%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE039+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:12:55 AM UTC 2025
% Result : Theorem 65.60s 65.78s
% Output : Proof 65.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE039+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 18:54:56 EDT 2025
% 0.14/0.37 % CPUTime :
% 65.60/65.78 % SZS status Theorem
% 65.60/65.78 % SZS output start Proof
% 65.60/65.78 tff(leq_type, type, (
% 65.60/65.78 leq: ( $i * $i ) > $o)).
% 65.60/65.78 tff(star_type, type, (
% 65.60/65.78 star: $i > $i)).
% 65.60/65.78 tff(tptp_fun_X0_0_type, type, (
% 65.60/65.78 tptp_fun_X0_0: $i)).
% 65.60/65.78 tff(multiplication_type, type, (
% 65.60/65.78 multiplication: ( $i * $i ) > $i)).
% 65.60/65.78 tff(addition_type, type, (
% 65.60/65.78 addition: ( $i * $i ) > $i)).
% 65.60/65.78 tff(one_type, type, (
% 65.60/65.78 one: $i)).
% 65.60/65.78 tff(1,plain,
% 65.60/65.78 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 65.60/65.78 inference(bind,[status(th)],[])).
% 65.60/65.78 tff(2,plain,
% 65.60/65.78 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 65.60/65.78 inference(quant_intro,[status(thm)],[1])).
% 65.60/65.78 tff(3,plain,
% 65.60/65.78 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 65.60/65.78 inference(rewrite,[status(thm)],[])).
% 65.60/65.78 tff(4,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','order')).
% 65.60/65.78 tff(5,plain,
% 65.60/65.78 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 65.60/65.78 inference(modus_ponens,[status(thm)],[4, 3])).
% 65.60/65.78 tff(6,plain,(
% 65.60/65.78 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 65.60/65.78 inference(skolemize,[status(sab)],[5])).
% 65.60/65.78 tff(7,plain,
% 65.60/65.78 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 65.60/65.78 inference(modus_ponens,[status(thm)],[6, 2])).
% 65.60/65.78 tff(8,plain,
% 65.60/65.78 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)))),
% 65.60/65.78 inference(quant_inst,[status(thm)],[])).
% 65.60/65.78 tff(9,plain,
% 65.60/65.78 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0))),
% 65.60/65.78 inference(unit_resolution,[status(thm)],[8, 7])).
% 65.60/65.78 tff(10,plain,
% 65.60/65.78 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 65.60/65.78 inference(bind,[status(th)],[])).
% 65.60/65.78 tff(11,plain,
% 65.60/65.78 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 65.60/65.78 inference(quant_intro,[status(thm)],[10])).
% 65.60/65.78 tff(12,plain,
% 65.60/65.78 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 65.60/65.78 inference(rewrite,[status(thm)],[])).
% 65.60/65.78 tff(13,axiom,(![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_right')).
% 65.60/65.78 tff(14,plain,
% 65.60/65.78 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 65.60/65.78 inference(modus_ponens,[status(thm)],[13, 12])).
% 65.60/65.78 tff(15,plain,(
% 65.60/65.78 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 65.60/65.78 inference(skolemize,[status(sab)],[14])).
% 65.60/65.78 tff(16,plain,
% 65.60/65.78 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 65.60/65.78 inference(modus_ponens,[status(thm)],[15, 11])).
% 65.60/65.78 tff(17,plain,
% 65.60/65.78 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 65.60/65.78 inference(quant_inst,[status(thm)],[])).
% 65.60/65.78 tff(18,plain,
% 65.60/65.78 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 65.60/65.78 inference(unit_resolution,[status(thm)],[17, 16])).
% 65.60/65.78 tff(19,plain,
% 65.60/65.78 ((~(leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)))) | (~leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))) | (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0))),
% 65.60/65.78 inference(tautology,[status(thm)],[])).
% 65.60/65.78 tff(20,plain,
% 65.60/65.78 ((~(leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)))) | (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0))),
% 65.60/65.78 inference(unit_resolution,[status(thm)],[19, 18])).
% 65.60/65.78 tff(21,plain,
% 65.60/65.78 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)),
% 65.60/65.78 inference(unit_resolution,[status(thm)],[20, 9])).
% 65.60/65.78 tff(22,plain,
% 65.60/65.78 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 65.60/65.78 inference(bind,[status(th)],[])).
% 65.60/65.78 tff(23,plain,
% 65.60/65.78 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 65.60/65.78 inference(quant_intro,[status(thm)],[22])).
% 65.60/65.78 tff(24,plain,
% 65.60/65.78 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 65.60/65.78 inference(rewrite,[status(thm)],[])).
% 65.60/65.78 tff(25,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 65.60/65.78 tff(26,plain,
% 65.60/65.78 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 65.60/65.78 inference(modus_ponens,[status(thm)],[25, 24])).
% 65.60/65.78 tff(27,plain,(
% 65.60/65.78 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 65.60/65.78 inference(skolemize,[status(sab)],[26])).
% 65.60/65.78 tff(28,plain,
% 65.60/65.78 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 65.60/65.78 inference(modus_ponens,[status(thm)],[27, 23])).
% 65.60/65.78 tff(29,plain,
% 65.60/65.78 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(X0!0, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), one))),
% 65.60/65.78 inference(quant_inst,[status(thm)],[])).
% 65.60/65.78 tff(30,plain,
% 65.60/65.78 (addition(one, multiplication(X0!0, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), one)),
% 65.60/65.78 inference(unit_resolution,[status(thm)],[29, 28])).
% 65.60/65.78 tff(31,plain,
% 65.60/65.78 (addition(multiplication(X0!0, star(X0!0)), one) = addition(one, multiplication(X0!0, star(X0!0)))),
% 65.60/65.78 inference(symmetry,[status(thm)],[30])).
% 65.60/65.78 tff(32,plain,
% 65.60/65.78 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 65.60/65.78 inference(monotonicity,[status(thm)],[31])).
% 65.60/65.78 tff(33,plain,
% 65.60/65.78 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = star(X0!0)),
% 65.60/65.78 inference(transitivity,[status(thm)],[32, 21])).
% 65.60/65.78 tff(34,plain,
% 65.60/65.78 (multiplication(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), star(star(X0!0))) = multiplication(star(X0!0), star(star(X0!0)))),
% 65.60/65.78 inference(monotonicity,[status(thm)],[33])).
% 65.60/65.78 tff(35,plain,
% 65.60/65.78 (^[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))))),
% 65.60/65.78 inference(bind,[status(th)],[])).
% 65.60/65.78 tff(36,plain,
% 65.60/65.78 (![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)))),
% 65.60/65.78 inference(quant_intro,[status(thm)],[35])).
% 65.60/65.78 tff(37,plain,
% 65.60/65.78 (![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)))),
% 65.60/65.78 inference(rewrite,[status(thm)],[])).
% 65.60/65.78 tff(38,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','left_distributivity')).
% 65.60/65.78 tff(39,plain,
% 65.60/65.78 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 65.60/65.78 inference(modus_ponens,[status(thm)],[38, 37])).
% 65.60/65.78 tff(40,plain,(
% 65.60/65.78 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 65.60/65.78 inference(skolemize,[status(sab)],[39])).
% 65.60/65.78 tff(41,plain,
% 65.60/65.78 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 65.60/65.78 inference(modus_ponens,[status(thm)],[40, 36])).
