%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN010-7 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:08:49 AM UTC 2025
% Result : Unsatisfiable 10.27s 10.43s
% Output : Proof 10.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : HEN010-7 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 17:15:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 10.27/10.43 % SZS status Unsatisfiable
% 10.27/10.43 % SZS output start Proof
% 10.27/10.43 tff(idQa_Q__idQ_idQa_type, type, (
% 10.27/10.43 idQa_Q__idQ_idQa: $i)).
% 10.27/10.43 tff(idQa_type, type, (
% 10.27/10.43 idQa: $i)).
% 10.27/10.43 tff(divide_type, type, (
% 10.27/10.43 divide: ( $i * $i ) > $i)).
% 10.27/10.43 tff(identity_type, type, (
% 10.27/10.43 identity: $i)).
% 10.27/10.43 tff(idQ_idQa_type, type, (
% 10.27/10.43 idQ_idQa: $i)).
% 10.27/10.43 tff(a_type, type, (
% 10.27/10.43 a: $i)).
% 10.27/10.43 tff(less_equal_type, type, (
% 10.27/10.43 less_equal: ( $i * $i ) > $o)).
% 10.27/10.43 tff(quotient_type, type, (
% 10.27/10.43 quotient: ( $i * $i * $i ) > $o)).
% 10.27/10.43 tff(zero_type, type, (
% 10.27/10.43 zero: $i)).
% 10.27/10.43 tff(1,plain,
% 10.27/10.43 (^[Y: $i, X: $i] : refl(quotient(X, Y, divide(X, Y)) <=> quotient(X, Y, divide(X, Y)))),
% 10.27/10.43 inference(bind,[status(th)],[])).
% 10.27/10.43 tff(2,plain,
% 10.27/10.43 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y)) <=> ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 10.27/10.43 inference(quant_intro,[status(thm)],[1])).
% 10.27/10.43 tff(3,plain,
% 10.27/10.43 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y)) <=> ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 10.27/10.43 inference(rewrite,[status(thm)],[])).
% 10.27/10.43 tff(4,axiom,(![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','closure')).
% 10.27/10.43 tff(5,plain,
% 10.27/10.43 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 10.27/10.43 tff(6,plain,(
% 10.27/10.43 ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 10.27/10.43 inference(skolemize,[status(sab)],[5])).
% 10.27/10.43 tff(7,plain,
% 10.27/10.43 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 10.27/10.43 tff(8,plain,
% 10.27/10.43 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.43 inference(quant_inst,[status(thm)],[])).
% 10.27/10.43 tff(9,plain,
% 10.27/10.43 (quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 10.27/10.43 tff(10,plain,
% 10.27/10.43 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(idQ_idQa, identity, divide(idQ_idQa, identity))),
% 10.27/10.43 inference(quant_inst,[status(thm)],[])).
% 10.27/10.43 tff(11,plain,
% 10.27/10.43 (quotient(idQ_idQa, identity, divide(idQ_idQa, identity))),
% 10.27/10.43 inference(unit_resolution,[status(thm)],[10, 7])).
% 10.27/10.43 tff(12,plain,
% 10.27/10.43 (quotient(identity, idQa, idQ_idQa) <=> quotient(identity, idQa, idQ_idQa)),
% 10.27/10.43 inference(rewrite,[status(thm)],[])).
% 10.27/10.43 tff(13,axiom,(quotient(identity, idQa, idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_idQa')).
% 10.27/10.43 tff(14,plain,
% 10.27/10.43 (quotient(identity, idQa, idQ_idQa)),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[13, 12])).
% 10.27/10.43 tff(15,plain,
% 10.27/10.43 (^[Z: $i, Y: $i, X: $i] : refl(((~quotient(X, Y, Z)) | less_equal(Z, X)) <=> ((~quotient(X, Y, Z)) | less_equal(Z, X)))),
% 10.27/10.43 inference(bind,[status(th)],[])).
% 10.27/10.43 tff(16,plain,
% 10.27/10.43 (![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))),
% 10.27/10.43 inference(quant_intro,[status(thm)],[15])).
% 10.27/10.43 tff(17,plain,
% 10.27/10.43 (![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))),
% 10.27/10.43 inference(rewrite,[status(thm)],[])).
% 10.27/10.43 tff(18,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')).
% 10.27/10.43 tff(19,plain,
% 10.27/10.43 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 10.27/10.43 tff(20,plain,(
% 10.27/10.43 ![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 10.27/10.43 inference(skolemize,[status(sab)],[19])).
% 10.27/10.43 tff(21,plain,
% 10.27/10.43 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[20, 16])).
% 10.27/10.43 tff(22,plain,
% 10.27/10.43 (((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, identity))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, identity))),
% 10.27/10.43 inference(rewrite,[status(thm)],[])).
% 10.27/10.43 tff(23,plain,
% 10.27/10.43 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, identity))),
% 10.27/10.43 inference(quant_inst,[status(thm)],[])).
% 10.27/10.43 tff(24,plain,
% 10.27/10.43 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, identity)),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[23, 22])).
% 10.27/10.43 tff(25,plain,
% 10.27/10.43 (less_equal(idQ_idQa, identity)),
% 10.27/10.43 inference(unit_resolution,[status(thm)],[24, 21, 14])).
% 10.27/10.43 tff(26,plain,
% 10.27/10.43 (^[Y: $i, X: $i] : refl(((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ((~less_equal(X, Y)) | quotient(X, Y, zero)))),
% 10.27/10.43 inference(bind,[status(th)],[])).
% 10.27/10.43 tff(27,plain,
% 10.27/10.43 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 10.27/10.43 inference(quant_intro,[status(thm)],[26])).
% 10.27/10.43 tff(28,plain,
% 10.27/10.43 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 10.27/10.43 inference(rewrite,[status(thm)],[])).
% 10.27/10.43 tff(29,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')).
% 10.27/10.43 tff(30,plain,
% 10.27/10.43 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[29, 28])).
% 10.27/10.43 tff(31,plain,(
% 10.27/10.43 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 10.27/10.43 inference(skolemize,[status(sab)],[30])).
% 10.27/10.43 tff(32,plain,
% 10.27/10.43 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[31, 27])).
% 10.27/10.43 tff(33,plain,
% 10.27/10.43 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(idQ_idQa, identity)) | quotient(idQ_idQa, identity, zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(idQ_idQa, identity)) | quotient(idQ_idQa, identity, zero))),
% 10.27/10.43 inference(rewrite,[status(thm)],[])).
% 10.27/10.43 tff(34,plain,
% 10.27/10.43 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(idQ_idQa, identity)) | quotient(idQ_idQa, identity, zero))),
% 10.27/10.43 inference(quant_inst,[status(thm)],[])).
