%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE040+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 112.55s 112.72s
% Output : Proof 112.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE040+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n009.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 18:55:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 112.55/112.72 % SZS status Theorem
% 112.55/112.72 % SZS output start Proof
% 112.55/112.72 tff(star_type, type, (
% 112.55/112.72 star: $i > $i)).
% 112.55/112.72 tff(tptp_fun_X0_0_type, type, (
% 112.55/112.72 tptp_fun_X0_0: $i)).
% 112.55/112.72 tff(addition_type, type, (
% 112.55/112.72 addition: ( $i * $i ) > $i)).
% 112.55/112.72 tff(multiplication_type, type, (
% 112.55/112.72 multiplication: ( $i * $i ) > $i)).
% 112.55/112.72 tff(one_type, type, (
% 112.55/112.72 one: $i)).
% 112.55/112.72 tff(leq_type, type, (
% 112.55/112.72 leq: ( $i * $i ) > $o)).
% 112.55/112.72 tff(1,plain,
% 112.55/112.72 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 112.55/112.72 inference(bind,[status(th)],[])).
% 112.55/112.72 tff(2,plain,
% 112.55/112.72 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 112.55/112.72 inference(quant_intro,[status(thm)],[1])).
% 112.55/112.72 tff(3,plain,
% 112.55/112.72 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 112.55/112.72 inference(rewrite,[status(thm)],[])).
% 112.55/112.72 tff(4,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','order')).
% 112.55/112.72 tff(5,plain,
% 112.55/112.72 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[4, 3])).
% 112.55/112.72 tff(6,plain,(
% 112.55/112.72 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 112.55/112.72 inference(skolemize,[status(sab)],[5])).
% 112.55/112.72 tff(7,plain,
% 112.55/112.72 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[6, 2])).
% 112.55/112.72 tff(8,plain,
% 112.55/112.72 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) <=> (addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) = star(X0!0)))),
% 112.55/112.72 inference(quant_inst,[status(thm)],[])).
% 112.55/112.72 tff(9,plain,
% 112.55/112.72 (leq(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) <=> (addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) = star(X0!0))),
% 112.55/112.72 inference(unit_resolution,[status(thm)],[8, 7])).
% 112.55/112.72 tff(10,plain,
% 112.55/112.72 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 112.55/112.72 inference(bind,[status(th)],[])).
% 112.55/112.72 tff(11,plain,
% 112.55/112.72 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 112.55/112.72 inference(quant_intro,[status(thm)],[10])).
% 112.55/112.72 tff(12,plain,
% 112.55/112.72 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 112.55/112.72 inference(rewrite,[status(thm)],[])).
% 112.55/112.72 tff(13,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 112.55/112.72 tff(14,plain,
% 112.55/112.72 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[13, 12])).
% 112.55/112.72 tff(15,plain,(
% 112.55/112.72 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 112.55/112.72 inference(skolemize,[status(sab)],[14])).
% 112.55/112.72 tff(16,plain,
% 112.55/112.72 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[15, 11])).
% 112.55/112.72 tff(17,plain,
% 112.55/112.72 ((~![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))),
% 112.55/112.72 inference(quant_inst,[status(thm)],[])).
% 112.55/112.72 tff(18,plain,
% 112.55/112.72 (addition(one, multiplication(X0!0, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), one)),
% 112.55/112.72 inference(unit_resolution,[status(thm)],[17, 16])).
% 112.55/112.72 tff(19,plain,
% 112.55/112.72 (addition(multiplication(X0!0, star(X0!0)), one) = addition(one, multiplication(X0!0, star(X0!0)))),
% 112.55/112.72 inference(symmetry,[status(thm)],[18])).
% 112.55/112.72 tff(20,plain,
% 112.55/112.72 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 112.55/112.72 inference(monotonicity,[status(thm)],[19])).
% 112.55/112.72 tff(21,plain,
% 112.55/112.72 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 112.55/112.72 inference(symmetry,[status(thm)],[20])).
