%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE159+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:13:07 AM UTC 2025
% Result : Theorem 0.54s 0.75s
% Output : Proof 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE159+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:05:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.54/0.75 % SZS status Theorem
% 0.54/0.75 % SZS output start Proof
% 0.54/0.75 tff(multiplication_type, type, (
% 0.54/0.75 multiplication: ( $i * $i ) > $i)).
% 0.54/0.75 tff(tptp_fun_X0_2_type, type, (
% 0.54/0.75 tptp_fun_X0_2: $i)).
% 0.54/0.75 tff(star_type, type, (
% 0.54/0.75 star: $i > $i)).
% 0.54/0.75 tff(tptp_fun_X2_0_type, type, (
% 0.54/0.75 tptp_fun_X2_0: $i)).
% 0.54/0.75 tff(addition_type, type, (
% 0.54/0.75 addition: ( $i * $i ) > $i)).
% 0.54/0.75 tff(tptp_fun_X1_1_type, type, (
% 0.54/0.75 tptp_fun_X1_1: $i)).
% 0.54/0.75 tff(one_type, type, (
% 0.54/0.75 one: $i)).
% 0.54/0.75 tff(leq_type, type, (
% 0.54/0.75 leq: ( $i * $i ) > $o)).
% 0.54/0.75 tff(1,plain,
% 0.54/0.75 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(2,plain,
% 0.54/0.75 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[1])).
% 0.54/0.75 tff(3,plain,
% 0.54/0.75 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(4,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 0.54/0.75 tff(5,plain,
% 0.54/0.75 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.54/0.75 tff(6,plain,(
% 0.54/0.75 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.54/0.75 inference(skolemize,[status(sab)],[5])).
% 0.54/0.75 tff(7,plain,
% 0.54/0.75 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.54/0.75 tff(8,plain,
% 0.54/0.75 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(X2!0, star(X2!0))) = star(X2!0))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(9,plain,
% 0.54/0.75 (addition(one, multiplication(X2!0, star(X2!0))) = star(X2!0)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.54/0.75 tff(10,plain,
% 0.54/0.75 (multiplication(addition(one, multiplication(X2!0, star(X2!0))), X0!2) = multiplication(star(X2!0), X0!2)),
% 0.54/0.75 inference(monotonicity,[status(thm)],[9])).
% 0.54/0.75 tff(11,plain,
% 0.54/0.75 (^[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))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(12,plain,
% 0.54/0.75 (![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)))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[11])).
% 0.54/0.75 tff(13,plain,
% 0.54/0.75 (![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)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(14,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/KLE004+0.ax','distributivity2')).
% 0.54/0.75 tff(15,plain,
% 0.54/0.75 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.54/0.75 tff(16,plain,(
% 0.54/0.75 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.54/0.75 inference(skolemize,[status(sab)],[15])).
% 0.54/0.75 tff(17,plain,
% 0.54/0.75 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.54/0.75 tff(18,plain,
% 0.54/0.75 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, multiplication(X2!0, star(X2!0))), X0!2) = addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(19,plain,
% 0.54/0.75 (multiplication(addition(one, multiplication(X2!0, star(X2!0))), X0!2) = addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.54/0.75 tff(20,plain,
% 0.54/0.75 (addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = multiplication(addition(one, multiplication(X2!0, star(X2!0))), X0!2)),
% 0.54/0.75 inference(symmetry,[status(thm)],[19])).
% 0.54/0.75 tff(21,plain,
% 0.54/0.75 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(22,plain,
% 0.54/0.75 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[21])).
% 0.54/0.75 tff(23,plain,
% 0.54/0.75 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(24,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.54/0.75 tff(25,plain,
% 0.54/0.75 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.54/0.75 tff(26,plain,(
% 0.54/0.75 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.54/0.75 inference(skolemize,[status(sab)],[25])).
% 0.54/0.75 tff(27,plain,
% 0.54/0.75 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.54/0.75 tff(28,plain,
% 0.54/0.75 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(29,plain,
% 0.54/0.75 (addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.54/0.75 tff(30,plain,
% 0.54/0.75 (addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2)) = addition(multiplication(one, X0!2), multiplication(multiplication(X2!0, star(X2!0)), X0!2))),
% 0.54/0.75 inference(symmetry,[status(thm)],[29])).