% 10.27/10.43 tff(35,plain,
% 10.27/10.43 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(idQ_idQa, identity)) | quotient(idQ_idQa, identity, zero)),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 10.27/10.43 tff(36,plain,
% 10.27/10.43 (quotient(idQ_idQa, identity, zero)),
% 10.27/10.43 inference(unit_resolution,[status(thm)],[35, 32, 25])).
% 10.27/10.43 tff(37,plain,
% 10.27/10.43 (^[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))))),
% 10.27/10.43 inference(bind,[status(th)],[])).
% 10.27/10.43 tff(38,plain,
% 10.27/10.43 (![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)))),
% 10.27/10.43 inference(quant_intro,[status(thm)],[37])).
% 10.27/10.43 tff(39,plain,
% 10.27/10.43 (![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)))),
% 10.27/10.43 inference(rewrite,[status(thm)],[])).
% 10.27/10.43 tff(40,plain,
% 10.27/10.43 (^[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))))),
% 10.27/10.43 inference(bind,[status(th)],[])).
% 10.27/10.43 tff(41,plain,
% 10.27/10.43 (![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)))),
% 10.27/10.43 inference(quant_intro,[status(thm)],[40])).
% 10.27/10.43 tff(42,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')).
% 10.27/10.43 tff(43,plain,
% 10.27/10.43 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[42, 41])).
% 10.27/10.43 tff(44,plain,
% 10.27/10.43 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[43, 39])).
% 10.27/10.43 tff(45,plain,(
% 10.27/10.43 ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 10.27/10.43 inference(skolemize,[status(sab)],[44])).
% 10.27/10.43 tff(46,plain,
% 10.27/10.43 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[45, 38])).
% 10.27/10.43 tff(47,plain,
% 10.27/10.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, identity, zero)) | (~quotient(idQ_idQa, identity, divide(idQ_idQa, identity))) | (zero = divide(idQ_idQa, identity)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQ_idQa, identity, zero)) | (~quotient(idQ_idQa, identity, divide(idQ_idQa, identity))) | (zero = divide(idQ_idQa, identity)))),
% 10.27/10.43 inference(rewrite,[status(thm)],[])).
% 10.27/10.43 tff(48,plain,
% 10.27/10.43 (((~quotient(idQ_idQa, identity, zero)) | (zero = divide(idQ_idQa, identity)) | (~quotient(idQ_idQa, identity, divide(idQ_idQa, identity)))) <=> ((~quotient(idQ_idQa, identity, zero)) | (~quotient(idQ_idQa, identity, divide(idQ_idQa, identity))) | (zero = divide(idQ_idQa, identity)))),
% 10.27/10.43 inference(rewrite,[status(thm)],[])).
% 10.27/10.43 tff(49,plain,
% 10.27/10.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, identity, zero)) | (zero = divide(idQ_idQa, identity)) | (~quotient(idQ_idQa, identity, divide(idQ_idQa, identity))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, identity, zero)) | (~quotient(idQ_idQa, identity, divide(idQ_idQa, identity))) | (zero = divide(idQ_idQa, identity))))),
% 10.27/10.43 inference(monotonicity,[status(thm)],[48])).
% 10.27/10.43 tff(50,plain,
% 10.27/10.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, identity, zero)) | (zero = divide(idQ_idQa, identity)) | (~quotient(idQ_idQa, identity, divide(idQ_idQa, identity))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQ_idQa, identity, zero)) | (~quotient(idQ_idQa, identity, divide(idQ_idQa, identity))) | (zero = divide(idQ_idQa, identity)))),
% 10.27/10.43 inference(transitivity,[status(thm)],[49, 47])).
% 10.27/10.43 tff(51,plain,
% 10.27/10.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, identity, zero)) | (zero = divide(idQ_idQa, identity)) | (~quotient(idQ_idQa, identity, divide(idQ_idQa, identity))))),
% 10.27/10.43 inference(quant_inst,[status(thm)],[])).
% 10.27/10.43 tff(52,plain,
% 10.27/10.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQ_idQa, identity, zero)) | (~quotient(idQ_idQa, identity, divide(idQ_idQa, identity))) | (zero = divide(idQ_idQa, identity))),
% 10.27/10.43 inference(modus_ponens,[status(thm)],[51, 50])).
% 10.27/10.43 tff(53,plain,
% 10.27/10.43 (zero = divide(idQ_idQa, identity)),
% 10.27/10.43 inference(unit_resolution,[status(thm)],[52, 46, 36, 11])).
% 10.27/10.43 tff(54,plain,
% 10.27/10.43 (divide(idQ_idQa, identity) = zero),
% 10.27/10.43 inference(symmetry,[status(thm)],[53])).
% 10.27/10.43 tff(55,plain,
% 10.27/10.43 (quotient(a, divide(idQ_idQa, identity), a) <=> quotient(a, zero, a)),
% 10.27/10.43 inference(monotonicity,[status(thm)],[54])).
% 10.27/10.43 tff(56,plain,
% 10.27/10.43 (quotient(a, zero, a) <=> quotient(a, divide(idQ_idQa, identity), a)),
% 10.27/10.43 inference(symmetry,[status(thm)],[55])).
% 10.27/10.43 tff(57,plain,
% 10.27/10.43 (^[X: $i] : refl(quotient(X, zero, X) <=> quotient(X, zero, X))),
% 10.27/10.43 inference(bind,[status(th)],[])).
% 10.27/10.43 tff(58,plain,
% 10.27/10.43 (![X: $i] : quotient(X, zero, X) <=> ![X: $i] : quotient(X, zero, X)),
% 10.27/10.43 inference(quant_intro,[status(thm)],[57])).
% 10.27/10.43 tff(59,plain,
% 10.27/10.43 (![X: $i] : quotient(X, zero, X) <=> ![X: $i] : quotient(X, zero, X)),
% 10.27/10.43 inference(rewrite,[status(thm)],[])).
% 10.27/10.43 tff(60,axiom,(![X: $i] : quotient(X, zero, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x_divde_zero_is_x')).
% 10.27/10.43 tff(61,plain,
% 10.27/10.43 (![X: $i] : quotient(X, zero, X)),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 10.27/10.44 tff(62,plain,(
% 10.27/10.44 ![X: $i] : quotient(X, zero, X)),
% 10.27/10.44 inference(skolemize,[status(sab)],[61])).
% 10.27/10.44 tff(63,plain,
% 10.27/10.44 (![X: $i] : quotient(X, zero, X)),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[62, 58])).
