%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE039+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 52.06s 52.23s
% Output : Proof 52.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE039+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 18:55:20 EDT 2025
% 0.13/0.34 % CPUTime :
% 52.06/52.23 % SZS status Theorem
% 52.06/52.23 % SZS output start Proof
% 52.06/52.23 tff(leq_type, type, (
% 52.06/52.23 leq: ( $i * $i ) > $o)).
% 52.06/52.23 tff(star_type, type, (
% 52.06/52.23 star: $i > $i)).
% 52.06/52.23 tff(tptp_fun_X0_0_type, type, (
% 52.06/52.23 tptp_fun_X0_0: $i)).
% 52.06/52.23 tff(multiplication_type, type, (
% 52.06/52.23 multiplication: ( $i * $i ) > $i)).
% 52.06/52.23 tff(addition_type, type, (
% 52.06/52.23 addition: ( $i * $i ) > $i)).
% 52.06/52.23 tff(one_type, type, (
% 52.06/52.23 one: $i)).
% 52.06/52.23 tff(1,plain,
% 52.06/52.23 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 52.06/52.23 inference(bind,[status(th)],[])).
% 52.06/52.23 tff(2,plain,
% 52.06/52.23 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 52.06/52.23 inference(quant_intro,[status(thm)],[1])).
% 52.06/52.23 tff(3,plain,
% 52.06/52.23 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 52.06/52.23 inference(rewrite,[status(thm)],[])).
% 52.06/52.23 tff(4,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','order')).
% 52.06/52.23 tff(5,plain,
% 52.06/52.23 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 52.06/52.23 inference(modus_ponens,[status(thm)],[4, 3])).
% 52.06/52.23 tff(6,plain,(
% 52.06/52.23 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 52.06/52.23 inference(skolemize,[status(sab)],[5])).
% 52.06/52.23 tff(7,plain,
% 52.06/52.23 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 52.06/52.23 inference(modus_ponens,[status(thm)],[6, 2])).
% 52.06/52.23 tff(8,plain,
% 52.06/52.23 ((~![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))))),
% 52.06/52.23 inference(quant_inst,[status(thm)],[])).
% 52.06/52.23 tff(9,plain,
% 52.06/52.23 (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)))),
% 52.06/52.23 inference(unit_resolution,[status(thm)],[8, 7])).
% 52.06/52.23 tff(10,plain,
% 52.06/52.23 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 52.06/52.23 inference(bind,[status(th)],[])).
% 52.06/52.23 tff(11,plain,
% 52.06/52.23 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 52.06/52.23 inference(quant_intro,[status(thm)],[10])).
% 52.06/52.23 tff(12,plain,
% 52.06/52.23 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 52.06/52.23 inference(rewrite,[status(thm)],[])).
% 52.06/52.23 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')).
% 52.06/52.23 tff(14,plain,
% 52.06/52.23 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 52.06/52.23 inference(modus_ponens,[status(thm)],[13, 12])).
% 52.06/52.23 tff(15,plain,(
% 52.06/52.23 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 52.06/52.23 inference(skolemize,[status(sab)],[14])).
% 52.06/52.23 tff(16,plain,
% 52.06/52.23 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 52.06/52.23 inference(modus_ponens,[status(thm)],[15, 11])).
% 52.06/52.23 tff(17,plain,
% 52.06/52.23 ((~![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)))),
% 52.06/52.23 inference(quant_inst,[status(thm)],[])).
% 52.06/52.23 tff(18,plain,
% 52.06/52.23 (leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 52.06/52.23 inference(unit_resolution,[status(thm)],[17, 16])).
% 52.06/52.23 tff(19,plain,
% 52.06/52.23 ((~(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)))),
% 52.06/52.23 inference(tautology,[status(thm)],[])).
% 52.06/52.23 tff(20,plain,
% 52.06/52.23 ((~(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)))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[19, 18])).
% 52.06/52.24 tff(21,plain,
% 52.06/52.24 (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = star(star(X0!0))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[20, 9])).
% 52.06/52.24 tff(22,plain,
% 52.06/52.24 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 52.06/52.24 inference(bind,[status(th)],[])).
% 52.06/52.24 tff(23,plain,
% 52.06/52.24 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 52.06/52.24 inference(quant_intro,[status(thm)],[22])).
% 52.06/52.24 tff(24,plain,
% 52.06/52.24 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 52.06/52.24 inference(rewrite,[status(thm)],[])).
% 52.06/52.24 tff(25,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 52.06/52.24 tff(26,plain,
% 52.06/52.24 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[25, 24])).
% 52.06/52.24 tff(27,plain,(
% 52.06/52.24 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 52.06/52.24 inference(skolemize,[status(sab)],[26])).
% 52.06/52.24 tff(28,plain,
% 52.06/52.24 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[27, 23])).
% 52.06/52.24 tff(29,plain,
% 52.06/52.24 ((~![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))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(30,plain,
% 52.06/52.24 (addition(one, multiplication(star(X0!0), star(star(X0!0)))) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[29, 28])).
% 52.06/52.24 tff(31,plain,
% 52.06/52.24 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(one, multiplication(star(X0!0), star(star(X0!0))))),
% 52.06/52.24 inference(symmetry,[status(thm)],[30])).
% 52.06/52.24 tff(32,plain,
% 52.06/52.24 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(33,plain,
% 52.06/52.24 (leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0)))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[32, 7])).
% 52.06/52.24 tff(34,plain,
% 52.06/52.24 (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)))),
% 52.06/52.24 inference(monotonicity,[status(thm)],[31])).
% 52.06/52.24 tff(35,plain,
% 52.06/52.24 (^[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)))),
% 52.06/52.24 inference(bind,[status(th)],[])).
% 52.06/52.24 tff(36,plain,
% 52.06/52.24 (![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))),
% 52.06/52.24 inference(quant_intro,[status(thm)],[35])).
% 52.06/52.24 tff(37,plain,
% 52.06/52.24 (![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))),
% 52.06/52.24 inference(rewrite,[status(thm)],[])).
% 52.06/52.24 tff(38,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')).
% 52.06/52.24 tff(39,plain,
% 52.06/52.24 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[38, 37])).
% 52.06/52.24 tff(40,plain,(
% 52.06/52.24 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 52.06/52.24 inference(skolemize,[status(sab)],[39])).
% 52.06/52.24 tff(41,plain,
% 52.06/52.24 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[40, 36])).
% 52.06/52.24 tff(42,plain,
% 52.06/52.24 ((~![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))))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(43,plain,
% 52.06/52.24 (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)))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[42, 41])).
% 52.06/52.24 tff(44,plain,
% 52.06/52.24 ((~![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))))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(45,plain,
% 52.06/52.24 (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)))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[44, 7])).
% 52.06/52.24 tff(46,plain,
% 52.06/52.24 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 52.06/52.24 inference(bind,[status(th)],[])).
% 52.06/52.24 tff(47,plain,
% 52.06/52.24 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 52.06/52.24 inference(quant_intro,[status(thm)],[46])).
% 52.06/52.24 tff(48,plain,
% 52.06/52.24 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 52.06/52.24 inference(rewrite,[status(thm)],[])).
% 52.06/52.24 tff(49,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 52.06/52.24 tff(50,plain,
% 52.06/52.24 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[49, 48])).
% 52.06/52.24 tff(51,plain,(
% 52.06/52.24 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 52.06/52.24 inference(skolemize,[status(sab)],[50])).
% 52.06/52.24 tff(52,plain,
% 52.06/52.24 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[51, 47])).
% 52.06/52.24 tff(53,plain,
% 52.06/52.24 ((~![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)))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(54,plain,
% 52.06/52.24 (leq(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[53, 52])).
% 52.06/52.24 tff(55,plain,
% 52.06/52.24 ((~(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)))),
% 52.06/52.24 inference(tautology,[status(thm)],[])).
% 52.06/52.24 tff(56,plain,
% 52.06/52.24 ((~(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)))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[55, 54])).
% 52.06/52.24 tff(57,plain,
% 52.06/52.24 (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = star(star(X0!0))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[56, 45])).
% 52.06/52.24 tff(58,plain,
% 52.06/52.24 ((~![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))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(59,plain,
% 52.06/52.24 (addition(one, multiplication(star(star(X0!0)), star(X0!0))) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[58, 28])).
% 52.06/52.24 tff(60,plain,
% 52.06/52.24 (addition(multiplication(star(star(X0!0)), star(X0!0)), one) = addition(one, multiplication(star(star(X0!0)), star(X0!0)))),
% 52.06/52.24 inference(symmetry,[status(thm)],[59])).
% 52.06/52.24 tff(61,plain,
% 52.06/52.24 (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)))),
% 52.06/52.24 inference(monotonicity,[status(thm)],[60])).
% 52.06/52.24 tff(62,plain,
% 52.06/52.24 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))) = star(star(X0!0))),
% 52.06/52.24 inference(transitivity,[status(thm)],[61, 57])).
% 52.06/52.24 tff(63,plain,
% 52.06/52.24 (multiplication(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = multiplication(star(X0!0), star(star(X0!0)))),
% 52.06/52.24 inference(monotonicity,[status(thm)],[62])).
% 52.06/52.24 tff(64,plain,
% 52.06/52.24 (^[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))))),
% 52.06/52.24 inference(bind,[status(th)],[])).
% 52.06/52.24 tff(65,plain,
% 52.06/52.24 (![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)))),
% 52.06/52.24 inference(quant_intro,[status(thm)],[64])).
% 52.06/52.24 tff(66,plain,
% 52.06/52.24 (![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)))),
% 52.06/52.24 inference(rewrite,[status(thm)],[])).
% 52.06/52.24 tff(67,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')).
% 52.06/52.24 tff(68,plain,
% 52.06/52.24 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[67, 66])).
% 52.06/52.24 tff(69,plain,(
% 52.06/52.24 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 52.06/52.24 inference(skolemize,[status(sab)],[68])).
% 52.06/52.24 tff(70,plain,
% 52.06/52.24 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[69, 65])).
% 52.06/52.24 tff(71,plain,
% 52.06/52.24 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(72,plain,
% 52.06/52.24 (multiplication(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[71, 70])).
% 52.06/52.24 tff(73,plain,
% 52.06/52.24 (addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))))),
% 52.06/52.24 inference(symmetry,[status(thm)],[72])).
% 52.06/52.24 tff(74,plain,
% 52.06/52.24 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 52.06/52.24 inference(bind,[status(th)],[])).
% 52.06/52.24 tff(75,plain,
% 52.06/52.24 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 52.06/52.24 inference(quant_intro,[status(thm)],[74])).
% 52.06/52.24 tff(76,plain,
% 52.06/52.24 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 52.06/52.24 inference(rewrite,[status(thm)],[])).
% 52.06/52.24 tff(77,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 52.06/52.24 tff(78,plain,
% 52.06/52.24 (![A: $i] : (addition(A, A) = A)),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[77, 76])).
% 52.06/52.24 tff(79,plain,(
% 52.06/52.24 ![A: $i] : (addition(A, A) = A)),
% 52.06/52.24 inference(skolemize,[status(sab)],[78])).
% 52.06/52.24 tff(80,plain,
% 52.06/52.24 (![A: $i] : (addition(A, A) = A)),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[79, 75])).
% 52.06/52.24 tff(81,plain,
% 52.06/52.24 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(82,plain,
% 52.06/52.24 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[81, 80])).
% 52.06/52.24 tff(83,plain,
% 52.06/52.24 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = multiplication(star(X0!0), star(star(X0!0)))),
% 52.06/52.24 inference(transitivity,[status(thm)],[82, 73, 63])).
% 52.06/52.24 tff(84,plain,
% 52.06/52.24 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), 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))))),
% 52.06/52.24 inference(monotonicity,[status(thm)],[83])).
% 52.06/52.24 tff(85,plain,
% 52.06/52.24 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0)))))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(86,plain,
% 52.06/52.24 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0))))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[85, 41])).
% 52.06/52.24 tff(87,plain,
% 52.06/52.24 (addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), star(star(X0!0)))),
% 52.06/52.24 inference(transitivity,[status(thm)],[73, 63])).
% 52.06/52.24 tff(88,plain,
% 52.06/52.24 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), 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))))),
% 52.06/52.24 inference(monotonicity,[status(thm)],[87])).
% 52.06/52.24 tff(89,plain,
% 52.06/52.24 (addition(multiplication(star(X0!0), star(star(X0!0))), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 52.06/52.24 inference(symmetry,[status(thm)],[88])).
% 52.06/52.24 tff(90,plain,
% 52.06/52.24 (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))))),
% 52.06/52.24 inference(symmetry,[status(thm)],[43])).
% 52.06/52.24 tff(91,plain,
% 52.06/52.24 (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)))),
% 52.06/52.24 inference(symmetry,[status(thm)],[34])).
% 52.06/52.24 tff(92,plain,
% 52.06/52.24 (star(star(X0!0)) = addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 52.06/52.24 inference(symmetry,[status(thm)],[21])).
% 52.06/52.24 tff(93,plain,
% 52.06/52.24 (star(star(X0!0)) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 52.06/52.24 inference(transitivity,[status(thm)],[92, 91, 90, 89])).
% 52.06/52.24 tff(94,plain,
% 52.06/52.24 (multiplication(star(X0!0), star(star(X0!0))) = multiplication(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))))),
% 52.06/52.24 inference(symmetry,[status(thm)],[63])).
% 52.06/52.24 tff(95,plain,
% 52.06/52.24 (multiplication(star(X0!0), star(star(X0!0))) = addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))),
% 52.06/52.24 inference(transitivity,[status(thm)],[94, 72])).
% 52.06/52.24 tff(96,plain,
% 52.06/52.24 (addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))))),
% 52.06/52.24 inference(monotonicity,[status(thm)],[95, 93])).
% 52.06/52.24 tff(97,plain,
% 52.06/52.24 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))),
% 52.06/52.24 inference(monotonicity,[status(thm)],[87, 62])).
% 52.06/52.24 tff(98,plain,
% 52.06/52.24 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(99,plain,
% 52.06/52.24 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0)))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[98, 41])).
% 52.06/52.24 tff(100,plain,
% 52.06/52.24 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))))),
% 52.06/52.24 inference(symmetry,[status(thm)],[99])).
% 52.06/52.24 tff(101,plain,
% 52.06/52.24 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))) = addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(102,plain,
% 52.06/52.24 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))) = addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[101, 28])).
% 52.06/52.24 tff(103,plain,
% 52.06/52.24 (addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0)))),
% 52.06/52.24 inference(symmetry,[status(thm)],[102])).
