TSTP Solution File: HEN003-4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HEN003-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 22:39:45 EDT 2022
% Result : Unsatisfiable 0.22s 0.44s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : HEN003-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n003.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 31 21:41:08 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 0.22/0.44 % SZS status Unsatisfiable
% 0.22/0.44 % SZS output start Proof
% 0.22/0.44 tff(less_equal_type, type, (
% 0.22/0.44 less_equal: ( $i * $i ) > $o)).
% 0.22/0.44 tff(zero_type, type, (
% 0.22/0.44 zero: $i)).
% 0.22/0.44 tff(divide_type, type, (
% 0.22/0.44 divide: ( $i * $i ) > $i)).
% 0.22/0.44 tff(a_type, type, (
% 0.22/0.44 a: $i)).
% 0.22/0.44 tff(1,plain,
% 0.22/0.44 (^[Y: $i, X: $i] : refl(less_equal(divide(X, Y), X) <=> less_equal(divide(X, Y), X))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(2,plain,
% 0.22/0.44 (![Y: $i, X: $i] : less_equal(divide(X, Y), X) <=> ![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 0.22/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.44 tff(3,plain,
% 0.22/0.44 (![Y: $i, X: $i] : less_equal(divide(X, Y), X) <=> ![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(4,axiom,(![Y: $i, X: $i] : less_equal(divide(X, Y), X)), file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax','quotient_smaller_than_numerator')).
% 0.22/0.44 tff(5,plain,
% 0.22/0.44 (![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.44 tff(6,plain,(
% 0.22/0.44 ![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 0.22/0.44 inference(skolemize,[status(sab)],[5])).
% 0.22/0.44 tff(7,plain,
% 0.22/0.44 (![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.44 tff(8,plain,
% 0.22/0.44 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(a, zero), a)),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(9,plain,
% 0.22/0.44 (less_equal(divide(a, zero), a)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.22/0.44 tff(10,plain,
% 0.22/0.44 (^[Y: $i, X: $i] : refl(((~less_equal(X, Y)) | (divide(X, Y) = zero)) <=> ((~less_equal(X, Y)) | (divide(X, Y) = zero)))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(11,plain,
% 0.22/0.44 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.44 tff(12,plain,
% 0.22/0.44 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(13,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')).
% 0.22/0.44 tff(14,plain,
% 0.22/0.44 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.22/0.44 tff(15,plain,(
% 0.22/0.44 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 0.22/0.44 inference(skolemize,[status(sab)],[14])).
% 0.22/0.44 tff(16,plain,
% 0.22/0.44 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.22/0.44 tff(17,plain,
% 0.22/0.44 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(a, zero), a)) | (divide(divide(a, zero), a) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(a, zero), a)) | (divide(divide(a, zero), a) = zero))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(18,plain,
% 0.22/0.44 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(a, zero), a)) | (divide(divide(a, zero), a) = zero))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(19,plain,
% 0.22/0.44 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(a, zero), a)) | (divide(divide(a, zero), a) = zero)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.44 tff(20,plain,
% 0.22/0.44 ((~less_equal(divide(a, zero), a)) | (divide(divide(a, zero), a) = zero)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[19, 16])).
% 0.22/0.44 tff(21,plain,
% 0.22/0.44 (divide(divide(a, zero), a) = zero),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[20, 9])).
% 0.22/0.44 tff(22,plain,
% 0.22/0.44 (zero = divide(divide(a, zero), a)),
% 0.22/0.44 inference(symmetry,[status(thm)],[21])).
% 0.22/0.44 tff(23,plain,
% 0.22/0.44 (^[X: $i] : refl((divide(zero, X) = zero) <=> (divide(zero, X) = zero))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(24,plain,
% 0.22/0.44 (![X: $i] : (divide(zero, X) = zero) <=> ![X: $i] : (divide(zero, X) = zero)),
% 0.22/0.44 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.44 tff(25,plain,
% 0.22/0.44 (![X: $i] : (divide(zero, X) = zero) <=> ![X: $i] : (divide(zero, X) = zero)),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(26,axiom,(![X: $i] : (divide(zero, X) = zero)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','zero_divide_anything_is_zero')).
% 0.22/0.44 tff(27,plain,
% 0.22/0.44 (![X: $i] : (divide(zero, X) = zero)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.22/0.44 tff(28,plain,(
% 0.22/0.44 ![X: $i] : (divide(zero, X) = zero)),
% 0.22/0.44 inference(skolemize,[status(sab)],[27])).