% 65.60/65.78 tff(42,plain,
% 65.60/65.78 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), star(star(X0!0))) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(43,plain,
% 65.60/65.79 (multiplication(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), star(star(X0!0))) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[42, 41])).
% 65.60/65.79 tff(44,plain,
% 65.60/65.79 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), star(star(X0!0)))),
% 65.60/65.79 inference(symmetry,[status(thm)],[43])).
% 65.60/65.79 tff(45,plain,
% 65.60/65.79 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 65.60/65.79 inference(bind,[status(th)],[])).
% 65.60/65.79 tff(46,plain,
% 65.60/65.79 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 65.60/65.79 inference(quant_intro,[status(thm)],[45])).
% 65.60/65.79 tff(47,plain,
% 65.60/65.79 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 65.60/65.79 inference(rewrite,[status(thm)],[])).
% 65.60/65.79 tff(48,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 65.60/65.79 tff(49,plain,
% 65.60/65.79 (![A: $i] : (addition(A, A) = A)),
% 65.60/65.79 inference(modus_ponens,[status(thm)],[48, 47])).
% 65.60/65.79 tff(50,plain,(
% 65.60/65.79 ![A: $i] : (addition(A, A) = A)),
% 65.60/65.79 inference(skolemize,[status(sab)],[49])).
% 65.60/65.79 tff(51,plain,
% 65.60/65.79 (![A: $i] : (addition(A, A) = A)),
% 65.60/65.79 inference(modus_ponens,[status(thm)],[50, 46])).
% 65.60/65.79 tff(52,plain,
% 65.60/65.79 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(53,plain,
% 65.60/65.79 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[52, 51])).
% 65.60/65.79 tff(54,plain,
% 65.60/65.79 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))) = multiplication(star(X0!0), star(star(X0!0)))),
% 65.60/65.79 inference(transitivity,[status(thm)],[53, 44, 34])).
% 65.60/65.79 tff(55,plain,
% 65.60/65.79 (addition(addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0)))) = addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0))))),
% 65.60/65.79 inference(monotonicity,[status(thm)],[54])).
% 65.60/65.79 tff(56,plain,
% 65.60/65.79 (^[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)))),
% 65.60/65.79 inference(bind,[status(th)],[])).
% 65.60/65.79 tff(57,plain,
% 65.60/65.79 (![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))),
% 65.60/65.79 inference(quant_intro,[status(thm)],[56])).
% 65.60/65.79 tff(58,plain,
% 65.60/65.79 (![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))),
% 65.60/65.79 inference(rewrite,[status(thm)],[])).
% 65.60/65.79 tff(59,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_associativity')).
% 65.60/65.79 tff(60,plain,
% 65.60/65.79 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 65.60/65.79 inference(modus_ponens,[status(thm)],[59, 58])).
% 65.60/65.79 tff(61,plain,(
% 65.60/65.79 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 65.60/65.79 inference(skolemize,[status(sab)],[60])).
% 65.60/65.79 tff(62,plain,
% 65.60/65.79 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 65.60/65.79 inference(modus_ponens,[status(thm)],[61, 57])).
% 65.60/65.79 tff(63,plain,
% 65.60/65.79 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0)))))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(64,plain,
% 65.60/65.79 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0))))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[63, 62])).
% 65.60/65.79 tff(65,plain,
% 65.60/65.79 (addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), star(star(X0!0)))),
% 65.60/65.79 inference(transitivity,[status(thm)],[44, 34])).
% 65.60/65.79 tff(66,plain,
% 65.60/65.79 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))) = addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0))))),
% 65.60/65.79 inference(monotonicity,[status(thm)],[65])).
% 65.60/65.79 tff(67,plain,
% 65.60/65.79 (addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))) = addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 65.60/65.79 inference(symmetry,[status(thm)],[66])).
% 65.60/65.79 tff(68,plain,
% 65.60/65.79 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(69,plain,
% 65.60/65.79 (addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[68, 62])).
% 65.60/65.79 tff(70,plain,
% 65.60/65.79 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))) = addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0))))),
% 65.60/65.79 inference(symmetry,[status(thm)],[69])).
% 65.60/65.79 tff(71,plain,
% 65.60/65.79 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(star(X0!0), star(star(X0!0)))) = addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(72,plain,
% 65.60/65.79 (addition(one, multiplication(star(X0!0), star(star(X0!0)))) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[71, 28])).
% 65.60/65.79 tff(73,plain,
% 65.60/65.79 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(one, multiplication(star(X0!0), star(star(X0!0))))),
% 65.60/65.79 inference(symmetry,[status(thm)],[72])).
% 65.60/65.79 tff(74,plain,
% 65.60/65.79 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))) = addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 65.60/65.79 inference(monotonicity,[status(thm)],[73])).
% 65.60/65.79 tff(75,plain,
% 65.60/65.79 (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))),
% 65.60/65.79 inference(symmetry,[status(thm)],[74])).
% 65.60/65.79 tff(76,plain,
% 65.60/65.79 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0))))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(77,plain,
% 65.60/65.79 (leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0)))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[76, 7])).
% 65.60/65.79 tff(78,plain,
% 65.60/65.79 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(79,plain,
% 65.60/65.79 (leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[78, 16])).
% 65.60/65.79 tff(80,plain,
% 65.60/65.79 ((~(leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0))))) | (~leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))) | (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0)))),
% 65.60/65.79 inference(tautology,[status(thm)],[])).
% 65.60/65.79 tff(81,plain,
% 65.60/65.79 ((~(leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0))))) | (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0)))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[80, 79])).
% 65.60/65.79 tff(82,plain,
% 65.60/65.79 (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[81, 77])).
% 65.60/65.79 tff(83,plain,
% 65.60/65.79 (star(star(X0!0)) = addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 65.60/65.79 inference(symmetry,[status(thm)],[82])).
% 65.60/65.79 tff(84,plain,
% 65.60/65.79 (star(star(X0!0)) = addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 65.60/65.79 inference(transitivity,[status(thm)],[83, 75, 70, 67])).
% 65.60/65.79 tff(85,plain,
% 65.60/65.79 (multiplication(star(X0!0), star(star(X0!0))) = multiplication(addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)), star(star(X0!0)))),
% 65.60/65.79 inference(symmetry,[status(thm)],[34])).
% 65.60/65.79 tff(86,plain,
% 65.60/65.79 (multiplication(star(X0!0), star(star(X0!0))) = addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))),
% 65.60/65.79 inference(transitivity,[status(thm)],[85, 43])).
% 65.60/65.79 tff(87,plain,
% 65.60/65.79 (addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))) = addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))))),
% 65.60/65.79 inference(monotonicity,[status(thm)],[86, 84])).
% 65.60/65.79 tff(88,plain,
% 65.60/65.79 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0))))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(89,plain,
% 65.60/65.79 (leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0)))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[88, 7])).
% 65.60/65.79 tff(90,plain,
% 65.60/65.79 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 65.60/65.79 inference(bind,[status(th)],[])).
% 65.60/65.79 tff(91,plain,
% 65.60/65.79 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 65.60/65.79 inference(quant_intro,[status(thm)],[90])).
% 65.60/65.79 tff(92,plain,
% 65.60/65.79 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 65.60/65.79 inference(rewrite,[status(thm)],[])).
% 65.60/65.79 tff(93,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 65.60/65.79 tff(94,plain,
% 65.60/65.79 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 65.60/65.79 inference(modus_ponens,[status(thm)],[93, 92])).
