%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN005-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Sat Jun 21 05:08:46 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : HEN005-2 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 17:14:31 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.53 % SZS status Unsatisfiable
% 0.21/0.53 % SZS output start Proof
% 0.21/0.53 tff(quotient_type, type, (
% 0.21/0.53 quotient: ( $i * $i * $i ) > $o)).
% 0.21/0.53 tff(divide_type, type, (
% 0.21/0.53 divide: ( $i * $i ) > $i)).
% 0.21/0.53 tff(zero_type, type, (
% 0.21/0.53 zero: $i)).
% 0.21/0.53 tff(z_type, type, (
% 0.21/0.53 z: $i)).
% 0.21/0.53 tff(x_type, type, (
% 0.21/0.53 x: $i)).
% 0.21/0.53 tff(less_equal_type, type, (
% 0.21/0.53 less_equal: ( $i * $i ) > $o)).
% 0.21/0.53 tff(y_type, type, (
% 0.21/0.53 y: $i)).
% 0.21/0.53 tff(1,plain,
% 0.21/0.53 (^[Y: $i, X: $i] : refl(quotient(X, Y, divide(X, Y)) <=> quotient(X, Y, divide(X, Y)))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(2,plain,
% 0.21/0.53 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y)) <=> ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.53 tff(3,plain,
% 0.21/0.53 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y)) <=> ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(4,axiom,(![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','closure')).
% 0.21/0.53 tff(5,plain,
% 0.21/0.53 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.53 tff(6,plain,(
% 0.21/0.53 ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.21/0.53 inference(skolemize,[status(sab)],[5])).
% 0.21/0.53 tff(7,plain,
% 0.21/0.53 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.53 tff(8,plain,
% 0.21/0.53 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(9,plain,
% 0.21/0.53 (quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.53 tff(10,plain,
% 0.21/0.53 (^[X: $i] : refl(quotient(X, X, zero) <=> quotient(X, X, zero))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(11,plain,
% 0.21/0.53 (![X: $i] : quotient(X, X, zero) <=> ![X: $i] : quotient(X, X, zero)),
% 0.21/0.53 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.53 tff(12,plain,
% 0.21/0.53 (![X: $i] : quotient(X, X, zero) <=> ![X: $i] : quotient(X, X, zero)),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(13,axiom,(![X: $i] : quotient(X, X, zero)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x_divide_x_is_zero')).
% 0.21/0.53 tff(14,plain,
% 0.21/0.53 (![X: $i] : quotient(X, X, zero)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.53 tff(15,plain,(
% 0.21/0.53 ![X: $i] : quotient(X, X, zero)),
% 0.21/0.53 inference(skolemize,[status(sab)],[14])).
% 0.21/0.53 tff(16,plain,
% 0.21/0.53 (![X: $i] : quotient(X, X, zero)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.53 tff(17,plain,
% 0.21/0.53 ((~![X: $i] : quotient(X, X, zero)) | quotient(divide(z, zero), divide(z, zero), zero)),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(18,plain,
% 0.21/0.53 (quotient(divide(z, zero), divide(z, zero), zero)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.53 tff(19,plain,
% 0.21/0.53 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))) <=> ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(20,plain,
% 0.21/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.53 tff(21,plain,
% 0.21/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(22,plain,
% 0.21/0.53 (^[W: $i, Z: $i, Y: $i, X: $i] : rewrite((((~quotient(X, Y, Z)) | (~quotient(X, Y, W))) | (Z = W)) <=> ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(23,plain,
% 0.21/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (((~quotient(X, Y, Z)) | (~quotient(X, Y, W))) | (Z = W)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.53 tff(24,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~quotient(X, Y, Z)) | (~quotient(X, Y, W))) | (Z = W))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','well_defined')).
% 0.21/0.54 tff(25,plain,
% 0.21/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.54 tff(26,plain,
% 0.21/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.54 tff(27,plain,(
% 0.21/0.54 ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.21/0.54 inference(skolemize,[status(sab)],[26])).
