%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE053+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:12:57 AM UTC 2025
% Result : Theorem 1.07s 1.23s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE053+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 18:56:56 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.07/1.23 % SZS status Theorem
% 1.07/1.23 % SZS output start Proof
% 1.07/1.23 tff(domain_type, type, (
% 1.07/1.23 domain: $i > $i)).
% 1.07/1.23 tff(tptp_fun_X0_0_type, type, (
% 1.07/1.23 tptp_fun_X0_0: $i)).
% 1.07/1.23 tff(multiplication_type, type, (
% 1.07/1.23 multiplication: ( $i * $i ) > $i)).
% 1.07/1.23 tff(one_type, type, (
% 1.07/1.23 one: $i)).
% 1.07/1.23 tff(addition_type, type, (
% 1.07/1.23 addition: ( $i * $i ) > $i)).
% 1.07/1.23 tff(1,plain,
% 1.07/1.23 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(2,plain,
% 1.07/1.23 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.07/1.23 inference(quant_intro,[status(thm)],[1])).
% 1.07/1.23 tff(3,plain,
% 1.07/1.23 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(4,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 1.07/1.23 tff(5,plain,
% 1.07/1.23 (![A: $i] : (multiplication(one, A) = A)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.07/1.23 tff(6,plain,(
% 1.07/1.23 ![A: $i] : (multiplication(one, A) = A)),
% 1.07/1.23 inference(skolemize,[status(sab)],[5])).
% 1.07/1.23 tff(7,plain,
% 1.07/1.23 (![A: $i] : (multiplication(one, A) = A)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.07/1.23 tff(8,plain,
% 1.07/1.23 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!0) = X0!0)),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(9,plain,
% 1.07/1.23 (multiplication(one, X0!0) = X0!0),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.07/1.23 tff(10,plain,
% 1.07/1.23 (X0!0 = multiplication(one, X0!0)),
% 1.07/1.23 inference(symmetry,[status(thm)],[9])).
% 1.07/1.23 tff(11,plain,
% 1.07/1.23 (domain(X0!0) = domain(multiplication(one, X0!0))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[10])).
% 1.07/1.23 tff(12,plain,
% 1.07/1.23 (domain(multiplication(one, X0!0)) = domain(X0!0)),
% 1.07/1.23 inference(symmetry,[status(thm)],[11])).
% 1.07/1.23 tff(13,plain,
% 1.07/1.23 (^[X0: $i, X1: $i] : refl((domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(14,plain,
% 1.07/1.23 (![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))))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[13])).
% 1.07/1.23 tff(15,plain,
% 1.07/1.23 (![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))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(16,axiom,(![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain2')).
% 1.07/1.23 tff(17,plain,
% 1.07/1.23 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.07/1.23 tff(18,plain,(
% 1.07/1.23 ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 1.07/1.23 inference(skolemize,[status(sab)],[17])).
% 1.07/1.23 tff(19,plain,
% 1.07/1.23 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.07/1.23 tff(20,plain,
% 1.07/1.23 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(one, X0!0)) = domain(multiplication(one, domain(X0!0))))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(21,plain,
% 1.07/1.23 (domain(multiplication(one, X0!0)) = domain(multiplication(one, domain(X0!0)))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[20, 19])).
% 1.07/1.23 tff(22,plain,
% 1.07/1.23 (domain(multiplication(one, domain(X0!0))) = domain(multiplication(one, X0!0))),
% 1.07/1.23 inference(symmetry,[status(thm)],[21])).
% 1.07/1.23 tff(23,plain,
% 1.07/1.23 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(domain(X0!0), domain(X0!0))) = addition(domain(X0!0), domain(X0!0)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(24,plain,
% 1.07/1.23 (multiplication(one, addition(domain(X0!0), domain(X0!0))) = addition(domain(X0!0), domain(X0!0))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[23, 7])).
% 1.07/1.23 tff(25,plain,
% 1.07/1.23 (^[X0: $i] : refl((addition(domain(X0), one) = one) <=> (addition(domain(X0), one) = one))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(26,plain,
% 1.07/1.23 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 1.07/1.23 inference(quant_intro,[status(thm)],[25])).
% 1.07/1.23 tff(27,plain,
% 1.07/1.23 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(28,axiom,(![X0: $i] : (addition(domain(X0), one) = one)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain3')).
% 1.07/1.23 tff(29,plain,
% 1.07/1.23 (![X0: $i] : (addition(domain(X0), one) = one)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.07/1.23 tff(30,plain,(
% 1.07/1.23 ![X0: $i] : (addition(domain(X0), one) = one)),
% 1.07/1.23 inference(skolemize,[status(sab)],[29])).
