%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE045+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:12:56 AM UTC 2025
% Result : Theorem 8.28s 8.45s
% Output : Proof 8.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : KLE045+1 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 18:55:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 8.28/8.45 % SZS status Theorem
% 8.28/8.45 % SZS output start Proof
% 8.28/8.45 tff(multiplication_type, type, (
% 8.28/8.45 multiplication: ( $i * $i ) > $i)).
% 8.28/8.45 tff(star_type, type, (
% 8.28/8.45 star: $i > $i)).
% 8.28/8.45 tff(tptp_fun_X1_1_type, type, (
% 8.28/8.45 tptp_fun_X1_1: $i)).
% 8.28/8.45 tff(tptp_fun_X2_0_type, type, (
% 8.28/8.45 tptp_fun_X2_0: $i)).
% 8.28/8.45 tff(addition_type, type, (
% 8.28/8.45 addition: ( $i * $i ) > $i)).
% 8.28/8.45 tff(tptp_fun_X0_2_type, type, (
% 8.28/8.45 tptp_fun_X0_2: $i)).
% 8.28/8.45 tff(one_type, type, (
% 8.28/8.45 one: $i)).
% 8.28/8.45 tff(leq_type, type, (
% 8.28/8.45 leq: ( $i * $i ) > $o)).
% 8.28/8.45 tff(1,plain,
% 8.28/8.45 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 8.28/8.45 inference(bind,[status(th)],[])).
% 8.28/8.45 tff(2,plain,
% 8.28/8.45 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 8.28/8.45 inference(quant_intro,[status(thm)],[1])).
% 8.28/8.45 tff(3,plain,
% 8.28/8.45 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 8.28/8.45 inference(rewrite,[status(thm)],[])).
% 8.28/8.45 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 8.28/8.45 tff(5,plain,
% 8.28/8.45 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 8.28/8.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 8.28/8.45 tff(6,plain,(
% 8.28/8.45 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 8.28/8.45 inference(skolemize,[status(sab)],[5])).
% 8.28/8.45 tff(7,plain,
% 8.28/8.45 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 8.28/8.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 8.28/8.45 tff(8,plain,
% 8.28/8.45 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(X1!1, star(X1!1))) = addition(multiplication(X1!1, star(X1!1)), one))),
% 8.28/8.45 inference(quant_inst,[status(thm)],[])).
% 8.28/8.45 tff(9,plain,
% 8.28/8.45 (addition(one, multiplication(X1!1, star(X1!1))) = addition(multiplication(X1!1, star(X1!1)), one)),
% 8.28/8.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 8.28/8.45 tff(10,plain,
% 8.28/8.45 (addition(multiplication(X1!1, star(X1!1)), one) = addition(one, multiplication(X1!1, star(X1!1)))),
% 8.28/8.45 inference(symmetry,[status(thm)],[9])).
% 8.28/8.45 tff(11,plain,
% 8.28/8.45 (addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)) = addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1))),
% 8.28/8.45 inference(monotonicity,[status(thm)],[10])).
% 8.28/8.45 tff(12,plain,
% 8.28/8.45 (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))),
% 8.28/8.45 inference(symmetry,[status(thm)],[11])).
% 8.28/8.45 tff(13,plain,
% 8.28/8.45 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 8.28/8.45 inference(bind,[status(th)],[])).
% 8.28/8.45 tff(14,plain,
% 8.28/8.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 8.28/8.45 inference(quant_intro,[status(thm)],[13])).
% 8.28/8.45 tff(15,plain,
% 8.28/8.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 8.28/8.45 inference(rewrite,[status(thm)],[])).
% 8.28/8.45 tff(16,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','order')).
% 8.28/8.45 tff(17,plain,
% 8.28/8.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 8.28/8.45 inference(modus_ponens,[status(thm)],[16, 15])).
% 8.28/8.45 tff(18,plain,(
% 8.28/8.45 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 8.28/8.45 inference(skolemize,[status(sab)],[17])).
% 8.28/8.45 tff(19,plain,
% 8.28/8.45 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 8.28/8.45 inference(modus_ponens,[status(thm)],[18, 14])).
% 8.28/8.45 tff(20,plain,
% 8.28/8.45 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) <=> (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1)))),
% 8.28/8.45 inference(quant_inst,[status(thm)],[])).
% 8.28/8.45 tff(21,plain,
% 8.28/8.45 (leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) <=> (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1))),
% 8.28/8.45 inference(unit_resolution,[status(thm)],[20, 19])).
% 8.28/8.45 tff(22,plain,
% 8.28/8.45 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 8.28/8.45 inference(bind,[status(th)],[])).
% 8.28/8.45 tff(23,plain,
% 8.28/8.45 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 8.28/8.45 inference(quant_intro,[status(thm)],[22])).
% 8.28/8.45 tff(24,plain,
% 8.28/8.45 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 8.28/8.45 inference(rewrite,[status(thm)],[])).
% 8.28/8.45 tff(25,axiom,(![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_unfold_right')).
% 8.28/8.45 tff(26,plain,
% 8.28/8.45 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 8.28/8.45 inference(modus_ponens,[status(thm)],[25, 24])).
% 8.28/8.45 tff(27,plain,(
% 8.28/8.45 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 8.28/8.45 inference(skolemize,[status(sab)],[26])).
% 8.28/8.45 tff(28,plain,
% 8.28/8.45 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[27, 23])).
% 8.28/8.46 tff(29,plain,
% 8.28/8.46 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(30,plain,
% 8.28/8.46 (leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[29, 28])).