% 10.27/10.44 tff(64,plain,
% 10.27/10.44 ((~![X: $i] : quotient(X, zero, X)) | quotient(a, zero, a)),
% 10.27/10.44 inference(quant_inst,[status(thm)],[])).
% 10.27/10.44 tff(65,plain,
% 10.27/10.44 (quotient(a, zero, a)),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[64, 63])).
% 10.27/10.44 tff(66,plain,
% 10.27/10.44 (quotient(a, divide(idQ_idQa, identity), a)),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[65, 56])).
% 10.27/10.44 tff(67,plain,
% 10.27/10.44 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))),
% 10.27/10.44 inference(quant_inst,[status(thm)],[])).
% 10.27/10.44 tff(68,plain,
% 10.27/10.44 (quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[67, 7])).
% 10.27/10.44 tff(69,plain,
% 10.27/10.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((a = divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(a, divide(idQ_idQa, identity), a)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (a = divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(a, divide(idQ_idQa, identity), a)))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(70,plain,
% 10.27/10.44 (((~quotient(a, divide(idQ_idQa, identity), a)) | (a = divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity))))) <=> ((a = divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(a, divide(idQ_idQa, identity), a)))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(71,plain,
% 10.27/10.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(a, divide(idQ_idQa, identity), a)) | (a = divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((a = divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(a, divide(idQ_idQa, identity), a))))),
% 10.27/10.44 inference(monotonicity,[status(thm)],[70])).
% 10.27/10.44 tff(72,plain,
% 10.27/10.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(a, divide(idQ_idQa, identity), a)) | (a = divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (a = divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(a, divide(idQ_idQa, identity), a)))),
% 10.27/10.44 inference(transitivity,[status(thm)],[71, 69])).
% 10.27/10.44 tff(73,plain,
% 10.27/10.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(a, divide(idQ_idQa, identity), a)) | (a = divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.44 inference(quant_inst,[status(thm)],[])).
% 10.27/10.44 tff(74,plain,
% 10.27/10.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (a = divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(a, divide(idQ_idQa, identity), a))),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 10.27/10.44 tff(75,plain,
% 10.27/10.44 ((a = divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), a))),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[74, 46, 68])).
% 10.27/10.44 tff(76,plain,
% 10.27/10.44 (a = divide(a, divide(idQ_idQa, identity))),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[75, 66])).
% 10.27/10.44 tff(77,plain,
% 10.27/10.44 (divide(a, divide(idQ_idQa, identity)) = a),
% 10.27/10.44 inference(symmetry,[status(thm)],[76])).
% 10.27/10.44 tff(78,plain,
% 10.27/10.44 (quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa) <=> quotient(identity, a, idQa)),
% 10.27/10.44 inference(monotonicity,[status(thm)],[77])).
% 10.27/10.44 tff(79,plain,
% 10.27/10.44 (quotient(identity, a, idQa) <=> quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)),
% 10.27/10.44 inference(symmetry,[status(thm)],[78])).
% 10.27/10.44 tff(80,plain,
% 10.27/10.44 (quotient(identity, a, idQa) <=> quotient(identity, a, idQa)),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(81,axiom,(quotient(identity, a, idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_a')).
% 10.27/10.44 tff(82,plain,
% 10.27/10.44 (quotient(identity, a, idQa)),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[81, 80])).
% 10.27/10.44 tff(83,plain,
% 10.27/10.44 (quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[82, 79])).
% 10.27/10.44 tff(84,plain,
% 10.27/10.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity))))) | (idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity))))) | (idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(85,plain,
% 10.27/10.44 (((~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity)))))) <=> ((~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity))))) | (idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(86,plain,
% 10.27/10.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity))))) | (idQa = divide(identity, divide(a, divide(idQ_idQa, identity))))))),
% 10.27/10.44 inference(monotonicity,[status(thm)],[85])).
% 10.27/10.44 tff(87,plain,
% 10.27/10.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity))))) | (idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.44 inference(transitivity,[status(thm)],[86, 84])).
% 10.27/10.44 tff(88,plain,
% 10.27/10.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity))))))),
% 10.27/10.44 inference(quant_inst,[status(thm)],[])).
% 10.27/10.44 tff(89,plain,
% 10.27/10.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), divide(identity, divide(a, divide(idQ_idQa, identity))))) | (idQa = divide(identity, divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[88, 87])).
% 10.27/10.44 tff(90,plain,
% 10.27/10.44 (idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[89, 46, 83, 9])).
% 10.27/10.44 tff(91,plain,
% 10.27/10.44 (divide(identity, divide(a, divide(idQ_idQa, identity))) = idQa),
% 10.27/10.44 inference(symmetry,[status(thm)],[90])).
% 10.27/10.44 tff(92,plain,
% 10.27/10.44 (less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity)))) <=> less_equal(idQa_Q__idQ_idQa, idQa)),
% 10.27/10.44 inference(monotonicity,[status(thm)],[91])).
% 10.27/10.44 tff(93,plain,
% 10.27/10.44 (less_equal(idQa_Q__idQ_idQa, idQa) <=> less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.44 inference(symmetry,[status(thm)],[92])).
% 10.27/10.44 tff(94,plain,
% 10.27/10.44 (quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa) <=> quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(95,axiom,(quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_idQ_idQa')).
% 10.27/10.44 tff(96,plain,
% 10.27/10.44 (quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 10.27/10.44 tff(97,plain,
% 10.27/10.44 (((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(idQa_Q__idQ_idQa, idQa))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(idQa_Q__idQ_idQa, idQa))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(98,plain,
% 10.27/10.44 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(idQa_Q__idQ_idQa, idQa))),
% 10.27/10.44 inference(quant_inst,[status(thm)],[])).
% 10.27/10.44 tff(99,plain,
% 10.27/10.44 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(idQa_Q__idQ_idQa, idQa)),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[98, 97])).
% 10.27/10.44 tff(100,plain,
% 10.27/10.44 (less_equal(idQa_Q__idQ_idQa, idQa)),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[99, 21, 96])).
% 10.27/10.44 tff(101,plain,
% 10.27/10.44 (less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[100, 93])).
% 10.27/10.44 tff(102,plain,
% 10.27/10.44 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.44 inference(quant_inst,[status(thm)],[])).
% 10.27/10.44 tff(103,plain,
% 10.27/10.44 (quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[102, 7])).
% 10.27/10.44 tff(104,plain,
% 10.27/10.44 (quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa) <=> quotient(idQ_idQa, zero, idQ_idQa)),
% 10.27/10.44 inference(monotonicity,[status(thm)],[54])).