% 112.55/112.72 tff(22,plain,
% 112.55/112.72 ((~![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)))),
% 112.55/112.72 inference(quant_inst,[status(thm)],[])).
% 112.55/112.72 tff(23,plain,
% 112.55/112.72 (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))),
% 112.55/112.72 inference(unit_resolution,[status(thm)],[22, 7])).
% 112.55/112.72 tff(24,plain,
% 112.55/112.72 (^[A: $i] : refl(leq(addition(one, multiplication(A, star(A))), star(A)) <=> leq(addition(one, multiplication(A, star(A))), star(A)))),
% 112.55/112.72 inference(bind,[status(th)],[])).
% 112.55/112.72 tff(25,plain,
% 112.55/112.72 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 112.55/112.72 inference(quant_intro,[status(thm)],[24])).
% 112.55/112.72 tff(26,plain,
% 112.55/112.72 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 112.55/112.72 inference(rewrite,[status(thm)],[])).
% 112.55/112.72 tff(27,axiom,(![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_right')).
% 112.55/112.72 tff(28,plain,
% 112.55/112.72 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[27, 26])).
% 112.55/112.72 tff(29,plain,(
% 112.55/112.72 ![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 112.55/112.72 inference(skolemize,[status(sab)],[28])).
% 112.55/112.72 tff(30,plain,
% 112.55/112.72 (![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[29, 25])).
% 112.55/112.72 tff(31,plain,
% 112.55/112.72 ((~![A: $i] : leq(addition(one, multiplication(A, star(A))), star(A))) | leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 112.55/112.72 inference(quant_inst,[status(thm)],[])).
% 112.55/112.72 tff(32,plain,
% 112.55/112.72 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 112.55/112.72 inference(unit_resolution,[status(thm)],[31, 30])).
% 112.55/112.72 tff(33,plain,
% 112.55/112.72 ((~(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))),
% 112.55/112.72 inference(tautology,[status(thm)],[])).
% 112.55/112.72 tff(34,plain,
% 112.55/112.72 ((~(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))),
% 112.55/112.72 inference(unit_resolution,[status(thm)],[33, 32])).
% 112.55/112.72 tff(35,plain,
% 112.55/112.72 (addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) = star(X0!0)),
% 112.55/112.72 inference(unit_resolution,[status(thm)],[34, 23])).
% 112.55/112.72 tff(36,plain,
% 112.55/112.72 (star(X0!0) = addition(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 112.55/112.72 inference(symmetry,[status(thm)],[35])).
% 112.55/112.72 tff(37,plain,
% 112.55/112.72 (star(X0!0) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 112.55/112.72 inference(transitivity,[status(thm)],[36, 21])).
% 112.55/112.72 tff(38,plain,
% 112.55/112.72 (multiplication(star(X0!0), star(X0!0)) = multiplication(star(X0!0), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 112.55/112.72 inference(monotonicity,[status(thm)],[37])).
% 112.55/112.72 tff(39,plain,
% 112.55/112.72 (multiplication(star(X0!0), addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 112.55/112.72 inference(symmetry,[status(thm)],[38])).
% 112.55/112.72 tff(40,plain,
% 112.55/112.72 (^[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))))),
% 112.55/112.72 inference(bind,[status(th)],[])).
% 112.55/112.72 tff(41,plain,
% 112.55/112.72 (![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)))),
% 112.55/112.72 inference(quant_intro,[status(thm)],[40])).
% 112.55/112.72 tff(42,plain,
% 112.55/112.72 (![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)))),
% 112.55/112.72 inference(rewrite,[status(thm)],[])).
% 112.55/112.72 tff(43,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')).
% 112.55/112.72 tff(44,plain,
% 112.55/112.72 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[43, 42])).
% 112.55/112.72 tff(45,plain,(
% 112.55/112.72 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 112.55/112.72 inference(skolemize,[status(sab)],[44])).
% 112.55/112.72 tff(46,plain,
% 112.55/112.72 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[45, 41])).