% 65.60/65.79 tff(95,plain,(
% 65.60/65.79 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 65.60/65.79 inference(skolemize,[status(sab)],[94])).
% 65.60/65.79 tff(96,plain,
% 65.60/65.79 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 65.60/65.79 inference(modus_ponens,[status(thm)],[95, 91])).
% 65.60/65.79 tff(97,plain,
% 65.60/65.79 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(98,plain,
% 65.60/65.79 (leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[97, 96])).
% 65.60/65.79 tff(99,plain,
% 65.60/65.79 ((~(leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0))))) | (~leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))) | (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0)))),
% 65.60/65.79 inference(tautology,[status(thm)],[])).
% 65.60/65.79 tff(100,plain,
% 65.60/65.79 ((~(leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) <=> (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0))))) | (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0)))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[99, 98])).
% 65.60/65.79 tff(101,plain,
% 65.60/65.79 (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[100, 89])).
% 65.60/65.79 tff(102,plain,
% 65.60/65.79 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(star(star(X0!0)), star(X0!0))) = addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(103,plain,
% 65.60/65.79 (addition(one, multiplication(star(star(X0!0)), star(X0!0))) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[102, 28])).
% 65.60/65.79 tff(104,plain,
% 65.60/65.79 (addition(multiplication(star(star(X0!0)), star(X0!0)), one) = addition(one, multiplication(star(star(X0!0)), star(X0!0)))),
% 65.60/65.79 inference(symmetry,[status(thm)],[103])).
% 65.60/65.79 tff(105,plain,
% 65.60/65.79 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))) = addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 65.60/65.79 inference(monotonicity,[status(thm)],[104])).
% 65.60/65.79 tff(106,plain,
% 65.60/65.79 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(107,plain,
% 65.60/65.79 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[106, 28])).
% 65.60/65.79 tff(108,plain,
% 65.60/65.79 (addition(star(star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))),
% 65.60/65.79 inference(symmetry,[status(thm)],[107])).
% 65.60/65.79 tff(109,plain,
% 65.60/65.79 (addition(star(star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = star(star(X0!0))),
% 65.60/65.79 inference(transitivity,[status(thm)],[108, 105, 101])).
% 65.60/65.79 tff(110,plain,
% 65.60/65.79 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(star(star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))),
% 65.60/65.79 inference(monotonicity,[status(thm)],[65, 109])).
% 65.60/65.79 tff(111,plain,
% 65.60/65.79 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(star(star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(112,plain,
% 65.60/65.79 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(star(star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[111, 62])).
% 65.60/65.79 tff(113,plain,
% 65.60/65.79 (addition(addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), addition(star(star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 65.60/65.79 inference(symmetry,[status(thm)],[112])).
% 65.60/65.79 tff(114,plain,
% 65.60/65.79 (multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = multiplication(star(star(X0!0)), star(X0!0))),
% 65.60/65.79 inference(monotonicity,[status(thm)],[33])).
% 65.60/65.79 tff(115,plain,
% 65.60/65.79 (^[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))))),
% 65.60/65.79 inference(bind,[status(th)],[])).
% 65.60/65.79 tff(116,plain,
% 65.60/65.79 (![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)))),
% 65.60/65.79 inference(quant_intro,[status(thm)],[115])).
% 65.60/65.79 tff(117,plain,
% 65.60/65.79 (![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)))),
% 65.60/65.79 inference(rewrite,[status(thm)],[])).
% 65.60/65.79 tff(118,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','right_distributivity')).
% 65.60/65.79 tff(119,plain,
% 65.60/65.79 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 65.60/65.79 inference(modus_ponens,[status(thm)],[118, 117])).
% 65.60/65.79 tff(120,plain,(
% 65.60/65.79 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 65.60/65.79 inference(skolemize,[status(sab)],[119])).
% 65.60/65.79 tff(121,plain,
% 65.60/65.79 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 65.60/65.79 inference(modus_ponens,[status(thm)],[120, 116])).
% 65.60/65.79 tff(122,plain,
% 65.60/65.79 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(123,plain,
% 65.60/65.79 (multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[122, 121])).
% 65.60/65.79 tff(124,plain,
% 65.60/65.79 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))) = multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 65.60/65.79 inference(symmetry,[status(thm)],[123])).
% 65.60/65.79 tff(125,plain,
% 65.60/65.79 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))) = multiplication(star(star(X0!0)), star(X0!0))),
% 65.60/65.79 inference(transitivity,[status(thm)],[124, 114])).
% 65.60/65.79 tff(126,plain,
% 65.60/65.79 (addition(one, addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(one, multiplication(star(star(X0!0)), star(X0!0)))),
% 65.60/65.79 inference(monotonicity,[status(thm)],[125])).
% 65.60/65.79 tff(127,plain,
% 65.60/65.79 (addition(one, addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 65.60/65.79 inference(transitivity,[status(thm)],[126, 103])).
% 65.60/65.79 tff(128,plain,
% 65.60/65.79 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(129,plain,
% 65.60/65.79 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[128, 28])).
% 65.60/65.79 tff(130,plain,
% 65.60/65.79 (addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 65.60/65.79 inference(symmetry,[status(thm)],[129])).
% 65.60/65.79 tff(131,plain,
% 65.60/65.79 (addition(addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 65.60/65.79 inference(monotonicity,[status(thm)],[130, 127])).
% 65.60/65.79 tff(132,plain,
% 65.60/65.79 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), one), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 65.60/65.79 inference(quant_inst,[status(thm)],[])).
% 65.60/65.79 tff(133,plain,
% 65.60/65.79 (addition(addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), one), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))),
% 65.60/65.79 inference(unit_resolution,[status(thm)],[132, 62])).
% 65.60/65.79 tff(134,plain,
% 65.60/65.79 (addition(addition(addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), one), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 65.60/65.79 inference(symmetry,[status(thm)],[133])).
% 65.60/65.79 tff(135,plain,
% 65.60/65.79 (addition(addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))),
% 65.60/65.79 inference(monotonicity,[status(thm)],[65])).
% 65.60/65.79 tff(136,plain,
% 65.60/65.79 (addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))),
% 65.60/65.80 inference(transitivity,[status(thm)],[130, 135])).
% 65.60/65.80 tff(137,plain,
% 65.60/65.80 (addition(addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), one) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))), one)),
% 65.60/65.80 inference(monotonicity,[status(thm)],[136])).
% 65.60/65.80 tff(138,plain,
% 65.60/65.80 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))), one) = addition(addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), one)),
% 65.60/65.80 inference(symmetry,[status(thm)],[137])).
% 65.60/65.80 tff(139,plain,
% 65.60/65.80 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))), one))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(140,plain,
% 65.60/65.80 (addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))), one)),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[139, 28])).
% 65.60/65.80 tff(141,plain,
% 65.60/65.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))) = addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(142,plain,
% 65.60/65.80 (addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))) = addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[141, 62])).
% 65.60/65.80 tff(143,plain,
% 65.60/65.80 (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))))),
% 65.60/65.80 inference(symmetry,[status(thm)],[142])).
% 65.60/65.80 tff(144,plain,
% 65.60/65.80 (star(star(X0!0)) = addition(addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), one)),
% 65.60/65.80 inference(transitivity,[status(thm)],[83, 143, 140, 138])).
% 65.60/65.80 tff(145,plain,
% 65.60/65.80 (addition(star(star(X0!0)), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(addition(star(star(X0!0)), addition(multiplication(addition(multiplication(X0!0, star(X0!0)), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))), one), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[144])).
