%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE043+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:12:56 AM UTC 2025
% Result : Theorem 0.43s 0.59s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE043+2 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:00:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.43/0.59 % SZS status Theorem
% 0.43/0.59 % SZS output start Proof
% 0.43/0.59 tff(addition_type, type, (
% 0.43/0.59 addition: ( $i * $i ) > $i)).
% 0.43/0.59 tff(tptp_fun_X1_0_type, type, (
% 0.43/0.59 tptp_fun_X1_0: $i)).
% 0.43/0.59 tff(multiplication_type, type, (
% 0.43/0.59 multiplication: ( $i * $i ) > $i)).
% 0.43/0.59 tff(star_type, type, (
% 0.43/0.59 star: $i > $i)).
% 0.43/0.59 tff(tptp_fun_X0_1_type, type, (
% 0.43/0.59 tptp_fun_X0_1: $i)).
% 0.43/0.59 tff(leq_type, type, (
% 0.43/0.59 leq: ( $i * $i ) > $o)).
% 0.43/0.59 tff(one_type, type, (
% 0.43/0.59 one: $i)).
% 0.43/0.59 tff(1,plain,
% 0.43/0.59 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(2,plain,
% 0.43/0.59 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.43/0.59 inference(quant_intro,[status(thm)],[1])).
% 0.43/0.59 tff(3,plain,
% 0.43/0.59 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(4,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 0.43/0.59 tff(5,plain,
% 0.43/0.59 (![A: $i] : (addition(A, A) = A)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.43/0.59 tff(6,plain,(
% 0.43/0.59 ![A: $i] : (addition(A, A) = A)),
% 0.43/0.59 inference(skolemize,[status(sab)],[5])).
% 0.43/0.59 tff(7,plain,
% 0.43/0.59 (![A: $i] : (addition(A, A) = A)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.43/0.59 tff(8,plain,
% 0.43/0.59 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(9,plain,
% 0.43/0.59 (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.43/0.59 tff(10,plain,
% 0.43/0.59 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(11,plain,
% 0.43/0.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[10])).
% 0.43/0.59 tff(12,plain,
% 0.43/0.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(13,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 0.43/0.59 tff(14,plain,
% 0.43/0.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.43/0.59 tff(15,plain,(
% 0.43/0.59 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.43/0.59 inference(skolemize,[status(sab)],[14])).
% 0.43/0.59 tff(16,plain,
% 0.43/0.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.43/0.59 tff(17,plain,
% 0.43/0.59 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(18,plain,
% 0.43/0.59 (addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.43/0.59 tff(19,plain,
% 0.43/0.59 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(20,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[19])).
% 0.43/0.59 tff(21,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(22,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','multiplicative_associativity')).
% 0.43/0.59 tff(23,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.43/0.59 tff(24,plain,(
% 0.43/0.59 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.43/0.59 inference(skolemize,[status(sab)],[23])).
% 0.43/0.59 tff(25,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.43/0.59 tff(26,plain,
% 0.43/0.59 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!1, multiplication(star(X0!1), X1!0)) = multiplication(multiplication(X0!1, star(X0!1)), X1!0))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(27,plain,
% 0.43/0.59 (multiplication(X0!1, multiplication(star(X0!1), X1!0)) = multiplication(multiplication(X0!1, star(X0!1)), X1!0)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.43/0.59 tff(28,plain,
% 0.43/0.59 (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[18])).
% 0.43/0.59 tff(29,plain,
% 0.43/0.59 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(30,plain,
% 0.43/0.59 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[29])).
% 0.43/0.59 tff(31,plain,
% 0.43/0.59 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(32,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','order')).
% 0.43/0.59 tff(33,plain,
% 0.43/0.59 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.43/0.59 tff(34,plain,(
% 0.43/0.59 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.43/0.59 inference(skolemize,[status(sab)],[33])).