% 0.54/0.75 tff(31,plain,
% 0.54/0.75 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(32,plain,
% 0.54/0.75 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.54/0.75 inference(quant_intro,[status(thm)],[31])).
% 0.54/0.75 tff(33,plain,
% 0.54/0.75 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(34,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 0.54/0.75 tff(35,plain,
% 0.54/0.75 (![A: $i] : (multiplication(one, A) = A)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.54/0.75 tff(36,plain,(
% 0.54/0.75 ![A: $i] : (multiplication(one, A) = A)),
% 0.54/0.75 inference(skolemize,[status(sab)],[35])).
% 0.54/0.75 tff(37,plain,
% 0.54/0.75 (![A: $i] : (multiplication(one, A) = A)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.54/0.75 tff(38,plain,
% 0.54/0.75 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(39,plain,
% 0.54/0.75 (multiplication(one, X0!2) = X0!2),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.54/0.75 tff(40,plain,
% 0.54/0.75 (X0!2 = multiplication(one, X0!2)),
% 0.54/0.75 inference(symmetry,[status(thm)],[39])).
% 0.54/0.75 tff(41,plain,
% 0.54/0.75 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(42,plain,
% 0.54/0.75 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.54/0.75 inference(quant_intro,[status(thm)],[41])).
% 0.54/0.75 tff(43,plain,
% 0.54/0.75 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(44,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.54/0.75 tff(45,plain,
% 0.54/0.75 (![A: $i] : (addition(A, A) = A)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.54/0.75 tff(46,plain,(
% 0.54/0.75 ![A: $i] : (addition(A, A) = A)),
% 0.54/0.75 inference(skolemize,[status(sab)],[45])).
% 0.54/0.75 tff(47,plain,
% 0.54/0.75 (![A: $i] : (addition(A, A) = A)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.54/0.75 tff(48,plain,
% 0.54/0.75 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!2, X0!2) = X0!2)),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(49,plain,
% 0.54/0.75 (addition(X0!2, X0!2) = X0!2),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.54/0.75 tff(50,plain,
% 0.54/0.75 (addition(X0!2, X0!2) = multiplication(one, X0!2)),
% 0.54/0.75 inference(transitivity,[status(thm)],[49, 40])).
% 0.54/0.75 tff(51,plain,
% 0.54/0.75 (addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), addition(X0!2, X0!2)) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[50])).
% 0.54/0.75 tff(52,plain,
% 0.54/0.75 (^[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)))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(53,plain,
% 0.54/0.75 (![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))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[52])).
% 0.54/0.75 tff(54,plain,
% 0.54/0.75 (![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))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(55,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_associativity')).
% 0.54/0.75 tff(56,plain,
% 0.54/0.75 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.54/0.75 tff(57,plain,(
% 0.54/0.75 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.54/0.75 inference(skolemize,[status(sab)],[56])).
% 0.54/0.75 tff(58,plain,
% 0.54/0.75 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.54/0.75 tff(59,plain,
% 0.54/0.75 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), addition(X0!2, X0!2)) = addition(addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2), X0!2))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(60,plain,
% 0.54/0.75 (addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), addition(X0!2, X0!2)) = addition(addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2), X0!2)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.54/0.75 tff(61,plain,
% 0.54/0.75 (addition(addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2), X0!2) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), addition(X0!2, X0!2))),
% 0.54/0.75 inference(symmetry,[status(thm)],[60])).
% 0.54/0.75 tff(62,plain,
% 0.54/0.75 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(63,plain,
% 0.54/0.75 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.54/0.75 inference(quant_intro,[status(thm)],[62])).
% 0.54/0.75 tff(64,plain,
% 0.54/0.75 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(65,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 0.54/0.75 tff(66,plain,
% 0.54/0.75 (![A: $i] : (multiplication(A, one) = A)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.54/0.75 tff(67,plain,(
% 0.54/0.75 ![A: $i] : (multiplication(A, one) = A)),
% 0.54/0.75 inference(skolemize,[status(sab)],[66])).
% 0.54/0.75 tff(68,plain,
% 0.54/0.75 (![A: $i] : (multiplication(A, one) = A)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.54/0.76 tff(69,plain,
% 0.54/0.76 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!2, one) = X0!2)),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(70,plain,
% 0.54/0.76 (multiplication(X0!2, one) = X0!2),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.54/0.76 tff(71,plain,
% 0.54/0.76 (addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[40])).
