%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE061+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:12:58 AM UTC 2025
% Result : Theorem 1.64s 1.80s
% Output : Proof 1.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE061+1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 18:56:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.64/1.80 % SZS status Theorem
% 1.64/1.80 % SZS output start Proof
% 1.64/1.80 tff(domain_type, type, (
% 1.64/1.80 domain: $i > $i)).
% 1.64/1.80 tff(tptp_fun_X0_0_type, type, (
% 1.64/1.80 tptp_fun_X0_0: $i)).
% 1.64/1.80 tff(multiplication_type, type, (
% 1.64/1.80 multiplication: ( $i * $i ) > $i)).
% 1.64/1.80 tff(one_type, type, (
% 1.64/1.80 one: $i)).
% 1.64/1.80 tff(addition_type, type, (
% 1.64/1.80 addition: ( $i * $i ) > $i)).
% 1.64/1.80 tff(zero_type, type, (
% 1.64/1.80 zero: $i)).
% 1.64/1.80 tff(1,plain,
% 1.64/1.80 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 1.64/1.80 inference(bind,[status(th)],[])).
% 1.64/1.80 tff(2,plain,
% 1.64/1.80 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.64/1.80 inference(quant_intro,[status(thm)],[1])).
% 1.64/1.80 tff(3,plain,
% 1.64/1.80 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 1.64/1.80 tff(5,plain,
% 1.64/1.80 (![A: $i] : (multiplication(one, A) = A)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.64/1.80 tff(6,plain,(
% 1.64/1.80 ![A: $i] : (multiplication(one, A) = A)),
% 1.64/1.80 inference(skolemize,[status(sab)],[5])).
% 1.64/1.80 tff(7,plain,
% 1.64/1.80 (![A: $i] : (multiplication(one, A) = A)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.64/1.80 tff(8,plain,
% 1.64/1.80 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!0) = X0!0)),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(9,plain,
% 1.64/1.80 (multiplication(one, X0!0) = X0!0),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.64/1.80 tff(10,plain,
% 1.64/1.80 (X0!0 = multiplication(one, X0!0)),
% 1.64/1.80 inference(symmetry,[status(thm)],[9])).
% 1.64/1.80 tff(11,plain,
% 1.64/1.80 (domain(X0!0) = domain(multiplication(one, X0!0))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[10])).
% 1.64/1.80 tff(12,plain,
% 1.64/1.80 (domain(multiplication(one, X0!0)) = domain(X0!0)),
% 1.64/1.80 inference(symmetry,[status(thm)],[11])).
% 1.64/1.80 tff(13,plain,
% 1.64/1.80 (^[X0: $i, X1: $i] : refl((domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))))),
% 1.64/1.80 inference(bind,[status(th)],[])).
% 1.64/1.80 tff(14,plain,
% 1.64/1.80 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 1.64/1.80 inference(quant_intro,[status(thm)],[13])).
% 1.64/1.80 tff(15,plain,
% 1.64/1.80 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(16,axiom,(![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain2')).
% 1.64/1.80 tff(17,plain,
% 1.64/1.80 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.64/1.80 tff(18,plain,(
% 1.64/1.80 ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 1.64/1.80 inference(skolemize,[status(sab)],[17])).
% 1.64/1.80 tff(19,plain,
% 1.64/1.80 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.64/1.80 tff(20,plain,
% 1.64/1.80 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(one, X0!0)) = domain(multiplication(one, domain(X0!0))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(21,plain,
% 1.64/1.80 (domain(multiplication(one, X0!0)) = domain(multiplication(one, domain(X0!0)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[20, 19])).
% 1.64/1.80 tff(22,plain,
% 1.64/1.80 (domain(multiplication(one, domain(X0!0))) = domain(multiplication(one, X0!0))),
% 1.64/1.80 inference(symmetry,[status(thm)],[21])).
