%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE055+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 0.49s 0.69s
% Output : Proof 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE055+1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 18:56:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.49/0.69 % SZS status Theorem
% 0.49/0.69 % SZS output start Proof
% 0.49/0.69 tff(domain_type, type, (
% 0.49/0.69 domain: $i > $i)).
% 0.49/0.69 tff(tptp_fun_X0_0_type, type, (
% 0.49/0.69 tptp_fun_X0_0: $i)).
% 0.49/0.69 tff(addition_type, type, (
% 0.49/0.69 addition: ( $i * $i ) > $i)).
% 0.49/0.69 tff(zero_type, type, (
% 0.49/0.69 zero: $i)).
% 0.49/0.69 tff(multiplication_type, type, (
% 0.49/0.69 multiplication: ( $i * $i ) > $i)).
% 0.49/0.69 tff(one_type, type, (
% 0.49/0.69 one: $i)).
% 0.49/0.69 tff(1,plain,
% 0.49/0.69 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(2,plain,
% 0.49/0.69 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.49/0.69 inference(quant_intro,[status(thm)],[1])).
% 0.49/0.69 tff(3,plain,
% 0.49/0.69 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(4,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.49/0.69 tff(5,plain,
% 0.49/0.69 (![A: $i] : (addition(A, A) = A)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.49/0.69 tff(6,plain,(
% 0.49/0.69 ![A: $i] : (addition(A, A) = A)),
% 0.49/0.69 inference(skolemize,[status(sab)],[5])).
% 0.49/0.69 tff(7,plain,
% 0.49/0.69 (![A: $i] : (addition(A, A) = A)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.49/0.69 tff(8,plain,
% 0.49/0.69 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!0, X0!0) = X0!0)),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(9,plain,
% 0.49/0.69 (addition(X0!0, X0!0) = X0!0),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.49/0.69 tff(10,plain,
% 0.49/0.69 (X0!0 = addition(X0!0, X0!0)),
% 0.49/0.69 inference(symmetry,[status(thm)],[9])).
% 0.49/0.69 tff(11,plain,
% 0.49/0.69 (domain(X0!0) = domain(addition(X0!0, X0!0))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[10])).
% 0.49/0.69 tff(12,plain,
% 0.49/0.69 (domain(addition(X0!0, X0!0)) = domain(X0!0)),
% 0.49/0.69 inference(symmetry,[status(thm)],[11])).
% 0.49/0.69 tff(13,plain,
% 0.49/0.69 (^[X0: $i, X1: $i] : refl((domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(14,plain,
% 0.49/0.69 (![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)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[13])).
% 0.49/0.69 tff(15,plain,
% 0.49/0.69 (![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)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(16,axiom,(![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain5')).
% 0.49/0.69 tff(17,plain,
% 0.49/0.69 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.49/0.69 tff(18,plain,(
% 0.49/0.69 ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.49/0.69 inference(skolemize,[status(sab)],[17])).
% 0.49/0.69 tff(19,plain,
% 0.49/0.69 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.49/0.69 tff(20,plain,
% 0.49/0.69 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(X0!0, X0!0)) = addition(domain(X0!0), domain(X0!0)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(21,plain,
% 0.49/0.70 (domain(addition(X0!0, X0!0)) = addition(domain(X0!0), domain(X0!0))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.49/0.70 tff(22,plain,
% 0.49/0.70 (addition(domain(X0!0), domain(X0!0)) = domain(addition(X0!0, X0!0))),
% 0.49/0.70 inference(symmetry,[status(thm)],[21])).
% 0.49/0.70 tff(23,plain,
% 0.49/0.70 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(24,plain,
% 0.49/0.70 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.49/0.70 inference(quant_intro,[status(thm)],[23])).
% 0.49/0.70 tff(25,plain,
% 0.49/0.70 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(26,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.49/0.70 tff(27,plain,
% 0.49/0.70 (![A: $i] : (addition(A, zero) = A)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.49/0.70 tff(28,plain,(
% 0.49/0.70 ![A: $i] : (addition(A, zero) = A)),
% 0.49/0.70 inference(skolemize,[status(sab)],[27])).