% 8.28/8.46 tff(31,plain,
% 8.28/8.46 ((~(leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) <=> (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1)))) | (~leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1))) | (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1))),
% 8.28/8.46 inference(tautology,[status(thm)],[])).
% 8.28/8.46 tff(32,plain,
% 8.28/8.46 ((~(leq(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) <=> (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1)))) | (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[31, 30])).
% 8.28/8.46 tff(33,plain,
% 8.28/8.46 (addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1)) = star(X1!1)),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[32, 21])).
% 8.28/8.46 tff(34,plain,
% 8.28/8.46 (star(X1!1) = addition(addition(one, multiplication(X1!1, star(X1!1))), star(X1!1))),
% 8.28/8.46 inference(symmetry,[status(thm)],[33])).
% 8.28/8.46 tff(35,plain,
% 8.28/8.46 (star(X1!1) = addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))),
% 8.28/8.46 inference(transitivity,[status(thm)],[34, 12])).
% 8.28/8.46 tff(36,plain,
% 8.28/8.46 (multiplication(X1!1, star(X1!1)) = multiplication(X1!1, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[35])).
% 8.28/8.46 tff(37,plain,
% 8.28/8.46 (multiplication(X1!1, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = multiplication(X1!1, star(X1!1))),
% 8.28/8.46 inference(symmetry,[status(thm)],[36])).
% 8.28/8.46 tff(38,plain,
% 8.28/8.46 (^[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))))),
% 8.28/8.46 inference(bind,[status(th)],[])).
% 8.28/8.46 tff(39,plain,
% 8.28/8.46 (![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)))),
% 8.28/8.46 inference(quant_intro,[status(thm)],[38])).
% 8.28/8.46 tff(40,plain,
% 8.28/8.46 (![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)))),
% 8.28/8.46 inference(rewrite,[status(thm)],[])).
% 8.28/8.46 tff(41,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')).
% 8.28/8.46 tff(42,plain,
% 8.28/8.46 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[41, 40])).
% 8.28/8.46 tff(43,plain,(
% 8.28/8.46 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 8.28/8.46 inference(skolemize,[status(sab)],[42])).
% 8.28/8.46 tff(44,plain,
% 8.28/8.46 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[43, 39])).
% 8.28/8.46 tff(45,plain,
% 8.28/8.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!1, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(46,plain,
% 8.28/8.46 (multiplication(X1!1, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[45, 44])).
% 8.28/8.46 tff(47,plain,
% 8.28/8.46 (addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))) = multiplication(X1!1, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)))),
% 8.28/8.46 inference(symmetry,[status(thm)],[46])).
% 8.28/8.46 tff(48,plain,
% 8.28/8.46 (addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))) = multiplication(X1!1, star(X1!1))),
% 8.28/8.46 inference(transitivity,[status(thm)],[47, 37])).
% 8.28/8.46 tff(49,plain,
% 8.28/8.46 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1))) = addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1)))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[48])).
% 8.28/8.46 tff(50,plain,
% 8.28/8.46 (addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1))) = addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))),
% 8.28/8.46 inference(symmetry,[status(thm)],[49])).
% 8.28/8.46 tff(51,plain,
% 8.28/8.46 (^[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)))),
% 8.28/8.46 inference(bind,[status(th)],[])).
% 8.28/8.46 tff(52,plain,
% 8.28/8.46 (![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))),
% 8.28/8.46 inference(quant_intro,[status(thm)],[51])).
% 8.28/8.46 tff(53,plain,
% 8.28/8.46 (![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))),
% 8.28/8.46 inference(rewrite,[status(thm)],[])).
% 8.28/8.46 tff(54,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')).
% 8.28/8.46 tff(55,plain,
% 8.28/8.46 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[54, 53])).
% 8.28/8.46 tff(56,plain,(
% 8.28/8.46 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 8.28/8.46 inference(skolemize,[status(sab)],[55])).
% 8.28/8.46 tff(57,plain,
% 8.28/8.46 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[56, 52])).
% 8.28/8.46 tff(58,plain,
% 8.28/8.46 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1))) = addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(59,plain,
% 8.28/8.46 (addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1))) = addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[58, 57])).
% 8.28/8.46 tff(60,plain,
% 8.28/8.46 (addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)) = addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1)))),
% 8.28/8.46 inference(symmetry,[status(thm)],[59])).
% 8.28/8.46 tff(61,plain,
% 8.28/8.46 (star(X1!1) = addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))),
% 8.28/8.46 inference(transitivity,[status(thm)],[34, 12, 60, 50])).
% 8.28/8.46 tff(62,plain,
% 8.28/8.46 (multiplication(X1!1, star(X1!1)) = addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))),
% 8.28/8.46 inference(transitivity,[status(thm)],[36, 46])).
% 8.28/8.46 tff(63,plain,
% 8.28/8.46 (addition(multiplication(X1!1, star(X1!1)), star(X1!1)) = addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1))))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[62, 61])).
% 8.28/8.46 tff(64,plain,
% 8.28/8.46 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))) = addition(multiplication(X1!1, star(X1!1)), star(X1!1))),
% 8.28/8.46 inference(symmetry,[status(thm)],[63])).
% 8.28/8.46 tff(65,plain,
% 8.28/8.46 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))) = addition(addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(one, star(X1!1))))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(66,plain,
% 8.28/8.46 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))) = addition(addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(one, star(X1!1)))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[65, 57])).
% 8.28/8.46 tff(67,plain,
% 8.28/8.46 (addition(addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(one, star(X1!1))) = addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1))))),
% 8.28/8.46 inference(symmetry,[status(thm)],[66])).