% 0.22/0.44 tff(29,plain,
% 0.22/0.44 (![X: $i] : (divide(zero, X) = zero)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.22/0.44 tff(30,plain,
% 0.22/0.44 ((~![X: $i] : (divide(zero, X) = zero)) | (divide(zero, a) = zero)),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(31,plain,
% 0.22/0.44 (divide(zero, a) = zero),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.22/0.44 tff(32,plain,
% 0.22/0.44 (divide(divide(a, a), divide(zero, a)) = divide(divide(a, a), zero)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[31])).
% 0.22/0.44 tff(33,plain,
% 0.22/0.44 (divide(divide(a, a), zero) = divide(divide(a, a), divide(zero, a))),
% 0.22/0.44 inference(symmetry,[status(thm)],[32])).
% 0.22/0.44 tff(34,plain,
% 0.22/0.44 (less_equal(divide(divide(a, a), zero), zero) <=> less_equal(divide(divide(a, a), divide(zero, a)), divide(divide(a, zero), a))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[33, 22])).
% 0.22/0.44 tff(35,plain,
% 0.22/0.44 (less_equal(divide(divide(a, a), divide(zero, a)), divide(divide(a, zero), a)) <=> less_equal(divide(divide(a, a), zero), zero)),
% 0.22/0.44 inference(symmetry,[status(thm)],[34])).
% 0.22/0.44 tff(36,plain,
% 0.22/0.44 (^[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)))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(37,plain,
% 0.22/0.44 (![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))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[36])).
% 0.22/0.44 tff(38,plain,
% 0.22/0.44 (![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))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(39,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')).
% 0.22/0.44 tff(40,plain,
% 0.22/0.44 (![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.22/0.44 tff(41,plain,(
% 0.22/0.44 ![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))),
% 0.22/0.44 inference(skolemize,[status(sab)],[40])).
% 0.22/0.44 tff(42,plain,
% 0.22/0.44 (![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.22/0.44 tff(43,plain,
% 0.22/0.44 ((~![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))) | less_equal(divide(divide(a, a), divide(zero, a)), divide(divide(a, zero), a))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(44,plain,
% 0.22/0.44 (less_equal(divide(divide(a, a), divide(zero, a)), divide(divide(a, zero), a))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.22/0.44 tff(45,plain,
% 0.22/0.44 (less_equal(divide(divide(a, a), zero), zero)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[44, 35])).
% 0.22/0.44 tff(46,assumption,(~less_equal(divide(divide(a, a), zero), zero)), introduced(assumption)).
% 0.22/0.44 tff(47,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.22/0.44 tff(48,plain,(less_equal(divide(divide(a, a), zero), zero)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(49,assumption,(less_equal(divide(divide(a, a), zero), zero)), introduced(assumption)).
% 0.22/0.44 tff(50,plain,
% 0.22/0.44 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(a, a), zero), divide(a, a))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(51,plain,
% 0.22/0.44 (less_equal(divide(divide(a, a), zero), divide(a, a))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[50, 7])).
% 0.22/0.44 tff(52,plain,
% 0.22/0.45 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(a, a), zero), divide(a, a))) | (divide(divide(divide(a, a), zero), divide(a, a)) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(a, a), zero), divide(a, a))) | (divide(divide(divide(a, a), zero), divide(a, a)) = zero))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(53,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(divide(a, a), zero), divide(a, a))) | (divide(divide(divide(a, a), zero), divide(a, a)) = zero))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(54,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(divide(a, a), zero), divide(a, a))) | (divide(divide(divide(a, a), zero), divide(a, a)) = zero)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.22/0.45 tff(55,plain,
% 0.22/0.45 (divide(divide(divide(a, a), zero), divide(a, a)) = zero),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[54, 16, 51])).
% 0.22/0.45 tff(56,plain,
% 0.22/0.45 (zero = divide(divide(divide(a, a), zero), divide(a, a))),
% 0.22/0.45 inference(symmetry,[status(thm)],[55])).
% 0.22/0.45 tff(57,plain,
% 0.22/0.45 (less_equal(zero, divide(divide(a, a), zero)) <=> less_equal(divide(divide(divide(a, a), zero), divide(a, a)), divide(divide(a, a), zero))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[56])).
% 0.22/0.45 tff(58,plain,
% 0.22/0.45 (less_equal(divide(divide(divide(a, a), zero), divide(a, a)), divide(divide(a, a), zero)) <=> less_equal(zero, divide(divide(a, a), zero))),
% 0.22/0.45 inference(symmetry,[status(thm)],[57])).