% 0.49/0.70 tff(29,plain,
% 0.49/0.70 (![A: $i] : (addition(A, zero) = A)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.49/0.70 tff(30,plain,
% 0.49/0.70 ((~![A: $i] : (addition(A, zero) = A)) | (addition(addition(domain(X0!0), domain(X0!0)), zero) = addition(domain(X0!0), domain(X0!0)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(31,plain,
% 0.49/0.70 (addition(addition(domain(X0!0), domain(X0!0)), zero) = addition(domain(X0!0), domain(X0!0))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.49/0.70 tff(32,plain,
% 0.49/0.70 (addition(domain(X0!0), domain(X0!0)) = domain(X0!0)),
% 0.49/0.70 inference(transitivity,[status(thm)],[22, 12])).
% 0.49/0.70 tff(33,plain,
% 0.49/0.70 (addition(addition(domain(X0!0), domain(X0!0)), zero) = addition(domain(X0!0), zero)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[32])).
% 0.49/0.70 tff(34,plain,
% 0.49/0.70 (addition(domain(X0!0), zero) = addition(addition(domain(X0!0), domain(X0!0)), zero)),
% 0.49/0.70 inference(symmetry,[status(thm)],[33])).
% 0.49/0.70 tff(35,plain,
% 0.49/0.70 ((domain(zero) = zero) <=> (domain(zero) = zero)),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(36,axiom,(domain(zero) = zero), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain4')).
% 0.49/0.70 tff(37,plain,
% 0.49/0.70 (domain(zero) = zero),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.49/0.70 tff(38,plain,
% 0.49/0.70 (zero = domain(zero)),
% 0.49/0.70 inference(symmetry,[status(thm)],[37])).
% 0.49/0.70 tff(39,plain,
% 0.49/0.70 (multiplication(zero, zero) = multiplication(domain(zero), zero)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[38])).
% 0.49/0.70 tff(40,plain,
% 0.49/0.70 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(41,plain,
% 0.49/0.70 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.49/0.70 inference(quant_intro,[status(thm)],[40])).
% 0.49/0.70 tff(42,plain,
% 0.49/0.70 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(43,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 0.49/0.70 tff(44,plain,
% 0.49/0.70 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.49/0.70 tff(45,plain,(
% 0.49/0.70 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.49/0.70 inference(skolemize,[status(sab)],[44])).
% 0.49/0.70 tff(46,plain,
% 0.49/0.70 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.49/0.70 tff(47,plain,
% 0.49/0.70 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, zero) = zero)),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(48,plain,
% 0.49/0.70 (multiplication(zero, zero) = zero),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.49/0.70 tff(49,plain,
% 0.49/0.70 (zero = multiplication(zero, zero)),
% 0.49/0.70 inference(symmetry,[status(thm)],[48])).
% 0.49/0.70 tff(50,plain,
% 0.49/0.70 (zero = multiplication(domain(zero), zero)),
% 0.49/0.70 inference(transitivity,[status(thm)],[49, 39])).
% 0.49/0.70 tff(51,plain,
% 0.49/0.70 (domain(X0!0) = addition(domain(X0!0), domain(X0!0))),
% 0.49/0.70 inference(transitivity,[status(thm)],[11, 21])).
% 0.49/0.70 tff(52,plain,
% 0.49/0.70 (addition(domain(X0!0), zero) = addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[51, 50])).
% 0.49/0.70 tff(53,plain,
% 0.49/0.70 (addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)) = addition(domain(X0!0), zero)),
% 0.49/0.70 inference(symmetry,[status(thm)],[52])).
% 0.49/0.70 tff(54,plain,
% 0.49/0.70 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(55,plain,
% 0.49/0.70 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.49/0.70 inference(quant_intro,[status(thm)],[54])).
% 0.49/0.70 tff(56,plain,
% 0.49/0.70 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(57,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 0.49/0.70 tff(58,plain,
% 0.49/0.70 (![A: $i] : (multiplication(A, one) = A)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.49/0.70 tff(59,plain,(
% 0.49/0.70 ![A: $i] : (multiplication(A, one) = A)),
% 0.49/0.70 inference(skolemize,[status(sab)],[58])).
% 0.49/0.70 tff(60,plain,
% 0.49/0.70 (![A: $i] : (multiplication(A, one) = A)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.49/0.70 tff(61,plain,
% 0.49/0.70 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), one) = addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(62,plain,
% 0.49/0.70 (multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), one) = addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.49/0.70 tff(63,plain,
% 0.49/0.70 (addition(domain(X0!0), domain(X0!0)) = addition(addition(domain(X0!0), domain(X0!0)), zero)),
% 0.49/0.70 inference(symmetry,[status(thm)],[31])).
