%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE137+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:04 AM UTC 2025
% Result : Theorem 0.70s 0.87s
% Output : Proof 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE137+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:04:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.70/0.87 % SZS status Theorem
% 0.70/0.87 % SZS output start Proof
% 0.70/0.87 tff(strong_iteration_type, type, (
% 0.70/0.87 strong_iteration: $i > $i)).
% 0.70/0.87 tff(one_type, type, (
% 0.70/0.87 one: $i)).
% 0.70/0.87 tff(addition_type, type, (
% 0.70/0.87 addition: ( $i * $i ) > $i)).
% 0.70/0.87 tff(tptp_fun_X0_0_type, type, (
% 0.70/0.87 tptp_fun_X0_0: $i)).
% 0.70/0.87 tff(multiplication_type, type, (
% 0.70/0.87 multiplication: ( $i * $i ) > $i)).
% 0.70/0.87 tff(zero_type, type, (
% 0.70/0.87 zero: $i)).
% 0.70/0.87 tff(star_type, type, (
% 0.70/0.87 star: $i > $i)).
% 0.70/0.87 tff(leq_type, type, (
% 0.70/0.87 leq: ( $i * $i ) > $o)).
% 0.70/0.87 tff(1,plain,
% 0.70/0.87 (^[A: $i] : refl((strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))) <=> (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(2,plain,
% 0.70/0.87 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))) <=> ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[1])).
% 0.70/0.87 tff(3,plain,
% 0.70/0.87 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))) <=> ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(4,axiom,(![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','isolation')).
% 0.70/0.87 tff(5,plain,
% 0.70/0.87 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.70/0.87 tff(6,plain,(
% 0.70/0.87 ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[5])).
% 0.70/0.87 tff(7,plain,
% 0.70/0.87 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.70/0.87 tff(8,plain,
% 0.70/0.87 ((~![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))) | (strong_iteration(one) = addition(star(one), multiplication(strong_iteration(one), zero)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(9,plain,
% 0.70/0.87 (strong_iteration(one) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.70/0.87 tff(10,plain,
% 0.70/0.87 (addition(star(one), multiplication(strong_iteration(one), zero)) = strong_iteration(one)),
% 0.70/0.87 inference(symmetry,[status(thm)],[9])).
% 0.70/0.87 tff(11,plain,
% 0.70/0.87 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(12,plain,
% 0.70/0.87 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[11])).
% 0.70/0.87 tff(13,plain,
% 0.70/0.87 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(14,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.70/0.87 tff(15,plain,
% 0.70/0.87 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.70/0.87 tff(16,plain,(
% 0.70/0.87 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.70/0.87 inference(skolemize,[status(sab)],[15])).
% 0.70/0.87 tff(17,plain,
% 0.70/0.87 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.70/0.87 tff(18,plain,
% 0.70/0.87 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(one), multiplication(strong_iteration(one), zero)) = addition(multiplication(strong_iteration(one), zero), star(one)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(19,plain,
% 0.70/0.87 (addition(star(one), multiplication(strong_iteration(one), zero)) = addition(multiplication(strong_iteration(one), zero), star(one))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.70/0.87 tff(20,plain,
% 0.70/0.87 (addition(multiplication(strong_iteration(one), zero), star(one)) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 0.70/0.87 inference(symmetry,[status(thm)],[19])).
% 0.70/0.87 tff(21,plain,
% 0.70/0.87 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(22,plain,
% 0.70/0.87 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[21])).
% 0.70/0.87 tff(23,plain,
% 0.70/0.87 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(24,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 0.70/0.87 tff(25,plain,
% 0.70/0.87 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.70/0.87 tff(26,plain,(
% 0.70/0.87 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.70/0.87 inference(skolemize,[status(sab)],[25])).
% 0.70/0.87 tff(27,plain,
% 0.70/0.87 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.70/0.87 tff(28,plain,
% 0.70/0.87 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(one, star(one))) = star(one))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(29,plain,
% 0.70/0.87 (addition(one, multiplication(one, star(one))) = star(one)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.70/0.87 tff(30,plain,
% 0.70/0.87 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(31,plain,
% 0.70/0.87 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[30])).
% 0.70/0.87 tff(32,plain,
% 0.70/0.87 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(33,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 0.70/0.87 tff(34,plain,
% 0.70/0.87 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.70/0.87 tff(35,plain,(
% 0.70/0.87 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.70/0.87 inference(skolemize,[status(sab)],[34])).
% 0.70/0.87 tff(36,plain,
% 0.70/0.87 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.70/0.87 tff(37,plain,
% 0.70/0.87 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(one) = addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(38,plain,
% 0.70/0.87 (strong_iteration(one) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.70/0.87 tff(39,plain,
% 0.70/0.87 (multiplication(strong_iteration(one), zero) = multiplication(addition(multiplication(one, strong_iteration(one)), one), zero)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[38])).
% 0.70/0.87 tff(40,plain,
% 0.70/0.87 (multiplication(addition(multiplication(one, strong_iteration(one)), one), zero) = multiplication(strong_iteration(one), zero)),
% 0.70/0.87 inference(symmetry,[status(thm)],[39])).
% 0.70/0.87 tff(41,plain,
% 0.70/0.87 (^[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))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(42,plain,
% 0.70/0.87 (![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)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[41])).
% 0.70/0.87 tff(43,plain,
% 0.70/0.87 (![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)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(44,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity2')).
% 0.70/0.87 tff(45,plain,
% 0.70/0.87 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.70/0.87 tff(46,plain,(
% 0.70/0.87 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[45])).
% 0.70/0.87 tff(47,plain,
% 0.70/0.87 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.70/0.87 tff(48,plain,
% 0.70/0.87 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(one, strong_iteration(one)), one), zero) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(49,plain,
% 0.70/0.87 (multiplication(addition(multiplication(one, strong_iteration(one)), one), zero) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.70/0.87 tff(50,plain,
% 0.70/0.87 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(addition(multiplication(one, strong_iteration(one)), one), zero)),
% 0.70/0.87 inference(symmetry,[status(thm)],[49])).
% 0.70/0.87 tff(51,plain,
% 0.70/0.87 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(strong_iteration(one), zero)),
% 0.70/0.87 inference(transitivity,[status(thm)],[50, 40])).
% 0.70/0.87 tff(52,plain,
% 0.70/0.87 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, multiplication(one, star(one)))) = addition(multiplication(strong_iteration(one), zero), star(one))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[51, 29])).
% 0.70/0.87 tff(53,plain,
% 0.70/0.87 (^[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)))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(54,plain,
% 0.70/0.87 (![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))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[53])).
% 0.70/0.87 tff(55,plain,
% 0.70/0.87 (![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))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(56,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_associativity')).
% 0.70/0.87 tff(57,plain,
% 0.70/0.87 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.70/0.87 tff(58,plain,(
% 0.70/0.87 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.70/0.87 inference(skolemize,[status(sab)],[57])).
% 0.70/0.87 tff(59,plain,
% 0.70/0.87 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.70/0.87 tff(60,plain,
% 0.70/0.87 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, multiplication(one, star(one)))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), multiplication(one, star(one))))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(61,plain,
% 0.70/0.87 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, multiplication(one, star(one)))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), multiplication(one, star(one)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.70/0.87 tff(62,plain,
% 0.70/0.87 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), multiplication(one, star(one))) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, multiplication(one, star(one))))),
% 0.70/0.87 inference(symmetry,[status(thm)],[61])).
% 0.70/0.87 tff(63,plain,
% 0.70/0.87 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(64,plain,
% 0.70/0.87 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.70/0.87 inference(quant_intro,[status(thm)],[63])).
% 0.70/0.87 tff(65,plain,
% 0.70/0.87 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(66,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 0.70/0.87 tff(67,plain,
% 0.70/0.87 (![A: $i] : (multiplication(one, A) = A)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.70/0.87 tff(68,plain,(
% 0.70/0.87 ![A: $i] : (multiplication(one, A) = A)),
% 0.70/0.87 inference(skolemize,[status(sab)],[67])).
% 0.70/0.87 tff(69,plain,
% 0.70/0.87 (![A: $i] : (multiplication(one, A) = A)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.70/0.87 tff(70,plain,
% 0.70/0.87 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(one)) = star(one))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(71,plain,
% 0.70/0.87 (multiplication(one, star(one)) = star(one)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.70/0.87 tff(72,plain,
% 0.70/0.87 (star(one) = multiplication(one, star(one))),
% 0.70/0.87 inference(symmetry,[status(thm)],[71])).
% 0.70/0.87 tff(73,plain,
% 0.70/0.87 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(one, star(one))) = addition(multiplication(one, star(one)), one))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(74,plain,
% 0.70/0.87 (addition(one, multiplication(one, star(one))) = addition(multiplication(one, star(one)), one)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[73, 17])).
% 0.70/0.87 tff(75,plain,
% 0.70/0.87 (addition(multiplication(one, star(one)), one) = addition(one, multiplication(one, star(one)))),
% 0.70/0.87 inference(symmetry,[status(thm)],[74])).
% 0.70/0.87 tff(76,plain,
% 0.70/0.87 (addition(star(one), one) = addition(multiplication(one, star(one)), one)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[72])).
% 0.70/0.87 tff(77,plain,
% 0.70/0.87 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(78,plain,
% 0.70/0.87 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[77])).
% 0.70/0.87 tff(79,plain,
% 0.70/0.87 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(80,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','order')).
% 0.70/0.87 tff(81,plain,
% 0.70/0.87 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.70/0.87 tff(82,plain,(
% 0.70/0.87 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.70/0.87 inference(skolemize,[status(sab)],[81])).
% 0.70/0.87 tff(83,plain,
% 0.70/0.87 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.70/0.87 tff(84,plain,
% 0.70/0.87 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(star(one), one) <=> (addition(star(one), one) = one))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(85,plain,
% 0.70/0.87 (leq(star(one), one) <=> (addition(star(one), one) = one)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.70/0.87 tff(86,plain,
% 0.70/0.87 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(87,plain,
% 0.70/0.87 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.70/0.87 inference(quant_intro,[status(thm)],[86])).