% 0.43/0.59 tff(35,plain,
% 0.43/0.59 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.43/0.59 tff(36,plain,
% 0.43/0.59 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(37,plain,
% 0.43/0.59 (leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.43/0.59 tff(38,plain,
% 0.43/0.59 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(X0!1, star(X0!1))) = addition(multiplication(X0!1, star(X0!1)), one))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(39,plain,
% 0.43/0.59 (addition(one, multiplication(X0!1, star(X0!1))) = addition(multiplication(X0!1, star(X0!1)), one)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[38, 16])).
% 0.43/0.59 tff(40,plain,
% 0.43/0.59 (addition(multiplication(X0!1, star(X0!1)), one) = addition(one, multiplication(X0!1, star(X0!1)))),
% 0.43/0.59 inference(symmetry,[status(thm)],[39])).
% 0.43/0.59 tff(41,plain,
% 0.43/0.59 (addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1)) = addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[40])).
% 0.43/0.59 tff(42,plain,
% 0.43/0.59 (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1))),
% 0.43/0.59 inference(symmetry,[status(thm)],[41])).
% 0.43/0.59 tff(43,plain,
% 0.43/0.59 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) <=> (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1)))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(44,plain,
% 0.43/0.59 (leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) <=> (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[43, 35])).
% 0.43/0.59 tff(45,plain,
% 0.43/0.59 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(46,plain,
% 0.43/0.59 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[45])).
% 0.43/0.59 tff(47,plain,
% 0.43/0.59 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(48,axiom,(![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_unfold_right')).
% 0.43/0.59 tff(49,plain,
% 0.43/0.59 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.43/0.59 tff(50,plain,(
% 0.43/0.59 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.43/0.59 inference(skolemize,[status(sab)],[49])).
% 0.43/0.59 tff(51,plain,
% 0.43/0.59 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.43/0.59 tff(52,plain,
% 0.43/0.59 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(53,plain,
% 0.43/0.59 (leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.43/0.59 tff(54,plain,
% 0.43/0.59 ((~(leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) <=> (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1)))) | (~leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1))) | (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1))),
% 0.43/0.59 inference(tautology,[status(thm)],[])).
% 0.43/0.59 tff(55,plain,
% 0.43/0.59 ((~(leq(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) <=> (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1)))) | (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.43/0.59 tff(56,plain,
% 0.43/0.59 (addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1)) = star(X0!1)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[55, 44])).
% 0.43/0.59 tff(57,plain,
% 0.43/0.59 (star(X0!1) = addition(addition(one, multiplication(X0!1, star(X0!1))), star(X0!1))),
% 0.43/0.59 inference(symmetry,[status(thm)],[56])).
% 0.43/0.59 tff(58,plain,
% 0.43/0.59 (star(X0!1) = addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1))),
% 0.43/0.59 inference(transitivity,[status(thm)],[57, 42])).
% 0.43/0.59 tff(59,plain,
% 0.43/0.59 (multiplication(star(X0!1), X1!0) = multiplication(addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1)), X1!0)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[58])).
% 0.43/0.59 tff(60,plain,
% 0.43/0.59 (multiplication(addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1)), X1!0) = multiplication(star(X0!1), X1!0)),
% 0.43/0.59 inference(symmetry,[status(thm)],[59])).
% 0.43/0.59 tff(61,plain,
% 0.43/0.59 (^[A: $i, B: $i, C: $i] : refl((multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(62,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[61])).
% 0.43/0.59 tff(63,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(64,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','left_distributivity')).
% 0.43/0.59 tff(65,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.43/0.59 tff(66,plain,(
% 0.43/0.59 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.43/0.59 inference(skolemize,[status(sab)],[65])).
% 0.43/0.59 tff(67,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.43/0.59 tff(68,plain,
% 0.43/0.59 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1)), X1!0) = addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(69,plain,
% 0.43/0.59 (multiplication(addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1)), X1!0) = addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.43/0.59 tff(70,plain,
% 0.43/0.59 (addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)) = multiplication(addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1)), X1!0)),
% 0.43/0.59 inference(symmetry,[status(thm)],[69])).
% 0.43/0.59 tff(71,plain,
% 0.43/0.59 (addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)),
% 0.43/0.59 inference(transitivity,[status(thm)],[70, 60])).
