%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE044+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 3.89s 4.08s
% Output : Proof 3.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE044+2 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 18:56:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 3.89/4.08 % SZS status Theorem
% 3.89/4.08 % SZS output start Proof
% 3.89/4.08 tff(leq_type, type, (
% 3.89/4.08 leq: ( $i * $i ) > $o)).
% 3.89/4.08 tff(star_type, type, (
% 3.89/4.08 star: $i > $i)).
% 3.89/4.08 tff(tptp_fun_X0_0_type, type, (
% 3.89/4.08 tptp_fun_X0_0: $i)).
% 3.89/4.08 tff(multiplication_type, type, (
% 3.89/4.08 multiplication: ( $i * $i ) > $i)).
% 3.89/4.08 tff(addition_type, type, (
% 3.89/4.08 addition: ( $i * $i ) > $i)).
% 3.89/4.08 tff(one_type, type, (
% 3.89/4.08 one: $i)).
% 3.89/4.08 tff(1,plain,
% 3.89/4.08 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 3.89/4.08 inference(bind,[status(th)],[])).
% 3.89/4.08 tff(2,plain,
% 3.89/4.08 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 3.89/4.08 inference(quant_intro,[status(thm)],[1])).
% 3.89/4.08 tff(3,plain,
% 3.89/4.08 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 3.89/4.08 inference(rewrite,[status(thm)],[])).
% 3.89/4.08 tff(4,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','multiplicative_left_identity')).
% 3.89/4.08 tff(5,plain,
% 3.89/4.08 (![A: $i] : (multiplication(one, A) = A)),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.89/4.08 tff(6,plain,(
% 3.89/4.08 ![A: $i] : (multiplication(one, A) = A)),
% 3.89/4.08 inference(skolemize,[status(sab)],[5])).
% 3.89/4.08 tff(7,plain,
% 3.89/4.08 (![A: $i] : (multiplication(one, A) = A)),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.89/4.08 tff(8,plain,
% 3.89/4.08 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(addition(one, X0!0))) = star(addition(one, X0!0)))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(9,plain,
% 3.89/4.08 (multiplication(one, star(addition(one, X0!0))) = star(addition(one, X0!0))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.89/4.08 tff(10,plain,
% 3.89/4.08 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 3.89/4.08 inference(bind,[status(th)],[])).
% 3.89/4.08 tff(11,plain,
% 3.89/4.08 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.89/4.08 inference(quant_intro,[status(thm)],[10])).
% 3.89/4.08 tff(12,plain,
% 3.89/4.08 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.89/4.08 inference(rewrite,[status(thm)],[])).
% 3.89/4.08 tff(13,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 3.89/4.08 tff(14,plain,
% 3.89/4.08 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[13, 12])).
% 3.89/4.08 tff(15,plain,(
% 3.89/4.08 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.89/4.08 inference(skolemize,[status(sab)],[14])).
% 3.89/4.08 tff(16,plain,
% 3.89/4.08 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[15, 11])).
% 3.89/4.08 tff(17,plain,
% 3.89/4.08 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, X0!0) = addition(X0!0, one))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(18,plain,
% 3.89/4.08 (addition(one, X0!0) = addition(X0!0, one)),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[17, 16])).
% 3.89/4.08 tff(19,plain,
% 3.89/4.08 (addition(X0!0, one) = addition(one, X0!0)),
% 3.89/4.08 inference(symmetry,[status(thm)],[18])).
% 3.89/4.08 tff(20,plain,
% 3.89/4.08 (star(addition(X0!0, one)) = star(addition(one, X0!0))),
% 3.89/4.08 inference(monotonicity,[status(thm)],[19])).
% 3.89/4.08 tff(21,plain,
% 3.89/4.08 (multiplication(one, star(addition(X0!0, one))) = multiplication(one, star(addition(one, X0!0)))),
% 3.89/4.08 inference(monotonicity,[status(thm)],[20])).
% 3.89/4.08 tff(22,plain,
% 3.89/4.08 (multiplication(one, star(addition(X0!0, one))) = star(addition(one, X0!0))),
% 3.89/4.08 inference(transitivity,[status(thm)],[21, 9])).
% 3.89/4.08 tff(23,plain,
% 3.89/4.08 (leq(multiplication(one, star(addition(X0!0, one))), star(X0!0)) <=> leq(star(addition(one, X0!0)), star(X0!0))),
% 3.89/4.08 inference(monotonicity,[status(thm)],[22])).
% 3.89/4.08 tff(24,plain,
% 3.89/4.08 (leq(star(addition(one, X0!0)), star(X0!0)) <=> leq(multiplication(one, star(addition(X0!0, one))), star(X0!0))),
% 3.89/4.08 inference(symmetry,[status(thm)],[23])).
% 3.89/4.08 tff(25,plain,
% 3.89/4.08 ((~leq(star(addition(one, X0!0)), star(X0!0))) <=> (~leq(multiplication(one, star(addition(X0!0, one))), star(X0!0)))),
% 3.89/4.08 inference(monotonicity,[status(thm)],[24])).
% 3.89/4.08 tff(26,plain,
% 3.89/4.08 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 3.89/4.08 inference(bind,[status(th)],[])).
% 3.89/4.08 tff(27,plain,
% 3.89/4.08 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 3.89/4.08 inference(quant_intro,[status(thm)],[26])).
% 3.89/4.08 tff(28,plain,
% 3.89/4.08 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 3.89/4.08 inference(rewrite,[status(thm)],[])).