% 1.64/1.80 tff(23,plain,
% 1.64/1.80 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(domain(X0!0), domain(X0!0))) = addition(domain(X0!0), domain(X0!0)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(24,plain,
% 1.64/1.80 (multiplication(one, addition(domain(X0!0), domain(X0!0))) = addition(domain(X0!0), domain(X0!0))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[23, 7])).
% 1.64/1.80 tff(25,plain,
% 1.64/1.80 (^[X0: $i] : refl((addition(domain(X0), one) = one) <=> (addition(domain(X0), one) = one))),
% 1.64/1.80 inference(bind,[status(th)],[])).
% 1.64/1.80 tff(26,plain,
% 1.64/1.80 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 1.64/1.80 inference(quant_intro,[status(thm)],[25])).
% 1.64/1.80 tff(27,plain,
% 1.64/1.80 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(28,axiom,(![X0: $i] : (addition(domain(X0), one) = one)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain3')).
% 1.64/1.80 tff(29,plain,
% 1.64/1.80 (![X0: $i] : (addition(domain(X0), one) = one)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.64/1.80 tff(30,plain,(
% 1.64/1.80 ![X0: $i] : (addition(domain(X0), one) = one)),
% 1.64/1.80 inference(skolemize,[status(sab)],[29])).
% 1.64/1.80 tff(31,plain,
% 1.64/1.80 (![X0: $i] : (addition(domain(X0), one) = one)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.64/1.80 tff(32,plain,
% 1.64/1.80 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(one), one) = one)),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(33,plain,
% 1.64/1.80 (addition(domain(one), one) = one),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[32, 31])).
% 1.64/1.80 tff(34,plain,
% 1.64/1.80 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(X0!0), one) = one)),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(35,plain,
% 1.64/1.80 (addition(domain(X0!0), one) = one),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[34, 31])).
% 1.64/1.80 tff(36,plain,
% 1.64/1.80 (one = addition(domain(X0!0), one)),
% 1.64/1.80 inference(symmetry,[status(thm)],[35])).
% 1.64/1.80 tff(37,plain,
% 1.64/1.80 (domain(one) = domain(addition(domain(X0!0), one))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[36])).
% 1.64/1.80 tff(38,plain,
% 1.64/1.80 (domain(addition(domain(X0!0), one)) = domain(one)),
% 1.64/1.80 inference(symmetry,[status(thm)],[37])).
% 1.64/1.80 tff(39,plain,
% 1.64/1.80 (^[X0: $i, X1: $i] : refl((domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))))),
% 1.64/1.80 inference(bind,[status(th)],[])).
% 1.64/1.80 tff(40,plain,
% 1.64/1.80 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 1.64/1.80 inference(quant_intro,[status(thm)],[39])).
% 1.64/1.80 tff(41,plain,
% 1.64/1.80 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(42,axiom,(![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain5')).
% 1.64/1.80 tff(43,plain,
% 1.64/1.80 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.64/1.80 tff(44,plain,(
% 1.64/1.80 ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 1.64/1.80 inference(skolemize,[status(sab)],[43])).
% 1.64/1.80 tff(45,plain,
% 1.64/1.80 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.64/1.80 tff(46,plain,
% 1.64/1.80 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(domain(X0!0), one)) = addition(domain(domain(X0!0)), domain(one)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(47,plain,
% 1.64/1.80 (domain(addition(domain(X0!0), one)) = addition(domain(domain(X0!0)), domain(one))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[46, 45])).
% 1.64/1.80 tff(48,plain,
% 1.64/1.80 (addition(domain(domain(X0!0)), domain(one)) = domain(addition(domain(X0!0), one))),
% 1.64/1.80 inference(symmetry,[status(thm)],[47])).
% 1.64/1.80 tff(49,plain,
% 1.64/1.80 (addition(domain(domain(X0!0)), domain(one)) = domain(one)),
% 1.64/1.80 inference(transitivity,[status(thm)],[48, 38])).
% 1.64/1.80 tff(50,plain,
% 1.64/1.80 (addition(addition(domain(domain(X0!0)), domain(one)), one) = addition(domain(one), one)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[49])).
