TSTP Solution File: HEN012-3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HEN012-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:39:56 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN012-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 21:44:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(less_equal_type, type, (
% 0.19/0.39 less_equal: ( $i * $i ) > $o)).
% 0.19/0.39 tff(zero_type, type, (
% 0.19/0.39 zero: $i)).
% 0.19/0.39 tff(divide_type, type, (
% 0.19/0.39 divide: ( $i * $i ) > $i)).
% 0.19/0.39 tff(a_type, type, (
% 0.19/0.39 a: $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[Y: $i, X: $i] : refl(less_equal(divide(X, Y), X) <=> less_equal(divide(X, Y), X))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![Y: $i, X: $i] : less_equal(divide(X, Y), X) <=> ![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![Y: $i, X: $i] : less_equal(divide(X, Y), X) <=> ![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 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')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![Y: $i, X: $i] : less_equal(divide(X, Y), X)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(a, a), zero), divide(a, a))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (less_equal(divide(divide(a, a), zero), divide(a, a))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (^[Y: $i, X: $i] : refl(((~less_equal(X, Y)) | (divide(X, Y) = zero)) <=> ((~less_equal(X, Y)) | (divide(X, Y) = zero)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 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')).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.39 tff(15,plain,(
% 0.19/0.39 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 0.19/0.39 inference(skolemize,[status(sab)],[14])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (((~![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))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~![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))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((~![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)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (divide(divide(divide(a, a), zero), divide(a, a)) = zero),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (zero = divide(divide(divide(a, a), zero), divide(a, a))),
% 0.19/0.39 inference(symmetry,[status(thm)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (less_equal(zero, divide(divide(a, a), zero)) <=> less_equal(divide(divide(divide(a, a), zero), divide(a, a)), divide(divide(a, a), zero))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (less_equal(divide(divide(divide(a, a), zero), divide(a, a)), divide(divide(a, a), zero)) <=> less_equal(zero, divide(divide(a, a), zero))),
% 0.19/0.40 inference(symmetry,[status(thm)],[22])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 ((~![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))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (less_equal(divide(divide(divide(a, a), zero), divide(a, a)), divide(divide(a, a), zero))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[24, 7])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (less_equal(zero, divide(divide(a, a), zero))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(a, zero), a)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (less_equal(divide(a, zero), a)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[27, 7])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (((~![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(a, zero), a)) | (divide(divide(a, zero), a) = zero))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(a, zero), a)) | (divide(divide(a, zero), a) = zero)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 ((~less_equal(divide(a, zero), a)) | (divide(divide(a, zero), a) = zero)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[31, 16])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (divide(divide(a, zero), a) = zero),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[32, 28])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (zero = divide(divide(a, zero), a)),
% 0.19/0.40 inference(symmetry,[status(thm)],[33])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(a, a), a)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (less_equal(divide(a, a), a)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[35, 7])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (((~![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(divide(a, a), a)) | (divide(divide(a, a), a) = zero))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(divide(a, a), a)) | (divide(divide(a, a), a) = zero)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (divide(divide(a, a), a) = zero),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[39, 16, 36])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (zero = divide(divide(a, a), a)),
% 0.19/0.40 inference(symmetry,[status(thm)],[40])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (divide(zero, a) = divide(divide(divide(a, a), a), a)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (divide(divide(divide(a, a), a), a) = divide(zero, a)),
% 0.19/0.40 inference(symmetry,[status(thm)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (less_equal(divide(divide(divide(a, a), a), a), zero) <=> less_equal(divide(zero, a), zero)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (less_equal(divide(zero, a), zero) <=> less_equal(divide(divide(divide(a, a), a), a), zero)),
% 0.19/0.40 inference(symmetry,[status(thm)],[44])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(zero, a), zero)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (less_equal(divide(zero, a), zero)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 7])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (less_equal(divide(divide(divide(a, a), a), a), zero)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[47, 45])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (divide(divide(divide(a, a), a), divide(a, a)) = divide(zero, divide(a, a))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (divide(zero, divide(a, a)) = divide(divide(divide(a, a), a), divide(a, a))),
