%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HEN010-2 : 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 0.92s 1.16s
% Output : Proof 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : HEN010-2 : TPTP v9.0.0. Released v1.0.0.
% 0.01/0.12 % 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 17:15:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.92/1.16 % SZS status Unsatisfiable
% 0.92/1.16 % SZS output start Proof
% 0.92/1.16 tff(less_equal_type, type, (
% 0.92/1.16 less_equal: ( $i * $i ) > $o)).
% 0.92/1.16 tff(divide_type, type, (
% 0.92/1.16 divide: ( $i * $i ) > $i)).
% 0.92/1.16 tff(a_type, type, (
% 0.92/1.16 a: $i)).
% 0.92/1.16 tff(zero_type, type, (
% 0.92/1.16 zero: $i)).
% 0.92/1.16 tff(idQa_type, type, (
% 0.92/1.16 idQa: $i)).
% 0.92/1.16 tff(quotient_type, type, (
% 0.92/1.16 quotient: ( $i * $i * $i ) > $o)).
% 0.92/1.16 tff(identity_type, type, (
% 0.92/1.16 identity: $i)).
% 0.92/1.16 tff(idQa_Q__idQ_idQa_type, type, (
% 0.92/1.16 idQa_Q__idQ_idQa: $i)).
% 0.92/1.16 tff(idQ_idQa_type, type, (
% 0.92/1.16 idQ_idQa: $i)).
% 0.92/1.16 tff(1,plain,
% 0.92/1.16 (^[Y: $i, X: $i] : refl(quotient(X, Y, divide(X, Y)) <=> quotient(X, Y, divide(X, Y)))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(2,plain,
% 0.92/1.16 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y)) <=> ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[1])).
% 0.92/1.16 tff(3,plain,
% 0.92/1.16 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y)) <=> ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(4,axiom,(![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','closure')).
% 0.92/1.16 tff(5,plain,
% 0.92/1.16 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.92/1.16 tff(6,plain,(
% 0.92/1.16 ![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.92/1.16 inference(skolemize,[status(sab)],[5])).
% 0.92/1.16 tff(7,plain,
% 0.92/1.16 (![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.92/1.16 tff(8,plain,
% 0.92/1.16 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(9,plain,
% 0.92/1.16 (quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.92/1.16 tff(10,plain,
% 0.92/1.16 (^[X: $i] : refl(quotient(X, zero, X) <=> quotient(X, zero, X))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(11,plain,
% 0.92/1.16 (![X: $i] : quotient(X, zero, X) <=> ![X: $i] : quotient(X, zero, X)),
% 0.92/1.16 inference(quant_intro,[status(thm)],[10])).
% 0.92/1.16 tff(12,plain,
% 0.92/1.16 (![X: $i] : quotient(X, zero, X) <=> ![X: $i] : quotient(X, zero, X)),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(13,axiom,(![X: $i] : quotient(X, zero, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x_divde_zero_is_x')).
% 0.92/1.16 tff(14,plain,
% 0.92/1.16 (![X: $i] : quotient(X, zero, X)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.92/1.16 tff(15,plain,(
% 0.92/1.16 ![X: $i] : quotient(X, zero, X)),
% 0.92/1.16 inference(skolemize,[status(sab)],[14])).
% 0.92/1.16 tff(16,plain,
% 0.92/1.16 (![X: $i] : quotient(X, zero, X)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.92/1.16 tff(17,plain,
% 0.92/1.16 ((~![X: $i] : quotient(X, zero, X)) | quotient(idQa, zero, idQa)),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(18,plain,
% 0.92/1.16 (quotient(idQa, zero, idQa)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.92/1.16 tff(19,plain,
% 0.92/1.16 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(idQa, zero, divide(idQa, zero))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(20,plain,
% 0.92/1.16 (quotient(idQa, zero, divide(idQa, zero))),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[19, 7])).
% 0.92/1.16 tff(21,plain,
% 0.92/1.16 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))) <=> ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(22,plain,
% 0.92/1.16 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[21])).
% 0.92/1.16 tff(23,plain,
% 0.92/1.16 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(24,plain,
% 0.92/1.16 (^[W: $i, Z: $i, Y: $i, X: $i] : rewrite((((~quotient(X, Y, Z)) | (~quotient(X, Y, W))) | (Z = W)) <=> ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W))))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(25,plain,
% 0.92/1.16 (![W: $i, Z: $i, Y: $i, X: $i] : (((~quotient(X, Y, Z)) | (~quotient(X, Y, W))) | (Z = W)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[24])).
% 0.92/1.16 tff(26,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~quotient(X, Y, Z)) | (~quotient(X, Y, W))) | (Z = W))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','well_defined')).
% 0.92/1.16 tff(27,plain,
% 0.92/1.16 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.92/1.16 tff(28,plain,
% 0.92/1.16 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.92/1.16 tff(29,plain,(
% 0.92/1.16 ![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.92/1.16 inference(skolemize,[status(sab)],[28])).
% 0.92/1.16 tff(30,plain,
% 0.92/1.16 (![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.92/1.16 tff(31,plain,
% 0.92/1.16 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((idQa = divide(idQa, zero)) | (~quotient(idQa, zero, idQa)) | (~quotient(idQa, zero, divide(idQa, zero))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (idQa = divide(idQa, zero)) | (~quotient(idQa, zero, idQa)) | (~quotient(idQa, zero, divide(idQa, zero))))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(32,plain,
% 0.92/1.16 (((~quotient(idQa, zero, idQa)) | (idQa = divide(idQa, zero)) | (~quotient(idQa, zero, divide(idQa, zero)))) <=> ((idQa = divide(idQa, zero)) | (~quotient(idQa, zero, idQa)) | (~quotient(idQa, zero, divide(idQa, zero))))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(33,plain,
% 0.92/1.16 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, zero, idQa)) | (idQa = divide(idQa, zero)) | (~quotient(idQa, zero, divide(idQa, zero))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((idQa = divide(idQa, zero)) | (~quotient(idQa, zero, idQa)) | (~quotient(idQa, zero, divide(idQa, zero)))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[32])).