% 1.64/1.80 tff(51,plain,
% 1.64/1.80 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 1.64/1.80 inference(bind,[status(th)],[])).
% 1.64/1.80 tff(52,plain,
% 1.64/1.80 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.64/1.80 inference(quant_intro,[status(thm)],[51])).
% 1.64/1.80 tff(53,plain,
% 1.64/1.80 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(54,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 1.64/1.80 tff(55,plain,
% 1.64/1.80 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.64/1.80 tff(56,plain,(
% 1.64/1.80 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.64/1.80 inference(skolemize,[status(sab)],[55])).
% 1.64/1.80 tff(57,plain,
% 1.64/1.80 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[56, 52])).
% 1.64/1.80 tff(58,plain,
% 1.64/1.80 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(domain(domain(X0!0)), domain(one)), one) = addition(one, addition(domain(domain(X0!0)), domain(one))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(59,plain,
% 1.64/1.80 (addition(addition(domain(domain(X0!0)), domain(one)), one) = addition(one, addition(domain(domain(X0!0)), domain(one)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[58, 57])).
% 1.64/1.80 tff(60,plain,
% 1.64/1.80 (addition(one, addition(domain(domain(X0!0)), domain(one))) = addition(addition(domain(domain(X0!0)), domain(one)), one)),
% 1.64/1.80 inference(symmetry,[status(thm)],[59])).
% 1.64/1.80 tff(61,plain,
% 1.64/1.80 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 1.64/1.80 inference(bind,[status(th)],[])).
% 1.64/1.80 tff(62,plain,
% 1.64/1.80 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 1.64/1.80 inference(quant_intro,[status(thm)],[61])).
% 1.64/1.80 tff(63,plain,
% 1.64/1.80 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(64,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 1.64/1.80 tff(65,plain,
% 1.64/1.80 (![A: $i] : (multiplication(A, one) = A)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.64/1.80 tff(66,plain,(
% 1.64/1.80 ![A: $i] : (multiplication(A, one) = A)),
% 1.64/1.80 inference(skolemize,[status(sab)],[65])).
% 1.64/1.80 tff(67,plain,
% 1.64/1.80 (![A: $i] : (multiplication(A, one) = A)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[66, 62])).
% 1.64/1.80 tff(68,plain,
% 1.64/1.80 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(addition(domain(domain(X0!0)), domain(one)), one) = addition(domain(domain(X0!0)), domain(one)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(69,plain,
% 1.64/1.80 (multiplication(addition(domain(domain(X0!0)), domain(one)), one) = addition(domain(domain(X0!0)), domain(one))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[68, 67])).
% 1.64/1.80 tff(70,plain,
% 1.64/1.80 (multiplication(addition(domain(domain(X0!0)), domain(one)), one) = multiplication(domain(one), one)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[49])).
% 1.64/1.80 tff(71,plain,
% 1.64/1.80 (multiplication(domain(one), one) = multiplication(addition(domain(domain(X0!0)), domain(one)), one)),
% 1.64/1.80 inference(symmetry,[status(thm)],[70])).
% 1.64/1.80 tff(72,plain,
% 1.64/1.80 (multiplication(domain(one), one) = addition(domain(domain(X0!0)), domain(one))),
% 1.64/1.80 inference(transitivity,[status(thm)],[71, 69])).
% 1.64/1.80 tff(73,plain,
% 1.64/1.80 (addition(one, multiplication(domain(one), one)) = addition(one, addition(domain(domain(X0!0)), domain(one)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[72])).
% 1.64/1.80 tff(74,plain,
% 1.64/1.80 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 1.64/1.80 inference(bind,[status(th)],[])).
% 1.64/1.80 tff(75,plain,
% 1.64/1.80 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 1.64/1.80 inference(quant_intro,[status(thm)],[74])).
% 1.64/1.80 tff(76,plain,
% 1.64/1.80 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(77,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain1')).