% 1.07/1.23 tff(31,plain,
% 1.07/1.23 (![X0: $i] : (addition(domain(X0), one) = one)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.07/1.23 tff(32,plain,
% 1.07/1.23 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(one), one) = one)),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(33,plain,
% 1.07/1.23 (addition(domain(one), one) = one),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[32, 31])).
% 1.07/1.23 tff(34,plain,
% 1.07/1.23 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(X0!0), one) = one)),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(35,plain,
% 1.07/1.23 (addition(domain(X0!0), one) = one),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[34, 31])).
% 1.07/1.23 tff(36,plain,
% 1.07/1.23 (one = addition(domain(X0!0), one)),
% 1.07/1.23 inference(symmetry,[status(thm)],[35])).
% 1.07/1.23 tff(37,plain,
% 1.07/1.23 (domain(one) = domain(addition(domain(X0!0), one))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[36])).
% 1.07/1.23 tff(38,plain,
% 1.07/1.23 (domain(addition(domain(X0!0), one)) = domain(one)),
% 1.07/1.23 inference(symmetry,[status(thm)],[37])).
% 1.07/1.23 tff(39,plain,
% 1.07/1.23 (^[X0: $i, X1: $i] : refl((domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(40,plain,
% 1.07/1.23 (![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)))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[39])).
% 1.07/1.23 tff(41,plain,
% 1.07/1.23 (![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)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(42,axiom,(![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain5')).
% 1.07/1.23 tff(43,plain,
% 1.07/1.23 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.07/1.23 tff(44,plain,(
% 1.07/1.23 ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 1.07/1.23 inference(skolemize,[status(sab)],[43])).
% 1.07/1.23 tff(45,plain,
% 1.07/1.23 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.07/1.23 tff(46,plain,
% 1.07/1.23 ((~![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)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(47,plain,
% 1.07/1.23 (domain(addition(domain(X0!0), one)) = addition(domain(domain(X0!0)), domain(one))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[46, 45])).
% 1.07/1.23 tff(48,plain,
% 1.07/1.23 (addition(domain(domain(X0!0)), domain(one)) = domain(addition(domain(X0!0), one))),
% 1.07/1.23 inference(symmetry,[status(thm)],[47])).
% 1.07/1.23 tff(49,plain,
% 1.07/1.23 (addition(domain(domain(X0!0)), domain(one)) = domain(one)),
% 1.07/1.23 inference(transitivity,[status(thm)],[48, 38])).
% 1.07/1.23 tff(50,plain,
% 1.07/1.23 (addition(addition(domain(domain(X0!0)), domain(one)), one) = addition(domain(one), one)),
% 1.07/1.23 inference(monotonicity,[status(thm)],[49])).
% 1.07/1.23 tff(51,plain,
% 1.07/1.23 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(52,plain,
% 1.07/1.24 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[51])).
% 1.07/1.24 tff(53,plain,
% 1.07/1.24 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(54,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 1.07/1.24 tff(55,plain,
% 1.07/1.24 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.07/1.24 tff(56,plain,(
% 1.07/1.24 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.07/1.24 inference(skolemize,[status(sab)],[55])).
% 1.07/1.24 tff(57,plain,
% 1.07/1.24 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[56, 52])).
% 1.07/1.24 tff(58,plain,
% 1.07/1.24 ((~![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))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(59,plain,
% 1.07/1.24 (addition(addition(domain(domain(X0!0)), domain(one)), one) = addition(one, addition(domain(domain(X0!0)), domain(one)))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[58, 57])).
% 1.07/1.24 tff(60,plain,
% 1.07/1.24 (addition(one, addition(domain(domain(X0!0)), domain(one))) = addition(addition(domain(domain(X0!0)), domain(one)), one)),
% 1.07/1.24 inference(symmetry,[status(thm)],[59])).
% 1.07/1.24 tff(61,plain,
% 1.07/1.24 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(62,plain,
% 1.07/1.24 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 1.07/1.24 inference(quant_intro,[status(thm)],[61])).
% 1.07/1.24 tff(63,plain,
% 1.07/1.24 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(64,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 1.07/1.24 tff(65,plain,
% 1.07/1.24 (![A: $i] : (multiplication(A, one) = A)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.07/1.24 tff(66,plain,(
% 1.07/1.24 ![A: $i] : (multiplication(A, one) = A)),
% 1.07/1.24 inference(skolemize,[status(sab)],[65])).
% 1.07/1.24 tff(67,plain,
% 1.07/1.24 (![A: $i] : (multiplication(A, one) = A)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[66, 62])).