% 65.60/65.80 tff(146,plain,
% 65.60/65.80 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(147,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[146, 28])).
% 65.60/65.80 tff(148,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), star(X0!0)) = multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 65.60/65.80 inference(symmetry,[status(thm)],[114])).
% 65.60/65.80 tff(149,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), star(X0!0)) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))),
% 65.60/65.80 inference(transitivity,[status(thm)],[148, 123])).
% 65.60/65.80 tff(150,plain,
% 65.60/65.80 (addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[149])).
% 65.60/65.80 tff(151,plain,
% 65.60/65.80 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 65.60/65.80 inference(bind,[status(th)],[])).
% 65.60/65.80 tff(152,plain,
% 65.60/65.80 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 65.60/65.80 inference(quant_intro,[status(thm)],[151])).
% 65.60/65.80 tff(153,plain,
% 65.60/65.80 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 65.60/65.80 inference(rewrite,[status(thm)],[])).
% 65.60/65.80 tff(154,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_right_identity')).
% 65.60/65.80 tff(155,plain,
% 65.60/65.80 (![A: $i] : (multiplication(A, one) = A)),
% 65.60/65.80 inference(modus_ponens,[status(thm)],[154, 153])).
% 65.60/65.80 tff(156,plain,(
% 65.60/65.80 ![A: $i] : (multiplication(A, one) = A)),
% 65.60/65.80 inference(skolemize,[status(sab)],[155])).
% 65.60/65.80 tff(157,plain,
% 65.60/65.80 (![A: $i] : (multiplication(A, one) = A)),
% 65.60/65.80 inference(modus_ponens,[status(thm)],[156, 152])).
% 65.60/65.80 tff(158,plain,
% 65.60/65.80 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(star(star(X0!0)), one) = star(star(X0!0)))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(159,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), one) = star(star(X0!0))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[158, 157])).
% 65.60/65.80 tff(160,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), multiplication(star(star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0)))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[125, 159])).
% 65.60/65.80 tff(161,plain,
% 65.60/65.80 (addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(star(star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), multiplication(star(star(X0!0)), one))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[149])).
% 65.60/65.80 tff(162,plain,
% 65.60/65.80 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(star(X0!0)), addition(star(X0!0), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(star(star(X0!0)), one)))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(163,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), addition(star(X0!0), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(star(star(X0!0)), one))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[162, 121])).
% 65.60/65.80 tff(164,plain,
% 65.60/65.80 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(X0!0)) = addition(star(X0!0), one))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(165,plain,
% 65.60/65.80 (addition(one, star(X0!0)) = addition(star(X0!0), one)),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[164, 28])).
% 65.60/65.80 tff(166,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), addition(one, star(X0!0))) = multiplication(star(star(X0!0)), addition(star(X0!0), one))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[165])).
% 65.60/65.80 tff(167,plain,
% 65.60/65.80 ((~![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), star(X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(168,plain,
% 65.60/65.80 (addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[167, 62])).
% 65.60/65.80 tff(169,plain,
% 65.60/65.80 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 65.60/65.80 inference(symmetry,[status(thm)],[168])).
% 65.60/65.80 tff(170,plain,
% 65.60/65.80 ((~![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)))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(171,plain,
% 65.60/65.80 (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))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[170, 7])).
% 65.60/65.80 tff(172,plain,
% 65.60/65.80 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(173,plain,
% 65.60/65.80 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[172, 96])).
% 65.60/65.80 tff(174,plain,
% 65.60/65.80 ((~(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))),
% 65.60/65.80 inference(tautology,[status(thm)],[])).
% 65.60/65.80 tff(175,plain,
% 65.60/65.80 ((~(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))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[174, 173])).
% 65.60/65.80 tff(176,plain,
% 65.60/65.80 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[175, 171])).
% 65.60/65.80 tff(177,plain,
% 65.60/65.80 (star(X0!0) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 65.60/65.80 inference(symmetry,[status(thm)],[176])).
% 65.60/65.80 tff(178,plain,
% 65.60/65.80 (star(X0!0) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 65.60/65.80 inference(transitivity,[status(thm)],[177, 169])).
% 65.60/65.80 tff(179,plain,
% 65.60/65.80 (addition(one, star(X0!0)) = addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[178])).
% 65.60/65.80 tff(180,plain,
% 65.60/65.80 (addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))) = addition(one, star(X0!0))),
% 65.60/65.80 inference(symmetry,[status(thm)],[179])).
% 65.60/65.80 tff(181,plain,
% 65.60/65.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))) = addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0))))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(182,plain,
% 65.60/65.80 (addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))) = addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[181, 62])).
% 65.60/65.80 tff(183,plain,
% 65.60/65.80 (addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))))),
% 65.60/65.80 inference(symmetry,[status(thm)],[182])).
% 65.60/65.80 tff(184,plain,
% 65.60/65.80 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(185,plain,
% 65.60/65.80 (addition(one, one) = one),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[184, 51])).
% 65.60/65.80 tff(186,plain,
% 65.60/65.80 (addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[185])).
% 65.60/65.80 tff(187,plain,
% 65.60/65.80 (addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(addition(one, one), addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 65.60/65.80 inference(symmetry,[status(thm)],[186])).
% 65.60/65.80 tff(188,plain,
% 65.60/65.80 (star(X0!0) = addition(one, star(X0!0))),
% 65.60/65.80 inference(transitivity,[status(thm)],[177, 169, 187, 183, 180])).
% 65.60/65.80 tff(189,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), star(X0!0)) = multiplication(star(star(X0!0)), addition(one, star(X0!0)))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[188])).
% 65.60/65.80 tff(190,plain,
% 65.60/65.80 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))) = star(star(X0!0))),
% 65.60/65.80 inference(transitivity,[status(thm)],[124, 114, 189, 166, 163, 161, 160, 150, 147, 145, 134, 131, 113, 110, 87, 64, 55, 69, 74, 82])).
% 65.60/65.80 tff(191,plain,
% 65.60/65.80 (multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)) = multiplication(star(star(X0!0)), star(X0!0))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[190])).
% 65.60/65.80 tff(192,plain,
% 65.60/65.80 (multiplication(multiplication(star(star(X0!0)), star(X0!0)), star(X0!0)) = multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[149])).
% 65.60/65.80 tff(193,plain,
% 65.60/65.80 (^[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)))),
% 65.60/65.80 inference(bind,[status(th)],[])).
% 65.60/65.80 tff(194,plain,
% 65.60/65.80 (![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))),
% 65.60/65.80 inference(quant_intro,[status(thm)],[193])).
% 65.60/65.80 tff(195,plain,
% 65.60/65.80 (![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))),
% 65.60/65.80 inference(rewrite,[status(thm)],[])).
% 65.60/65.80 tff(196,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_associativity')).
% 65.60/65.80 tff(197,plain,
% 65.60/65.80 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 65.60/65.80 inference(modus_ponens,[status(thm)],[196, 195])).
% 65.60/65.80 tff(198,plain,(
% 65.60/65.80 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 65.60/65.80 inference(skolemize,[status(sab)],[197])).
% 65.60/65.80 tff(199,plain,
% 65.60/65.80 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 65.60/65.80 inference(modus_ponens,[status(thm)],[198, 194])).
% 65.60/65.80 tff(200,plain,
% 65.60/65.80 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))) = multiplication(multiplication(star(star(X0!0)), star(X0!0)), star(X0!0)))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(201,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))) = multiplication(multiplication(star(star(X0!0)), star(X0!0)), star(X0!0))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[200, 199])).