% 10.27/10.44 tff(105,plain,
% 10.27/10.44 (quotient(idQ_idQa, zero, idQ_idQa) <=> quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)),
% 10.27/10.44 inference(symmetry,[status(thm)],[104])).
% 10.27/10.44 tff(106,plain,
% 10.27/10.44 ((~![X: $i] : quotient(X, zero, X)) | quotient(idQ_idQa, zero, idQ_idQa)),
% 10.27/10.44 inference(quant_inst,[status(thm)],[])).
% 10.27/10.44 tff(107,plain,
% 10.27/10.44 (quotient(idQ_idQa, zero, idQ_idQa)),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[106, 63])).
% 10.27/10.44 tff(108,plain,
% 10.27/10.44 (quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[107, 105])).
% 10.27/10.44 tff(109,assumption,(~less_equal(identity, identity)), introduced(assumption)).
% 10.27/10.44 tff(110,plain,
% 10.27/10.44 (^[X: $i] : refl(less_equal(X, identity) <=> less_equal(X, identity))),
% 10.27/10.44 inference(bind,[status(th)],[])).
% 10.27/10.44 tff(111,plain,
% 10.27/10.44 (![X: $i] : less_equal(X, identity) <=> ![X: $i] : less_equal(X, identity)),
% 10.27/10.44 inference(quant_intro,[status(thm)],[110])).
% 10.27/10.44 tff(112,plain,
% 10.27/10.44 (![X: $i] : less_equal(X, identity) <=> ![X: $i] : less_equal(X, identity)),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(113,axiom,(![X: $i] : less_equal(X, identity)), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','identity_is_largest')).
% 10.27/10.44 tff(114,plain,
% 10.27/10.44 (![X: $i] : less_equal(X, identity)),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[113, 112])).
% 10.27/10.44 tff(115,plain,(
% 10.27/10.44 ![X: $i] : less_equal(X, identity)),
% 10.27/10.44 inference(skolemize,[status(sab)],[114])).
% 10.27/10.44 tff(116,plain,
% 10.27/10.44 (![X: $i] : less_equal(X, identity)),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[115, 111])).
% 10.27/10.44 tff(117,plain,
% 10.27/10.44 ((~![X: $i] : less_equal(X, identity)) | less_equal(identity, identity)),
% 10.27/10.44 inference(quant_inst,[status(thm)],[])).
% 10.27/10.44 tff(118,plain,
% 10.27/10.44 ($false),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[117, 116, 109])).
% 10.27/10.44 tff(119,plain,(less_equal(identity, identity)), inference(lemma,lemma(discharge,[]))).
% 10.27/10.44 tff(120,plain,
% 10.27/10.44 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : refl((less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) <=> (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))))),
% 10.27/10.44 inference(bind,[status(th)],[])).
% 10.27/10.44 tff(121,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 10.27/10.44 inference(quant_intro,[status(thm)],[120])).
% 10.27/10.44 tff(122,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(123,plain,
% 10.27/10.44 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : trans(monotonicity(rewrite((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) <=> ((~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))), (((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) | less_equal(W1, W2)) <=> (((~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) | less_equal(W1, W2)))), rewrite((((~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))), (((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))))),
% 10.27/10.44 inference(bind,[status(th)],[])).
% 10.27/10.44 tff(124,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) | less_equal(W1, W2)) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 10.27/10.44 inference(quant_intro,[status(thm)],[123])).
% 10.27/10.44 tff(125,axiom,(![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~less_equal(X, Y)) | (~quotient(X, Z, W1))) | (~quotient(Y, Z, W2))) | less_equal(W1, W2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','xLEy_implies_xQzLEyQz')).
% 10.27/10.44 tff(126,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 10.27/10.44 tff(127,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[126, 122])).
% 10.27/10.44 tff(128,plain,(
% 10.27/10.44 ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 10.27/10.44 inference(skolemize,[status(sab)],[127])).
% 10.27/10.44 tff(129,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[128, 121])).
% 10.27/10.44 tff(130,plain,
% 10.27/10.44 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(131,plain,
% 10.27/10.44 ((less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)) | (~quotient(identity, a, idQa))) <=> (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(132,plain,
% 10.27/10.44 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)) | (~quotient(identity, a, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa))))),
% 10.27/10.44 inference(monotonicity,[status(thm)],[131])).
% 10.27/10.44 tff(133,plain,
% 10.27/10.44 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)) | (~quotient(identity, a, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)))),
% 10.27/10.44 inference(transitivity,[status(thm)],[132, 130])).
% 10.27/10.44 tff(134,plain,
% 10.27/10.44 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa)) | (~quotient(identity, a, idQa)))),
% 10.27/10.44 inference(quant_inst,[status(thm)],[])).
% 10.27/10.44 tff(135,plain,
% 10.27/10.44 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | less_equal(idQa, idQa) | (~less_equal(identity, identity)) | (~quotient(identity, a, idQa))),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[134, 133])).
% 10.27/10.44 tff(136,plain,
% 10.27/10.44 (less_equal(idQa, idQa) | (~less_equal(identity, identity))),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[135, 129, 82])).
% 10.27/10.44 tff(137,plain,
% 10.27/10.44 (less_equal(idQa, idQa)),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[136, 119])).
% 10.27/10.44 tff(138,plain,
% 10.27/10.44 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : refl((less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) <=> (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))))),
% 10.27/10.44 inference(bind,[status(th)],[])).
% 10.27/10.44 tff(139,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 10.27/10.44 inference(quant_intro,[status(thm)],[138])).
% 10.27/10.44 tff(140,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(141,plain,
% 10.27/10.44 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) <=> ((~less_equal(W1, Z)) | (~quotient(X, Y, W1)))), ((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) <=> (((~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | (~quotient(X, Z, W2))))), rewrite((((~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | (~quotient(X, Z, W2))) <=> ((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))), ((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) <=> ((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))))), (((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) | less_equal(W2, Y)) <=> (((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | less_equal(W2, Y)))), rewrite((((~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1))) | less_equal(W2, Y)) <=> (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))), (((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) | less_equal(W2, Y)) <=> (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))))),
% 10.27/10.44 inference(bind,[status(th)],[])).
% 10.27/10.44 tff(142,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) | less_equal(W2, Y)) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 10.27/10.44 inference(quant_intro,[status(thm)],[141])).
% 10.27/10.44 tff(143,axiom,(![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~quotient(X, Y, W1)) | (~less_equal(W1, Z))) | (~quotient(X, Z, W2))) | less_equal(W2, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','xQyLEz_implies_xQzLEy')).
% 10.27/10.44 tff(144,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[143, 142])).
