%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE141+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.53s 0.75s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE141+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:03:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.53/0.75 % SZS status Theorem
% 0.53/0.75 % SZS output start Proof
% 0.53/0.75 tff(strong_iteration_type, type, (
% 0.53/0.75 strong_iteration: $i > $i)).
% 0.53/0.75 tff(one_type, type, (
% 0.53/0.75 one: $i)).
% 0.53/0.75 tff(multiplication_type, type, (
% 0.53/0.75 multiplication: ( $i * $i ) > $i)).
% 0.53/0.75 tff(tptp_fun_X0_0_type, type, (
% 0.53/0.75 tptp_fun_X0_0: $i)).
% 0.53/0.75 tff(addition_type, type, (
% 0.53/0.75 addition: ( $i * $i ) > $i)).
% 0.53/0.75 tff(zero_type, type, (
% 0.53/0.75 zero: $i)).
% 0.53/0.75 tff(star_type, type, (
% 0.53/0.75 star: $i > $i)).
% 0.53/0.75 tff(leq_type, type, (
% 0.53/0.75 leq: ( $i * $i ) > $o)).
% 0.53/0.75 tff(1,plain,
% 0.53/0.75 (^[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))))),
% 0.53/0.75 inference(bind,[status(th)],[])).
% 0.53/0.75 tff(2,plain,
% 0.53/0.75 (![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)))),
% 0.53/0.75 inference(quant_intro,[status(thm)],[1])).
% 0.53/0.75 tff(3,plain,
% 0.53/0.75 (![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)))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 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')).
% 0.53/0.75 tff(5,plain,
% 0.53/0.75 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.53/0.75 tff(6,plain,(
% 0.53/0.75 ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.53/0.75 inference(skolemize,[status(sab)],[5])).
% 0.53/0.75 tff(7,plain,
% 0.53/0.75 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.53/0.75 tff(8,plain,
% 0.53/0.75 ((~![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))) | (strong_iteration(one) = addition(star(one), multiplication(strong_iteration(one), zero)))),
% 0.53/0.75 inference(quant_inst,[status(thm)],[])).
% 0.53/0.75 tff(9,plain,
% 0.53/0.75 (strong_iteration(one) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.53/0.75 tff(10,plain,
% 0.53/0.75 (addition(star(one), multiplication(strong_iteration(one), zero)) = strong_iteration(one)),
% 0.53/0.75 inference(symmetry,[status(thm)],[9])).
% 0.53/0.75 tff(11,plain,
% 0.53/0.75 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.53/0.75 inference(bind,[status(th)],[])).
% 0.53/0.75 tff(12,plain,
% 0.53/0.75 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.53/0.75 inference(quant_intro,[status(thm)],[11])).
% 0.53/0.75 tff(13,plain,
% 0.53/0.75 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(14,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 0.53/0.75 tff(15,plain,
% 0.53/0.75 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.53/0.75 tff(16,plain,(
% 0.53/0.75 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.53/0.75 inference(skolemize,[status(sab)],[15])).
% 0.53/0.75 tff(17,plain,
% 0.53/0.75 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.53/0.75 tff(18,plain,
% 0.53/0.75 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(one) = addition(multiplication(one, strong_iteration(one)), one))),
% 0.53/0.75 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(19,plain,
% 0.60/0.76 (strong_iteration(one) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.60/0.76 tff(20,plain,
% 0.60/0.76 (multiplication(strong_iteration(one), zero) = multiplication(addition(multiplication(one, strong_iteration(one)), one), zero)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[19])).
% 0.60/0.76 tff(21,plain,
% 0.60/0.76 (multiplication(addition(multiplication(one, strong_iteration(one)), one), zero) = multiplication(strong_iteration(one), zero)),
% 0.60/0.76 inference(symmetry,[status(thm)],[20])).
% 0.60/0.76 tff(22,plain,
% 0.60/0.76 (^[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))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(23,plain,
% 0.60/0.76 (![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)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[22])).
% 0.60/0.76 tff(24,plain,
% 0.60/0.76 (![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)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(25,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')).
% 0.60/0.76 tff(26,plain,
% 0.60/0.76 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.60/0.76 tff(27,plain,(
% 0.60/0.76 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.60/0.76 inference(skolemize,[status(sab)],[26])).
% 0.60/0.76 tff(28,plain,
% 0.60/0.76 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.60/0.76 tff(29,plain,
% 0.60/0.76 ((~![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)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(30,plain,
% 0.60/0.76 (multiplication(addition(multiplication(one, strong_iteration(one)), one), zero) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.60/0.76 tff(31,plain,
% 0.60/0.76 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(addition(multiplication(one, strong_iteration(one)), one), zero)),
% 0.60/0.76 inference(symmetry,[status(thm)],[30])).