% 65.60/65.80 tff(202,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))) = addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0))))),
% 65.60/65.80 inference(transitivity,[status(thm)],[201, 192, 191, 189, 166, 163, 161, 160, 150, 147, 145, 134, 131, 113, 110, 87, 64, 55])).
% 65.60/65.80 tff(203,plain,
% 65.60/65.80 (leq(multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) <=> leq(addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))), star(X0!0))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[202])).
% 65.60/65.80 tff(204,plain,
% 65.60/65.80 (leq(addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))), star(X0!0)) <=> leq(multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 65.60/65.80 inference(symmetry,[status(thm)],[203])).
% 65.60/65.80 tff(205,plain,
% 65.60/65.80 ((~leq(addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))), star(X0!0))) <=> (~leq(multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0)))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[204])).
% 65.60/65.80 tff(206,plain,
% 65.60/65.80 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 65.60/65.80 inference(bind,[status(th)],[])).
% 65.60/65.80 tff(207,plain,
% 65.60/65.80 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 65.60/65.80 inference(quant_intro,[status(thm)],[206])).
% 65.60/65.80 tff(208,plain,
% 65.60/65.80 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 65.60/65.80 inference(rewrite,[status(thm)],[])).
% 65.60/65.80 tff(209,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_left_identity')).
% 65.60/65.80 tff(210,plain,
% 65.60/65.80 (![A: $i] : (multiplication(one, A) = A)),
% 65.60/65.80 inference(modus_ponens,[status(thm)],[209, 208])).
% 65.60/65.80 tff(211,plain,(
% 65.60/65.80 ![A: $i] : (multiplication(one, A) = A)),
% 65.60/65.80 inference(skolemize,[status(sab)],[210])).
% 65.60/65.80 tff(212,plain,
% 65.60/65.80 (![A: $i] : (multiplication(one, A) = A)),
% 65.60/65.80 inference(modus_ponens,[status(thm)],[211, 207])).
% 65.60/65.80 tff(213,plain,
% 65.60/65.80 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(X0!0)) = star(X0!0))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(214,plain,
% 65.60/65.80 (multiplication(one, star(X0!0)) = star(X0!0)),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[213, 212])).
% 65.60/65.80 tff(215,plain,
% 65.60/65.80 (multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)) = addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0))))),
% 65.60/65.80 inference(transitivity,[status(thm)],[191, 189, 166, 163, 161, 160, 150, 147, 145, 134, 131, 113, 110, 87, 64, 55])).
% 65.60/65.80 tff(216,plain,
% 65.60/65.80 (leq(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) <=> leq(addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))), star(X0!0))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[215, 214])).
% 65.60/65.80 tff(217,plain,
% 65.60/65.80 ((~leq(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0)))) <=> (~leq(addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))), star(X0!0)))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[216])).
% 65.60/65.80 tff(218,plain,
% 65.60/65.80 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) <=> (addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) = multiplication(one, star(X0!0))))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(219,plain,
% 65.60/65.80 (leq(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) <=> (addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) = multiplication(one, star(X0!0)))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[218, 7])).
% 65.60/65.80 tff(220,plain,
% 65.60/65.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(221,plain,
% 65.60/65.80 (addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[220, 62])).
% 65.60/65.80 tff(222,plain,
% 65.60/65.80 (addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))) = star(X0!0)),
% 65.60/65.80 inference(transitivity,[status(thm)],[221, 21])).
% 65.60/65.80 tff(223,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = multiplication(star(star(X0!0)), star(X0!0))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[222])).
% 65.60/65.80 tff(224,plain,
% 65.60/65.80 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(star(X0!0)), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(225,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[224, 121])).
% 65.60/65.80 tff(226,plain,
% 65.60/65.80 (addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = multiplication(star(star(X0!0)), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(symmetry,[status(thm)],[225])).
% 65.60/65.80 tff(227,plain,
% 65.60/65.80 (star(star(X0!0)) = multiplication(star(star(X0!0)), one)),
% 65.60/65.80 inference(symmetry,[status(thm)],[159])).
% 65.60/65.80 tff(228,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), multiplication(star(star(X0!0)), one)) = addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[104, 159])).
% 65.60/65.80 tff(229,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), multiplication(star(star(X0!0)), one)) = multiplication(star(star(X0!0)), one)),
% 65.60/65.80 inference(transitivity,[status(thm)],[228, 101, 227])).
% 65.60/65.80 tff(230,plain,
% 65.60/65.80 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[229])).
% 65.60/65.80 tff(231,plain,
% 65.60/65.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(232,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[231, 62])).
% 65.60/65.80 tff(233,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), star(X0!0)) = multiplication(star(star(X0!0)), addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(symmetry,[status(thm)],[223])).
% 65.60/65.80 tff(234,plain,
% 65.60/65.80 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))) = addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(transitivity,[status(thm)],[124, 114, 233, 225])).
% 65.60/65.80 tff(235,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[234])).
% 65.60/65.80 tff(236,plain,
% 65.60/65.80 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(237,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[236, 28])).
% 65.60/65.80 tff(238,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 65.60/65.80 inference(monotonicity,[status(thm)],[125])).
% 65.60/65.80 tff(239,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one)) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[238])).
% 65.60/65.80 tff(240,plain,
% 65.60/65.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one)) = addition(addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))), one))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(241,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one)) = addition(addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))), one)),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[240, 62])).
% 65.60/65.80 tff(242,plain,
% 65.60/65.80 (addition(addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))), one) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one))),
% 65.60/65.80 inference(symmetry,[status(thm)],[241])).
% 65.60/65.80 tff(243,plain,
% 65.60/65.80 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(quant_inst,[status(thm)],[])).
% 65.60/65.80 tff(244,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))),
% 65.60/65.80 inference(unit_resolution,[status(thm)],[243, 51])).
% 65.60/65.80 tff(245,plain,
% 65.60/65.80 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(symmetry,[status(thm)],[244])).
% 65.60/65.80 tff(246,plain,
% 65.60/65.80 (multiplication(star(star(X0!0)), star(X0!0)) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))))),
% 65.60/65.80 inference(transitivity,[status(thm)],[148, 123, 245])).
% 65.60/65.80 tff(247,plain,
% 65.60/65.80 (addition(multiplication(star(star(X0!0)), star(X0!0)), one) = addition(addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))), one)),
% 65.60/65.80 inference(monotonicity,[status(thm)],[246])).
% 65.60/65.80 tff(248,plain,
% 65.60/65.80 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))) = star(star(X0!0))),
% 65.60/65.80 inference(transitivity,[status(thm)],[105, 101])).
% 65.60/65.80 tff(249,plain,
% 65.60/65.80 (multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)) = multiplication(star(star(X0!0)), star(X0!0))),
% 65.60/65.80 inference(monotonicity,[status(thm)],[248])).
% 65.60/65.80 tff(250,plain,
% 65.60/65.80 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(251,plain,
% 65.60/65.81 (multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[250, 41])).
% 65.60/65.81 tff(252,plain,
% 65.60/65.81 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))) = multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0))),
% 65.60/65.81 inference(symmetry,[status(thm)],[251])).
% 65.60/65.81 tff(253,plain,
% 65.60/65.81 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[125])).