% 0.21/0.54 tff(28,plain,
% 0.21/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.21/0.54 tff(29,plain,
% 0.21/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((zero = divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(z, zero), divide(z, zero), zero)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (zero = divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(z, zero), divide(z, zero), zero)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(30,plain,
% 0.21/0.54 (((~quotient(divide(z, zero), divide(z, zero), zero)) | (zero = divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero))))) <=> ((zero = divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(z, zero), divide(z, zero), zero)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(31,plain,
% 0.21/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(divide(z, zero), divide(z, zero), zero)) | (zero = divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((zero = divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(z, zero), divide(z, zero), zero))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[30])).
% 0.21/0.54 tff(32,plain,
% 0.21/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(divide(z, zero), divide(z, zero), zero)) | (zero = divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (zero = divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(z, zero), divide(z, zero), zero)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[31, 29])).
% 0.21/0.54 tff(33,plain,
% 0.21/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(divide(z, zero), divide(z, zero), zero)) | (zero = divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero)))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(34,plain,
% 0.21/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (zero = divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(z, zero), divide(z, zero), divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(z, zero), divide(z, zero), zero))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.54 tff(35,plain,
% 0.21/0.54 (zero = divide(divide(z, zero), divide(z, zero))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[34, 28, 18, 9])).
% 0.21/0.54 tff(36,plain,
% 0.21/0.54 (divide(divide(z, zero), divide(z, zero)) = zero),
% 0.21/0.54 inference(symmetry,[status(thm)],[35])).
% 0.21/0.54 tff(37,plain,
% 0.21/0.54 (quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero))) <=> quotient(zero, z, zero)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[36, 36])).
% 0.21/0.54 tff(38,plain,
% 0.21/0.54 (quotient(zero, z, zero) <=> quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))),
% 0.21/0.54 inference(symmetry,[status(thm)],[37])).
% 0.21/0.54 tff(39,assumption,(~less_equal(zero, z)), introduced(assumption)).
% 0.21/0.54 tff(40,plain,
% 0.21/0.54 (^[X: $i] : refl(less_equal(zero, X) <=> less_equal(zero, X))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(41,plain,
% 0.21/0.54 (![X: $i] : less_equal(zero, X) <=> ![X: $i] : less_equal(zero, X)),
% 0.21/0.54 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.54 tff(42,plain,
% 0.21/0.54 (![X: $i] : less_equal(zero, X) <=> ![X: $i] : less_equal(zero, X)),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(43,axiom,(![X: $i] : less_equal(zero, X)), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','zero_is_smallest')).
% 0.21/0.54 tff(44,plain,
% 0.21/0.54 (![X: $i] : less_equal(zero, X)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.54 tff(45,plain,(
% 0.21/0.54 ![X: $i] : less_equal(zero, X)),
% 0.21/0.54 inference(skolemize,[status(sab)],[44])).
% 0.21/0.54 tff(46,plain,
% 0.21/0.54 (![X: $i] : less_equal(zero, X)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.54 tff(47,plain,
% 0.21/0.54 ((~![X: $i] : less_equal(zero, X)) | less_equal(zero, z)),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(48,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[47, 46, 39])).
% 0.21/0.54 tff(49,plain,(less_equal(zero, z)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(50,plain,
% 0.21/0.54 (^[Y: $i, X: $i] : refl(((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ((~less_equal(X, Y)) | quotient(X, Y, zero)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(51,plain,
% 0.21/0.54 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.54 tff(52,plain,
% 0.21/0.54 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(53,axiom,(![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','quotient_less_equal')).
% 0.21/0.54 tff(54,plain,
% 0.21/0.54 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.54 tff(55,plain,(
% 0.21/0.54 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.21/0.54 inference(skolemize,[status(sab)],[54])).
% 0.21/0.54 tff(56,plain,
% 0.21/0.54 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.21/0.54 tff(57,plain,
% 0.21/0.54 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(zero, z)) | quotient(zero, z, zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(zero, z)) | quotient(zero, z, zero))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(58,plain,
% 0.21/0.54 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(zero, z)) | quotient(zero, z, zero))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(59,plain,
% 0.21/0.54 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(zero, z)) | quotient(zero, z, zero)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.54 tff(60,plain,
% 0.21/0.54 (quotient(zero, z, zero)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[59, 56, 49])).
% 0.21/0.54 tff(61,plain,
% 0.21/0.54 (quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[60, 38])).