% 0.92/1.16 tff(34,plain,
% 0.92/1.16 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, zero, idQa)) | (idQa = divide(idQa, zero)) | (~quotient(idQa, zero, divide(idQa, zero))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (idQa = divide(idQa, zero)) | (~quotient(idQa, zero, idQa)) | (~quotient(idQa, zero, divide(idQa, zero))))),
% 0.92/1.16 inference(transitivity,[status(thm)],[33, 31])).
% 0.92/1.16 tff(35,plain,
% 0.92/1.16 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQa, zero, idQa)) | (idQa = divide(idQa, zero)) | (~quotient(idQa, zero, divide(idQa, zero))))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(36,plain,
% 0.92/1.16 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (idQa = divide(idQa, zero)) | (~quotient(idQa, zero, idQa)) | (~quotient(idQa, zero, divide(idQa, zero)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.92/1.16 tff(37,plain,
% 0.92/1.16 (idQa = divide(idQa, zero)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[36, 30, 20, 18])).
% 0.92/1.16 tff(38,plain,
% 0.92/1.16 (divide(idQa, zero) = idQa),
% 0.92/1.16 inference(symmetry,[status(thm)],[37])).
% 0.92/1.16 tff(39,plain,
% 0.92/1.16 (quotient(identity, a, divide(idQa, zero)) <=> quotient(identity, a, idQa)),
% 0.92/1.16 inference(monotonicity,[status(thm)],[38])).
% 0.92/1.16 tff(40,plain,
% 0.92/1.16 (quotient(identity, a, idQa) <=> quotient(identity, a, divide(idQa, zero))),
% 0.92/1.16 inference(symmetry,[status(thm)],[39])).
% 0.92/1.16 tff(41,plain,
% 0.92/1.16 (quotient(identity, a, idQa) <=> quotient(identity, a, idQa)),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(42,axiom,(quotient(identity, a, idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_a')).
% 0.92/1.16 tff(43,plain,
% 0.92/1.16 (quotient(identity, a, idQa)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.92/1.16 tff(44,plain,
% 0.92/1.16 (quotient(identity, a, divide(idQa, zero))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.92/1.16 tff(45,plain,
% 0.92/1.16 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(zero, zero, divide(zero, zero))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(46,plain,
% 0.92/1.16 (quotient(zero, zero, divide(zero, zero))),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[45, 7])).
% 0.92/1.16 tff(47,plain,
% 0.92/1.16 (quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa) <=> quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(48,axiom,(quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_idQ_idQa')).
% 0.92/1.16 tff(49,plain,
% 0.92/1.16 (quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.92/1.16 tff(50,plain,
% 0.92/1.16 (^[Z: $i, Y: $i, X: $i] : refl(((~quotient(X, Y, Z)) | less_equal(Z, X)) <=> ((~quotient(X, Y, Z)) | less_equal(Z, X)))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(51,plain,
% 0.92/1.16 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[50])).
% 0.92/1.16 tff(52,plain,
% 0.92/1.16 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(53,axiom,(![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','divisor_existence')).
% 0.92/1.16 tff(54,plain,
% 0.92/1.16 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.92/1.16 tff(55,plain,(
% 0.92/1.16 ![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.92/1.16 inference(skolemize,[status(sab)],[54])).
% 0.92/1.16 tff(56,plain,
% 0.92/1.16 (![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.92/1.16 tff(57,plain,
% 0.92/1.16 (((~![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))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(58,plain,
% 0.92/1.16 ((~![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))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(59,plain,
% 0.92/1.16 ((~![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)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.92/1.16 tff(60,plain,
% 0.92/1.16 (less_equal(idQa_Q__idQ_idQa, idQa)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[59, 56, 49])).
% 0.92/1.16 tff(61,plain,
% 0.92/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(identity, a, idQa)) | less_equal(idQa, identity))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(identity, a, idQa)) | less_equal(idQa, identity))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(62,plain,
% 0.92/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | ((~quotient(identity, a, idQa)) | less_equal(idQa, identity))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(63,plain,
% 0.92/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | less_equal(Z, X))) | (~quotient(identity, a, idQa)) | less_equal(idQa, identity)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.92/1.16 tff(64,plain,
% 0.92/1.16 (less_equal(idQa, identity)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[63, 56, 43])).
% 0.92/1.16 tff(65,plain,
% 0.92/1.16 (![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)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(66,plain,
% 0.92/1.16 (![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)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(67,plain,
% 0.92/1.16 (^[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))))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(68,plain,
% 0.92/1.16 (![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)))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[67])).
% 0.92/1.16 tff(69,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')).
% 0.92/1.16 tff(70,plain,
% 0.92/1.16 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.92/1.16 tff(71,plain,
% 0.92/1.16 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.92/1.16 tff(72,plain,(
% 0.92/1.16 ![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 0.92/1.16 inference(skolemize,[status(sab)],[71])).
