21/99.97 ($false),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[344, 119, 80, 338, 337])).
% 155.21/99.97 tff(346,plain,(divide(divide(c, b), zero) = divide(c, b)), inference(lemma,lemma(discharge,[]))).
% 155.21/99.97 tff(347,plain,
% 155.21/99.97 (divide(c, b) = divide(divide(c, b), zero)),
% 155.21/99.97 inference(symmetry,[status(thm)],[346])).
% 155.21/99.97 tff(348,plain,
% 155.21/99.97 (divide(divide(c, b), divide(c, a)) = divide(divide(divide(c, b), zero), divide(c, a))),
% 155.21/99.97 inference(monotonicity,[status(thm)],[347])).
% 155.21/99.97 tff(349,plain,
% 155.21/99.97 (divide(divide(divide(c, b), zero), divide(c, a)) = divide(divide(c, b), divide(c, a))),
% 155.21/99.97 inference(symmetry,[status(thm)],[348])).
% 155.21/99.97 tff(350,plain,
% 155.21/99.97 (divide(divide(divide(divide(c, b), zero), divide(c, a)), zero) = divide(divide(divide(c, b), divide(c, a)), zero)),
% 155.21/99.97 inference(monotonicity,[status(thm)],[349])).
% 155.21/99.97 tff(351,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(c, a), b), divide(c, a))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(352,plain,
% 155.21/99.97 (less_equal(divide(divide(c, a), b), divide(c, a))),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[351, 18])).
% 155.21/99.97 tff(353,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, a), b), divide(c, a))) | (divide(divide(divide(c, a), b), divide(c, a)) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, a), b), divide(c, a))) | (divide(divide(divide(c, a), b), divide(c, a)) = zero))),
% 155.21/99.97 inference(rewrite,[status(thm)],[])).
% 155.21/99.97 tff(354,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, a), b), divide(c, a))) | (divide(divide(divide(c, a), b), divide(c, a)) = zero))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(355,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, a), b), divide(c, a))) | (divide(divide(divide(c, a), b), divide(c, a)) = zero)),
% 155.21/99.97 inference(modus_ponens,[status(thm)],[354, 353])).
% 155.21/99.97 tff(356,plain,
% 155.21/99.97 (divide(divide(divide(c, a), b), divide(c, a)) = zero),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[355, 27, 352])).
% 155.21/99.97 tff(357,plain,
% 155.21/99.97 (divide(divide(divide(divide(c, b), zero), divide(c, a)), divide(divide(divide(c, a), b), divide(c, a))) = divide(divide(divide(divide(c, b), zero), divide(c, a)), zero)),
% 155.21/99.97 inference(monotonicity,[status(thm)],[356])).
% 155.21/99.97 tff(358,plain,
% 155.21/99.97 (divide(divide(divide(divide(c, b), zero), divide(c, a)), divide(divide(divide(c, a), b), divide(c, a))) = divide(divide(divide(c, b), divide(c, a)), zero)),
% 155.21/99.97 inference(transitivity,[status(thm)],[357, 350])).
% 155.21/99.97 tff(359,plain,
% 155.21/99.97 (less_equal(divide(divide(divide(divide(c, b), zero), divide(c, a)), divide(divide(divide(c, a), b), divide(c, a))), divide(divide(divide(divide(c, b), zero), divide(divide(c, a), b)), divide(c, a))) <=> less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)),
% 155.21/99.97 inference(monotonicity,[status(thm)],[358, 63])).
% 155.21/99.97 tff(360,plain,
% 155.21/99.97 (less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero) <=> less_equal(divide(divide(divide(divide(c, b), zero), divide(c, a)), divide(divide(divide(c, a), b), divide(c, a))), divide(divide(divide(divide(c, b), zero), divide(divide(c, a), b)), divide(c, a)))),
% 155.21/99.97 inference(symmetry,[status(thm)],[359])).
% 155.21/99.97 tff(361,plain,
% 155.21/99.97 ((~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)) <=> (~less_equal(divide(divide(divide(divide(c, b), zero), divide(c, a)), divide(divide(divide(c, a), b), divide(c, a))), divide(divide(divide(divide(c, b), zero), divide(divide(c, a), b)), divide(c, a))))),
% 155.21/99.97 inference(monotonicity,[status(thm)],[360])).
% 155.21/99.97 tff(362,assumption,(~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)), introduced(assumption)).
