%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE160+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:07 AM UTC 2025
% Result : Theorem 0.54s 0.73s
% Output : Proof 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE160+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:05:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.54/0.73 % SZS status Theorem
% 0.54/0.73 % SZS output start Proof
% 0.54/0.73 tff(multiplication_type, type, (
% 0.54/0.73 multiplication: ( $i * $i ) > $i)).
% 0.54/0.73 tff(star_type, type, (
% 0.54/0.73 star: $i > $i)).
% 0.54/0.73 tff(tptp_fun_X2_0_type, type, (
% 0.54/0.73 tptp_fun_X2_0: $i)).
% 0.54/0.73 tff(tptp_fun_X1_1_type, type, (
% 0.54/0.73 tptp_fun_X1_1: $i)).
% 0.54/0.73 tff(addition_type, type, (
% 0.54/0.73 addition: ( $i * $i ) > $i)).
% 0.54/0.73 tff(tptp_fun_X0_2_type, type, (
% 0.54/0.73 tptp_fun_X0_2: $i)).
% 0.54/0.73 tff(one_type, type, (
% 0.54/0.73 one: $i)).
% 0.54/0.73 tff(leq_type, type, (
% 0.54/0.73 leq: ( $i * $i ) > $o)).
% 0.54/0.73 tff(1,plain,
% 0.54/0.73 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(2,plain,
% 0.54/0.73 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[1])).
% 0.54/0.73 tff(3,plain,
% 0.54/0.73 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(4,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 0.54/0.73 tff(5,plain,
% 0.54/0.73 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.54/0.73 tff(6,plain,(
% 0.54/0.73 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.54/0.73 inference(skolemize,[status(sab)],[5])).
% 0.54/0.73 tff(7,plain,
% 0.54/0.73 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.54/0.73 tff(8,plain,
% 0.54/0.73 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(X2!0, star(X2!0))) = star(X2!0))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(9,plain,
% 0.54/0.73 (addition(one, multiplication(X2!0, star(X2!0))) = star(X2!0)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.54/0.73 tff(10,plain,
% 0.54/0.73 (multiplication(X1!1, addition(one, multiplication(X2!0, star(X2!0)))) = multiplication(X1!1, star(X2!0))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[9])).
% 0.54/0.73 tff(11,plain,
% 0.54/0.73 (^[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))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(12,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[11])).
% 0.54/0.73 tff(13,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(14,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity1')).
% 0.54/0.73 tff(15,plain,
% 0.54/0.73 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.54/0.73 tff(16,plain,(
% 0.54/0.73 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.54/0.73 inference(skolemize,[status(sab)],[15])).
% 0.54/0.73 tff(17,plain,
% 0.54/0.73 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.54/0.73 tff(18,plain,
% 0.54/0.73 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!1, addition(one, multiplication(X2!0, star(X2!0)))) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0)))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(19,plain,
% 0.54/0.73 (multiplication(X1!1, addition(one, multiplication(X2!0, star(X2!0)))) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.54/0.73 tff(20,plain,
% 0.54/0.73 (addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0)))) = multiplication(X1!1, addition(one, multiplication(X2!0, star(X2!0))))),
% 0.54/0.73 inference(symmetry,[status(thm)],[19])).
% 0.54/0.73 tff(21,plain,
% 0.54/0.73 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(22,plain,
% 0.54/0.73 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[21])).
% 0.54/0.73 tff(23,plain,
% 0.54/0.73 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(24,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.54/0.73 tff(25,plain,
% 0.54/0.73 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.54/0.73 tff(26,plain,(
% 0.54/0.73 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.54/0.73 inference(skolemize,[status(sab)],[25])).
% 0.54/0.73 tff(27,plain,
% 0.54/0.73 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.54/0.73 tff(28,plain,
% 0.54/0.73 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0)))) = addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(29,plain,
% 0.54/0.73 (addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0)))) = addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.54/0.73 tff(30,plain,
% 0.54/0.73 (addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one)) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(X2!0, star(X2!0))))),
% 0.54/0.73 inference(symmetry,[status(thm)],[29])).