% 0.22/0.45 tff(59,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(divide(a, a), zero), divide(a, a)), divide(divide(a, a), zero))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(60,plain,
% 0.22/0.45 (less_equal(divide(divide(divide(a, a), zero), divide(a, a)), divide(divide(a, a), zero))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[59, 7])).
% 0.22/0.45 tff(61,plain,
% 0.22/0.45 (less_equal(zero, divide(divide(a, a), zero))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[60, 58])).
% 0.22/0.45 tff(62,assumption,(~(divide(divide(a, a), zero) = zero)), introduced(assumption)).
% 0.22/0.45 tff(63,plain,
% 0.22/0.45 (![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)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(64,plain,
% 0.22/0.45 (![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)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(65,plain,
% 0.22/0.45 (^[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))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(66,plain,
% 0.22/0.45 (![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)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[65])).
% 0.22/0.45 tff(67,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')).
% 0.22/0.45 tff(68,plain,
% 0.22/0.45 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.22/0.45 tff(69,plain,
% 0.22/0.45 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.22/0.45 tff(70,plain,(
% 0.22/0.45 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.22/0.45 inference(skolemize,[status(sab)],[69])).
% 0.22/0.45 tff(71,plain,
% 0.22/0.45 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.22/0.45 tff(72,plain,
% 0.22/0.45 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(a, a), zero) = zero) | (~less_equal(divide(divide(a, a), zero), zero)) | (~less_equal(zero, divide(divide(a, a), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(a, a), zero) = zero) | (~less_equal(divide(divide(a, a), zero), zero)) | (~less_equal(zero, divide(divide(a, a), zero))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(73,plain,
% 0.22/0.45 (((~less_equal(divide(divide(a, a), zero), zero)) | (divide(divide(a, a), zero) = zero) | (~less_equal(zero, divide(divide(a, a), zero)))) <=> ((divide(divide(a, a), zero) = zero) | (~less_equal(divide(divide(a, a), zero), zero)) | (~less_equal(zero, divide(divide(a, a), zero))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(74,plain,
% 0.22/0.45 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(a, a), zero), zero)) | (divide(divide(a, a), zero) = zero) | (~less_equal(zero, divide(divide(a, a), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(a, a), zero) = zero) | (~less_equal(divide(divide(a, a), zero), zero)) | (~less_equal(zero, divide(divide(a, a), zero)))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[73])).
% 0.22/0.45 tff(75,plain,
% 0.22/0.45 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(a, a), zero), zero)) | (divide(divide(a, a), zero) = zero) | (~less_equal(zero, divide(divide(a, a), zero))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(a, a), zero) = zero) | (~less_equal(divide(divide(a, a), zero), zero)) | (~less_equal(zero, divide(divide(a, a), zero))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[74, 72])).
% 0.22/0.45 tff(76,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(divide(a, a), zero), zero)) | (divide(divide(a, a), zero) = zero) | (~less_equal(zero, divide(divide(a, a), zero))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(77,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(a, a), zero) = zero) | (~less_equal(divide(divide(a, a), zero), zero)) | (~less_equal(zero, divide(divide(a, a), zero)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.22/0.45 tff(78,plain,
% 0.22/0.45 ((~less_equal(divide(divide(a, a), zero), zero)) | (~less_equal(zero, divide(divide(a, a), zero)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[77, 71, 62])).
% 0.22/0.45 tff(79,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[78, 61, 49])).
% 0.22/0.45 tff(80,plain,((~less_equal(divide(divide(a, a), zero), zero)) | (divide(divide(a, a), zero) = zero)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(81,plain,
% 0.22/0.45 (divide(divide(a, a), zero) = zero),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[80, 48])).
% 0.22/0.45 tff(82,plain,
% 0.22/0.45 (^[Y: $i, X: $i] : refl(((~(divide(X, Y) = zero)) | less_equal(X, Y)) <=> ((~(divide(X, Y) = zero)) | less_equal(X, Y)))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(83,plain,
% 0.22/0.45 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[82])).
% 0.22/0.45 tff(84,plain,
% 0.22/0.45 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(85,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')).
% 0.22/0.45 tff(86,plain,
% 0.22/0.45 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.22/0.45 tff(87,plain,(
% 0.22/0.45 ![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 0.22/0.45 inference(skolemize,[status(sab)],[86])).