% 155.21/99.97 tff(363,plain,
% 155.21/99.97 (~less_equal(divide(divide(divide(divide(c, b), zero), divide(c, a)), divide(divide(divide(c, a), b), divide(c, a))), divide(divide(divide(divide(c, b), zero), divide(divide(c, a), b)), divide(c, a)))),
% 155.21/99.97 inference(modus_ponens,[status(thm)],[362, 361])).
% 155.21/99.97 tff(364,assumption,(less_equal(divide(divide(divide(divide(c, b), zero), divide(c, a)), divide(divide(divide(c, a), b), divide(c, a))), divide(divide(divide(divide(c, b), zero), divide(divide(c, a), b)), divide(c, a)))), introduced(assumption)).
% 155.21/99.97 tff(365,plain,
% 155.21/99.97 ($false),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[364, 363])).
% 155.21/99.97 tff(366,plain,((~less_equal(divide(divide(divide(divide(c, b), zero), divide(c, a)), divide(divide(divide(c, a), b), divide(c, a))), divide(divide(divide(divide(c, b), zero), divide(divide(c, a), b)), divide(c, a)))) | less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)), inference(lemma,lemma(discharge,[]))).
% 155.21/99.97 tff(367,plain,
% 155.21/99.97 (less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[366, 11])).
% 155.21/99.97 tff(368,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a)))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(369,plain,
% 155.21/99.97 (less_equal(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a)))),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[368, 18])).
% 155.21/99.97 tff(370,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a)))) | (divide(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a))) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a)))) | (divide(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a))) = zero))),
% 155.21/99.97 inference(rewrite,[status(thm)],[])).
% 155.21/99.97 tff(371,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a)))) | (divide(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a))) = zero))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(372,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a)))) | (divide(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a))) = zero)),
% 155.21/99.97 inference(modus_ponens,[status(thm)],[371, 370])).
% 155.21/99.97 tff(373,plain,
% 155.21/99.97 (divide(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a))) = zero),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[372, 27, 369])).
% 155.21/99.97 tff(374,plain,
% 155.21/99.97 (zero = divide(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a)))),
% 155.21/99.97 inference(symmetry,[status(thm)],[373])).
% 155.21/99.97 tff(375,plain,
% 155.21/99.97 (less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero)) <=> less_equal(divide(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, a)), zero))),
% 155.21/99.97 inference(monotonicity,[status(thm)],[374])).
% 155.21/99.97 tff(376,plain,
% 155.21/99.97 (less_equal(divide(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, a)), zero)) <=> less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero))),
% 155.21/99.97 inference(symmetry,[status(thm)],[375])).
% 155.21/99.97 tff(377,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, a)), zero))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(378,plain,
% 155.21/99.97 (less_equal(divide(divide(divide(divide(c, b), divide(c, a)), zero), divide(divide(c, b), divide(c, a))), divide(divide(divide(c, b), divide(c, a)), zero))),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[377, 18])).
% 155.21/99.97 tff(379,plain,
% 155.21/99.97 (less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero))),
% 155.21/99.97 inference(modus_ponens,[status(thm)],[378, 376])).
% 155.21/99.97 tff(380,assumption,(~(divide(divide(divide(c, b), divide(c, a)), zero) = zero)), introduced(assumption)).
% 155.21/99.97 tff(381,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(divide(c, b), divide(c, a)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(c, a)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)))),
% 155.21/99.97 inference(rewrite,[status(thm)],[])).
% 155.21/99.97 tff(382,plain,
% 155.21/99.97 (((~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)) | (divide(divide(divide(c, b), divide(c, a)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero)))) <=> ((divide(divide(divide(c, b), divide(c, a)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)))),
% 155.21/99.97 inference(rewrite,[status(thm)],[])).
% 155.21/99.97 tff(383,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)) | (divide(divide(divide(c, b), divide(c, a)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(divide(c, b), divide(c, a)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero))))),
% 155.21/99.97 inference(monotonicity,[status(thm)],[382])).
% 155.21/99.97 tff(384,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)) | (divide(divide(divide(c, b), divide(c, a)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(c, a)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)))),
% 155.21/99.97 inference(transitivity,[status(thm)],[383, 381])).