% 8.28/8.46 tff(68,plain,
% 8.28/8.46 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 8.28/8.46 inference(bind,[status(th)],[])).
% 8.28/8.46 tff(69,plain,
% 8.28/8.46 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 8.28/8.46 inference(quant_intro,[status(thm)],[68])).
% 8.28/8.46 tff(70,plain,
% 8.28/8.46 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 8.28/8.46 inference(rewrite,[status(thm)],[])).
% 8.28/8.46 tff(71,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 8.28/8.46 tff(72,plain,
% 8.28/8.46 (![A: $i] : (addition(A, A) = A)),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[71, 70])).
% 8.28/8.46 tff(73,plain,(
% 8.28/8.46 ![A: $i] : (addition(A, A) = A)),
% 8.28/8.46 inference(skolemize,[status(sab)],[72])).
% 8.28/8.46 tff(74,plain,
% 8.28/8.46 (![A: $i] : (addition(A, A) = A)),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[73, 69])).
% 8.28/8.46 tff(75,plain,
% 8.28/8.46 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))) = addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(76,plain,
% 8.28/8.46 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))) = addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[75, 74])).
% 8.28/8.46 tff(77,plain,
% 8.28/8.46 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))) = multiplication(X1!1, star(X1!1))),
% 8.28/8.46 inference(transitivity,[status(thm)],[76, 47, 37])).
% 8.28/8.46 tff(78,plain,
% 8.28/8.46 (addition(addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(one, star(X1!1))) = addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1)))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[77])).
% 8.28/8.46 tff(79,plain,
% 8.28/8.46 (addition(multiplication(X1!1, star(X1!1)), addition(one, star(X1!1))) = addition(addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(one, star(X1!1)))),
% 8.28/8.46 inference(symmetry,[status(thm)],[78])).
% 8.28/8.46 tff(80,plain,
% 8.28/8.46 (star(X1!1) = addition(multiplication(X1!1, star(X1!1)), star(X1!1))),
% 8.28/8.46 inference(transitivity,[status(thm)],[34, 12, 60, 79, 67, 64])).
% 8.28/8.46 tff(81,plain,
% 8.28/8.46 (multiplication(X2!0, star(X1!1)) = multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[80])).
% 8.28/8.46 tff(82,plain,
% 8.28/8.46 (multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))) = multiplication(X2!0, star(X1!1))),
% 8.28/8.46 inference(symmetry,[status(thm)],[81])).
% 8.28/8.46 tff(83,plain,
% 8.28/8.46 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1)) = addition(multiplication(X1!1, star(X1!1)), star(X1!1))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[48])).
% 8.28/8.46 tff(84,plain,
% 8.28/8.46 (addition(multiplication(X1!1, star(X1!1)), star(X1!1)) = addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1))),
% 8.28/8.46 inference(symmetry,[status(thm)],[83])).
% 8.28/8.46 tff(85,plain,
% 8.28/8.46 (multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1))) = multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1)))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[84])).
% 8.28/8.46 tff(86,plain,
% 8.28/8.46 (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1))) = multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), star(X1!1)))),
% 8.28/8.46 inference(symmetry,[status(thm)],[85])).
% 8.28/8.46 tff(87,plain,
% 8.28/8.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, star(X1!1))))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(88,plain,
% 8.28/8.46 (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, star(X1!1)))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[87, 44])).
% 8.28/8.46 tff(89,plain,
% 8.28/8.46 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), star(X1!1)))),
% 8.28/8.46 inference(symmetry,[status(thm)],[88])).
% 8.28/8.46 tff(90,plain,
% 8.28/8.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X2!0, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(91,plain,
% 8.28/8.46 (multiplication(X2!0, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[90, 44])).
% 8.28/8.46 tff(92,plain,
% 8.28/8.46 (addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)) = star(X1!1)),
% 8.28/8.46 inference(transitivity,[status(thm)],[11, 33])).
% 8.28/8.46 tff(93,plain,
% 8.28/8.46 (multiplication(X2!0, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1))) = multiplication(X2!0, star(X1!1))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[92])).
% 8.28/8.46 tff(94,plain,
% 8.28/8.46 (multiplication(X2!0, star(X1!1)) = multiplication(X2!0, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)))),
% 8.28/8.46 inference(symmetry,[status(thm)],[93])).
% 8.28/8.46 tff(95,plain,
% 8.28/8.46 (multiplication(X2!0, star(X1!1)) = addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))),
% 8.28/8.46 inference(transitivity,[status(thm)],[94, 91])).
% 8.28/8.46 tff(96,plain,
% 8.28/8.46 (^[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))))),
% 8.28/8.46 inference(bind,[status(th)],[])).
% 8.28/8.46 tff(97,plain,
% 8.28/8.46 (![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)))),
% 8.28/8.46 inference(quant_intro,[status(thm)],[96])).
% 8.28/8.46 tff(98,plain,
% 8.28/8.46 (![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)))),
% 8.28/8.46 inference(rewrite,[status(thm)],[])).
% 8.28/8.46 tff(99,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')).
% 8.28/8.46 tff(100,plain,
% 8.28/8.46 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[99, 98])).
% 8.28/8.46 tff(101,plain,(
% 8.28/8.46 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 8.28/8.46 inference(skolemize,[status(sab)],[100])).
% 8.28/8.46 tff(102,plain,
% 8.28/8.46 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[101, 97])).