% 10.27/10.44 tff(145,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[144, 140])).
% 10.27/10.44 tff(146,plain,(
% 10.27/10.44 ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 10.27/10.44 inference(skolemize,[status(sab)],[145])).
% 10.27/10.44 tff(147,plain,
% 10.27/10.44 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[146, 139])).
% 10.27/10.44 tff(148,plain,
% 10.27/10.44 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | ((~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa)))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(149,plain,
% 10.27/10.44 ((less_equal(idQ_idQa, a) | (~quotient(identity, idQa, idQ_idQa)) | (~less_equal(idQa, idQa)) | (~quotient(identity, a, idQa))) <=> ((~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa)))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(150,plain,
% 10.27/10.44 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (less_equal(idQ_idQa, a) | (~quotient(identity, idQa, idQ_idQa)) | (~less_equal(idQa, idQa)) | (~quotient(identity, a, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | ((~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa))))),
% 10.27/10.44 inference(monotonicity,[status(thm)],[149])).
% 10.27/10.44 tff(151,plain,
% 10.27/10.44 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (less_equal(idQ_idQa, a) | (~quotient(identity, idQa, idQ_idQa)) | (~less_equal(idQa, idQa)) | (~quotient(identity, a, idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa)))),
% 10.27/10.44 inference(transitivity,[status(thm)],[150, 148])).
% 10.27/10.44 tff(152,plain,
% 10.27/10.44 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (less_equal(idQ_idQa, a) | (~quotient(identity, idQa, idQ_idQa)) | (~less_equal(idQa, idQa)) | (~quotient(identity, a, idQa)))),
% 10.27/10.44 inference(quant_inst,[status(thm)],[])).
% 10.27/10.44 tff(153,plain,
% 10.27/10.44 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W2, Y) | (~quotient(X, Z, W2)) | (~less_equal(W1, Z)) | (~quotient(X, Y, W1)))) | (~quotient(identity, a, idQa)) | (~quotient(identity, idQa, idQ_idQa)) | less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa))),
% 10.27/10.44 inference(modus_ponens,[status(thm)],[152, 151])).
% 10.27/10.44 tff(154,plain,
% 10.27/10.44 (less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa))),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[153, 147, 82, 14])).
% 10.27/10.44 tff(155,plain,
% 10.27/10.44 (less_equal(idQ_idQa, a)),
% 10.27/10.44 inference(unit_resolution,[status(thm)],[154, 137])).
% 10.27/10.44 tff(156,plain,
% 10.27/10.44 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | ((~less_equal(idQ_idQa, a)) | (~quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)) | less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (~less_equal(idQ_idQa, a)) | (~quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)) | less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(157,plain,
% 10.27/10.44 ((less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity))) | (~less_equal(idQ_idQa, a)) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa))) <=> ((~less_equal(idQ_idQa, a)) | (~quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)) | less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.44 inference(rewrite,[status(thm)],[])).
% 10.27/10.44 tff(158,plain,
% 10.27/10.44 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity))) | (~less_equal(idQ_idQa, a)) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | ((~less_equal(idQ_idQa, a)) | (~quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)) | less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity))))))),
% 10.27/10.44 inference(monotonicity,[status(thm)],[157])).
% 10.27/10.44 tff(159,plain,
% 10.27/10.44 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity))) | (~less_equal(idQ_idQa, a)) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (~less_equal(idQ_idQa, a)) | (~quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)) | less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.45 inference(transitivity,[status(thm)],[158, 156])).
% 10.27/10.45 tff(160,plain,
% 10.27/10.45 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity))) | (~less_equal(idQ_idQa, a)) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)))),
% 10.27/10.45 inference(quant_inst,[status(thm)],[])).
% 10.27/10.45 tff(161,plain,
% 10.27/10.45 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (~less_equal(idQ_idQa, a)) | (~quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)) | less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[160, 159])).
% 10.27/10.45 tff(162,plain,
% 10.27/10.45 ((~quotient(idQ_idQa, divide(idQ_idQa, identity), idQ_idQa)) | less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity)))),
% 10.27/10.45 inference(unit_resolution,[status(thm)],[161, 129, 155, 68])).
% 10.27/10.45 tff(163,plain,
% 10.27/10.45 (less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity)))),
% 10.27/10.45 inference(unit_resolution,[status(thm)],[162, 108])).
% 10.27/10.45 tff(164,plain,
% 10.27/10.45 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : refl((less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) <=> (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))))),
% 10.27/10.45 inference(bind,[status(th)],[])).
% 10.27/10.45 tff(165,plain,
% 10.27/10.45 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 10.27/10.45 inference(quant_intro,[status(thm)],[164])).
% 10.27/10.45 tff(166,plain,
% 10.27/10.45 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(167,plain,
% 10.27/10.45 (^[Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : trans(monotonicity(rewrite((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) <=> ((~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))), (((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) | less_equal(W1, W2)) <=> (((~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) | less_equal(W1, W2)))), rewrite((((~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))), (((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) | less_equal(W1, W2)) <=> (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))))),
% 10.27/10.45 inference(bind,[status(th)],[])).
% 10.27/10.45 tff(168,plain,
% 10.27/10.45 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) | less_equal(W1, W2)) <=> ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 10.27/10.45 inference(quant_intro,[status(thm)],[167])).
% 10.27/10.45 tff(169,axiom,(![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : ((((~less_equal(X, Y)) | (~quotient(Z, Y, W1))) | (~quotient(Z, X, W2))) | less_equal(W1, W2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','xLEy_implies_zQyLEzQx')).
% 10.27/10.45 tff(170,plain,
% 10.27/10.45 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[169, 168])).
% 10.27/10.45 tff(171,plain,
% 10.27/10.45 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[170, 166])).
% 10.27/10.45 tff(172,plain,(
% 10.27/10.45 ![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 10.27/10.45 inference(skolemize,[status(sab)],[171])).
% 10.27/10.45 tff(173,plain,
% 10.27/10.45 (![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[172, 165])).
% 10.27/10.45 tff(174,plain,
% 10.27/10.45 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | ((~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))))),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(175,plain,
% 10.27/10.45 ((less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity))))) <=> ((~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))))),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(176,plain,
% 10.27/10.45 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity)))))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | ((~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity)))))))),
% 10.27/10.45 inference(monotonicity,[status(thm)],[175])).
% 10.27/10.45 tff(177,plain,
% 10.27/10.45 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity)))))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))))),
% 10.27/10.45 inference(transitivity,[status(thm)],[176, 174])).