% 0.92/1.16 tff(73,plain,
% 0.92/1.16 (![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.92/1.16 tff(74,plain,
% 0.92/1.16 (((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(idQa_Q__idQ_idQa, idQa)) | less_equal(idQa_Q__idQ_idQa, identity) | (~less_equal(idQa, identity)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | less_equal(idQa_Q__idQ_idQa, identity) | (~less_equal(idQa, identity)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(75,plain,
% 0.92/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(idQa_Q__idQ_idQa, idQa)) | less_equal(idQa_Q__idQ_idQa, identity) | (~less_equal(idQa, identity)))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(76,plain,
% 0.92/1.16 ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | less_equal(idQa_Q__idQ_idQa, identity) | (~less_equal(idQa, identity))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.92/1.16 tff(77,plain,
% 0.92/1.16 (less_equal(idQa_Q__idQ_idQa, identity)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[76, 73, 64, 60])).
% 0.92/1.16 tff(78,plain,
% 0.92/1.16 (^[Y: $i, X: $i] : refl(((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ((~less_equal(X, Y)) | quotient(X, Y, zero)))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(79,plain,
% 0.92/1.16 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[78])).
% 0.92/1.16 tff(80,plain,
% 0.92/1.16 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero)) <=> ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(81,axiom,(![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','quotient_less_equal')).
% 0.92/1.16 tff(82,plain,
% 0.92/1.16 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.92/1.16 tff(83,plain,(
% 0.92/1.16 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.92/1.16 inference(skolemize,[status(sab)],[82])).
% 0.92/1.16 tff(84,plain,
% 0.92/1.16 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.92/1.16 tff(85,plain,
% 0.92/1.16 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(idQa_Q__idQ_idQa, identity)) | quotient(idQa_Q__idQ_idQa, identity, zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(idQa_Q__idQ_idQa, identity)) | quotient(idQa_Q__idQ_idQa, identity, zero))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(86,plain,
% 0.92/1.16 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(idQa_Q__idQ_idQa, identity)) | quotient(idQa_Q__idQ_idQa, identity, zero))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(87,plain,
% 0.92/1.16 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(idQa_Q__idQ_idQa, identity)) | quotient(idQa_Q__idQ_idQa, identity, zero)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.92/1.16 tff(88,plain,
% 0.92/1.16 (quotient(idQa_Q__idQ_idQa, identity, zero)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[87, 84, 77])).
% 0.92/1.16 tff(89,plain,
% 0.92/1.16 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(idQa, identity)) | quotient(idQa, identity, zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(idQa, identity)) | quotient(idQa, identity, zero))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(90,plain,
% 0.92/1.16 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(idQa, identity)) | quotient(idQa, identity, zero))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(91,plain,
% 0.92/1.16 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(idQa, identity)) | quotient(idQa, identity, zero)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.92/1.16 tff(92,plain,
% 0.92/1.16 (quotient(idQa, identity, zero)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[91, 84, 64])).
% 0.92/1.16 tff(93,plain,
% 0.92/1.16 (^[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))))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(94,plain,
% 0.92/1.16 (![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)))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[93])).
% 0.92/1.16 tff(95,plain,
% 0.92/1.16 (![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)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(96,plain,
% 0.92/1.16 (^[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)))))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(97,plain,
% 0.92/1.16 (![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)))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[96])).
% 0.92/1.16 tff(98,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')).
% 0.92/1.16 tff(99,plain,
% 0.92/1.16 (![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)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.92/1.17 tff(100,plain,
% 0.92/1.17 (![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)))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.92/1.17 tff(101,plain,(
% 0.92/1.17 ![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)))),
% 0.92/1.17 inference(skolemize,[status(sab)],[100])).
% 0.92/1.17 tff(102,plain,
% 0.92/1.17 (![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)))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.92/1.17 tff(103,plain,
% 0.92/1.17 (((~![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_Q__idQ_idQa, idQa)) | less_equal(zero, zero) | (~quotient(idQa, identity, zero)) | (~quotient(idQa_Q__idQ_idQa, identity, zero)))) <=> ((~![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_Q__idQ_idQa, idQa)) | less_equal(zero, zero) | (~quotient(idQa, identity, zero)) | (~quotient(idQa_Q__idQ_idQa, identity, zero)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(104,plain,
% 0.92/1.17 ((less_equal(zero, zero) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~quotient(idQa, identity, zero)) | (~quotient(idQa_Q__idQ_idQa, identity, zero))) <=> ((~less_equal(idQa_Q__idQ_idQa, idQa)) | less_equal(zero, zero) | (~quotient(idQa, identity, zero)) | (~quotient(idQa_Q__idQ_idQa, identity, zero)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(105,plain,
% 0.92/1.17 (((~![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(zero, zero) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~quotient(idQa, identity, zero)) | (~quotient(idQa_Q__idQ_idQa, identity, zero)))) <=> ((~![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_Q__idQ_idQa, idQa)) | less_equal(zero, zero) | (~quotient(idQa, identity, zero)) | (~quotient(idQa_Q__idQ_idQa, identity, zero))))),
% 0.92/1.17 inference(monotonicity,[status(thm)],[104])).
% 0.92/1.17 tff(106,plain,
% 0.92/1.17 (((~![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(zero, zero) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~quotient(idQa, identity, zero)) | (~quotient(idQa_Q__idQ_idQa, identity, zero)))) <=> ((~![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_Q__idQ_idQa, idQa)) | less_equal(zero, zero) | (~quotient(idQa, identity, zero)) | (~quotient(idQa_Q__idQ_idQa, identity, zero)))),
% 0.92/1.17 inference(transitivity,[status(thm)],[105, 103])).
% 0.92/1.17 tff(107,plain,
% 0.92/1.17 ((~![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(zero, zero) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~quotient(idQa, identity, zero)) | (~quotient(idQa_Q__idQ_idQa, identity, zero)))),
% 0.92/1.17 inference(quant_inst,[status(thm)],[])).