% 0.54/0.76 tff(72,plain,
% 0.54/0.76 (addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2)) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2)),
% 0.54/0.76 inference(symmetry,[status(thm)],[71])).
% 0.54/0.76 tff(73,plain,
% 0.54/0.76 (multiplication(star(X2!0), X0!2) = multiplication(addition(one, multiplication(X2!0, star(X2!0))), X0!2)),
% 0.54/0.76 inference(symmetry,[status(thm)],[10])).
% 0.54/0.76 tff(74,plain,
% 0.54/0.76 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(75,plain,
% 0.54/0.76 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[74])).
% 0.54/0.76 tff(76,plain,
% 0.54/0.76 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(77,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 0.54/0.76 tff(78,plain,
% 0.54/0.76 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.54/0.76 tff(79,plain,(
% 0.54/0.76 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.54/0.76 inference(skolemize,[status(sab)],[78])).
% 0.54/0.76 tff(80,plain,
% 0.54/0.76 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.54/0.76 tff(81,plain,
% 0.54/0.76 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(X2!0), X2!0)) = star(X2!0))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(82,plain,
% 0.54/0.76 (addition(one, multiplication(star(X2!0), X2!0)) = star(X2!0)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.54/0.76 tff(83,plain,
% 0.54/0.76 (star(X2!0) = addition(one, multiplication(star(X2!0), X2!0))),
% 0.54/0.76 inference(symmetry,[status(thm)],[82])).
% 0.54/0.76 tff(84,plain,
% 0.54/0.76 (multiplication(star(X2!0), X0!2) = multiplication(addition(one, multiplication(star(X2!0), X2!0)), X0!2)),
% 0.54/0.76 inference(monotonicity,[status(thm)],[83])).
% 0.54/0.76 tff(85,plain,
% 0.54/0.76 (multiplication(addition(one, multiplication(star(X2!0), X2!0)), X0!2) = multiplication(star(X2!0), X0!2)),
% 0.54/0.76 inference(symmetry,[status(thm)],[84])).
% 0.54/0.76 tff(86,plain,
% 0.54/0.76 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, multiplication(star(X2!0), X2!0)), X0!2) = addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(87,plain,
% 0.54/0.76 (multiplication(addition(one, multiplication(star(X2!0), X2!0)), X0!2) = addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[86, 17])).
% 0.54/0.76 tff(88,plain,
% 0.54/0.76 (addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)) = multiplication(addition(one, multiplication(star(X2!0), X2!0)), X0!2)),
% 0.54/0.76 inference(symmetry,[status(thm)],[87])).
% 0.54/0.76 tff(89,plain,
% 0.54/0.76 (addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2)),
% 0.54/0.76 inference(transitivity,[status(thm)],[88, 85, 73, 19, 29, 72])).
% 0.54/0.76 tff(90,plain,
% 0.54/0.76 (addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), multiplication(X0!2, one)) = addition(addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2), X0!2)),
% 0.54/0.76 inference(monotonicity,[status(thm)],[89, 70])).
% 0.54/0.76 tff(91,plain,
% 0.54/0.76 (X0!2 = multiplication(X0!2, one)),
% 0.54/0.76 inference(symmetry,[status(thm)],[70])).
% 0.54/0.76 tff(92,plain,
% 0.54/0.76 (multiplication(X2!0, star(X2!0)) = multiplication(X2!0, addition(one, multiplication(star(X2!0), X2!0)))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[83])).
% 0.54/0.76 tff(93,plain,
% 0.54/0.76 (multiplication(X2!0, addition(one, multiplication(star(X2!0), X2!0))) = multiplication(X2!0, star(X2!0))),
% 0.54/0.76 inference(symmetry,[status(thm)],[92])).
% 0.54/0.76 tff(94,plain,
% 0.54/0.76 (^[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))))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(95,plain,
% 0.54/0.76 (![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)))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[94])).
% 0.54/0.76 tff(96,plain,
% 0.54/0.76 (![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)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(97,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/KLE004+0.ax','distributivity1')).