% 1.64/1.80 tff(78,plain,
% 1.64/1.80 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.64/1.80 tff(79,plain,(
% 1.64/1.80 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 1.64/1.80 inference(skolemize,[status(sab)],[78])).
% 1.64/1.80 tff(80,plain,
% 1.64/1.80 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[79, 75])).
% 1.64/1.80 tff(81,plain,
% 1.64/1.80 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(one, multiplication(domain(one), one)) = multiplication(domain(one), one))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(82,plain,
% 1.64/1.80 (addition(one, multiplication(domain(one), one)) = multiplication(domain(one), one)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[81, 80])).
% 1.64/1.80 tff(83,plain,
% 1.64/1.80 (multiplication(domain(one), one) = addition(one, multiplication(domain(one), one))),
% 1.64/1.80 inference(symmetry,[status(thm)],[82])).
% 1.64/1.80 tff(84,plain,
% 1.64/1.80 (addition(domain(domain(X0!0)), domain(one)) = multiplication(addition(domain(domain(X0!0)), domain(one)), one)),
% 1.64/1.80 inference(symmetry,[status(thm)],[69])).
% 1.64/1.80 tff(85,plain,
% 1.64/1.80 (addition(domain(domain(X0!0)), domain(one)) = one),
% 1.64/1.80 inference(transitivity,[status(thm)],[84, 70, 83, 73, 60, 50, 33])).
% 1.64/1.80 tff(86,plain,
% 1.64/1.80 (multiplication(addition(domain(domain(X0!0)), domain(one)), addition(domain(X0!0), domain(X0!0))) = multiplication(one, addition(domain(X0!0), domain(X0!0)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[85])).
% 1.64/1.80 tff(87,plain,
% 1.64/1.80 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 1.64/1.80 inference(bind,[status(th)],[])).
% 1.64/1.80 tff(88,plain,
% 1.64/1.80 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.64/1.80 inference(quant_intro,[status(thm)],[87])).
% 1.64/1.80 tff(89,plain,
% 1.64/1.80 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(90,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 1.64/1.80 tff(91,plain,
% 1.64/1.80 (![A: $i] : (addition(A, A) = A)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.64/1.80 tff(92,plain,(
% 1.64/1.80 ![A: $i] : (addition(A, A) = A)),
% 1.64/1.80 inference(skolemize,[status(sab)],[91])).
% 1.64/1.80 tff(93,plain,
% 1.64/1.80 (![A: $i] : (addition(A, A) = A)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[92, 88])).
% 1.64/1.80 tff(94,plain,
% 1.64/1.80 ((~![A: $i] : (addition(A, A) = A)) | (addition(domain(X0!0), domain(X0!0)) = domain(X0!0))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(95,plain,
% 1.64/1.80 (addition(domain(X0!0), domain(X0!0)) = domain(X0!0)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[94, 93])).
% 1.64/1.80 tff(96,plain,
% 1.64/1.80 (domain(X0!0) = addition(domain(X0!0), domain(X0!0))),
% 1.64/1.80 inference(symmetry,[status(thm)],[95])).
% 1.64/1.80 tff(97,plain,
% 1.64/1.80 (addition(one, addition(domain(domain(X0!0)), domain(one))) = addition(one, multiplication(domain(one), one))),
% 1.64/1.80 inference(symmetry,[status(thm)],[73])).
% 1.64/1.80 tff(98,plain,
% 1.64/1.80 (addition(domain(one), one) = addition(addition(domain(domain(X0!0)), domain(one)), one)),
% 1.64/1.80 inference(symmetry,[status(thm)],[50])).
% 1.64/1.80 tff(99,plain,
% 1.64/1.80 (one = addition(domain(one), one)),
% 1.64/1.80 inference(symmetry,[status(thm)],[33])).
% 1.64/1.80 tff(100,plain,
% 1.64/1.80 (one = addition(domain(domain(X0!0)), domain(one))),
% 1.64/1.80 inference(transitivity,[status(thm)],[99, 98, 59, 97, 82, 71, 69])).