% 0.54/0.73 tff(31,plain,
% 0.54/0.73 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(32,plain,
% 0.54/0.73 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.54/0.73 inference(quant_intro,[status(thm)],[31])).
% 0.54/0.73 tff(33,plain,
% 0.54/0.73 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(34,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 0.54/0.73 tff(35,plain,
% 0.54/0.73 (![A: $i] : (multiplication(A, one) = A)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.54/0.73 tff(36,plain,(
% 0.54/0.73 ![A: $i] : (multiplication(A, one) = A)),
% 0.54/0.73 inference(skolemize,[status(sab)],[35])).
% 0.54/0.73 tff(37,plain,
% 0.54/0.73 (![A: $i] : (multiplication(A, one) = A)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.54/0.73 tff(38,plain,
% 0.54/0.73 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X1!1, one) = X1!1)),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(39,plain,
% 0.54/0.73 (multiplication(X1!1, one) = X1!1),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.54/0.73 tff(40,plain,
% 0.54/0.73 (X1!1 = multiplication(X1!1, one)),
% 0.54/0.73 inference(symmetry,[status(thm)],[39])).
% 0.54/0.73 tff(41,plain,
% 0.54/0.73 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(42,plain,
% 0.54/0.73 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.54/0.73 inference(quant_intro,[status(thm)],[41])).
% 0.54/0.73 tff(43,plain,
% 0.54/0.73 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(44,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.54/0.73 tff(45,plain,
% 0.54/0.73 (![A: $i] : (addition(A, A) = A)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.54/0.73 tff(46,plain,(
% 0.54/0.73 ![A: $i] : (addition(A, A) = A)),
% 0.54/0.73 inference(skolemize,[status(sab)],[45])).
% 0.54/0.73 tff(47,plain,
% 0.54/0.73 (![A: $i] : (addition(A, A) = A)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.54/0.73 tff(48,plain,
% 0.54/0.73 ((~![A: $i] : (addition(A, A) = A)) | (addition(X1!1, X1!1) = X1!1)),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(49,plain,
% 0.54/0.73 (addition(X1!1, X1!1) = X1!1),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.54/0.73 tff(50,plain,
% 0.54/0.73 (addition(X1!1, X1!1) = multiplication(X1!1, one)),
% 0.54/0.73 inference(transitivity,[status(thm)],[49, 40])).
% 0.54/0.73 tff(51,plain,
% 0.54/0.73 (^[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)))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(52,plain,
% 0.54/0.73 (![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))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[51])).
% 0.54/0.73 tff(53,plain,
% 0.54/0.73 (![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))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(54,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.54/0.73 tff(55,plain,
% 0.54/0.73 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.54/0.73 tff(56,plain,(
% 0.54/0.73 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.54/0.73 inference(skolemize,[status(sab)],[55])).
% 0.54/0.73 tff(57,plain,
% 0.54/0.73 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.54/0.73 tff(58,plain,
% 0.54/0.73 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X1!1, multiplication(X2!0, star(X2!0))) = multiplication(multiplication(X1!1, X2!0), star(X2!0)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(59,plain,
% 0.54/0.73 (multiplication(X1!1, multiplication(X2!0, star(X2!0))) = multiplication(multiplication(X1!1, X2!0), star(X2!0))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.54/0.73 tff(60,plain,
% 0.54/0.73 (multiplication(multiplication(X1!1, X2!0), star(X2!0)) = multiplication(X1!1, multiplication(X2!0, star(X2!0)))),
% 0.54/0.73 inference(symmetry,[status(thm)],[59])).
% 0.54/0.73 tff(61,plain,
% 0.54/0.73 (addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), addition(X1!1, X1!1)) = addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[60, 50])).