% 112.55/112.72 tff(47,plain,
% 112.55/112.72 ((~![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))))),
% 112.55/112.72 inference(quant_inst,[status(thm)],[])).
% 112.55/112.72 tff(48,plain,
% 112.55/112.72 (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)))),
% 112.55/112.72 inference(unit_resolution,[status(thm)],[47, 46])).
% 112.55/112.72 tff(49,plain,
% 112.55/112.72 (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)))),
% 112.55/112.72 inference(symmetry,[status(thm)],[48])).
% 112.55/112.72 tff(50,plain,
% 112.55/112.72 (addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 112.55/112.72 inference(transitivity,[status(thm)],[49, 39])).
% 112.55/112.72 tff(51,plain,
% 112.55/112.72 (leq(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) <=> leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 112.55/112.72 inference(monotonicity,[status(thm)],[50])).
% 112.55/112.72 tff(52,plain,
% 112.55/112.72 (leq(multiplication(star(X0!0), star(X0!0)), star(X0!0)) <=> leq(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 112.55/112.72 inference(symmetry,[status(thm)],[51])).
% 112.55/112.72 tff(53,plain,
% 112.55/112.72 (multiplication(X0!0, star(X0!0)) = multiplication(X0!0, addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 112.55/112.72 inference(monotonicity,[status(thm)],[37])).
% 112.55/112.72 tff(54,plain,
% 112.55/112.72 (multiplication(X0!0, addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 112.55/112.72 inference(symmetry,[status(thm)],[53])).
% 112.55/112.72 tff(55,plain,
% 112.55/112.72 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))))),
% 112.55/112.72 inference(quant_inst,[status(thm)],[])).
% 112.55/112.72 tff(56,plain,
% 112.55/112.72 (multiplication(X0!0, addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) = addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))),
% 112.55/112.72 inference(unit_resolution,[status(thm)],[55, 46])).
% 112.55/112.72 tff(57,plain,
% 112.55/112.72 (addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)))),
% 112.55/112.72 inference(symmetry,[status(thm)],[56])).
% 112.55/112.72 tff(58,plain,
% 112.55/112.72 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 112.55/112.72 inference(bind,[status(th)],[])).
% 112.55/112.72 tff(59,plain,
% 112.55/112.72 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 112.55/112.72 inference(quant_intro,[status(thm)],[58])).
% 112.55/112.72 tff(60,plain,
% 112.55/112.72 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 112.55/112.72 inference(rewrite,[status(thm)],[])).
% 112.55/112.72 tff(61,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 112.55/112.72 tff(62,plain,
% 112.55/112.72 (![A: $i] : (addition(A, A) = A)),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[61, 60])).
% 112.55/112.72 tff(63,plain,(
% 112.55/112.72 ![A: $i] : (addition(A, A) = A)),
% 112.55/112.72 inference(skolemize,[status(sab)],[62])).
% 112.55/112.72 tff(64,plain,
% 112.55/112.72 (![A: $i] : (addition(A, A) = A)),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[63, 59])).
% 112.55/112.72 tff(65,plain,
% 112.55/112.72 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))) = addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))))),
% 112.55/112.72 inference(quant_inst,[status(thm)],[])).
% 112.55/112.72 tff(66,plain,
% 112.55/112.72 (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))) = addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))),
% 112.55/112.72 inference(unit_resolution,[status(thm)],[65, 64])).
% 112.55/112.72 tff(67,plain,
% 112.55/112.72 (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))) = multiplication(X0!0, star(X0!0))),
% 112.55/112.72 inference(transitivity,[status(thm)],[66, 57, 54])).
% 112.55/112.72 tff(68,plain,
% 112.55/112.72 (addition(addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 112.55/112.72 inference(monotonicity,[status(thm)],[67])).
% 112.55/112.72 tff(69,plain,
% 112.55/112.72 (^[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)))),
% 112.55/112.72 inference(bind,[status(th)],[])).
% 112.55/112.72 tff(70,plain,
% 112.55/112.72 (![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))),
% 112.55/112.72 inference(quant_intro,[status(thm)],[69])).