% 8.28/8.46 tff(103,plain,
% 8.28/8.46 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X2!0, X1!1), multiplication(X0!2, X2!0)), star(X1!1)) = addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1))))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(104,plain,
% 8.28/8.46 (multiplication(addition(multiplication(X2!0, X1!1), multiplication(X0!2, X2!0)), star(X1!1)) = addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[103, 102])).
% 8.28/8.46 tff(105,plain,
% 8.28/8.46 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1)))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(106,plain,
% 8.28/8.46 (leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[105, 19])).
% 8.28/8.46 tff(107,plain,
% 8.28/8.46 ((~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1)))))),
% 8.28/8.46 inference(rewrite,[status(thm)],[])).
% 8.28/8.46 tff(108,plain,
% 8.28/8.46 ((~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X2), multiplication(X2, X1)) => leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1)))))),
% 8.28/8.46 inference(rewrite,[status(thm)],[])).
% 8.28/8.46 tff(109,axiom,(~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X2), multiplication(X2, X1)) => leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 8.28/8.46 tff(110,plain,
% 8.28/8.46 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[109, 108])).
% 8.28/8.46 tff(111,plain,
% 8.28/8.46 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[110, 107])).
% 8.28/8.46 tff(112,plain,
% 8.28/8.46 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[111, 107])).
% 8.28/8.46 tff(113,plain,
% 8.28/8.46 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X2), multiplication(X2, X1))) | leq(multiplication(star(X0), X2), multiplication(X2, star(X1))))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[112, 107])).
% 8.28/8.46 tff(114,plain,(
% 8.28/8.46 ~((~leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1))) | leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1))))),
% 8.28/8.46 inference(skolemize,[status(sab)],[113])).
% 8.28/8.46 tff(115,plain,
% 8.28/8.46 (leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1))),
% 8.28/8.46 inference(or_elim,[status(thm)],[114])).
% 8.28/8.46 tff(116,plain,
% 8.28/8.46 ((~(leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1)))) | (~leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1))) | (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1))),
% 8.28/8.46 inference(tautology,[status(thm)],[])).
% 8.28/8.46 tff(117,plain,
% 8.28/8.46 ((~(leq(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1)))) | (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[116, 115])).
% 8.28/8.46 tff(118,plain,
% 8.28/8.46 (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = multiplication(X2!0, X1!1)),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[117, 106])).
% 8.28/8.46 tff(119,plain,
% 8.28/8.46 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = addition(multiplication(X2!0, X1!1), multiplication(X0!2, X2!0)))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(120,plain,
% 8.28/8.46 (addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1)) = addition(multiplication(X2!0, X1!1), multiplication(X0!2, X2!0))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[119, 7])).
% 8.28/8.46 tff(121,plain,
% 8.28/8.46 (addition(multiplication(X2!0, X1!1), multiplication(X0!2, X2!0)) = addition(multiplication(X0!2, X2!0), multiplication(X2!0, X1!1))),
% 8.28/8.46 inference(symmetry,[status(thm)],[120])).
% 8.28/8.46 tff(122,plain,
% 8.28/8.46 (addition(multiplication(X2!0, X1!1), multiplication(X0!2, X2!0)) = multiplication(X2!0, X1!1)),
% 8.28/8.46 inference(transitivity,[status(thm)],[121, 118])).
% 8.28/8.46 tff(123,plain,
% 8.28/8.46 (multiplication(addition(multiplication(X2!0, X1!1), multiplication(X0!2, X2!0)), star(X1!1)) = multiplication(multiplication(X2!0, X1!1), star(X1!1))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[122])).
% 8.28/8.46 tff(124,plain,
% 8.28/8.46 (multiplication(multiplication(X2!0, X1!1), star(X1!1)) = multiplication(addition(multiplication(X2!0, X1!1), multiplication(X0!2, X2!0)), star(X1!1))),
% 8.28/8.46 inference(symmetry,[status(thm)],[123])).
% 8.28/8.46 tff(125,plain,
% 8.28/8.46 (^[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)))),
% 8.28/8.46 inference(bind,[status(th)],[])).
% 8.28/8.46 tff(126,plain,
% 8.28/8.46 (![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))),
% 8.28/8.46 inference(quant_intro,[status(thm)],[125])).
% 8.28/8.46 tff(127,plain,
% 8.28/8.46 (![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))),
% 8.28/8.46 inference(rewrite,[status(thm)],[])).
% 8.28/8.46 tff(128,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')).
% 8.28/8.46 tff(129,plain,
% 8.28/8.46 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[128, 127])).
% 8.28/8.46 tff(130,plain,(
% 8.28/8.46 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 8.28/8.46 inference(skolemize,[status(sab)],[129])).
% 8.28/8.46 tff(131,plain,
% 8.28/8.46 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 8.28/8.46 inference(modus_ponens,[status(thm)],[130, 126])).
% 8.28/8.46 tff(132,plain,
% 8.28/8.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X2!0, multiplication(X1!1, star(X1!1))) = multiplication(multiplication(X2!0, X1!1), star(X1!1)))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(133,plain,
% 8.28/8.46 (multiplication(X2!0, multiplication(X1!1, star(X1!1))) = multiplication(multiplication(X2!0, X1!1), star(X1!1))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[132, 131])).
% 8.28/8.46 tff(134,plain,
% 8.28/8.46 (multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))) = multiplication(X2!0, multiplication(X1!1, star(X1!1)))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[48])).
% 8.28/8.46 tff(135,plain,
% 8.28/8.46 (multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))) = addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.46 inference(transitivity,[status(thm)],[134, 133, 124, 104])).
% 8.28/8.46 tff(136,plain,
% 8.28/8.46 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, star(X1!1))) = addition(addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1))), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[135, 95])).