% 0.21/0.54 tff(62,plain,
% 0.21/0.54 (quotient(z, divide(divide(z, zero), divide(z, zero)), divide(z, zero)) <=> quotient(z, zero, divide(z, zero))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.54 tff(63,plain,
% 0.21/0.54 (quotient(z, zero, divide(z, zero)) <=> quotient(z, divide(divide(z, zero), divide(z, zero)), divide(z, zero))),
% 0.21/0.54 inference(symmetry,[status(thm)],[62])).
% 0.21/0.54 tff(64,plain,
% 0.21/0.54 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(z, zero, divide(z, zero))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(65,plain,
% 0.21/0.54 (quotient(z, zero, divide(z, zero))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[64, 7])).
% 0.21/0.54 tff(66,plain,
% 0.21/0.54 (quotient(z, divide(divide(z, zero), divide(z, zero)), divide(z, zero))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[65, 63])).
% 0.21/0.54 tff(67,plain,
% 0.21/0.54 (quotient(z, divide(divide(z, zero), divide(z, zero)), z) <=> quotient(z, zero, z)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.54 tff(68,plain,
% 0.21/0.54 (quotient(z, zero, z) <=> quotient(z, divide(divide(z, zero), divide(z, zero)), z)),
% 0.21/0.54 inference(symmetry,[status(thm)],[67])).
% 0.21/0.54 tff(69,plain,
% 0.21/0.54 (^[X: $i] : refl(quotient(X, zero, X) <=> quotient(X, zero, X))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(70,plain,
% 0.21/0.54 (![X: $i] : quotient(X, zero, X) <=> ![X: $i] : quotient(X, zero, X)),
% 0.21/0.54 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.54 tff(71,plain,
% 0.21/0.54 (![X: $i] : quotient(X, zero, X) <=> ![X: $i] : quotient(X, zero, X)),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(72,axiom,(![X: $i] : quotient(X, zero, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x_divde_zero_is_x')).
% 0.21/0.54 tff(73,plain,
% 0.21/0.54 (![X: $i] : quotient(X, zero, X)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.54 tff(74,plain,(
% 0.21/0.54 ![X: $i] : quotient(X, zero, X)),
% 0.21/0.54 inference(skolemize,[status(sab)],[73])).
% 0.21/0.54 tff(75,plain,
% 0.21/0.54 (![X: $i] : quotient(X, zero, X)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.21/0.54 tff(76,plain,
% 0.21/0.54 ((~![X: $i] : quotient(X, zero, X)) | quotient(z, zero, z)),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(77,plain,
% 0.21/0.54 (quotient(z, zero, z)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.54 tff(78,plain,
% 0.21/0.54 (quotient(z, divide(divide(z, zero), divide(z, zero)), z)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[77, 68])).
% 0.21/0.54 tff(79,plain,
% 0.21/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(z, divide(divide(z, zero), divide(z, zero)), divide(z, zero))) | (divide(z, zero) = z) | (~quotient(z, divide(divide(z, zero), divide(z, zero)), z)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(z, divide(divide(z, zero), divide(z, zero)), divide(z, zero))) | (divide(z, zero) = z) | (~quotient(z, divide(divide(z, zero), divide(z, zero)), z)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(80,plain,
% 0.21/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(z, divide(divide(z, zero), divide(z, zero)), divide(z, zero))) | (divide(z, zero) = z) | (~quotient(z, divide(divide(z, zero), divide(z, zero)), z)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(81,plain,
% 0.21/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(z, divide(divide(z, zero), divide(z, zero)), divide(z, zero))) | (divide(z, zero) = z) | (~quotient(z, divide(divide(z, zero), divide(z, zero)), z))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.54 tff(82,plain,
% 0.21/0.54 ((~quotient(z, divide(divide(z, zero), divide(z, zero)), divide(z, zero))) | (divide(z, zero) = z) | (~quotient(z, divide(divide(z, zero), divide(z, zero)), z))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[81, 28])).
% 0.21/0.54 tff(83,plain,
% 0.21/0.54 (divide(z, zero) = z),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[82, 78, 66])).
% 0.21/0.54 tff(84,plain,
% 0.21/0.54 (z = divide(z, zero)),
% 0.21/0.54 inference(symmetry,[status(thm)],[83])).