% 0.43/0.59 tff(72,plain,
% 0.43/0.59 (addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0))) = addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[71])).
% 0.43/0.59 tff(73,plain,
% 0.43/0.59 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0))) = addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0)))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(74,plain,
% 0.43/0.59 (addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0))) = addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[73, 16])).
% 0.43/0.59 tff(75,plain,
% 0.43/0.59 (addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0)) = addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)))),
% 0.43/0.60 inference(symmetry,[status(thm)],[74])).
% 0.43/0.60 tff(76,plain,
% 0.43/0.60 (multiplication(X0!1, star(X0!1)) = multiplication(X0!1, addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1)))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[58])).
% 0.43/0.60 tff(77,plain,
% 0.43/0.60 (multiplication(X0!1, addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1))) = multiplication(X0!1, star(X0!1))),
% 0.43/0.60 inference(symmetry,[status(thm)],[76])).
% 0.43/0.60 tff(78,plain,
% 0.43/0.60 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(79,plain,
% 0.43/0.60 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[78])).
% 0.43/0.60 tff(80,plain,
% 0.43/0.60 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(81,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','right_distributivity')).
% 0.43/0.60 tff(82,plain,
% 0.43/0.60 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.43/0.60 tff(83,plain,(
% 0.43/0.60 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[82])).
% 0.43/0.60 tff(84,plain,
% 0.43/0.60 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.43/0.60 tff(85,plain,
% 0.43/0.60 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1))) = addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(86,plain,
% 0.43/0.60 (multiplication(X0!1, addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1))) = addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1)))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.43/0.60 tff(87,plain,
% 0.43/0.60 (addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))) = multiplication(X0!1, addition(addition(multiplication(X0!1, star(X0!1)), one), star(X0!1)))),
% 0.43/0.60 inference(symmetry,[status(thm)],[86])).
% 0.43/0.60 tff(88,plain,
% 0.43/0.60 (addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))) = multiplication(X0!1, star(X0!1))),
% 0.43/0.60 inference(transitivity,[status(thm)],[87, 77])).
% 0.43/0.60 tff(89,plain,
% 0.43/0.60 (addition(addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))), one) = addition(multiplication(X0!1, star(X0!1)), one)),
% 0.43/0.60 inference(monotonicity,[status(thm)],[88])).
% 0.43/0.60 tff(90,plain,
% 0.43/0.60 (multiplication(addition(addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))), one), X1!0) = multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0)),
% 0.43/0.60 inference(monotonicity,[status(thm)],[89])).
% 0.43/0.60 tff(91,plain,
% 0.43/0.60 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))), one), X1!0) = addition(multiplication(addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))), X1!0), multiplication(one, X1!0)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(92,plain,
% 0.43/0.60 (multiplication(addition(addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))), one), X1!0) = addition(multiplication(addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))), X1!0), multiplication(one, X1!0))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[91, 67])).
% 0.43/0.60 tff(93,plain,
% 0.43/0.60 (addition(multiplication(addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))), X1!0), multiplication(one, X1!0)) = multiplication(addition(addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))), one), X1!0)),
% 0.43/0.60 inference(symmetry,[status(thm)],[92])).
% 0.43/0.60 tff(94,plain,
% 0.43/0.60 (multiplication(addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))), X1!0) = multiplication(multiplication(X0!1, star(X0!1)), X1!0)),
% 0.43/0.60 inference(monotonicity,[status(thm)],[88])).
% 0.43/0.60 tff(95,plain,
% 0.43/0.60 (multiplication(multiplication(X0!1, star(X0!1)), X1!0) = multiplication(addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))), X1!0)),
% 0.43/0.60 inference(symmetry,[status(thm)],[94])).
% 0.43/0.60 tff(96,plain,
% 0.43/0.60 (addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(one, X1!0)) = addition(multiplication(addition(multiplication(X0!1, addition(multiplication(X0!1, star(X0!1)), one)), multiplication(X0!1, star(X0!1))), X1!0), multiplication(one, X1!0))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[95])).