% 0.49/0.70 tff(64,plain,
% 0.49/0.70 (addition(domain(X0!0), domain(X0!0)) = addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero))),
% 0.49/0.70 inference(transitivity,[status(thm)],[63, 33, 52])).
% 0.49/0.70 tff(65,plain,
% 0.49/0.70 (multiplication(addition(domain(X0!0), domain(X0!0)), one) = multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), one)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[64])).
% 0.49/0.70 tff(66,plain,
% 0.49/0.70 ((~![X0: $i] : ((~(addition(X0, one) = one)) | (addition(X0, domain(X0)) = domain(X0)))) <=> (~![X0: $i] : ((~(addition(X0, one) = one)) | (addition(X0, domain(X0)) = domain(X0))))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(67,plain,
% 0.49/0.70 ((~![X0: $i] : ((addition(X0, one) = one) => (addition(X0, domain(X0)) = domain(X0)))) <=> (~![X0: $i] : ((~(addition(X0, one) = one)) | (addition(X0, domain(X0)) = domain(X0))))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(68,axiom,(~![X0: $i] : ((addition(X0, one) = one) => (addition(X0, domain(X0)) = domain(X0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.49/0.70 tff(69,plain,
% 0.49/0.70 (~![X0: $i] : ((~(addition(X0, one) = one)) | (addition(X0, domain(X0)) = domain(X0)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.49/0.70 tff(70,plain,
% 0.49/0.70 (~![X0: $i] : ((~(addition(X0, one) = one)) | (addition(X0, domain(X0)) = domain(X0)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.49/0.70 tff(71,plain,
% 0.49/0.70 (~![X0: $i] : ((~(addition(X0, one) = one)) | (addition(X0, domain(X0)) = domain(X0)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.49/0.70 tff(72,plain,
% 0.49/0.70 (~![X0: $i] : ((~(addition(X0, one) = one)) | (addition(X0, domain(X0)) = domain(X0)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[71, 66])).
% 0.49/0.70 tff(73,plain,(
% 0.49/0.70 ~((~(addition(X0!0, one) = one)) | (addition(X0!0, domain(X0!0)) = domain(X0!0)))),
% 0.49/0.70 inference(skolemize,[status(sab)],[72])).
% 0.49/0.70 tff(74,plain,
% 0.49/0.70 (addition(X0!0, one) = one),
% 0.49/0.70 inference(or_elim,[status(thm)],[73])).
% 0.49/0.70 tff(75,plain,
% 0.49/0.70 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(76,plain,
% 0.49/0.70 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[75])).
% 0.49/0.70 tff(77,plain,
% 0.49/0.70 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(78,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.49/0.70 tff(79,plain,
% 0.49/0.70 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.49/0.70 tff(80,plain,(
% 0.49/0.70 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.49/0.70 inference(skolemize,[status(sab)],[79])).
% 0.49/0.70 tff(81,plain,
% 0.49/0.70 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.49/0.70 tff(82,plain,
% 0.49/0.70 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!0, one) = addition(one, X0!0))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(83,plain,
% 0.49/0.70 (addition(X0!0, one) = addition(one, X0!0)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.49/0.70 tff(84,plain,
% 0.49/0.70 (addition(one, X0!0) = addition(X0!0, one)),
% 0.49/0.70 inference(symmetry,[status(thm)],[83])).
% 0.49/0.70 tff(85,plain,
% 0.49/0.70 (addition(one, X0!0) = one),
% 0.49/0.70 inference(transitivity,[status(thm)],[84, 74])).
% 0.49/0.70 tff(86,plain,
% 0.49/0.70 (addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)) = addition(domain(X0!0), domain(X0!0))),
% 0.49/0.70 inference(transitivity,[status(thm)],[53, 34, 31])).
% 0.49/0.70 tff(87,plain,
% 0.49/0.70 (multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), addition(one, X0!0)) = multiplication(addition(domain(X0!0), domain(X0!0)), one)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[86, 85])).
% 0.49/0.70 tff(88,plain,
% 0.49/0.70 (^[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))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(89,plain,
% 0.49/0.70 (![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)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[88])).