% 52.06/52.24 tff(104,plain,
% 52.06/52.24 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(105,plain,
% 52.06/52.24 (addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[104, 41])).
% 52.06/52.24 tff(106,plain,
% 52.06/52.24 (addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(star(star(X0!0)), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 52.06/52.24 inference(symmetry,[status(thm)],[105])).
% 52.06/52.24 tff(107,plain,
% 52.06/52.24 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), 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), addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(108,plain,
% 52.06/52.24 (addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), 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), addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[107, 28])).
% 52.06/52.24 tff(109,plain,
% 52.06/52.24 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.06/52.24 inference(symmetry,[status(thm)],[108])).
% 52.06/52.24 tff(110,plain,
% 52.06/52.24 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(111,plain,
% 52.06/52.24 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[110, 28])).
% 52.06/52.24 tff(112,plain,
% 52.06/52.24 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), 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)))),
% 52.06/52.24 inference(monotonicity,[status(thm)],[87])).
% 52.06/52.24 tff(113,plain,
% 52.06/52.24 (addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 52.06/52.24 inference(symmetry,[status(thm)],[112])).
% 52.06/52.24 tff(114,plain,
% 52.06/52.24 (addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.24 inference(transitivity,[status(thm)],[113, 111])).
% 52.06/52.24 tff(115,plain,
% 52.06/52.24 (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))),
% 52.06/52.24 inference(monotonicity,[status(thm)],[62])).
% 52.06/52.24 tff(116,plain,
% 52.06/52.24 (^[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))))),
% 52.06/52.24 inference(bind,[status(th)],[])).
% 52.06/52.24 tff(117,plain,
% 52.06/52.24 (![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)))),
% 52.06/52.24 inference(quant_intro,[status(thm)],[116])).
% 52.06/52.24 tff(118,plain,
% 52.06/52.24 (![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)))),
% 52.06/52.24 inference(rewrite,[status(thm)],[])).
% 52.06/52.24 tff(119,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')).
% 52.06/52.24 tff(120,plain,
% 52.06/52.24 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[119, 118])).
% 52.06/52.24 tff(121,plain,(
% 52.06/52.24 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 52.06/52.24 inference(skolemize,[status(sab)],[120])).
% 52.06/52.24 tff(122,plain,
% 52.06/52.24 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 52.06/52.24 inference(modus_ponens,[status(thm)],[121, 117])).
% 52.06/52.24 tff(123,plain,
% 52.06/52.24 ((~![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))))),
% 52.06/52.24 inference(quant_inst,[status(thm)],[])).
% 52.06/52.24 tff(124,plain,
% 52.06/52.24 (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)))),
% 52.06/52.24 inference(unit_resolution,[status(thm)],[123, 122])).
% 52.06/52.24 tff(125,plain,
% 52.06/52.24 (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))),
% 52.06/52.24 inference(symmetry,[status(thm)],[124])).
% 52.06/52.24 tff(126,plain,
% 52.06/52.24 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))) = multiplication(star(star(X0!0)), star(X0!0))),
% 52.06/52.24 inference(transitivity,[status(thm)],[125, 115])).
% 52.06/52.24 tff(127,plain,
% 52.06/52.24 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 52.06/52.24 inference(monotonicity,[status(thm)],[126])).
% 52.06/52.24 tff(128,plain,
% 52.06/52.24 (addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.06/52.24 inference(monotonicity,[status(thm)],[127, 114])).
% 52.06/52.25 tff(129,plain,
% 52.06/52.25 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(130,plain,
% 52.06/52.25 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[129, 41])).
% 52.06/52.25 tff(131,plain,
% 52.06/52.25 ((~![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))))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(132,plain,
% 52.06/52.25 (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)))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[131, 41])).
% 52.06/52.25 tff(133,plain,
% 52.06/52.25 (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))))),
% 52.06/52.25 inference(symmetry,[status(thm)],[132])).
% 52.06/52.25 tff(134,plain,
% 52.06/52.25 (star(star(X0!0)) = addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0))))),
% 52.06/52.25 inference(transitivity,[status(thm)],[92, 133])).
% 52.06/52.25 tff(135,plain,
% 52.06/52.25 (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))),
% 52.06/52.25 inference(symmetry,[status(thm)],[115])).
% 52.06/52.25 tff(136,plain,
% 52.06/52.25 (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)))),
% 52.06/52.25 inference(transitivity,[status(thm)],[135, 124])).
% 52.06/52.25 tff(137,plain,
% 52.06/52.25 (addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), star(star(X0!0)))))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[136, 134])).
% 52.06/52.25 tff(138,plain,
% 52.06/52.25 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 52.06/52.25 inference(bind,[status(th)],[])).
% 52.06/52.25 tff(139,plain,
% 52.06/52.25 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 52.06/52.25 inference(quant_intro,[status(thm)],[138])).
% 52.06/52.25 tff(140,plain,
% 52.06/52.25 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 52.06/52.25 inference(rewrite,[status(thm)],[])).
% 52.06/52.25 tff(141,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_right_identity')).
% 52.06/52.25 tff(142,plain,
% 52.06/52.25 (![A: $i] : (multiplication(A, one) = A)),
% 52.06/52.25 inference(modus_ponens,[status(thm)],[141, 140])).
% 52.06/52.25 tff(143,plain,(
% 52.06/52.25 ![A: $i] : (multiplication(A, one) = A)),
% 52.06/52.25 inference(skolemize,[status(sab)],[142])).
% 52.06/52.25 tff(144,plain,
% 52.06/52.25 (![A: $i] : (multiplication(A, one) = A)),
% 52.06/52.25 inference(modus_ponens,[status(thm)],[143, 139])).
% 52.06/52.25 tff(145,plain,
% 52.06/52.25 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(star(star(X0!0)), one) = star(star(X0!0)))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(146,plain,
% 52.06/52.25 (multiplication(star(star(X0!0)), one) = star(star(X0!0))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[145, 144])).
% 52.06/52.25 tff(147,plain,
% 52.06/52.25 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), 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)))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[126, 146])).
% 52.06/52.25 tff(148,plain,
% 52.06/52.25 (addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(star(star(X0!0)), one)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), multiplication(star(star(X0!0)), one))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[136])).
% 52.06/52.25 tff(149,plain,
% 52.06/52.25 ((~![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)))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(150,plain,
% 52.06/52.25 (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))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[149, 70])).
% 52.06/52.25 tff(151,plain,
% 52.06/52.25 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(X0!0)) = addition(star(X0!0), one))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(152,plain,
% 52.06/52.25 (addition(one, star(X0!0)) = addition(star(X0!0), one)),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[151, 28])).
% 52.06/52.25 tff(153,plain,
% 52.06/52.25 (multiplication(star(star(X0!0)), addition(one, star(X0!0))) = multiplication(star(star(X0!0)), addition(star(X0!0), one))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[152])).
% 52.06/52.25 tff(154,plain,
% 52.06/52.25 ((~![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)))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(155,plain,
% 52.06/52.25 (addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[154, 41])).
% 52.06/52.25 tff(156,plain,
% 52.06/52.25 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 52.06/52.25 inference(symmetry,[status(thm)],[155])).
% 52.06/52.25 tff(157,plain,
% 52.06/52.25 ((~![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)))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(158,plain,
% 52.06/52.25 (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))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[157, 7])).
% 52.06/52.25 tff(159,plain,
% 52.06/52.25 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(160,plain,
% 52.06/52.25 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[159, 52])).
% 52.06/52.25 tff(161,plain,
% 52.06/52.25 ((~(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))),
% 52.06/52.25 inference(tautology,[status(thm)],[])).
% 52.06/52.25 tff(162,plain,
% 52.06/52.25 ((~(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))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[161, 160])).
% 52.06/52.25 tff(163,plain,
% 52.06/52.25 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[162, 158])).
% 52.06/52.25 tff(164,plain,
% 52.06/52.25 (star(X0!0) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 52.06/52.25 inference(symmetry,[status(thm)],[163])).
% 52.06/52.25 tff(165,plain,
% 52.06/52.25 (star(X0!0) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 52.06/52.25 inference(transitivity,[status(thm)],[164, 156])).
% 52.06/52.25 tff(166,plain,
% 52.06/52.25 (addition(one, star(X0!0)) = addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[165])).
% 52.06/52.25 tff(167,plain,
% 52.06/52.25 (addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))) = addition(one, star(X0!0))),
% 52.06/52.25 inference(symmetry,[status(thm)],[166])).
% 52.06/52.25 tff(168,plain,
% 52.06/52.25 ((~![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))))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(169,plain,
% 52.06/52.25 (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)))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[168, 41])).
% 52.06/52.25 tff(170,plain,
% 52.06/52.25 (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))))),
% 52.06/52.25 inference(symmetry,[status(thm)],[169])).
% 52.06/52.25 tff(171,plain,
% 52.06/52.25 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(172,plain,
% 52.06/52.25 (addition(one, one) = one),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[171, 80])).
% 52.06/52.25 tff(173,plain,
% 52.06/52.25 (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)))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[172])).
% 52.06/52.25 tff(174,plain,
% 52.06/52.25 (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)))),
% 52.06/52.25 inference(symmetry,[status(thm)],[173])).
% 52.06/52.25 tff(175,plain,
% 52.06/52.25 (star(X0!0) = addition(one, star(X0!0))),
% 52.06/52.25 inference(transitivity,[status(thm)],[164, 156, 174, 170, 167])).
% 52.06/52.25 tff(176,plain,
% 52.06/52.25 (multiplication(star(star(X0!0)), star(X0!0)) = multiplication(star(star(X0!0)), addition(one, star(X0!0)))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[175])).
% 52.06/52.25 tff(177,plain,
% 52.06/52.25 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(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))))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(178,plain,
% 52.06/52.25 (addition(one, addition(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)))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[177, 41])).
% 52.06/52.25 tff(179,plain,
% 52.06/52.25 (addition(addition(one, one), addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0)))) = addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[172])).
% 52.06/52.25 tff(180,plain,
% 52.06/52.25 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))) = addition(addition(one, one), addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0)))))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(181,plain,
% 52.06/52.25 (addition(one, addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))) = addition(addition(one, one), addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[180, 41])).
% 52.06/52.25 tff(182,plain,
% 52.06/52.25 (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))),
% 52.06/52.25 inference(symmetry,[status(thm)],[178])).
% 52.06/52.25 tff(183,plain,
% 52.06/52.25 (star(star(X0!0)) = addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 52.06/52.25 inference(symmetry,[status(thm)],[57])).
% 52.06/52.25 tff(184,plain,
% 52.06/52.25 (star(star(X0!0)) = addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0))))),
% 52.06/52.25 inference(transitivity,[status(thm)],[183, 182])).
% 52.06/52.25 tff(185,plain,
% 52.06/52.25 (addition(one, star(star(X0!0))) = addition(one, addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), star(star(X0!0)))))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[184])).
% 52.06/52.25 tff(186,plain,
% 52.06/52.25 (addition(one, star(star(X0!0))) = star(star(X0!0))),
% 52.06/52.25 inference(transitivity,[status(thm)],[185, 181, 179, 178, 57])).
% 52.06/52.25 tff(187,plain,
% 52.06/52.25 (multiplication(addition(one, star(star(X0!0))), star(X0!0)) = multiplication(star(star(X0!0)), star(X0!0))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[186])).
% 52.06/52.25 tff(188,plain,
% 52.06/52.25 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(star(X0!0))) = addition(star(star(X0!0)), one))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(189,plain,
% 52.06/52.25 (addition(one, star(star(X0!0))) = addition(star(star(X0!0)), one)),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[188, 28])).
% 52.06/52.25 tff(190,plain,
% 52.06/52.25 (addition(star(star(X0!0)), one) = addition(one, star(star(X0!0)))),
% 52.06/52.25 inference(symmetry,[status(thm)],[189])).
% 52.06/52.25 tff(191,plain,
% 52.06/52.25 (multiplication(addition(star(star(X0!0)), one), star(X0!0)) = multiplication(addition(one, star(star(X0!0))), star(X0!0))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[190])).
% 52.06/52.25 tff(192,plain,
% 52.06/52.25 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(star(star(X0!0)), one), star(X0!0)) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(one, star(X0!0))))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(193,plain,
% 52.06/52.25 (multiplication(addition(star(star(X0!0)), one), star(X0!0)) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(one, star(X0!0)))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[192, 122])).
% 52.06/52.25 tff(194,plain,
% 52.06/52.25 (addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(one, star(X0!0))) = multiplication(addition(star(star(X0!0)), one), star(X0!0))),
% 52.06/52.25 inference(symmetry,[status(thm)],[193])).
% 52.06/52.25 tff(195,plain,
% 52.06/52.25 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), multiplication(one, star(X0!0))) = addition(multiplication(star(star(X0!0)), star(X0!0)), multiplication(one, star(X0!0)))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[126])).
% 52.06/52.25 tff(196,plain,
% 52.06/52.25 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 52.06/52.25 inference(bind,[status(th)],[])).
% 52.06/52.25 tff(197,plain,
% 52.06/52.25 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 52.06/52.25 inference(quant_intro,[status(thm)],[196])).
% 52.06/52.25 tff(198,plain,
% 52.06/52.25 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 52.06/52.25 inference(rewrite,[status(thm)],[])).
% 52.06/52.25 tff(199,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_left_identity')).
% 52.06/52.25 tff(200,plain,
% 52.06/52.25 (![A: $i] : (multiplication(one, A) = A)),
% 52.06/52.25 inference(modus_ponens,[status(thm)],[199, 198])).
% 52.06/52.25 tff(201,plain,(
% 52.06/52.25 ![A: $i] : (multiplication(one, A) = A)),
% 52.06/52.25 inference(skolemize,[status(sab)],[200])).
% 52.06/52.25 tff(202,plain,
% 52.06/52.25 (![A: $i] : (multiplication(one, A) = A)),
% 52.06/52.25 inference(modus_ponens,[status(thm)],[201, 197])).
% 52.06/52.25 tff(203,plain,
% 52.06/52.25 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(X0!0)) = star(X0!0))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(204,plain,
% 52.06/52.25 (multiplication(one, star(X0!0)) = star(X0!0)),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[203, 202])).
% 52.06/52.25 tff(205,plain,
% 52.06/52.25 (star(X0!0) = multiplication(one, star(X0!0))),
% 52.06/52.25 inference(symmetry,[status(thm)],[204])).