% 65.60/65.81 tff(254,plain,
% 65.60/65.81 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))) = multiplication(star(star(X0!0)), star(X0!0))),
% 65.60/65.81 inference(transitivity,[status(thm)],[253, 252, 249])).
% 65.60/65.81 tff(255,plain,
% 65.60/65.81 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))), one) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 65.60/65.81 inference(monotonicity,[status(thm)],[254])).
% 65.60/65.81 tff(256,plain,
% 65.60/65.81 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))), one))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(257,plain,
% 65.60/65.81 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0)))), one)),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[256, 62])).
% 65.60/65.81 tff(258,plain,
% 65.60/65.81 (addition(multiplication(star(star(X0!0)), star(X0!0)), one) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one)),
% 65.60/65.81 inference(symmetry,[status(thm)],[238])).
% 65.60/65.81 tff(259,plain,
% 65.60/65.81 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), one) = addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(260,plain,
% 65.60/65.81 (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), one) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[259, 157])).
% 65.60/65.81 tff(261,plain,
% 65.60/65.81 (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), one) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one)),
% 65.60/65.81 inference(transitivity,[status(thm)],[260, 258])).
% 65.60/65.81 tff(262,plain,
% 65.60/65.81 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(star(X0!0), X0!0)) = addition(multiplication(star(X0!0), X0!0), one))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(263,plain,
% 65.60/65.81 (addition(one, multiplication(star(X0!0), X0!0)) = addition(multiplication(star(X0!0), X0!0), one)),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[262, 28])).
% 65.60/65.81 tff(264,plain,
% 65.60/65.81 (addition(multiplication(star(X0!0), X0!0), one) = addition(one, multiplication(star(X0!0), X0!0))),
% 65.60/65.81 inference(symmetry,[status(thm)],[263])).
% 65.60/65.81 tff(265,plain,
% 65.60/65.81 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[264])).
% 65.60/65.81 tff(266,plain,
% 65.60/65.81 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = star(X0!0)),
% 65.60/65.81 inference(transitivity,[status(thm)],[265, 176])).
% 65.60/65.81 tff(267,plain,
% 65.60/65.81 (addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[264, 266])).
% 65.60/65.81 tff(268,plain,
% 65.60/65.81 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one)), star(X0!0)))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(269,plain,
% 65.60/65.81 (addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one)), star(X0!0))),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[268, 62])).
% 65.60/65.81 tff(270,plain,
% 65.60/65.81 (addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one)), star(X0!0)) = addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 65.60/65.81 inference(symmetry,[status(thm)],[269])).
% 65.60/65.81 tff(271,plain,
% 65.60/65.81 (addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one)), star(X0!0)) = star(X0!0)),
% 65.60/65.81 inference(transitivity,[status(thm)],[270, 267, 176])).
% 65.60/65.81 tff(272,plain,
% 65.60/65.81 (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one)), star(X0!0))) = multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[271])).
% 65.60/65.81 tff(273,plain,
% 65.60/65.81 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one)), star(X0!0))) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one))), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0))))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(274,plain,
% 65.60/65.81 (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one)), star(X0!0))) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one))), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)))),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[273, 121])).
% 65.60/65.81 tff(275,plain,
% 65.60/65.81 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one))), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0))) = multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one)), star(X0!0)))),
% 65.60/65.81 inference(symmetry,[status(thm)],[274])).
% 65.60/65.81 tff(276,plain,
% 65.60/65.81 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one))), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0))) = multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0))),
% 65.60/65.81 inference(transitivity,[status(thm)],[275, 272])).
% 65.60/65.81 tff(277,plain,
% 65.60/65.81 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one))), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0))), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), one)) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[276, 261])).
% 65.60/65.81 tff(278,plain,
% 65.60/65.81 (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)) = multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one)), star(X0!0)))),
% 65.60/65.81 inference(symmetry,[status(thm)],[272])).
% 65.60/65.81 tff(279,plain,
% 65.60/65.81 (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one))), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)))),
% 65.60/65.81 inference(transitivity,[status(thm)],[278, 274])).
% 65.60/65.81 tff(280,plain,
% 65.60/65.81 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), one)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), X0!0), one))), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0))), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), one))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[279])).
% 65.60/65.81 tff(281,plain,
% 65.60/65.81 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), one)) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), one)))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(282,plain,
% 65.60/65.81 (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), one)) = addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), one))),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[281, 121])).
% 65.60/65.81 tff(283,plain,
% 65.60/65.81 (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(one, star(X0!0))) = multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), one))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[165])).
% 65.60/65.81 tff(284,plain,
% 65.60/65.81 (multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)) = multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(one, star(X0!0)))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[188])).
% 65.60/65.81 tff(285,plain,
% 65.60/65.81 (multiplication(addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one), star(X0!0)) = multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[238])).
% 65.60/65.81 tff(286,plain,
% 65.60/65.81 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one), star(X0!0)) = addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(287,plain,
% 65.60/65.81 (multiplication(addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one), star(X0!0)) = addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0)))),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[286, 41])).
% 65.60/65.81 tff(288,plain,
% 65.60/65.81 (addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) = multiplication(addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), one), star(X0!0))),
% 65.60/65.81 inference(symmetry,[status(thm)],[287])).
% 65.60/65.81 tff(289,plain,
% 65.60/65.81 (addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) = star(star(X0!0))),
% 65.60/65.81 inference(transitivity,[status(thm)],[288, 285, 284, 283, 282, 280, 277, 257, 255, 247, 242, 239, 237, 235, 232, 230, 226, 223, 189, 166, 163, 161, 160, 150, 147, 145, 134, 131, 113, 110, 87, 64, 55, 69, 74, 82])).
% 65.60/65.81 tff(290,plain,
% 65.60/65.81 ((addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) = multiplication(one, star(X0!0))) <=> (star(star(X0!0)) = star(X0!0))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[289, 214])).
% 65.60/65.81 tff(291,plain,
% 65.60/65.81 ((star(star(X0!0)) = star(X0!0)) <=> (addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) = multiplication(one, star(X0!0)))),
% 65.60/65.81 inference(symmetry,[status(thm)],[290])).
% 65.60/65.81 tff(292,plain,
% 65.60/65.81 ((~(star(star(X0!0)) = star(X0!0))) <=> (~(addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) = multiplication(one, star(X0!0))))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[291])).
% 65.60/65.81 tff(293,plain,
% 65.60/65.81 ((~![X0: $i] : (star(star(X0)) = star(X0))) <=> (~![X0: $i] : (star(star(X0)) = star(X0)))),
% 65.60/65.81 inference(rewrite,[status(thm)],[])).
% 65.60/65.81 tff(294,axiom,(~![X0: $i] : (star(star(X0)) = star(X0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 65.60/65.81 tff(295,plain,
% 65.60/65.81 (~![X0: $i] : (star(star(X0)) = star(X0))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[294, 293])).
% 65.60/65.81 tff(296,plain,
% 65.60/65.81 (~![X0: $i] : (star(star(X0)) = star(X0))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[295, 293])).
% 65.60/65.81 tff(297,plain,
% 65.60/65.81 (~![X0: $i] : (star(star(X0)) = star(X0))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[296, 293])).
% 65.60/65.81 tff(298,plain,
% 65.60/65.81 (~![X0: $i] : (star(star(X0)) = star(X0))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[297, 293])).
% 65.60/65.81 tff(299,plain,(
% 65.60/65.81 ~(star(star(X0!0)) = star(X0!0))),
% 65.60/65.81 inference(skolemize,[status(sab)],[298])).