% 0.92/1.17 tff(108,plain,
% 0.92/1.17 ((~![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_Q__idQ_idQa, idQa)) | less_equal(zero, zero) | (~quotient(idQa, identity, zero)) | (~quotient(idQa_Q__idQ_idQa, identity, zero))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.92/1.17 tff(109,plain,
% 0.92/1.17 (less_equal(zero, zero)),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[108, 102, 60, 92, 88])).
% 0.92/1.17 tff(110,plain,
% 0.92/1.17 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(zero, zero)) | quotient(zero, zero, zero))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(zero, zero)) | quotient(zero, zero, zero))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(111,plain,
% 1.01/1.17 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | ((~less_equal(zero, zero)) | quotient(zero, zero, zero))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(112,plain,
% 1.01/1.17 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | quotient(X, Y, zero))) | (~less_equal(zero, zero)) | quotient(zero, zero, zero)),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.01/1.17 tff(113,plain,
% 1.01/1.17 (quotient(zero, zero, zero)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[112, 84, 109])).
% 1.01/1.17 tff(114,plain,
% 1.01/1.17 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((zero = divide(zero, zero)) | (~quotient(zero, zero, zero)) | (~quotient(zero, zero, divide(zero, zero))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (zero = divide(zero, zero)) | (~quotient(zero, zero, zero)) | (~quotient(zero, zero, divide(zero, zero))))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(115,plain,
% 1.01/1.17 (((~quotient(zero, zero, zero)) | (zero = divide(zero, zero)) | (~quotient(zero, zero, divide(zero, zero)))) <=> ((zero = divide(zero, zero)) | (~quotient(zero, zero, zero)) | (~quotient(zero, zero, divide(zero, zero))))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(116,plain,
% 1.01/1.17 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(zero, zero, zero)) | (zero = divide(zero, zero)) | (~quotient(zero, zero, divide(zero, zero))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((zero = divide(zero, zero)) | (~quotient(zero, zero, zero)) | (~quotient(zero, zero, divide(zero, zero)))))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[115])).
% 1.01/1.17 tff(117,plain,
% 1.01/1.17 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(zero, zero, zero)) | (zero = divide(zero, zero)) | (~quotient(zero, zero, divide(zero, zero))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (zero = divide(zero, zero)) | (~quotient(zero, zero, zero)) | (~quotient(zero, zero, divide(zero, zero))))),
% 1.01/1.17 inference(transitivity,[status(thm)],[116, 114])).
% 1.01/1.17 tff(118,plain,
% 1.01/1.17 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(zero, zero, zero)) | (zero = divide(zero, zero)) | (~quotient(zero, zero, divide(zero, zero))))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(119,plain,
% 1.01/1.17 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (zero = divide(zero, zero)) | (~quotient(zero, zero, zero)) | (~quotient(zero, zero, divide(zero, zero)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.01/1.17 tff(120,plain,
% 1.01/1.17 (zero = divide(zero, zero)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[119, 30, 113, 46])).
% 1.01/1.17 tff(121,plain,
% 1.01/1.17 (divide(zero, zero) = zero),
% 1.01/1.17 inference(symmetry,[status(thm)],[120])).
% 1.01/1.17 tff(122,plain,
% 1.01/1.17 (quotient(a, a, divide(zero, zero)) <=> quotient(a, a, zero)),
% 1.01/1.17 inference(monotonicity,[status(thm)],[121])).
% 1.01/1.17 tff(123,plain,
% 1.01/1.17 (quotient(a, a, zero) <=> quotient(a, a, divide(zero, zero))),
% 1.01/1.17 inference(symmetry,[status(thm)],[122])).
% 1.01/1.17 tff(124,assumption,(~quotient(a, a, zero)), introduced(assumption)).
% 1.01/1.17 tff(125,plain,
% 1.01/1.17 (^[X: $i] : refl(quotient(X, X, zero) <=> quotient(X, X, zero))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(126,plain,
% 1.01/1.17 (![X: $i] : quotient(X, X, zero) <=> ![X: $i] : quotient(X, X, zero)),
% 1.01/1.17 inference(quant_intro,[status(thm)],[125])).
% 1.01/1.17 tff(127,plain,
% 1.01/1.17 (![X: $i] : quotient(X, X, zero) <=> ![X: $i] : quotient(X, X, zero)),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(128,axiom,(![X: $i] : quotient(X, X, zero)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x_divide_x_is_zero')).
% 1.01/1.17 tff(129,plain,
% 1.01/1.17 (![X: $i] : quotient(X, X, zero)),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.01/1.17 tff(130,plain,(
% 1.01/1.17 ![X: $i] : quotient(X, X, zero)),
% 1.01/1.17 inference(skolemize,[status(sab)],[129])).
% 1.01/1.17 tff(131,plain,
% 1.01/1.17 (![X: $i] : quotient(X, X, zero)),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[130, 126])).
% 1.01/1.17 tff(132,plain,
% 1.01/1.17 ((~![X: $i] : quotient(X, X, zero)) | quotient(a, a, zero)),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(133,plain,
% 1.01/1.17 ($false),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[132, 131, 124])).
% 1.01/1.17 tff(134,plain,(quotient(a, a, zero)), inference(lemma,lemma(discharge,[]))).
% 1.01/1.17 tff(135,plain,
% 1.01/1.17 (quotient(a, a, divide(zero, zero))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[134, 123])).
% 1.01/1.17 tff(136,plain,
% 1.01/1.17 (quotient(divide(idQa, zero), divide(zero, zero), divide(idQa, zero)) <=> quotient(idQa, zero, divide(idQa, zero))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[38, 121])).
% 1.01/1.17 tff(137,plain,
% 1.01/1.17 (quotient(idQa, zero, divide(idQa, zero)) <=> quotient(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))),
% 1.01/1.17 inference(symmetry,[status(thm)],[136])).