% 0.43/0.60 tff(97,plain,
% 0.43/0.60 (addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(one, X1!0)) = multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0)),
% 0.43/0.60 inference(transitivity,[status(thm)],[96, 93, 90])).
% 0.43/0.60 tff(98,plain,
% 0.43/0.60 (addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(one, X1!0))) = addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[97])).
% 0.43/0.60 tff(99,plain,
% 0.43/0.60 (^[C: $i, B: $i, A: $i] : refl((addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> (addition(A, addition(B, C)) = addition(addition(A, B), C)))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(100,plain,
% 0.43/0.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[99])).
% 0.43/0.60 tff(101,plain,
% 0.43/0.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(102,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_associativity')).
% 0.43/0.60 tff(103,plain,
% 0.43/0.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.43/0.60 tff(104,plain,(
% 0.43/0.60 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.43/0.60 inference(skolemize,[status(sab)],[103])).
% 0.43/0.60 tff(105,plain,
% 0.43/0.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.43/0.60 tff(106,plain,
% 0.43/0.60 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(one, X1!0))) = addition(addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(one, X1!0)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(107,plain,
% 0.43/0.60 (addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(one, X1!0))) = addition(addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(one, X1!0))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.43/0.60 tff(108,plain,
% 0.43/0.60 (addition(addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(one, X1!0)) = addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), multiplication(one, X1!0)))),
% 0.43/0.60 inference(symmetry,[status(thm)],[107])).
% 0.43/0.60 tff(109,plain,
% 0.43/0.60 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(110,plain,
% 0.43/0.60 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.43/0.60 inference(quant_intro,[status(thm)],[109])).
% 0.43/0.60 tff(111,plain,
% 0.43/0.60 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(112,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','multiplicative_left_identity')).
% 0.43/0.60 tff(113,plain,
% 0.43/0.60 (![A: $i] : (multiplication(one, A) = A)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.43/0.60 tff(114,plain,(
% 0.43/0.60 ![A: $i] : (multiplication(one, A) = A)),
% 0.43/0.60 inference(skolemize,[status(sab)],[113])).
% 0.43/0.60 tff(115,plain,
% 0.43/0.60 (![A: $i] : (multiplication(one, A) = A)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.43/0.60 tff(116,plain,
% 0.43/0.60 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!0) = X1!0)),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(117,plain,
% 0.43/0.60 (multiplication(one, X1!0) = X1!0),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.43/0.60 tff(118,plain,
% 0.43/0.60 (X1!0 = multiplication(one, X1!0)),
% 0.43/0.60 inference(symmetry,[status(thm)],[117])).
% 0.43/0.60 tff(119,plain,
% 0.43/0.60 (addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = addition(multiplication(star(X0!1), X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[71])).
% 0.43/0.60 tff(120,plain,
% 0.43/0.60 (addition(multiplication(star(X0!1), X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), multiplication(multiplication(X0!1, star(X0!1)), X1!0))),
% 0.43/0.60 inference(symmetry,[status(thm)],[119])).
% 0.43/0.60 tff(121,plain,
% 0.43/0.60 (addition(addition(multiplication(star(X0!1), X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)), X1!0) = addition(addition(addition(multiplication(addition(multiplication(X0!1, star(X0!1)), one), X1!0), multiplication(star(X0!1), X1!0)), multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(one, X1!0))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[120, 118])).
% 0.43/0.60 tff(122,plain,
% 0.43/0.60 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X0!1), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(addition(multiplication(star(X0!1), X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)), X1!0))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(123,plain,
% 0.43/0.60 (addition(multiplication(star(X0!1), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(addition(multiplication(star(X0!1), X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)), X1!0)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[122, 105])).
% 0.43/0.60 tff(124,plain,
% 0.43/0.60 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0)) = addition(multiplication(star(X0!1), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(125,plain,
% 0.43/0.60 (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0)) = addition(multiplication(star(X0!1), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[124, 16])).