% 0.49/0.70 tff(90,plain,
% 0.49/0.70 (![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)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(91,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 0.49/0.70 tff(92,plain,
% 0.49/0.70 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.49/0.70 tff(93,plain,(
% 0.49/0.70 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.49/0.70 inference(skolemize,[status(sab)],[92])).
% 0.49/0.70 tff(94,plain,
% 0.49/0.70 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.49/0.70 tff(95,plain,
% 0.49/0.70 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), addition(one, X0!0)) = addition(multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), one), multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), X0!0)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(96,plain,
% 0.49/0.70 (multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), addition(one, X0!0)) = addition(multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), one), multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), X0!0))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.49/0.70 tff(97,plain,
% 0.49/0.70 (addition(multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), one), multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), X0!0)) = multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), addition(one, X0!0))),
% 0.49/0.70 inference(symmetry,[status(thm)],[96])).
% 0.49/0.70 tff(98,plain,
% 0.49/0.70 (addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)) = domain(X0!0)),
% 0.49/0.70 inference(transitivity,[status(thm)],[53, 34, 31, 22, 12])).
% 0.49/0.70 tff(99,plain,
% 0.49/0.70 (multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), X0!0) = multiplication(domain(X0!0), X0!0)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[98])).
% 0.49/0.70 tff(100,plain,
% 0.49/0.70 (multiplication(domain(X0!0), X0!0) = multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), X0!0)),
% 0.49/0.70 inference(symmetry,[status(thm)],[99])).
% 0.49/0.70 tff(101,plain,
% 0.49/0.70 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(102,plain,
% 0.49/0.70 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[101])).
% 0.49/0.70 tff(103,plain,
% 0.49/0.70 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(104,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain1')).
% 0.49/0.70 tff(105,plain,
% 0.49/0.70 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.49/0.70 tff(106,plain,(
% 0.49/0.70 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.49/0.70 inference(skolemize,[status(sab)],[105])).
% 0.49/0.70 tff(107,plain,
% 0.49/0.70 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.49/0.70 tff(108,plain,
% 0.49/0.70 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(X0!0, multiplication(domain(X0!0), X0!0)) = multiplication(domain(X0!0), X0!0))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(109,plain,
% 0.49/0.70 (addition(X0!0, multiplication(domain(X0!0), X0!0)) = multiplication(domain(X0!0), X0!0)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.49/0.70 tff(110,plain,
% 0.49/0.70 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(111,plain,
% 0.49/0.70 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.49/0.70 inference(quant_intro,[status(thm)],[110])).
% 0.49/0.70 tff(112,plain,
% 0.49/0.70 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(113,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 0.49/0.70 tff(114,plain,
% 0.49/0.70 (![A: $i] : (multiplication(one, A) = A)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.49/0.70 tff(115,plain,(
% 0.49/0.70 ![A: $i] : (multiplication(one, A) = A)),
% 0.49/0.70 inference(skolemize,[status(sab)],[114])).
% 0.49/0.70 tff(116,plain,
% 0.49/0.70 (![A: $i] : (multiplication(one, A) = A)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.49/0.70 tff(117,plain,
% 0.49/0.70 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!0) = X0!0)),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(118,plain,
% 0.49/0.70 (multiplication(one, X0!0) = X0!0),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.49/0.70 tff(119,plain,
% 0.49/0.70 (X0!0 = multiplication(one, X0!0)),
% 0.49/0.70 inference(symmetry,[status(thm)],[118])).
% 0.49/0.70 tff(120,plain,
% 0.49/0.70 (addition(X0!0, multiplication(domain(X0!0), X0!0)) = addition(multiplication(one, X0!0), multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), X0!0))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[119, 100])).
% 0.49/0.70 tff(121,plain,
% 0.49/0.70 (addition(multiplication(one, X0!0), multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), X0!0)) = addition(X0!0, multiplication(domain(X0!0), X0!0))),
% 0.49/0.70 inference(symmetry,[status(thm)],[120])).
% 0.49/0.70 tff(122,plain,
% 0.49/0.70 (^[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))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(123,plain,
% 0.49/0.70 (![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)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[122])).
% 0.49/0.70 tff(124,plain,
% 0.49/0.70 (![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)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(125,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')).
% 0.49/0.70 tff(126,plain,
% 0.49/0.70 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.49/0.70 tff(127,plain,(
% 0.49/0.70 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.49/0.70 inference(skolemize,[status(sab)],[126])).