% 1.01/1.17 tff(138,plain,
% 1.01/1.17 (quotient(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[20, 137])).
% 1.01/1.17 tff(139,plain,
% 1.01/1.17 (^[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))))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(140,plain,
% 1.01/1.17 (![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)))),
% 1.01/1.17 inference(quant_intro,[status(thm)],[139])).
% 1.01/1.17 tff(141,plain,
% 1.01/1.17 (![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)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(142,plain,
% 1.01/1.17 (^[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)))))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(143,plain,
% 1.01/1.17 (![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)))),
% 1.01/1.17 inference(quant_intro,[status(thm)],[142])).
% 1.01/1.17 tff(144,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')).
% 1.01/1.17 tff(145,plain,
% 1.01/1.17 (![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)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.01/1.17 tff(146,plain,
% 1.01/1.17 (![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)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[145, 141])).
% 1.01/1.17 tff(147,plain,(
% 1.01/1.17 ![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)))),
% 1.01/1.17 inference(skolemize,[status(sab)],[146])).
% 1.01/1.17 tff(148,plain,
% 1.01/1.17 (![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)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[147, 140])).
% 1.01/1.17 tff(149,plain,
% 1.01/1.17 (((~![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(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))) | (~quotient(a, a, divide(zero, zero))) | (~quotient(identity, a, divide(idQa, zero))) | less_equal(divide(idQa, zero), divide(divide(idQa, zero), a)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))))) <=> ((~![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(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))) | (~quotient(a, a, divide(zero, zero))) | (~quotient(identity, a, divide(idQa, zero))) | less_equal(divide(idQa, zero), divide(divide(idQa, zero), a)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(150,plain,
% 1.01/1.17 ((less_equal(divide(idQa, zero), divide(divide(idQa, zero), a)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))) | (~quotient(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))) | (~quotient(identity, a, divide(idQa, zero))) | (~quotient(a, a, divide(zero, zero))) | (~quotient(identity, a, divide(idQa, zero)))) <=> ((~quotient(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))) | (~quotient(a, a, divide(zero, zero))) | (~quotient(identity, a, divide(idQa, zero))) | less_equal(divide(idQa, zero), divide(divide(idQa, zero), a)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(151,plain,
% 1.01/1.17 (((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(divide(idQa, zero), divide(divide(idQa, zero), a)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))) | (~quotient(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))) | (~quotient(identity, a, divide(idQa, zero))) | (~quotient(a, a, divide(zero, zero))) | (~quotient(identity, a, divide(idQa, zero))))) <=> ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | ((~quotient(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))) | (~quotient(a, a, divide(zero, zero))) | (~quotient(identity, a, divide(idQa, zero))) | less_equal(divide(idQa, zero), divide(divide(idQa, zero), a)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a)))))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[150])).
% 1.01/1.17 tff(152,plain,
% 1.01/1.17 (((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(divide(idQa, zero), divide(divide(idQa, zero), a)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))) | (~quotient(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))) | (~quotient(identity, a, divide(idQa, zero))) | (~quotient(a, a, divide(zero, zero))) | (~quotient(identity, a, divide(idQa, zero))))) <=> ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (~quotient(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))) | (~quotient(a, a, divide(zero, zero))) | (~quotient(identity, a, divide(idQa, zero))) | less_equal(divide(idQa, zero), divide(divide(idQa, zero), a)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))))),
% 1.01/1.17 inference(transitivity,[status(thm)],[151, 149])).
% 1.01/1.17 tff(153,plain,
% 1.01/1.17 ((~![Z: $i, Y: $i, V1: $i, V5: $i, X: $i, V2: $i, V3: $i, V4: $i] : (less_equal(V4, V5) | (~quotient(V1, Z, V5)) | (~quotient(V3, V2, V4)) | (~quotient(X, Z, V3)) | (~quotient(Y, Z, V2)) | (~quotient(X, Y, V1)))) | (less_equal(divide(idQa, zero), divide(divide(idQa, zero), a)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))) | (~quotient(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))) | (~quotient(identity, a, divide(idQa, zero))) | (~quotient(a, a, divide(zero, zero))) | (~quotient(identity, a, divide(idQa, zero))))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(154,plain,
% 1.01/1.17 ((~![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(divide(idQa, zero), divide(zero, zero), divide(idQa, zero))) | (~quotient(a, a, divide(zero, zero))) | (~quotient(identity, a, divide(idQa, zero))) | less_equal(divide(idQa, zero), divide(divide(idQa, zero), a)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.01/1.17 tff(155,plain,
% 1.01/1.17 (less_equal(divide(idQa, zero), divide(divide(idQa, zero), a))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[154, 148, 138, 135, 44, 9])).
% 1.01/1.17 tff(156,plain,
% 1.01/1.17 ((~![X: $i] : quotient(X, zero, X)) | quotient(idQ_idQa, zero, idQ_idQa)),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(157,plain,
% 1.01/1.17 (quotient(idQ_idQa, zero, idQ_idQa)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[156, 16])).
% 1.01/1.17 tff(158,plain,
% 1.01/1.17 ((~![Y: $i, X: $i] : quotient(X, Y, divide(X, Y))) | quotient(idQ_idQa, zero, divide(idQ_idQa, zero))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(159,plain,
% 1.01/1.17 (quotient(idQ_idQa, zero, divide(idQ_idQa, zero))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[158, 7])).
% 1.01/1.17 tff(160,plain,
% 1.01/1.17 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))) | (~quotient(idQ_idQa, zero, idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, zero)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))) | (~quotient(idQ_idQa, zero, idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, zero)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(161,plain,
% 1.01/1.17 (((~quotient(idQ_idQa, zero, idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, zero)) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero)))) <=> ((~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))) | (~quotient(idQ_idQa, zero, idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, zero)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(162,plain,
% 1.01/1.17 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, zero, idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, zero)) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))) | (~quotient(idQ_idQa, zero, idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, zero))))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[161])).