% 1.64/1.80 tff(101,plain,
% 1.64/1.80 (multiplication(one, domain(X0!0)) = multiplication(addition(domain(domain(X0!0)), domain(one)), addition(domain(X0!0), domain(X0!0)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[100, 96])).
% 1.64/1.80 tff(102,plain,
% 1.64/1.80 (multiplication(one, domain(X0!0)) = addition(domain(X0!0), domain(X0!0))),
% 1.64/1.80 inference(transitivity,[status(thm)],[101, 86, 24])).
% 1.64/1.80 tff(103,plain,
% 1.64/1.80 (domain(multiplication(one, domain(X0!0))) = domain(addition(domain(X0!0), domain(X0!0)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[102])).
% 1.64/1.80 tff(104,plain,
% 1.64/1.80 (domain(addition(domain(X0!0), domain(X0!0))) = domain(multiplication(one, domain(X0!0)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[103])).
% 1.64/1.80 tff(105,plain,
% 1.64/1.80 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 1.64/1.80 inference(bind,[status(th)],[])).
% 1.64/1.80 tff(106,plain,
% 1.64/1.80 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 1.64/1.80 inference(quant_intro,[status(thm)],[105])).
% 1.64/1.80 tff(107,plain,
% 1.64/1.80 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(108,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 1.64/1.80 tff(109,plain,
% 1.64/1.80 (![A: $i] : (multiplication(zero, A) = zero)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.64/1.80 tff(110,plain,(
% 1.64/1.80 ![A: $i] : (multiplication(zero, A) = zero)),
% 1.64/1.80 inference(skolemize,[status(sab)],[109])).
% 1.64/1.80 tff(111,plain,
% 1.64/1.80 (![A: $i] : (multiplication(zero, A) = zero)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[110, 106])).
% 1.64/1.80 tff(112,plain,
% 1.64/1.80 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, zero) = zero)),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(113,plain,
% 1.64/1.80 (multiplication(zero, zero) = zero),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[112, 111])).
% 1.64/1.80 tff(114,plain,
% 1.64/1.80 ((domain(zero) = zero) <=> (domain(zero) = zero)),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(115,axiom,(domain(zero) = zero), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain4')).
% 1.64/1.80 tff(116,plain,
% 1.64/1.80 (domain(zero) = zero),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[115, 114])).
% 1.64/1.80 tff(117,plain,
% 1.64/1.80 (zero = domain(zero)),
% 1.64/1.80 inference(symmetry,[status(thm)],[116])).
% 1.64/1.80 tff(118,plain,
% 1.64/1.80 (multiplication(zero, zero) = multiplication(domain(zero), zero)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[117])).
% 1.64/1.80 tff(119,plain,
% 1.64/1.80 (multiplication(domain(zero), zero) = multiplication(zero, zero)),
% 1.64/1.80 inference(symmetry,[status(thm)],[118])).
% 1.64/1.80 tff(120,plain,
% 1.64/1.80 (multiplication(domain(zero), zero) = zero),
% 1.64/1.80 inference(transitivity,[status(thm)],[119, 113])).
% 1.64/1.80 tff(121,plain,
% 1.64/1.80 (addition(domain(X0!0), multiplication(domain(zero), zero)) = addition(domain(X0!0), zero)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[120])).
% 1.64/1.80 tff(122,plain,
% 1.64/1.80 (addition(domain(X0!0), zero) = addition(domain(X0!0), multiplication(domain(zero), zero))),
% 1.64/1.80 inference(symmetry,[status(thm)],[121])).
% 1.64/1.80 tff(123,plain,
% 1.64/1.80 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 1.64/1.80 inference(bind,[status(th)],[])).
% 1.64/1.80 tff(124,plain,
% 1.64/1.80 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 1.64/1.80 inference(quant_intro,[status(thm)],[123])).