% 1.07/1.24 tff(68,plain,
% 1.07/1.24 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(addition(domain(domain(X0!0)), domain(one)), one) = addition(domain(domain(X0!0)), domain(one)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(69,plain,
% 1.07/1.24 (multiplication(addition(domain(domain(X0!0)), domain(one)), one) = addition(domain(domain(X0!0)), domain(one))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[68, 67])).
% 1.07/1.24 tff(70,plain,
% 1.07/1.24 (multiplication(addition(domain(domain(X0!0)), domain(one)), one) = multiplication(domain(one), one)),
% 1.07/1.24 inference(monotonicity,[status(thm)],[49])).
% 1.07/1.24 tff(71,plain,
% 1.07/1.24 (multiplication(domain(one), one) = multiplication(addition(domain(domain(X0!0)), domain(one)), one)),
% 1.07/1.24 inference(symmetry,[status(thm)],[70])).
% 1.07/1.24 tff(72,plain,
% 1.07/1.24 (multiplication(domain(one), one) = addition(domain(domain(X0!0)), domain(one))),
% 1.07/1.24 inference(transitivity,[status(thm)],[71, 69])).
% 1.07/1.24 tff(73,plain,
% 1.07/1.24 (addition(one, multiplication(domain(one), one)) = addition(one, addition(domain(domain(X0!0)), domain(one)))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[72])).
% 1.07/1.24 tff(74,plain,
% 1.07/1.24 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(75,plain,
% 1.07/1.24 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[74])).
% 1.07/1.24 tff(76,plain,
% 1.07/1.24 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(77,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain1')).
% 1.07/1.24 tff(78,plain,
% 1.07/1.24 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.07/1.24 tff(79,plain,(
% 1.07/1.24 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 1.07/1.24 inference(skolemize,[status(sab)],[78])).
% 1.07/1.24 tff(80,plain,
% 1.07/1.24 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[79, 75])).
% 1.07/1.24 tff(81,plain,
% 1.07/1.24 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(one, multiplication(domain(one), one)) = multiplication(domain(one), one))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(82,plain,
% 1.07/1.24 (addition(one, multiplication(domain(one), one)) = multiplication(domain(one), one)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[81, 80])).
% 1.07/1.24 tff(83,plain,
% 1.07/1.24 (multiplication(domain(one), one) = addition(one, multiplication(domain(one), one))),
% 1.07/1.24 inference(symmetry,[status(thm)],[82])).
% 1.07/1.24 tff(84,plain,
% 1.07/1.24 (addition(domain(domain(X0!0)), domain(one)) = multiplication(addition(domain(domain(X0!0)), domain(one)), one)),
% 1.07/1.24 inference(symmetry,[status(thm)],[69])).
% 1.07/1.24 tff(85,plain,
% 1.07/1.24 (addition(domain(domain(X0!0)), domain(one)) = one),
% 1.07/1.24 inference(transitivity,[status(thm)],[84, 70, 83, 73, 60, 50, 33])).
% 1.07/1.24 tff(86,plain,
% 1.07/1.24 (multiplication(addition(domain(domain(X0!0)), domain(one)), addition(domain(X0!0), domain(X0!0))) = multiplication(one, addition(domain(X0!0), domain(X0!0)))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[85])).
% 1.07/1.24 tff(87,plain,
% 1.07/1.24 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(88,plain,
% 1.07/1.24 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.07/1.24 inference(quant_intro,[status(thm)],[87])).
% 1.07/1.24 tff(89,plain,
% 1.07/1.24 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(90,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 1.07/1.24 tff(91,plain,
% 1.07/1.24 (![A: $i] : (addition(A, A) = A)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.07/1.24 tff(92,plain,(
% 1.07/1.24 ![A: $i] : (addition(A, A) = A)),
% 1.07/1.24 inference(skolemize,[status(sab)],[91])).
% 1.07/1.24 tff(93,plain,
% 1.07/1.24 (![A: $i] : (addition(A, A) = A)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[92, 88])).
% 1.07/1.24 tff(94,plain,
% 1.07/1.24 ((~![A: $i] : (addition(A, A) = A)) | (addition(domain(X0!0), domain(X0!0)) = domain(X0!0))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(95,plain,
% 1.07/1.24 (addition(domain(X0!0), domain(X0!0)) = domain(X0!0)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[94, 93])).
% 1.07/1.24 tff(96,plain,
% 1.07/1.24 (domain(X0!0) = addition(domain(X0!0), domain(X0!0))),
% 1.07/1.24 inference(symmetry,[status(thm)],[95])).
% 1.07/1.24 tff(97,plain,
% 1.07/1.24 (addition(one, addition(domain(domain(X0!0)), domain(one))) = addition(one, multiplication(domain(one), one))),
% 1.07/1.24 inference(symmetry,[status(thm)],[73])).