% 52.06/52.25 tff(206,plain,
% 52.06/52.25 (addition(multiplication(star(star(X0!0)), star(X0!0)), star(X0!0)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), multiplication(one, star(X0!0)))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[136, 205])).
% 52.06/52.25 tff(207,plain,
% 52.06/52.25 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)) = addition(multiplication(star(star(X0!0)), star(X0!0)), star(X0!0))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[126])).
% 52.06/52.25 tff(208,plain,
% 52.06/52.25 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(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)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0)))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(209,plain,
% 52.06/52.25 (addition(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)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), star(X0!0))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[208, 28])).
% 52.06/52.25 tff(210,plain,
% 52.06/52.25 ((~![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))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(211,plain,
% 52.06/52.25 (addition(one, multiplication(star(X0!0), X0!0)) = addition(multiplication(star(X0!0), X0!0), one)),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[210, 28])).
% 52.06/52.25 tff(212,plain,
% 52.06/52.25 (addition(multiplication(star(X0!0), X0!0), one) = addition(one, multiplication(star(X0!0), X0!0))),
% 52.06/52.25 inference(symmetry,[status(thm)],[211])).
% 52.06/52.25 tff(213,plain,
% 52.06/52.25 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[212])).
% 52.06/52.25 tff(214,plain,
% 52.06/52.25 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(215,plain,
% 52.06/52.25 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(star(X0!0), X0!0), one))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[214, 28])).
% 52.06/52.25 tff(216,plain,
% 52.06/52.25 (addition(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 52.06/52.25 inference(symmetry,[status(thm)],[215])).
% 52.06/52.25 tff(217,plain,
% 52.06/52.25 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 52.06/52.25 inference(symmetry,[status(thm)],[213])).
% 52.06/52.25 tff(218,plain,
% 52.06/52.25 (star(X0!0) = addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 52.06/52.25 inference(transitivity,[status(thm)],[164, 217])).
% 52.06/52.25 tff(219,plain,
% 52.06/52.25 (multiplication(star(X0!0), X0!0) = multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0)),
% 52.06/52.25 inference(monotonicity,[status(thm)],[218])).
% 52.06/52.25 tff(220,plain,
% 52.06/52.25 (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0) = multiplication(star(X0!0), X0!0)),
% 52.06/52.25 inference(symmetry,[status(thm)],[219])).
% 52.06/52.25 tff(221,plain,
% 52.06/52.25 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(222,plain,
% 52.06/52.25 (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[221, 122])).
% 52.06/52.25 tff(223,plain,
% 52.06/52.25 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)) = multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), X0!0)),
% 52.06/52.25 inference(symmetry,[status(thm)],[222])).
% 52.06/52.25 tff(224,plain,
% 52.06/52.25 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)) = multiplication(star(X0!0), X0!0)),
% 52.06/52.25 inference(transitivity,[status(thm)],[223, 220])).
% 52.06/52.25 tff(225,plain,
% 52.06/52.25 (addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one) = addition(multiplication(star(X0!0), X0!0), one)),
% 52.06/52.25 inference(monotonicity,[status(thm)],[224])).
% 52.06/52.25 tff(226,plain,
% 52.06/52.25 (addition(star(X0!0), addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one)) = addition(star(X0!0), addition(multiplication(star(X0!0), X0!0), one))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[225])).
% 52.06/52.25 tff(227,plain,
% 52.06/52.25 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one)) = addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(228,plain,
% 52.06/52.25 (addition(star(X0!0), addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one)) = addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one)),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[227, 41])).
% 52.06/52.25 tff(229,plain,
% 52.06/52.25 (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one) = addition(star(X0!0), addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one))),
% 52.06/52.25 inference(symmetry,[status(thm)],[228])).
% 52.06/52.25 tff(230,plain,
% 52.06/52.25 (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one) = star(X0!0)),
% 52.06/52.25 inference(transitivity,[status(thm)],[229, 226, 216, 213, 163])).
% 52.06/52.25 tff(231,plain,
% 52.06/52.25 (addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(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))))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[230])).
% 52.06/52.25 tff(232,plain,
% 52.06/52.25 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(233,plain,
% 52.06/52.25 (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[232, 41])).
% 52.06/52.25 tff(234,plain,
% 52.06/52.25 (addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(one, multiplication(star(star(X0!0)), star(X0!0)))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[126])).
% 52.06/52.25 tff(235,plain,
% 52.06/52.25 (addition(one, multiplication(star(star(X0!0)), star(X0!0))) = addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.25 inference(symmetry,[status(thm)],[234])).
% 52.06/52.25 tff(236,plain,
% 52.06/52.25 (addition(multiplication(star(star(X0!0)), star(X0!0)), one) = addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.25 inference(transitivity,[status(thm)],[60, 235])).
% 52.06/52.25 tff(237,plain,
% 52.06/52.25 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))))),
% 52.06/52.25 inference(quant_inst,[status(thm)],[])).
% 52.06/52.25 tff(238,plain,
% 52.06/52.25 (addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 52.06/52.25 inference(unit_resolution,[status(thm)],[237, 28])).
% 52.06/52.25 tff(239,plain,
% 52.06/52.25 (addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(multiplication(star(X0!0), X0!0), star(X0!0))),
% 52.06/52.25 inference(monotonicity,[status(thm)],[224])).
% 52.06/52.25 tff(240,plain,
% 52.06/52.25 (addition(multiplication(star(X0!0), X0!0), star(X0!0)) = addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0))),
% 52.06/52.25 inference(symmetry,[status(thm)],[239])).
% 52.06/52.25 tff(241,plain,
% 52.06/52.25 (addition(multiplication(star(X0!0), X0!0), star(X0!0)) = addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 52.06/52.25 inference(transitivity,[status(thm)],[240, 238])).
% 52.06/52.25 tff(242,plain,
% 52.06/52.25 (addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[241, 236])).
% 52.06/52.26 tff(243,plain,
% 52.06/52.26 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(244,plain,
% 52.06/52.26 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[243, 80])).
% 52.06/52.26 tff(245,plain,
% 52.06/52.26 (addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 52.06/52.26 inference(transitivity,[status(thm)],[234, 59])).
% 52.06/52.26 tff(246,plain,
% 52.06/52.26 (addition(addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), 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)), star(X0!0)), one))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[245])).
% 52.06/52.26 tff(247,plain,
% 52.06/52.26 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(248,plain,
% 52.06/52.26 (addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[247, 41])).
% 52.06/52.26 tff(249,plain,
% 52.06/52.26 (addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 52.06/52.26 inference(transitivity,[status(thm)],[248, 246, 244])).
% 52.06/52.26 tff(250,plain,
% 52.06/52.26 (addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))) = addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0))),
% 52.06/52.26 inference(symmetry,[status(thm)],[238])).
% 52.06/52.26 tff(251,plain,
% 52.06/52.26 (addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))) = addition(multiplication(star(X0!0), X0!0), star(X0!0))),
% 52.06/52.26 inference(transitivity,[status(thm)],[250, 239])).
% 52.06/52.26 tff(252,plain,
% 52.06/52.26 (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(multiplication(star(X0!0), X0!0), star(X0!0)), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[251, 249])).
% 52.06/52.26 tff(253,plain,
% 52.06/52.26 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(254,plain,
% 52.06/52.26 (addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[253, 41])).
% 52.06/52.26 tff(255,plain,
% 52.06/52.26 (addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), addition(one, addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))))),
% 52.06/52.26 inference(symmetry,[status(thm)],[254])).
% 52.06/52.26 tff(256,plain,
% 52.06/52.26 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), 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(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(257,plain,
% 52.06/52.26 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), 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(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[256, 28])).
% 52.06/52.26 tff(258,plain,
% 52.06/52.26 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.06/52.26 inference(symmetry,[status(thm)],[257])).
% 52.06/52.26 tff(259,plain,
% 52.06/52.26 (addition(star(X0!0), addition(multiplication(star(X0!0), X0!0), one)) = addition(star(X0!0), addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one))),
% 52.06/52.26 inference(symmetry,[status(thm)],[226])).
% 52.06/52.26 tff(260,plain,
% 52.06/52.26 (star(X0!0) = addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one)),
% 52.06/52.26 inference(transitivity,[status(thm)],[164, 217, 215, 259, 228])).
% 52.06/52.26 tff(261,plain,
% 52.06/52.26 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(star(X0!0), addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[260, 258])).
% 52.06/52.26 tff(262,plain,
% 52.06/52.26 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(263,plain,
% 52.06/52.26 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[262, 41])).
% 52.06/52.26 tff(264,plain,
% 52.06/52.26 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 52.06/52.26 inference(symmetry,[status(thm)],[263])).
% 52.06/52.26 tff(265,plain,
% 52.06/52.26 ((~![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)))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(266,plain,
% 52.06/52.26 (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))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[265, 7])).
% 52.06/52.26 tff(267,plain,
% 52.06/52.26 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(268,plain,
% 52.06/52.26 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[267, 16])).
% 52.06/52.26 tff(269,plain,
% 52.06/52.26 ((~(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))),
% 52.06/52.26 inference(tautology,[status(thm)],[])).
% 52.06/52.26 tff(270,plain,
% 52.06/52.26 ((~(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))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[269, 268])).
% 52.06/52.26 tff(271,plain,
% 52.06/52.26 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[270, 266])).
% 52.06/52.26 tff(272,plain,
% 52.06/52.26 ((~![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)))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(273,plain,
% 52.06/52.26 (addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[272, 41])).
% 52.06/52.26 tff(274,plain,
% 52.06/52.26 (addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))) = star(X0!0)),
% 52.06/52.26 inference(transitivity,[status(thm)],[273, 271])).
% 52.06/52.26 tff(275,plain,
% 52.06/52.26 (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))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[274])).
% 52.06/52.26 tff(276,plain,
% 52.06/52.26 ((~![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)))))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(277,plain,
% 52.06/52.26 (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))))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[276, 70])).
% 52.06/52.26 tff(278,plain,
% 52.06/52.26 (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))))),
% 52.06/52.26 inference(symmetry,[status(thm)],[277])).
% 52.06/52.26 tff(279,plain,
% 52.06/52.26 (addition(multiplication(star(star(X0!0)), one), multiplication(star(star(X0!0)), addition(multiplication(X0!0, 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)))),
% 52.06/52.26 inference(transitivity,[status(thm)],[278, 275, 135, 124])).
% 52.06/52.26 tff(280,plain,
% 52.06/52.26 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(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(X0!0)))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(281,plain,
% 52.06/52.26 (addition(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(X0!0))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[280, 28])).
% 52.06/52.26 tff(282,plain,
% 52.06/52.26 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.06/52.26 inference(symmetry,[status(thm)],[281])).
% 52.06/52.26 tff(283,plain,
% 52.06/52.26 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), 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))))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[282, 279])).
% 52.06/52.26 tff(284,plain,
% 52.06/52.26 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), 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))))) = addition(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(285,plain,
% 52.06/52.26 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), 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))))) = addition(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[284, 41])).
% 52.06/52.26 tff(286,plain,
% 52.06/52.26 (addition(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), 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), 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)))))),
% 52.06/52.26 inference(symmetry,[status(thm)],[285])).
% 52.06/52.26 tff(287,plain,
% 52.06/52.26 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one)) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), star(star(X0!0)))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[146])).
% 52.06/52.26 tff(288,plain,
% 52.06/52.26 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), star(star(X0!0))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one))),
% 52.06/52.26 inference(symmetry,[status(thm)],[287])).
% 52.06/52.26 tff(289,plain,
% 52.06/52.26 ((~![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(star(X0!0), star(star(X0!0)))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), star(star(X0!0))))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(290,plain,
% 52.06/52.26 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), star(star(X0!0)))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), star(star(X0!0)))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[289, 41])).
% 52.06/52.26 tff(291,plain,
% 52.06/52.26 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(X0!0), star(star(X0!0))) = addition(star(star(X0!0)), star(X0!0)))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(292,plain,
% 52.06/52.26 (addition(star(X0!0), star(star(X0!0))) = addition(star(star(X0!0)), star(X0!0))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[291, 28])).
% 52.06/52.26 tff(293,plain,
% 52.06/52.26 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), star(X0!0)))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[292])).
% 52.06/52.26 tff(294,plain,
% 52.06/52.26 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), star(X0!0))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), star(star(X0!0))))),
% 52.06/52.26 inference(symmetry,[status(thm)],[293])).
% 52.06/52.26 tff(295,plain,
% 52.06/52.26 ((~![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(star(star(X0!0)), star(X0!0))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(296,plain,
% 52.06/52.26 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), star(X0!0))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[295, 41])).
% 52.06/52.26 tff(297,plain,
% 52.06/52.26 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(star(X0!0)), star(X0!0)))),
% 52.06/52.26 inference(symmetry,[status(thm)],[296])).
% 52.06/52.26 tff(298,plain,
% 52.06/52.26 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0)) = addition(star(star(X0!0)), star(X0!0))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[62])).
% 52.06/52.26 tff(299,plain,
% 52.06/52.26 (addition(star(star(X0!0)), star(X0!0)) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))), star(X0!0))),
% 52.06/52.26 inference(symmetry,[status(thm)],[298])).
% 52.06/52.26 tff(300,plain,
% 52.06/52.26 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))) = star(star(X0!0))),
% 52.06/52.26 inference(transitivity,[status(thm)],[34, 21])).
% 52.06/52.26 tff(301,plain,
% 52.06/52.26 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))), star(X0!0)) = addition(star(star(X0!0)), star(X0!0))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[300])).
% 52.06/52.26 tff(302,plain,
% 52.06/52.26 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(star(X0!0)), star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))), star(X0!0)))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(303,plain,
% 52.06/52.26 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(star(X0!0)), star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))), star(X0!0))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[302, 41])).
% 52.06/52.26 tff(304,plain,
% 52.06/52.26 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(X0!0), star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(star(X0!0)), star(X0!0)))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[292])).
% 52.06/52.26 tff(305,plain,
% 52.06/52.26 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(X0!0), star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), star(star(X0!0))))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(306,plain,
% 52.06/52.26 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(X0!0), star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), star(star(X0!0)))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[305, 41])).
% 52.06/52.26 tff(307,plain,
% 52.06/52.26 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(star(X0!0), star(star(X0!0))))),
% 52.06/52.26 inference(symmetry,[status(thm)],[306])).
% 52.06/52.26 tff(308,plain,
% 52.06/52.26 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), multiplication(star(star(X0!0)), one)) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), star(star(X0!0)))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[146])).