% 0.70/0.87 tff(88,plain,
% 0.70/0.87 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(89,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 0.70/0.87 tff(90,plain,
% 0.70/0.87 (![A: $i] : (multiplication(A, one) = A)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.70/0.87 tff(91,plain,(
% 0.70/0.87 ![A: $i] : (multiplication(A, one) = A)),
% 0.70/0.87 inference(skolemize,[status(sab)],[90])).
% 0.70/0.87 tff(92,plain,
% 0.70/0.87 (![A: $i] : (multiplication(A, one) = A)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.70/0.87 tff(93,plain,
% 0.70/0.87 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(star(one), one) = star(one))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(94,plain,
% 0.70/0.87 (multiplication(star(one), one) = star(one)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.70/0.87 tff(95,plain,
% 0.70/0.87 (star(one) = multiplication(star(one), one)),
% 0.70/0.87 inference(symmetry,[status(thm)],[94])).
% 0.70/0.87 tff(96,plain,
% 0.70/0.87 (leq(star(one), one) <=> leq(multiplication(star(one), one), one)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[95])).
% 0.70/0.87 tff(97,plain,
% 0.70/0.87 (leq(multiplication(star(one), one), one) <=> leq(star(one), one)),
% 0.70/0.87 inference(symmetry,[status(thm)],[96])).
% 0.70/0.87 tff(98,plain,
% 0.70/0.87 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(99,plain,
% 0.70/0.87 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.70/0.87 inference(quant_intro,[status(thm)],[98])).
% 0.70/0.87 tff(100,plain,
% 0.70/0.87 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(101,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.70/0.87 tff(102,plain,
% 0.70/0.87 (![A: $i] : (addition(A, A) = A)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.70/0.87 tff(103,plain,(
% 0.70/0.87 ![A: $i] : (addition(A, A) = A)),
% 0.70/0.87 inference(skolemize,[status(sab)],[102])).
% 0.70/0.87 tff(104,plain,
% 0.70/0.87 (![A: $i] : (addition(A, A) = A)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.70/0.87 tff(105,plain,
% 0.70/0.87 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(106,plain,
% 0.70/0.87 (addition(one, one) = one),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.70/0.87 tff(107,plain,
% 0.70/0.87 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, one) = one)),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(108,plain,
% 0.70/0.87 (multiplication(one, one) = one),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[107, 69])).
% 0.70/0.87 tff(109,plain,
% 0.70/0.87 (addition(multiplication(one, one), one) = addition(one, one)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[108])).
% 0.70/0.87 tff(110,plain,
% 0.70/0.87 (addition(multiplication(one, one), one) = one),
% 0.70/0.87 inference(transitivity,[status(thm)],[109, 106])).
% 0.70/0.87 tff(111,plain,
% 0.70/0.87 (leq(addition(multiplication(one, one), one), one) <=> leq(one, one)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[110])).
% 0.70/0.87 tff(112,plain,
% 0.70/0.87 (leq(one, one) <=> leq(addition(multiplication(one, one), one), one)),
% 0.70/0.87 inference(symmetry,[status(thm)],[111])).
% 0.70/0.87 tff(113,plain,
% 0.70/0.87 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(one, one) <=> (addition(one, one) = one))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(114,plain,
% 0.70/0.87 (leq(one, one) <=> (addition(one, one) = one)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[113, 83])).
% 0.70/0.87 tff(115,plain,
% 0.70/0.87 ((~(leq(one, one) <=> (addition(one, one) = one))) | leq(one, one) | (~(addition(one, one) = one))),
% 0.70/0.87 inference(tautology,[status(thm)],[])).
% 0.70/0.87 tff(116,plain,
% 0.70/0.87 (leq(one, one)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[115, 106, 114])).
% 0.70/0.87 tff(117,plain,
% 0.70/0.87 (leq(addition(multiplication(one, one), one), one)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.70/0.87 tff(118,plain,
% 0.70/0.87 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(119,plain,
% 0.70/0.87 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[118])).
% 0.70/0.87 tff(120,plain,
% 0.70/0.87 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(121,plain,
% 0.70/0.87 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C)) <=> ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(122,plain,
% 0.70/0.87 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[121])).
% 0.70/0.87 tff(123,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_induction1')).
% 0.70/0.87 tff(124,plain,
% 0.70/0.87 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.70/0.87 tff(125,plain,
% 0.70/0.87 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.70/0.87 tff(126,plain,(
% 0.70/0.87 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.70/0.87 inference(skolemize,[status(sab)],[125])).
% 0.70/0.87 tff(127,plain,
% 0.70/0.87 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.70/0.87 tff(128,plain,
% 0.70/0.87 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(star(one), one), one))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(star(one), one), one))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(129,plain,
% 0.70/0.87 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(star(one), one), one))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(130,plain,
% 0.70/0.87 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(star(one), one), one)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.70/0.87 tff(131,plain,
% 0.70/0.87 ((~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(star(one), one), one)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[130, 127])).
% 0.70/0.87 tff(132,plain,
% 0.70/0.87 (leq(multiplication(star(one), one), one)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[131, 117])).
% 0.70/0.87 tff(133,plain,
% 0.70/0.87 (leq(star(one), one)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[132, 97])).
% 0.70/0.87 tff(134,plain,
% 0.70/0.87 ((~(leq(star(one), one) <=> (addition(star(one), one) = one))) | (~leq(star(one), one)) | (addition(star(one), one) = one)),
% 0.70/0.87 inference(tautology,[status(thm)],[])).
% 0.70/0.87 tff(135,plain,
% 0.70/0.87 (addition(star(one), one) = one),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[134, 133, 85])).
% 0.70/0.87 tff(136,plain,
% 0.70/0.87 (one = addition(star(one), one)),
% 0.70/0.87 inference(symmetry,[status(thm)],[135])).
% 0.70/0.87 tff(137,plain,
% 0.70/0.87 (addition(one, one) = multiplication(one, star(one))),
% 0.70/0.87 inference(transitivity,[status(thm)],[106, 136, 76, 75, 29, 72])).
% 0.70/0.87 tff(138,plain,
% 0.70/0.87 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), addition(one, one)) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), multiplication(one, star(one)))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[137])).
% 0.70/0.87 tff(139,plain,
% 0.70/0.87 (one = addition(one, one)),
% 0.70/0.87 inference(symmetry,[status(thm)],[106])).
% 0.70/0.87 tff(140,plain,
% 0.70/0.87 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[139])).
% 0.70/0.87 tff(141,plain,
% 0.70/0.87 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one)),
% 0.70/0.87 inference(symmetry,[status(thm)],[140])).
% 0.70/0.87 tff(142,plain,
% 0.70/0.87 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)), addition(one, one)) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), addition(one, one))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[141])).
% 0.70/0.87 tff(143,plain,
% 0.70/0.87 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(one, one), addition(one, one))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)), addition(one, one)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(144,plain,
% 0.70/0.87 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(one, one), addition(one, one))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)), addition(one, one))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[143, 59])).
% 0.70/0.87 tff(145,plain,
% 0.70/0.87 (addition(addition(one, one), addition(one, one)) = addition(one, one)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[106, 106])).
% 0.70/0.87 tff(146,plain,
% 0.70/0.87 (addition(one, one) = addition(addition(one, one), addition(one, one))),
% 0.70/0.87 inference(symmetry,[status(thm)],[145])).
% 0.70/0.87 tff(147,plain,
% 0.70/0.87 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(one, one), addition(one, one)))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[146])).
% 0.70/0.87 tff(148,plain,
% 0.70/0.87 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one) = addition(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(149,plain,
% 0.70/0.87 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one) = addition(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[148, 17])).
% 0.70/0.87 tff(150,plain,
% 0.70/0.87 (addition(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one)),
% 0.70/0.87 inference(symmetry,[status(thm)],[149])).
% 0.70/0.87 tff(151,plain,
% 0.70/0.87 (addition(addition(one, one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[106])).
% 0.70/0.87 tff(152,plain,
% 0.70/0.87 (addition(multiplication(one, strong_iteration(one)), one) = strong_iteration(one)),
% 0.70/0.87 inference(symmetry,[status(thm)],[38])).
% 0.70/0.87 tff(153,plain,
% 0.70/0.87 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(154,plain,
% 0.70/0.87 (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[153, 69])).
% 0.70/0.87 tff(155,plain,
% 0.70/0.87 (multiplication(one, strong_iteration(one)) = multiplication(one, addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[38])).
% 0.70/0.87 tff(156,plain,
% 0.70/0.87 (multiplication(one, strong_iteration(one)) = strong_iteration(one)),
% 0.70/0.87 inference(transitivity,[status(thm)],[155, 154, 152])).
% 0.70/0.87 tff(157,plain,
% 0.70/0.87 (multiplication(multiplication(one, strong_iteration(one)), zero) = multiplication(strong_iteration(one), zero)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[156])).
% 0.70/0.87 tff(158,plain,
% 0.70/0.87 (multiplication(strong_iteration(one), zero) = multiplication(multiplication(one, strong_iteration(one)), zero)),
% 0.70/0.87 inference(symmetry,[status(thm)],[157])).
% 0.70/0.87 tff(159,plain,
% 0.70/0.87 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(multiplication(one, strong_iteration(one)), zero)),
% 0.70/0.87 inference(transitivity,[status(thm)],[50, 40, 158])).
% 0.70/0.87 tff(160,plain,
% 0.70/0.87 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), multiplication(one, zero)) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[159])).
% 0.70/0.87 tff(161,plain,
% 0.70/0.87 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), multiplication(one, zero)) = addition(multiplication(one, zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(162,plain,
% 0.70/0.87 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), multiplication(one, zero)) = addition(multiplication(one, zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[161, 17])).
% 0.70/0.87 tff(163,plain,
% 0.70/0.87 (addition(multiplication(one, zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), multiplication(one, zero))),
% 0.70/0.87 inference(symmetry,[status(thm)],[162])).
% 0.70/0.87 tff(164,plain,
% 0.70/0.87 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, zero) = zero)),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(165,plain,
% 0.70/0.88 (multiplication(one, zero) = zero),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[164, 69])).
% 0.70/0.88 tff(166,plain,
% 0.70/0.88 (zero = multiplication(one, zero)),
% 0.70/0.88 inference(symmetry,[status(thm)],[165])).
% 0.70/0.88 tff(167,plain,
% 0.70/0.88 (addition(zero, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(multiplication(one, zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[166])).