% 1.01/1.17 tff(163,plain,
% 1.01/1.17 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, zero, idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, zero)) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))) | (~quotient(idQ_idQa, zero, idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, zero)))),
% 1.01/1.17 inference(transitivity,[status(thm)],[162, 160])).
% 1.01/1.17 tff(164,plain,
% 1.01/1.17 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | ((~quotient(idQ_idQa, zero, idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, zero)) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(165,plain,
% 1.01/1.17 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~quotient(X, Y, Z)) | (Z = W) | (~quotient(X, Y, W)))) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))) | (~quotient(idQ_idQa, zero, idQ_idQa)) | (idQ_idQa = divide(idQ_idQa, zero))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[164, 163])).
% 1.01/1.17 tff(166,plain,
% 1.01/1.17 (idQ_idQa = divide(idQ_idQa, zero)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[165, 30, 159, 157])).
% 1.01/1.17 tff(167,plain,
% 1.01/1.17 (divide(idQ_idQa, zero) = idQ_idQa),
% 1.01/1.17 inference(symmetry,[status(thm)],[166])).
% 1.01/1.17 tff(168,plain,
% 1.01/1.17 (quotient(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa) <=> quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa)),
% 1.01/1.17 inference(monotonicity,[status(thm)],[38, 167])).
% 1.01/1.17 tff(169,plain,
% 1.01/1.17 (quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa) <=> quotient(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)),
% 1.01/1.17 inference(symmetry,[status(thm)],[168])).
% 1.01/1.17 tff(170,plain,
% 1.01/1.17 (quotient(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[49, 169])).
% 1.01/1.17 tff(171,plain,
% 1.01/1.17 ((~![X: $i] : quotient(X, zero, X)) | quotient(a, zero, a)),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(172,plain,
% 1.01/1.17 (quotient(a, zero, a)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[171, 16])).
% 1.01/1.17 tff(173,assumption,(~less_equal(identity, identity)), introduced(assumption)).
% 1.01/1.17 tff(174,plain,
% 1.01/1.17 (^[X: $i] : refl(less_equal(X, identity) <=> less_equal(X, identity))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(175,plain,
% 1.01/1.17 (![X: $i] : less_equal(X, identity) <=> ![X: $i] : less_equal(X, identity)),
% 1.01/1.17 inference(quant_intro,[status(thm)],[174])).
% 1.01/1.17 tff(176,plain,
% 1.01/1.17 (![X: $i] : less_equal(X, identity) <=> ![X: $i] : less_equal(X, identity)),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(177,axiom,(![X: $i] : less_equal(X, identity)), file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax','identity_is_largest')).
% 1.01/1.17 tff(178,plain,
% 1.01/1.17 (![X: $i] : less_equal(X, identity)),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[177, 176])).
% 1.01/1.17 tff(179,plain,(
% 1.01/1.17 ![X: $i] : less_equal(X, identity)),
% 1.01/1.17 inference(skolemize,[status(sab)],[178])).
% 1.01/1.17 tff(180,plain,
% 1.01/1.17 (![X: $i] : less_equal(X, identity)),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[179, 175])).
% 1.01/1.17 tff(181,plain,
% 1.01/1.17 ((~![X: $i] : less_equal(X, identity)) | less_equal(identity, identity)),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(182,plain,
% 1.01/1.17 ($false),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[181, 180, 173])).
% 1.01/1.17 tff(183,plain,(less_equal(identity, identity)), inference(lemma,lemma(discharge,[]))).
% 1.01/1.17 tff(184,plain,
% 1.01/1.17 (((~![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)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(185,plain,
% 1.01/1.17 ((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)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(186,plain,
% 1.01/1.17 (((~![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))))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[185])).
% 1.01/1.17 tff(187,plain,
% 1.01/1.17 (((~![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)))),
% 1.01/1.17 inference(transitivity,[status(thm)],[186, 184])).
% 1.01/1.17 tff(188,plain,
% 1.01/1.17 ((~![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)))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(189,plain,
% 1.01/1.17 ((~![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))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.01/1.17 tff(190,plain,
% 1.01/1.17 (less_equal(idQa, idQa) | (~less_equal(identity, identity))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[189, 102, 43])).
% 1.01/1.18 tff(191,plain,
% 1.01/1.18 (less_equal(idQa, idQa)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[190, 183])).
% 1.01/1.18 tff(192,plain,
% 1.01/1.18 (quotient(identity, idQa, idQ_idQa) <=> quotient(identity, idQa, idQ_idQa)),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(193,axiom,(quotient(identity, idQa, idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','identity_divide_idQa')).
% 1.01/1.18 tff(194,plain,
% 1.01/1.18 (quotient(identity, idQa, idQ_idQa)),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.01/1.18 tff(195,plain,
% 1.01/1.18 (^[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))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(196,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[195])).
% 1.01/1.18 tff(197,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(198,plain,
% 1.01/1.18 (^[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)))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(199,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[198])).
% 1.01/1.18 tff(200,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')).
% 1.01/1.18 tff(201,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.01/1.18 tff(202,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[201, 197])).
% 1.01/1.18 tff(203,plain,(
% 1.01/1.18 ![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)))),
% 1.01/1.18 inference(skolemize,[status(sab)],[202])).
% 1.01/1.18 tff(204,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[203, 196])).
% 1.01/1.18 tff(205,plain,
% 1.01/1.18 (((~![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)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(206,plain,
% 1.01/1.18 ((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)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(207,plain,
% 1.01/1.18 (((~![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))))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[206])).