% 112.55/112.72 tff(71,plain,
% 112.55/112.72 (![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))),
% 112.55/112.72 inference(rewrite,[status(thm)],[])).
% 112.55/112.72 tff(72,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')).
% 112.55/112.72 tff(73,plain,
% 112.55/112.72 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[72, 71])).
% 112.55/112.72 tff(74,plain,(
% 112.55/112.72 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 112.55/112.72 inference(skolemize,[status(sab)],[73])).
% 112.55/112.72 tff(75,plain,
% 112.55/112.72 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 112.55/112.72 inference(modus_ponens,[status(thm)],[74, 70])).
% 112.55/112.72 tff(76,plain,
% 112.55/112.72 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0))))),
% 112.55/112.72 inference(quant_inst,[status(thm)],[])).
% 112.55/112.72 tff(77,plain,
% 112.55/112.72 (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))) = addition(addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))), addition(one, star(X0!0)))),
% 112.55/112.72 inference(unit_resolution,[status(thm)],[76, 75])).
% 112.55/112.72 tff(78,plain,
% 112.55/112.72 (addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))) = multiplication(X0!0, star(X0!0))),
% 112.55/112.72 inference(transitivity,[status(thm)],[57, 54])).
% 112.55/112.72 tff(79,plain,
% 112.55/112.72 (addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 112.55/112.72 inference(monotonicity,[status(thm)],[78])).
% 112.55/112.72 tff(80,plain,
% 112.55/112.72 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))),
% 112.55/112.72 inference(symmetry,[status(thm)],[79])).
% 112.55/112.72 tff(81,plain,
% 112.55/112.72 ((~![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)))),
% 112.55/112.72 inference(quant_inst,[status(thm)],[])).
% 112.55/112.72 tff(82,plain,
% 112.55/112.72 (addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))) = addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 112.55/112.72 inference(unit_resolution,[status(thm)],[81, 75])).
% 112.55/112.72 tff(83,plain,
% 112.55/112.72 (addition(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 112.55/112.72 inference(symmetry,[status(thm)],[82])).
% 112.55/112.72 tff(84,plain,
% 112.55/112.72 (star(X0!0) = addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0)))),
% 112.55/112.72 inference(transitivity,[status(thm)],[36, 21, 83, 80])).
% 112.55/112.72 tff(85,plain,
% 112.55/112.72 (multiplication(X0!0, star(X0!0)) = addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0)))),
% 112.55/112.72 inference(transitivity,[status(thm)],[53, 56])).
% 112.55/112.72 tff(86,plain,
% 112.55/112.72 (addition(multiplication(X0!0, star(X0!0)), star(X0!0)) = addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(addition(multiplication(X0!0, addition(multiplication(X0!0, star(X0!0)), one)), multiplication(X0!0, star(X0!0))), addition(one, star(X0!0))))),
% 112.55/112.72 inference(monotonicity,[status(thm)],[85, 84])).
% 112.55/112.72 tff(87,plain,
% 112.55/112.72 (addition(multiplication(X0!0, star(X0!0)), star(X0!0)) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 112.55/112.72 inference(transitivity,[status(thm)],[86, 77, 68])).
% 112.55/112.72 tff(88,plain,
% 112.55/112.73 (leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0)) <=> leq(addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))), star(X0!0))),
% 112.55/112.73 inference(monotonicity,[status(thm)],[87])).
% 112.55/112.73 tff(89,plain,
% 112.55/112.73 (leq(addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))), star(X0!0)) <=> leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))),
% 112.55/112.73 inference(symmetry,[status(thm)],[88])).
% 112.55/112.73 tff(90,plain,
% 112.55/112.73 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 112.55/112.73 inference(bind,[status(th)],[])).
% 112.55/112.73 tff(91,plain,
% 112.55/112.73 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 112.55/112.73 inference(quant_intro,[status(thm)],[90])).
% 112.55/112.73 tff(92,plain,
% 112.55/112.73 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 112.55/112.73 inference(rewrite,[status(thm)],[])).