% 0.70/0.88 tff(168,plain,
% 0.70/0.88 (addition(zero, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.70/0.88 inference(transitivity,[status(thm)],[167, 163, 160])).
% 0.70/0.88 tff(169,plain,
% 0.70/0.88 (addition(one, addition(zero, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))) = addition(addition(one, one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[139, 168])).
% 0.70/0.88 tff(170,plain,
% 0.70/0.88 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(zero, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))) = addition(addition(one, zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(171,plain,
% 0.70/0.88 (addition(one, addition(zero, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))) = addition(addition(one, zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[170, 59])).
% 0.70/0.88 tff(172,plain,
% 0.70/0.88 (addition(addition(one, zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(one, addition(zero, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))))),
% 0.70/0.88 inference(symmetry,[status(thm)],[171])).
% 0.70/0.88 tff(173,plain,
% 0.70/0.88 (addition(one, zero) = addition(addition(one, one), zero)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[139])).
% 0.70/0.88 tff(174,plain,
% 0.70/0.88 (addition(addition(one, one), zero) = addition(one, zero)),
% 0.70/0.88 inference(symmetry,[status(thm)],[173])).
% 0.70/0.88 tff(175,plain,
% 0.70/0.88 (addition(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(one, zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[174])).
% 0.70/0.88 tff(176,plain,
% 0.70/0.88 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) <=> (addition(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(177,plain,
% 0.70/0.88 (leq(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) <=> (addition(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[176, 83])).
% 0.70/0.88 tff(178,plain,
% 0.70/0.88 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(179,plain,
% 0.70/0.88 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.70/0.88 inference(quant_intro,[status(thm)],[178])).
% 0.70/0.88 tff(180,plain,
% 0.70/0.88 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(181,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_identity')).
% 0.70/0.88 tff(182,plain,
% 0.70/0.88 (![A: $i] : (addition(A, zero) = A)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.70/0.88 tff(183,plain,(
% 0.70/0.88 ![A: $i] : (addition(A, zero) = A)),
% 0.70/0.88 inference(skolemize,[status(sab)],[182])).
% 0.70/0.88 tff(184,plain,
% 0.70/0.88 (![A: $i] : (addition(A, zero) = A)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.70/0.88 tff(185,plain,
% 0.70/0.88 ((~![A: $i] : (addition(A, zero) = A)) | (addition(addition(one, one), zero) = addition(one, one))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(186,plain,
% 0.70/0.88 (addition(addition(one, one), zero) = addition(one, one)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.70/0.88 tff(187,plain,
% 0.70/0.88 (addition(addition(one, one), zero) = one),
% 0.70/0.88 inference(transitivity,[status(thm)],[186, 106])).
% 0.70/0.88 tff(188,plain,
% 0.70/0.88 (leq(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) <=> leq(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[187])).
% 0.70/0.88 tff(189,plain,
% 0.70/0.88 (leq(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) <=> leq(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(symmetry,[status(thm)],[188])).
% 0.70/0.88 tff(190,plain,
% 0.70/0.88 (strong_iteration(addition(one, one)) = strong_iteration(one)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[106])).
% 0.70/0.88 tff(191,plain,
% 0.70/0.88 (multiplication(strong_iteration(addition(one, one)), zero) = multiplication(strong_iteration(one), zero)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[190])).
% 0.70/0.88 tff(192,plain,
% 0.70/0.88 (multiplication(strong_iteration(addition(one, one)), zero) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.70/0.88 inference(transitivity,[status(thm)],[191, 39, 49])).
% 0.70/0.88 tff(193,plain,
% 0.70/0.88 (leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero)) <=> leq(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[106, 192])).
% 0.70/0.88 tff(194,plain,
% 0.70/0.88 (leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero)) <=> leq(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[193, 189])).
% 0.70/0.88 tff(195,plain,
% 0.70/0.88 (multiplication(addition(one, one), addition(one, one)) = multiplication(one, one)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[106, 106])).
% 0.70/0.88 tff(196,plain,
% 0.70/0.88 (multiplication(addition(one, one), addition(one, one)) = addition(one, one)),
% 0.70/0.88 inference(transitivity,[status(thm)],[195, 108, 139])).
% 0.70/0.88 tff(197,plain,
% 0.70/0.88 (addition(multiplication(addition(one, one), addition(one, one)), zero) = addition(addition(one, one), zero)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[196])).
% 0.70/0.88 tff(198,plain,
% 0.70/0.88 (addition(multiplication(addition(one, one), addition(one, one)), zero) = one),
% 0.70/0.88 inference(transitivity,[status(thm)],[197, 186, 106])).
% 0.70/0.88 tff(199,plain,
% 0.70/0.88 (leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero)) <=> leq(one, one)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[106, 198])).
% 0.70/0.88 tff(200,plain,
% 0.70/0.88 (leq(one, one) <=> leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))),
% 0.70/0.88 inference(symmetry,[status(thm)],[199])).
% 0.70/0.88 tff(201,plain,
% 0.70/0.88 (leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[116, 200])).
% 0.70/0.88 tff(202,plain,
% 0.70/0.88 (^[A: $i, B: $i, C: $i] : refl(((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B))) <=> ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(203,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B))) <=> ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[202])).
% 0.70/0.88 tff(204,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B))) <=> ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(205,plain,
% 0.70/0.88 (^[A: $i, B: $i, C: $i] : rewrite((leq(C, addition(multiplication(A, C), B)) => leq(C, multiplication(strong_iteration(A), B))) <=> ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(206,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : (leq(C, addition(multiplication(A, C), B)) => leq(C, multiplication(strong_iteration(A), B))) <=> ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[205])).
% 0.70/0.88 tff(207,axiom,(![A: $i, B: $i, C: $i] : (leq(C, addition(multiplication(A, C), B)) => leq(C, multiplication(strong_iteration(A), B)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','infty_coinduction')).
% 0.70/0.88 tff(208,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.70/0.88 tff(209,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.70/0.88 tff(210,plain,(
% 0.70/0.88 ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.70/0.88 inference(skolemize,[status(sab)],[209])).
% 0.70/0.88 tff(211,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.70/0.88 tff(212,plain,
% 0.70/0.88 (((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))) | leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))) | leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(213,plain,
% 0.70/0.88 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))) | leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(214,plain,
% 0.70/0.88 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))) | leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.70/0.88 tff(215,plain,
% 0.70/0.88 ((~leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))) | leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[214, 211])).
% 0.70/0.88 tff(216,plain,
% 0.70/0.88 (leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[215, 201])).
% 0.70/0.88 tff(217,plain,
% 0.70/0.88 (leq(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[216, 194])).
% 0.70/0.88 tff(218,plain,
% 0.70/0.88 ((~(leq(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) <=> (addition(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))))) | (~leq(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))) | (addition(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(tautology,[status(thm)],[])).
% 0.70/0.88 tff(219,plain,
% 0.70/0.88 (addition(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[218, 217, 177])).
% 0.70/0.88 tff(220,plain,
% 0.70/0.88 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = addition(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.88 inference(symmetry,[status(thm)],[219])).
% 0.70/0.88 tff(221,plain,
% 0.70/0.88 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) <=> (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) = zero))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(222,plain,
% 0.70/0.88 (leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) <=> (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) = zero)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[221, 83])).
% 0.70/0.88 tff(223,plain,
% 0.70/0.88 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(224,plain,
% 0.70/0.88 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[223])).
% 0.70/0.88 tff(225,plain,
% 0.70/0.88 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(226,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 0.70/0.88 tff(227,plain,
% 0.70/0.88 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.70/0.88 tff(228,plain,(
% 0.70/0.88 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.70/0.88 inference(skolemize,[status(sab)],[227])).
% 0.70/0.88 tff(229,plain,
% 0.70/0.88 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[228, 224])).
% 0.70/0.88 tff(230,plain,
% 0.70/0.88 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(one), one)) = star(one))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(231,plain,
% 0.70/0.88 (addition(one, multiplication(star(one), one)) = star(one)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.70/0.88 tff(232,plain,
% 0.70/0.88 (star(one) = addition(one, multiplication(star(one), one))),
% 0.70/0.88 inference(symmetry,[status(thm)],[231])).
% 0.70/0.88 tff(233,plain,
% 0.70/0.88 (multiplication(star(one), zero) = multiplication(addition(one, multiplication(star(one), one)), zero)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[232])).
% 0.70/0.88 tff(234,plain,
% 0.70/0.88 (multiplication(addition(one, multiplication(star(one), one)), zero) = multiplication(star(one), zero)),
% 0.70/0.88 inference(symmetry,[status(thm)],[233])).
% 0.70/0.88 tff(235,plain,
% 0.70/0.88 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, multiplication(star(one), one)), zero) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(236,plain,
% 0.70/0.88 (multiplication(addition(one, multiplication(star(one), one)), zero) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[235, 47])).
% 0.70/0.88 tff(237,plain,
% 0.70/0.88 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(addition(one, multiplication(star(one), one)), zero)),
% 0.70/0.88 inference(symmetry,[status(thm)],[236])).
% 0.70/0.88 tff(238,plain,
% 0.70/0.88 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(star(one), zero)),
% 0.70/0.88 inference(transitivity,[status(thm)],[237, 234])).
% 0.70/0.88 tff(239,plain,
% 0.70/0.88 (leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) <=> leq(multiplication(star(one), zero), zero)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[238])).
% 0.70/0.88 tff(240,plain,
% 0.70/0.88 (leq(multiplication(star(one), zero), zero) <=> leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.70/0.88 inference(symmetry,[status(thm)],[239])).
% 0.70/0.88 tff(241,plain,
% 0.70/0.88 ((~![A: $i] : (addition(A, A) = A)) | (addition(zero, zero) = zero)),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(242,plain,
% 0.70/0.88 (addition(zero, zero) = zero),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[241, 104])).
% 0.70/0.88 tff(243,plain,
% 0.70/0.88 (addition(multiplication(one, zero), multiplication(one, zero)) = addition(zero, zero)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[165, 165])).
% 0.70/0.88 tff(244,plain,
% 0.70/0.88 (addition(multiplication(one, zero), zero) = addition(multiplication(one, zero), multiplication(one, zero))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[166])).
% 0.70/0.88 tff(245,plain,
% 0.70/0.88 (addition(multiplication(one, zero), zero) = zero),
% 0.70/0.88 inference(transitivity,[status(thm)],[244, 243, 242])).