% 1.07/1.24 tff(98,plain,
% 1.07/1.24 (addition(domain(one), one) = addition(addition(domain(domain(X0!0)), domain(one)), one)),
% 1.07/1.24 inference(symmetry,[status(thm)],[50])).
% 1.07/1.24 tff(99,plain,
% 1.07/1.24 (one = addition(domain(one), one)),
% 1.07/1.24 inference(symmetry,[status(thm)],[33])).
% 1.07/1.24 tff(100,plain,
% 1.07/1.24 (one = addition(domain(domain(X0!0)), domain(one))),
% 1.07/1.24 inference(transitivity,[status(thm)],[99, 98, 59, 97, 82, 71, 69])).
% 1.07/1.24 tff(101,plain,
% 1.07/1.24 (multiplication(one, domain(X0!0)) = multiplication(addition(domain(domain(X0!0)), domain(one)), addition(domain(X0!0), domain(X0!0)))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[100, 96])).
% 1.07/1.24 tff(102,plain,
% 1.07/1.24 (multiplication(one, domain(X0!0)) = addition(domain(X0!0), domain(X0!0))),
% 1.07/1.24 inference(transitivity,[status(thm)],[101, 86, 24])).
% 1.07/1.24 tff(103,plain,
% 1.07/1.24 (domain(multiplication(one, domain(X0!0))) = domain(addition(domain(X0!0), domain(X0!0)))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[102])).
% 1.07/1.24 tff(104,plain,
% 1.07/1.24 (domain(addition(domain(X0!0), domain(X0!0))) = domain(multiplication(one, domain(X0!0)))),
% 1.07/1.24 inference(symmetry,[status(thm)],[103])).
% 1.07/1.24 tff(105,plain,
% 1.07/1.24 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(domain(X0!0), domain(X0!0))) = addition(domain(domain(X0!0)), domain(domain(X0!0))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(106,plain,
% 1.07/1.24 (domain(addition(domain(X0!0), domain(X0!0))) = addition(domain(domain(X0!0)), domain(domain(X0!0)))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[105, 45])).
% 1.07/1.24 tff(107,plain,
% 1.07/1.24 (addition(domain(domain(X0!0)), domain(domain(X0!0))) = domain(addition(domain(X0!0), domain(X0!0)))),
% 1.07/1.24 inference(symmetry,[status(thm)],[106])).
% 1.07/1.24 tff(108,plain,
% 1.07/1.24 ((~![A: $i] : (addition(A, A) = A)) | (addition(domain(domain(X0!0)), domain(domain(X0!0))) = domain(domain(X0!0)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(109,plain,
% 1.07/1.24 (addition(domain(domain(X0!0)), domain(domain(X0!0))) = domain(domain(X0!0))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[108, 93])).
% 1.07/1.24 tff(110,plain,
% 1.07/1.24 (domain(domain(X0!0)) = addition(domain(domain(X0!0)), domain(domain(X0!0)))),
% 1.07/1.24 inference(symmetry,[status(thm)],[109])).
% 1.07/1.24 tff(111,plain,
% 1.07/1.24 (domain(domain(X0!0)) = domain(X0!0)),
% 1.07/1.24 inference(transitivity,[status(thm)],[110, 107, 104, 22, 12])).
% 1.07/1.24 tff(112,plain,
% 1.07/1.24 ((~![X0: $i] : (domain(domain(X0)) = domain(X0))) <=> (~![X0: $i] : (domain(domain(X0)) = domain(X0)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(113,axiom,(~![X0: $i] : (domain(domain(X0)) = domain(X0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 1.07/1.24 tff(114,plain,
% 1.07/1.24 (~![X0: $i] : (domain(domain(X0)) = domain(X0))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.07/1.24 tff(115,plain,
% 1.07/1.24 (~![X0: $i] : (domain(domain(X0)) = domain(X0))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[114, 112])).
% 1.07/1.24 tff(116,plain,
% 1.07/1.24 (~![X0: $i] : (domain(domain(X0)) = domain(X0))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[115, 112])).
% 1.07/1.24 tff(117,plain,
% 1.07/1.24 (~![X0: $i] : (domain(domain(X0)) = domain(X0))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[116, 112])).
% 1.07/1.24 tff(118,plain,(
% 1.07/1.24 ~(domain(domain(X0!0)) = domain(X0!0))),
% 1.07/1.24 inference(skolemize,[status(sab)],[117])).
% 1.07/1.24 tff(119,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[118, 111])).
% 1.07/1.24 % SZS output end Proof
% 1.07/1.24 % E exiting
%------------------------------------------------------------------------------