% 0.54/0.76 tff(98,plain,
% 0.54/0.76 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.54/0.76 tff(99,plain,(
% 0.54/0.76 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.54/0.76 inference(skolemize,[status(sab)],[98])).
% 0.54/0.76 tff(100,plain,
% 0.54/0.76 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.54/0.76 tff(101,plain,
% 0.54/0.76 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X2!0, addition(one, multiplication(star(X2!0), X2!0))) = addition(multiplication(X2!0, one), multiplication(X2!0, multiplication(star(X2!0), X2!0))))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(102,plain,
% 0.54/0.76 (multiplication(X2!0, addition(one, multiplication(star(X2!0), X2!0))) = addition(multiplication(X2!0, one), multiplication(X2!0, multiplication(star(X2!0), X2!0)))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.54/0.76 tff(103,plain,
% 0.54/0.76 (addition(multiplication(X2!0, one), multiplication(X2!0, multiplication(star(X2!0), X2!0))) = multiplication(X2!0, addition(one, multiplication(star(X2!0), X2!0)))),
% 0.54/0.76 inference(symmetry,[status(thm)],[102])).
% 0.54/0.76 tff(104,plain,
% 0.54/0.76 (^[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)))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(105,plain,
% 0.54/0.76 (![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))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[104])).
% 0.54/0.76 tff(106,plain,
% 0.54/0.76 (![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))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(107,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.54/0.76 tff(108,plain,
% 0.54/0.76 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.54/0.76 tff(109,plain,(
% 0.54/0.76 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.54/0.76 inference(skolemize,[status(sab)],[108])).
% 0.54/0.76 tff(110,plain,
% 0.54/0.76 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.54/0.76 tff(111,plain,
% 0.54/0.76 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X2!0, multiplication(star(X2!0), X2!0)) = multiplication(multiplication(X2!0, star(X2!0)), X2!0))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(112,plain,
% 0.54/0.76 (multiplication(X2!0, multiplication(star(X2!0), X2!0)) = multiplication(multiplication(X2!0, star(X2!0)), X2!0)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.54/0.76 tff(113,plain,
% 0.54/0.76 (multiplication(multiplication(X2!0, star(X2!0)), X2!0) = multiplication(X2!0, multiplication(star(X2!0), X2!0))),
% 0.54/0.76 inference(symmetry,[status(thm)],[112])).
% 0.54/0.76 tff(114,plain,
% 0.54/0.76 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X2!0, one) = X2!0)),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(115,plain,
% 0.54/0.76 (multiplication(X2!0, one) = X2!0),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[114, 68])).
% 0.54/0.76 tff(116,plain,
% 0.54/0.76 (X2!0 = multiplication(X2!0, one)),
% 0.54/0.76 inference(symmetry,[status(thm)],[115])).
% 0.54/0.76 tff(117,plain,
% 0.54/0.76 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X2!0) = X2!0)),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(118,plain,
% 0.54/0.76 (multiplication(one, X2!0) = X2!0),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[117, 37])).
% 0.54/0.76 tff(119,plain,
% 0.54/0.76 (multiplication(one, X2!0) = multiplication(X2!0, one)),
% 0.54/0.76 inference(transitivity,[status(thm)],[118, 116])).
% 0.54/0.76 tff(120,plain,
% 0.54/0.76 (addition(multiplication(one, X2!0), multiplication(multiplication(X2!0, star(X2!0)), X2!0)) = addition(multiplication(X2!0, one), multiplication(X2!0, multiplication(star(X2!0), X2!0)))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[119, 113])).
% 0.54/0.76 tff(121,plain,
% 0.54/0.76 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, multiplication(X2!0, star(X2!0))), X2!0) = addition(multiplication(one, X2!0), multiplication(multiplication(X2!0, star(X2!0)), X2!0)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(122,plain,
% 0.54/0.76 (multiplication(addition(one, multiplication(X2!0, star(X2!0))), X2!0) = addition(multiplication(one, X2!0), multiplication(multiplication(X2!0, star(X2!0)), X2!0))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[121, 17])).
% 0.54/0.76 tff(123,plain,
% 0.54/0.76 (star(X2!0) = addition(one, multiplication(X2!0, star(X2!0)))),
% 0.54/0.76 inference(symmetry,[status(thm)],[9])).