% 0.21/0.54 tff(85,plain,
% 0.21/0.54 (quotient(x, z, divide(x, divide(z, zero))) <=> quotient(x, divide(z, zero), divide(x, divide(z, zero)))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.54 tff(86,plain,
% 0.21/0.54 (quotient(x, divide(z, zero), divide(x, divide(z, zero))) <=> quotient(x, z, divide(x, divide(z, zero)))),
% 0.21/0.54 inference(symmetry,[status(thm)],[85])).
% 0.21/0.54 tff(87,plain,
% 0.21/0.54 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(x, divide(z, zero), divide(x, divide(z, zero)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(88,plain,
% 0.21/0.54 (quotient(x, divide(z, zero), divide(x, divide(z, zero)))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[87, 7])).
% 0.21/0.54 tff(89,plain,
% 0.21/0.54 (quotient(x, z, divide(x, divide(z, zero)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[88, 86])).
% 0.21/0.54 tff(90,plain,
% 0.21/0.54 (quotient(y, z, divide(divide(z, zero), divide(z, zero))) <=> quotient(y, z, zero)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.54 tff(91,plain,
% 0.21/0.54 (quotient(y, z, zero) <=> quotient(y, z, divide(divide(z, zero), divide(z, zero)))),
% 0.21/0.54 inference(symmetry,[status(thm)],[90])).
% 0.21/0.54 tff(92,plain,
% 0.21/0.54 (less_equal(y, z) <=> less_equal(y, z)),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(93,axiom,(less_equal(y, z)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','yLEz')).
% 0.21/0.54 tff(94,plain,
% 0.21/0.54 (less_equal(y, z)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.54 tff(95,plain,
% 0.21/0.54 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(y, z)) | quotient(y, z, zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(y, z)) | quotient(y, z, zero))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(96,plain,
% 0.21/0.54 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(y, z)) | quotient(y, z, zero))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(97,plain,
% 0.21/0.54 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(y, z)) | quotient(y, z, zero)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.54 tff(98,plain,
% 0.21/0.54 (quotient(y, z, zero)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[97, 56, 94])).
% 0.21/0.54 tff(99,plain,
% 0.21/0.54 (quotient(y, z, divide(divide(z, zero), divide(z, zero)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.21/0.54 tff(100,plain,
% 0.21/0.54 (quotient(x, y, divide(divide(z, zero), divide(z, zero))) <=> quotient(x, y, zero)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.54 tff(101,plain,
% 0.21/0.54 (quotient(x, y, zero) <=> quotient(x, y, divide(divide(z, zero), divide(z, zero)))),
% 0.21/0.54 inference(symmetry,[status(thm)],[100])).
% 0.21/0.54 tff(102,plain,
% 0.21/0.54 (less_equal(x, y) <=> less_equal(x, y)),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(103,axiom,(less_equal(x, y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','xLEy')).
% 0.21/0.54 tff(104,plain,
% 0.21/0.54 (less_equal(x, y)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.54 tff(105,plain,
% 0.21/0.54 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(x, y)) | quotient(x, y, zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(x, y)) | quotient(x, y, zero))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(106,plain,
% 0.21/0.54 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(x, y)) | quotient(x, y, zero))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(107,plain,
% 0.21/0.54 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(x, y)) | quotient(x, y, zero)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.54 tff(108,plain,
% 0.21/0.54 (quotient(x, y, zero)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[107, 56, 104])).
% 0.21/0.54 tff(109,plain,
% 0.21/0.54 (quotient(x, y, divide(divide(z, zero), divide(z, zero)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.21/0.54 tff(110,plain,
% 0.21/0.54 (quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero))) <=> quotient(divide(x, divide(z, zero)), zero, divide(x, divide(z, zero)))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.54 tff(111,plain,
% 0.21/0.54 (quotient(divide(x, divide(z, zero)), zero, divide(x, divide(z, zero))) <=> quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))),
% 0.21/0.54 inference(symmetry,[status(thm)],[110])).
% 0.21/0.54 tff(112,plain,
% 0.21/0.54 ((~![X: $i] : quotient(X, zero, X)) | quotient(divide(x, divide(z, zero)), zero, divide(x, divide(z, zero)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(113,plain,
% 0.21/0.54 (quotient(divide(x, divide(z, zero)), zero, divide(x, divide(z, zero)))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[112, 75])).
% 0.21/0.54 tff(114,plain,
% 0.21/0.54 (quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[113, 111])).