% 0.70/0.88 tff(246,plain,
% 0.70/0.88 (leq(addition(multiplication(one, zero), zero), zero) <=> leq(zero, zero)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[245])).
% 0.70/0.88 tff(247,plain,
% 0.70/0.88 (leq(zero, zero) <=> leq(addition(multiplication(one, zero), zero), zero)),
% 0.70/0.88 inference(symmetry,[status(thm)],[246])).
% 0.70/0.88 tff(248,plain,
% 0.70/0.88 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(zero, zero) <=> (addition(zero, zero) = zero))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(249,plain,
% 0.70/0.88 (leq(zero, zero) <=> (addition(zero, zero) = zero)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[248, 83])).
% 0.70/0.88 tff(250,plain,
% 0.70/0.88 ((~(leq(zero, zero) <=> (addition(zero, zero) = zero))) | leq(zero, zero) | (~(addition(zero, zero) = zero))),
% 0.70/0.88 inference(tautology,[status(thm)],[])).
% 0.70/0.88 tff(251,plain,
% 0.70/0.88 (leq(zero, zero)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[250, 242, 249])).
% 0.70/0.88 tff(252,plain,
% 0.70/0.88 (leq(addition(multiplication(one, zero), zero), zero)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.70/0.88 tff(253,plain,
% 0.70/0.88 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(one, zero), zero), zero)) | leq(multiplication(star(one), zero), zero))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(one, zero), zero), zero)) | leq(multiplication(star(one), zero), zero))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(254,plain,
% 0.70/0.88 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(one, zero), zero), zero)) | leq(multiplication(star(one), zero), zero))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(255,plain,
% 0.70/0.88 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(one, zero), zero), zero)) | leq(multiplication(star(one), zero), zero)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.70/0.88 tff(256,plain,
% 0.70/0.88 ((~leq(addition(multiplication(one, zero), zero), zero)) | leq(multiplication(star(one), zero), zero)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[255, 127])).
% 0.70/0.88 tff(257,plain,
% 0.70/0.88 (leq(multiplication(star(one), zero), zero)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[256, 252])).
% 0.70/0.88 tff(258,plain,
% 0.70/0.88 (leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[257, 240])).
% 0.70/0.88 tff(259,plain,
% 0.70/0.88 ((~(leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) <=> (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) = zero))) | (~leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)) | (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) = zero)),
% 0.70/0.88 inference(tautology,[status(thm)],[])).
% 0.70/0.88 tff(260,plain,
% 0.70/0.88 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) = zero),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[259, 258, 222])).
% 0.70/0.88 tff(261,plain,
% 0.70/0.88 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(262,plain,
% 0.70/0.88 (addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[261, 17])).
% 0.70/0.88 tff(263,plain,
% 0.70/0.88 (multiplication(multiplication(one, star(one)), zero) = multiplication(star(one), zero)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[71])).
% 0.70/0.88 tff(264,plain,
% 0.70/0.88 (multiplication(star(one), zero) = multiplication(multiplication(one, star(one)), zero)),
% 0.70/0.88 inference(symmetry,[status(thm)],[263])).
% 0.70/0.88 tff(265,plain,
% 0.70/0.88 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(multiplication(one, star(one)), zero)),
% 0.70/0.88 inference(transitivity,[status(thm)],[237, 234, 264])).
% 0.70/0.88 tff(266,plain,
% 0.70/0.88 (addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[166, 265])).
% 0.70/0.88 tff(267,plain,
% 0.70/0.88 (addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero)) = addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.88 inference(symmetry,[status(thm)],[266])).
% 0.70/0.88 tff(268,plain,
% 0.70/0.88 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, multiplication(one, star(one))), zero) = addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(269,plain,
% 0.70/0.88 (multiplication(addition(one, multiplication(one, star(one))), zero) = addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[268, 47])).
% 0.70/0.88 tff(270,plain,
% 0.70/0.88 (multiplication(addition(one, multiplication(one, star(one))), zero) = multiplication(star(one), zero)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[29])).
% 0.70/0.88 tff(271,plain,
% 0.70/0.88 (multiplication(star(one), zero) = multiplication(addition(one, multiplication(one, star(one))), zero)),
% 0.70/0.88 inference(symmetry,[status(thm)],[270])).
% 0.70/0.88 tff(272,plain,
% 0.70/0.88 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = zero),
% 0.70/0.88 inference(transitivity,[status(thm)],[237, 234, 271, 269, 267, 262, 260])).
% 0.70/0.88 tff(273,plain,
% 0.70/0.88 (multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(strong_iteration(one), zero)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[272])).
% 0.70/0.88 tff(274,plain,
% 0.70/0.88 (addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero)) = multiplication(addition(one, multiplication(one, star(one))), zero)),
% 0.70/0.88 inference(symmetry,[status(thm)],[269])).
% 0.70/0.88 tff(275,plain,
% 0.70/0.88 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) = addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.88 inference(symmetry,[status(thm)],[262])).
% 0.70/0.88 tff(276,plain,
% 0.70/0.88 (zero = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.70/0.88 inference(symmetry,[status(thm)],[260])).
% 0.70/0.88 tff(277,plain,
% 0.70/0.88 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(278,plain,
% 0.70/0.88 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.70/0.88 inference(quant_intro,[status(thm)],[277])).
% 0.70/0.88 tff(279,plain,
% 0.70/0.88 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(280,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 0.70/0.88 tff(281,plain,
% 0.70/0.88 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.70/0.88 tff(282,plain,(
% 0.70/0.88 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.70/0.88 inference(skolemize,[status(sab)],[281])).
% 0.70/0.88 tff(283,plain,
% 0.70/0.88 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[282, 278])).
% 0.70/0.88 tff(284,plain,
% 0.70/0.88 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = zero)),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(285,plain,
% 0.70/0.88 (multiplication(zero, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = zero),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[284, 283])).
% 0.70/0.88 tff(286,plain,
% 0.70/0.88 (multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(zero, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[272])).
% 0.70/0.88 tff(287,plain,
% 0.70/0.88 (multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))),
% 0.70/0.88 inference(transitivity,[status(thm)],[286, 285, 276, 275, 266, 274, 270, 233, 236])).
% 0.70/0.88 tff(288,plain,
% 0.70/0.88 (addition(multiplication(one, star(one)), one) = addition(star(one), one)),
% 0.70/0.88 inference(symmetry,[status(thm)],[76])).
% 0.70/0.88 tff(289,plain,
% 0.70/0.88 (star(one) = addition(one, multiplication(one, star(one)))),
% 0.70/0.88 inference(symmetry,[status(thm)],[29])).
% 0.70/0.88 tff(290,plain,
% 0.70/0.88 (star(one) = one),
% 0.70/0.88 inference(transitivity,[status(thm)],[289, 74, 288, 135])).
% 0.70/0.88 tff(291,plain,
% 0.70/0.88 (strong_iteration(star(one)) = strong_iteration(one)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[290])).
% 0.70/0.88 tff(292,plain,
% 0.70/0.88 (multiplication(star(one), one) = multiplication(star(one), addition(one, one))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[139])).
% 0.70/0.88 tff(293,plain,
% 0.70/0.88 (multiplication(star(one), addition(one, one)) = multiplication(star(one), one)),
% 0.70/0.88 inference(symmetry,[status(thm)],[292])).
% 0.70/0.88 tff(294,plain,
% 0.70/0.88 (addition(one, one) = addition(addition(one, one), zero)),
% 0.70/0.88 inference(symmetry,[status(thm)],[186])).
% 0.70/0.88 tff(295,plain,
% 0.70/0.88 (multiplication(star(one), addition(one, one)) = multiplication(star(one), addition(addition(one, one), zero))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[294])).
% 0.70/0.88 tff(296,plain,
% 0.70/0.88 (multiplication(star(one), addition(addition(one, one), zero)) = multiplication(star(one), addition(one, one))),
% 0.70/0.88 inference(symmetry,[status(thm)],[295])).
% 0.70/0.88 tff(297,plain,
% 0.70/0.88 (^[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))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(298,plain,
% 0.70/0.88 (![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)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[297])).
% 0.70/0.88 tff(299,plain,
% 0.70/0.88 (![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)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(300,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity1')).
% 0.70/0.88 tff(301,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.70/0.88 tff(302,plain,(
% 0.70/0.88 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.70/0.88 inference(skolemize,[status(sab)],[301])).
% 0.70/0.88 tff(303,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.70/0.88 tff(304,plain,
% 0.70/0.88 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(one), addition(addition(one, one), zero)) = addition(multiplication(star(one), addition(one, one)), multiplication(star(one), zero)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(305,plain,
% 0.70/0.88 (multiplication(star(one), addition(addition(one, one), zero)) = addition(multiplication(star(one), addition(one, one)), multiplication(star(one), zero))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.70/0.88 tff(306,plain,
% 0.70/0.88 (addition(multiplication(star(one), addition(one, one)), multiplication(star(one), zero)) = multiplication(star(one), addition(addition(one, one), zero))),
% 0.70/0.88 inference(symmetry,[status(thm)],[305])).
% 0.70/0.88 tff(307,plain,
% 0.70/0.88 (multiplication(star(one), addition(one, one)) = star(one)),
% 0.70/0.88 inference(transitivity,[status(thm)],[293, 94])).
% 0.70/0.88 tff(308,plain,
% 0.70/0.88 (addition(multiplication(star(one), addition(one, one)), multiplication(star(one), zero)) = addition(star(one), multiplication(star(one), zero))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[307])).
% 0.70/0.88 tff(309,plain,
% 0.70/0.88 (addition(star(one), multiplication(star(one), zero)) = addition(multiplication(star(one), addition(one, one)), multiplication(star(one), zero))),
% 0.70/0.88 inference(symmetry,[status(thm)],[308])).
% 0.70/0.88 tff(310,plain,
% 0.70/0.88 (multiplication(star(one), zero) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))),
% 0.70/0.88 inference(transitivity,[status(thm)],[233, 236])).
% 0.70/0.88 tff(311,plain,
% 0.70/0.88 (addition(star(one), multiplication(star(one), zero)) = addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[310])).
% 0.70/0.88 tff(312,plain,
% 0.70/0.88 (addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(star(one), multiplication(star(one), zero))),
% 0.70/0.88 inference(symmetry,[status(thm)],[311])).