% 1.64/1.80 tff(125,plain,
% 1.64/1.80 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(126,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 1.64/1.80 tff(127,plain,
% 1.64/1.80 (![A: $i] : (addition(A, zero) = A)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.64/1.80 tff(128,plain,(
% 1.64/1.80 ![A: $i] : (addition(A, zero) = A)),
% 1.64/1.80 inference(skolemize,[status(sab)],[127])).
% 1.64/1.80 tff(129,plain,
% 1.64/1.80 (![A: $i] : (addition(A, zero) = A)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[128, 124])).
% 1.64/1.80 tff(130,plain,
% 1.64/1.80 ((~![A: $i] : (addition(A, zero) = A)) | (addition(domain(X0!0), zero) = domain(X0!0))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(131,plain,
% 1.64/1.80 (addition(domain(X0!0), zero) = domain(X0!0)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[130, 129])).
% 1.64/1.80 tff(132,plain,
% 1.64/1.80 (domain(X0!0) = addition(domain(X0!0), zero)),
% 1.64/1.80 inference(symmetry,[status(thm)],[131])).
% 1.64/1.80 tff(133,plain,
% 1.64/1.80 (addition(domain(X0!0), domain(X0!0)) = addition(domain(X0!0), multiplication(domain(zero), zero))),
% 1.64/1.80 inference(transitivity,[status(thm)],[95, 132, 122])).
% 1.64/1.80 tff(134,plain,
% 1.64/1.80 (domain(addition(domain(X0!0), domain(X0!0))) = domain(addition(domain(X0!0), multiplication(domain(zero), zero)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[133])).
% 1.64/1.80 tff(135,plain,
% 1.64/1.80 (domain(addition(domain(X0!0), multiplication(domain(zero), zero))) = domain(addition(domain(X0!0), domain(X0!0)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[134])).
% 1.64/1.80 tff(136,plain,
% 1.64/1.80 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(domain(X0!0), multiplication(domain(zero), zero))) = addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(137,plain,
% 1.64/1.80 (domain(addition(domain(X0!0), multiplication(domain(zero), zero))) = addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[136, 45])).
% 1.64/1.80 tff(138,plain,
% 1.64/1.80 (addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))) = domain(addition(domain(X0!0), multiplication(domain(zero), zero)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[137])).
% 1.64/1.80 tff(139,plain,
% 1.64/1.80 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(140,plain,
% 1.64/1.80 (multiplication(one, addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[139, 7])).
% 1.64/1.80 tff(141,plain,
% 1.64/1.80 (multiplication(addition(domain(domain(X0!0)), domain(one)), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = multiplication(one, addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[85])).
% 1.64/1.80 tff(142,plain,
% 1.64/1.80 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), one) = one)),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(143,plain,
% 1.64/1.80 (addition(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), one) = one),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[142, 31])).
% 1.64/1.80 tff(144,plain,
% 1.64/1.80 (domain(domain(X0!0)) = domain(addition(domain(X0!0), domain(X0!0)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[96])).
% 1.64/1.80 tff(145,plain,
% 1.64/1.80 (domain(addition(domain(X0!0), domain(X0!0))) = domain(domain(X0!0))),
% 1.64/1.80 inference(symmetry,[status(thm)],[144])).
% 1.64/1.80 tff(146,plain,
% 1.64/1.80 (addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))) = domain(domain(X0!0))),
% 1.64/1.80 inference(transitivity,[status(thm)],[138, 135, 145])).
% 1.64/1.80 tff(147,plain,
% 1.64/1.80 (domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = domain(domain(domain(X0!0)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[146])).
% 1.64/1.80 tff(148,plain,
% 1.64/1.80 (domain(domain(domain(X0!0))) = domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[147])).
% 1.64/1.80 tff(149,plain,
% 1.64/1.80 (addition(domain(domain(domain(X0!0))), one) = addition(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), one)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[148])).