% 155.21/99.97 tff(385,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero)) | (divide(divide(divide(c, b), divide(c, a)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero))))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(386,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(divide(c, b), divide(c, a)), zero) = zero) | (~less_equal(zero, divide(divide(divide(c, b), divide(c, a)), zero))) | (~less_equal(divide(divide(divide(c, b), divide(c, a)), zero), zero))),
% 155.21/99.97 inference(modus_ponens,[status(thm)],[385, 384])).
% 155.21/99.97 tff(387,plain,
% 155.21/99.97 ($false),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[386, 119, 380, 379, 367])).
% 155.21/99.97 tff(388,plain,(divide(divide(divide(c, b), divide(c, a)), zero) = zero), inference(lemma,lemma(discharge,[]))).
% 155.21/99.97 tff(389,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(divide(c, b), divide(c, a)), zero) = zero)) | less_equal(divide(divide(c, b), divide(c, a)), zero))) <=> ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(divide(c, b), divide(c, a)), zero) = zero)) | less_equal(divide(divide(c, b), divide(c, a)), zero))),
% 155.21/99.97 inference(rewrite,[status(thm)],[])).
% 155.21/99.97 tff(390,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(divide(c, b), divide(c, a)), zero) = zero)) | less_equal(divide(divide(c, b), divide(c, a)), zero))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(391,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(divide(c, b), divide(c, a)), zero) = zero)) | less_equal(divide(divide(c, b), divide(c, a)), zero)),
% 155.21/99.97 inference(modus_ponens,[status(thm)],[390, 389])).
% 155.21/99.97 tff(392,plain,
% 155.21/99.97 ((~(divide(divide(divide(c, b), divide(c, a)), zero) = zero)) | less_equal(divide(divide(c, b), divide(c, a)), zero)),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[391, 136])).
% 155.21/99.97 tff(393,plain,
% 155.21/99.97 (less_equal(divide(divide(c, b), divide(c, a)), zero)),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[392, 388])).
% 155.21/99.97 tff(394,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(c, b), divide(c, a)), divide(c, b))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(395,plain,
% 155.21/99.97 (less_equal(divide(divide(c, b), divide(c, a)), divide(c, b))),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[394, 18])).
% 155.21/99.97 tff(396,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), divide(c, a)), divide(c, b))) | (divide(divide(divide(c, b), divide(c, a)), divide(c, b)) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), divide(c, a)), divide(c, b))) | (divide(divide(divide(c, b), divide(c, a)), divide(c, b)) = zero))),
% 155.21/99.97 inference(rewrite,[status(thm)],[])).
% 155.21/99.97 tff(397,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(c, b), divide(c, a)), divide(c, b))) | (divide(divide(divide(c, b), divide(c, a)), divide(c, b)) = zero))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(398,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(c, b), divide(c, a)), divide(c, b))) | (divide(divide(divide(c, b), divide(c, a)), divide(c, b)) = zero)),
% 155.21/99.97 inference(modus_ponens,[status(thm)],[397, 396])).
% 155.21/99.97 tff(399,plain,
% 155.21/99.97 (divide(divide(divide(c, b), divide(c, a)), divide(c, b)) = zero),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[398, 27, 395])).
% 155.21/99.97 tff(400,plain,
% 155.21/99.97 (zero = divide(divide(divide(c, b), divide(c, a)), divide(c, b))),
% 155.21/99.97 inference(symmetry,[status(thm)],[399])).
% 155.21/99.97 tff(401,plain,
% 155.21/99.97 (less_equal(zero, divide(divide(c, b), divide(c, a))) <=> less_equal(divide(divide(divide(c, b), divide(c, a)), divide(c, b)), divide(divide(c, b), divide(c, a)))),
% 155.21/99.97 inference(monotonicity,[status(thm)],[400])).
% 155.21/99.97 tff(402,plain,
% 155.21/99.97 (less_equal(divide(divide(divide(c, b), divide(c, a)), divide(c, b)), divide(divide(c, b), divide(c, a))) <=> less_equal(zero, divide(divide(c, b), divide(c, a)))),
% 155.21/99.97 inference(symmetry,[status(thm)],[401])).
% 155.21/99.97 tff(403,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(divide(c, b), divide(c, a)), divide(c, b)), divide(divide(c, b), divide(c, a)))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(404,plain,
% 155.21/99.97 (less_equal(divide(divide(divide(c, b), divide(c, a)), divide(c, b)), divide(divide(c, b), divide(c, a)))),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[403, 18])).