% 0.21/0.54 tff(115,plain,
% 0.21/0.54 (^[Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : refl((less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) <=> (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(116,plain,
% 0.21/0.54 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) <=> ![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.54 tff(117,plain,
% 0.21/0.54 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) <=> ![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(118,plain,
% 0.21/0.54 (^[Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) <=> ((~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))), (((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) <=> (((~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | (~quotient(V3, V2, V4))))), rewrite((((~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | (~quotient(V3, V2, V4))) <=> ((~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))), (((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) <=> ((~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))))), ((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) <=> (((~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | (~quotient(V1, Z, V5))))), rewrite((((~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | (~quotient(V1, Z, V5))) <=> ((~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))), ((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) <=> ((~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))))), (((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) | less_equal(V4, V5)) <=> (((~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | less_equal(V4, V5)))), rewrite((((~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1))) | less_equal(V4, V5)) <=> (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))), (((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) | less_equal(V4, V5)) <=> (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(119,plain,
% 0.21/0.55 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : ((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) | less_equal(V4, V5)) <=> ![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[118])).
% 0.21/0.55 tff(120,axiom,(![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : ((((((~quotient(X, Y, V1)) | (~quotient(Y, Z, V2))) | (~quotient(X, Z, V3))) | (~quotient(V3, V2, V4))) | (~quotient(V1, Z, V5))) | less_equal(V4, V5))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','quotient_property')).
% 0.21/0.55 tff(121,plain,
% 0.21/0.55 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.55 tff(122,plain,
% 0.21/0.55 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.21/0.55 tff(123,plain,(
% 0.21/0.55 ![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 0.21/0.55 inference(skolemize,[status(sab)],[122])).
% 0.21/0.55 tff(124,plain,
% 0.21/0.55 (![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.21/0.55 tff(125,plain,
% 0.21/0.55 (((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))) | (~quotient(y, z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(x, y, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~quotient(x, z, divide(x, divide(z, zero)))))) <=> ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))) | (~quotient(y, z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(x, y, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~quotient(x, z, divide(x, divide(z, zero)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(126,plain,
% 0.21/0.55 ((less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~quotient(x, z, divide(x, divide(z, zero)))) | (~quotient(y, z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(x, y, divide(divide(z, zero), divide(z, zero))))) <=> (less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))) | (~quotient(y, z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(x, y, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~quotient(x, z, divide(x, divide(z, zero)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(127,plain,
% 0.21/0.55 (((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~quotient(x, z, divide(x, divide(z, zero)))) | (~quotient(y, z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(x, y, divide(divide(z, zero), divide(z, zero)))))) <=> ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))) | (~quotient(y, z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(x, y, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~quotient(x, z, divide(x, divide(z, zero))))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.55 tff(128,plain,
% 0.21/0.55 (((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~quotient(x, z, divide(x, divide(z, zero)))) | (~quotient(y, z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(x, y, divide(divide(z, zero), divide(z, zero)))))) <=> ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))) | (~quotient(y, z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(x, y, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~quotient(x, z, divide(x, divide(z, zero)))))),
% 0.21/0.55 inference(transitivity,[status(thm)],[127, 125])).
% 0.21/0.55 tff(129,plain,
% 0.21/0.55 ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))) | (~quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~quotient(x, z, divide(x, divide(z, zero)))) | (~quotient(y, z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(x, y, divide(divide(z, zero), divide(z, zero)))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(130,plain,
% 0.21/0.55 ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))) | (~quotient(y, z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(x, y, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~quotient(x, z, divide(x, divide(z, zero))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.55 tff(131,plain,
% 0.21/0.55 (less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))) | (~quotient(y, z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(divide(divide(z, zero), divide(z, zero)), z, divide(divide(z, zero), divide(z, zero)))) | (~quotient(x, z, divide(x, divide(z, zero))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[130, 124, 114, 109])).
% 0.21/0.55 tff(132,plain,
% 0.21/0.55 (less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[131, 99, 89, 61])).
% 0.21/0.55 tff(133,plain,
% 0.21/0.55 (quotient(divide(x, divide(z, zero)), x, divide(divide(z, zero), divide(z, zero))) <=> quotient(divide(x, divide(z, zero)), x, zero)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.55 tff(134,plain,
% 0.21/0.55 (quotient(divide(x, divide(z, zero)), x, zero) <=> quotient(divide(x, divide(z, zero)), x, divide(divide(z, zero), divide(z, zero)))),
% 0.21/0.55 inference(symmetry,[status(thm)],[133])).