% 52.06/52.26 tff(309,plain,
% 52.06/52.26 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), multiplication(star(star(X0!0)), one)) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one))),
% 52.06/52.26 inference(transitivity,[status(thm)],[308, 307, 304, 303, 301, 299, 297, 294, 290, 288])).
% 52.06/52.26 tff(310,plain,
% 52.06/52.26 (addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))) = addition(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[309])).
% 52.06/52.26 tff(311,plain,
% 52.06/52.26 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), 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))))) = addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0)))))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(312,plain,
% 52.06/52.26 (addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), 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))))) = addition(addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)), multiplication(star(star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), star(X0!0))))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[311, 41])).
% 52.06/52.26 tff(313,plain,
% 52.06/52.26 (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))))),
% 52.06/52.26 inference(symmetry,[status(thm)],[275])).
% 52.06/52.26 tff(314,plain,
% 52.06/52.26 (addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), 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))))),
% 52.06/52.26 inference(transitivity,[status(thm)],[125, 115, 313, 277])).
% 52.06/52.26 tff(315,plain,
% 52.06/52.26 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 52.06/52.26 inference(quant_inst,[status(thm)],[])).
% 52.06/52.26 tff(316,plain,
% 52.06/52.26 (addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))),
% 52.06/52.26 inference(unit_resolution,[status(thm)],[315, 28])).
% 52.06/52.26 tff(317,plain,
% 52.06/52.26 (addition(addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), 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)))))),
% 52.06/52.26 inference(monotonicity,[status(thm)],[316, 314])).
% 52.06/52.26 tff(318,plain,
% 52.06/52.26 (addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(one, multiplication(star(X0!0), star(star(X0!0))))),
% 52.06/52.27 inference(monotonicity,[status(thm)],[87])).
% 52.06/52.27 tff(319,plain,
% 52.06/52.27 (addition(one, multiplication(star(X0!0), star(star(X0!0)))) = addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.27 inference(symmetry,[status(thm)],[318])).
% 52.06/52.27 tff(320,plain,
% 52.06/52.27 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.27 inference(transitivity,[status(thm)],[31, 319])).
% 52.06/52.27 tff(321,plain,
% 52.06/52.27 (addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.06/52.27 inference(monotonicity,[status(thm)],[320])).
% 52.06/52.27 tff(322,plain,
% 52.06/52.27 (addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.06/52.27 inference(symmetry,[status(thm)],[321])).
% 52.06/52.27 tff(323,plain,
% 52.06/52.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.06/52.27 inference(quant_inst,[status(thm)],[])).
% 52.06/52.27 tff(324,plain,
% 52.06/52.27 (addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.27 inference(unit_resolution,[status(thm)],[323, 41])).
% 52.06/52.27 tff(325,plain,
% 52.06/52.27 (addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(star(X0!0), addition(one, addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.06/52.27 inference(symmetry,[status(thm)],[324])).
% 52.06/52.27 tff(326,plain,
% 52.06/52.27 (addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.06/52.27 inference(transitivity,[status(thm)],[325, 322])).
% 52.06/52.27 tff(327,plain,
% 52.06/52.27 (addition(addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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)))) = addition(addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.27 inference(monotonicity,[status(thm)],[326])).
% 52.06/52.27 tff(328,plain,
% 52.06/52.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(star(X0!0), one), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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))))) = addition(addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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)))))),
% 52.06/52.27 inference(quant_inst,[status(thm)],[])).
% 52.06/52.27 tff(329,plain,
% 52.06/52.27 (addition(addition(star(X0!0), one), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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))))) = addition(addition(addition(star(X0!0), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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))))),
% 52.06/52.27 inference(unit_resolution,[status(thm)],[328, 41])).
% 52.06/52.27 tff(330,plain,
% 52.06/52.27 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.06/52.27 inference(quant_inst,[status(thm)],[])).
% 52.06/52.27 tff(331,plain,
% 52.06/52.27 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.27 inference(unit_resolution,[status(thm)],[330, 28])).
% 52.06/52.27 tff(332,plain,
% 52.06/52.27 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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))))),
% 52.06/52.27 inference(symmetry,[status(thm)],[331])).
% 52.06/52.27 tff(333,plain,
% 52.06/52.27 (addition(addition(star(X0!0), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), one), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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)))))),
% 52.06/52.27 inference(monotonicity,[status(thm)],[332])).
% 52.06/52.27 tff(334,plain,
% 52.06/52.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(star(X0!0), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.06/52.27 inference(quant_inst,[status(thm)],[])).
% 52.06/52.27 tff(335,plain,
% 52.06/52.27 (addition(addition(star(X0!0), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.27 inference(unit_resolution,[status(thm)],[334, 41])).
% 52.06/52.27 tff(336,plain,
% 52.06/52.27 (addition(addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(star(X0!0), one), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.06/52.27 inference(symmetry,[status(thm)],[335])).
% 52.06/52.27 tff(337,plain,
% 52.06/52.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 52.06/52.27 inference(quant_inst,[status(thm)],[])).
% 52.06/52.27 tff(338,plain,
% 52.06/52.27 (addition(star(X0!0), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.27 inference(unit_resolution,[status(thm)],[337, 41])).
% 52.06/52.27 tff(339,plain,
% 52.06/52.27 (addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(star(X0!0), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 52.06/52.27 inference(monotonicity,[status(thm)],[236])).
% 52.06/52.27 tff(340,plain,
% 52.06/52.27 (addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.27 inference(transitivity,[status(thm)],[339, 338])).
% 52.06/52.27 tff(341,plain,
% 52.06/52.27 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(addition(star(X0!0), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.27 inference(monotonicity,[status(thm)],[340])).
% 52.06/52.27 tff(342,plain,
% 52.06/52.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.06/52.27 inference(quant_inst,[status(thm)],[])).
% 52.06/52.27 tff(343,plain,
% 52.06/52.27 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.27 inference(unit_resolution,[status(thm)],[342, 41])).
% 52.06/52.27 tff(344,plain,
% 52.06/52.27 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), 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), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.06/52.27 inference(quant_inst,[status(thm)],[])).
% 52.06/52.27 tff(345,plain,
% 52.06/52.27 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), 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), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.06/52.27 inference(unit_resolution,[status(thm)],[344, 28])).
% 52.06/52.27 tff(346,plain,
% 52.06/52.27 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.06/52.27 inference(monotonicity,[status(thm)],[245])).
% 52.06/52.27 tff(347,plain,
% 52.06/52.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 52.06/52.27 inference(quant_inst,[status(thm)],[])).
% 52.06/52.27 tff(348,plain,
% 52.06/52.27 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.27 inference(unit_resolution,[status(thm)],[347, 41])).
% 52.06/52.27 tff(349,plain,
% 52.06/52.27 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))))),
% 52.06/52.27 inference(symmetry,[status(thm)],[348])).
% 52.06/52.27 tff(350,plain,
% 52.06/52.27 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 52.06/52.27 inference(monotonicity,[status(thm)],[87])).
% 52.06/52.27 tff(351,plain,
% 52.06/52.27 (addition(multiplication(star(X0!0), star(star(X0!0))), one) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one)),
% 52.06/52.27 inference(symmetry,[status(thm)],[350])).
% 52.06/52.27 tff(352,plain,
% 52.06/52.27 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.27 inference(monotonicity,[status(thm)],[351])).
% 52.06/52.27 tff(353,plain,
% 52.06/52.27 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.06/52.27 inference(quant_inst,[status(thm)],[])).
% 52.06/52.27 tff(354,plain,
% 52.06/52.27 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.06/52.27 inference(unit_resolution,[status(thm)],[353, 28])).
% 52.06/52.27 tff(355,plain,
% 52.06/52.27 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))))),
% 52.06/52.27 inference(symmetry,[status(thm)],[354])).
% 52.06/52.27 tff(356,plain,
% 52.06/52.27 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.06/52.27 inference(quant_inst,[status(thm)],[])).
% 52.06/52.27 tff(357,plain,
% 52.06/52.27 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 52.06/52.27 inference(unit_resolution,[status(thm)],[356, 80])).
% 52.06/52.27 tff(358,plain,
% 52.06/52.27 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.06/52.27 inference(monotonicity,[status(thm)],[350])).
% 52.06/52.27 tff(359,plain,
% 52.06/52.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.06/52.27 inference(quant_inst,[status(thm)],[])).
% 52.06/52.27 tff(360,plain,
% 52.06/52.27 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.06/52.27 inference(unit_resolution,[status(thm)],[359, 41])).
% 52.06/52.27 tff(361,plain,
% 52.06/52.27 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 52.06/52.27 inference(transitivity,[status(thm)],[360, 358, 357])).
% 52.06/52.27 tff(362,plain,
% 52.06/52.27 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.06/52.27 inference(monotonicity,[status(thm)],[361])).
% 52.06/52.27 tff(363,plain,
% 52.06/52.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))))),
% 52.13/52.27 inference(quant_inst,[status(thm)],[])).
% 52.13/52.27 tff(364,plain,
% 52.13/52.27 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.27 inference(unit_resolution,[status(thm)],[363, 41])).
% 52.13/52.27 tff(365,plain,
% 52.13/52.27 (addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))))),
% 52.13/52.27 inference(symmetry,[status(thm)],[364])).
% 52.13/52.27 tff(366,plain,
% 52.13/52.27 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.27 inference(monotonicity,[status(thm)],[331])).
% 52.13/52.27 tff(367,plain,
% 52.13/52.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))))),
% 52.13/52.27 inference(quant_inst,[status(thm)],[])).
% 52.13/52.27 tff(368,plain,
% 52.13/52.27 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(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)))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[367, 41])).
% 52.13/52.28 tff(369,plain,
% 52.13/52.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.28 inference(quant_inst,[status(thm)],[])).
% 52.13/52.28 tff(370,plain,
% 52.13/52.28 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[369, 41])).
% 52.13/52.28 tff(371,plain,
% 52.13/52.28 (addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.28 inference(symmetry,[status(thm)],[370])).
% 52.13/52.28 tff(372,plain,
% 52.13/52.28 (addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[127])).
% 52.13/52.28 tff(373,plain,
% 52.13/52.28 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.13/52.28 inference(symmetry,[status(thm)],[372])).
% 52.13/52.28 tff(374,plain,
% 52.13/52.28 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.28 inference(transitivity,[status(thm)],[373, 371])).
% 52.13/52.28 tff(375,plain,
% 52.13/52.28 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, addition(multiplication(star(X0!0), star(star(X0!0))), one))))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[374])).
% 52.13/52.28 tff(376,plain,
% 52.13/52.28 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.28 inference(quant_inst,[status(thm)],[])).
% 52.13/52.28 tff(377,plain,
% 52.13/52.28 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[376, 28])).
% 52.13/52.28 tff(378,plain,
% 52.13/52.28 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[351])).
% 52.13/52.28 tff(379,plain,
% 52.13/52.28 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.13/52.28 inference(symmetry,[status(thm)],[378])).
% 52.13/52.28 tff(380,plain,
% 52.13/52.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 52.13/52.28 inference(quant_inst,[status(thm)],[])).
% 52.13/52.28 tff(381,plain,
% 52.13/52.28 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[380, 41])).
% 52.13/52.28 tff(382,plain,
% 52.13/52.28 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.13/52.28 inference(transitivity,[status(thm)],[381, 379, 377])).
% 52.13/52.28 tff(383,plain,
% 52.13/52.28 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[382])).
% 52.13/52.28 tff(384,plain,
% 52.13/52.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))))),
% 52.13/52.28 inference(quant_inst,[status(thm)],[])).
% 52.13/52.28 tff(385,plain,
% 52.13/52.28 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[384, 41])).
% 52.13/52.28 tff(386,plain,
% 52.13/52.28 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))))),
% 52.13/52.28 inference(symmetry,[status(thm)],[385])).
% 52.13/52.28 tff(387,plain,
% 52.13/52.28 (addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.13/52.28 inference(symmetry,[status(thm)],[82])).
% 52.13/52.28 tff(388,plain,
% 52.13/52.28 (addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one))) = addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[387])).
% 52.13/52.28 tff(389,plain,
% 52.13/52.28 (addition(addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, addition(multiplication(star(star(X0!0)), star(X0!0)), one)))),
% 52.13/52.28 inference(symmetry,[status(thm)],[381])).
% 52.13/52.28 tff(390,plain,
% 52.13/52.28 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), addition(multiplication(star(star(X0!0)), star(X0!0)), one))),
% 52.13/52.28 inference(symmetry,[status(thm)],[377])).
% 52.13/52.28 tff(391,plain,
% 52.13/52.28 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.13/52.28 inference(transitivity,[status(thm)],[390, 378, 389, 388, 386, 383, 375, 368, 366, 365, 362, 355, 352, 349, 346, 345])).
% 52.13/52.28 tff(392,plain,
% 52.13/52.28 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[391])).
% 52.13/52.28 tff(393,plain,
% 52.13/52.28 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0)))),
% 52.13/52.28 inference(quant_inst,[status(thm)],[])).
% 52.13/52.28 tff(394,plain,
% 52.13/52.28 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0))),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[393, 28])).
% 52.13/52.28 tff(395,plain,
% 52.13/52.28 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0)) = addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.28 inference(symmetry,[status(thm)],[394])).
% 52.13/52.28 tff(396,plain,
% 52.13/52.28 ((~![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(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0)))),
% 52.13/52.28 inference(quant_inst,[status(thm)],[])).
% 52.13/52.28 tff(397,plain,
% 52.13/52.28 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0))),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[396, 41])).
% 52.13/52.28 tff(398,plain,
% 52.13/52.28 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[316])).
% 52.13/52.28 tff(399,plain,
% 52.13/52.28 (addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)) = addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.13/52.28 inference(symmetry,[status(thm)],[316])).
% 52.13/52.28 tff(400,plain,
% 52.13/52.28 ((~![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))),
% 52.13/52.28 inference(quant_inst,[status(thm)],[])).
% 52.13/52.28 tff(401,plain,
% 52.13/52.28 (addition(one, multiplication(X0!0, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), one)),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[400, 28])).
% 52.13/52.28 tff(402,plain,
% 52.13/52.28 (addition(multiplication(X0!0, star(X0!0)), one) = addition(one, multiplication(X0!0, star(X0!0)))),
% 52.13/52.28 inference(symmetry,[status(thm)],[401])).
% 52.13/52.28 tff(403,plain,
% 52.13/52.28 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[402])).
% 52.13/52.28 tff(404,plain,
% 52.13/52.28 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = star(X0!0)),
% 52.13/52.28 inference(transitivity,[status(thm)],[403, 271])).