% 0.49/0.70 tff(128,plain,
% 0.49/0.70 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.49/0.70 tff(129,plain,
% 0.49/0.70 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero))), X0!0) = addition(multiplication(one, X0!0), multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), X0!0)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(130,plain,
% 0.49/0.70 (multiplication(addition(one, addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero))), X0!0) = addition(multiplication(one, X0!0), multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), X0!0))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.49/0.70 tff(131,plain,
% 0.49/0.70 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(addition(domain(X0!0), domain(one)), one) = addition(domain(X0!0), domain(one)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(132,plain,
% 0.49/0.70 (multiplication(addition(domain(X0!0), domain(one)), one) = addition(domain(X0!0), domain(one))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[131, 60])).
% 0.49/0.70 tff(133,plain,
% 0.49/0.70 (one = addition(X0!0, one)),
% 0.49/0.70 inference(symmetry,[status(thm)],[74])).
% 0.49/0.70 tff(134,plain,
% 0.49/0.70 (domain(one) = domain(addition(X0!0, one))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[133])).
% 0.49/0.70 tff(135,plain,
% 0.49/0.70 (domain(addition(X0!0, one)) = domain(one)),
% 0.49/0.70 inference(symmetry,[status(thm)],[134])).
% 0.49/0.70 tff(136,plain,
% 0.49/0.70 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(X0!0, one)) = addition(domain(X0!0), domain(one)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(137,plain,
% 0.49/0.70 (domain(addition(X0!0, one)) = addition(domain(X0!0), domain(one))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[136, 19])).
% 0.49/0.70 tff(138,plain,
% 0.49/0.70 (addition(domain(X0!0), domain(one)) = domain(addition(X0!0, one))),
% 0.49/0.70 inference(symmetry,[status(thm)],[137])).
% 0.49/0.70 tff(139,plain,
% 0.49/0.70 (addition(domain(X0!0), domain(one)) = domain(one)),
% 0.49/0.70 inference(transitivity,[status(thm)],[138, 135])).
% 0.49/0.70 tff(140,plain,
% 0.49/0.70 (multiplication(addition(domain(X0!0), domain(one)), one) = multiplication(domain(one), one)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[139])).
% 0.49/0.70 tff(141,plain,
% 0.49/0.70 (multiplication(domain(one), one) = multiplication(addition(domain(X0!0), domain(one)), one)),
% 0.49/0.70 inference(symmetry,[status(thm)],[140])).
% 0.49/0.70 tff(142,plain,
% 0.49/0.70 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(one, multiplication(domain(one), one)) = multiplication(domain(one), one))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(143,plain,
% 0.49/0.70 (addition(one, multiplication(domain(one), one)) = multiplication(domain(one), one)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[142, 107])).
% 0.49/0.70 tff(144,plain,
% 0.49/0.70 (multiplication(domain(one), one) = addition(domain(X0!0), domain(one))),
% 0.49/0.70 inference(transitivity,[status(thm)],[141, 132])).
% 0.49/0.70 tff(145,plain,
% 0.49/0.70 (addition(one, multiplication(domain(one), one)) = addition(one, addition(domain(X0!0), domain(one)))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[144])).
% 0.49/0.70 tff(146,plain,
% 0.49/0.70 (addition(one, addition(domain(X0!0), domain(one))) = addition(one, multiplication(domain(one), one))),
% 0.49/0.70 inference(symmetry,[status(thm)],[145])).
% 0.49/0.70 tff(147,plain,
% 0.49/0.70 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(domain(X0!0), domain(one)), one) = addition(one, addition(domain(X0!0), domain(one))))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(148,plain,
% 0.49/0.70 (addition(addition(domain(X0!0), domain(one)), one) = addition(one, addition(domain(X0!0), domain(one)))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[147, 81])).
% 0.49/0.70 tff(149,plain,
% 0.49/0.70 (addition(addition(domain(X0!0), domain(one)), one) = addition(domain(one), one)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[139])).
% 0.49/0.70 tff(150,plain,
% 0.49/0.70 (addition(domain(one), one) = addition(addition(domain(X0!0), domain(one)), one)),
% 0.49/0.70 inference(symmetry,[status(thm)],[149])).
% 0.49/0.70 tff(151,plain,
% 0.49/0.70 (^[X0: $i] : refl((addition(domain(X0), one) = one) <=> (addition(domain(X0), one) = one))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(152,plain,
% 0.49/0.70 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 0.49/0.70 inference(quant_intro,[status(thm)],[151])).