% 3.89/4.08 tff(29,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 3.89/4.08 tff(30,plain,
% 3.89/4.08 (![A: $i] : (addition(A, A) = A)),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[29, 28])).
% 3.89/4.08 tff(31,plain,(
% 3.89/4.08 ![A: $i] : (addition(A, A) = A)),
% 3.89/4.08 inference(skolemize,[status(sab)],[30])).
% 3.89/4.08 tff(32,plain,
% 3.89/4.08 (![A: $i] : (addition(A, A) = A)),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[31, 27])).
% 3.89/4.08 tff(33,plain,
% 3.89/4.08 ((~![A: $i] : (addition(A, A) = A)) | (addition(star(addition(one, X0!0)), star(addition(one, X0!0))) = star(addition(one, X0!0)))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(34,plain,
% 3.89/4.08 (addition(star(addition(one, X0!0)), star(addition(one, X0!0))) = star(addition(one, X0!0))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[33, 32])).
% 3.89/4.08 tff(35,plain,
% 3.89/4.08 (^[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))))),
% 3.89/4.08 inference(bind,[status(th)],[])).
% 3.89/4.08 tff(36,plain,
% 3.89/4.08 (![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)))),
% 3.89/4.08 inference(quant_intro,[status(thm)],[35])).
% 3.89/4.08 tff(37,plain,
% 3.89/4.08 (![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)))),
% 3.89/4.08 inference(rewrite,[status(thm)],[])).
% 3.89/4.08 tff(38,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')).
% 3.89/4.08 tff(39,plain,
% 3.89/4.08 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[38, 37])).
% 3.89/4.08 tff(40,plain,(
% 3.89/4.08 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 3.89/4.08 inference(skolemize,[status(sab)],[39])).
% 3.89/4.08 tff(41,plain,
% 3.89/4.08 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[40, 36])).
% 3.89/4.08 tff(42,plain,
% 3.89/4.08 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one), star(addition(one, X0!0)))) = addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0)))))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(43,plain,
% 3.89/4.08 (multiplication(X0!0, addition(addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one), star(addition(one, X0!0)))) = addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[42, 41])).
% 3.89/4.08 tff(44,plain,
% 3.89/4.08 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 3.89/4.08 inference(bind,[status(th)],[])).
% 3.89/4.08 tff(45,plain,
% 3.89/4.08 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 3.89/4.08 inference(quant_intro,[status(thm)],[44])).
% 3.89/4.08 tff(46,plain,
% 3.89/4.08 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 3.89/4.08 inference(rewrite,[status(thm)],[])).
% 3.89/4.08 tff(47,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','order')).
% 3.89/4.08 tff(48,plain,
% 3.89/4.08 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[47, 46])).
% 3.89/4.08 tff(49,plain,(
% 3.89/4.08 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 3.89/4.08 inference(skolemize,[status(sab)],[48])).
% 3.89/4.08 tff(50,plain,
% 3.89/4.08 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[49, 45])).
% 3.89/4.08 tff(51,plain,
% 3.89/4.08 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0))) <=> (addition(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0))) = star(addition(one, X0!0))))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(52,plain,
% 3.89/4.08 (leq(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0))) <=> (addition(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0))) = star(addition(one, X0!0)))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[51, 50])).
% 3.89/4.08 tff(53,plain,
% 3.89/4.08 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 3.89/4.08 inference(bind,[status(th)],[])).
% 3.89/4.08 tff(54,plain,
% 3.89/4.08 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 3.89/4.08 inference(quant_intro,[status(thm)],[53])).
% 3.89/4.08 tff(55,plain,
% 3.89/4.08 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 3.89/4.08 inference(rewrite,[status(thm)],[])).
% 3.89/4.08 tff(56,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 3.89/4.08 tff(57,plain,
% 3.89/4.08 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[56, 55])).
% 3.89/4.08 tff(58,plain,(
% 3.89/4.08 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 3.89/4.08 inference(skolemize,[status(sab)],[57])).
% 3.89/4.08 tff(59,plain,
% 3.89/4.08 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[58, 54])).
% 3.89/4.08 tff(60,plain,
% 3.89/4.08 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0)))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(61,plain,
% 3.89/4.08 (leq(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0)))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[60, 59])).
% 3.89/4.08 tff(62,plain,
% 3.89/4.08 ((~(leq(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0))) <=> (addition(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0))) = star(addition(one, X0!0))))) | (~leq(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0)))) | (addition(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0))) = star(addition(one, X0!0)))),
% 3.89/4.08 inference(tautology,[status(thm)],[])).
% 3.89/4.08 tff(63,plain,
% 3.89/4.08 ((~(leq(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0))) <=> (addition(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0))) = star(addition(one, X0!0))))) | (addition(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0))) = star(addition(one, X0!0)))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[62, 61])).
% 3.89/4.08 tff(64,plain,
% 3.89/4.08 (addition(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0))) = star(addition(one, X0!0))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[63, 52])).
% 3.89/4.08 tff(65,plain,
% 3.89/4.08 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))) = addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(66,plain,
% 3.89/4.08 (addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))) = addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[65, 16])).
% 3.89/4.08 tff(67,plain,
% 3.89/4.08 (addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one) = addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0)))),
% 3.89/4.08 inference(symmetry,[status(thm)],[66])).
% 3.89/4.08 tff(68,plain,
% 3.89/4.08 (addition(addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one), star(addition(one, X0!0))) = addition(addition(one, multiplication(star(addition(one, X0!0)), addition(one, X0!0))), star(addition(one, X0!0)))),
% 3.89/4.08 inference(monotonicity,[status(thm)],[67])).