% 10.27/10.45 tff(178,plain,
% 10.27/10.45 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.45 inference(quant_inst,[status(thm)],[])).
% 10.27/10.45 tff(179,plain,
% 10.27/10.45 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~quotient(Z, X, W2)) | (~quotient(Z, Y, W1)) | (~less_equal(X, Y)))) | (~quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)) | less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~less_equal(idQ_idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[178, 177])).
% 10.27/10.45 tff(180,plain,
% 10.27/10.45 (less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)),
% 10.27/10.45 inference(unit_resolution,[status(thm)],[179, 173, 96, 163, 103])).
% 10.27/10.45 tff(181,plain,
% 10.27/10.45 (less_equal(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity)))) <=> less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.45 inference(monotonicity,[status(thm)],[90])).
% 10.27/10.45 tff(182,plain,
% 10.27/10.45 (quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity)) <=> quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), zero)),
% 10.27/10.45 inference(monotonicity,[status(thm)],[54])).
% 10.27/10.45 tff(183,plain,
% 10.27/10.45 (quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), zero) <=> quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))),
% 10.27/10.45 inference(symmetry,[status(thm)],[182])).
% 10.27/10.45 tff(184,plain,
% 10.27/10.45 (^[X: $i] : refl(quotient(X, X, zero) <=> quotient(X, X, zero))),
% 10.27/10.45 inference(bind,[status(th)],[])).
% 10.27/10.45 tff(185,plain,
% 10.27/10.45 (![X: $i] : quotient(X, X, zero) <=> ![X: $i] : quotient(X, X, zero)),
% 10.27/10.45 inference(quant_intro,[status(thm)],[184])).
% 10.27/10.45 tff(186,plain,
% 10.27/10.45 (![X: $i] : quotient(X, X, zero) <=> ![X: $i] : quotient(X, X, zero)),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(187,axiom,(![X: $i] : quotient(X, X, zero)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x_divide_x_is_zero')).
% 10.27/10.45 tff(188,plain,
% 10.27/10.45 (![X: $i] : quotient(X, X, zero)),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[187, 186])).
% 10.27/10.45 tff(189,plain,(
% 10.27/10.45 ![X: $i] : quotient(X, X, zero)),
% 10.27/10.45 inference(skolemize,[status(sab)],[188])).
% 10.27/10.45 tff(190,plain,
% 10.27/10.45 (![X: $i] : quotient(X, X, zero)),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[189, 185])).
% 10.27/10.45 tff(191,plain,
% 10.27/10.45 ((~![X: $i] : quotient(X, X, zero)) | quotient(a, a, zero)),
% 10.27/10.45 inference(quant_inst,[status(thm)],[])).
% 10.27/10.45 tff(192,plain,
% 10.27/10.45 (quotient(a, a, zero)),
% 10.27/10.45 inference(unit_resolution,[status(thm)],[191, 190])).
% 10.27/10.45 tff(193,plain,
% 10.27/10.45 (^[Y: $i, X: $i] : refl(((~quotient(X, Y, zero)) | less_equal(X, Y)) <=> ((~quotient(X, Y, zero)) | less_equal(X, Y)))),
% 10.27/10.45 inference(bind,[status(th)],[])).
% 10.27/10.45 tff(194,plain,
% 10.27/10.45 (![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))),
% 10.27/10.45 inference(quant_intro,[status(thm)],[193])).
% 10.27/10.45 tff(195,plain,
% 10.27/10.45 (![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y)) <=> ![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(196,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')).
% 10.27/10.45 tff(197,plain,
% 10.27/10.45 (![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[196, 195])).
% 10.27/10.45 tff(198,plain,(
% 10.27/10.45 ![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))),
% 10.27/10.45 inference(skolemize,[status(sab)],[197])).
% 10.27/10.45 tff(199,plain,
% 10.27/10.45 (![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[198, 194])).
% 10.27/10.45 tff(200,plain,
% 10.27/10.45 (((~![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))) | ((~quotient(a, a, zero)) | less_equal(a, a))) <=> ((~![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))) | (~quotient(a, a, zero)) | less_equal(a, a))),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(201,plain,
% 10.27/10.45 ((~![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))) | ((~quotient(a, a, zero)) | less_equal(a, a))),
% 10.27/10.45 inference(quant_inst,[status(thm)],[])).
% 10.27/10.45 tff(202,plain,
% 10.27/10.45 ((~![Y: $i, X: $i] : ((~quotient(X, Y, zero)) | less_equal(X, Y))) | (~quotient(a, a, zero)) | less_equal(a, a)),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[201, 200])).
% 10.27/10.45 tff(203,plain,
% 10.27/10.45 (less_equal(a, a)),
% 10.27/10.45 inference(unit_resolution,[status(thm)],[202, 199, 192])).
% 10.27/10.45 tff(204,plain,
% 10.27/10.45 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | ((~less_equal(a, a)) | less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (~less_equal(a, a)) | less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(205,plain,
% 10.27/10.45 ((less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity))) | (~less_equal(a, a)) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity))))) <=> ((~less_equal(a, a)) | less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(206,plain,
% 10.27/10.45 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity))) | (~less_equal(a, a)) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | ((~less_equal(a, a)) | less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity))))))),
% 10.27/10.45 inference(monotonicity,[status(thm)],[205])).
% 10.27/10.45 tff(207,plain,
% 10.27/10.45 (((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity))) | (~less_equal(a, a)) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))) <=> ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (~less_equal(a, a)) | less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.45 inference(transitivity,[status(thm)],[206, 204])).
% 10.27/10.45 tff(208,plain,
% 10.27/10.45 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity))) | (~less_equal(a, a)) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.45 inference(quant_inst,[status(thm)],[])).
% 10.27/10.45 tff(209,plain,
% 10.27/10.45 ((~![Z: $i, Y: $i, W2: $i, W1: $i, X: $i] : (less_equal(W1, W2) | (~less_equal(X, Y)) | (~quotient(Y, Z, W2)) | (~quotient(X, Z, W1)))) | (~less_equal(a, a)) | less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity))) | (~quotient(a, divide(idQ_idQa, identity), divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[208, 207])).
% 10.27/10.45 tff(210,plain,
% 10.27/10.45 (less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)))),
% 10.27/10.45 inference(unit_resolution,[status(thm)],[209, 129, 203, 68])).
% 10.27/10.45 tff(211,plain,
% 10.27/10.45 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)))) | quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)))) | quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), zero))),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(212,plain,
% 10.27/10.45 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)))) | quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), zero))),
% 10.27/10.45 inference(quant_inst,[status(thm)],[])).