% 52.13/52.28 tff(405,plain,
% 52.13/52.28 (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))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[404])).
% 52.13/52.28 tff(406,plain,
% 52.13/52.28 ((~![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))))),
% 52.13/52.28 inference(quant_inst,[status(thm)],[])).
% 52.13/52.28 tff(407,plain,
% 52.13/52.28 (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)))),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[406, 70])).
% 52.13/52.28 tff(408,plain,
% 52.13/52.28 (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)))),
% 52.13/52.28 inference(symmetry,[status(thm)],[407])).
% 52.13/52.28 tff(409,plain,
% 52.13/52.28 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), 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)))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[126])).
% 52.13/52.28 tff(410,plain,
% 52.13/52.28 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))) = multiplication(star(star(X0!0)), star(X0!0))),
% 52.13/52.28 inference(transitivity,[status(thm)],[409, 408, 405])).
% 52.13/52.28 tff(411,plain,
% 52.13/52.28 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), one) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 52.13/52.28 inference(monotonicity,[status(thm)],[410])).
% 52.13/52.28 tff(412,plain,
% 52.13/52.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one)) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), one))),
% 52.13/52.28 inference(quant_inst,[status(thm)],[])).
% 52.13/52.28 tff(413,plain,
% 52.13/52.28 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one)) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), one)),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[412, 41])).
% 52.13/52.28 tff(414,plain,
% 52.13/52.28 (addition(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)), multiplication(star(star(X0!0)), star(X0!0))), one)),
% 52.13/52.28 inference(symmetry,[status(thm)],[127])).
% 52.13/52.28 tff(415,plain,
% 52.13/52.28 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[60, 300])).
% 52.13/52.28 tff(416,plain,
% 52.13/52.28 ((~![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(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))))),
% 52.13/52.28 inference(quant_inst,[status(thm)],[])).
% 52.13/52.28 tff(417,plain,
% 52.13/52.28 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0)))),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[416, 41])).
% 52.13/52.28 tff(418,plain,
% 52.13/52.28 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))))),
% 52.13/52.28 inference(symmetry,[status(thm)],[417])).
% 52.13/52.28 tff(419,plain,
% 52.13/52.28 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))) = star(star(X0!0))),
% 52.13/52.28 inference(transitivity,[status(thm)],[418, 415, 57])).
% 52.13/52.28 tff(420,plain,
% 52.13/52.28 (multiplication(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[419])).
% 52.13/52.28 tff(421,plain,
% 52.13/52.28 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))))),
% 52.13/52.28 inference(quant_inst,[status(thm)],[])).
% 52.13/52.28 tff(422,plain,
% 52.13/52.28 (multiplication(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)))),
% 52.13/52.28 inference(unit_resolution,[status(thm)],[421, 122])).
% 52.13/52.28 tff(423,plain,
% 52.13/52.28 (addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))) = multiplication(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one))),
% 52.13/52.28 inference(symmetry,[status(thm)],[422])).
% 52.13/52.28 tff(424,plain,
% 52.13/52.28 (addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))) = multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 52.13/52.28 inference(transitivity,[status(thm)],[423, 420])).
% 52.13/52.28 tff(425,plain,
% 52.13/52.28 (addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), one))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[424, 414])).
% 52.13/52.28 tff(426,plain,
% 52.13/52.28 (addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), star(X0!0)), one)),
% 52.13/52.28 inference(transitivity,[status(thm)],[425, 413, 411])).
% 52.13/52.28 tff(427,plain,
% 52.13/52.28 (addition(addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(star(X0!0), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.28 inference(monotonicity,[status(thm)],[426, 399])).
% 52.13/52.28 tff(428,plain,
% 52.13/52.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))) = addition(addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(429,plain,
% 52.13/52.29 (addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))) = addition(addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[428, 41])).
% 52.13/52.29 tff(430,plain,
% 52.13/52.29 (addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(X0!0)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 52.13/52.29 inference(symmetry,[status(thm)],[397])).
% 52.13/52.29 tff(431,plain,
% 52.13/52.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(432,plain,
% 52.13/52.29 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[431, 41])).
% 52.13/52.29 tff(433,plain,
% 52.13/52.29 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.29 inference(symmetry,[status(thm)],[432])).
% 52.13/52.29 tff(434,plain,
% 52.13/52.29 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0)))),
% 52.13/52.29 inference(transitivity,[status(thm)],[433, 394, 430])).
% 52.13/52.29 tff(435,plain,
% 52.13/52.29 (multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(addition(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))), addition(multiplication(X0!0, star(X0!0)), one))),
% 52.13/52.29 inference(symmetry,[status(thm)],[420])).
% 52.13/52.29 tff(436,plain,
% 52.13/52.29 (multiplication(X0!0, star(X0!0)) = multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 52.13/52.29 inference(monotonicity,[status(thm)],[218])).
% 52.13/52.29 tff(437,plain,
% 52.13/52.29 (multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 52.13/52.29 inference(symmetry,[status(thm)],[436])).
% 52.13/52.29 tff(438,plain,
% 52.13/52.29 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(439,plain,
% 52.13/52.29 (multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[438, 70])).
% 52.13/52.29 tff(440,plain,
% 52.13/52.29 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 52.13/52.29 inference(symmetry,[status(thm)],[439])).
% 52.13/52.29 tff(441,plain,
% 52.13/52.29 (addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 52.13/52.29 inference(transitivity,[status(thm)],[440, 437])).
% 52.13/52.29 tff(442,plain,
% 52.13/52.29 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one) = addition(multiplication(X0!0, star(X0!0)), one)),
% 52.13/52.29 inference(monotonicity,[status(thm)],[441])).
% 52.13/52.29 tff(443,plain,
% 52.13/52.29 (addition(multiplication(X0!0, star(X0!0)), one) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)),
% 52.13/52.29 inference(symmetry,[status(thm)],[442])).
% 52.13/52.29 tff(444,plain,
% 52.13/52.29 (multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one))),
% 52.13/52.29 inference(monotonicity,[status(thm)],[443])).
% 52.13/52.29 tff(445,plain,
% 52.13/52.29 (multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)) = multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 52.13/52.29 inference(symmetry,[status(thm)],[444])).
% 52.13/52.29 tff(446,plain,
% 52.13/52.29 ((~![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, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(447,plain,
% 52.13/52.29 (multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one)) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[446, 70])).
% 52.13/52.29 tff(448,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)) = multiplication(star(star(X0!0)), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), one))),
% 52.13/52.29 inference(symmetry,[status(thm)],[447])).
% 52.13/52.29 tff(449,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), star(star(X0!0)))),
% 52.13/52.29 inference(monotonicity,[status(thm)],[146])).
% 52.13/52.29 tff(450,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), star(star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one))),
% 52.13/52.29 inference(symmetry,[status(thm)],[449])).
% 52.13/52.29 tff(451,plain,
% 52.13/52.29 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(star(star(X0!0)), one), star(star(X0!0))) <=> (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0))))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(452,plain,
% 52.13/52.29 (leq(multiplication(star(star(X0!0)), one), star(star(X0!0))) <=> (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0)))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[451, 7])).
% 52.13/52.29 tff(453,plain,
% 52.13/52.29 (leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))) <=> leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 52.13/52.29 inference(monotonicity,[status(thm)],[31])).
% 52.13/52.29 tff(454,plain,
% 52.13/52.29 (leq(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) <=> leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))),
% 52.13/52.29 inference(symmetry,[status(thm)],[453])).
% 52.13/52.29 tff(455,plain,
% 52.13/52.29 (leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))),
% 52.13/52.29 inference(modus_ponens,[status(thm)],[18, 454])).
% 52.13/52.29 tff(456,plain,
% 52.13/52.29 (^[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)))),
% 52.13/52.29 inference(bind,[status(th)],[])).
% 52.13/52.29 tff(457,plain,
% 52.13/52.29 (![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))),
% 52.13/52.29 inference(quant_intro,[status(thm)],[456])).
% 52.13/52.29 tff(458,plain,
% 52.13/52.29 (![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))),
% 52.13/52.29 inference(rewrite,[status(thm)],[])).
% 52.13/52.29 tff(459,plain,
% 52.13/52.29 (^[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)))),
% 52.13/52.29 inference(bind,[status(th)],[])).
% 52.13/52.29 tff(460,plain,
% 52.13/52.29 (![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))),
% 52.13/52.29 inference(quant_intro,[status(thm)],[459])).
% 52.13/52.29 tff(461,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')).
% 52.13/52.29 tff(462,plain,
% 52.13/52.29 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 52.13/52.29 inference(modus_ponens,[status(thm)],[461, 460])).
% 52.13/52.29 tff(463,plain,
% 52.13/52.29 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 52.13/52.29 inference(modus_ponens,[status(thm)],[462, 458])).
% 52.13/52.29 tff(464,plain,(
% 52.13/52.29 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 52.13/52.29 inference(skolemize,[status(sab)],[463])).
% 52.13/52.29 tff(465,plain,
% 52.13/52.29 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 52.13/52.29 inference(modus_ponens,[status(thm)],[464, 457])).
% 52.13/52.29 tff(466,plain,
% 52.13/52.29 (((~![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(star(X0!0))), one), star(star(X0!0)))) | leq(multiplication(star(star(X0!0)), one), star(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(star(X0!0))), one), star(star(X0!0)))) | leq(multiplication(star(star(X0!0)), one), star(star(X0!0))))),
% 52.13/52.29 inference(rewrite,[status(thm)],[])).
% 52.13/52.29 tff(467,plain,
% 52.13/52.29 ((~![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(star(X0!0))), one), star(star(X0!0)))) | leq(multiplication(star(star(X0!0)), one), star(star(X0!0))))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(468,plain,
% 52.13/52.29 ((~![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(star(X0!0))), one), star(star(X0!0)))) | leq(multiplication(star(star(X0!0)), one), star(star(X0!0)))),
% 52.13/52.29 inference(modus_ponens,[status(thm)],[467, 466])).
% 52.13/52.29 tff(469,plain,
% 52.13/52.29 ((~leq(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) | leq(multiplication(star(star(X0!0)), one), star(star(X0!0)))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[468, 465])).
% 52.13/52.29 tff(470,plain,
% 52.13/52.29 (leq(multiplication(star(star(X0!0)), one), star(star(X0!0)))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[469, 455])).
% 52.13/52.29 tff(471,plain,
% 52.13/52.29 ((~(leq(multiplication(star(star(X0!0)), one), star(star(X0!0))) <=> (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0))))) | (~leq(multiplication(star(star(X0!0)), one), star(star(X0!0)))) | (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0)))),
% 52.13/52.29 inference(tautology,[status(thm)],[])).
% 52.13/52.29 tff(472,plain,
% 52.13/52.29 ((~(leq(multiplication(star(star(X0!0)), one), star(star(X0!0))) <=> (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0))))) | (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0)))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[471, 470])).
% 52.13/52.29 tff(473,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), one), star(star(X0!0))) = star(star(X0!0))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[472, 452])).
% 52.13/52.29 tff(474,plain,
% 52.13/52.29 (star(star(X0!0)) = addition(multiplication(star(star(X0!0)), one), star(star(X0!0)))),
% 52.13/52.29 inference(symmetry,[status(thm)],[473])).
% 52.13/52.29 tff(475,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), star(star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(multiplication(star(star(X0!0)), one), star(star(X0!0))))),
% 52.13/52.29 inference(monotonicity,[status(thm)],[474])).
% 52.13/52.29 tff(476,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(multiplication(star(star(X0!0)), one), star(star(X0!0)))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), star(star(X0!0)))),
% 52.13/52.29 inference(symmetry,[status(thm)],[475])).
% 52.13/52.29 tff(477,plain,
% 52.13/52.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(multiplication(star(star(X0!0)), one), star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)), star(star(X0!0))))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(478,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(multiplication(star(star(X0!0)), one), star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)), star(star(X0!0)))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[477, 41])).
% 52.13/52.29 tff(479,plain,
% 52.13/52.29 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)), star(star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(multiplication(star(star(X0!0)), one), star(star(X0!0))))),
% 52.13/52.29 inference(symmetry,[status(thm)],[478])).
% 52.13/52.29 tff(480,plain,
% 52.13/52.29 (addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0)))) = addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0))))),
% 52.13/52.29 inference(monotonicity,[status(thm)],[126])).
% 52.13/52.29 tff(481,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0)))) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))),
% 52.13/52.29 inference(symmetry,[status(thm)],[480])).
% 52.13/52.29 tff(482,plain,
% 52.13/52.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(483,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[482, 41])).
% 52.13/52.29 tff(484,plain,
% 52.13/52.29 (addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))) = addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0))))),
% 52.13/52.29 inference(symmetry,[status(thm)],[483])).
% 52.13/52.29 tff(485,plain,
% 52.13/52.29 (addition(addition(one, multiplication(star(star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))),
% 52.13/52.29 inference(symmetry,[status(thm)],[61])).
% 52.13/52.29 tff(486,plain,
% 52.13/52.29 (star(star(X0!0)) = addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))),
% 52.13/52.29 inference(transitivity,[status(thm)],[183, 485, 484, 481])).
% 52.13/52.29 tff(487,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)) = multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 52.13/52.29 inference(transitivity,[status(thm)],[448, 445])).
% 52.13/52.29 tff(488,plain,
% 52.13/52.29 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)), star(star(X0!0))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0)))))),
% 52.13/52.29 inference(monotonicity,[status(thm)],[487, 486])).
% 52.13/52.29 tff(489,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), multiplication(star(star(X0!0)), one)), star(star(X0!0)))),
% 52.13/52.29 inference(symmetry,[status(thm)],[488])).
% 52.13/52.29 tff(490,plain,
% 52.13/52.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0)))))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(491,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0))))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0))))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[490, 41])).
% 52.13/52.29 tff(492,plain,
% 52.13/52.29 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0)))) = addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0))), addition(one, star(star(X0!0)))))),
% 52.13/52.29 inference(symmetry,[status(thm)],[491])).
% 52.13/52.29 tff(493,plain,
% 52.13/52.29 (addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0)))) = addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0))))),
% 52.13/52.29 inference(monotonicity,[status(thm)],[410])).
% 52.13/52.29 tff(494,plain,
% 52.13/52.29 (addition(multiplication(star(star(X0!0)), star(X0!0)), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(X0!0)), multiplication(star(star(X0!0)), star(X0!0)))), addition(one, star(star(X0!0))))),
% 52.13/52.29 inference(symmetry,[status(thm)],[493])).