% 3.89/4.08 tff(69,plain,
% 3.89/4.08 (addition(addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one), star(addition(one, X0!0))) = star(addition(one, X0!0))),
% 3.89/4.08 inference(transitivity,[status(thm)],[68, 64])).
% 3.89/4.08 tff(70,plain,
% 3.89/4.08 (multiplication(X0!0, addition(addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one), star(addition(one, X0!0)))) = multiplication(X0!0, star(addition(one, X0!0)))),
% 3.89/4.08 inference(monotonicity,[status(thm)],[69])).
% 3.89/4.08 tff(71,plain,
% 3.89/4.08 (multiplication(X0!0, star(addition(one, X0!0))) = multiplication(X0!0, addition(addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one), star(addition(one, X0!0))))),
% 3.89/4.08 inference(symmetry,[status(thm)],[70])).
% 3.89/4.08 tff(72,plain,
% 3.89/4.08 (multiplication(X0!0, star(addition(one, X0!0))) = addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))),
% 3.89/4.08 inference(transitivity,[status(thm)],[71, 43])).
% 3.89/4.08 tff(73,plain,
% 3.89/4.08 (addition(multiplication(X0!0, star(addition(one, X0!0))), one) = addition(addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0)))), one)),
% 3.89/4.08 inference(monotonicity,[status(thm)],[72])).
% 3.89/4.08 tff(74,plain,
% 3.89/4.08 (addition(addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0)))), one) = addition(multiplication(X0!0, star(addition(one, X0!0))), one)),
% 3.89/4.08 inference(symmetry,[status(thm)],[73])).
% 3.89/4.08 tff(75,plain,
% 3.89/4.08 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0)))), one) = addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(76,plain,
% 3.89/4.08 (addition(addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0)))), one) = addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0)))))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[75, 16])).
% 3.89/4.08 tff(77,plain,
% 3.89/4.08 (addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))) = addition(addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0)))), one)),
% 3.89/4.08 inference(symmetry,[status(thm)],[76])).
% 3.89/4.08 tff(78,plain,
% 3.89/4.08 (addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))) = addition(multiplication(X0!0, star(addition(one, X0!0))), one)),
% 3.89/4.08 inference(transitivity,[status(thm)],[77, 74])).
% 3.89/4.08 tff(79,plain,
% 3.89/4.08 (leq(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) <=> leq(addition(multiplication(X0!0, star(addition(one, X0!0))), one), star(addition(one, X0!0)))),
% 3.89/4.08 inference(monotonicity,[status(thm)],[78, 34])).
% 3.89/4.08 tff(80,plain,
% 3.89/4.08 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) <=> (addition(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) = addition(star(addition(one, X0!0)), star(addition(one, X0!0)))))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(81,plain,
% 3.89/4.08 (leq(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) <=> (addition(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) = addition(star(addition(one, X0!0)), star(addition(one, X0!0))))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[80, 50])).
% 3.89/4.08 tff(82,plain,
% 3.89/4.08 (star(addition(one, X0!0)) = addition(star(addition(one, X0!0)), star(addition(one, X0!0)))),
% 3.89/4.08 inference(symmetry,[status(thm)],[34])).
% 3.89/4.08 tff(83,plain,
% 3.89/4.08 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0))) <=> (addition(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0))) = star(addition(one, X0!0))))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(84,plain,
% 3.89/4.08 (leq(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0))) <=> (addition(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0))) = star(addition(one, X0!0)))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[83, 50])).
% 3.89/4.08 tff(85,plain,
% 3.89/4.08 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 3.89/4.08 inference(bind,[status(th)],[])).
% 3.89/4.08 tff(86,plain,
% 3.89/4.08 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 3.89/4.08 inference(quant_intro,[status(thm)],[85])).
% 3.89/4.08 tff(87,plain,
% 3.89/4.08 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 3.89/4.08 inference(rewrite,[status(thm)],[])).
% 3.89/4.08 tff(88,axiom,(![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_unfold_right')).
% 3.89/4.08 tff(89,plain,
% 3.89/4.08 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[88, 87])).
% 3.89/4.08 tff(90,plain,(
% 3.89/4.08 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 3.89/4.08 inference(skolemize,[status(sab)],[89])).
% 3.89/4.08 tff(91,plain,
% 3.89/4.08 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[90, 86])).
% 3.89/4.08 tff(92,plain,
% 3.89/4.08 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0)))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(93,plain,
% 3.89/4.08 (leq(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0)))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[92, 91])).
% 3.89/4.08 tff(94,plain,
% 3.89/4.08 ((~(leq(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0))) <=> (addition(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0))) = star(addition(one, X0!0))))) | (~leq(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0)))) | (addition(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0))) = star(addition(one, X0!0)))),
% 3.89/4.08 inference(tautology,[status(thm)],[])).
% 3.89/4.08 tff(95,plain,
% 3.89/4.08 ((~(leq(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0))) <=> (addition(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0))) = star(addition(one, X0!0))))) | (addition(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0))) = star(addition(one, X0!0)))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[94, 93])).
% 3.89/4.08 tff(96,plain,
% 3.89/4.08 (addition(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0))) = star(addition(one, X0!0))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[95, 84])).
% 3.89/4.08 tff(97,plain,
% 3.89/4.08 (^[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))))),
% 3.89/4.08 inference(bind,[status(th)],[])).
% 3.89/4.08 tff(98,plain,
% 3.89/4.08 (![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)))),
% 3.89/4.08 inference(quant_intro,[status(thm)],[97])).