% 0.54/0.73 tff(62,plain,
% 0.54/0.73 (^[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)))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(63,plain,
% 0.54/0.73 (![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))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[62])).
% 0.54/0.73 tff(64,plain,
% 0.54/0.73 (![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))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(65,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_associativity')).
% 0.54/0.73 tff(66,plain,
% 0.54/0.73 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.54/0.73 tff(67,plain,(
% 0.54/0.73 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.54/0.73 inference(skolemize,[status(sab)],[66])).
% 0.54/0.73 tff(68,plain,
% 0.54/0.73 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.54/0.73 tff(69,plain,
% 0.54/0.73 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), addition(X1!1, X1!1)) = addition(addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1), X1!1))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(70,plain,
% 0.54/0.73 (addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), addition(X1!1, X1!1)) = addition(addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1), X1!1)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.54/0.73 tff(71,plain,
% 0.54/0.73 (addition(addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1), X1!1) = addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), addition(X1!1, X1!1))),
% 0.54/0.73 inference(symmetry,[status(thm)],[70])).
% 0.54/0.73 tff(72,plain,
% 0.54/0.73 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(73,plain,
% 0.54/0.73 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.54/0.73 inference(quant_intro,[status(thm)],[72])).
% 0.54/0.73 tff(74,plain,
% 0.54/0.73 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(75,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 0.54/0.73 tff(76,plain,
% 0.54/0.73 (![A: $i] : (multiplication(one, A) = A)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.54/0.73 tff(77,plain,(
% 0.54/0.73 ![A: $i] : (multiplication(one, A) = A)),
% 0.54/0.73 inference(skolemize,[status(sab)],[76])).
% 0.54/0.73 tff(78,plain,
% 0.54/0.73 (![A: $i] : (multiplication(one, A) = A)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.54/0.73 tff(79,plain,
% 0.54/0.73 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!1) = X1!1)),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(80,plain,
% 0.54/0.73 (multiplication(one, X1!1) = X1!1),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.54/0.73 tff(81,plain,
% 0.54/0.73 (addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1) = addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[60, 40])).
% 0.54/0.73 tff(82,plain,
% 0.54/0.73 (addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one)) = addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1)),
% 0.54/0.73 inference(symmetry,[status(thm)],[81])).
% 0.54/0.73 tff(83,plain,
% 0.54/0.73 (multiplication(X1!1, star(X2!0)) = multiplication(X1!1, addition(one, multiplication(X2!0, star(X2!0))))),
% 0.54/0.73 inference(symmetry,[status(thm)],[10])).
% 0.54/0.73 tff(84,plain,
% 0.54/0.73 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(85,plain,
% 0.54/0.73 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[84])).
% 0.54/0.73 tff(86,plain,
% 0.54/0.73 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(87,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 0.54/0.73 tff(88,plain,
% 0.54/0.73 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.54/0.73 tff(89,plain,(
% 0.54/0.73 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.54/0.73 inference(skolemize,[status(sab)],[88])).
% 0.54/0.73 tff(90,plain,
% 0.54/0.73 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.54/0.73 tff(91,plain,
% 0.54/0.73 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(X2!0), X2!0)) = star(X2!0))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(92,plain,
% 0.54/0.73 (addition(one, multiplication(star(X2!0), X2!0)) = star(X2!0)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.54/0.73 tff(93,plain,
% 0.54/0.73 (star(X2!0) = addition(one, multiplication(star(X2!0), X2!0))),
% 0.54/0.73 inference(symmetry,[status(thm)],[92])).
% 0.54/0.73 tff(94,plain,
% 0.54/0.73 (multiplication(X1!1, star(X2!0)) = multiplication(X1!1, addition(one, multiplication(star(X2!0), X2!0)))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[93])).
% 0.54/0.73 tff(95,plain,
% 0.54/0.73 (multiplication(X1!1, addition(one, multiplication(star(X2!0), X2!0))) = multiplication(X1!1, star(X2!0))),
% 0.54/0.73 inference(symmetry,[status(thm)],[94])).