% 0.43/0.60 tff(126,plain,
% 0.43/0.60 (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)),
% 0.43/0.60 inference(transitivity,[status(thm)],[28, 125, 123, 121, 108, 98, 75, 72, 70, 60])).
% 0.43/0.60 tff(127,assumption,(~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))), introduced(assumption)).
% 0.43/0.60 tff(128,plain,
% 0.43/0.60 ((~(leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))) | leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) | (~(addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))),
% 0.43/0.60 inference(tautology,[status(thm)],[])).
% 0.43/0.60 tff(129,plain,
% 0.43/0.60 ((~(leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))) | (~(addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.43/0.60 tff(130,plain,
% 0.43/0.60 (~(addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[129, 37])).
% 0.43/0.60 tff(131,plain,
% 0.43/0.60 ($false),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[130, 126])).
% 0.43/0.60 tff(132,plain,(leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.60 tff(133,plain,
% 0.43/0.60 ((~(leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))) | (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0))),
% 0.46/0.60 inference(tautology,[status(thm)],[])).
% 0.46/0.60 tff(134,plain,
% 0.46/0.60 ((~(leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) <=> (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)))) | (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.46/0.60 tff(135,plain,
% 0.46/0.60 (addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)) = multiplication(star(X0!1), X1!0)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[134, 37])).
% 0.46/0.60 tff(136,plain,
% 0.46/0.60 (multiplication(star(X0!1), X1!0) = addition(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))),
% 0.46/0.60 inference(symmetry,[status(thm)],[135])).
% 0.46/0.60 tff(137,plain,
% 0.46/0.60 (multiplication(star(X0!1), X1!0) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0))),
% 0.46/0.60 inference(transitivity,[status(thm)],[136, 28])).
% 0.46/0.60 tff(138,plain,
% 0.46/0.60 (multiplication(X0!1, multiplication(star(X0!1), X1!0)) = multiplication(X0!1, addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0)))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[137])).
% 0.46/0.60 tff(139,plain,
% 0.46/0.60 (multiplication(X0!1, addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0))) = multiplication(X0!1, multiplication(star(X0!1), X1!0))),
% 0.46/0.60 inference(symmetry,[status(thm)],[138])).
% 0.46/0.60 tff(140,plain,
% 0.46/0.60 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0))) = addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.60 tff(141,plain,
% 0.46/0.60 (multiplication(X0!1, addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0))) = addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[140, 84])).
% 0.46/0.60 tff(142,plain,
% 0.46/0.60 (addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))) = multiplication(X0!1, addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), multiplication(star(X0!1), X1!0)))),
% 0.46/0.60 inference(symmetry,[status(thm)],[141])).
% 0.46/0.60 tff(143,plain,
% 0.46/0.60 (addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))) = multiplication(multiplication(X0!1, star(X0!1)), X1!0)),
% 0.46/0.60 inference(transitivity,[status(thm)],[142, 139, 27])).
% 0.46/0.60 tff(144,plain,
% 0.46/0.60 (addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[143])).
% 0.46/0.60 tff(145,plain,
% 0.46/0.60 (addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)),
% 0.46/0.60 inference(transitivity,[status(thm)],[144, 18])).
% 0.46/0.60 tff(146,plain,
% 0.46/0.60 (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[145])).
% 0.46/0.60 tff(147,plain,
% 0.46/0.60 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.61 tff(148,plain,
% 0.46/0.61 (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[147, 105])).
% 0.46/0.61 tff(149,plain,
% 0.46/0.61 (addition(addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[148])).
% 0.46/0.61 tff(150,plain,
% 0.46/0.61 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) = addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.46/0.61 inference(quant_inst,[status(thm)],[])).
% 0.46/0.61 tff(151,plain,
% 0.46/0.61 (multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) = addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[150, 84])).
% 0.46/0.61 tff(152,plain,
% 0.46/0.61 (addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) = multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.46/0.61 inference(symmetry,[status(thm)],[151])).
% 0.46/0.61 tff(153,plain,
% 0.46/0.61 (addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) = addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[152])).