% 3.89/4.08 tff(99,plain,
% 3.89/4.08 (![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)))),
% 3.89/4.08 inference(rewrite,[status(thm)],[])).
% 3.89/4.08 tff(100,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')).
% 3.89/4.08 tff(101,plain,
% 3.89/4.08 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[100, 99])).
% 3.89/4.08 tff(102,plain,(
% 3.89/4.08 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 3.89/4.08 inference(skolemize,[status(sab)],[101])).
% 3.89/4.08 tff(103,plain,
% 3.89/4.08 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[102, 98])).
% 3.89/4.08 tff(104,plain,
% 3.89/4.08 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!0, one), star(addition(one, X0!0))) = addition(multiplication(X0!0, star(addition(one, X0!0))), multiplication(one, star(addition(one, X0!0)))))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(105,plain,
% 3.89/4.08 (multiplication(addition(X0!0, one), star(addition(one, X0!0))) = addition(multiplication(X0!0, star(addition(one, X0!0))), multiplication(one, star(addition(one, X0!0))))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[104, 103])).
% 3.89/4.08 tff(106,plain,
% 3.89/4.08 (multiplication(addition(one, X0!0), star(addition(one, X0!0))) = multiplication(addition(X0!0, one), star(addition(one, X0!0)))),
% 3.89/4.08 inference(monotonicity,[status(thm)],[18])).
% 3.89/4.08 tff(107,plain,
% 3.89/4.08 (multiplication(addition(one, X0!0), star(addition(one, X0!0))) = addition(multiplication(X0!0, star(addition(one, X0!0))), multiplication(one, star(addition(one, X0!0))))),
% 3.89/4.08 inference(transitivity,[status(thm)],[106, 105])).
% 3.89/4.08 tff(108,plain,
% 3.89/4.08 (addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))) = addition(one, addition(multiplication(X0!0, star(addition(one, X0!0))), multiplication(one, star(addition(one, X0!0)))))),
% 3.89/4.08 inference(monotonicity,[status(thm)],[107])).
% 3.89/4.08 tff(109,plain,
% 3.89/4.08 (addition(one, addition(multiplication(X0!0, star(addition(one, X0!0))), multiplication(one, star(addition(one, X0!0))))) = addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0))))),
% 3.89/4.08 inference(symmetry,[status(thm)],[108])).
% 3.89/4.08 tff(110,plain,
% 3.89/4.08 (^[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)))),
% 3.89/4.08 inference(bind,[status(th)],[])).
% 3.89/4.08 tff(111,plain,
% 3.89/4.08 (![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))),
% 3.89/4.08 inference(quant_intro,[status(thm)],[110])).
% 3.89/4.08 tff(112,plain,
% 3.89/4.08 (![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))),
% 3.89/4.08 inference(rewrite,[status(thm)],[])).
% 3.89/4.08 tff(113,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')).
% 3.89/4.08 tff(114,plain,
% 3.89/4.08 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[113, 112])).
% 3.89/4.08 tff(115,plain,(
% 3.89/4.08 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 3.89/4.08 inference(skolemize,[status(sab)],[114])).
% 3.89/4.08 tff(116,plain,
% 3.89/4.08 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 3.89/4.08 inference(modus_ponens,[status(thm)],[115, 111])).
% 3.89/4.08 tff(117,plain,
% 3.89/4.08 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(X0!0, star(addition(one, X0!0))), multiplication(one, star(addition(one, X0!0))))) = addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), multiplication(one, star(addition(one, X0!0)))))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.08 tff(118,plain,
% 3.89/4.08 (addition(one, addition(multiplication(X0!0, star(addition(one, X0!0))), multiplication(one, star(addition(one, X0!0))))) = addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), multiplication(one, star(addition(one, X0!0))))),
% 3.89/4.08 inference(unit_resolution,[status(thm)],[117, 116])).
% 3.89/4.08 tff(119,plain,
% 3.89/4.08 (addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), multiplication(one, star(addition(one, X0!0)))) = addition(one, addition(multiplication(X0!0, star(addition(one, X0!0))), multiplication(one, star(addition(one, X0!0)))))),
% 3.89/4.08 inference(symmetry,[status(thm)],[118])).
% 3.89/4.08 tff(120,plain,
% 3.89/4.08 (star(addition(one, X0!0)) = multiplication(one, star(addition(one, X0!0)))),
% 3.89/4.08 inference(symmetry,[status(thm)],[9])).
% 3.89/4.08 tff(121,plain,
% 3.89/4.08 (addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), star(addition(one, X0!0))) = addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), multiplication(one, star(addition(one, X0!0))))),
% 3.89/4.08 inference(monotonicity,[status(thm)],[120])).
% 3.89/4.08 tff(122,plain,
% 3.89/4.08 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), star(addition(one, X0!0))) = addition(star(addition(one, X0!0)), addition(one, multiplication(X0!0, star(addition(one, X0!0))))))),
% 3.89/4.08 inference(quant_inst,[status(thm)],[])).
% 3.89/4.09 tff(123,plain,
% 3.89/4.09 (addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), star(addition(one, X0!0))) = addition(star(addition(one, X0!0)), addition(one, multiplication(X0!0, star(addition(one, X0!0)))))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[122, 16])).
% 3.89/4.09 tff(124,plain,
% 3.89/4.09 (addition(star(addition(one, X0!0)), addition(one, multiplication(X0!0, star(addition(one, X0!0))))) = addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), star(addition(one, X0!0)))),
% 3.89/4.09 inference(symmetry,[status(thm)],[123])).