% 10.27/10.45 tff(213,plain,
% 10.27/10.45 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)))) | quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), zero)),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[212, 211])).
% 10.27/10.45 tff(214,plain,
% 10.27/10.45 (quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), zero)),
% 10.27/10.45 inference(unit_resolution,[status(thm)],[213, 32, 210])).
% 10.27/10.45 tff(215,plain,
% 10.27/10.45 (quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[214, 183])).
% 10.27/10.45 tff(216,plain,
% 10.27/10.45 (quotient(idQa, divide(idQ_idQa, identity), idQa) <=> quotient(idQa, zero, idQa)),
% 10.27/10.45 inference(monotonicity,[status(thm)],[54])).
% 10.27/10.45 tff(217,plain,
% 10.27/10.45 (quotient(idQa, zero, idQa) <=> quotient(idQa, divide(idQ_idQa, identity), idQa)),
% 10.27/10.45 inference(symmetry,[status(thm)],[216])).
% 10.27/10.45 tff(218,plain,
% 10.27/10.45 ((~![X: $i] : quotient(X, zero, X)) | quotient(idQa, zero, idQa)),
% 10.27/10.45 inference(quant_inst,[status(thm)],[])).
% 10.27/10.45 tff(219,plain,
% 10.27/10.45 (quotient(idQa, zero, idQa)),
% 10.27/10.45 inference(unit_resolution,[status(thm)],[218, 63])).
% 10.27/10.45 tff(220,plain,
% 10.27/10.45 (quotient(idQa, divide(idQ_idQa, identity), idQa)),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[219, 217])).
% 10.27/10.45 tff(221,plain,
% 10.27/10.45 (^[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))))),
% 10.27/10.45 inference(bind,[status(th)],[])).
% 10.27/10.45 tff(222,plain,
% 10.27/10.45 (![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)))),
% 10.27/10.45 inference(quant_intro,[status(thm)],[221])).
% 10.27/10.45 tff(223,plain,
% 10.27/10.45 (![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)))),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(224,plain,
% 10.27/10.45 (^[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)))))),
% 10.27/10.45 inference(bind,[status(th)],[])).
% 10.27/10.45 tff(225,plain,
% 10.27/10.45 (![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)))),
% 10.27/10.45 inference(quant_intro,[status(thm)],[224])).
% 10.27/10.45 tff(226,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')).
% 10.27/10.45 tff(227,plain,
% 10.27/10.45 (![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)))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[226, 225])).
% 10.27/10.45 tff(228,plain,
% 10.27/10.45 (![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)))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[227, 223])).
% 10.27/10.45 tff(229,plain,(
% 10.27/10.45 ![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)))),
% 10.27/10.45 inference(skolemize,[status(sab)],[228])).
% 10.27/10.45 tff(230,plain,
% 10.27/10.45 (![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)))),
% 10.27/10.45 inference(modus_ponens,[status(thm)],[229, 222])).
% 10.27/10.45 tff(231,plain,
% 10.27/10.45 (((~![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)))) | ((~quotient(idQa, divide(idQ_idQa, identity), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))) | less_equal(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))))) <=> ((~![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)))) | (~quotient(idQa, divide(idQ_idQa, identity), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))) | less_equal(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))))),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(232,plain,
% 10.27/10.45 ((less_equal(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~quotient(idQa, divide(idQ_idQa, identity), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa))) <=> ((~quotient(idQa, divide(idQ_idQa, identity), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))) | less_equal(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))))),
% 10.27/10.45 inference(rewrite,[status(thm)],[])).
% 10.27/10.45 tff(233,plain,
% 10.27/10.45 (((~![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(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~quotient(idQa, divide(idQ_idQa, identity), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)))) <=> ((~![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)))) | ((~quotient(idQa, divide(idQ_idQa, identity), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))) | less_equal(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity)))))))),
% 10.27/10.46 inference(monotonicity,[status(thm)],[232])).
% 10.27/10.46 tff(234,plain,
% 10.27/10.46 (((~![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(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~quotient(idQa, divide(idQ_idQa, identity), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)))) <=> ((~![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)))) | (~quotient(idQa, divide(idQ_idQa, identity), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))) | less_equal(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))))),
% 10.27/10.46 inference(transitivity,[status(thm)],[233, 231])).
% 10.27/10.46 tff(235,plain,
% 10.27/10.46 ((~![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(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~quotient(idQa, divide(idQ_idQa, identity), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)))),
% 10.27/10.46 inference(quant_inst,[status(thm)],[])).
% 10.27/10.46 tff(236,plain,
% 10.27/10.46 ((~![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)))) | (~quotient(idQa, divide(idQ_idQa, identity), idQa)) | (~quotient(identity, divide(a, divide(idQ_idQa, identity)), idQa)) | (~quotient(divide(a, divide(idQ_idQa, identity)), divide(a, divide(idQ_idQa, identity)), divide(idQ_idQa, identity))) | less_equal(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity)))) | (~quotient(idQa, divide(a, divide(idQ_idQa, identity)), divide(idQa, divide(a, divide(idQ_idQa, identity)))))),
% 10.27/10.46 inference(modus_ponens,[status(thm)],[235, 234])).
% 10.27/10.46 tff(237,plain,
% 10.27/10.46 (less_equal(idQa, divide(idQa, divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.46 inference(unit_resolution,[status(thm)],[236, 230, 220, 83, 215, 103])).
% 10.27/10.46 tff(238,plain,
% 10.27/10.46 (less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))),
% 10.27/10.46 inference(modus_ponens,[status(thm)],[237, 181])).
% 10.27/10.46 tff(239,plain,
% 10.27/10.46 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 10.27/10.46 inference(rewrite,[status(thm)],[])).
% 10.27/10.46 tff(240,plain,
% 10.27/10.46 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 10.27/10.46 inference(rewrite,[status(thm)],[])).
% 10.27/10.46 tff(241,plain,
% 10.27/10.46 (^[Z: $i, Y: $i, X: $i] : rewrite((((~less_equal(X, Y)) | (~less_equal(Y, Z))) | less_equal(X, Z)) <=> ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z))))),
% 10.27/10.46 inference(bind,[status(th)],[])).
% 10.27/10.46 tff(242,plain,
% 10.27/10.46 (![Z: $i, Y: $i, X: $i] : (((~less_equal(X, Y)) | (~less_equal(Y, Z))) | less_equal(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 10.27/10.46 inference(quant_intro,[status(thm)],[241])).
% 10.27/10.46 tff(243,axiom,(![Z: $i, Y: $i, X: $i] : (((~less_equal(X, Y)) | (~less_equal(Y, Z))) | less_equal(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity_of_less_equal')).