% 65.60/65.81 tff(300,plain,
% 65.60/65.81 (~(addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) = multiplication(one, star(X0!0)))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[299, 292])).
% 65.60/65.81 tff(301,plain,
% 65.60/65.81 ((~(leq(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) <=> (addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) = multiplication(one, star(X0!0))))) | (~leq(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0)))) | (addition(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0))) = multiplication(one, star(X0!0)))),
% 65.60/65.81 inference(tautology,[status(thm)],[])).
% 65.60/65.81 tff(302,plain,
% 65.60/65.81 (~leq(multiplication(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)), multiplication(one, star(X0!0)))),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[301, 300, 219])).
% 65.60/65.81 tff(303,plain,
% 65.60/65.81 (~leq(addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))), star(X0!0))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[302, 217])).
% 65.60/65.81 tff(304,plain,
% 65.60/65.81 (~leq(multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[303, 205])).
% 65.60/65.81 tff(305,plain,
% 65.60/65.81 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(star(X0!0), one), star(X0!0)) <=> (addition(multiplication(star(X0!0), one), star(X0!0)) = star(X0!0)))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(306,plain,
% 65.60/65.81 (leq(multiplication(star(X0!0), one), star(X0!0)) <=> (addition(multiplication(star(X0!0), one), star(X0!0)) = star(X0!0))),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[305, 7])).
% 65.60/65.81 tff(307,plain,
% 65.60/65.81 (leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) <=> leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[31])).
% 65.60/65.81 tff(308,plain,
% 65.60/65.81 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 65.60/65.81 inference(symmetry,[status(thm)],[307])).
% 65.60/65.81 tff(309,plain,
% 65.60/65.81 (leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[18, 308])).
% 65.60/65.81 tff(310,plain,
% 65.60/65.81 (^[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)))),
% 65.60/65.81 inference(bind,[status(th)],[])).
% 65.60/65.81 tff(311,plain,
% 65.60/65.81 (![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))),
% 65.60/65.81 inference(quant_intro,[status(thm)],[310])).
% 65.60/65.81 tff(312,plain,
% 65.60/65.81 (![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))),
% 65.60/65.81 inference(rewrite,[status(thm)],[])).
% 65.60/65.81 tff(313,plain,
% 65.60/65.81 (^[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)))),
% 65.60/65.81 inference(bind,[status(th)],[])).
% 65.60/65.81 tff(314,plain,
% 65.60/65.81 (![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))),
% 65.60/65.81 inference(quant_intro,[status(thm)],[313])).
% 65.60/65.81 tff(315,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), B) => leq(multiplication(star(A), C), B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_induction_left')).
% 65.60/65.81 tff(316,plain,
% 65.60/65.81 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[315, 314])).
% 65.60/65.81 tff(317,plain,
% 65.60/65.81 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[316, 312])).
% 65.60/65.81 tff(318,plain,(
% 65.60/65.81 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 65.60/65.81 inference(skolemize,[status(sab)],[317])).
% 65.60/65.81 tff(319,plain,
% 65.60/65.81 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[318, 311])).
% 65.60/65.81 tff(320,plain,
% 65.60/65.81 (((~![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(X0!0)), one), star(X0!0))) | leq(multiplication(star(X0!0), one), star(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(X0!0)), one), star(X0!0))) | leq(multiplication(star(X0!0), one), star(X0!0)))),
% 65.60/65.81 inference(rewrite,[status(thm)],[])).
% 65.60/65.81 tff(321,plain,
% 65.60/65.81 ((~![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(X0!0)), one), star(X0!0))) | leq(multiplication(star(X0!0), one), star(X0!0)))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(322,plain,
% 65.60/65.81 ((~![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(X0!0)), one), star(X0!0))) | leq(multiplication(star(X0!0), one), star(X0!0))),
% 65.60/65.81 inference(modus_ponens,[status(thm)],[321, 320])).
% 65.60/65.81 tff(323,plain,
% 65.60/65.81 ((~leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) | leq(multiplication(star(X0!0), one), star(X0!0))),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[322, 319])).
% 65.60/65.81 tff(324,plain,
% 65.60/65.81 (leq(multiplication(star(X0!0), one), star(X0!0))),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[323, 309])).
% 65.60/65.81 tff(325,plain,
% 65.60/65.81 ((~(leq(multiplication(star(X0!0), one), star(X0!0)) <=> (addition(multiplication(star(X0!0), one), star(X0!0)) = star(X0!0)))) | (~leq(multiplication(star(X0!0), one), star(X0!0))) | (addition(multiplication(star(X0!0), one), star(X0!0)) = star(X0!0))),
% 65.60/65.81 inference(tautology,[status(thm)],[])).
% 65.60/65.81 tff(326,plain,
% 65.60/65.81 ((~(leq(multiplication(star(X0!0), one), star(X0!0)) <=> (addition(multiplication(star(X0!0), one), star(X0!0)) = star(X0!0)))) | (addition(multiplication(star(X0!0), one), star(X0!0)) = star(X0!0))),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[325, 324])).
% 65.60/65.81 tff(327,plain,
% 65.60/65.81 (addition(multiplication(star(X0!0), one), star(X0!0)) = star(X0!0)),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[326, 306])).
% 65.60/65.81 tff(328,plain,
% 65.60/65.81 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(star(X0!0), one) = star(X0!0))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(329,plain,
% 65.60/65.81 (multiplication(star(X0!0), one) = star(X0!0)),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[328, 157])).
% 65.60/65.81 tff(330,plain,
% 65.60/65.81 (star(X0!0) = multiplication(star(X0!0), one)),
% 65.60/65.81 inference(symmetry,[status(thm)],[329])).
% 65.60/65.81 tff(331,plain,
% 65.60/65.81 (addition(star(X0!0), star(X0!0)) = addition(multiplication(star(X0!0), one), star(X0!0))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[330])).
% 65.60/65.81 tff(332,plain,
% 65.60/65.81 (addition(star(X0!0), star(X0!0)) = star(X0!0)),
% 65.60/65.81 inference(transitivity,[status(thm)],[331, 327])).
% 65.60/65.81 tff(333,plain,
% 65.60/65.81 (multiplication(star(X0!0), addition(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[332])).
% 65.60/65.81 tff(334,plain,
% 65.60/65.81 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(star(X0!0), star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(335,plain,
% 65.60/65.81 (multiplication(star(X0!0), addition(star(X0!0), star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0)))),
% 65.60/65.81 inference(unit_resolution,[status(thm)],[334, 121])).
% 65.60/65.81 tff(336,plain,
% 65.60/65.81 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), addition(star(X0!0), star(X0!0)))),
% 65.60/65.81 inference(symmetry,[status(thm)],[335])).
% 65.60/65.81 tff(337,plain,
% 65.60/65.81 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 65.60/65.81 inference(transitivity,[status(thm)],[336, 333])).
% 65.60/65.81 tff(338,plain,
% 65.60/65.81 (leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) <=> leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[337])).
% 65.60/65.81 tff(339,plain,
% 65.60/65.81 (leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)) <=> leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 65.60/65.81 inference(symmetry,[status(thm)],[338])).
% 65.60/65.81 tff(340,plain,
% 65.60/65.81 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 65.60/65.81 inference(symmetry,[status(thm)],[32])).
% 65.60/65.81 tff(341,plain,
% 65.60/65.81 (star(X0!0) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 65.60/65.81 inference(symmetry,[status(thm)],[21])).