% 0.46/0.61 tff(154,plain,
% 0.46/0.61 (addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) = addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[153])).
% 0.46/0.61 tff(155,plain,
% 0.46/0.61 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[154])).
% 0.46/0.61 tff(156,plain,
% 0.46/0.61 (addition(addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[155])).
% 0.46/0.61 tff(157,plain,
% 0.46/0.61 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X1!0, addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.46/0.61 inference(quant_inst,[status(thm)],[])).
% 0.46/0.61 tff(158,plain,
% 0.46/0.61 (addition(X1!0, addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(X1!0, addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[157, 105])).
% 0.46/0.61 tff(159,plain,
% 0.46/0.61 (addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))) = multiplication(X0!1, multiplication(star(X0!1), X1!0))),
% 0.46/0.61 inference(transitivity,[status(thm)],[142, 139])).
% 0.46/0.61 tff(160,plain,
% 0.46/0.61 (addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0) = addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))),
% 0.46/0.61 inference(symmetry,[status(thm)],[18])).
% 0.46/0.61 tff(161,plain,
% 0.46/0.61 (multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[160])).
% 0.46/0.61 tff(162,plain,
% 0.46/0.61 (multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) = multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.61 inference(symmetry,[status(thm)],[161])).
% 0.46/0.61 tff(163,plain,
% 0.46/0.61 (addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) = multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.61 inference(transitivity,[status(thm)],[152, 162])).
% 0.46/0.61 tff(164,plain,
% 0.46/0.61 (addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[163, 159])).
% 0.46/0.61 tff(165,plain,
% 0.46/0.61 (addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = multiplication(multiplication(X0!1, star(X0!1)), X1!0)),
% 0.46/0.61 inference(transitivity,[status(thm)],[164, 142, 139, 27])).
% 0.46/0.61 tff(166,plain,
% 0.46/0.61 (addition(X1!0, addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[165])).
% 0.46/0.61 tff(167,plain,
% 0.46/0.61 (addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = addition(X1!0, addition(addition(multiplication(X0!1, X1!0), multiplication(X0!1, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[166])).
% 0.46/0.61 tff(168,plain,
% 0.46/0.61 (addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0) = addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(transitivity,[status(thm)],[160, 167, 158, 156])).
% 0.46/0.61 tff(169,plain,
% 0.46/0.61 (addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), X1!0)),
% 0.46/0.61 inference(monotonicity,[status(thm)],[168])).
% 0.46/0.61 tff(170,plain,
% 0.46/0.61 (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), X1!0) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0)),
% 0.46/0.61 inference(symmetry,[status(thm)],[169])).
% 0.46/0.61 tff(171,plain,
% 0.46/0.61 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), X1!0)) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), X1!0))),
% 0.46/0.61 inference(quant_inst,[status(thm)],[])).
% 0.46/0.61 tff(172,plain,
% 0.46/0.61 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), X1!0)) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), X1!0)),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[171, 105])).
% 0.46/0.61 tff(173,plain,
% 0.46/0.61 (addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), X1!0) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)),
% 0.46/0.61 inference(monotonicity,[status(thm)],[143])).
% 0.46/0.61 tff(174,plain,
% 0.46/0.61 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0) = addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))))),
% 0.46/0.61 inference(quant_inst,[status(thm)],[])).
% 0.46/0.61 tff(175,plain,
% 0.46/0.61 (addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0) = addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[174, 16])).
% 0.46/0.61 tff(176,plain,
% 0.46/0.61 (addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) = addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0)),
% 0.46/0.61 inference(symmetry,[status(thm)],[175])).
% 0.46/0.61 tff(177,plain,
% 0.46/0.61 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), X1!0)) = addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[176, 173])).
% 0.46/0.61 tff(178,plain,
% 0.46/0.61 (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), X1!0))),
% 0.46/0.61 inference(symmetry,[status(thm)],[177])).
% 0.46/0.61 tff(179,plain,
% 0.46/0.61 (addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[144])).