% 155.21/99.97 tff(405,plain,
% 155.21/99.97 (less_equal(zero, divide(divide(c, b), divide(c, a)))),
% 155.21/99.97 inference(modus_ponens,[status(thm)],[404, 402])).
% 155.21/99.97 tff(406,plain,
% 155.21/99.97 ((~less_equal(divide(c, b), divide(c, a))) <=> (~less_equal(divide(c, b), divide(c, a)))),
% 155.21/99.97 inference(rewrite,[status(thm)],[])).
% 155.21/99.97 tff(407,axiom,(~less_equal(divide(c, b), divide(c, a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_c_divide_b_LE_c_divide_a')).
% 155.21/99.97 tff(408,plain,
% 155.21/99.97 (~less_equal(divide(c, b), divide(c, a))),
% 155.21/99.97 inference(modus_ponens,[status(thm)],[407, 406])).
% 155.21/99.97 tff(409,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(c, b), divide(c, a)) = zero)) | less_equal(divide(c, b), divide(c, a)))) <=> ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(c, b), divide(c, a)) = zero)) | less_equal(divide(c, b), divide(c, a)))),
% 155.21/99.97 inference(rewrite,[status(thm)],[])).
% 155.21/99.97 tff(410,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(c, b), divide(c, a)) = zero)) | less_equal(divide(c, b), divide(c, a)))),
% 155.21/99.97 inference(quant_inst,[status(thm)],[])).
% 155.21/99.97 tff(411,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(c, b), divide(c, a)) = zero)) | less_equal(divide(c, b), divide(c, a))),
% 155.21/99.97 inference(modus_ponens,[status(thm)],[410, 409])).
% 155.21/99.97 tff(412,plain,
% 155.21/99.97 (~(divide(divide(c, b), divide(c, a)) = zero)),
% 155.21/99.97 inference(unit_resolution,[status(thm)],[411, 136, 408])).
% 155.21/99.97 tff(413,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(c, b), divide(c, a)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, a)))) | (~less_equal(divide(divide(c, b), divide(c, a)), zero)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(c, b), divide(c, a)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, a)))) | (~less_equal(divide(divide(c, b), divide(c, a)), zero)))),
% 155.21/99.97 inference(rewrite,[status(thm)],[])).
% 155.21/99.97 tff(414,plain,
% 155.21/99.97 (((~less_equal(divide(divide(c, b), divide(c, a)), zero)) | (divide(divide(c, b), divide(c, a)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, a))))) <=> ((divide(divide(c, b), divide(c, a)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, a)))) | (~less_equal(divide(divide(c, b), divide(c, a)), zero)))),
% 155.21/99.97 inference(rewrite,[status(thm)],[])).
% 155.21/99.97 tff(415,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(c, b), divide(c, a)), zero)) | (divide(divide(c, b), divide(c, a)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, a)))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(c, b), divide(c, a)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, a)))) | (~less_equal(divide(divide(c, b), divide(c, a)), zero))))),
% 155.21/99.97 inference(monotonicity,[status(thm)],[414])).
% 155.21/99.97 tff(416,plain,
% 155.21/99.97 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(c, b), divide(c, a)), zero)) | (divide(divide(c, b), divide(c, a)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, a)))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(c, b), divide(c, a)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, a)))) | (~less_equal(divide(divide(c, b), divide(c, a)), zero)))),
% 155.21/99.97 inference(transitivity,[status(thm)],[415, 413])).
% 155.21/99.97 tff(417,plain,
% 155.21/99.97 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(c, b), divide(c, a)), zero)) | (divide(divide(c, b), divide(c, a)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, a)))))),
% 155.21/99.98 inference(quant_inst,[status(thm)],[])).
% 155.21/99.98 tff(418,plain,
% 155.21/99.98 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(c, b), divide(c, a)) = zero) | (~less_equal(zero, divide(divide(c, b), divide(c, a)))) | (~less_equal(divide(divide(c, b), divide(c, a)), zero))),
% 155.21/99.98 inference(modus_ponens,[status(thm)],[417, 416])).
% 155.21/99.98 tff(419,plain,
% 155.21/99.98 ($false),
% 155.21/99.98 inference(unit_resolution,[status(thm)],[418, 119, 412, 405, 393])).
% 155.21/99.98 % SZS output end Proof
%------------------------------------------------------------------------------