% 0.54/0.76 tff(124,plain,
% 0.54/0.76 (multiplication(star(X2!0), X2!0) = multiplication(addition(one, multiplication(X2!0, star(X2!0))), X2!0)),
% 0.54/0.76 inference(monotonicity,[status(thm)],[123])).
% 0.54/0.76 tff(125,plain,
% 0.54/0.76 (multiplication(star(X2!0), X2!0) = multiplication(X2!0, star(X2!0))),
% 0.54/0.76 inference(transitivity,[status(thm)],[124, 122, 120, 103, 93])).
% 0.54/0.76 tff(126,plain,
% 0.54/0.76 (multiplication(multiplication(star(X2!0), X2!0), X0!2) = multiplication(multiplication(X2!0, star(X2!0)), X0!2)),
% 0.54/0.76 inference(monotonicity,[status(thm)],[125])).
% 0.54/0.76 tff(127,plain,
% 0.54/0.76 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(star(X2!0), multiplication(X2!0, X0!2)) = multiplication(multiplication(star(X2!0), X2!0), X0!2))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(128,plain,
% 0.54/0.76 (multiplication(star(X2!0), multiplication(X2!0, X0!2)) = multiplication(multiplication(star(X2!0), X2!0), X0!2)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[127, 110])).
% 0.54/0.76 tff(129,plain,
% 0.54/0.76 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(130,plain,
% 0.54/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[129])).
% 0.54/0.76 tff(131,plain,
% 0.54/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(132,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','order')).
% 0.54/0.76 tff(133,plain,
% 0.54/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.54/0.76 tff(134,plain,(
% 0.54/0.76 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.54/0.76 inference(skolemize,[status(sab)],[133])).
% 0.54/0.76 tff(135,plain,
% 0.54/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.54/0.76 tff(136,plain,
% 0.54/0.76 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(137,plain,
% 0.54/0.76 (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.54/0.76 tff(138,plain,
% 0.54/0.76 ((~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(139,plain,
% 0.54/0.76 ((~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X2, X0)) => leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(140,axiom,(~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X2, X0)) => leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.54/0.76 tff(141,plain,
% 0.54/0.76 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.54/0.76 tff(142,plain,
% 0.54/0.76 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[141, 138])).
% 0.54/0.76 tff(143,plain,
% 0.54/0.76 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.54/0.76 tff(144,plain,
% 0.54/0.76 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, star(X1)), multiplication(star(X2), X0)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[143, 138])).
% 0.54/0.76 tff(145,plain,(
% 0.54/0.76 ~((~leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) | leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2)))),
% 0.54/0.76 inference(skolemize,[status(sab)],[144])).
% 0.54/0.76 tff(146,plain,
% 0.54/0.76 (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))),
% 0.54/0.76 inference(or_elim,[status(thm)],[145])).
% 0.54/0.76 tff(147,plain,
% 0.54/0.76 ((~(leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))) | (~leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) | (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.54/0.76 inference(tautology,[status(thm)],[])).
% 0.54/0.76 tff(148,plain,
% 0.54/0.76 ((~(leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))) | (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.54/0.76 tff(149,plain,
% 0.54/0.76 (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[148, 137])).
% 0.54/0.76 tff(150,plain,
% 0.54/0.76 (multiplication(star(X2!0), addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) = multiplication(star(X2!0), multiplication(X2!0, X0!2))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[149])).
% 0.54/0.76 tff(151,plain,
% 0.54/0.76 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X2!0), addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) = addition(multiplication(star(X2!0), multiplication(X0!2, X1!1)), multiplication(star(X2!0), multiplication(X2!0, X0!2))))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(152,plain,
% 0.54/0.76 (multiplication(star(X2!0), addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) = addition(multiplication(star(X2!0), multiplication(X0!2, X1!1)), multiplication(star(X2!0), multiplication(X2!0, X0!2)))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[151, 100])).
% 0.54/0.76 tff(153,plain,
% 0.54/0.76 (addition(multiplication(star(X2!0), multiplication(X0!2, X1!1)), multiplication(star(X2!0), multiplication(X2!0, X0!2))) = multiplication(star(X2!0), addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)))),
% 0.54/0.76 inference(symmetry,[status(thm)],[152])).