% 0.60/0.76 tff(32,plain,
% 0.60/0.76 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(strong_iteration(one), zero)),
% 0.60/0.76 inference(transitivity,[status(thm)],[31, 21])).
% 0.60/0.76 tff(33,plain,
% 0.60/0.76 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(34,plain,
% 0.60/0.76 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[33])).
% 0.60/0.76 tff(35,plain,
% 0.60/0.76 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(36,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 0.60/0.76 tff(37,plain,
% 0.60/0.76 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.60/0.76 tff(38,plain,(
% 0.60/0.76 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.60/0.76 inference(skolemize,[status(sab)],[37])).
% 0.60/0.76 tff(39,plain,
% 0.60/0.76 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.60/0.76 tff(40,plain,
% 0.60/0.76 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(one, star(one))) = star(one))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(41,plain,
% 0.60/0.76 (addition(one, multiplication(one, star(one))) = star(one)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.60/0.76 tff(42,plain,
% 0.60/0.76 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(43,plain,
% 0.60/0.76 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[42])).
% 0.60/0.76 tff(44,plain,
% 0.60/0.76 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(45,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.60/0.76 tff(46,plain,
% 0.60/0.76 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.60/0.76 tff(47,plain,(
% 0.60/0.76 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.60/0.76 inference(skolemize,[status(sab)],[46])).
% 0.60/0.76 tff(48,plain,
% 0.60/0.76 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.60/0.76 tff(49,plain,
% 0.60/0.76 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(one, star(one))) = addition(multiplication(one, star(one)), one))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(50,plain,
% 0.60/0.76 (addition(one, multiplication(one, star(one))) = addition(multiplication(one, star(one)), one)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.60/0.76 tff(51,plain,
% 0.60/0.76 (addition(multiplication(one, star(one)), one) = addition(one, multiplication(one, star(one)))),
% 0.60/0.76 inference(symmetry,[status(thm)],[50])).
% 0.60/0.76 tff(52,plain,
% 0.60/0.76 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(53,plain,
% 0.60/0.76 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.60/0.76 inference(quant_intro,[status(thm)],[52])).
% 0.60/0.76 tff(54,plain,
% 0.60/0.76 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(55,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 0.60/0.76 tff(56,plain,
% 0.60/0.76 (![A: $i] : (multiplication(one, A) = A)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.60/0.76 tff(57,plain,(
% 0.60/0.76 ![A: $i] : (multiplication(one, A) = A)),
% 0.60/0.76 inference(skolemize,[status(sab)],[56])).
% 0.60/0.76 tff(58,plain,
% 0.60/0.76 (![A: $i] : (multiplication(one, A) = A)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.60/0.76 tff(59,plain,
% 0.60/0.76 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(one)) = star(one))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(60,plain,
% 0.60/0.76 (multiplication(one, star(one)) = star(one)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.60/0.76 tff(61,plain,
% 0.60/0.76 (star(one) = multiplication(one, star(one))),
% 0.60/0.76 inference(symmetry,[status(thm)],[60])).
% 0.60/0.76 tff(62,plain,
% 0.60/0.76 (addition(star(one), one) = addition(multiplication(one, star(one)), one)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[61])).
% 0.60/0.76 tff(63,plain,
% 0.60/0.76 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(64,plain,
% 0.60/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[63])).
% 0.60/0.76 tff(65,plain,
% 0.60/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(66,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','order')).
% 0.60/0.76 tff(67,plain,
% 0.60/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.60/0.76 tff(68,plain,(
% 0.60/0.76 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.60/0.76 inference(skolemize,[status(sab)],[67])).
% 0.60/0.76 tff(69,plain,
% 0.60/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.60/0.76 tff(70,plain,
% 0.60/0.76 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(star(one), one) <=> (addition(star(one), one) = one))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(71,plain,
% 0.60/0.76 (leq(star(one), one) <=> (addition(star(one), one) = one)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.60/0.76 tff(72,plain,
% 0.60/0.76 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(73,plain,
% 0.60/0.76 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.60/0.76 inference(quant_intro,[status(thm)],[72])).
% 0.60/0.76 tff(74,plain,
% 0.60/0.76 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(75,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 0.60/0.76 tff(76,plain,
% 0.60/0.76 (![A: $i] : (multiplication(A, one) = A)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.60/0.76 tff(77,plain,(
% 0.60/0.76 ![A: $i] : (multiplication(A, one) = A)),
% 0.60/0.76 inference(skolemize,[status(sab)],[76])).