% 1.64/1.80 tff(150,plain,
% 1.64/1.80 (addition(domain(domain(domain(X0!0))), one) = addition(domain(domain(X0!0)), domain(one))),
% 1.64/1.80 inference(transitivity,[status(thm)],[149, 143, 99, 98, 59, 97, 82, 71, 69])).
% 1.64/1.80 tff(151,plain,
% 1.64/1.80 (multiplication(addition(domain(domain(domain(X0!0))), one), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = multiplication(addition(domain(domain(X0!0)), domain(one)), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[150])).
% 1.64/1.80 tff(152,plain,
% 1.64/1.80 (^[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))))),
% 1.64/1.80 inference(bind,[status(th)],[])).
% 1.64/1.80 tff(153,plain,
% 1.64/1.80 (![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)))),
% 1.64/1.80 inference(quant_intro,[status(thm)],[152])).
% 1.64/1.80 tff(154,plain,
% 1.64/1.80 (![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)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(155,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/KLE001+0.ax','left_distributivity')).
% 1.64/1.80 tff(156,plain,
% 1.64/1.80 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.64/1.80 tff(157,plain,(
% 1.64/1.80 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.64/1.80 inference(skolemize,[status(sab)],[156])).
% 1.64/1.80 tff(158,plain,
% 1.64/1.80 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[157, 153])).
% 1.64/1.80 tff(159,plain,
% 1.64/1.80 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(domain(domain(domain(X0!0))), one), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = addition(multiplication(domain(domain(domain(X0!0))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), multiplication(one, addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(160,plain,
% 1.64/1.80 (multiplication(addition(domain(domain(domain(X0!0))), one), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = addition(multiplication(domain(domain(domain(X0!0))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), multiplication(one, addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[159, 158])).
% 1.64/1.80 tff(161,plain,
% 1.64/1.80 (addition(multiplication(domain(domain(domain(X0!0))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), multiplication(one, addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))) = multiplication(addition(domain(domain(domain(X0!0))), one), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[160])).
% 1.64/1.80 tff(162,plain,
% 1.64/1.80 (addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))) = multiplication(one, addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[140])).
% 1.64/1.80 tff(163,plain,
% 1.64/1.80 (multiplication(domain(domain(domain(X0!0))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[148])).
% 1.64/1.80 tff(164,plain,
% 1.64/1.80 (multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = multiplication(domain(domain(domain(X0!0))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[163])).
% 1.64/1.80 tff(165,plain,
% 1.64/1.80 (addition(multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = addition(multiplication(domain(domain(domain(X0!0))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), multiplication(one, addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[164, 162])).
% 1.64/1.80 tff(166,plain,
% 1.64/1.80 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))), multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))) = addition(multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(167,plain,
% 1.64/1.80 (addition(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))), multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))) = addition(multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[166, 57])).
% 1.64/1.80 tff(168,plain,
% 1.64/1.80 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))), multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))) = multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(169,plain,
% 1.64/1.80 (addition(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))), multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))) = multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[168, 80])).
% 1.64/1.80 tff(170,plain,
% 1.64/1.80 (multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = addition(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))), multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[169])).
% 1.64/1.80 tff(171,plain,
% 1.64/1.80 (domain(addition(domain(X0!0), domain(X0!0))) = addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[134, 137])).
% 1.64/1.80 tff(172,plain,
% 1.64/1.80 (multiplication(one, domain(addition(domain(X0!0), domain(X0!0)))) = multiplication(addition(domain(domain(X0!0)), domain(one)), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[100, 171])).
% 1.64/1.80 tff(173,plain,
% 1.64/1.80 (multiplication(addition(domain(domain(X0!0)), domain(one)), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = multiplication(one, domain(addition(domain(X0!0), domain(X0!0))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[172])).
% 1.64/1.80 tff(174,plain,
% 1.64/1.80 (multiplication(one, addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = multiplication(addition(domain(domain(X0!0)), domain(one)), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[141])).
% 1.64/1.80 tff(175,plain,
% 1.64/1.80 (domain(domain(X0!0)) = multiplication(one, domain(addition(domain(X0!0), domain(X0!0))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[144, 134, 137, 162, 174, 173])).