% 52.13/52.29 tff(495,plain,
% 52.13/52.29 (star(star(X0!0)) = addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)))),
% 52.13/52.29 inference(transitivity,[status(thm)],[183, 485, 484, 494, 492, 489, 479, 476, 450, 448, 445, 435, 422])).
% 52.13/52.29 tff(496,plain,
% 52.13/52.29 (addition(star(star(X0!0)), addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one))) = addition(addition(multiplication(addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(multiplication(star(X0!0), star(star(X0!0))), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(X0!0))))),
% 52.13/52.29 inference(monotonicity,[status(thm)],[495, 434])).
% 52.13/52.29 tff(497,plain,
% 52.13/52.29 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))) = addition(star(star(X0!0)), addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one))))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(498,plain,
% 52.13/52.29 (addition(addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))) = addition(star(star(X0!0)), addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[497, 28])).
% 52.13/52.29 tff(499,plain,
% 52.13/52.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0))))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(500,plain,
% 52.13/52.29 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))) = addition(addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(multiplication(star(X0!0), star(star(X0!0))), one)), star(star(X0!0)))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[499, 41])).
% 52.13/52.29 tff(501,plain,
% 52.13/52.29 (star(star(X0!0)) = addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0)))),
% 52.13/52.29 inference(transitivity,[status(thm)],[92, 91])).
% 52.13/52.29 tff(502,plain,
% 52.13/52.29 (addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), addition(addition(multiplication(star(X0!0), star(star(X0!0))), one), star(star(X0!0))))),
% 52.13/52.29 inference(monotonicity,[status(thm)],[501])).
% 52.13/52.29 tff(503,plain,
% 52.13/52.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0))))),
% 52.13/52.29 inference(quant_inst,[status(thm)],[])).
% 52.13/52.29 tff(504,plain,
% 52.13/52.29 (addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))) = addition(addition(star(X0!0), addition(multiplication(star(star(X0!0)), star(X0!0)), one)), star(star(X0!0)))),
% 52.13/52.29 inference(unit_resolution,[status(thm)],[503, 41])).
% 52.13/52.29 tff(505,plain,
% 52.13/52.29 (star(star(X0!0)) = addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0)))),
% 52.13/52.29 inference(transitivity,[status(thm)],[183, 485])).
% 52.13/52.29 tff(506,plain,
% 52.13/52.29 (addition(star(X0!0), star(star(X0!0))) = addition(star(X0!0), addition(addition(multiplication(star(star(X0!0)), star(X0!0)), one), star(star(X0!0))))),
% 52.13/52.29 inference(monotonicity,[status(thm)],[505])).
% 52.13/52.29 tff(507,plain,
% 52.13/52.29 (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))),
% 52.13/52.29 inference(transitivity,[status(thm)],[506, 504, 502, 500, 498, 496, 429, 427, 398, 397, 395, 392, 343, 341, 336, 333, 329, 327, 317, 312, 310, 286, 283, 264, 261, 255, 252, 242, 233, 231, 209, 207, 206, 195, 194, 191, 187, 176, 153, 150, 148, 147, 137, 130, 128, 109, 106, 103, 100, 97, 96, 86, 84, 43, 34, 21])).
% 52.13/52.30 tff(508,assumption,(~leq(star(X0!0), star(star(X0!0)))), introduced(assumption)).
% 52.13/52.30 tff(509,plain,
% 52.13/52.30 ((~(leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))) | leq(star(X0!0), star(star(X0!0))) | (~(addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))),
% 52.13/52.30 inference(tautology,[status(thm)],[])).
% 52.13/52.30 tff(510,plain,
% 52.13/52.30 ((~(leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))) | (~(addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[509, 508])).
% 52.13/52.30 tff(511,plain,
% 52.13/52.30 (~(addition(star(X0!0), star(star(X0!0))) = star(star(X0!0)))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[510, 33])).
% 52.13/52.30 tff(512,plain,
% 52.13/52.30 ($false),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[511, 507])).
% 52.13/52.30 tff(513,plain,(leq(star(X0!0), star(star(X0!0)))), inference(lemma,lemma(discharge,[]))).
% 52.13/52.30 tff(514,plain,
% 52.13/52.30 ((~(leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))) | (~leq(star(X0!0), star(star(X0!0)))) | (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0)))),
% 52.13/52.30 inference(tautology,[status(thm)],[])).
% 52.13/52.30 tff(515,plain,
% 52.13/52.30 ((~(leq(star(X0!0), star(star(X0!0))) <=> (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))))) | (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0)))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[514, 513])).
% 52.13/52.30 tff(516,plain,
% 52.13/52.30 (addition(star(X0!0), star(star(X0!0))) = star(star(X0!0))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[515, 33])).
% 52.13/52.30 tff(517,plain,
% 52.13/52.30 (multiplication(star(X0!0), addition(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), star(star(X0!0)))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[516])).
% 52.13/52.30 tff(518,plain,
% 52.13/52.30 ((~![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(star(X0!0)))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(519,plain,
% 52.13/52.30 (multiplication(star(X0!0), addition(star(X0!0), star(star(X0!0)))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[518, 70])).
% 52.13/52.30 tff(520,plain,
% 52.13/52.30 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), addition(star(X0!0), star(star(X0!0))))),
% 52.13/52.30 inference(symmetry,[status(thm)],[519])).
% 52.13/52.30 tff(521,plain,
% 52.13/52.30 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(star(X0!0), star(star(X0!0)))),
% 52.13/52.30 inference(transitivity,[status(thm)],[520, 517])).
% 52.13/52.30 tff(522,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one) = addition(multiplication(star(X0!0), star(star(X0!0))), one)),
% 52.13/52.30 inference(monotonicity,[status(thm)],[521])).
% 52.13/52.30 tff(523,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one) = addition(one, multiplication(star(X0!0), star(star(X0!0))))),
% 52.13/52.30 inference(transitivity,[status(thm)],[522, 31])).
% 52.13/52.30 tff(524,plain,
% 52.13/52.30 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), 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)))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[523])).
% 52.13/52.30 tff(525,plain,
% 52.13/52.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), star(star(X0!0))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(526,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), star(star(X0!0)))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[525, 41])).
% 52.13/52.30 tff(527,plain,
% 52.13/52.30 (multiplication(star(X0!0), star(star(X0!0))) = multiplication(star(X0!0), addition(star(X0!0), star(star(X0!0))))),
% 52.13/52.30 inference(symmetry,[status(thm)],[517])).
% 52.13/52.30 tff(528,plain,
% 52.13/52.30 ((~![A: $i] : (addition(A, A) = A)) | (addition(star(X0!0), star(X0!0)) = star(X0!0))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(529,plain,
% 52.13/52.30 (addition(star(X0!0), star(X0!0)) = star(X0!0)),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[528, 80])).
% 52.13/52.30 tff(530,plain,
% 52.13/52.30 (multiplication(addition(star(X0!0), star(X0!0)), star(star(X0!0))) = multiplication(star(X0!0), star(star(X0!0)))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[529])).
% 52.13/52.30 tff(531,plain,
% 52.13/52.30 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(star(X0!0), star(X0!0)), star(star(X0!0))) = addition(multiplication(star(X0!0), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(532,plain,
% 52.13/52.30 (multiplication(addition(star(X0!0), star(X0!0)), star(star(X0!0))) = addition(multiplication(star(X0!0), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[531, 122])).
% 52.13/52.30 tff(533,plain,
% 52.13/52.30 (addition(multiplication(star(X0!0), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(addition(star(X0!0), star(X0!0)), star(star(X0!0)))),
% 52.13/52.30 inference(symmetry,[status(thm)],[532])).
% 52.13/52.30 tff(534,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[521, 521])).
% 52.13/52.30 tff(535,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))),
% 52.13/52.30 inference(transitivity,[status(thm)],[534, 533, 530, 527, 519])).
% 52.13/52.30 tff(536,plain,
% 52.13/52.30 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[535])).
% 52.13/52.30 tff(537,plain,
% 52.13/52.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0)))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(538,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0))))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[537, 41])).
% 52.13/52.30 tff(539,plain,
% 52.13/52.30 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 52.13/52.30 inference(symmetry,[status(thm)],[526])).
% 52.13/52.30 tff(540,plain,
% 52.13/52.30 (addition(addition(one, multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), one), star(star(X0!0)))),
% 52.13/52.30 inference(symmetry,[status(thm)],[524])).
% 52.13/52.30 tff(541,plain,
% 52.13/52.30 (star(star(X0!0)) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))),
% 52.13/52.30 inference(transitivity,[status(thm)],[92, 540, 539])).
% 52.13/52.30 tff(542,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[541])).
% 52.13/52.30 tff(543,plain,
% 52.13/52.30 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(544,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[543, 28])).
% 52.13/52.30 tff(545,plain,
% 52.13/52.30 (addition(star(star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 52.13/52.30 inference(symmetry,[status(thm)],[544])).
% 52.13/52.30 tff(546,plain,
% 52.13/52.30 ((~![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)))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(547,plain,
% 52.13/52.30 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[546, 41])).
% 52.13/52.30 tff(548,plain,
% 52.13/52.30 (multiplication(X0!0, addition(star(X0!0), star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[529])).
% 52.13/52.30 tff(549,plain,
% 52.13/52.30 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(star(X0!0), star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(550,plain,
% 52.13/52.30 (multiplication(X0!0, addition(star(X0!0), star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0)))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[549, 70])).
% 52.13/52.30 tff(551,plain,
% 52.13/52.30 (addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, addition(star(X0!0), star(X0!0)))),
% 52.13/52.30 inference(symmetry,[status(thm)],[550])).
% 52.13/52.30 tff(552,plain,
% 52.13/52.30 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, star(X0!0)))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[441, 441])).
% 52.13/52.30 tff(553,plain,
% 52.13/52.30 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = multiplication(X0!0, star(X0!0))),
% 52.13/52.30 inference(transitivity,[status(thm)],[552, 551, 548])).
% 52.13/52.30 tff(554,plain,
% 52.13/52.30 (addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), 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)))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[553])).
% 52.13/52.30 tff(555,plain,
% 52.13/52.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(556,plain,
% 52.13/52.30 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0)))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[555, 41])).
% 52.13/52.30 tff(557,plain,
% 52.13/52.30 (addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), 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)))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[441])).
% 52.13/52.30 tff(558,plain,
% 52.13/52.30 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))),
% 52.13/52.30 inference(symmetry,[status(thm)],[557])).
% 52.13/52.30 tff(559,plain,
% 52.13/52.30 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 52.13/52.30 inference(symmetry,[status(thm)],[547])).
% 52.13/52.30 tff(560,plain,
% 52.13/52.30 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 52.13/52.30 inference(symmetry,[status(thm)],[403])).
% 52.13/52.30 tff(561,plain,
% 52.13/52.30 (star(X0!0) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 52.13/52.30 inference(symmetry,[status(thm)],[271])).
% 52.13/52.30 tff(562,plain,
% 52.13/52.30 (star(X0!0) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))),
% 52.13/52.30 inference(transitivity,[status(thm)],[561, 560, 559, 558])).
% 52.13/52.30 tff(563,plain,
% 52.13/52.30 (multiplication(X0!0, star(X0!0)) = addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))),
% 52.13/52.30 inference(transitivity,[status(thm)],[436, 439])).
% 52.13/52.30 tff(564,plain,
% 52.13/52.30 (addition(multiplication(X0!0, star(X0!0)), star(X0!0)) = addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[563, 562])).
% 52.13/52.30 tff(565,plain,
% 52.13/52.30 (addition(multiplication(X0!0, star(X0!0)), star(X0!0)) = star(X0!0)),
% 52.13/52.30 inference(transitivity,[status(thm)],[564, 556, 554, 547, 403, 271])).
% 52.13/52.30 tff(566,plain,
% 52.13/52.30 (multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(star(X0!0))) = multiplication(star(X0!0), star(star(X0!0)))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[565])).
% 52.13/52.30 tff(567,plain,
% 52.13/52.30 (multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))),
% 52.13/52.30 inference(transitivity,[status(thm)],[566, 527, 519])).
% 52.13/52.30 tff(568,plain,
% 52.13/52.30 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(star(X0!0))) = star(star(X0!0)))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(569,plain,
% 52.13/52.30 (multiplication(one, star(star(X0!0))) = star(star(X0!0))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[568, 202])).
% 52.13/52.30 tff(570,plain,
% 52.13/52.30 (addition(multiplication(one, star(star(X0!0))), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(star(X0!0)))) = addition(star(star(X0!0)), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[569, 567])).
% 52.13/52.30 tff(571,plain,
% 52.13/52.30 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(multiplication(one, star(star(X0!0))), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(star(X0!0)))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(572,plain,
% 52.13/52.30 (multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), star(star(X0!0))) = addition(multiplication(one, star(star(X0!0))), multiplication(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(star(X0!0))))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[571, 122])).
% 52.13/52.30 tff(573,plain,
% 52.13/52.30 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))),
% 52.13/52.30 inference(symmetry,[status(thm)],[273])).
% 52.13/52.30 tff(574,plain,
% 52.13/52.30 (star(X0!0) = addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0)))),
% 52.13/52.30 inference(transitivity,[status(thm)],[561, 573])).
% 52.13/52.30 tff(575,plain,
% 52.13/52.30 (multiplication(star(X0!0), star(star(X0!0))) = multiplication(addition(one, addition(multiplication(X0!0, star(X0!0)), star(X0!0))), star(star(X0!0)))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[574])).
% 52.13/52.30 tff(576,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = star(X0!0)),
% 52.13/52.30 inference(transitivity,[status(thm)],[213, 163])).
% 52.13/52.30 tff(577,plain,
% 52.13/52.30 (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), star(star(X0!0))) = multiplication(star(X0!0), star(star(X0!0)))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[576])).
% 52.13/52.30 tff(578,plain,
% 52.13/52.30 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), star(star(X0!0))) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(579,plain,
% 52.13/52.30 (multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), star(star(X0!0))) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[578, 122])).
% 52.13/52.30 tff(580,plain,
% 52.13/52.30 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), star(star(X0!0)))),
% 52.13/52.30 inference(symmetry,[status(thm)],[579])).
% 52.13/52.30 tff(581,plain,
% 52.13/52.30 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0))), multiplication(star(X0!0), star(star(X0!0))))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[521])).
% 52.13/52.30 tff(582,plain,
% 52.13/52.30 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0)))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(583,plain,
% 52.13/52.30 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0))))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[582, 28])).