% 3.89/4.09 tff(125,plain,
% 3.89/4.09 (addition(star(addition(one, X0!0)), addition(one, multiplication(X0!0, star(addition(one, X0!0))))) = addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0))))),
% 3.89/4.09 inference(transitivity,[status(thm)],[124, 121, 119, 109])).
% 3.89/4.09 tff(126,plain,
% 3.89/4.09 (addition(addition(star(addition(one, X0!0)), addition(one, multiplication(X0!0, star(addition(one, X0!0))))), star(addition(one, X0!0))) = addition(addition(one, multiplication(addition(one, X0!0), star(addition(one, X0!0)))), star(addition(one, X0!0)))),
% 3.89/4.09 inference(monotonicity,[status(thm)],[125])).
% 3.89/4.09 tff(127,plain,
% 3.89/4.09 (addition(addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), star(addition(one, X0!0))), star(addition(one, X0!0))) = addition(addition(star(addition(one, X0!0)), addition(one, multiplication(X0!0, star(addition(one, X0!0))))), star(addition(one, X0!0)))),
% 3.89/4.09 inference(monotonicity,[status(thm)],[123])).
% 3.89/4.09 tff(128,plain,
% 3.89/4.09 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) = addition(addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), star(addition(one, X0!0))), star(addition(one, X0!0))))),
% 3.89/4.09 inference(quant_inst,[status(thm)],[])).
% 3.89/4.09 tff(129,plain,
% 3.89/4.09 (addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) = addition(addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), star(addition(one, X0!0))), star(addition(one, X0!0)))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[128, 116])).
% 3.89/4.09 tff(130,plain,
% 3.89/4.09 (addition(one, multiplication(X0!0, star(addition(one, X0!0)))) = addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0)))))),
% 3.89/4.09 inference(monotonicity,[status(thm)],[72])).
% 3.89/4.09 tff(131,plain,
% 3.89/4.09 (addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))) = addition(one, multiplication(X0!0, star(addition(one, X0!0))))),
% 3.89/4.09 inference(symmetry,[status(thm)],[130])).
% 3.89/4.09 tff(132,plain,
% 3.89/4.09 (addition(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) = addition(addition(one, multiplication(X0!0, star(addition(one, X0!0)))), addition(star(addition(one, X0!0)), star(addition(one, X0!0))))),
% 3.89/4.09 inference(monotonicity,[status(thm)],[131])).
% 3.89/4.09 tff(133,plain,
% 3.89/4.09 (addition(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) = addition(star(addition(one, X0!0)), star(addition(one, X0!0)))),
% 3.89/4.09 inference(transitivity,[status(thm)],[132, 129, 127, 126, 96, 82])).
% 3.89/4.09 tff(134,plain,
% 3.89/4.09 ((~(leq(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) <=> (addition(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) = addition(star(addition(one, X0!0)), star(addition(one, X0!0)))))) | leq(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) | (~(addition(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0)))) = addition(star(addition(one, X0!0)), star(addition(one, X0!0)))))),
% 3.89/4.09 inference(tautology,[status(thm)],[])).
% 3.89/4.09 tff(135,plain,
% 3.89/4.09 (leq(addition(one, addition(multiplication(X0!0, addition(multiplication(star(addition(one, X0!0)), addition(one, X0!0)), one)), multiplication(X0!0, star(addition(one, X0!0))))), addition(star(addition(one, X0!0)), star(addition(one, X0!0))))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[134, 133, 81])).
% 3.89/4.09 tff(136,plain,
% 3.89/4.09 (leq(addition(multiplication(X0!0, star(addition(one, X0!0))), one), star(addition(one, X0!0)))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[135, 79])).
% 3.89/4.09 tff(137,plain,
% 3.89/4.09 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 3.89/4.09 inference(bind,[status(th)],[])).
% 3.89/4.09 tff(138,plain,
% 3.89/4.09 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 3.89/4.09 inference(quant_intro,[status(thm)],[137])).
% 3.89/4.09 tff(139,plain,
% 3.89/4.09 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 3.89/4.09 inference(rewrite,[status(thm)],[])).
% 3.89/4.09 tff(140,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','multiplicative_right_identity')).
% 3.89/4.09 tff(141,plain,
% 3.89/4.09 (![A: $i] : (multiplication(A, one) = A)),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[140, 139])).
% 3.89/4.09 tff(142,plain,(
% 3.89/4.09 ![A: $i] : (multiplication(A, one) = A)),
% 3.89/4.09 inference(skolemize,[status(sab)],[141])).
% 3.89/4.09 tff(143,plain,
% 3.89/4.09 (![A: $i] : (multiplication(A, one) = A)),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[142, 138])).
% 3.89/4.09 tff(144,plain,
% 3.89/4.09 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(star(X0!0), one) = star(X0!0))),
% 3.89/4.09 inference(quant_inst,[status(thm)],[])).
% 3.89/4.09 tff(145,plain,
% 3.89/4.09 (multiplication(star(X0!0), one) = star(X0!0)),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[144, 143])).
% 3.89/4.09 tff(146,plain,
% 3.89/4.09 (leq(multiplication(star(X0!0), one), star(addition(one, X0!0))) <=> leq(star(X0!0), star(addition(one, X0!0)))),
% 3.89/4.09 inference(monotonicity,[status(thm)],[145])).
% 3.89/4.09 tff(147,plain,
% 3.89/4.09 (leq(star(X0!0), star(addition(one, X0!0))) <=> leq(multiplication(star(X0!0), one), star(addition(one, X0!0)))),
% 3.89/4.09 inference(symmetry,[status(thm)],[146])).