% 1.01/1.18 tff(208,plain,
% 1.01/1.18 (((~![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)))),
% 1.01/1.18 inference(transitivity,[status(thm)],[207, 205])).
% 1.01/1.18 tff(209,plain,
% 1.01/1.18 ((~![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)))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(210,plain,
% 1.01/1.18 ((~![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))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.01/1.18 tff(211,plain,
% 1.01/1.18 (less_equal(idQ_idQa, a) | (~less_equal(idQa, idQa))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[210, 204, 43, 194])).
% 1.01/1.18 tff(212,plain,
% 1.01/1.18 (less_equal(idQ_idQa, a)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[211, 191])).
% 1.01/1.18 tff(213,plain,
% 1.01/1.18 (((~![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, zero, divide(idQ_idQa, zero))) | (~quotient(a, zero, a)) | less_equal(divide(idQ_idQa, zero), a))) <=> ((~![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, zero, divide(idQ_idQa, zero))) | (~quotient(a, zero, a)) | less_equal(divide(idQ_idQa, zero), a))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(214,plain,
% 1.01/1.18 ((less_equal(divide(idQ_idQa, zero), a) | (~less_equal(idQ_idQa, a)) | (~quotient(a, zero, a)) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero)))) <=> ((~less_equal(idQ_idQa, a)) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))) | (~quotient(a, zero, a)) | less_equal(divide(idQ_idQa, zero), a))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(215,plain,
% 1.01/1.18 (((~![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(idQ_idQa, zero), a) | (~less_equal(idQ_idQa, a)) | (~quotient(a, zero, a)) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))))) <=> ((~![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, zero, divide(idQ_idQa, zero))) | (~quotient(a, zero, a)) | less_equal(divide(idQ_idQa, zero), a)))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[214])).
% 1.01/1.18 tff(216,plain,
% 1.01/1.18 (((~![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(idQ_idQa, zero), a) | (~less_equal(idQ_idQa, a)) | (~quotient(a, zero, a)) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))))) <=> ((~![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, zero, divide(idQ_idQa, zero))) | (~quotient(a, zero, a)) | less_equal(divide(idQ_idQa, zero), a))),
% 1.01/1.18 inference(transitivity,[status(thm)],[215, 213])).
% 1.01/1.18 tff(217,plain,
% 1.01/1.18 ((~![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(idQ_idQa, zero), a) | (~less_equal(idQ_idQa, a)) | (~quotient(a, zero, a)) | (~quotient(idQ_idQa, zero, divide(idQ_idQa, zero))))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(218,plain,
% 1.01/1.18 ((~![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, zero, divide(idQ_idQa, zero))) | (~quotient(a, zero, a)) | less_equal(divide(idQ_idQa, zero), a)),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[217, 216])).
% 1.01/1.18 tff(219,plain,
% 1.01/1.18 (less_equal(divide(idQ_idQa, zero), a)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[218, 102, 212, 159, 172])).
% 1.01/1.18 tff(220,plain,
% 1.01/1.18 (^[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))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(221,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[220])).
% 1.01/1.18 tff(222,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(223,plain,
% 1.01/1.18 (^[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)))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(224,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[223])).
% 1.01/1.18 tff(225,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')).
% 1.01/1.18 tff(226,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[225, 224])).
% 1.01/1.18 tff(227,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[226, 222])).
% 1.01/1.18 tff(228,plain,(
% 1.01/1.18 ![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)))),
% 1.01/1.18 inference(skolemize,[status(sab)],[227])).
% 1.01/1.18 tff(229,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[228, 221])).
% 1.01/1.18 tff(230,plain,
% 1.01/1.18 (((~![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(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)) | (~less_equal(divide(idQ_idQa, zero), a)) | less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))))) <=> ((~![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(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)) | (~less_equal(divide(idQ_idQa, zero), a)) | less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(231,plain,
% 1.01/1.18 ((less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))) | (~less_equal(divide(idQ_idQa, zero), a))) <=> ((~quotient(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)) | (~less_equal(divide(idQ_idQa, zero), a)) | less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(232,plain,
% 1.01/1.18 (((~![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(divide(idQa, zero), a), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))) | (~less_equal(divide(idQ_idQa, zero), a)))) <=> ((~![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(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)) | (~less_equal(divide(idQ_idQa, zero), a)) | less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a)))))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[231])).
% 1.01/1.18 tff(233,plain,
% 1.01/1.18 (((~![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(divide(idQa, zero), a), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))) | (~less_equal(divide(idQ_idQa, zero), a)))) <=> ((~![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(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)) | (~less_equal(divide(idQ_idQa, zero), a)) | less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))))),
% 1.01/1.18 inference(transitivity,[status(thm)],[232, 230])).
% 1.01/1.18 tff(234,plain,
% 1.01/1.18 ((~![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(divide(idQa, zero), a), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a))) | (~less_equal(divide(idQ_idQa, zero), a)))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(235,plain,
% 1.01/1.18 ((~![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(divide(idQa, zero), divide(idQ_idQa, zero), idQa_Q__idQ_idQa)) | (~less_equal(divide(idQ_idQa, zero), a)) | less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa) | (~quotient(divide(idQa, zero), a, divide(divide(idQa, zero), a)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.01/1.18 tff(236,plain,
% 1.01/1.18 (less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[235, 229, 219, 170, 9])).
% 1.01/1.18 tff(237,plain,
% 1.01/1.18 (less_equal(idQa, idQa_Q__idQ_idQa) <=> less_equal(divide(idQa, zero), idQa_Q__idQ_idQa)),
% 1.01/1.18 inference(monotonicity,[status(thm)],[37])).