% 0.60/0.76 tff(78,plain,
% 0.60/0.76 (![A: $i] : (multiplication(A, one) = A)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.60/0.76 tff(79,plain,
% 0.60/0.76 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(star(one), one) = star(one))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(80,plain,
% 0.60/0.76 (multiplication(star(one), one) = star(one)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.60/0.76 tff(81,plain,
% 0.60/0.76 (star(one) = multiplication(star(one), one)),
% 0.60/0.76 inference(symmetry,[status(thm)],[80])).
% 0.60/0.76 tff(82,plain,
% 0.60/0.76 (leq(star(one), one) <=> leq(multiplication(star(one), one), one)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[81])).
% 0.60/0.76 tff(83,plain,
% 0.60/0.76 (leq(multiplication(star(one), one), one) <=> leq(star(one), one)),
% 0.60/0.76 inference(symmetry,[status(thm)],[82])).
% 0.60/0.76 tff(84,plain,
% 0.60/0.76 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(85,plain,
% 0.60/0.76 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.60/0.76 inference(quant_intro,[status(thm)],[84])).
% 0.60/0.76 tff(86,plain,
% 0.60/0.76 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(87,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.60/0.76 tff(88,plain,
% 0.60/0.76 (![A: $i] : (addition(A, A) = A)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.60/0.76 tff(89,plain,(
% 0.60/0.76 ![A: $i] : (addition(A, A) = A)),
% 0.60/0.76 inference(skolemize,[status(sab)],[88])).
% 0.60/0.76 tff(90,plain,
% 0.60/0.76 (![A: $i] : (addition(A, A) = A)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.60/0.76 tff(91,plain,
% 0.60/0.76 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(92,plain,
% 0.60/0.76 (addition(one, one) = one),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.60/0.76 tff(93,plain,
% 0.60/0.76 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, one) = one)),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(94,plain,
% 0.60/0.76 (multiplication(one, one) = one),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[93, 58])).
% 0.60/0.76 tff(95,plain,
% 0.60/0.76 (addition(multiplication(one, one), one) = addition(one, one)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[94])).
% 0.60/0.76 tff(96,plain,
% 0.60/0.76 (addition(multiplication(one, one), one) = one),
% 0.60/0.76 inference(transitivity,[status(thm)],[95, 92])).
% 0.60/0.76 tff(97,plain,
% 0.60/0.76 (leq(addition(multiplication(one, one), one), one) <=> leq(one, one)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[96])).
% 0.60/0.76 tff(98,plain,
% 0.60/0.76 (leq(one, one) <=> leq(addition(multiplication(one, one), one), one)),
% 0.60/0.76 inference(symmetry,[status(thm)],[97])).
% 0.60/0.76 tff(99,plain,
% 0.60/0.76 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(one, one) <=> (addition(one, one) = one))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(100,plain,
% 0.60/0.76 (leq(one, one) <=> (addition(one, one) = one)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[99, 69])).
% 0.60/0.76 tff(101,plain,
% 0.60/0.76 ((~(leq(one, one) <=> (addition(one, one) = one))) | leq(one, one) | (~(addition(one, one) = one))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(102,plain,
% 0.60/0.76 (leq(one, one)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[101, 92, 100])).
% 0.60/0.76 tff(103,plain,
% 0.60/0.76 (leq(addition(multiplication(one, one), one), one)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.60/0.76 tff(104,plain,
% 0.60/0.76 (^[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)))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(105,plain,
% 0.60/0.76 (![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))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[104])).
% 0.60/0.76 tff(106,plain,
% 0.60/0.76 (![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))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(107,plain,
% 0.60/0.76 (^[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)))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(108,plain,
% 0.60/0.76 (![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))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[107])).
% 0.60/0.76 tff(109,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')).
% 0.60/0.76 tff(110,plain,
% 0.60/0.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.60/0.76 tff(111,plain,
% 0.60/0.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.60/0.76 tff(112,plain,(
% 0.60/0.76 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.60/0.76 inference(skolemize,[status(sab)],[111])).
% 0.60/0.76 tff(113,plain,
% 0.60/0.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.60/0.76 tff(114,plain,
% 0.60/0.76 (((~![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))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(115,plain,
% 0.60/0.76 ((~![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))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(116,plain,
% 0.60/0.76 ((~![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)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.60/0.76 tff(117,plain,
% 0.60/0.76 ((~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(star(one), one), one)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.60/0.76 tff(118,plain,
% 0.60/0.76 (leq(multiplication(star(one), one), one)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[117, 103])).