% 3.89/4.09 tff(148,plain,
% 3.89/4.09 ((~leq(star(X0!0), star(addition(one, X0!0)))) <=> (~leq(multiplication(star(X0!0), one), star(addition(one, X0!0))))),
% 3.89/4.09 inference(monotonicity,[status(thm)],[147])).
% 3.89/4.09 tff(149,assumption,(~leq(star(X0!0), star(addition(one, X0!0)))), introduced(assumption)).
% 3.89/4.09 tff(150,plain,
% 3.89/4.09 (~leq(multiplication(star(X0!0), one), star(addition(one, X0!0)))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[149, 148])).
% 3.89/4.09 tff(151,plain,
% 3.89/4.09 (^[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)))),
% 3.89/4.09 inference(bind,[status(th)],[])).
% 3.89/4.09 tff(152,plain,
% 3.89/4.09 (![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))),
% 3.89/4.09 inference(quant_intro,[status(thm)],[151])).
% 3.89/4.09 tff(153,plain,
% 3.89/4.09 (![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))),
% 3.89/4.09 inference(rewrite,[status(thm)],[])).
% 3.89/4.09 tff(154,plain,
% 3.89/4.09 (^[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)))),
% 3.89/4.09 inference(bind,[status(th)],[])).
% 3.89/4.09 tff(155,plain,
% 3.89/4.09 (![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))),
% 3.89/4.09 inference(quant_intro,[status(thm)],[154])).
% 3.89/4.09 tff(156,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')).
% 3.89/4.09 tff(157,plain,
% 3.89/4.09 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[156, 155])).
% 3.89/4.09 tff(158,plain,
% 3.89/4.09 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[157, 153])).
% 3.89/4.09 tff(159,plain,(
% 3.89/4.09 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 3.89/4.09 inference(skolemize,[status(sab)],[158])).
% 3.89/4.09 tff(160,plain,
% 3.89/4.09 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[159, 152])).
% 3.89/4.09 tff(161,plain,
% 3.89/4.09 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!0, star(addition(one, X0!0))), one), star(addition(one, X0!0)))) | leq(multiplication(star(X0!0), one), star(addition(one, X0!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!0, star(addition(one, X0!0))), one), star(addition(one, X0!0)))) | leq(multiplication(star(X0!0), one), star(addition(one, X0!0))))),
% 3.89/4.09 inference(rewrite,[status(thm)],[])).
% 3.89/4.09 tff(162,plain,
% 3.89/4.09 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!0, star(addition(one, X0!0))), one), star(addition(one, X0!0)))) | leq(multiplication(star(X0!0), one), star(addition(one, X0!0))))),
% 3.89/4.09 inference(quant_inst,[status(thm)],[])).
% 3.89/4.09 tff(163,plain,
% 3.89/4.09 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!0, star(addition(one, X0!0))), one), star(addition(one, X0!0)))) | leq(multiplication(star(X0!0), one), star(addition(one, X0!0)))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[162, 161])).
% 3.89/4.09 tff(164,plain,
% 3.89/4.09 ((~leq(addition(multiplication(X0!0, star(addition(one, X0!0))), one), star(addition(one, X0!0)))) | leq(multiplication(star(X0!0), one), star(addition(one, X0!0)))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[163, 160])).
% 3.89/4.09 tff(165,plain,
% 3.89/4.09 (~leq(addition(multiplication(X0!0, star(addition(one, X0!0))), one), star(addition(one, X0!0)))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[164, 150])).
% 3.89/4.09 tff(166,plain,
% 3.89/4.09 ($false),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[165, 136])).
% 3.89/4.09 tff(167,plain,(leq(star(X0!0), star(addition(one, X0!0)))), inference(lemma,lemma(discharge,[]))).
% 3.89/4.09 tff(168,plain,
% 3.89/4.09 ((~(~((~leq(star(addition(one, X0!0)), star(X0!0))) | (~leq(star(X0!0), star(addition(one, X0!0))))))) <=> ((~leq(star(addition(one, X0!0)), star(X0!0))) | (~leq(star(X0!0), star(addition(one, X0!0)))))),
% 3.89/4.09 inference(rewrite,[status(thm)],[])).
% 3.89/4.09 tff(169,plain,
% 3.89/4.09 ((leq(star(addition(one, X0!0)), star(X0!0)) & leq(star(X0!0), star(addition(one, X0!0)))) <=> (~((~leq(star(addition(one, X0!0)), star(X0!0))) | (~leq(star(X0!0), star(addition(one, X0!0))))))),
% 3.89/4.09 inference(rewrite,[status(thm)],[])).
% 3.89/4.09 tff(170,plain,
% 3.89/4.09 ((~(leq(star(addition(one, X0!0)), star(X0!0)) & leq(star(X0!0), star(addition(one, X0!0))))) <=> (~(~((~leq(star(addition(one, X0!0)), star(X0!0))) | (~leq(star(X0!0), star(addition(one, X0!0)))))))),
% 3.89/4.09 inference(monotonicity,[status(thm)],[169])).
% 3.89/4.09 tff(171,plain,
% 3.89/4.09 ((~(leq(star(addition(one, X0!0)), star(X0!0)) & leq(star(X0!0), star(addition(one, X0!0))))) <=> ((~leq(star(addition(one, X0!0)), star(X0!0))) | (~leq(star(X0!0), star(addition(one, X0!0)))))),
% 3.89/4.09 inference(transitivity,[status(thm)],[170, 168])).