% 0.54/0.73 tff(96,plain,
% 0.54/0.73 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!1, addition(one, multiplication(star(X2!0), X2!0))) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(97,plain,
% 0.54/0.73 (multiplication(X1!1, addition(one, multiplication(star(X2!0), X2!0))) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0)))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[96, 17])).
% 0.54/0.73 tff(98,plain,
% 0.54/0.73 (addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))) = multiplication(X1!1, addition(one, multiplication(star(X2!0), X2!0)))),
% 0.54/0.73 inference(symmetry,[status(thm)],[97])).
% 0.54/0.73 tff(99,plain,
% 0.54/0.73 (addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))) = addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1)),
% 0.54/0.73 inference(transitivity,[status(thm)],[98, 95, 83, 19, 29, 82])).
% 0.54/0.73 tff(100,plain,
% 0.54/0.73 (addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), multiplication(one, X1!1)) = addition(addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1), X1!1)),
% 0.54/0.73 inference(monotonicity,[status(thm)],[99, 80])).
% 0.54/0.73 tff(101,plain,
% 0.54/0.73 (X1!1 = multiplication(one, X1!1)),
% 0.54/0.73 inference(symmetry,[status(thm)],[80])).
% 0.54/0.73 tff(102,plain,
% 0.54/0.73 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(103,plain,
% 0.54/0.73 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[102])).
% 0.54/0.73 tff(104,plain,
% 0.54/0.73 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(105,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','order')).
% 0.54/0.73 tff(106,plain,
% 0.54/0.73 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.54/0.73 tff(107,plain,(
% 0.54/0.73 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.54/0.73 inference(skolemize,[status(sab)],[106])).
% 0.54/0.73 tff(108,plain,
% 0.54/0.73 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.54/0.73 tff(109,plain,
% 0.54/0.73 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(110,plain,
% 0.54/0.73 (leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.54/0.73 tff(111,plain,
% 0.54/0.73 ((~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2)))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(112,plain,
% 0.54/0.73 ((~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X1, X2)) => leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2)))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(113,axiom,(~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X1, X2)) => leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.54/0.73 tff(114,plain,
% 0.54/0.73 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.54/0.73 tff(115,plain,
% 0.54/0.73 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[114, 111])).
% 0.54/0.73 tff(116,plain,
% 0.54/0.73 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.54/0.73 tff(117,plain,
% 0.54/0.73 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X1, X2))) | leq(multiplication(star(X0), X1), multiplication(X1, star(X2))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[116, 111])).
% 0.54/0.73 tff(118,plain,(
% 0.54/0.73 ~((~leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0))) | leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0))))),
% 0.54/0.73 inference(skolemize,[status(sab)],[117])).
% 0.54/0.73 tff(119,plain,
% 0.54/0.73 (leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0))),
% 0.54/0.73 inference(or_elim,[status(thm)],[118])).
% 0.54/0.73 tff(120,plain,
% 0.54/0.73 ((~(leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)))) | (~leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0))) | (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0))),
% 0.54/0.73 inference(tautology,[status(thm)],[])).
% 0.54/0.73 tff(121,plain,
% 0.54/0.73 ((~(leq(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)))) | (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.54/0.73 tff(122,plain,
% 0.54/0.73 (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[121, 110])).
% 0.54/0.73 tff(123,plain,
% 0.54/0.73 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)), star(X2!0)) = multiplication(multiplication(X1!1, X2!0), star(X2!0))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[122])).
% 0.54/0.73 tff(124,plain,
% 0.54/0.73 (^[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))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(125,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[124])).
% 0.54/0.73 tff(126,plain,
% 0.54/0.73 (![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)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(127,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity2')).
% 0.54/0.73 tff(128,plain,
% 0.54/0.73 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.54/0.73 tff(129,plain,(
% 0.54/0.73 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.54/0.73 inference(skolemize,[status(sab)],[128])).