% 52.13/52.30 tff(584,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0)))) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.13/52.30 inference(symmetry,[status(thm)],[583])).
% 52.13/52.30 tff(585,plain,
% 52.13/52.30 (addition(multiplication(star(X0!0), X0!0), one) = addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one)),
% 52.13/52.30 inference(symmetry,[status(thm)],[225])).
% 52.13/52.30 tff(586,plain,
% 52.13/52.30 (multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0))) = multiplication(addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one), star(star(X0!0)))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[585])).
% 52.13/52.30 tff(587,plain,
% 52.13/52.30 (multiplication(addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one), star(star(X0!0))) = multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0)))),
% 52.13/52.30 inference(symmetry,[status(thm)],[586])).
% 52.13/52.30 tff(588,plain,
% 52.13/52.30 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one), star(star(X0!0))) = addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), multiplication(one, star(star(X0!0)))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(589,plain,
% 52.13/52.30 (multiplication(addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one), star(star(X0!0))) = addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), multiplication(one, star(star(X0!0))))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[588, 122])).
% 52.13/52.30 tff(590,plain,
% 52.13/52.30 (addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), multiplication(one, star(star(X0!0)))) = multiplication(addition(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), one), star(star(X0!0)))),
% 52.13/52.30 inference(symmetry,[status(thm)],[589])).
% 52.13/52.30 tff(591,plain,
% 52.13/52.30 (addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), multiplication(one, star(star(X0!0)))) = multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0)))),
% 52.13/52.30 inference(transitivity,[status(thm)],[590, 587])).
% 52.13/52.30 tff(592,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), multiplication(one, star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0))))),
% 52.13/52.30 inference(monotonicity,[status(thm)],[591])).
% 52.13/52.30 tff(593,plain,
% 52.13/52.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), multiplication(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0)))), multiplication(one, star(star(X0!0)))))),
% 52.13/52.30 inference(quant_inst,[status(thm)],[])).
% 52.13/52.30 tff(594,plain,
% 52.13/52.30 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), multiplication(one, star(star(X0!0))))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0)))), multiplication(one, star(star(X0!0))))),
% 52.13/52.30 inference(unit_resolution,[status(thm)],[593, 41])).
% 52.13/52.30 tff(595,plain,
% 52.13/52.30 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0)))), multiplication(one, star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), multiplication(one, star(star(X0!0)))))),
% 52.13/52.30 inference(symmetry,[status(thm)],[594])).
% 52.13/52.30 tff(596,plain,
% 52.13/52.30 (star(star(X0!0)) = multiplication(one, star(star(X0!0)))),
% 52.13/52.30 inference(symmetry,[status(thm)],[569])).
% 52.13/52.30 tff(597,plain,
% 52.13/52.30 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0)))))),
% 52.13/52.31 inference(quant_inst,[status(thm)],[])).
% 52.13/52.31 tff(598,plain,
% 52.13/52.31 (addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))))),
% 52.13/52.31 inference(unit_resolution,[status(thm)],[597, 28])).
% 52.13/52.31 tff(599,plain,
% 52.13/52.31 (addition(addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), star(star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0)))), multiplication(one, star(star(X0!0))))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[598, 596])).
% 52.13/52.31 tff(600,plain,
% 52.13/52.31 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))) = addition(addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), star(star(X0!0))))),
% 52.13/52.31 inference(quant_inst,[status(thm)],[])).
% 52.13/52.31 tff(601,plain,
% 52.13/52.31 (addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))) = addition(addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), star(star(X0!0)))),
% 52.13/52.31 inference(unit_resolution,[status(thm)],[600, 41])).
% 52.13/52.31 tff(602,plain,
% 52.13/52.31 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0))))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 52.13/52.31 inference(symmetry,[status(thm)],[542])).
% 52.13/52.31 tff(603,plain,
% 52.13/52.31 (addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0)))) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))))),
% 52.13/52.31 inference(symmetry,[status(thm)],[538])).
% 52.13/52.31 tff(604,plain,
% 52.13/52.31 (addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(one, star(star(X0!0)))) = addition(addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))), addition(one, star(star(X0!0))))),
% 52.13/52.31 inference(symmetry,[status(thm)],[536])).
% 52.13/52.31 tff(605,plain,
% 52.13/52.31 (star(star(X0!0)) = addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0)))),
% 52.13/52.31 inference(transitivity,[status(thm)],[92, 540, 539, 604, 603, 602])).
% 52.13/52.31 tff(606,plain,
% 52.13/52.31 (addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), star(star(X0!0))) = addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), addition(addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))), star(star(X0!0))))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[605])).
% 52.13/52.31 tff(607,plain,
% 52.13/52.31 (addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), multiplication(one, star(star(X0!0)))) = addition(multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(star(X0!0))), star(star(X0!0)))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[569])).
% 52.13/52.31 tff(608,plain,
% 52.13/52.31 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))) = star(star(X0!0))),
% 52.13/52.31 inference(transitivity,[status(thm)],[520, 517, 575, 572, 570, 545, 542, 538, 536, 526, 524, 21])).
% 52.13/52.31 tff(609,plain,
% 52.13/52.31 (multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))) = multiplication(addition(multiplication(star(X0!0), X0!0), one), star(star(X0!0)))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[608])).
% 52.13/52.31 tff(610,plain,
% 52.13/52.31 (multiplication(star(X0!0), star(star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0))))),
% 52.13/52.31 inference(transitivity,[status(thm)],[527, 519])).
% 52.13/52.31 tff(611,plain,
% 52.13/52.31 (multiplication(addition(multiplication(star(X0!0), X0!0), one), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), star(star(X0!0)))))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[610])).
% 52.13/52.31 tff(612,plain,
% 52.13/52.31 (^[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)))),
% 52.13/52.31 inference(bind,[status(th)],[])).
% 52.13/52.31 tff(613,plain,
% 52.13/52.31 (![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))),
% 52.13/52.31 inference(quant_intro,[status(thm)],[612])).
% 52.13/52.31 tff(614,plain,
% 52.13/52.31 (![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))),
% 52.13/52.31 inference(rewrite,[status(thm)],[])).
% 52.13/52.31 tff(615,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')).
% 52.13/52.31 tff(616,plain,
% 52.13/52.31 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 52.13/52.31 inference(modus_ponens,[status(thm)],[615, 614])).
% 52.13/52.31 tff(617,plain,(
% 52.13/52.31 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 52.13/52.31 inference(skolemize,[status(sab)],[616])).
% 52.13/52.31 tff(618,plain,
% 52.13/52.31 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 52.13/52.31 inference(modus_ponens,[status(thm)],[617, 613])).
% 52.13/52.31 tff(619,plain,
% 52.13/52.31 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(star(X0!0), X0!0), one), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), star(star(X0!0))))),
% 52.13/52.31 inference(quant_inst,[status(thm)],[])).
% 52.13/52.31 tff(620,plain,
% 52.13/52.31 (multiplication(addition(multiplication(star(X0!0), X0!0), one), multiplication(star(X0!0), star(star(X0!0)))) = multiplication(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), star(star(X0!0)))),
% 52.13/52.31 inference(unit_resolution,[status(thm)],[619, 618])).
% 52.13/52.31 tff(621,plain,
% 52.13/52.31 (multiplication(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), star(star(X0!0))) = multiplication(addition(multiplication(star(X0!0), X0!0), one), multiplication(star(X0!0), star(star(X0!0))))),
% 52.13/52.31 inference(symmetry,[status(thm)],[620])).
% 52.13/52.31 tff(622,plain,
% 52.13/52.31 (addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[212, 404])).
% 52.13/52.31 tff(623,plain,
% 52.13/52.31 ((~![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(X0!0, star(X0!0)), one), star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)))),
% 52.13/52.31 inference(quant_inst,[status(thm)],[])).
% 52.13/52.31 tff(624,plain,
% 52.13/52.31 (addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0))),
% 52.13/52.31 inference(unit_resolution,[status(thm)],[623, 41])).
% 52.13/52.31 tff(625,plain,
% 52.13/52.31 (addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)) = addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 52.13/52.31 inference(symmetry,[status(thm)],[624])).
% 52.13/52.31 tff(626,plain,
% 52.13/52.31 (addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)) = star(X0!0)),
% 52.13/52.31 inference(transitivity,[status(thm)],[625, 622, 163])).
% 52.13/52.31 tff(627,plain,
% 52.13/52.31 (multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0))) = multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[626])).
% 52.13/52.31 tff(628,plain,
% 52.13/52.31 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0))) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))))),
% 52.13/52.31 inference(quant_inst,[status(thm)],[])).
% 52.13/52.31 tff(629,plain,
% 52.13/52.31 (multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0))) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 52.13/52.31 inference(unit_resolution,[status(thm)],[628, 70])).
% 52.13/52.31 tff(630,plain,
% 52.13/52.31 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)))),
% 52.13/52.31 inference(symmetry,[status(thm)],[629])).
% 52.13/52.31 tff(631,plain,
% 52.13/52.31 (addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))) = multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 52.13/52.31 inference(transitivity,[status(thm)],[630, 627])).
% 52.13/52.31 tff(632,plain,
% 52.13/52.31 (multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))), star(star(X0!0))) = multiplication(multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)), star(star(X0!0)))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[631])).
% 52.13/52.31 tff(633,plain,
% 52.13/52.31 (multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)))),
% 52.13/52.31 inference(symmetry,[status(thm)],[627])).
% 52.13/52.31 tff(634,plain,
% 52.13/52.31 (addition(one, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))) = addition(one, multiplication(star(X0!0), X0!0))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[224])).
% 52.13/52.31 tff(635,plain,
% 52.13/52.31 (addition(one, multiplication(star(X0!0), X0!0)) = addition(one, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 52.13/52.31 inference(symmetry,[status(thm)],[634])).
% 52.13/52.31 tff(636,plain,
% 52.13/52.31 (addition(multiplication(star(X0!0), X0!0), one) = addition(one, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)))),
% 52.13/52.31 inference(transitivity,[status(thm)],[212, 635])).
% 52.13/52.31 tff(637,plain,
% 52.13/52.31 (multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)) = multiplication(addition(one, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), star(X0!0))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[636])).
% 52.13/52.31 tff(638,plain,
% 52.13/52.31 (multiplication(addition(one, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), star(X0!0)) = multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))),
% 52.13/52.31 inference(symmetry,[status(thm)],[637])).
% 52.13/52.31 tff(639,plain,
% 52.13/52.31 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), star(X0!0)) = addition(multiplication(one, star(X0!0)), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0))))),
% 52.13/52.31 inference(quant_inst,[status(thm)],[])).
% 52.13/52.31 tff(640,plain,
% 52.13/52.31 (multiplication(addition(one, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), star(X0!0)) = addition(multiplication(one, star(X0!0)), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)))),
% 52.13/52.31 inference(unit_resolution,[status(thm)],[639, 122])).
% 52.13/52.31 tff(641,plain,
% 52.13/52.31 (addition(multiplication(one, star(X0!0)), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0))) = multiplication(addition(one, addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0))), star(X0!0))),
% 52.13/52.31 inference(symmetry,[status(thm)],[640])).
% 52.13/52.31 tff(642,plain,
% 52.13/52.31 (addition(multiplication(one, star(X0!0)), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0))) = addition(star(X0!0), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[204])).
% 52.13/52.31 tff(643,plain,
% 52.13/52.31 (addition(star(X0!0), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0))) = addition(multiplication(one, star(X0!0)), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)))),
% 52.13/52.31 inference(symmetry,[status(thm)],[642])).
% 52.13/52.31 tff(644,plain,
% 52.13/52.31 (multiplication(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = multiplication(star(X0!0), multiplication(X0!0, star(X0!0)))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[441])).
% 52.13/52.31 tff(645,plain,
% 52.13/52.31 (multiplication(star(X0!0), multiplication(X0!0, star(X0!0))) = multiplication(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 52.13/52.31 inference(symmetry,[status(thm)],[644])).
% 52.13/52.31 tff(646,plain,
% 52.13/52.31 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(star(X0!0), multiplication(X0!0, star(X0!0))) = multiplication(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 52.13/52.31 inference(quant_inst,[status(thm)],[])).
% 52.13/52.31 tff(647,plain,
% 52.13/52.31 (multiplication(star(X0!0), multiplication(X0!0, star(X0!0))) = multiplication(multiplication(star(X0!0), X0!0), star(X0!0))),
% 52.13/52.31 inference(unit_resolution,[status(thm)],[646, 618])).
% 52.13/52.31 tff(648,plain,
% 52.13/52.31 (multiplication(multiplication(star(X0!0), X0!0), star(X0!0)) = multiplication(star(X0!0), multiplication(X0!0, star(X0!0)))),
% 52.13/52.31 inference(symmetry,[status(thm)],[647])).
% 52.13/52.31 tff(649,plain,
% 52.13/52.31 (multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)) = multiplication(multiplication(star(X0!0), X0!0), star(X0!0))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[224])).
% 52.13/52.31 tff(650,plain,
% 52.13/52.31 (multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)) = multiplication(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))),
% 52.13/52.31 inference(transitivity,[status(thm)],[649, 648, 645])).
% 52.13/52.31 tff(651,plain,
% 52.13/52.31 (addition(star(X0!0), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0))) = addition(star(X0!0), multiplication(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[650])).
% 52.13/52.31 tff(652,plain,
% 52.13/52.31 (addition(star(X0!0), multiplication(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(star(X0!0), multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), X0!0), multiplication(star(X0!0), X0!0)), star(X0!0)))),
% 52.13/52.31 inference(symmetry,[status(thm)],[651])).
% 52.13/52.31 tff(653,plain,
% 52.13/52.31 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(star(X0!0), one) = star(X0!0))),
% 52.13/52.31 inference(quant_inst,[status(thm)],[])).
% 52.13/52.31 tff(654,plain,
% 52.13/52.31 (multiplication(star(X0!0), one) = star(X0!0)),
% 52.13/52.31 inference(unit_resolution,[status(thm)],[653, 144])).
% 52.13/52.31 tff(655,plain,
% 52.13/52.31 (star(X0!0) = multiplication(star(X0!0), one)),
% 52.13/52.31 inference(symmetry,[status(thm)],[654])).
% 52.13/52.31 tff(656,plain,
% 52.13/52.31 (addition(star(X0!0), multiplication(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[655])).