% 0.70/0.88 tff(313,plain,
% 0.70/0.88 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(314,plain,
% 0.70/0.88 (addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[313, 17])).
% 0.70/0.88 tff(315,plain,
% 0.70/0.88 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)) = addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.88 inference(symmetry,[status(thm)],[314])).
% 0.70/0.88 tff(316,plain,
% 0.70/0.88 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)) = star(one)),
% 0.70/0.88 inference(transitivity,[status(thm)],[315, 312, 309, 306, 296, 293, 94])).
% 0.70/0.88 tff(317,plain,
% 0.70/0.88 (strong_iteration(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))) = strong_iteration(star(one))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[316])).
% 0.70/0.88 tff(318,plain,
% 0.70/0.88 (strong_iteration(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))) = strong_iteration(one)),
% 0.70/0.88 inference(transitivity,[status(thm)],[317, 291])).
% 0.70/0.88 tff(319,plain,
% 0.70/0.88 (multiplication(strong_iteration(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[318, 287])).
% 0.70/0.88 tff(320,plain,
% 0.70/0.88 (strong_iteration(star(one)) = strong_iteration(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)))),
% 0.70/0.88 inference(symmetry,[status(thm)],[317])).
% 0.70/0.88 tff(321,plain,
% 0.70/0.88 (strong_iteration(one) = strong_iteration(star(one))),
% 0.70/0.89 inference(symmetry,[status(thm)],[291])).
% 0.70/0.89 tff(322,plain,
% 0.70/0.89 (addition(multiplication(one, strong_iteration(one)), one) = strong_iteration(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)))),
% 0.70/0.89 inference(transitivity,[status(thm)],[152, 321, 320])).
% 0.70/0.89 tff(323,plain,
% 0.70/0.89 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(strong_iteration(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[322])).
% 0.70/0.89 tff(324,plain,
% 0.70/0.89 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 0.70/0.89 inference(bind,[status(th)],[])).
% 0.70/0.89 tff(325,plain,
% 0.70/0.89 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.70/0.89 inference(quant_intro,[status(thm)],[324])).
% 0.70/0.89 tff(326,plain,
% 0.70/0.89 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(327,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.70/0.89 tff(328,plain,
% 0.70/0.89 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.70/0.89 tff(329,plain,(
% 0.70/0.89 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.70/0.89 inference(skolemize,[status(sab)],[328])).
% 0.70/0.89 tff(330,plain,
% 0.70/0.89 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[329, 325])).
% 0.70/0.89 tff(331,plain,
% 0.70/0.89 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(332,plain,
% 0.70/0.89 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[331, 330])).
% 0.70/0.89 tff(333,plain,
% 0.70/0.89 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.70/0.89 inference(symmetry,[status(thm)],[332])).
% 0.70/0.89 tff(334,plain,
% 0.70/0.89 (multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[152])).
% 0.70/0.89 tff(335,plain,
% 0.70/0.89 (multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.89 inference(symmetry,[status(thm)],[334])).
% 0.70/0.89 tff(336,plain,
% 0.70/0.89 (multiplication(strong_iteration(one), zero) = multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.89 inference(symmetry,[status(thm)],[273])).
% 0.70/0.89 tff(337,plain,
% 0.70/0.89 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.89 inference(transitivity,[status(thm)],[50, 40, 336, 335])).
% 0.70/0.89 tff(338,plain,
% 0.70/0.89 (multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[337])).
% 0.70/0.89 tff(339,plain,
% 0.70/0.89 (addition(addition(one, zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.89 inference(symmetry,[status(thm)],[175])).
% 0.70/0.89 tff(340,plain,
% 0.70/0.89 (addition(addition(one, one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(one, addition(zero, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))))),
% 0.70/0.89 inference(symmetry,[status(thm)],[169])).
% 0.70/0.89 tff(341,plain,
% 0.70/0.89 (addition(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(one, one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.89 inference(symmetry,[status(thm)],[151])).
% 0.70/0.89 tff(342,plain,
% 0.70/0.89 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(one, one), addition(one, one))) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one))),
% 0.70/0.89 inference(symmetry,[status(thm)],[147])).
% 0.70/0.89 tff(343,plain,
% 0.70/0.89 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)), addition(one, one)) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(one, one), addition(one, one)))),
% 0.70/0.89 inference(symmetry,[status(thm)],[144])).
% 0.70/0.89 tff(344,plain,
% 0.70/0.89 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), addition(one, one)) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)), addition(one, one))),
% 0.70/0.89 inference(symmetry,[status(thm)],[142])).
% 0.70/0.89 tff(345,plain,
% 0.70/0.89 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), multiplication(one, star(one))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), addition(one, one))),
% 0.70/0.89 inference(symmetry,[status(thm)],[138])).
% 0.70/0.89 tff(346,plain,
% 0.70/0.89 (addition(multiplication(strong_iteration(one), zero), star(one)) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, multiplication(one, star(one))))),
% 0.70/0.89 inference(symmetry,[status(thm)],[52])).
% 0.70/0.89 tff(347,plain,
% 0.70/0.89 (strong_iteration(one) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.70/0.89 inference(transitivity,[status(thm)],[9, 19, 346, 61, 345, 344, 343, 342, 141, 149, 341, 340, 171, 339, 219])).
% 0.70/0.89 tff(348,plain,
% 0.70/0.89 (multiplication(strong_iteration(one), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[347])).
% 0.70/0.89 tff(349,plain,
% 0.70/0.89 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(one, strong_iteration(one)), one) = addition(one, multiplication(one, strong_iteration(one))))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(350,plain,
% 0.70/0.89 (addition(multiplication(one, strong_iteration(one)), one) = addition(one, multiplication(one, strong_iteration(one)))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[349, 17])).
% 0.70/0.89 tff(351,plain,
% 0.70/0.89 (addition(one, multiplication(one, strong_iteration(one))) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.70/0.89 inference(symmetry,[status(thm)],[350])).
% 0.70/0.89 tff(352,plain,
% 0.70/0.89 (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = multiplication(one, strong_iteration(one))),
% 0.70/0.89 inference(symmetry,[status(thm)],[155])).
% 0.70/0.89 tff(353,plain,
% 0.70/0.89 (addition(multiplication(one, strong_iteration(one)), one) = multiplication(one, addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.89 inference(symmetry,[status(thm)],[154])).
% 0.70/0.89 tff(354,plain,
% 0.70/0.89 (addition(multiplication(one, strong_iteration(one)), one) = multiplication(one, strong_iteration(one))),
% 0.70/0.89 inference(transitivity,[status(thm)],[353, 352])).
% 0.70/0.89 tff(355,plain,
% 0.70/0.89 (addition(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(one, multiplication(one, strong_iteration(one)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[354])).
% 0.70/0.89 tff(356,plain,
% 0.70/0.89 (addition(one, addition(multiplication(one, strong_iteration(one)), one)) = multiplication(one, strong_iteration(one))),
% 0.70/0.89 inference(transitivity,[status(thm)],[355, 351, 353, 352])).
% 0.70/0.89 tff(357,plain,
% 0.70/0.89 (addition(one, addition(one, addition(multiplication(one, strong_iteration(one)), one))) = addition(one, multiplication(one, strong_iteration(one)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[356])).
% 0.70/0.89 tff(358,plain,
% 0.70/0.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(multiplication(one, strong_iteration(one)), one))) = addition(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(359,plain,
% 0.70/0.89 (addition(one, addition(one, addition(multiplication(one, strong_iteration(one)), one))) = addition(addition(one, one), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[358, 59])).
% 0.70/0.89 tff(360,plain,
% 0.70/0.89 (addition(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)) = addition(one, addition(one, addition(multiplication(one, strong_iteration(one)), one)))),
% 0.70/0.89 inference(symmetry,[status(thm)],[359])).
% 0.70/0.89 tff(361,plain,
% 0.70/0.89 (multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), zero) = multiplication(strong_iteration(one), zero)),
% 0.70/0.89 inference(monotonicity,[status(thm)],[10])).
% 0.70/0.89 tff(362,plain,
% 0.70/0.89 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), zero) = addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(363,plain,
% 0.70/0.89 (multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), zero) = addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[362, 47])).
% 0.70/0.89 tff(364,plain,
% 0.70/0.89 (addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)) = multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), zero)),
% 0.70/0.89 inference(symmetry,[status(thm)],[363])).
% 0.70/0.89 tff(365,plain,
% 0.70/0.89 (addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)) = multiplication(strong_iteration(one), zero)),
% 0.70/0.89 inference(transitivity,[status(thm)],[364, 361])).
% 0.70/0.89 tff(366,plain,
% 0.70/0.89 (addition(addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)), star(one)) = addition(multiplication(strong_iteration(one), zero), star(one))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[365])).
% 0.70/0.89 tff(367,plain,
% 0.70/0.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(one), zero), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))) = addition(addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)), star(one)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(368,plain,
% 0.70/0.89 (addition(multiplication(star(one), zero), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))) = addition(addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)), star(one))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[367, 59])).
% 0.70/0.89 tff(369,plain,
% 0.70/0.89 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))) = addition(multiplication(star(one), zero), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[238])).
% 0.70/0.89 tff(370,plain,
% 0.70/0.89 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.70/0.89 inference(transitivity,[status(thm)],[369, 368, 366, 20, 10, 38])).
% 0.70/0.89 tff(371,plain,
% 0.70/0.89 (addition(addition(one, one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))) = addition(addition(one, one), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[370])).
% 0.70/0.89 tff(372,plain,
% 0.70/0.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(one, one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))) = addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(373,plain,
% 0.70/0.89 (addition(addition(one, one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))) = addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[372, 59])).
% 0.70/0.89 tff(374,plain,
% 0.70/0.89 (addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))) = addition(addition(one, one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))))),
% 0.70/0.89 inference(symmetry,[status(thm)],[373])).
% 0.70/0.89 tff(375,plain,
% 0.70/0.89 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, zero) = zero)),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(376,plain,
% 0.70/0.89 (multiplication(zero, zero) = zero),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[375, 283])).
% 0.70/0.89 tff(377,plain,
% 0.70/0.89 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, zero)) = multiplication(strong_iteration(one), zero)),
% 0.70/0.89 inference(monotonicity,[status(thm)],[152, 376])).