% 8.28/8.46 tff(137,plain,
% 8.28/8.46 (addition(addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1))), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, star(X1!1)))),
% 8.28/8.46 inference(symmetry,[status(thm)],[136])).
% 8.28/8.46 tff(138,plain,
% 8.28/8.46 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))) = addition(addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1))), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(139,plain,
% 8.28/8.46 (addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))) = addition(addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), multiplication(multiplication(X0!2, X2!0), star(X1!1))), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[138, 57])).
% 8.28/8.46 tff(140,plain,
% 8.28/8.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!2, multiplication(X2!0, star(X1!1))) = multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.46 inference(quant_inst,[status(thm)],[])).
% 8.28/8.46 tff(141,plain,
% 8.28/8.46 (multiplication(X0!2, multiplication(X2!0, star(X1!1))) = multiplication(multiplication(X0!2, X2!0), star(X1!1))),
% 8.28/8.46 inference(unit_resolution,[status(thm)],[140, 131])).
% 8.28/8.46 tff(142,plain,
% 8.28/8.46 (multiplication(multiplication(X0!2, X2!0), star(X1!1)) = multiplication(X0!2, multiplication(X2!0, star(X1!1)))),
% 8.28/8.46 inference(symmetry,[status(thm)],[141])).
% 8.28/8.46 tff(143,plain,
% 8.28/8.46 (addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1))) = addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))),
% 8.28/8.46 inference(monotonicity,[status(thm)],[142])).
% 8.28/8.46 tff(144,plain,
% 8.28/8.46 (addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, addition(addition(multiplication(X1!1, star(X1!1)), one), star(X1!1)))),
% 8.28/8.46 inference(symmetry,[status(thm)],[91])).
% 8.28/8.46 tff(145,plain,
% 8.28/8.46 (addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))),
% 8.28/8.46 inference(transitivity,[status(thm)],[144, 93])).
% 8.28/8.47 tff(146,plain,
% 8.28/8.47 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1)))) = addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[145, 143])).
% 8.28/8.47 tff(147,plain,
% 8.28/8.47 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1)))) = addition(addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), X2!0), multiplication(multiplication(X0!2, X2!0), star(X1!1))))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(148,plain,
% 8.28/8.47 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1)))) = addition(addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), X2!0), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[147, 57])).
% 8.28/8.47 tff(149,plain,
% 8.28/8.47 (addition(addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), X2!0), multiplication(multiplication(X0!2, X2!0), star(X1!1))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1))))),
% 8.28/8.47 inference(symmetry,[status(thm)],[148])).
% 8.28/8.47 tff(150,plain,
% 8.28/8.47 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 8.28/8.47 inference(bind,[status(th)],[])).
% 8.28/8.47 tff(151,plain,
% 8.28/8.47 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 8.28/8.47 inference(quant_intro,[status(thm)],[150])).
% 8.28/8.47 tff(152,plain,
% 8.28/8.47 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 8.28/8.47 inference(rewrite,[status(thm)],[])).
% 8.28/8.47 tff(153,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','multiplicative_right_identity')).
% 8.28/8.47 tff(154,plain,
% 8.28/8.47 (![A: $i] : (multiplication(A, one) = A)),
% 8.28/8.47 inference(modus_ponens,[status(thm)],[153, 152])).
% 8.28/8.47 tff(155,plain,(
% 8.28/8.47 ![A: $i] : (multiplication(A, one) = A)),
% 8.28/8.47 inference(skolemize,[status(sab)],[154])).
% 8.28/8.47 tff(156,plain,
% 8.28/8.47 (![A: $i] : (multiplication(A, one) = A)),
% 8.28/8.47 inference(modus_ponens,[status(thm)],[155, 151])).
% 8.28/8.47 tff(157,plain,
% 8.28/8.47 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X2!0, one) = X2!0)),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(158,plain,
% 8.28/8.47 (multiplication(X2!0, one) = X2!0),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[157, 156])).
% 8.28/8.47 tff(159,plain,
% 8.28/8.47 (X2!0 = multiplication(X2!0, one)),
% 8.28/8.47 inference(symmetry,[status(thm)],[158])).
% 8.28/8.47 tff(160,plain,
% 8.28/8.47 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), X2!0) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), multiplication(X2!0, one))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[159])).
% 8.28/8.47 tff(161,plain,
% 8.28/8.47 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), multiplication(X2!0, one)) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), X2!0)),
% 8.28/8.47 inference(symmetry,[status(thm)],[160])).
% 8.28/8.47 tff(162,plain,
% 8.28/8.47 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), multiplication(X2!0, one)) = addition(multiplication(X2!0, star(X1!1)), multiplication(X2!0, one))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[145])).
% 8.28/8.47 tff(163,plain,
% 8.28/8.47 (addition(multiplication(X2!0, star(X1!1)), multiplication(X2!0, one)) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), multiplication(X2!0, one))),
% 8.28/8.47 inference(symmetry,[status(thm)],[162])).
% 8.28/8.47 tff(164,plain,
% 8.28/8.47 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X2!0, addition(star(X1!1), one)) = addition(multiplication(X2!0, star(X1!1)), multiplication(X2!0, one)))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(165,plain,
% 8.28/8.47 (multiplication(X2!0, addition(star(X1!1), one)) = addition(multiplication(X2!0, star(X1!1)), multiplication(X2!0, one))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[164, 44])).
% 8.28/8.47 tff(166,plain,
% 8.28/8.47 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(X1!1)) = addition(star(X1!1), one))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(167,plain,
% 8.28/8.47 (addition(one, star(X1!1)) = addition(star(X1!1), one)),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[166, 7])).