% 112.55/112.73 tff(93,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_right_identity')).
% 112.55/112.73 tff(94,plain,
% 112.55/112.73 (![A: $i] : (multiplication(A, one) = A)),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[93, 92])).
% 112.55/112.73 tff(95,plain,(
% 112.55/112.73 ![A: $i] : (multiplication(A, one) = A)),
% 112.55/112.73 inference(skolemize,[status(sab)],[94])).
% 112.55/112.73 tff(96,plain,
% 112.55/112.73 (![A: $i] : (multiplication(A, one) = A)),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[95, 91])).
% 112.55/112.73 tff(97,plain,
% 112.55/112.73 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(star(X0!0), one) = star(X0!0))),
% 112.55/112.73 inference(quant_inst,[status(thm)],[])).
% 112.55/112.73 tff(98,plain,
% 112.55/112.73 (multiplication(star(X0!0), one) = star(X0!0)),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[97, 96])).
% 112.55/112.73 tff(99,plain,
% 112.55/112.73 (multiplication(star(X0!0), one) = addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0)))),
% 112.55/112.73 inference(transitivity,[status(thm)],[98, 36, 21, 83])).
% 112.55/112.73 tff(100,plain,
% 112.55/112.73 (leq(multiplication(star(X0!0), one), star(X0!0)) <=> leq(addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))), star(X0!0))),
% 112.55/112.73 inference(monotonicity,[status(thm)],[99])).
% 112.55/112.73 tff(101,plain,
% 112.55/112.73 (leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0)) <=> leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0))),
% 112.55/112.73 inference(monotonicity,[status(thm)],[19])).
% 112.55/112.73 tff(102,plain,
% 112.55/112.73 (leq(addition(one, multiplication(X0!0, star(X0!0))), star(X0!0)) <=> leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 112.55/112.73 inference(symmetry,[status(thm)],[101])).
% 112.55/112.73 tff(103,plain,
% 112.55/112.73 (leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[32, 102])).
% 112.55/112.73 tff(104,plain,
% 112.55/112.73 (^[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)))),
% 112.55/112.73 inference(bind,[status(th)],[])).
% 112.55/112.73 tff(105,plain,
% 112.55/112.73 (![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))),
% 112.55/112.73 inference(quant_intro,[status(thm)],[104])).
% 112.55/112.73 tff(106,plain,
% 112.55/112.73 (![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))),
% 112.55/112.73 inference(rewrite,[status(thm)],[])).
% 112.55/112.73 tff(107,plain,
% 112.55/112.73 (^[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)))),
% 112.55/112.73 inference(bind,[status(th)],[])).
% 112.55/112.73 tff(108,plain,
% 112.55/112.73 (![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))),
% 112.55/112.73 inference(quant_intro,[status(thm)],[107])).
% 112.55/112.73 tff(109,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')).
% 112.55/112.73 tff(110,plain,
% 112.55/112.73 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[109, 108])).
% 112.55/112.73 tff(111,plain,
% 112.55/112.73 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[110, 106])).
% 112.55/112.73 tff(112,plain,(
% 112.55/112.73 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 112.55/112.73 inference(skolemize,[status(sab)],[111])).
% 112.55/112.73 tff(113,plain,
% 112.55/112.73 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[112, 105])).
% 112.55/112.73 tff(114,plain,
% 112.55/112.73 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) | leq(multiplication(star(X0!0), one), star(X0!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) | leq(multiplication(star(X0!0), one), star(X0!0)))),
% 112.55/112.73 inference(rewrite,[status(thm)],[])).
% 112.55/112.73 tff(115,plain,
% 112.55/112.73 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | ((~leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) | leq(multiplication(star(X0!0), one), star(X0!0)))),
% 112.55/112.73 inference(quant_inst,[status(thm)],[])).
% 112.55/112.73 tff(116,plain,
% 112.55/112.73 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), B)) | leq(multiplication(star(A), C), B))) | (~leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) | leq(multiplication(star(X0!0), one), star(X0!0))),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[115, 114])).