% 3.89/4.09 tff(172,plain,
% 3.89/4.09 ((~![X0: $i] : (leq(star(addition(one, X0)), star(X0)) & leq(star(X0), star(addition(one, X0))))) <=> (~![X0: $i] : (leq(star(addition(one, X0)), star(X0)) & leq(star(X0), star(addition(one, X0)))))),
% 3.89/4.09 inference(rewrite,[status(thm)],[])).
% 3.89/4.09 tff(173,axiom,(~![X0: $i] : (leq(star(addition(one, X0)), star(X0)) & leq(star(X0), star(addition(one, X0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 3.89/4.09 tff(174,plain,
% 3.89/4.09 (~![X0: $i] : (leq(star(addition(one, X0)), star(X0)) & leq(star(X0), star(addition(one, X0))))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[173, 172])).
% 3.89/4.09 tff(175,plain,
% 3.89/4.09 (~![X0: $i] : (leq(star(addition(one, X0)), star(X0)) & leq(star(X0), star(addition(one, X0))))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[174, 172])).
% 3.89/4.09 tff(176,plain,
% 3.89/4.09 (~![X0: $i] : (leq(star(addition(one, X0)), star(X0)) & leq(star(X0), star(addition(one, X0))))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[175, 172])).
% 3.89/4.09 tff(177,plain,
% 3.89/4.09 (~![X0: $i] : (leq(star(addition(one, X0)), star(X0)) & leq(star(X0), star(addition(one, X0))))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[176, 172])).
% 3.89/4.09 tff(178,plain,(
% 3.89/4.09 ~(leq(star(addition(one, X0!0)), star(X0!0)) & leq(star(X0!0), star(addition(one, X0!0))))),
% 3.89/4.09 inference(skolemize,[status(sab)],[177])).
% 3.89/4.09 tff(179,plain,
% 3.89/4.09 ((~leq(star(addition(one, X0!0)), star(X0!0))) | (~leq(star(X0!0), star(addition(one, X0!0))))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[178, 171])).
% 3.89/4.09 tff(180,plain,
% 3.89/4.09 (~leq(star(addition(one, X0!0)), star(X0!0))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[179, 167])).
% 3.89/4.09 tff(181,plain,
% 3.89/4.09 (~leq(multiplication(one, star(addition(X0!0, one))), star(X0!0))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[180, 25])).
% 3.89/4.09 tff(182,plain,
% 3.89/4.09 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)))),
% 3.89/4.09 inference(quant_inst,[status(thm)],[])).
% 3.89/4.09 tff(183,plain,
% 3.89/4.09 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[182, 50])).
% 3.89/4.09 tff(184,plain,
% 3.89/4.09 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 3.89/4.09 inference(quant_inst,[status(thm)],[])).
% 3.89/4.09 tff(185,plain,
% 3.89/4.09 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[184, 59])).
% 3.89/4.09 tff(186,plain,
% 3.89/4.09 ((~(leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)))) | (~leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))) | (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0))),
% 3.89/4.09 inference(tautology,[status(thm)],[])).
% 3.89/4.09 tff(187,plain,
% 3.89/4.09 ((~(leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) <=> (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)))) | (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[186, 185])).
% 3.89/4.09 tff(188,plain,
% 3.89/4.09 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[187, 183])).
% 3.89/4.09 tff(189,plain,
% 3.89/4.09 (addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(star(X0!0), one)) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 3.89/4.09 inference(monotonicity,[status(thm)],[145])).
% 3.89/4.09 tff(190,plain,
% 3.89/4.09 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(star(X0!0), one))) = addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(star(X0!0), one)))),
% 3.89/4.09 inference(quant_inst,[status(thm)],[])).
% 3.89/4.09 tff(191,plain,
% 3.89/4.09 (addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(star(X0!0), one))) = addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(star(X0!0), one))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[190, 116])).
% 3.89/4.09 tff(192,plain,
% 3.89/4.09 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(star(X0!0), one))) = addition(addition(multiplication(star(X0!0), X0!0), multiplication(star(X0!0), one)), one))),
% 3.89/4.09 inference(quant_inst,[status(thm)],[])).
% 3.89/4.09 tff(193,plain,
% 3.89/4.09 (addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(star(X0!0), one))) = addition(addition(multiplication(star(X0!0), X0!0), multiplication(star(X0!0), one)), one)),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[192, 16])).
% 3.89/4.09 tff(194,plain,
% 3.89/4.09 (addition(addition(multiplication(star(X0!0), X0!0), multiplication(star(X0!0), one)), one) = addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(star(X0!0), one)))),
% 3.89/4.09 inference(symmetry,[status(thm)],[193])).
% 3.89/4.09 tff(195,plain,
% 3.89/4.09 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(X0!0, one)) = addition(multiplication(star(X0!0), X0!0), multiplication(star(X0!0), one)))),
% 3.89/4.09 inference(quant_inst,[status(thm)],[])).
% 3.89/4.09 tff(196,plain,
% 3.89/4.09 (multiplication(star(X0!0), addition(X0!0, one)) = addition(multiplication(star(X0!0), X0!0), multiplication(star(X0!0), one))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[195, 41])).
% 3.89/4.09 tff(197,plain,
% 3.89/4.09 (addition(multiplication(star(X0!0), addition(X0!0, one)), one) = addition(addition(multiplication(star(X0!0), X0!0), multiplication(star(X0!0), one)), one)),
% 3.89/4.09 inference(monotonicity,[status(thm)],[196])).