% 10.27/10.46 tff(244,plain,
% 10.27/10.46 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 10.27/10.46 inference(modus_ponens,[status(thm)],[243, 242])).
% 10.27/10.46 tff(245,plain,
% 10.27/10.46 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 10.27/10.46 inference(modus_ponens,[status(thm)],[244, 240])).
% 10.27/10.46 tff(246,plain,(
% 10.27/10.46 ![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 10.27/10.46 inference(skolemize,[status(sab)],[245])).
% 10.27/10.46 tff(247,plain,
% 10.27/10.46 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 10.27/10.46 inference(modus_ponens,[status(thm)],[246, 239])).
% 10.27/10.46 tff(248,plain,
% 10.27/10.46 (((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)) | less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)) | less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa))),
% 10.27/10.46 inference(rewrite,[status(thm)],[])).
% 10.27/10.46 tff(249,plain,
% 10.27/10.46 (((~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa))) <=> ((~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)) | less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa))),
% 10.27/10.46 inference(rewrite,[status(thm)],[])).
% 10.27/10.46 tff(250,plain,
% 10.27/10.46 (((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)) | less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)))),
% 10.27/10.46 inference(monotonicity,[status(thm)],[249])).
% 10.27/10.46 tff(251,plain,
% 10.27/10.46 (((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)) | less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa))),
% 10.27/10.46 inference(transitivity,[status(thm)],[250, 248])).
% 10.27/10.46 tff(252,plain,
% 10.27/10.46 ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa) | (~less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)))),
% 10.27/10.46 inference(quant_inst,[status(thm)],[])).
% 10.27/10.46 tff(253,plain,
% 10.27/10.46 ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), divide(idQa, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(idQa, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)) | less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)),
% 10.27/10.46 inference(modus_ponens,[status(thm)],[252, 251])).
% 10.27/10.46 tff(254,plain,
% 10.27/10.46 (less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)),
% 10.27/10.46 inference(unit_resolution,[status(thm)],[253, 247, 238, 180])).
% 10.27/10.46 tff(255,plain,
% 10.27/10.46 (![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)))),
% 10.27/10.46 inference(rewrite,[status(thm)],[])).
% 10.27/10.46 tff(256,plain,
% 10.27/10.46 (![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)))),
% 10.27/10.46 inference(rewrite,[status(thm)],[])).
% 10.27/10.46 tff(257,plain,
% 10.27/10.46 (^[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))))),
% 10.27/10.46 inference(bind,[status(th)],[])).
% 10.27/10.46 tff(258,plain,
% 10.27/10.46 (![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)))),
% 10.27/10.46 inference(quant_intro,[status(thm)],[257])).
% 10.27/10.46 tff(259,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')).
% 10.27/10.46 tff(260,plain,
% 10.27/10.46 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 10.27/10.46 inference(modus_ponens,[status(thm)],[259, 258])).
% 10.27/10.46 tff(261,plain,
% 10.27/10.46 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 10.27/10.46 inference(modus_ponens,[status(thm)],[260, 256])).
% 10.27/10.46 tff(262,plain,(
% 10.27/10.46 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 10.27/10.46 inference(skolemize,[status(sab)],[261])).
% 10.27/10.46 tff(263,plain,
% 10.27/10.46 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 10.27/10.46 inference(modus_ponens,[status(thm)],[262, 255])).
% 10.27/10.46 tff(264,plain,
% 10.27/10.46 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((idQa_Q__idQ_idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa_Q__idQ_idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)))),
% 10.27/10.46 inference(rewrite,[status(thm)],[])).
% 10.27/10.46 tff(265,plain,
% 10.27/10.46 (((~less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))) | (idQa_Q__idQ_idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa))) <=> ((idQa_Q__idQ_idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)))),
% 10.27/10.46 inference(rewrite,[status(thm)],[])).
% 10.27/10.46 tff(266,plain,
% 10.27/10.46 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))) | (idQa_Q__idQ_idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((idQa_Q__idQ_idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa))))),
% 10.27/10.46 inference(monotonicity,[status(thm)],[265])).
% 10.27/10.46 tff(267,plain,
% 10.27/10.46 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))) | (idQa_Q__idQ_idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa_Q__idQ_idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)))),
% 10.27/10.46 inference(transitivity,[status(thm)],[266, 264])).
% 10.27/10.46 tff(268,plain,
% 10.27/10.46 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))) | (idQa_Q__idQ_idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa)))),
% 10.27/10.46 inference(quant_inst,[status(thm)],[])).
% 10.27/10.46 tff(269,plain,
% 10.27/10.46 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa_Q__idQ_idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))) | (~less_equal(idQa_Q__idQ_idQa, divide(identity, divide(a, divide(idQ_idQa, identity))))) | (~less_equal(divide(identity, divide(a, divide(idQ_idQa, identity))), idQa_Q__idQ_idQa))),
% 10.27/10.46 inference(modus_ponens,[status(thm)],[268, 267])).
% 10.27/10.46 tff(270,plain,
% 10.27/10.46 (idQa_Q__idQ_idQa = divide(identity, divide(a, divide(idQ_idQa, identity)))),
% 10.27/10.46 inference(unit_resolution,[status(thm)],[269, 263, 254, 101])).
% 10.27/10.46 tff(271,plain,
% 10.27/10.46 (divide(identity, divide(a, divide(idQ_idQa, identity))) = idQa_Q__idQ_idQa),
% 10.27/10.46 inference(symmetry,[status(thm)],[270])).
% 10.27/10.46 tff(272,plain,
% 10.27/10.46 (idQa = idQa_Q__idQ_idQa),
% 10.27/10.46 inference(transitivity,[status(thm)],[90, 271])).
% 10.27/10.46 tff(273,plain,
% 10.27/10.46 ((~(idQa = idQa_Q__idQ_idQa)) <=> (~(idQa = idQa_Q__idQ_idQa))),
% 10.27/10.48 inference(rewrite,[status(thm)],[])).
% 10.27/10.48 tff(274,axiom,(~(idQa = idQa_Q__idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_idQa_equals_idQa_Q__idQ_idQa')).
% 10.27/10.48 tff(275,plain,
% 10.27/10.48 (~(idQa = idQa_Q__idQ_idQa)),
% 10.27/10.48 inference(modus_ponens,[status(thm)],[274, 273])).
% 10.27/10.48 tff(276,plain,
% 10.27/10.48 ($false),
% 10.27/10.48 inference(unit_resolution,[status(thm)],[275, 272])).
% 10.27/10.48 % SZS output end Proof
% 10.27/10.48 % E exiting
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