% 0.54/0.73 tff(130,plain,
% 0.54/0.73 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.54/0.73 tff(131,plain,
% 0.54/0.73 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)), star(X2!0)) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(132,plain,
% 0.54/0.73 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)), star(X2!0)) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0)))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.54/0.73 tff(133,plain,
% 0.54/0.73 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(X1!1, X2!0)), star(X2!0))),
% 0.54/0.73 inference(symmetry,[status(thm)],[132])).
% 0.54/0.73 tff(134,plain,
% 0.54/0.73 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))) = multiplication(X1!1, multiplication(X2!0, star(X2!0)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[133, 123, 60])).
% 0.54/0.73 tff(135,plain,
% 0.54/0.73 (addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))), X1!1) = addition(multiplication(X1!1, multiplication(X2!0, star(X2!0))), multiplication(X1!1, one))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[134, 40])).
% 0.54/0.73 tff(136,plain,
% 0.54/0.73 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1)) = addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))), X1!1))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(137,plain,
% 0.54/0.73 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1)) = addition(addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), multiplication(multiplication(X1!1, X2!0), star(X2!0))), X1!1)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[136, 68])).
% 0.54/0.73 tff(138,plain,
% 0.54/0.73 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0)))) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(multiplication(X1!1, X2!0), star(X2!0)), X1!1))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[99])).
% 0.54/0.73 tff(139,plain,
% 0.54/0.73 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0)))) = addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), multiplication(multiplication(X0!2, X1!1), star(X2!0))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(140,plain,
% 0.54/0.74 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0)))) = addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), multiplication(multiplication(X0!2, X1!1), star(X2!0)))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[139, 27])).
% 0.54/0.74 tff(141,plain,
% 0.54/0.74 (addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), multiplication(multiplication(X0!2, X1!1), star(X2!0))) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))))),
% 0.54/0.74 inference(symmetry,[status(thm)],[140])).
% 0.54/0.74 tff(142,plain,
% 0.54/0.74 (addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), multiplication(multiplication(X0!2, X1!1), star(X2!0))) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[141, 138, 137, 135, 30, 20, 10, 94, 97])).
% 0.54/0.74 tff(143,plain,
% 0.54/0.74 (addition(addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), multiplication(multiplication(X0!2, X1!1), star(X2!0))), X1!1) = addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), multiplication(one, X1!1))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[142, 101])).
% 0.54/0.74 tff(144,plain,
% 0.54/0.74 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1)) = addition(addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), multiplication(multiplication(X0!2, X1!1), star(X2!0))), X1!1))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(145,plain,
% 0.54/0.74 (addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1)) = addition(addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), multiplication(multiplication(X0!2, X1!1), star(X2!0))), X1!1)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[144, 68])).
% 0.54/0.74 tff(146,plain,
% 0.54/0.74 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!2, multiplication(X1!1, star(X2!0))) = multiplication(multiplication(X0!2, X1!1), star(X2!0)))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(147,plain,
% 0.54/0.74 (multiplication(X0!2, multiplication(X1!1, star(X2!0))) = multiplication(multiplication(X0!2, X1!1), star(X2!0))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[146, 57])).
% 0.54/0.74 tff(148,plain,
% 0.54/0.74 (multiplication(multiplication(X0!2, X1!1), star(X2!0)) = multiplication(X0!2, multiplication(X1!1, star(X2!0)))),
% 0.54/0.74 inference(symmetry,[status(thm)],[147])).
% 0.54/0.74 tff(149,plain,
% 0.54/0.74 (addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1) = addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1)),
% 0.54/0.74 inference(monotonicity,[status(thm)],[148])).
% 0.54/0.74 tff(150,plain,
% 0.54/0.74 (addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1)),
% 0.54/0.74 inference(symmetry,[status(thm)],[149])).
% 0.54/0.74 tff(151,plain,
% 0.54/0.74 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1) = addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(152,plain,
% 0.54/0.74 (addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1) = addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[151, 27])).