% 65.60/65.81 tff(342,plain,
% 65.60/65.81 (star(X0!0) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 65.60/65.81 inference(transitivity,[status(thm)],[341, 340])).
% 65.60/65.81 tff(343,plain,
% 65.60/65.81 (multiplication(X0!0, star(X0!0)) = multiplication(X0!0, addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 65.60/65.81 inference(monotonicity,[status(thm)],[342])).
% 65.60/65.81 tff(344,plain,
% 65.60/65.81 (multiplication(X0!0, addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 65.60/65.81 inference(symmetry,[status(thm)],[343])).
% 65.60/65.81 tff(345,plain,
% 65.60/65.81 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))))),
% 65.60/65.81 inference(quant_inst,[status(thm)],[])).
% 65.60/65.81 tff(346,plain,
% 65.60/65.81 (multiplication(X0!0, addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))),
% 65.60/65.82 inference(unit_resolution,[status(thm)],[345, 121])).
% 65.60/65.82 tff(347,plain,
% 65.60/65.82 (addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 65.60/65.82 inference(symmetry,[status(thm)],[346])).
% 65.60/65.82 tff(348,plain,
% 65.60/65.82 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))) = addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))))),
% 65.60/65.82 inference(quant_inst,[status(thm)],[])).
% 65.60/65.82 tff(349,plain,
% 65.60/65.82 (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))) = addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))),
% 65.60/65.82 inference(unit_resolution,[status(thm)],[348, 51])).
% 65.60/65.82 tff(350,plain,
% 65.60/65.82 (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))) = multiplication(X0!0, star(X0!0))),
% 65.60/65.82 inference(transitivity,[status(thm)],[349, 347, 344])).
% 65.60/65.82 tff(351,plain,
% 65.60/65.82 (addition(addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 65.60/65.82 inference(monotonicity,[status(thm)],[350])).
% 65.60/65.82 tff(352,plain,
% 65.60/65.82 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0))))),
% 65.60/65.82 inference(quant_inst,[status(thm)],[])).
% 65.60/65.82 tff(353,plain,
% 65.60/65.82 (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0)))),
% 65.60/65.82 inference(unit_resolution,[status(thm)],[352, 62])).
% 65.60/65.82 tff(354,plain,
% 65.60/65.82 (addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 65.60/65.82 inference(transitivity,[status(thm)],[347, 344])).
% 65.60/65.82 tff(355,plain,
% 65.60/65.82 (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 65.60/65.82 inference(monotonicity,[status(thm)],[354])).
% 65.60/65.82 tff(356,plain,
% 65.60/65.82 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))),
% 65.60/65.82 inference(symmetry,[status(thm)],[355])).
% 65.60/65.82 tff(357,plain,
% 65.60/65.82 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 65.60/65.82 inference(quant_inst,[status(thm)],[])).
% 65.60/65.82 tff(358,plain,
% 65.60/65.82 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 65.60/65.82 inference(unit_resolution,[status(thm)],[357, 62])).
% 65.60/65.82 tff(359,plain,
% 65.60/65.82 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 65.60/65.82 inference(symmetry,[status(thm)],[358])).
% 65.60/65.82 tff(360,plain,
% 65.60/65.82 (star(X0!0) = addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))),
% 65.60/65.82 inference(transitivity,[status(thm)],[341, 340, 359, 356])).
% 65.60/65.82 tff(361,plain,
% 65.60/65.82 (multiplication(X0!0, star(X0!0)) = addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))),
% 65.60/65.82 inference(transitivity,[status(thm)],[343, 346])).
% 65.60/65.82 tff(362,plain,
% 65.60/65.82 (addition(multiplication(X0!0, star(X0!0)), star(X0!0)) = addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))))),
% 65.60/65.82 inference(monotonicity,[status(thm)],[361, 360])).
% 65.60/65.82 tff(363,plain,
% 65.60/65.82 (addition(multiplication(X0!0, star(X0!0)), star(X0!0)) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 65.60/65.82 inference(transitivity,[status(thm)],[362, 353, 351])).
% 65.60/65.82 tff(364,plain,
% 65.60/65.82 (leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0)) <=> leq(addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))), star(X0!0))),
% 65.60/65.82 inference(monotonicity,[status(thm)],[363])).
% 65.60/65.82 tff(365,plain,
% 65.60/65.82 (leq(addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))), star(X0!0)) <=> leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))),
% 65.60/65.82 inference(symmetry,[status(thm)],[364])).
% 65.60/65.82 tff(366,plain,
% 65.60/65.82 (multiplication(star(X0!0), one) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 65.60/65.82 inference(transitivity,[status(thm)],[329, 341, 340, 359])).
% 65.60/65.82 tff(367,plain,
% 65.60/65.82 (leq(multiplication(star(X0!0), one), star(X0!0)) <=> leq(addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))), star(X0!0))),
% 65.60/65.82 inference(monotonicity,[status(thm)],[366])).
% 65.60/65.82 tff(368,plain,
% 65.60/65.82 (leq(addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))), star(X0!0))),
% 65.60/65.82 inference(modus_ponens,[status(thm)],[324, 367])).
% 65.60/65.82 tff(369,plain,
% 65.60/65.82 (leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))),
% 65.60/65.82 inference(modus_ponens,[status(thm)],[368, 365])).
% 65.60/65.82 tff(370,plain,
% 65.60/65.82 (((~![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(X0!0)), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(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(X0!0)), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)))),
% 65.60/65.82 inference(rewrite,[status(thm)],[])).
% 65.60/65.82 tff(371,plain,
% 65.60/65.82 ((~![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(X0!0)), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)))),
% 65.60/65.82 inference(quant_inst,[status(thm)],[])).
% 65.60/65.82 tff(372,plain,
% 65.60/65.82 ((~![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(X0!0)), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 65.73/65.98 inference(modus_ponens,[status(thm)],[371, 370])).
% 65.73/65.98 tff(373,plain,
% 65.73/65.98 ((~leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))) | leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 65.73/65.98 inference(unit_resolution,[status(thm)],[372, 319])).
% 65.73/65.98 tff(374,plain,
% 65.73/65.98 (leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 65.73/65.98 inference(unit_resolution,[status(thm)],[373, 369])).
% 65.73/65.98 tff(375,plain,
% 65.73/65.98 (leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 65.73/65.98 inference(modus_ponens,[status(thm)],[374, 339])).
% 65.73/65.98 tff(376,plain,
% 65.73/65.98 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))) | leq(multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))) | leq(multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0)))),
% 65.73/65.98 inference(rewrite,[status(thm)],[])).
% 65.73/65.98 tff(377,plain,
% 65.73/65.98 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))) | leq(multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0)))),
% 65.73/65.98 inference(quant_inst,[status(thm)],[])).
% 65.73/65.98 tff(378,plain,
% 65.73/65.98 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))) | leq(multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 65.73/65.98 inference(modus_ponens,[status(thm)],[377, 376])).
% 65.73/65.98 tff(379,plain,
% 65.73/65.98 ((~leq(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))) | leq(multiplication(star(star(X0!0)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 65.73/65.98 inference(unit_resolution,[status(thm)],[378, 319])).
% 65.73/65.98 tff(380,plain,
% 65.73/65.98 ($false),
% 65.73/65.98 inference(unit_resolution,[status(thm)],[379, 375, 304])).
% 65.73/65.98 % SZS output end Proof
% 65.73/66.01 % E exiting
%------------------------------------------------------------------------------