% 0.21/0.55 tff(135,plain,
% 0.21/0.55 (^[Z: $i, Y: $i, X: $i] : refl(((~quotient(X, Y, Z)) | less_equal(Z, X)) <=> ((~quotient(X, Y, Z)) | less_equal(Z, X)))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(136,plain,
% 0.21/0.55 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.55 tff(137,plain,
% 0.21/0.55 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(138,axiom,(![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','divisor_existence')).
% 0.21/0.55 tff(139,plain,
% 0.21/0.55 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.55 tff(140,plain,(
% 0.21/0.55 ![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.21/0.55 inference(skolemize,[status(sab)],[139])).
% 0.21/0.55 tff(141,plain,
% 0.21/0.55 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.21/0.55 tff(142,plain,
% 0.21/0.55 (((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(x, divide(z, zero), divide(x, divide(z, zero)))) | less_equal(divide(x, divide(z, zero)), x))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(x, divide(z, zero), divide(x, divide(z, zero)))) | less_equal(divide(x, divide(z, zero)), x))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(143,plain,
% 0.21/0.55 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(x, divide(z, zero), divide(x, divide(z, zero)))) | less_equal(divide(x, divide(z, zero)), x))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(144,plain,
% 0.21/0.55 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(x, divide(z, zero), divide(x, divide(z, zero)))) | less_equal(divide(x, divide(z, zero)), x)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.21/0.55 tff(145,plain,
% 0.21/0.55 (less_equal(divide(x, divide(z, zero)), x)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[144, 141, 88])).
% 0.21/0.55 tff(146,plain,
% 0.21/0.55 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(divide(x, divide(z, zero)), x)) | quotient(divide(x, divide(z, zero)), x, zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(divide(x, divide(z, zero)), x)) | quotient(divide(x, divide(z, zero)), x, zero))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(147,plain,
% 0.21/0.55 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(divide(x, divide(z, zero)), x)) | quotient(divide(x, divide(z, zero)), x, zero))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(148,plain,
% 0.21/0.55 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(divide(x, divide(z, zero)), x)) | quotient(divide(x, divide(z, zero)), x, zero)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.55 tff(149,plain,
% 0.21/0.55 (quotient(divide(x, divide(z, zero)), x, zero)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[148, 56, 145])).
% 0.21/0.55 tff(150,plain,
% 0.21/0.55 (quotient(divide(x, divide(z, zero)), x, divide(divide(z, zero), divide(z, zero)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[149, 134])).
% 0.21/0.55 tff(151,plain,
% 0.21/0.55 (((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(divide(x, divide(z, zero)), x, divide(divide(z, zero), divide(z, zero)))) | less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(divide(x, divide(z, zero)), x, divide(divide(z, zero), divide(z, zero)))) | less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(152,plain,
% 0.21/0.55 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(divide(x, divide(z, zero)), x, divide(divide(z, zero), divide(z, zero)))) | less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(153,plain,
% 0.21/0.55 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(divide(x, divide(z, zero)), x, divide(divide(z, zero), divide(z, zero)))) | less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.55 tff(154,plain,
% 0.21/0.55 ((~quotient(divide(x, divide(z, zero)), x, divide(divide(z, zero), divide(z, zero)))) | less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[153, 141])).
% 0.21/0.55 tff(155,plain,
% 0.21/0.55 (less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[154, 150])).
% 0.21/0.55 tff(156,plain,
% 0.21/0.55 (![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)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(157,plain,
% 0.21/0.55 (![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)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(158,plain,
% 0.21/0.55 (^[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))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(159,plain,
% 0.21/0.55 (![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)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[158])).
% 0.21/0.55 tff(160,axiom,(![Y: $i, X: $i] : (((~less_equal(X, Y)) | (~less_equal(Y, X))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','less_equal_and_equal')).
% 0.21/0.55 tff(161,plain,
% 0.21/0.55 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.55 tff(162,plain,
% 0.21/0.55 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.21/0.55 tff(163,plain,(
% 0.21/0.55 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.21/0.55 inference(skolemize,[status(sab)],[162])).