% 0.46/0.61 tff(180,plain,
% 0.46/0.61 (addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0) = addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(transitivity,[status(thm)],[160, 179])).
% 0.46/0.61 tff(181,plain,
% 0.46/0.61 (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[175, 180])).
% 0.46/0.61 tff(182,plain,
% 0.46/0.61 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.61 inference(symmetry,[status(thm)],[181])).
% 0.46/0.61 tff(183,plain,
% 0.46/0.61 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.46/0.61 inference(quant_inst,[status(thm)],[])).
% 0.46/0.61 tff(184,plain,
% 0.46/0.61 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[183, 105])).
% 0.46/0.61 tff(185,plain,
% 0.46/0.61 (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(X1!0, addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[184])).
% 0.46/0.61 tff(186,plain,
% 0.46/0.61 (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0)),
% 0.46/0.61 inference(transitivity,[status(thm)],[185, 182, 178, 172, 170])).
% 0.46/0.61 tff(187,plain,
% 0.46/0.61 (addition(addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[186])).
% 0.46/0.61 tff(188,plain,
% 0.46/0.61 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.46/0.61 inference(quant_inst,[status(thm)],[])).
% 0.46/0.61 tff(189,plain,
% 0.46/0.61 (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))) = addition(addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[188, 105])).
% 0.46/0.61 tff(190,plain,
% 0.46/0.61 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(quant_inst,[status(thm)],[])).
% 0.46/0.61 tff(191,plain,
% 0.46/0.61 (addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[190, 7])).
% 0.46/0.61 tff(192,plain,
% 0.46/0.61 (addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))) = addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[191])).
% 0.46/0.61 tff(193,plain,
% 0.46/0.61 (addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))) = addition(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), X1!0), addition(addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0))), addition(multiplication(X0!1, addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)), multiplication(X0!1, multiplication(star(X0!1), X1!0)))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[192])).
% 0.46/0.62 tff(194,plain,
% 0.46/0.62 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[176])).
% 0.46/0.62 tff(195,plain,
% 0.46/0.62 (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)),
% 0.46/0.62 inference(transitivity,[status(thm)],[194, 181, 184, 193, 189, 187, 149, 146, 9])).
% 0.46/0.62 tff(196,plain,
% 0.46/0.62 (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.62 inference(symmetry,[status(thm)],[194])).
% 0.46/0.62 tff(197,plain,
% 0.46/0.62 ((addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) <=> (addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[196])).
% 0.46/0.62 tff(198,plain,
% 0.46/0.62 ((~(addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))) <=> (~(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[197])).
% 0.46/0.62 tff(199,plain,
% 0.46/0.62 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) <=> (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)))),
% 0.46/0.62 inference(quant_inst,[status(thm)],[])).
% 0.46/0.62 tff(200,plain,
% 0.46/0.62 (leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) <=> (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.62 inference(unit_resolution,[status(thm)],[199, 35])).
% 0.46/0.62 tff(201,plain,
% 0.46/0.62 (leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) <=> leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[160])).
% 0.46/0.62 tff(202,plain,
% 0.46/0.62 (leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) <=> leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.62 inference(symmetry,[status(thm)],[201])).
% 0.46/0.62 tff(203,plain,
% 0.46/0.62 ((~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) <=> (~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[202])).
% 0.46/0.62 tff(204,plain,
% 0.46/0.62 ((~(~((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))))) <=> ((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(205,plain,
% 0.46/0.62 ((leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) & leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))) <=> (~((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(206,plain,
% 0.46/0.62 ((~(leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) & leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))) <=> (~(~((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))))))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[205])).
% 0.46/0.62 tff(207,plain,
% 0.46/0.62 ((~(leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) & leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))) <=> ((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0))))),
% 0.46/0.62 inference(transitivity,[status(thm)],[206, 204])).
% 0.46/0.62 tff(208,plain,
% 0.46/0.62 ((~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))) <=> (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1))))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(209,axiom,(~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.46/0.62 tff(210,plain,
% 0.46/0.62 (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.46/0.62 tff(211,plain,
% 0.46/0.62 (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[210, 208])).