% 8.28/8.47 tff(168,plain,
% 8.28/8.47 (addition(star(X1!1), one) = addition(one, star(X1!1))),
% 8.28/8.47 inference(symmetry,[status(thm)],[167])).
% 8.28/8.47 tff(169,plain,
% 8.28/8.47 (multiplication(X2!0, addition(star(X1!1), one)) = multiplication(X2!0, addition(one, star(X1!1)))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[168])).
% 8.28/8.47 tff(170,plain,
% 8.28/8.47 (multiplication(X2!0, addition(one, star(X1!1))) = multiplication(X2!0, addition(star(X1!1), one))),
% 8.28/8.47 inference(symmetry,[status(thm)],[169])).
% 8.28/8.47 tff(171,plain,
% 8.28/8.47 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) <=> (addition(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) = star(X1!1)))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(172,plain,
% 8.28/8.47 (leq(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) <=> (addition(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) = star(X1!1))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[171, 19])).
% 8.28/8.47 tff(173,plain,
% 8.28/8.47 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 8.28/8.47 inference(bind,[status(th)],[])).
% 8.28/8.47 tff(174,plain,
% 8.28/8.47 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 8.28/8.47 inference(quant_intro,[status(thm)],[173])).
% 8.28/8.47 tff(175,plain,
% 8.28/8.47 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 8.28/8.47 inference(rewrite,[status(thm)],[])).
% 8.28/8.47 tff(176,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 8.28/8.47 tff(177,plain,
% 8.28/8.47 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 8.28/8.47 inference(modus_ponens,[status(thm)],[176, 175])).
% 8.28/8.47 tff(178,plain,(
% 8.28/8.47 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 8.28/8.47 inference(skolemize,[status(sab)],[177])).
% 8.28/8.47 tff(179,plain,
% 8.28/8.47 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 8.28/8.47 inference(modus_ponens,[status(thm)],[178, 174])).
% 8.28/8.47 tff(180,plain,
% 8.28/8.47 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(181,plain,
% 8.28/8.47 (leq(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[180, 179])).
% 8.28/8.47 tff(182,plain,
% 8.28/8.47 ((~(leq(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) <=> (addition(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) = star(X1!1)))) | (~leq(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1))) | (addition(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) = star(X1!1))),
% 8.28/8.47 inference(tautology,[status(thm)],[])).
% 8.28/8.47 tff(183,plain,
% 8.28/8.47 ((~(leq(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) <=> (addition(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) = star(X1!1)))) | (addition(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) = star(X1!1))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[182, 181])).
% 8.28/8.47 tff(184,plain,
% 8.28/8.47 (addition(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) = star(X1!1)),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[183, 172])).
% 8.28/8.47 tff(185,plain,
% 8.28/8.47 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(star(X1!1), X1!1), star(X1!1))) = addition(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(186,plain,
% 8.28/8.47 (addition(one, addition(multiplication(star(X1!1), X1!1), star(X1!1))) = addition(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[185, 57])).
% 8.28/8.47 tff(187,plain,
% 8.28/8.47 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(188,plain,
% 8.28/8.47 (addition(one, one) = one),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[187, 74])).
% 8.28/8.47 tff(189,plain,
% 8.28/8.47 (addition(addition(one, one), addition(multiplication(star(X1!1), X1!1), star(X1!1))) = addition(one, addition(multiplication(star(X1!1), X1!1), star(X1!1)))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[188])).
% 8.28/8.47 tff(190,plain,
% 8.28/8.47 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(multiplication(star(X1!1), X1!1), star(X1!1)))) = addition(addition(one, one), addition(multiplication(star(X1!1), X1!1), star(X1!1))))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(191,plain,
% 8.28/8.47 (addition(one, addition(one, addition(multiplication(star(X1!1), X1!1), star(X1!1)))) = addition(addition(one, one), addition(multiplication(star(X1!1), X1!1), star(X1!1)))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[190, 57])).
% 8.28/8.47 tff(192,plain,
% 8.28/8.47 (addition(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1)) = addition(one, addition(multiplication(star(X1!1), X1!1), star(X1!1)))),
% 8.28/8.47 inference(symmetry,[status(thm)],[186])).
% 8.28/8.47 tff(193,plain,
% 8.28/8.47 (star(X1!1) = addition(addition(one, multiplication(star(X1!1), X1!1)), star(X1!1))),
% 8.28/8.47 inference(symmetry,[status(thm)],[184])).
% 8.28/8.47 tff(194,plain,
% 8.28/8.47 (star(X1!1) = addition(one, addition(multiplication(star(X1!1), X1!1), star(X1!1)))),
% 8.28/8.47 inference(transitivity,[status(thm)],[193, 192])).
% 8.28/8.47 tff(195,plain,
% 8.28/8.47 (addition(one, star(X1!1)) = addition(one, addition(one, addition(multiplication(star(X1!1), X1!1), star(X1!1))))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[194])).
% 8.28/8.47 tff(196,plain,
% 8.28/8.47 (addition(one, star(X1!1)) = star(X1!1)),
% 8.28/8.47 inference(transitivity,[status(thm)],[195, 191, 189, 186, 184])).
% 8.28/8.47 tff(197,plain,
% 8.28/8.47 (multiplication(X2!0, addition(one, star(X1!1))) = multiplication(X2!0, star(X1!1))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[196])).
% 8.28/8.47 tff(198,plain,
% 8.28/8.47 (multiplication(X2!0, star(X1!1)) = multiplication(X2!0, addition(one, star(X1!1)))),
% 8.28/8.47 inference(symmetry,[status(thm)],[197])).