% 0.70/0.89 tff(378,plain,
% 0.70/0.89 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, zero)) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(379,plain,
% 0.70/0.89 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, zero)) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[378, 330])).
% 0.70/0.89 tff(380,plain,
% 0.70/0.89 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, zero))),
% 0.70/0.89 inference(symmetry,[status(thm)],[379])).
% 0.70/0.89 tff(381,plain,
% 0.70/0.89 (multiplication(multiplication(strong_iteration(one), zero), zero) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero)),
% 0.70/0.89 inference(monotonicity,[status(thm)],[39])).
% 0.70/0.89 tff(382,plain,
% 0.70/0.89 (multiplication(multiplication(strong_iteration(one), zero), zero) = multiplication(strong_iteration(one), zero)),
% 0.70/0.89 inference(transitivity,[status(thm)],[381, 380, 377])).
% 0.70/0.89 tff(383,plain,
% 0.70/0.89 (addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)) = addition(multiplication(strong_iteration(one), zero), star(one))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[382])).
% 0.70/0.89 tff(384,plain,
% 0.70/0.89 (addition(multiplication(strong_iteration(one), zero), star(one)) = addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))),
% 0.70/0.89 inference(symmetry,[status(thm)],[383])).
% 0.70/0.89 tff(385,plain,
% 0.70/0.89 (addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)) = multiplication(multiplication(one, strong_iteration(one)), zero)),
% 0.70/0.89 inference(transitivity,[status(thm)],[364, 361, 158])).
% 0.70/0.89 tff(386,plain,
% 0.70/0.89 (addition(addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)), multiplication(one, zero)) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[385])).
% 0.70/0.89 tff(387,plain,
% 0.70/0.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(one), zero), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero))) = addition(addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)), multiplication(one, zero)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(388,plain,
% 0.70/0.89 (addition(multiplication(star(one), zero), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero))) = addition(addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)), multiplication(one, zero))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[387, 59])).
% 0.70/0.89 tff(389,plain,
% 0.70/0.89 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero))) = addition(multiplication(star(one), zero), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[238])).
% 0.70/0.89 tff(390,plain,
% 0.70/0.89 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero))) = multiplication(strong_iteration(one), zero)),
% 0.70/0.89 inference(transitivity,[status(thm)],[389, 388, 386, 50, 40])).
% 0.70/0.89 tff(391,plain,
% 0.70/0.89 (addition(star(one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero)))) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[390])).
% 0.70/0.89 tff(392,plain,
% 0.70/0.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero)))) = addition(addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero))))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(393,plain,
% 0.70/0.89 (addition(star(one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero)))) = addition(addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero)))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[392, 59])).
% 0.70/0.89 tff(394,plain,
% 0.70/0.89 (addition(addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero))) = addition(star(one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero))))),
% 0.70/0.89 inference(symmetry,[status(thm)],[393])).
% 0.70/0.89 tff(395,plain,
% 0.70/0.89 (addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero)) = addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), zero)),
% 0.70/0.89 inference(monotonicity,[status(thm)],[381, 165])).
% 0.70/0.89 tff(396,plain,
% 0.70/0.89 (addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), zero) = addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero))),
% 0.70/0.89 inference(symmetry,[status(thm)],[395])).
% 0.70/0.89 tff(397,plain,
% 0.70/0.89 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), zero) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(398,plain,
% 0.70/0.89 (addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), zero) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[397, 184])).
% 0.70/0.89 tff(399,plain,
% 0.70/0.89 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero) = addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), zero)),
% 0.70/0.89 inference(symmetry,[status(thm)],[398])).
% 0.70/0.89 tff(400,plain,
% 0.70/0.89 (multiplication(strong_iteration(one), zero) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, zero))),
% 0.70/0.89 inference(symmetry,[status(thm)],[377])).
% 0.70/0.89 tff(401,plain,
% 0.70/0.89 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero))),
% 0.70/0.89 inference(transitivity,[status(thm)],[50, 40, 400, 379, 399, 396])).
% 0.70/0.89 tff(402,plain,
% 0.70/0.89 (addition(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(one, zero)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[315, 401])).
% 0.70/0.89 tff(403,plain,
% 0.70/0.89 (addition(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))),
% 0.70/0.89 inference(transitivity,[status(thm)],[402, 394, 391, 19, 384])).
% 0.70/0.89 tff(404,plain,
% 0.70/0.89 (addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))) = addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[403])).
% 0.70/0.89 tff(405,plain,
% 0.70/0.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))) = addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(406,plain,
% 0.70/0.89 (addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))) = addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[405, 59])).
% 0.70/0.89 tff(407,plain,
% 0.70/0.89 (addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))))),
% 0.70/0.90 inference(symmetry,[status(thm)],[406])).
% 0.70/0.90 tff(408,plain,
% 0.70/0.90 (addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = strong_iteration(one)),
% 0.70/0.90 inference(transitivity,[status(thm)],[407, 404, 374, 371, 360, 357, 351, 152])).
% 0.70/0.90 tff(409,plain,
% 0.70/0.90 (multiplication(addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(strong_iteration(one), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[408])).
% 0.70/0.90 tff(410,plain,
% 0.70/0.90 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = addition(multiplication(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)), multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(411,plain,
% 0.70/0.90 (multiplication(addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = addition(multiplication(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)), multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[410, 47])).
% 0.70/0.90 tff(412,plain,
% 0.70/0.90 (addition(multiplication(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)), multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.90 inference(symmetry,[status(thm)],[411])).
% 0.70/0.90 tff(413,plain,
% 0.70/0.90 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.90 inference(symmetry,[status(thm)],[338])).
% 0.70/0.90 tff(414,plain,
% 0.70/0.90 (multiplication(strong_iteration(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.70/0.90 inference(symmetry,[status(thm)],[323])).
% 0.70/0.90 tff(415,plain,
% 0.70/0.90 (multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(strong_iteration(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.70/0.90 inference(symmetry,[status(thm)],[319])).
% 0.70/0.90 tff(416,plain,
% 0.70/0.90 (addition(multiplication(one, strong_iteration(one)), one) = multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.90 inference(transitivity,[status(thm)],[152, 9, 19, 346, 61, 345, 344, 343, 342, 141, 149, 341, 340, 171, 339, 219, 50, 40, 336, 415, 414, 332, 413])).
% 0.70/0.90 tff(417,plain,
% 0.70/0.90 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(418,plain,
% 0.70/0.90 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[417, 104])).
% 0.70/0.90 tff(419,plain,
% 0.70/0.90 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(star(one), zero)),
% 0.70/0.90 inference(transitivity,[status(thm)],[418, 237, 234])).
% 0.70/0.90 tff(420,plain,
% 0.70/0.90 (addition(star(one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(star(one), multiplication(star(one), zero))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[419])).
% 0.70/0.90 tff(421,plain,
% 0.70/0.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(422,plain,
% 0.70/0.90 (addition(star(one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[421, 59])).
% 0.70/0.90 tff(423,plain,
% 0.70/0.90 (addition(addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(star(one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.70/0.90 inference(symmetry,[status(thm)],[422])).
% 0.70/0.90 tff(424,plain,
% 0.70/0.90 (multiplication(star(one), multiplication(zero, zero)) = multiplication(star(one), zero)),
% 0.70/0.90 inference(monotonicity,[status(thm)],[376])).
% 0.70/0.90 tff(425,plain,
% 0.70/0.90 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(star(one), multiplication(zero, zero)) = multiplication(multiplication(star(one), zero), zero))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(426,plain,
% 0.70/0.90 (multiplication(star(one), multiplication(zero, zero)) = multiplication(multiplication(star(one), zero), zero)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[425, 330])).
% 0.70/0.90 tff(427,plain,
% 0.70/0.90 (multiplication(multiplication(star(one), zero), zero) = multiplication(star(one), multiplication(zero, zero))),
% 0.70/0.90 inference(symmetry,[status(thm)],[426])).
% 0.70/0.90 tff(428,plain,
% 0.70/0.90 (multiplication(multiplication(star(one), zero), zero) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))),
% 0.70/0.90 inference(transitivity,[status(thm)],[427, 424, 233, 236])).
% 0.70/0.90 tff(429,plain,
% 0.70/0.90 (addition(addition(star(one), multiplication(star(one), zero)), multiplication(multiplication(star(one), zero), zero)) = addition(addition(star(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[311, 428])).
% 0.70/0.90 tff(430,plain,
% 0.70/0.90 (multiplication(star(one), zero) = multiplication(star(one), multiplication(zero, zero))),
% 0.70/0.90 inference(symmetry,[status(thm)],[424])).
% 0.70/0.90 tff(431,plain,
% 0.70/0.90 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(multiplication(star(one), zero), zero)),
% 0.70/0.90 inference(transitivity,[status(thm)],[237, 234, 430, 426])).
% 0.70/0.90 tff(432,plain,
% 0.70/0.90 (addition(star(one), one) = star(one)),
% 0.70/0.90 inference(transitivity,[status(thm)],[76, 75, 29])).
% 0.70/0.90 tff(433,plain,
% 0.70/0.90 (addition(addition(star(one), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(star(one), multiplication(star(one), zero))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[432, 238])).
% 0.70/0.90 tff(434,plain,
% 0.70/0.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(one), addition(one, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(star(one), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(435,plain,
% 0.70/0.90 (addition(star(one), addition(one, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(star(one), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[434, 59])).
% 0.70/0.90 tff(436,plain,
% 0.70/0.90 (addition(one, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[139])).
% 0.70/0.90 tff(437,plain,
% 0.70/0.90 (addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(one, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.90 inference(symmetry,[status(thm)],[436])).
% 0.70/0.90 tff(438,plain,
% 0.70/0.90 (addition(star(one), addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(star(one), addition(one, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[437])).
% 0.70/0.90 tff(439,plain,
% 0.70/0.90 (addition(star(one), addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(star(one), multiplication(star(one), zero))),
% 0.70/0.90 inference(transitivity,[status(thm)],[438, 435, 433])).
% 0.70/0.90 tff(440,plain,
% 0.70/0.90 (addition(addition(star(one), addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(star(one), multiplication(star(one), zero)), multiplication(multiplication(star(one), zero), zero))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[439, 431])).