% 0.54/0.74 tff(153,plain,
% 0.54/0.74 (addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))) = addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1)),
% 0.54/0.74 inference(symmetry,[status(thm)],[152])).
% 0.54/0.74 tff(154,plain,
% 0.54/0.74 (addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))) = addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1)),
% 0.54/0.74 inference(transitivity,[status(thm)],[153, 150])).
% 0.54/0.74 tff(155,plain,
% 0.54/0.74 (addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0))))) = addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), addition(multiplication(multiplication(X0!2, X1!1), star(X2!0)), X1!1))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[154])).
% 0.54/0.74 tff(156,plain,
% 0.54/0.74 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0)))) = addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0))))))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(157,plain,
% 0.54/0.74 (addition(addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0)))) = addition(addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))), addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[156, 27])).
% 0.54/0.74 tff(158,plain,
% 0.54/0.74 (multiplication(X1!1, star(X2!0)) = addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[94, 97])).
% 0.54/0.74 tff(159,plain,
% 0.54/0.74 (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = addition(addition(X1!1, multiplication(X0!2, multiplication(X1!1, star(X2!0)))), addition(multiplication(X1!1, one), multiplication(X1!1, multiplication(star(X2!0), X2!0))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[152, 158])).
% 0.54/0.74 tff(160,plain,
% 0.54/0.74 (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))),
% 0.54/0.74 inference(transitivity,[status(thm)],[159, 157, 155, 145, 143, 100, 71, 61, 30, 20, 10])).
% 0.54/0.74 tff(161,plain,
% 0.54/0.74 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) <=> (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(162,plain,
% 0.54/0.74 (leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) <=> (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0)))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[161, 108])).
% 0.54/0.74 tff(163,plain,
% 0.54/0.74 (~leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0)))),
% 0.54/0.74 inference(or_elim,[status(thm)],[118])).
% 0.54/0.74 tff(164,plain,
% 0.54/0.74 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(165,plain,
% 0.54/0.74 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[164])).
% 0.54/0.74 tff(166,plain,
% 0.54/0.74 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(167,plain,
% 0.54/0.74 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C)) <=> ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(168,plain,
% 0.54/0.74 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[167])).
% 0.54/0.74 tff(169,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_induction1')).
% 0.54/0.74 tff(170,plain,
% 0.54/0.74 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.54/0.74 tff(171,plain,
% 0.54/0.74 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.54/0.74 tff(172,plain,(
% 0.54/0.74 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.54/0.74 inference(skolemize,[status(sab)],[171])).
% 0.54/0.74 tff(173,plain,
% 0.54/0.74 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.54/0.74 tff(174,plain,
% 0.54/0.74 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0)))) | leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0)))) | leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(175,plain,
% 0.54/0.74 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0)))) | leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0))))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(176,plain,
% 0.54/0.74 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0)))) | leq(multiplication(star(X0!2), X1!1), multiplication(X1!1, star(X2!0)))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.54/0.74 tff(177,plain,
% 0.54/0.74 (~leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0)))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[176, 173, 163])).
% 0.54/0.74 tff(178,plain,
% 0.54/0.74 ((~(leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) <=> (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))))) | leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) | (~(addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))))),
% 0.54/0.74 inference(tautology,[status(thm)],[])).
% 0.54/0.74 tff(179,plain,
% 0.54/0.74 ((~(leq(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) <=> (addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))))) | (~(addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.54/0.74 tff(180,plain,
% 0.54/0.74 (~(addition(addition(multiplication(X0!2, multiplication(X1!1, star(X2!0))), X1!1), multiplication(X1!1, star(X2!0))) = multiplication(X1!1, star(X2!0)))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[179, 162])).
% 0.54/0.74 tff(181,plain,
% 0.54/0.74 ($false),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[180, 160])).
% 0.54/0.74 % SZS output end Proof
% 0.54/0.75 % E exiting
%------------------------------------------------------------------------------