% 8.28/8.47 tff(199,plain,
% 8.28/8.47 (addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), X2!0)),
% 8.28/8.47 inference(transitivity,[status(thm)],[144, 93, 198, 170, 165, 163, 161])).
% 8.28/8.47 tff(200,plain,
% 8.28/8.47 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1))) = addition(addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), X2!0), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[199])).
% 8.28/8.47 tff(201,plain,
% 8.28/8.47 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1))))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(202,plain,
% 8.28/8.47 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[201, 7])).
% 8.28/8.47 tff(203,plain,
% 8.28/8.47 (addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))) = addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 8.28/8.47 inference(transitivity,[status(thm)],[202, 200, 149, 146])).
% 8.28/8.47 tff(204,plain,
% 8.28/8.47 (multiplication(X2!0, multiplication(X1!1, star(X1!1))) = multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))))),
% 8.28/8.47 inference(symmetry,[status(thm)],[134])).
% 8.28/8.47 tff(205,plain,
% 8.28/8.47 (multiplication(multiplication(X2!0, X1!1), star(X1!1)) = multiplication(X2!0, multiplication(X1!1, star(X1!1)))),
% 8.28/8.47 inference(symmetry,[status(thm)],[133])).
% 8.28/8.47 tff(206,plain,
% 8.28/8.47 (multiplication(multiplication(X2!0, X1!1), star(X1!1)) = multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))))),
% 8.28/8.47 inference(transitivity,[status(thm)],[205, 204])).
% 8.28/8.47 tff(207,plain,
% 8.28/8.47 (addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[206, 203])).
% 8.28/8.47 tff(208,plain,
% 8.28/8.47 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))) = addition(multiplication(multiplication(X2!0, X1!1), star(X1!1)), addition(multiplication(multiplication(X0!2, X2!0), star(X1!1)), addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))))),
% 8.28/8.47 inference(symmetry,[status(thm)],[207])).
% 8.28/8.47 tff(209,plain,
% 8.28/8.47 (multiplication(X2!0, addition(one, star(X1!1))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), X2!0)),
% 8.28/8.47 inference(transitivity,[status(thm)],[170, 165, 163, 161])).
% 8.28/8.47 tff(210,plain,
% 8.28/8.47 (addition(multiplication(X2!0, addition(one, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1))) = addition(addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), X2!0), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[209])).
% 8.28/8.47 tff(211,plain,
% 8.28/8.47 (addition(addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), X2!0), multiplication(multiplication(X0!2, X2!0), star(X1!1))) = addition(multiplication(X2!0, addition(one, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.47 inference(symmetry,[status(thm)],[210])).
% 8.28/8.47 tff(212,plain,
% 8.28/8.47 (addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), addition(X2!0, multiplication(multiplication(X0!2, X2!0), star(X1!1))))),
% 8.28/8.47 inference(symmetry,[status(thm)],[146])).
% 8.28/8.47 tff(213,plain,
% 8.28/8.47 (addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))) = addition(multiplication(X2!0, addition(one, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.47 inference(transitivity,[status(thm)],[212, 148, 211])).
% 8.28/8.47 tff(214,plain,
% 8.28/8.47 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, addition(one, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1))))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[213])).
% 8.28/8.47 tff(215,plain,
% 8.28/8.47 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, addition(one, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1)))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 8.28/8.47 inference(symmetry,[status(thm)],[214])).
% 8.28/8.47 tff(216,plain,
% 8.28/8.47 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, addition(one, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1)))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, addition(one, star(X1!1)))), multiplication(multiplication(X0!2, X2!0), star(X1!1))))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(217,plain,
% 8.28/8.47 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, addition(one, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1)))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, addition(one, star(X1!1)))), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[216, 57])).
% 8.28/8.47 tff(218,plain,
% 8.28/8.47 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, addition(one, star(X1!1)))), multiplication(multiplication(X0!2, X2!0), star(X1!1))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), addition(multiplication(X2!0, addition(one, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1))))),
% 8.28/8.47 inference(symmetry,[status(thm)],[217])).
% 8.28/8.47 tff(219,plain,
% 8.28/8.47 (addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1))) = star(X1!1)),
% 8.28/8.47 inference(transitivity,[status(thm)],[49, 59, 11, 33])).
% 8.28/8.47 tff(220,plain,
% 8.28/8.47 (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))) = multiplication(X2!0, star(X1!1))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[219])).
% 8.28/8.47 tff(221,plain,
% 8.28/8.47 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, addition(one, star(X1!1)))))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(222,plain,
% 8.28/8.47 (multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1)))) = addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, addition(one, star(X1!1))))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[221, 44])).
% 8.28/8.47 tff(223,plain,
% 8.28/8.47 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, addition(one, star(X1!1)))) = multiplication(X2!0, addition(addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1))), addition(one, star(X1!1))))),
% 8.28/8.47 inference(symmetry,[status(thm)],[222])).
% 8.28/8.47 tff(224,plain,
% 8.28/8.47 (addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, addition(one, star(X1!1)))) = addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1)))),
% 8.28/8.47 inference(transitivity,[status(thm)],[223, 220, 94, 91])).
% 8.28/8.47 tff(225,plain,
% 8.28/8.47 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, addition(one, star(X1!1)))), multiplication(multiplication(X0!2, X2!0), star(X1!1))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[224])).