% 0.46/0.62 tff(212,plain,
% 0.46/0.62 (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[211, 208])).
% 0.46/0.62 tff(213,plain,
% 0.46/0.62 (~![X0: $i, X1: $i] : (leq(multiplication(star(X0), X1), addition(X1, multiplication(multiplication(X0, star(X0)), X1))) & leq(addition(X1, multiplication(multiplication(X0, star(X0)), X1)), multiplication(star(X0), X1)))),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[212, 208])).
% 0.46/0.62 tff(214,plain,(
% 0.46/0.62 ~(leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))) & leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))),
% 0.46/0.62 inference(skolemize,[status(sab)],[213])).
% 0.46/0.62 tff(215,plain,
% 0.46/0.62 ((~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | (~leq(addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)), multiplication(star(X0!1), X1!0)))),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[214, 207])).
% 0.46/0.62 tff(216,plain,
% 0.46/0.62 (~leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.46/0.62 inference(unit_resolution,[status(thm)],[215, 132])).
% 0.46/0.62 tff(217,plain,
% 0.46/0.62 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B)) <=> ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B)))),
% 0.46/0.62 inference(bind,[status(th)],[])).
% 0.46/0.62 tff(218,plain,
% 0.46/0.62 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.46/0.62 inference(quant_intro,[status(thm)],[217])).
% 0.46/0.62 tff(219,plain,
% 0.46/0.62 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(220,plain,
% 0.46/0.62 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, B), C), B) => leq(multiplication(star(A), C), B)) <=> ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B)))),
% 0.46/0.62 inference(bind,[status(th)],[])).
% 0.46/0.62 tff(221,plain,
% 0.46/0.62 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), B) => leq(multiplication(star(A), C), B)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.46/0.62 inference(quant_intro,[status(thm)],[220])).
% 0.46/0.62 tff(222,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), B) => leq(multiplication(star(A), C), B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_induction_left')).
% 0.46/0.62 tff(223,plain,
% 0.46/0.62 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.46/0.62 tff(224,plain,
% 0.46/0.62 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.46/0.62 tff(225,plain,(
% 0.46/0.62 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.46/0.62 inference(skolemize,[status(sab)],[224])).
% 0.46/0.62 tff(226,plain,
% 0.46/0.62 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[225, 218])).
% 0.46/0.62 tff(227,plain,
% 0.46/0.62 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(228,plain,
% 0.46/0.62 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))))),
% 0.46/0.62 inference(quant_inst,[status(thm)],[])).
% 0.46/0.62 tff(229,plain,
% 0.46/0.62 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))) | leq(multiplication(star(X0!1), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.46/0.62 tff(230,plain,
% 0.46/0.62 (~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 0.46/0.62 inference(unit_resolution,[status(thm)],[229, 226, 216])).
% 0.46/0.62 tff(231,plain,
% 0.46/0.62 (~leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[230, 203])).
% 0.46/0.62 tff(232,plain,
% 0.46/0.62 ((~(leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) <=> (addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)))) | leq(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) | (~(addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)))),
% 0.46/0.62 inference(tautology,[status(thm)],[])).
% 0.46/0.62 tff(233,plain,
% 0.46/0.62 (~(addition(addition(multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0))), X1!0), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.62 inference(unit_resolution,[status(thm)],[232, 231, 200])).
% 0.46/0.62 tff(234,plain,
% 0.46/0.62 (~(addition(addition(X1!0, multiplication(X0!1, addition(X1!0, multiplication(multiplication(X0!1, star(X0!1)), X1!0)))), addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0)) = addition(multiplication(multiplication(X0!1, star(X0!1)), X1!0), X1!0))),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[233, 198])).
% 0.46/0.62 tff(235,plain,
% 0.46/0.62 ($false),
% 0.46/0.62 inference(unit_resolution,[status(thm)],[234, 195])).
% 0.46/0.62 % SZS output end Proof
% 0.46/0.62 % E exiting
%------------------------------------------------------------------------------