% 0.54/0.76 tff(154,plain,
% 0.54/0.76 (multiplication(multiplication(star(X2!0), X2!0), X0!2) = multiplication(star(X2!0), multiplication(X2!0, X0!2))),
% 0.54/0.76 inference(symmetry,[status(thm)],[128])).
% 0.54/0.76 tff(155,plain,
% 0.54/0.76 (multiplication(multiplication(X2!0, star(X2!0)), X0!2) = multiplication(multiplication(star(X2!0), X2!0), X0!2)),
% 0.54/0.76 inference(symmetry,[status(thm)],[126])).
% 0.54/0.76 tff(156,plain,
% 0.54/0.76 (multiplication(multiplication(X2!0, star(X2!0)), X0!2) = multiplication(star(X2!0), multiplication(X2!0, X0!2))),
% 0.54/0.76 inference(transitivity,[status(thm)],[155, 154])).
% 0.54/0.76 tff(157,plain,
% 0.54/0.76 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(star(X2!0), multiplication(X0!2, X1!1)) = multiplication(multiplication(star(X2!0), X0!2), X1!1))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(158,plain,
% 0.54/0.76 (multiplication(star(X2!0), multiplication(X0!2, X1!1)) = multiplication(multiplication(star(X2!0), X0!2), X1!1)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[157, 110])).
% 0.54/0.76 tff(159,plain,
% 0.54/0.76 (multiplication(multiplication(star(X2!0), X0!2), X1!1) = multiplication(star(X2!0), multiplication(X0!2, X1!1))),
% 0.54/0.76 inference(symmetry,[status(thm)],[158])).
% 0.54/0.76 tff(160,plain,
% 0.54/0.76 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = addition(multiplication(star(X2!0), multiplication(X0!2, X1!1)), multiplication(star(X2!0), multiplication(X2!0, X0!2)))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[159, 156])).
% 0.54/0.76 tff(161,plain,
% 0.54/0.76 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), multiplication(multiplication(X2!0, star(X2!0)), X0!2)) = multiplication(multiplication(X2!0, star(X2!0)), X0!2)),
% 0.54/0.76 inference(transitivity,[status(thm)],[160, 153, 150, 128, 126])).
% 0.54/0.76 tff(162,plain,
% 0.54/0.76 (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), multiplication(multiplication(X2!0, star(X2!0)), X0!2)), X0!2) = addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), multiplication(one, X0!2))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[161, 40])).
% 0.54/0.76 tff(163,plain,
% 0.54/0.76 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2)) = addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), multiplication(multiplication(X2!0, star(X2!0)), X0!2)), X0!2))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(164,plain,
% 0.54/0.76 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2)) = addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), multiplication(multiplication(X2!0, star(X2!0)), X0!2)), X0!2)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[163, 58])).
% 0.54/0.76 tff(165,plain,
% 0.54/0.76 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2))) = addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(multiplication(X2!0, star(X2!0)), X0!2), X0!2))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[89])).
% 0.54/0.76 tff(166,plain,
% 0.54/0.76 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2))) = addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), multiplication(multiplication(star(X2!0), X0!2), X1!1)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(167,plain,
% 0.54/0.76 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2))) = addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), multiplication(multiplication(star(X2!0), X0!2), X1!1))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[166, 27])).
% 0.54/0.76 tff(168,plain,
% 0.54/0.76 (addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), multiplication(multiplication(star(X2!0), X0!2), X1!1)) = addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)))),
% 0.54/0.76 inference(symmetry,[status(thm)],[167])).
% 0.54/0.76 tff(169,plain,
% 0.54/0.76 (addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), multiplication(multiplication(star(X2!0), X0!2), X1!1)) = addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2))),
% 0.54/0.76 inference(transitivity,[status(thm)],[168, 165, 164, 162, 30, 20, 10, 84, 87])).
% 0.54/0.76 tff(170,plain,
% 0.54/0.76 (addition(addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), multiplication(multiplication(star(X2!0), X0!2), X1!1)), X0!2) = addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), multiplication(X0!2, one))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[169, 91])).
% 0.54/0.76 tff(171,plain,
% 0.54/0.76 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2)) = addition(addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), multiplication(multiplication(star(X2!0), X0!2), X1!1)), X0!2))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(172,plain,
% 0.54/0.76 (addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2)) = addition(addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), multiplication(multiplication(star(X2!0), X0!2), X1!1)), X0!2)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[171, 58])).