% 0.49/0.70 tff(153,plain,
% 0.49/0.70 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(154,axiom,(![X0: $i] : (addition(domain(X0), one) = one)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain3')).
% 0.49/0.70 tff(155,plain,
% 0.49/0.70 (![X0: $i] : (addition(domain(X0), one) = one)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.49/0.70 tff(156,plain,(
% 0.49/0.70 ![X0: $i] : (addition(domain(X0), one) = one)),
% 0.49/0.70 inference(skolemize,[status(sab)],[155])).
% 0.49/0.70 tff(157,plain,
% 0.49/0.70 (![X0: $i] : (addition(domain(X0), one) = one)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.49/0.70 tff(158,plain,
% 0.49/0.70 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(one), one) = one)),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(159,plain,
% 0.49/0.70 (addition(domain(one), one) = one),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.49/0.70 tff(160,plain,
% 0.49/0.70 (one = addition(domain(one), one)),
% 0.49/0.70 inference(symmetry,[status(thm)],[159])).
% 0.49/0.70 tff(161,plain,
% 0.49/0.70 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(X0!0), one) = one)),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(162,plain,
% 0.49/0.70 (addition(domain(X0!0), one) = one),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[161, 157])).
% 0.49/0.70 tff(163,plain,
% 0.49/0.70 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(zero), one) = one)),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(164,plain,
% 0.49/0.70 (addition(domain(zero), one) = one),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[163, 157])).
% 0.49/0.70 tff(165,plain,
% 0.49/0.70 (addition(zero, one) = addition(domain(zero), one)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[38])).
% 0.49/0.70 tff(166,plain,
% 0.49/0.70 (addition(zero, one) = one),
% 0.49/0.70 inference(transitivity,[status(thm)],[165, 164])).
% 0.49/0.70 tff(167,plain,
% 0.49/0.70 (addition(domain(X0!0), addition(zero, one)) = addition(domain(X0!0), one)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[166])).
% 0.49/0.70 tff(168,plain,
% 0.49/0.70 (^[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)))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(169,plain,
% 0.49/0.70 (![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))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[168])).
% 0.49/0.70 tff(170,plain,
% 0.49/0.70 (![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))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(171,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 0.49/0.70 tff(172,plain,
% 0.49/0.70 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.49/0.70 tff(173,plain,(
% 0.49/0.70 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.49/0.70 inference(skolemize,[status(sab)],[172])).
% 0.49/0.70 tff(174,plain,
% 0.49/0.70 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.49/0.70 tff(175,plain,
% 0.49/0.70 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(domain(X0!0), addition(zero, one)) = addition(addition(domain(X0!0), zero), one))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(176,plain,
% 0.49/0.70 (addition(domain(X0!0), addition(zero, one)) = addition(addition(domain(X0!0), zero), one)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.49/0.70 tff(177,plain,
% 0.49/0.70 (addition(addition(domain(X0!0), zero), one) = addition(domain(X0!0), addition(zero, one))),
% 0.49/0.70 inference(symmetry,[status(thm)],[176])).
% 0.49/0.70 tff(178,plain,
% 0.49/0.70 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(domain(X0!0), zero), one) = addition(one, addition(domain(X0!0), zero)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(179,plain,
% 0.49/0.70 (addition(addition(domain(X0!0), zero), one) = addition(one, addition(domain(X0!0), zero))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[178, 81])).
% 0.49/0.70 tff(180,plain,
% 0.49/0.70 (addition(one, addition(domain(X0!0), zero)) = addition(addition(domain(X0!0), zero), one)),
% 0.49/0.70 inference(symmetry,[status(thm)],[179])).
% 0.49/0.70 tff(181,plain,
% 0.49/0.70 (addition(one, addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero))) = addition(one, addition(domain(X0!0), zero))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[53])).
% 0.49/0.70 tff(182,plain,
% 0.49/0.70 (addition(one, addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero))) = addition(domain(X0!0), domain(one))),
% 0.49/0.70 inference(transitivity,[status(thm)],[181, 180, 177, 167, 162, 160, 150, 148, 146, 143, 141, 132])).
% 0.49/0.70 tff(183,plain,
% 0.49/0.70 (multiplication(addition(one, addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero))), X0!0) = multiplication(addition(domain(X0!0), domain(one)), X0!0)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[182])).