% 1.64/1.80 tff(176,plain,
% 1.64/1.80 (domain(domain(domain(X0!0))) = domain(multiplication(one, domain(addition(domain(X0!0), domain(X0!0)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[175])).
% 1.64/1.80 tff(177,plain,
% 1.64/1.80 (domain(multiplication(one, domain(addition(domain(X0!0), domain(X0!0))))) = domain(domain(domain(X0!0)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[176])).
% 1.64/1.80 tff(178,plain,
% 1.64/1.80 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(one, addition(domain(X0!0), domain(X0!0)))) = domain(multiplication(one, domain(addition(domain(X0!0), domain(X0!0))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(179,plain,
% 1.64/1.80 (domain(multiplication(one, addition(domain(X0!0), domain(X0!0)))) = domain(multiplication(one, domain(addition(domain(X0!0), domain(X0!0)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[178, 19])).
% 1.64/1.80 tff(180,plain,
% 1.64/1.80 (domain(multiplication(one, addition(domain(X0!0), domain(X0!0)))) = domain(addition(domain(X0!0), domain(X0!0)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[24])).
% 1.64/1.80 tff(181,plain,
% 1.64/1.80 (domain(addition(domain(X0!0), domain(X0!0))) = domain(multiplication(one, addition(domain(X0!0), domain(X0!0))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[180])).
% 1.64/1.80 tff(182,plain,
% 1.64/1.80 (addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))) = domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[138, 135, 181, 179, 177, 148])).
% 1.64/1.80 tff(183,plain,
% 1.64/1.80 (multiplication(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))) = multiplication(domain(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[182])).
% 1.64/1.80 tff(184,plain,
% 1.64/1.80 (domain(X0!0) = addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[11, 21, 103, 134, 137])).
% 1.64/1.80 tff(185,plain,
% 1.64/1.80 (multiplication(domain(X0!0), domain(X0!0)) = multiplication(addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))), addition(domain(domain(X0!0)), domain(multiplication(domain(zero), zero))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[184, 184])).
% 1.64/1.80 tff(186,plain,
% 1.64/1.80 (multiplication(domain(X0!0), domain(X0!0)) = domain(X0!0)),
% 1.64/1.80 inference(transitivity,[status(thm)],[185, 183, 170, 167, 165, 161, 151, 141, 140, 138, 135, 104, 22, 12])).
% 1.64/1.80 tff(187,plain,
% 1.64/1.80 ((~![X0: $i] : (multiplication(domain(X0), domain(X0)) = domain(X0))) <=> (~![X0: $i] : (multiplication(domain(X0), domain(X0)) = domain(X0)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(188,axiom,(~![X0: $i] : (multiplication(domain(X0), domain(X0)) = domain(X0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 1.64/1.80 tff(189,plain,
% 1.64/1.80 (~![X0: $i] : (multiplication(domain(X0), domain(X0)) = domain(X0))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.64/1.80 tff(190,plain,
% 1.64/1.80 (~![X0: $i] : (multiplication(domain(X0), domain(X0)) = domain(X0))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[189, 187])).
% 1.64/1.80 tff(191,plain,
% 1.64/1.80 (~![X0: $i] : (multiplication(domain(X0), domain(X0)) = domain(X0))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[190, 187])).
% 1.64/1.80 tff(192,plain,
% 1.64/1.80 (~![X0: $i] : (multiplication(domain(X0), domain(X0)) = domain(X0))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[191, 187])).
% 1.65/1.80 tff(193,plain,(
% 1.65/1.80 ~(multiplication(domain(X0!0), domain(X0!0)) = domain(X0!0))),
% 1.65/1.80 inference(skolemize,[status(sab)],[192])).
% 1.65/1.80 tff(194,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[193, 186])).
% 1.65/1.80 % SZS output end Proof
% 1.65/1.81 % E exiting
%------------------------------------------------------------------------------