% 1.01/1.18 tff(238,plain,
% 1.01/1.18 ((~less_equal(idQa, idQa_Q__idQ_idQa)) <=> (~less_equal(divide(idQa, zero), idQa_Q__idQ_idQa))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[237])).
% 1.01/1.18 tff(239,plain,
% 1.01/1.18 ((~(idQa = idQa_Q__idQ_idQa)) <=> (~(idQa = idQa_Q__idQ_idQa))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(240,axiom,(~(idQa = idQa_Q__idQ_idQa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_idQa_equals_idQa_Q__idQ_idQa')).
% 1.01/1.18 tff(241,plain,
% 1.01/1.18 (~(idQa = idQa_Q__idQ_idQa)),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[240, 239])).
% 1.01/1.18 tff(242,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(243,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(244,plain,
% 1.01/1.18 (^[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))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(245,plain,
% 1.01/1.18 (![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)))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[244])).
% 1.01/1.18 tff(246,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')).
% 1.01/1.18 tff(247,plain,
% 1.01/1.18 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[246, 245])).
% 1.01/1.18 tff(248,plain,
% 1.01/1.18 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[247, 243])).
% 1.01/1.18 tff(249,plain,(
% 1.01/1.18 ![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 1.01/1.18 inference(skolemize,[status(sab)],[248])).
% 1.01/1.18 tff(250,plain,
% 1.01/1.18 (![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[249, 242])).
% 1.01/1.18 tff(251,plain,
% 1.01/1.18 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(252,plain,
% 1.01/1.18 (((~less_equal(idQa, idQa_Q__idQ_idQa)) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa))) <=> ((idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(253,plain,
% 1.01/1.18 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa, idQa_Q__idQ_idQa)) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa))))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[252])).
% 1.01/1.18 tff(254,plain,
% 1.01/1.18 (((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa, idQa_Q__idQ_idQa)) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)))) <=> ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa)))),
% 1.01/1.18 inference(transitivity,[status(thm)],[253, 251])).
% 1.01/1.18 tff(255,plain,
% 1.01/1.18 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | ((~less_equal(idQa, idQa_Q__idQ_idQa)) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(256,plain,
% 1.01/1.18 ((~![Y: $i, X: $i] : ((~less_equal(X, Y)) | (X = Y) | (~less_equal(Y, X)))) | (idQa = idQa_Q__idQ_idQa) | (~less_equal(idQa_Q__idQ_idQa, idQa)) | (~less_equal(idQa, idQa_Q__idQ_idQa))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.01/1.18 tff(257,plain,
% 1.01/1.18 (~less_equal(idQa, idQa_Q__idQ_idQa)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[256, 250, 241, 60])).
% 1.01/1.18 tff(258,plain,
% 1.01/1.18 (~less_equal(divide(idQa, zero), idQa_Q__idQ_idQa)),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[257, 238])).
% 1.01/1.18 tff(259,plain,
% 1.01/1.18 (((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | (less_equal(divide(idQa, zero), idQa_Q__idQ_idQa) | (~less_equal(divide(idQa, zero), divide(divide(idQa, zero), a))) | (~less_equal(divide(divide(idQa, zero), a), 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(idQa, zero), idQa_Q__idQ_idQa) | (~less_equal(divide(idQa, zero), divide(divide(idQa, zero), a))) | (~less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(260,plain,
% 1.01/1.18 (((~less_equal(divide(idQa, zero), divide(divide(idQa, zero), a))) | less_equal(divide(idQa, zero), idQa_Q__idQ_idQa) | (~less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa))) <=> (less_equal(divide(idQa, zero), idQa_Q__idQ_idQa) | (~less_equal(divide(idQa, zero), divide(divide(idQa, zero), a))) | (~less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(261,plain,
% 1.01/1.18 (((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(divide(idQa, zero), divide(divide(idQa, zero), a))) | less_equal(divide(idQa, zero), idQa_Q__idQ_idQa) | (~less_equal(divide(divide(idQa, zero), a), 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(idQa, zero), idQa_Q__idQ_idQa) | (~less_equal(divide(idQa, zero), divide(divide(idQa, zero), a))) | (~less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa))))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[260])).
% 1.01/1.18 tff(262,plain,
% 1.01/1.18 (((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(divide(idQa, zero), divide(divide(idQa, zero), a))) | less_equal(divide(idQa, zero), idQa_Q__idQ_idQa) | (~less_equal(divide(divide(idQa, zero), a), 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(idQa, zero), idQa_Q__idQ_idQa) | (~less_equal(divide(idQa, zero), divide(divide(idQa, zero), a))) | (~less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa)))),
% 1.01/1.19 inference(transitivity,[status(thm)],[261, 259])).
% 1.01/1.19 tff(263,plain,
% 1.01/1.19 ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | ((~less_equal(divide(idQa, zero), divide(divide(idQa, zero), a))) | less_equal(divide(idQa, zero), idQa_Q__idQ_idQa) | (~less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa)))),
% 1.01/1.19 inference(quant_inst,[status(thm)],[])).
% 1.01/1.19 tff(264,plain,
% 1.01/1.19 ((~![Z: $i, Y: $i, X: $i] : ((~less_equal(X, Y)) | less_equal(X, Z) | (~less_equal(Y, Z)))) | less_equal(divide(idQa, zero), idQa_Q__idQ_idQa) | (~less_equal(divide(idQa, zero), divide(divide(idQa, zero), a))) | (~less_equal(divide(divide(idQa, zero), a), idQa_Q__idQ_idQa))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[263, 262])).
% 1.01/1.19 tff(265,plain,
% 1.01/1.19 ($false),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[264, 73, 258, 236, 155])).
% 1.01/1.19 % SZS output end Proof
% 1.01/1.19 % E exiting
%------------------------------------------------------------------------------