% 112.55/112.73 tff(117,plain,
% 112.55/112.73 ((~leq(addition(multiplication(X0!0, star(X0!0)), one), star(X0!0))) | leq(multiplication(star(X0!0), one), star(X0!0))),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[116, 113])).
% 112.55/112.73 tff(118,plain,
% 112.55/112.73 (leq(multiplication(star(X0!0), one), star(X0!0))),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[117, 103])).
% 112.55/112.73 tff(119,plain,
% 112.55/112.73 (leq(addition(multiplication(X0!0, star(X0!0)), addition(one, star(X0!0))), star(X0!0))),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[118, 100])).
% 112.55/112.73 tff(120,plain,
% 112.55/112.73 (leq(addition(multiplication(X0!0, star(X0!0)), star(X0!0)), star(X0!0))),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[119, 89])).
% 112.55/112.73 tff(121,plain,
% 112.55/112.73 (((~![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)))),
% 112.55/112.73 inference(rewrite,[status(thm)],[])).
% 112.55/112.73 tff(122,plain,
% 112.55/112.73 ((~![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)))),
% 112.55/112.73 inference(quant_inst,[status(thm)],[])).
% 112.55/112.73 tff(123,plain,
% 112.55/112.73 ((~![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))),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[122, 121])).
% 112.55/112.73 tff(124,plain,
% 112.55/112.73 ((~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))),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[123, 113])).
% 112.55/112.73 tff(125,plain,
% 112.55/112.73 (leq(multiplication(star(X0!0), star(X0!0)), star(X0!0))),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[124, 120])).
% 112.55/112.73 tff(126,plain,
% 112.55/112.73 (leq(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0))),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[125, 52])).
% 112.55/112.73 tff(127,plain,
% 112.55/112.73 ((~![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)))),
% 112.55/112.73 inference(quant_inst,[status(thm)],[])).
% 112.55/112.73 tff(128,plain,
% 112.55/112.73 (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))),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[127, 7])).
% 112.55/112.73 tff(129,plain,
% 112.55/112.73 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 112.55/112.73 inference(bind,[status(th)],[])).
% 112.55/112.73 tff(130,plain,
% 112.55/112.73 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 112.55/112.73 inference(quant_intro,[status(thm)],[129])).
% 112.55/112.73 tff(131,plain,
% 112.55/112.73 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 112.55/112.73 inference(rewrite,[status(thm)],[])).
% 112.55/112.73 tff(132,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 112.55/112.73 tff(133,plain,
% 112.55/112.73 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[132, 131])).
% 112.55/112.73 tff(134,plain,(
% 112.55/112.73 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 112.55/112.73 inference(skolemize,[status(sab)],[133])).
% 112.55/112.73 tff(135,plain,
% 112.55/112.73 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 112.55/112.73 inference(modus_ponens,[status(thm)],[134, 130])).
% 112.55/112.73 tff(136,plain,
% 112.55/112.73 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 112.55/112.73 inference(quant_inst,[status(thm)],[])).
% 112.55/112.73 tff(137,plain,
% 112.55/112.73 (leq(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[136, 135])).
% 112.55/112.73 tff(138,plain,
% 112.55/112.73 ((~(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))),
% 112.55/112.73 inference(tautology,[status(thm)],[])).
% 112.55/112.73 tff(139,plain,
% 112.55/112.73 ((~(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))),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[138, 137])).
% 112.55/112.73 tff(140,plain,
% 112.55/112.73 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = star(X0!0)),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[139, 128])).
% 112.55/112.73 tff(141,plain,
% 112.55/112.73 ((~![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)))),
% 112.55/112.73 inference(quant_inst,[status(thm)],[])).
% 112.55/112.73 tff(142,plain,
% 112.55/112.73 (addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[141, 75])).
% 112.55/112.73 tff(143,plain,
% 112.55/112.73 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 112.55/112.73 inference(quant_inst,[status(thm)],[])).