% 0.70/0.90 tff(441,plain,
% 0.70/0.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(one), addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(star(one), addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(442,plain,
% 0.70/0.90 (addition(star(one), addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(star(one), addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[441, 59])).
% 0.70/0.90 tff(443,plain,
% 0.70/0.90 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(one), addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), star(one)))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(444,plain,
% 0.70/0.90 (addition(star(one), addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), star(one))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[443, 17])).
% 0.70/0.90 tff(445,plain,
% 0.70/0.90 (addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), star(one)) = addition(star(one), addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.70/0.90 inference(symmetry,[status(thm)],[444])).
% 0.70/0.90 tff(446,plain,
% 0.70/0.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))) = addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), star(one)))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(447,plain,
% 0.70/0.90 (addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))) = addition(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), star(one))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[446, 59])).
% 0.70/0.90 tff(448,plain,
% 0.70/0.90 (addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))),
% 0.70/0.90 inference(transitivity,[status(thm)],[447, 445, 442, 440, 429, 423, 420, 311, 314])).
% 0.70/0.90 tff(449,plain,
% 0.70/0.90 (multiplication(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[448])).
% 0.70/0.90 tff(450,plain,
% 0.70/0.90 (multiplication(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.90 inference(symmetry,[status(thm)],[449])).
% 0.70/0.90 tff(451,plain,
% 0.70/0.90 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)) = one),
% 0.70/0.90 inference(transitivity,[status(thm)],[315, 312, 309, 306, 296, 293, 94, 289, 74, 288, 135])).
% 0.70/0.90 tff(452,plain,
% 0.70/0.90 (multiplication(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(one, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[451])).
% 0.70/0.90 tff(453,plain,
% 0.70/0.90 (multiplication(one, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.90 inference(symmetry,[status(thm)],[452])).
% 0.70/0.90 tff(454,plain,
% 0.70/0.90 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(455,plain,
% 0.70/0.90 (multiplication(one, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[454, 69])).
% 0.70/0.90 tff(456,plain,
% 0.70/0.90 (addition(addition(X0!0, multiplication(one, strong_iteration(one))), one) = multiplication(one, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.90 inference(symmetry,[status(thm)],[455])).
% 0.70/0.90 tff(457,plain,
% 0.70/0.90 (addition(X0!0, multiplication(one, strong_iteration(one))) = addition(X0!0, strong_iteration(one))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[156])).
% 0.70/0.90 tff(458,plain,
% 0.70/0.90 (addition(X0!0, strong_iteration(one)) = addition(X0!0, multiplication(one, strong_iteration(one)))),
% 0.70/0.90 inference(symmetry,[status(thm)],[457])).
% 0.70/0.90 tff(459,plain,
% 0.70/0.90 (addition(X0!0, strong_iteration(one)) = addition(X0!0, addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[38])).
% 0.70/0.90 tff(460,plain,
% 0.70/0.90 (addition(X0!0, addition(multiplication(one, strong_iteration(one)), one)) = addition(X0!0, strong_iteration(one))),
% 0.70/0.90 inference(symmetry,[status(thm)],[459])).
% 0.70/0.90 tff(461,plain,
% 0.70/0.90 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!0, addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(multiplication(one, strong_iteration(one)), one), X0!0))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(462,plain,
% 0.70/0.90 (addition(X0!0, addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(multiplication(one, strong_iteration(one)), one), X0!0)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[461, 17])).
% 0.70/0.90 tff(463,plain,
% 0.70/0.90 (addition(addition(multiplication(one, strong_iteration(one)), one), X0!0) = addition(X0!0, addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.90 inference(symmetry,[status(thm)],[462])).
% 0.70/0.90 tff(464,plain,
% 0.70/0.90 (addition(addition(multiplication(one, strong_iteration(one)), one), X0!0) = addition(X0!0, multiplication(one, strong_iteration(one)))),
% 0.70/0.90 inference(transitivity,[status(thm)],[463, 460, 458])).
% 0.70/0.90 tff(465,plain,
% 0.70/0.90 (addition(addition(addition(multiplication(one, strong_iteration(one)), one), X0!0), one) = addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)),
% 0.70/0.90 inference(monotonicity,[status(thm)],[464])).
% 0.70/0.90 tff(466,plain,
% 0.70/0.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, one)) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), X0!0), one))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(467,plain,
% 0.70/0.90 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, one)) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), X0!0), one)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[466, 59])).
% 0.70/0.90 tff(468,plain,
% 0.70/0.90 (addition(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.70/0.90 inference(transitivity,[status(thm)],[360, 357, 351])).
% 0.70/0.90 tff(469,plain,
% 0.70/0.90 (addition(addition(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), addition(X0!0, one)) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, one))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[468])).
% 0.70/0.90 tff(470,plain,
% 0.70/0.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(one, one), addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, one))) = addition(addition(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), addition(X0!0, one)))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(471,plain,
% 0.70/0.90 (addition(addition(one, one), addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, one))) = addition(addition(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), addition(X0!0, one))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[470, 59])).
% 0.70/0.90 tff(472,plain,
% 0.70/0.90 (addition(addition(addition(multiplication(one, strong_iteration(one)), one), X0!0), one) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, one))),
% 0.70/0.90 inference(symmetry,[status(thm)],[467])).
% 0.70/0.90 tff(473,plain,
% 0.70/0.90 (addition(addition(X0!0, multiplication(one, strong_iteration(one))), one) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), X0!0), one)),
% 0.70/0.90 inference(symmetry,[status(thm)],[465])).
% 0.70/0.90 tff(474,plain,
% 0.70/0.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!0, addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(475,plain,
% 0.70/0.90 (addition(X0!0, addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[474, 59])).
% 0.70/0.90 tff(476,plain,
% 0.70/0.90 (addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), one) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.70/0.90 inference(monotonicity,[status(thm)],[352])).
% 0.70/0.90 tff(477,plain,
% 0.70/0.90 (addition(addition(multiplication(one, strong_iteration(one)), one), one) = addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), one)),
% 0.70/0.90 inference(monotonicity,[status(thm)],[353])).
% 0.70/0.90 tff(478,plain,
% 0.70/0.90 (addition(addition(multiplication(one, strong_iteration(one)), one), one) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.70/0.90 inference(transitivity,[status(thm)],[477, 476])).
% 0.70/0.90 tff(479,plain,
% 0.70/0.90 (addition(addition(addition(multiplication(one, strong_iteration(one)), one), one), X0!0) = addition(addition(multiplication(one, strong_iteration(one)), one), X0!0)),
% 0.70/0.90 inference(monotonicity,[status(thm)],[478])).
% 0.70/0.90 tff(480,plain,
% 0.70/0.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(one, strong_iteration(one)), one), addition(one, X0!0)) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), one), X0!0))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(481,plain,
% 0.70/0.90 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(one, X0!0)) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), one), X0!0)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[480, 59])).
% 0.70/0.90 tff(482,plain,
% 0.70/0.90 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(one, strong_iteration(one)), one), addition(one, X0!0)) = addition(addition(one, X0!0), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(483,plain,
% 0.70/0.91 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(one, X0!0)) = addition(addition(one, X0!0), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[482, 17])).
% 0.70/0.91 tff(484,plain,
% 0.70/0.91 (addition(addition(one, X0!0), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(one, X0!0))),
% 0.70/0.91 inference(symmetry,[status(thm)],[483])).
% 0.70/0.91 tff(485,plain,
% 0.70/0.91 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!0, one) = addition(one, X0!0))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(486,plain,
% 0.70/0.91 (addition(X0!0, one) = addition(one, X0!0)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[485, 17])).
% 0.70/0.91 tff(487,plain,
% 0.70/0.91 (addition(addition(X0!0, one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))) = addition(addition(one, X0!0), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[486, 370])).
% 0.70/0.91 tff(488,plain,
% 0.70/0.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X0!0, one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))) = addition(addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(489,plain,
% 0.70/0.91 (addition(addition(X0!0, one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))) = addition(addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[488, 59])).
% 0.70/0.91 tff(490,plain,
% 0.70/0.91 (addition(addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))) = addition(addition(X0!0, one), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))))),
% 0.70/0.91 inference(symmetry,[status(thm)],[489])).
% 0.70/0.91 tff(491,plain,
% 0.70/0.91 (addition(multiplication(one, strong_iteration(one)), one) = addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))),
% 0.70/0.91 inference(transitivity,[status(thm)],[152, 9, 19, 384])).
% 0.70/0.91 tff(492,plain,
% 0.70/0.91 (addition(addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[491])).
% 0.70/0.91 tff(493,plain,
% 0.70/0.91 (addition(addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, one))),
% 0.70/0.91 inference(transitivity,[status(thm)],[492, 490, 487, 484, 481, 479, 463, 475, 473, 472])).
% 0.70/0.91 tff(494,plain,
% 0.70/0.91 (addition(addition(one, one), addition(addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, strong_iteration(one)), one))) = addition(addition(one, one), addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, one)))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[493])).
% 0.70/0.91 tff(495,plain,
% 0.70/0.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(one, one), addition(addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, strong_iteration(one)), one))) = addition(addition(addition(one, one), addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(496,plain,
% 0.70/0.91 (addition(addition(one, one), addition(addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, strong_iteration(one)), one))) = addition(addition(addition(one, one), addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[495, 59])).
% 0.70/0.91 tff(497,plain,
% 0.70/0.91 (addition(addition(addition(one, one), addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(one, one), addition(addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.70/0.91 inference(symmetry,[status(thm)],[496])).
% 0.70/0.91 tff(498,plain,
% 0.70/0.91 (addition(addition(addition(one, one), addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))), addition(multiplication(one, strong_iteration(one)), one)) = multiplication(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.70/0.91 inference(transitivity,[status(thm)],[497, 494, 471, 469, 467, 465, 456, 453, 450])).
% 0.70/0.91 tff(499,plain,
% 0.70/0.91 (addition(addition(addition(addition(one, one), addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))), addition(multiplication(one, strong_iteration(one)), one)), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(addition(addition(addition(one, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), star(one))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)), multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[498, 416])).
% 0.70/0.91 tff(500,plain,
% 0.70/0.91 (addition(addition(one, one), addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, one))) = addition(addition(one, one), addition(addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.70/0.91 inference(symmetry,[status(thm)],[494])).