% 0.19/0.40 inference(symmetry,[status(thm)],[49])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (less_equal(zero, divide(a, a)) <=> less_equal(divide(divide(a, a), a), divide(a, a))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (less_equal(divide(divide(a, a), a), divide(a, a)) <=> less_equal(zero, divide(a, a))),
% 0.19/0.40 inference(symmetry,[status(thm)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : less_equal(divide(X, Y), X)) | less_equal(divide(divide(a, a), a), divide(a, a))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (less_equal(divide(divide(a, a), a), divide(a, a))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[53, 7])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (less_equal(zero, divide(a, a))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[54, 52])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(zero, divide(a, a))) | (divide(zero, divide(a, a)) = zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(zero, divide(a, a))) | (divide(zero, divide(a, a)) = zero))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | ((~less_equal(zero, divide(a, a))) | (divide(zero, divide(a, a)) = zero))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (divide(X, Y) = zero))) | (~less_equal(zero, divide(a, a))) | (divide(zero, divide(a, a)) = zero)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 ((~less_equal(zero, divide(a, a))) | (divide(zero, divide(a, a)) = zero)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[58, 16])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (divide(zero, divide(a, a)) = zero),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[59, 55])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (zero = divide(zero, divide(a, a))),
% 0.19/0.40 inference(symmetry,[status(thm)],[60])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (zero = divide(divide(divide(a, a), a), divide(a, a))),
% 0.19/0.40 inference(transitivity,[status(thm)],[61, 50])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (less_equal(zero, divide(divide(divide(a, a), a), a)) <=> less_equal(divide(divide(divide(a, a), a), divide(a, a)), divide(divide(divide(a, a), a), a))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (less_equal(divide(divide(divide(a, a), a), divide(a, a)), divide(divide(divide(a, a), a), a)) <=> less_equal(zero, divide(divide(divide(a, a), a), a))),
% 0.19/0.40 inference(symmetry,[status(thm)],[63])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (^[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)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(68,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')).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.40 tff(70,plain,(
% 0.19/0.40 ![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))),
% 0.19/0.40 inference(skolemize,[status(sab)],[69])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((~![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(a, a), a), divide(a, a)), divide(divide(divide(a, a), a), a))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (less_equal(divide(divide(divide(a, a), a), divide(a, a)), divide(divide(divide(a, a), a), a))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (less_equal(zero, divide(divide(divide(a, a), a), a))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[73, 64])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.40 tff(79,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')).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.19/0.41 tff(82,plain,(
% 0.19/0.41 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[81])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(zero, divide(divide(divide(a, a), a), a))) | (zero = divide(divide(divide(a, a), a), a)) | (~less_equal(divide(divide(divide(a, a), a), a), zero)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (~less_equal(zero, divide(divide(divide(a, a), a), a))) | (zero = divide(divide(divide(a, a), a), a)) | (~less_equal(divide(divide(divide(a, a), a), a), zero)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(zero, divide(divide(divide(a, a), a), a))) | (zero = divide(divide(divide(a, a), a), a)) | (~less_equal(divide(divide(divide(a, a), a), a), zero)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (~less_equal(zero, divide(divide(divide(a, a), a), a))) | (zero = divide(divide(divide(a, a), a), a)) | (~less_equal(divide(divide(divide(a, a), a), a), zero))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 ((zero = divide(divide(divide(a, a), a), a)) | (~less_equal(divide(divide(divide(a, a), a), a), zero))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[86, 83, 74])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (zero = divide(divide(divide(a, a), a), a)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[87, 48])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (divide(divide(divide(a, a), a), a) = zero),
% 0.19/0.41 inference(symmetry,[status(thm)],[88])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (divide(zero, a) = zero),
% 0.19/0.41 inference(transitivity,[status(thm)],[42, 89])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (divide(divide(a, a), divide(zero, a)) = divide(divide(a, a), zero)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (divide(divide(a, a), zero) = divide(divide(a, a), divide(zero, a))),
% 0.19/0.41 inference(symmetry,[status(thm)],[91])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (less_equal(divide(divide(a, a), zero), zero) <=> less_equal(divide(divide(a, a), divide(zero, a)), divide(divide(a, zero), a))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[92, 34])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (less_equal(divide(divide(a, a), divide(zero, a)), divide(divide(a, zero), a)) <=> less_equal(divide(divide(a, a), zero), zero)),
% 0.19/0.41 inference(symmetry,[status(thm)],[93])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ((~![Z: $i, Y: $i, X: $i] : less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))) | less_equal(divide(divide(a, a), divide(zero, a)), divide(divide(a, zero), a))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (less_equal(divide(divide(a, a), divide(zero, a)), divide(divide(a, zero), a))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[95, 71])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (less_equal(divide(divide(a, a), zero), zero)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[96, 94])).