% 112.55/112.73 tff(144,plain,
% 112.55/112.73 (addition(one, one) = one),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[143, 64])).
% 112.55/112.73 tff(145,plain,
% 112.55/112.73 (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)))),
% 112.55/112.73 inference(monotonicity,[status(thm)],[144])).
% 112.55/112.73 tff(146,plain,
% 112.55/112.73 ((~![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))))),
% 112.55/112.73 inference(quant_inst,[status(thm)],[])).
% 112.55/112.73 tff(147,plain,
% 112.55/112.73 (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)))),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[146, 75])).
% 112.55/112.73 tff(148,plain,
% 112.55/112.73 (addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0)) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 112.55/112.73 inference(symmetry,[status(thm)],[142])).
% 112.55/112.73 tff(149,plain,
% 112.55/112.73 (star(X0!0) = addition(addition(one, multiplication(star(X0!0), X0!0)), star(X0!0))),
% 112.55/112.73 inference(symmetry,[status(thm)],[140])).
% 112.55/112.73 tff(150,plain,
% 112.55/112.73 (star(X0!0) = addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0)))),
% 112.55/112.73 inference(transitivity,[status(thm)],[149, 148])).
% 112.55/112.73 tff(151,plain,
% 112.55/112.73 (addition(one, star(X0!0)) = addition(one, addition(one, addition(multiplication(star(X0!0), X0!0), star(X0!0))))),
% 112.55/112.73 inference(monotonicity,[status(thm)],[150])).
% 112.55/112.73 tff(152,plain,
% 112.55/112.73 (addition(one, star(X0!0)) = star(X0!0)),
% 112.55/112.73 inference(transitivity,[status(thm)],[151, 147, 145, 142, 140])).
% 112.55/112.73 tff(153,plain,
% 112.55/112.73 (multiplication(star(X0!0), addition(one, star(X0!0))) = multiplication(star(X0!0), star(X0!0))),
% 112.55/112.73 inference(monotonicity,[status(thm)],[152])).
% 112.55/112.73 tff(154,plain,
% 112.55/112.73 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(X0!0)) = addition(star(X0!0), one))),
% 112.55/112.73 inference(quant_inst,[status(thm)],[])).
% 112.55/112.73 tff(155,plain,
% 112.55/112.73 (addition(one, star(X0!0)) = addition(star(X0!0), one)),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[154, 16])).
% 112.55/112.73 tff(156,plain,
% 112.55/112.73 (addition(star(X0!0), one) = addition(one, star(X0!0))),
% 112.55/112.73 inference(symmetry,[status(thm)],[155])).
% 112.55/112.73 tff(157,plain,
% 112.55/112.73 (multiplication(star(X0!0), addition(star(X0!0), one)) = multiplication(star(X0!0), addition(one, star(X0!0)))),
% 112.55/112.73 inference(monotonicity,[status(thm)],[156])).
% 112.55/112.73 tff(158,plain,
% 112.55/112.73 ((~![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), one)) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), one)))),
% 112.55/112.73 inference(quant_inst,[status(thm)],[])).
% 112.55/112.73 tff(159,plain,
% 112.55/112.73 (multiplication(star(X0!0), addition(star(X0!0), one)) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), one))),
% 112.55/112.73 inference(unit_resolution,[status(thm)],[158, 46])).
% 112.55/112.73 tff(160,plain,
% 112.55/112.73 (addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), one)) = multiplication(star(X0!0), addition(star(X0!0), one))),
% 112.55/112.73 inference(symmetry,[status(thm)],[159])).
% 112.55/112.73 tff(161,plain,
% 112.55/112.73 (addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), multiplication(star(X0!0), one)) = addition(multiplication(star(X0!0), star(X0!0)), multiplication(star(X0!0), one))),
% 112.55/112.73 inference(monotonicity,[status(thm)],[50])).
% 112.55/112.73 tff(162,plain,
% 112.55/112.73 (star(X0!0) = multiplication(star(X0!0), one)),
% 112.55/112.73 inference(symmetry,[status(thm)],[98])).