% 3.89/4.09 tff(198,plain,
% 3.89/4.09 (addition(multiplication(star(X0!0), addition(X0!0, one)), one) = star(X0!0)),
% 3.89/4.09 inference(transitivity,[status(thm)],[197, 194, 191, 189, 188])).
% 3.89/4.09 tff(199,plain,
% 3.89/4.09 (leq(addition(multiplication(star(X0!0), addition(X0!0, one)), one), star(X0!0)) <=> leq(star(X0!0), star(X0!0))),
% 3.89/4.09 inference(monotonicity,[status(thm)],[198])).
% 3.89/4.09 tff(200,plain,
% 3.89/4.09 (leq(star(X0!0), star(X0!0)) <=> leq(addition(multiplication(star(X0!0), addition(X0!0, one)), one), star(X0!0))),
% 3.89/4.09 inference(symmetry,[status(thm)],[199])).
% 3.89/4.09 tff(201,plain,
% 3.89/4.09 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(star(X0!0), star(X0!0)) <=> (addition(star(X0!0), star(X0!0)) = star(X0!0)))),
% 3.89/4.09 inference(quant_inst,[status(thm)],[])).
% 3.89/4.09 tff(202,plain,
% 3.89/4.09 (leq(star(X0!0), star(X0!0)) <=> (addition(star(X0!0), star(X0!0)) = star(X0!0))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[201, 50])).
% 3.89/4.09 tff(203,plain,
% 3.89/4.09 ((~![A: $i] : (addition(A, A) = A)) | (addition(star(X0!0), star(X0!0)) = star(X0!0))),
% 3.89/4.09 inference(quant_inst,[status(thm)],[])).
% 3.89/4.09 tff(204,plain,
% 3.89/4.09 (addition(star(X0!0), star(X0!0)) = star(X0!0)),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[203, 32])).
% 3.89/4.09 tff(205,plain,
% 3.89/4.09 ((~(leq(star(X0!0), star(X0!0)) <=> (addition(star(X0!0), star(X0!0)) = star(X0!0)))) | leq(star(X0!0), star(X0!0)) | (~(addition(star(X0!0), star(X0!0)) = star(X0!0)))),
% 3.89/4.09 inference(tautology,[status(thm)],[])).
% 3.89/4.09 tff(206,plain,
% 3.89/4.09 (leq(star(X0!0), star(X0!0))),
% 3.89/4.09 inference(unit_resolution,[status(thm)],[205, 204, 202])).
% 3.89/4.09 tff(207,plain,
% 3.89/4.09 (leq(addition(multiplication(star(X0!0), addition(X0!0, one)), one), star(X0!0))),
% 3.89/4.09 inference(modus_ponens,[status(thm)],[206, 200])).
% 3.89/4.09 tff(208,plain,
% 3.89/4.09 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 3.89/4.10 inference(bind,[status(th)],[])).
% 3.89/4.10 tff(209,plain,
% 3.89/4.10 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 3.89/4.10 inference(quant_intro,[status(thm)],[208])).
% 3.89/4.10 tff(210,plain,
% 3.89/4.10 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 3.89/4.10 inference(rewrite,[status(thm)],[])).
% 3.89/4.10 tff(211,plain,
% 3.89/4.10 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 3.89/4.10 inference(bind,[status(th)],[])).
% 3.89/4.10 tff(212,plain,
% 3.89/4.10 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 3.89/4.10 inference(quant_intro,[status(thm)],[211])).
% 3.89/4.10 tff(213,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_induction_right')).
% 3.89/4.10 tff(214,plain,
% 3.89/4.10 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 3.89/4.10 inference(modus_ponens,[status(thm)],[213, 212])).
% 3.89/4.10 tff(215,plain,
% 3.89/4.10 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 3.89/4.10 inference(modus_ponens,[status(thm)],[214, 210])).
% 3.89/4.10 tff(216,plain,(
% 3.89/4.10 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 3.89/4.10 inference(skolemize,[status(sab)],[215])).
% 3.89/4.10 tff(217,plain,
% 3.89/4.10 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 3.89/4.10 inference(modus_ponens,[status(thm)],[216, 209])).
% 3.89/4.10 tff(218,plain,
% 3.89/4.10 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X0!0), addition(X0!0, one)), one), star(X0!0))) | leq(multiplication(one, star(addition(X0!0, one))), star(X0!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X0!0), addition(X0!0, one)), one), star(X0!0))) | leq(multiplication(one, star(addition(X0!0, one))), star(X0!0)))),
% 3.89/4.10 inference(rewrite,[status(thm)],[])).
% 3.89/4.10 tff(219,plain,
% 3.89/4.10 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X0!0), addition(X0!0, one)), one), star(X0!0))) | leq(multiplication(one, star(addition(X0!0, one))), star(X0!0)))),
% 3.89/4.10 inference(quant_inst,[status(thm)],[])).
% 3.89/4.10 tff(220,plain,
% 3.89/4.10 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X0!0), addition(X0!0, one)), one), star(X0!0))) | leq(multiplication(one, star(addition(X0!0, one))), star(X0!0))),
% 3.89/4.10 inference(modus_ponens,[status(thm)],[219, 218])).
% 3.89/4.10 tff(221,plain,
% 3.89/4.10 ($false),
% 3.89/4.10 inference(unit_resolution,[status(thm)],[220, 217, 207, 181])).
% 3.89/4.10 % SZS output end Proof
% 3.89/4.10 % E exiting
%------------------------------------------------------------------------------