% 8.28/8.47 tff(226,plain,
% 8.28/8.47 (addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X1!1, star(X1!1)))), multiplication(X2!0, addition(one, star(X1!1)))), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.47 inference(symmetry,[status(thm)],[225])).
% 8.28/8.47 tff(227,plain,
% 8.28/8.47 (addition(addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), X2!0), multiplication(multiplication(X0!2, X2!0), star(X1!1))) = addition(addition(multiplication(X2!0, addition(multiplication(X1!1, star(X1!1)), one)), multiplication(X2!0, star(X1!1))), multiplication(multiplication(X0!2, X2!0), star(X1!1)))),
% 8.28/8.47 inference(symmetry,[status(thm)],[200])).
% 8.28/8.47 tff(228,plain,
% 8.28/8.47 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, star(X1!1))) = addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(229,plain,
% 8.28/8.47 (addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, star(X1!1))) = addition(multiplication(X2!0, star(X1!1)), addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[228, 7])).
% 8.28/8.47 tff(230,plain,
% 8.28/8.47 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0) = addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(231,plain,
% 8.28/8.47 (addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0) = addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1))))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[230, 7])).
% 8.28/8.47 tff(232,plain,
% 8.28/8.47 (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = addition(addition(X2!0, multiplication(X0!2, multiplication(X2!0, star(X1!1)))), multiplication(X2!0, star(X1!1)))),
% 8.28/8.47 inference(monotonicity,[status(thm)],[231])).
% 8.28/8.47 tff(233,plain,
% 8.28/8.47 (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))),
% 8.28/8.47 inference(transitivity,[status(thm)],[232, 229, 212, 148, 227, 226, 218, 215, 208, 139, 137, 89, 86, 82])).
% 8.28/8.47 tff(234,plain,
% 8.28/8.47 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) <=> (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))))),
% 8.28/8.47 inference(quant_inst,[status(thm)],[])).
% 8.28/8.47 tff(235,plain,
% 8.28/8.47 (leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) <=> (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1)))),
% 8.28/8.47 inference(unit_resolution,[status(thm)],[234, 19])).
% 8.28/8.47 tff(236,plain,
% 8.28/8.47 (~leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1)))),
% 8.28/8.47 inference(or_elim,[status(thm)],[114])).
% 8.28/8.47 tff(237,plain,
% 8.28/8.47 (^[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)))),
% 8.28/8.47 inference(bind,[status(th)],[])).
% 8.28/8.47 tff(238,plain,
% 8.28/8.47 (![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))),
% 8.28/8.47 inference(quant_intro,[status(thm)],[237])).
% 8.28/8.47 tff(239,plain,
% 8.28/8.47 (![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))),
% 8.28/8.47 inference(rewrite,[status(thm)],[])).
% 8.28/8.47 tff(240,plain,
% 8.28/8.47 (^[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)))),
% 8.28/8.47 inference(bind,[status(th)],[])).
% 8.28/8.47 tff(241,plain,
% 8.28/8.47 (![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))),
% 8.28/8.47 inference(quant_intro,[status(thm)],[240])).
% 8.28/8.47 tff(242,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')).
% 8.28/8.47 tff(243,plain,
% 8.28/8.47 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 8.28/8.47 inference(modus_ponens,[status(thm)],[242, 241])).
% 8.28/8.47 tff(244,plain,
% 8.28/8.47 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 8.28/8.47 inference(modus_ponens,[status(thm)],[243, 239])).
% 8.28/8.47 tff(245,plain,(
% 8.28/8.47 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 8.28/8.48 inference(skolemize,[status(sab)],[244])).
% 8.28/8.48 tff(246,plain,
% 8.28/8.48 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 8.28/8.48 inference(modus_ponens,[status(thm)],[245, 238])).
% 8.28/8.48 tff(247,plain,
% 8.28/8.48 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))) | leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))) | leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1))))),
% 8.28/8.48 inference(rewrite,[status(thm)],[])).
% 8.28/8.48 tff(248,plain,
% 8.28/8.48 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))) | leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1))))),
% 8.28/8.48 inference(quant_inst,[status(thm)],[])).
% 8.28/8.48 tff(249,plain,
% 8.28/8.48 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))) | leq(multiplication(star(X0!2), X2!0), multiplication(X2!0, star(X1!1)))),
% 8.28/8.48 inference(modus_ponens,[status(thm)],[248, 247])).
% 8.28/8.48 tff(250,plain,
% 8.28/8.48 (~leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1)))),
% 8.28/8.48 inference(unit_resolution,[status(thm)],[249, 246, 236])).
% 8.28/8.48 tff(251,plain,
% 8.28/8.48 ((~(leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) <=> (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))))) | leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) | (~(addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))))),
% 8.28/8.48 inference(tautology,[status(thm)],[])).
% 8.28/8.48 tff(252,plain,
% 8.28/8.48 ((~(leq(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) <=> (addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))))) | (~(addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1))))),
% 8.28/8.48 inference(unit_resolution,[status(thm)],[251, 250])).
% 8.28/8.48 tff(253,plain,
% 8.28/8.48 (~(addition(addition(multiplication(X0!2, multiplication(X2!0, star(X1!1))), X2!0), multiplication(X2!0, star(X1!1))) = multiplication(X2!0, star(X1!1)))),
% 8.28/8.48 inference(unit_resolution,[status(thm)],[252, 235])).
% 8.28/8.48 tff(254,plain,
% 8.28/8.48 ($false),
% 8.28/8.48 inference(unit_resolution,[status(thm)],[253, 233])).
% 8.28/8.48 % SZS output end Proof
% 8.28/8.48 % E exiting
%------------------------------------------------------------------------------