% 0.19/0.41 tff(98,assumption,(~less_equal(divide(divide(a, a), zero), zero)), introduced(assumption)).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.41 tff(100,plain,(less_equal(divide(divide(a, a), zero), zero)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(101,assumption,(~(divide(divide(a, a), zero) = zero)), introduced(assumption)).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(divide(a, a), zero) = zero) | (~less_equal(zero, divide(divide(a, a), zero))) | (~less_equal(divide(divide(a, a), zero), zero)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(a, a), zero) = zero) | (~less_equal(zero, divide(divide(a, a), zero))) | (~less_equal(divide(divide(a, a), zero), zero)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (((~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(zero, divide(divide(a, a), zero))) | (~less_equal(divide(divide(a, a), zero), zero)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (((~![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(zero, divide(divide(a, a), zero))) | (~less_equal(divide(divide(a, a), zero), zero))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (((~![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(zero, divide(divide(a, a), zero))) | (~less_equal(divide(divide(a, a), zero), zero)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[104, 102])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~![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))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(divide(a, a), zero) = zero) | (~less_equal(zero, divide(divide(a, a), zero))) | (~less_equal(divide(divide(a, a), zero), zero))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[107, 83, 101, 100, 26])).
% 0.19/0.41 tff(109,plain,(divide(divide(a, a), zero) = zero), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (^[Y: $i, X: $i] : refl(((~(divide(X, Y) = zero)) | less_equal(X, Y)) <=> ((~(divide(X, Y) = zero)) | less_equal(X, Y)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(113,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')).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.41 tff(115,plain,(
% 0.19/0.41 ![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 0.19/0.41 inference(skolemize,[status(sab)],[114])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (((~![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(divide(a, a), zero) = zero)) | less_equal(divide(a, a), zero))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(divide(a, a), zero) = zero)) | less_equal(divide(a, a), zero)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 ((~(divide(divide(a, a), zero) = zero)) | less_equal(divide(a, a), zero)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[119, 116])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (less_equal(divide(a, a), zero)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[120, 109])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 ((~less_equal(a, a)) <=> (~less_equal(a, a))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(123,axiom,(~less_equal(a, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_a_LE_a')).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (~less_equal(a, a)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(a, a) = zero)) | less_equal(a, a))) <=> ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(a, a) = zero)) | less_equal(a, a))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | ((~(divide(a, a) = zero)) | less_equal(a, a))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~(divide(X, Y) = zero)) | less_equal(X, Y))) | (~(divide(a, a) = zero)) | less_equal(a, a)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (~(divide(a, a) = zero)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[127, 116, 124])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (((~![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (((~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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (((~![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))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[130])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[131, 129])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 ((~![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))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(a, a) = zero) | (~less_equal(zero, divide(a, a))) | (~less_equal(divide(a, a), zero))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[134, 83, 128, 55, 121])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------