% 52.13/52.31 tff(657,plain,
% 52.13/52.31 (addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(star(X0!0), multiplication(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 52.13/52.31 inference(symmetry,[status(thm)],[656])).
% 52.13/52.31 tff(658,plain,
% 52.13/52.31 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))))),
% 52.13/52.31 inference(quant_inst,[status(thm)],[])).
% 52.13/52.31 tff(659,plain,
% 52.13/52.31 (multiplication(star(X0!0), addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = addition(multiplication(star(X0!0), one), multiplication(star(X0!0), addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 52.13/52.31 inference(unit_resolution,[status(thm)],[658, 70])).
% 52.13/52.31 tff(660,plain,
% 52.13/52.31 (addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(one, multiplication(X0!0, star(X0!0)))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[441])).
% 52.13/52.31 tff(661,plain,
% 52.13/52.31 (addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))) = addition(multiplication(X0!0, star(X0!0)), one)),
% 52.13/52.31 inference(transitivity,[status(thm)],[660, 401])).
% 52.13/52.31 tff(662,plain,
% 52.13/52.31 (multiplication(star(X0!0), addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0))))) = multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[661])).
% 52.13/52.31 tff(663,plain,
% 52.13/52.31 (multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(star(X0!0), addition(one, addition(multiplication(X0!0, addition(multiplication(star(X0!0), X0!0), one)), multiplication(X0!0, star(X0!0)))))),
% 52.13/52.31 inference(symmetry,[status(thm)],[662])).
% 52.13/52.31 tff(664,plain,
% 52.13/52.31 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 52.13/52.31 inference(symmetry,[status(thm)],[622])).
% 52.13/52.31 tff(665,plain,
% 52.13/52.31 (star(X0!0) = addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0))),
% 52.13/52.31 inference(transitivity,[status(thm)],[164, 664, 624])).
% 52.13/52.31 tff(666,plain,
% 52.13/52.31 (multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[665])).
% 52.13/52.31 tff(667,plain,
% 52.13/52.31 (multiplication(addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) = multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 52.13/52.31 inference(symmetry,[status(thm)],[666])).
% 52.13/52.31 tff(668,plain,
% 52.13/52.31 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))))),
% 52.13/52.31 inference(quant_inst,[status(thm)],[])).
% 52.13/52.31 tff(669,plain,
% 52.13/52.31 (multiplication(addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one)) = addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))),
% 52.13/52.31 inference(unit_resolution,[status(thm)],[668, 122])).
% 52.13/52.31 tff(670,plain,
% 52.13/52.31 (addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))) = multiplication(addition(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), star(X0!0)), addition(multiplication(X0!0, star(X0!0)), one))),
% 52.13/52.31 inference(symmetry,[status(thm)],[669])).
% 52.13/52.31 tff(671,plain,
% 52.13/52.31 (addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))) = addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0)))),
% 52.13/52.31 inference(transitivity,[status(thm)],[670, 667, 663, 659, 657, 652, 643, 641, 638, 633, 629])).
% 52.13/52.31 tff(672,plain,
% 52.13/52.31 (multiplication(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), star(star(X0!0))) = multiplication(addition(multiplication(addition(multiplication(star(X0!0), X0!0), one), addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one))), multiplication(addition(multiplication(star(X0!0), X0!0), one), star(X0!0))), star(star(X0!0)))),
% 52.13/52.31 inference(monotonicity,[status(thm)],[671])).
% 52.13/52.31 tff(673,plain,
% 52.13/52.31 (multiplication(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), star(star(X0!0))) = star(star(X0!0))),
% 52.13/52.31 inference(transitivity,[status(thm)],[672, 632, 621, 611, 609, 586, 589, 607, 606, 601, 599, 595, 592, 584, 581, 580, 577, 575, 572, 570, 545, 542, 538, 536, 526, 524, 21])).
% 52.13/52.31 tff(674,plain,
% 52.13/52.31 (leq(multiplication(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), star(star(X0!0))), star(X0!0)) <=> leq(star(star(X0!0)), star(X0!0))),
% 52.13/52.32 inference(monotonicity,[status(thm)],[673])).
% 52.13/52.32 tff(675,plain,
% 52.13/52.32 (leq(star(star(X0!0)), star(X0!0)) <=> leq(multiplication(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), star(star(X0!0))), star(X0!0))),
% 52.13/52.32 inference(symmetry,[status(thm)],[674])).
% 52.13/52.32 tff(676,plain,
% 52.13/52.32 ((~leq(star(star(X0!0)), star(X0!0))) <=> (~leq(multiplication(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), star(star(X0!0))), star(X0!0)))),
% 52.13/52.32 inference(monotonicity,[status(thm)],[675])).
% 52.13/52.32 tff(677,plain,
% 52.13/52.32 ((~(~((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0))))))) <=> ((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0)))))),
% 52.13/52.32 inference(rewrite,[status(thm)],[])).
% 52.13/52.32 tff(678,plain,
% 52.13/52.32 ((leq(star(star(X0!0)), star(X0!0)) & leq(star(X0!0), star(star(X0!0)))) <=> (~((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0))))))),
% 52.13/52.32 inference(rewrite,[status(thm)],[])).
% 52.13/52.32 tff(679,plain,
% 52.13/52.32 ((~(leq(star(star(X0!0)), star(X0!0)) & leq(star(X0!0), star(star(X0!0))))) <=> (~(~((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0)))))))),
% 52.13/52.32 inference(monotonicity,[status(thm)],[678])).
% 52.13/52.32 tff(680,plain,
% 52.13/52.32 ((~(leq(star(star(X0!0)), star(X0!0)) & leq(star(X0!0), star(star(X0!0))))) <=> ((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0)))))),
% 52.13/52.32 inference(transitivity,[status(thm)],[679, 677])).
% 52.13/52.32 tff(681,plain,
% 52.13/52.32 ((~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))) <=> (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0)))))),
% 52.13/52.32 inference(rewrite,[status(thm)],[])).
% 52.13/52.32 tff(682,axiom,(~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 52.13/52.32 tff(683,plain,
% 52.13/52.32 (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[682, 681])).
% 52.13/52.32 tff(684,plain,
% 52.13/52.32 (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[683, 681])).
% 52.13/52.32 tff(685,plain,
% 52.13/52.32 (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[684, 681])).
% 52.13/52.32 tff(686,plain,
% 52.13/52.32 (~![X0: $i] : (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[685, 681])).
% 52.13/52.32 tff(687,plain,(
% 52.13/52.32 ~(leq(star(star(X0!0)), star(X0!0)) & leq(star(X0!0), star(star(X0!0))))),
% 52.13/52.32 inference(skolemize,[status(sab)],[686])).
% 52.13/52.32 tff(688,plain,
% 52.13/52.32 ((~leq(star(star(X0!0)), star(X0!0))) | (~leq(star(X0!0), star(star(X0!0))))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[687, 680])).
% 52.13/52.32 tff(689,plain,
% 52.13/52.32 (~leq(star(star(X0!0)), star(X0!0))),
% 52.13/52.32 inference(unit_resolution,[status(thm)],[688, 513])).
% 52.13/52.32 tff(690,plain,
% 52.13/52.32 (~leq(multiplication(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), star(star(X0!0))), star(X0!0))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[689, 676])).
% 52.13/52.32 tff(691,plain,
% 52.13/52.32 (multiplication(star(X0!0), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 52.13/52.32 inference(monotonicity,[status(thm)],[404])).
% 52.13/52.32 tff(692,plain,
% 52.13/52.32 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X0!0), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))))),
% 52.13/52.32 inference(quant_inst,[status(thm)],[])).
% 52.13/52.32 tff(693,plain,
% 52.13/52.32 (multiplication(star(X0!0), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0)))),
% 52.13/52.32 inference(unit_resolution,[status(thm)],[692, 70])).
% 52.13/52.32 tff(694,plain,
% 52.13/52.32 (addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 52.13/52.32 inference(symmetry,[status(thm)],[693])).
% 52.13/52.32 tff(695,plain,
% 52.13/52.32 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))))),
% 52.13/52.32 inference(quant_inst,[status(thm)],[])).
% 52.13/52.32 tff(696,plain,
% 52.13/52.32 (addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))),
% 52.13/52.32 inference(unit_resolution,[status(thm)],[695, 28])).
% 52.13/52.32 tff(697,plain,
% 52.13/52.32 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))) = addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0)))),
% 52.13/52.32 inference(symmetry,[status(thm)],[696])).
% 52.13/52.32 tff(698,plain,
% 52.13/52.32 (addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))) = multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))),
% 52.13/52.32 inference(transitivity,[status(thm)],[670, 667])).
% 52.13/52.32 tff(699,plain,
% 52.13/52.32 (addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))),
% 52.13/52.32 inference(monotonicity,[status(thm)],[698])).
% 52.13/52.32 tff(700,plain,
% 52.13/52.32 (addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))) = multiplication(star(X0!0), star(X0!0))),
% 52.13/52.32 inference(transitivity,[status(thm)],[699, 697, 694, 691])).
% 52.13/52.32 tff(701,plain,
% 52.13/52.32 (leq(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))), star(X0!0)) <=> leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 52.13/52.32 inference(monotonicity,[status(thm)],[700])).
% 52.13/52.32 tff(702,plain,
% 52.13/52.32 (leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)) <=> leq(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))), star(X0!0))),
% 52.13/52.32 inference(symmetry,[status(thm)],[701])).
% 52.13/52.32 tff(703,plain,
% 52.13/52.32 (leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0)) <=> leq(star(X0!0), star(X0!0))),
% 52.13/52.32 inference(monotonicity,[status(thm)],[565])).
% 52.13/52.32 tff(704,plain,
% 52.13/52.32 (leq(star(X0!0), star(X0!0)) <=> leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))),
% 52.13/52.32 inference(symmetry,[status(thm)],[703])).
% 52.13/52.32 tff(705,plain,
% 52.13/52.32 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(star(X0!0), star(X0!0)) <=> (addition(star(X0!0), star(X0!0)) = star(X0!0)))),
% 52.13/52.32 inference(quant_inst,[status(thm)],[])).
% 52.13/52.32 tff(706,plain,
% 52.13/52.32 (leq(star(X0!0), star(X0!0)) <=> (addition(star(X0!0), star(X0!0)) = star(X0!0))),
% 52.13/52.32 inference(unit_resolution,[status(thm)],[705, 7])).
% 52.13/52.32 tff(707,plain,
% 52.13/52.32 ((~(leq(star(X0!0), star(X0!0)) <=> (addition(star(X0!0), star(X0!0)) = star(X0!0)))) | leq(star(X0!0), star(X0!0)) | (~(addition(star(X0!0), star(X0!0)) = star(X0!0)))),
% 52.13/52.32 inference(tautology,[status(thm)],[])).
% 52.13/52.32 tff(708,plain,
% 52.13/52.32 (leq(star(X0!0), star(X0!0))),
% 52.13/52.32 inference(unit_resolution,[status(thm)],[707, 529, 706])).
% 52.13/52.32 tff(709,plain,
% 52.13/52.32 (leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[708, 704])).
% 52.13/52.32 tff(710,plain,
% 52.13/52.32 (((~![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)))),
% 52.13/52.32 inference(rewrite,[status(thm)],[])).
% 52.13/52.32 tff(711,plain,
% 52.13/52.32 ((~![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)))),
% 52.13/52.32 inference(quant_inst,[status(thm)],[])).
% 52.13/52.32 tff(712,plain,
% 52.13/52.32 ((~![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))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[711, 710])).
% 52.13/52.32 tff(713,plain,
% 52.13/52.32 ((~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))),
% 52.13/52.32 inference(unit_resolution,[status(thm)],[712, 465])).
% 52.13/52.32 tff(714,plain,
% 52.13/52.32 (leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 52.13/52.32 inference(unit_resolution,[status(thm)],[713, 709])).
% 52.13/52.32 tff(715,plain,
% 52.13/52.32 (leq(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))), star(X0!0))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[714, 702])).
% 52.13/52.32 tff(716,plain,
% 52.13/52.32 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 52.13/52.32 inference(bind,[status(th)],[])).
% 52.13/52.32 tff(717,plain,
% 52.13/52.32 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 52.13/52.32 inference(quant_intro,[status(thm)],[716])).
% 52.13/52.32 tff(718,plain,
% 52.13/52.32 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 52.13/52.32 inference(rewrite,[status(thm)],[])).
% 52.13/52.32 tff(719,plain,
% 52.13/52.32 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 52.13/52.32 inference(bind,[status(th)],[])).
% 52.13/52.32 tff(720,plain,
% 52.13/52.32 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 52.13/52.32 inference(quant_intro,[status(thm)],[719])).
% 52.13/52.32 tff(721,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_induction_right')).
% 52.13/52.32 tff(722,plain,
% 52.13/52.32 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[721, 720])).
% 52.13/52.32 tff(723,plain,
% 52.13/52.32 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[722, 718])).
% 52.13/52.32 tff(724,plain,(
% 52.13/52.32 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 52.13/52.32 inference(skolemize,[status(sab)],[723])).
% 52.13/52.32 tff(725,plain,
% 52.13/52.32 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 52.13/52.32 inference(modus_ponens,[status(thm)],[724, 717])).
% 52.13/52.32 tff(726,plain,
% 52.13/52.32 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))), star(X0!0))) | leq(multiplication(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), star(star(X0!0))), star(X0!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))), star(X0!0))) | leq(multiplication(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), star(star(X0!0))), star(X0!0)))),
% 52.13/52.32 inference(rewrite,[status(thm)],[])).
% 52.13/52.32 tff(727,plain,
% 52.13/52.32 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))), star(X0!0))) | leq(multiplication(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), star(star(X0!0))), star(X0!0)))),
% 52.13/52.32 inference(quant_inst,[status(thm)],[])).
% 52.13/52.32 tff(728,plain,
% 52.13/52.32 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X0!0), star(X0!0)), addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)))), star(X0!0))) | leq(multiplication(addition(multiplication(addition(addition(multiplication(star(X0!0), X0!0), one), addition(multiplication(X0!0, star(X0!0)), one)), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one))), star(star(X0!0))), star(X0!0))),
% 52.13/52.35 inference(modus_ponens,[status(thm)],[727, 726])).
% 52.13/52.35 tff(729,plain,
% 52.13/52.35 ($false),
% 52.13/52.35 inference(unit_resolution,[status(thm)],[728, 725, 715, 690])).
% 52.13/52.35 % SZS output end Proof
% 52.13/52.35 % E exiting
%------------------------------------------------------------------------------