% 0.70/0.91 tff(501,plain,
% 0.70/0.91 (addition(addition(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), addition(X0!0, one)) = addition(addition(one, one), addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, one)))),
% 0.70/0.91 inference(symmetry,[status(thm)],[471])).
% 0.70/0.91 tff(502,plain,
% 0.70/0.91 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, one)) = addition(addition(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), addition(X0!0, one))),
% 0.70/0.91 inference(symmetry,[status(thm)],[469])).
% 0.70/0.91 tff(503,plain,
% 0.70/0.91 (addition(star(one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[51])).
% 0.70/0.91 tff(504,plain,
% 0.70/0.91 (addition(star(one), multiplication(strong_iteration(one), zero)) = addition(star(one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.91 inference(symmetry,[status(thm)],[503])).
% 0.70/0.91 tff(505,plain,
% 0.70/0.91 (addition(multiplication(one, strong_iteration(one)), one) = addition(star(one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.70/0.91 inference(transitivity,[status(thm)],[152, 9, 504])).
% 0.70/0.91 tff(506,plain,
% 0.70/0.91 (addition(addition(multiplication(one, strong_iteration(one)), one), zero) = addition(addition(star(one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))), multiplication(one, zero))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[505, 166])).
% 0.70/0.91 tff(507,plain,
% 0.70/0.91 (addition(addition(star(one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))), multiplication(one, zero)) = addition(addition(multiplication(one, strong_iteration(one)), one), zero)),
% 0.70/0.91 inference(symmetry,[status(thm)],[506])).
% 0.70/0.91 tff(508,plain,
% 0.70/0.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(one), addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), multiplication(one, zero))) = addition(addition(star(one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))), multiplication(one, zero)))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(509,plain,
% 0.70/0.91 (addition(star(one), addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), multiplication(one, zero))) = addition(addition(star(one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))), multiplication(one, zero))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[508, 59])).
% 0.70/0.91 tff(510,plain,
% 0.70/0.91 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), multiplication(one, zero)) = multiplication(strong_iteration(one), zero)),
% 0.70/0.91 inference(transitivity,[status(thm)],[160, 50, 40])).
% 0.70/0.91 tff(511,plain,
% 0.70/0.91 (addition(star(one), addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), multiplication(one, zero))) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[510])).
% 0.70/0.91 tff(512,plain,
% 0.70/0.91 (addition(star(one), multiplication(strong_iteration(one), zero)) = addition(star(one), addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), multiplication(one, zero)))),
% 0.70/0.91 inference(symmetry,[status(thm)],[511])).
% 0.70/0.91 tff(513,plain,
% 0.70/0.91 (addition(multiplication(one, strong_iteration(one)), one) = addition(addition(multiplication(one, strong_iteration(one)), one), zero)),
% 0.70/0.91 inference(transitivity,[status(thm)],[152, 9, 512, 509, 507])).
% 0.70/0.91 tff(514,plain,
% 0.70/0.91 (addition(addition(multiplication(one, strong_iteration(one)), one), X0!0) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0)),
% 0.70/0.91 inference(monotonicity,[status(thm)],[513])).
% 0.70/0.91 tff(515,plain,
% 0.70/0.91 (addition(addition(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0) = addition(addition(multiplication(one, strong_iteration(one)), one), X0!0)),
% 0.70/0.91 inference(symmetry,[status(thm)],[514])).
% 0.70/0.91 tff(516,plain,
% 0.70/0.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(one, strong_iteration(one)), one), addition(zero, X0!0)) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(517,plain,
% 0.70/0.91 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(zero, X0!0)) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[516, 59])).
% 0.70/0.91 tff(518,plain,
% 0.70/0.91 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(one, strong_iteration(one)), one), addition(zero, X0!0)) = addition(addition(zero, X0!0), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(519,plain,
% 0.70/0.91 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(zero, X0!0)) = addition(addition(zero, X0!0), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[518, 17])).
% 0.70/0.91 tff(520,plain,
% 0.70/0.91 (addition(addition(zero, X0!0), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(zero, X0!0))),
% 0.70/0.91 inference(symmetry,[status(thm)],[519])).
% 0.70/0.91 tff(521,plain,
% 0.70/0.91 (addition(addition(zero, X0!0), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(addition(one, one), addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(transitivity,[status(thm)],[520, 517, 515, 463, 475, 473, 472, 502, 501, 500, 496])).
% 0.70/0.91 tff(522,plain,
% 0.70/0.91 (addition(addition(addition(zero, X0!0), addition(multiplication(one, strong_iteration(one)), one)), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(addition(addition(one, one), addition(addition(X0!0, one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))), addition(multiplication(one, strong_iteration(one)), one)), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[521])).
% 0.70/0.91 tff(523,plain,
% 0.70/0.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(zero, X0!0), addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one))) = addition(addition(addition(zero, X0!0), addition(multiplication(one, strong_iteration(one)), one)), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(524,plain,
% 0.70/0.91 (addition(addition(zero, X0!0), addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one))) = addition(addition(addition(zero, X0!0), addition(multiplication(one, strong_iteration(one)), one)), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[523, 59])).
% 0.70/0.91 tff(525,plain,
% 0.70/0.91 (multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)) = multiplication(one, strong_iteration(one))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[106, 152])).
% 0.70/0.91 tff(526,plain,
% 0.70/0.91 (multiplication(one, strong_iteration(one)) = multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(symmetry,[status(thm)],[525])).
% 0.70/0.91 tff(527,plain,
% 0.70/0.91 (addition(multiplication(one, strong_iteration(one)), one) = multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(transitivity,[status(thm)],[353, 352, 526])).
% 0.70/0.91 tff(528,plain,
% 0.70/0.91 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[527, 527])).
% 0.70/0.91 tff(529,plain,
% 0.70/0.91 (addition(multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one))) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(symmetry,[status(thm)],[528])).
% 0.70/0.91 tff(530,plain,
% 0.70/0.91 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(one, one), addition(one, one)), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one))))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(531,plain,
% 0.70/0.91 (multiplication(addition(addition(one, one), addition(one, one)), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[530, 47])).
% 0.70/0.91 tff(532,plain,
% 0.70/0.91 (addition(addition(one, one), addition(one, one)) = one),
% 0.70/0.91 inference(transitivity,[status(thm)],[145, 106])).
% 0.70/0.91 tff(533,plain,
% 0.70/0.91 (multiplication(addition(addition(one, one), addition(one, one)), addition(multiplication(one, strong_iteration(one)), one)) = multiplication(one, strong_iteration(one))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[532, 152])).
% 0.70/0.91 tff(534,plain,
% 0.70/0.91 (multiplication(one, strong_iteration(one)) = multiplication(addition(addition(one, one), addition(one, one)), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(symmetry,[status(thm)],[533])).
% 0.70/0.91 tff(535,plain,
% 0.70/0.91 (addition(multiplication(one, strong_iteration(one)), one) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one))),
% 0.70/0.91 inference(transitivity,[status(thm)],[353, 352, 534, 531, 529])).
% 0.70/0.91 tff(536,plain,
% 0.70/0.91 (addition(addition(zero, X0!0), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(zero, X0!0), addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[535])).
% 0.70/0.91 tff(537,plain,
% 0.70/0.91 (addition(addition(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(zero, X0!0))),
% 0.70/0.91 inference(symmetry,[status(thm)],[517])).
% 0.70/0.91 tff(538,plain,
% 0.70/0.91 (addition(X0!0, strong_iteration(one)) = strong_iteration(one)),
% 0.70/0.91 inference(transitivity,[status(thm)],[459, 462, 514, 537, 519, 536, 524, 522, 499, 412, 409, 348, 338, 333, 323, 319, 273, 39, 49, 220, 175, 172, 169, 151, 150, 140, 147, 144, 142, 138, 62, 52, 20, 10])).
% 0.70/0.91 tff(539,plain,
% 0.70/0.91 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!0, strong_iteration(one)) <=> (addition(X0!0, strong_iteration(one)) = strong_iteration(one)))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(540,plain,
% 0.70/0.91 (leq(X0!0, strong_iteration(one)) <=> (addition(X0!0, strong_iteration(one)) = strong_iteration(one))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[539, 83])).
% 0.70/0.91 tff(541,plain,
% 0.70/0.91 ((~![X0: $i] : leq(X0, strong_iteration(one))) <=> (~![X0: $i] : leq(X0, strong_iteration(one)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(542,axiom,(~![X0: $i] : leq(X0, strong_iteration(one))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.70/0.91 tff(543,plain,
% 0.70/0.91 (~![X0: $i] : leq(X0, strong_iteration(one))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.70/0.91 tff(544,plain,
% 0.70/0.91 (~![X0: $i] : leq(X0, strong_iteration(one))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[543, 541])).
% 0.70/0.91 tff(545,plain,
% 0.70/0.91 (~![X0: $i] : leq(X0, strong_iteration(one))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[544, 541])).
% 0.70/0.91 tff(546,plain,
% 0.70/0.91 (~![X0: $i] : leq(X0, strong_iteration(one))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[545, 541])).
% 0.70/0.91 tff(547,plain,(
% 0.70/0.91 ~leq(X0!0, strong_iteration(one))),
% 0.70/0.91 inference(skolemize,[status(sab)],[546])).
% 0.70/0.91 tff(548,plain,
% 0.70/0.91 ((~(leq(X0!0, strong_iteration(one)) <=> (addition(X0!0, strong_iteration(one)) = strong_iteration(one)))) | leq(X0!0, strong_iteration(one)) | (~(addition(X0!0, strong_iteration(one)) = strong_iteration(one)))),
% 0.70/0.91 inference(tautology,[status(thm)],[])).
% 0.70/0.91 tff(549,plain,
% 0.70/0.91 ((~(leq(X0!0, strong_iteration(one)) <=> (addition(X0!0, strong_iteration(one)) = strong_iteration(one)))) | (~(addition(X0!0, strong_iteration(one)) = strong_iteration(one)))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[548, 547])).
% 0.70/0.91 tff(550,plain,
% 0.70/0.91 (~(addition(X0!0, strong_iteration(one)) = strong_iteration(one))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[549, 540])).
% 0.70/0.91 tff(551,plain,
% 0.70/0.91 ($false),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[550, 538])).
% 0.70/0.91 % SZS output end Proof
% 0.70/0.92 % E exiting
%------------------------------------------------------------------------------