% 0.21/0.55 tff(164,plain,
% 0.21/0.55 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.21/0.55 tff(165,plain,
% 0.21/0.55 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))) | (~less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))) | (~less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(166,plain,
% 0.21/0.55 (((~less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)))) | (divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))) | (~less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero))))) <=> ((divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))) | (~less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(167,plain,
% 0.21/0.55 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)))) | (divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))) | (~less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))) | (~less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[166])).
% 0.21/0.55 tff(168,plain,
% 0.21/0.55 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)))) | (divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))) | (~less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))) | (~less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)))))),
% 0.21/0.55 inference(transitivity,[status(thm)],[167, 165])).
% 0.21/0.55 tff(169,plain,
% 0.21/0.55 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero)))) | (divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))) | (~less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(170,plain,
% 0.21/0.55 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))) | (~less_equal(divide(divide(z, zero), divide(z, zero)), divide(x, divide(z, zero)))) | (~less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.21/0.55 tff(171,plain,
% 0.21/0.55 ((divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))) | (~less_equal(divide(x, divide(z, zero)), divide(divide(z, zero), divide(z, zero))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[170, 164, 155])).
% 0.21/0.55 tff(172,plain,
% 0.21/0.55 (divide(x, divide(z, zero)) = divide(divide(z, zero), divide(z, zero))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[171, 132])).
% 0.21/0.55 tff(173,plain,
% 0.21/0.55 (divide(x, divide(z, zero)) = zero),
% 0.21/0.55 inference(transitivity,[status(thm)],[172, 36])).
% 0.21/0.55 tff(174,plain,
% 0.21/0.55 (quotient(x, divide(z, zero), divide(x, divide(z, zero))) <=> quotient(x, z, zero)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[83, 173])).
% 0.21/0.56 tff(175,plain,
% 0.21/0.56 (quotient(x, z, zero) <=> quotient(x, divide(z, zero), divide(x, divide(z, zero)))),
% 0.21/0.56 inference(symmetry,[status(thm)],[174])).
% 0.21/0.56 tff(176,plain,
% 0.21/0.56 ((~quotient(x, z, zero)) <=> (~quotient(x, divide(z, zero), divide(x, divide(z, zero))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[175])).
% 0.21/0.56 tff(177,plain,
% 0.21/0.56 ((~less_equal(x, z)) <=> (~less_equal(x, z))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(178,axiom,(~less_equal(x, z)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_transitivity_of_less_equal')).
% 0.21/0.56 tff(179,plain,
% 0.21/0.56 (~less_equal(x, z)),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.56 tff(180,plain,
% 0.21/0.56 (^[Y: $i, X: $i] : refl(((~quotient(X, Y, zero)) | less_equal(X, Y)) <=> ((~quotient(X, Y, zero)) | less_equal(X, Y)))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(181,plain,
% 0.21/0.56 (![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[180])).
% 0.21/0.56 tff(182,plain,
% 0.21/0.56 (![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(183,axiom,(![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','less_equal_quotient')).
% 0.21/0.56 tff(184,plain,
% 0.21/0.56 (![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.21/0.56 tff(185,plain,(
% 0.21/0.56 ![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))),
% 0.21/0.56 inference(skolemize,[status(sab)],[184])).
% 0.21/0.56 tff(186,plain,
% 0.21/0.56 (![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.21/0.56 tff(187,plain,
% 0.21/0.56 (((~![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))) | ((~quotient(x, z, zero)) | less_equal(x, z))) <=> ((~![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))) | (~quotient(x, z, zero)) | less_equal(x, z))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(188,plain,
% 0.21/0.56 ((~![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))) | ((~quotient(x, z, zero)) | less_equal(x, z))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(189,plain,
% 0.21/0.56 ((~![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))) | (~quotient(x, z, zero)) | less_equal(x, z)),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.21/0.56 tff(190,plain,
% 0.21/0.56 (~quotient(x, z, zero)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[189, 186, 179])).
% 0.21/0.56 tff(191,plain,
% 0.21/0.56 (~quotient(x, divide(z, zero), divide(x, divide(z, zero)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[190, 176])).
% 0.21/0.56 tff(192,plain,
% 0.21/0.56 ($false),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[88, 191])).
% 0.21/0.56 % SZS output end Proof
% 0.21/0.56 % E exiting
%------------------------------------------------------------------------------