% 0.54/0.76 tff(173,plain,
% 0.54/0.76 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2) = addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(174,plain,
% 0.54/0.77 (addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2) = addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[173, 27])).
% 0.54/0.77 tff(175,plain,
% 0.54/0.77 (addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)) = addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2)),
% 0.54/0.77 inference(symmetry,[status(thm)],[174])).
% 0.54/0.77 tff(176,plain,
% 0.54/0.77 (addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1))) = addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[175])).
% 0.54/0.77 tff(177,plain,
% 0.54/0.77 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)), addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2))) = addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1))))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(178,plain,
% 0.54/0.77 (addition(addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)), addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2))) = addition(addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)), addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[177, 27])).
% 0.54/0.77 tff(179,plain,
% 0.54/0.77 (multiplication(star(X2!0), X0!2) = addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2))),
% 0.54/0.77 inference(transitivity,[status(thm)],[84, 87])).
% 0.54/0.77 tff(180,plain,
% 0.54/0.77 (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = addition(addition(X0!2, multiplication(multiplication(star(X2!0), X0!2), X1!1)), addition(multiplication(one, X0!2), multiplication(multiplication(star(X2!0), X2!0), X0!2)))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[174, 179])).
% 0.54/0.77 tff(181,plain,
% 0.54/0.77 (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)),
% 0.54/0.77 inference(transitivity,[status(thm)],[180, 178, 176, 172, 170, 90, 61, 51, 30, 20, 10])).
% 0.54/0.77 tff(182,plain,
% 0.54/0.77 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) <=> (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(183,plain,
% 0.54/0.77 (leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) <=> (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[182, 135])).
% 0.54/0.77 tff(184,plain,
% 0.54/0.77 (~leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2))),
% 0.54/0.77 inference(or_elim,[status(thm)],[145])).
% 0.54/0.77 tff(185,plain,
% 0.54/0.77 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)))),
% 0.54/0.77 inference(bind,[status(th)],[])).
% 0.54/0.77 tff(186,plain,
% 0.54/0.77 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.54/0.77 inference(quant_intro,[status(thm)],[185])).
% 0.54/0.77 tff(187,plain,
% 0.54/0.77 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(188,plain,
% 0.54/0.77 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C)) <=> ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)))),
% 0.54/0.77 inference(bind,[status(th)],[])).
% 0.54/0.77 tff(189,plain,
% 0.54/0.77 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.54/0.77 inference(quant_intro,[status(thm)],[188])).
% 0.54/0.77 tff(190,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_induction2')).
% 0.54/0.77 tff(191,plain,
% 0.54/0.77 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.54/0.77 tff(192,plain,
% 0.54/0.77 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.54/0.77 tff(193,plain,(
% 0.54/0.77 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.54/0.77 inference(skolemize,[status(sab)],[192])).
% 0.54/0.77 tff(194,plain,
% 0.54/0.77 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.54/0.77 tff(195,plain,
% 0.54/0.77 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | ((~leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2))) | leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | (~leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2))) | leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2)))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(196,plain,
% 0.54/0.77 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | ((~leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2))) | leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(197,plain,
% 0.54/0.77 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | (~leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2))) | leq(multiplication(X0!2, star(X1!1)), multiplication(star(X2!0), X0!2))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.54/0.77 tff(198,plain,
% 0.54/0.77 (~leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[197, 194, 184])).
% 0.54/0.77 tff(199,plain,
% 0.54/0.77 ((~(leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) <=> (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)))) | leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) | (~(addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)))),
% 0.54/0.77 inference(tautology,[status(thm)],[])).
% 0.54/0.77 tff(200,plain,
% 0.54/0.77 ((~(leq(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) <=> (addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)))) | (~(addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2)))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.54/0.77 tff(201,plain,
% 0.54/0.77 (~(addition(addition(multiplication(multiplication(star(X2!0), X0!2), X1!1), X0!2), multiplication(star(X2!0), X0!2)) = multiplication(star(X2!0), X0!2))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[200, 183])).
% 0.54/0.77 tff(202,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[201, 181])).
% 0.54/0.77 % SZS output end Proof
% 0.60/0.77 % E exiting
%------------------------------------------------------------------------------