% 0.49/0.70 tff(184,plain,
% 0.49/0.70 (multiplication(addition(domain(X0!0), domain(one)), X0!0) = multiplication(addition(one, addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero))), X0!0)),
% 0.49/0.70 inference(symmetry,[status(thm)],[183])).
% 0.49/0.70 tff(185,plain,
% 0.49/0.70 (addition(one, addition(domain(X0!0), domain(one))) = addition(addition(domain(X0!0), domain(one)), one)),
% 0.49/0.70 inference(symmetry,[status(thm)],[148])).
% 0.49/0.70 tff(186,plain,
% 0.49/0.70 (multiplication(domain(one), one) = addition(one, multiplication(domain(one), one))),
% 0.49/0.70 inference(symmetry,[status(thm)],[143])).
% 0.49/0.70 tff(187,plain,
% 0.49/0.70 (addition(domain(X0!0), domain(one)) = multiplication(addition(domain(X0!0), domain(one)), one)),
% 0.49/0.70 inference(symmetry,[status(thm)],[132])).
% 0.49/0.70 tff(188,plain,
% 0.49/0.70 (addition(domain(X0!0), domain(one)) = one),
% 0.49/0.70 inference(transitivity,[status(thm)],[187, 140, 186, 145, 185, 149, 159])).
% 0.49/0.70 tff(189,plain,
% 0.49/0.70 (multiplication(addition(domain(X0!0), domain(one)), X0!0) = multiplication(one, X0!0)),
% 0.49/0.71 inference(monotonicity,[status(thm)],[188])).
% 0.49/0.71 tff(190,plain,
% 0.49/0.71 (multiplication(one, X0!0) = multiplication(addition(domain(X0!0), domain(one)), X0!0)),
% 0.49/0.71 inference(symmetry,[status(thm)],[189])).
% 0.49/0.71 tff(191,plain,
% 0.49/0.71 (X0!0 = multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), X0!0)),
% 0.49/0.71 inference(transitivity,[status(thm)],[119, 190, 184, 130, 121, 109, 100])).
% 0.49/0.71 tff(192,plain,
% 0.49/0.71 (addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)) = multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), one)),
% 0.49/0.71 inference(symmetry,[status(thm)],[62])).
% 0.49/0.71 tff(193,plain,
% 0.49/0.71 (addition(domain(X0!0), zero) = multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), one)),
% 0.49/0.71 inference(transitivity,[status(thm)],[52, 192])).
% 0.49/0.71 tff(194,plain,
% 0.49/0.71 (addition(addition(domain(X0!0), zero), X0!0) = addition(multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), one), multiplication(addition(addition(domain(X0!0), domain(X0!0)), multiplication(domain(zero), zero)), X0!0))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[193, 191])).
% 0.49/0.71 tff(195,plain,
% 0.49/0.71 (domain(X0!0) = addition(domain(X0!0), zero)),
% 0.49/0.71 inference(transitivity,[status(thm)],[11, 21, 63, 33])).
% 0.49/0.71 tff(196,plain,
% 0.49/0.71 (addition(domain(X0!0), X0!0) = addition(addition(domain(X0!0), zero), X0!0)),
% 0.49/0.71 inference(monotonicity,[status(thm)],[195])).
% 0.49/0.71 tff(197,plain,
% 0.49/0.71 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!0, domain(X0!0)) = addition(domain(X0!0), X0!0))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(198,plain,
% 0.49/0.71 (addition(X0!0, domain(X0!0)) = addition(domain(X0!0), X0!0)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[197, 81])).
% 0.49/0.71 tff(199,plain,
% 0.49/0.71 (addition(X0!0, domain(X0!0)) = domain(X0!0)),
% 0.49/0.71 inference(transitivity,[status(thm)],[198, 196, 194, 97, 87, 65, 62, 53, 34, 31, 22, 12])).
% 0.49/0.71 tff(200,plain,
% 0.49/0.71 (~(addition(X0!0, domain(X0!0)) = domain(X0!0))),
% 0.49/0.71 inference(or_elim,[status(thm)],[73])).
% 0.49/0.71 tff(201,plain,
% 0.49/0.71 ($false),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.49/0.71 % SZS output end Proof
% 0.49/0.71 % E exiting
%------------------------------------------------------------------------------