% 0.22/0.45 tff(88,plain,
% 0.22/0.45 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.22/0.45 tff(89,plain,
% 0.22/0.45 (((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(a, a), zero) = zero)) | less_equal(divide(a, a), zero))) <=> ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(a, a), zero) = zero)) | less_equal(divide(a, a), zero))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(90,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(a, a), zero) = zero)) | less_equal(divide(a, a), zero))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(91,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(a, a), zero) = zero)) | less_equal(divide(a, a), zero)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.22/0.45 tff(92,plain,
% 0.22/0.45 ((~(divide(divide(a, a), zero) = zero)) | less_equal(divide(a, a), zero)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[91, 88])).
% 0.22/0.45 tff(93,plain,
% 0.22/0.45 (less_equal(divide(a, a), zero)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[92, 81])).
% 0.22/0.45 tff(94,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(a, a), a)),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(95,plain,
% 0.22/0.45 (less_equal(divide(a, a), a)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[94, 7])).
% 0.22/0.45 tff(96,plain,
% 0.22/0.45 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(a, a), a)) | (divide(divide(a, a), a) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(a, a), a)) | (divide(divide(a, a), a) = zero))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(97,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(a, a), a)) | (divide(divide(a, a), a) = zero))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(98,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(a, a), a)) | (divide(divide(a, a), a) = zero)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.22/0.45 tff(99,plain,
% 0.22/0.45 (divide(divide(a, a), a) = zero),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[98, 16, 95])).
% 0.22/0.45 tff(100,plain,
% 0.22/0.45 (zero = divide(divide(a, a), a)),
% 0.22/0.45 inference(symmetry,[status(thm)],[99])).
% 0.22/0.45 tff(101,plain,
% 0.22/0.45 (less_equal(zero, divide(a, a)) <=> less_equal(divide(divide(a, a), a), divide(a, a))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[100])).
% 0.22/0.45 tff(102,plain,
% 0.22/0.45 (less_equal(divide(divide(a, a), a), divide(a, a)) <=> less_equal(zero, divide(a, a))),
% 0.22/0.45 inference(symmetry,[status(thm)],[101])).
% 0.22/0.45 tff(103,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(a, a), a), divide(a, a))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(104,plain,
% 0.22/0.45 (less_equal(divide(divide(a, a), a), divide(a, a))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[103, 7])).
% 0.22/0.45 tff(105,plain,
% 0.22/0.45 (less_equal(zero, divide(a, a))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[104, 102])).
% 0.22/0.45 tff(106,plain,
% 0.22/0.45 ((~(divide(a, a) = zero)) <=> (~(divide(a, a) = zero))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(107,axiom,(~(divide(a, a) = zero)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_x_divide_x_is_zero')).
% 0.22/0.45 tff(108,plain,
% 0.22/0.45 (~(divide(a, a) = zero)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.22/0.45 tff(109,plain,
% 0.22/0.45 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(a, a) = zero) | (~less_equal(zero, divide(a, a))) | (~less_equal(divide(a, a), zero)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(a, a) = zero) | (~less_equal(zero, divide(a, a))) | (~less_equal(divide(a, a), zero)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(110,plain,
% 0.22/0.46 (((~less_equal(divide(a, a), zero)) | (divide(a, a) = zero) | (~less_equal(zero, divide(a, a)))) <=> ((divide(a, a) = zero) | (~less_equal(zero, divide(a, a))) | (~less_equal(divide(a, a), zero)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(111,plain,
% 0.22/0.46 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(a, a), zero)) | (divide(a, a) = zero) | (~less_equal(zero, divide(a, a))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(a, a) = zero) | (~less_equal(zero, divide(a, a))) | (~less_equal(divide(a, a), zero))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[110])).
% 0.22/0.46 tff(112,plain,
% 0.22/0.46 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(a, a), zero)) | (divide(a, a) = zero) | (~less_equal(zero, divide(a, a))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(a, a) = zero) | (~less_equal(zero, divide(a, a))) | (~less_equal(divide(a, a), zero)))),
% 0.22/0.46 inference(transitivity,[status(thm)],[111, 109])).
% 0.22/0.46 tff(113,plain,
% 0.22/0.46 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(a, a), zero)) | (divide(a, a) = zero) | (~less_equal(zero, divide(a, a))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(114,plain,
% 0.22/0.46 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(a, a) = zero) | (~less_equal(zero, divide(a, a))) | (~less_equal(divide(a, a), zero))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.22/0.46 tff(115,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[114, 71, 108, 105, 93])).
% 0.22/0.46 % SZS output end Proof
%------------------------------------------------------------------------------