% 112.55/112.73 tff(163,plain,
% 112.55/112.73 (addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) = addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), multiplication(star(X0!0), one))),
% 112.55/112.73 inference(monotonicity,[status(thm)],[162])).
% 112.55/112.73 tff(164,plain,
% 112.55/112.73 (addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) = multiplication(star(X0!0), star(X0!0))),
% 112.64/112.85 inference(transitivity,[status(thm)],[163, 161, 160, 157, 153])).
% 112.64/112.85 tff(165,plain,
% 112.64/112.85 ((addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) = star(X0!0)) <=> (multiplication(star(X0!0), star(X0!0)) = star(X0!0))),
% 112.64/112.85 inference(monotonicity,[status(thm)],[164])).
% 112.64/112.85 tff(166,plain,
% 112.64/112.85 ((multiplication(star(X0!0), star(X0!0)) = star(X0!0)) <=> (addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) = star(X0!0))),
% 112.64/112.85 inference(symmetry,[status(thm)],[165])).
% 112.64/112.85 tff(167,plain,
% 112.64/112.85 ((~(multiplication(star(X0!0), star(X0!0)) = star(X0!0))) <=> (~(addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) = star(X0!0)))),
% 112.64/112.85 inference(monotonicity,[status(thm)],[166])).
% 112.64/112.85 tff(168,plain,
% 112.64/112.85 ((~![X0: $i] : (multiplication(star(X0), star(X0)) = star(X0))) <=> (~![X0: $i] : (multiplication(star(X0), star(X0)) = star(X0)))),
% 112.64/112.85 inference(rewrite,[status(thm)],[])).
% 112.64/112.85 tff(169,axiom,(~![X0: $i] : (multiplication(star(X0), star(X0)) = star(X0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 112.64/112.85 tff(170,plain,
% 112.64/112.85 (~![X0: $i] : (multiplication(star(X0), star(X0)) = star(X0))),
% 112.64/112.85 inference(modus_ponens,[status(thm)],[169, 168])).
% 112.64/112.85 tff(171,plain,
% 112.64/112.85 (~![X0: $i] : (multiplication(star(X0), star(X0)) = star(X0))),
% 112.64/112.85 inference(modus_ponens,[status(thm)],[170, 168])).
% 112.64/112.85 tff(172,plain,
% 112.64/112.85 (~![X0: $i] : (multiplication(star(X0), star(X0)) = star(X0))),
% 112.64/112.85 inference(modus_ponens,[status(thm)],[171, 168])).
% 112.64/112.85 tff(173,plain,
% 112.64/112.85 (~![X0: $i] : (multiplication(star(X0), star(X0)) = star(X0))),
% 112.64/112.85 inference(modus_ponens,[status(thm)],[172, 168])).
% 112.64/112.85 tff(174,plain,(
% 112.64/112.85 ~(multiplication(star(X0!0), star(X0!0)) = star(X0!0))),
% 112.64/112.85 inference(skolemize,[status(sab)],[173])).
% 112.64/112.85 tff(175,plain,
% 112.64/112.85 (~(addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) = star(X0!0))),
% 112.64/112.85 inference(modus_ponens,[status(thm)],[174, 167])).
% 112.64/112.85 tff(176,plain,
% 112.64/112.85 ((~(leq(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) <=> (addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) = star(X0!0)))) | (~leq(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0))) | (addition(addition(multiplication(star(X0!0), addition(multiplication(X0!0, star(X0!0)), one)), multiplication(star(X0!0), star(X0!0))), star(X0!0)) = star(X0!0))),
% 112.64/112.85 inference(tautology,[status(thm)],[])).
% 112.64/112.85 tff(177,plain,
% 112.64/112.85 ($false),
% 112.64/112.85 inference(unit_resolution,[status(thm)],[176, 175, 126, 9])).
% 112.64/112.85 % SZS output end Proof
% 112.74/112.92 % E exiting
%------------------------------------------------------------------------------