% 0.60/0.76 tff(119,plain,
% 0.60/0.76 (leq(star(one), one)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[118, 83])).
% 0.60/0.76 tff(120,plain,
% 0.60/0.76 ((~(leq(star(one), one) <=> (addition(star(one), one) = one))) | (~leq(star(one), one)) | (addition(star(one), one) = one)),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(121,plain,
% 0.60/0.76 (addition(star(one), one) = one),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[120, 119, 71])).
% 0.60/0.76 tff(122,plain,
% 0.60/0.76 (one = addition(star(one), one)),
% 0.60/0.76 inference(symmetry,[status(thm)],[121])).
% 0.60/0.76 tff(123,plain,
% 0.60/0.76 (addition(one, one) = star(one)),
% 0.60/0.76 inference(transitivity,[status(thm)],[92, 122, 62, 51, 41])).
% 0.60/0.76 tff(124,plain,
% 0.60/0.76 (addition(addition(one, one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[123, 32])).
% 0.60/0.76 tff(125,plain,
% 0.60/0.76 (addition(multiplication(one, strong_iteration(one)), one) = strong_iteration(one)),
% 0.60/0.76 inference(symmetry,[status(thm)],[19])).
% 0.60/0.76 tff(126,plain,
% 0.60/0.76 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(127,plain,
% 0.60/0.76 (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[126, 58])).
% 0.60/0.76 tff(128,plain,
% 0.60/0.76 (multiplication(one, strong_iteration(one)) = multiplication(one, addition(multiplication(one, strong_iteration(one)), one))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[19])).
% 0.60/0.76 tff(129,plain,
% 0.60/0.76 (multiplication(one, strong_iteration(one)) = strong_iteration(one)),
% 0.60/0.76 inference(transitivity,[status(thm)],[128, 127, 125])).
% 0.60/0.76 tff(130,plain,
% 0.60/0.76 (multiplication(multiplication(one, strong_iteration(one)), zero) = multiplication(strong_iteration(one), zero)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[129])).
% 0.60/0.76 tff(131,plain,
% 0.60/0.76 (multiplication(strong_iteration(one), zero) = multiplication(multiplication(one, strong_iteration(one)), zero)),
% 0.60/0.76 inference(symmetry,[status(thm)],[130])).
% 0.60/0.76 tff(132,plain,
% 0.60/0.76 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(multiplication(one, strong_iteration(one)), zero)),
% 0.60/0.76 inference(transitivity,[status(thm)],[31, 21, 131])).
% 0.60/0.76 tff(133,plain,
% 0.60/0.76 (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))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[132])).
% 0.60/0.76 tff(134,plain,
% 0.60/0.76 ((~![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))))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(135,plain,
% 0.60/0.76 (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)))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[134, 48])).
% 0.61/0.76 tff(136,plain,
% 0.61/0.76 (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))),
% 0.61/0.76 inference(symmetry,[status(thm)],[135])).
% 0.61/0.76 tff(137,plain,
% 0.61/0.76 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, zero) = zero)),
% 0.61/0.76 inference(quant_inst,[status(thm)],[])).
% 0.61/0.76 tff(138,plain,
% 0.61/0.76 (multiplication(one, zero) = zero),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[137, 58])).
% 0.61/0.76 tff(139,plain,
% 0.61/0.76 (zero = multiplication(one, zero)),
% 0.61/0.76 inference(symmetry,[status(thm)],[138])).
% 0.61/0.76 tff(140,plain,
% 0.61/0.76 (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)))),
% 0.61/0.76 inference(monotonicity,[status(thm)],[139])).
% 0.61/0.76 tff(141,plain,
% 0.61/0.76 (addition(zero, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.61/0.76 inference(transitivity,[status(thm)],[140, 136, 133])).
% 0.61/0.76 tff(142,plain,
% 0.61/0.76 (one = addition(one, one)),
% 0.61/0.76 inference(symmetry,[status(thm)],[92])).
% 0.61/0.76 tff(143,plain,
% 0.61/0.76 (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)))),
% 0.61/0.76 inference(monotonicity,[status(thm)],[142, 141])).
% 0.61/0.76 tff(144,plain,
% 0.61/0.76 (^[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)))),
% 0.61/0.76 inference(bind,[status(th)],[])).
% 0.61/0.76 tff(145,plain,
% 0.61/0.76 (![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))),
% 0.61/0.76 inference(quant_intro,[status(thm)],[144])).
% 0.61/0.76 tff(146,plain,
% 0.61/0.76 (![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))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(147,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')).
% 0.61/0.76 tff(148,plain,
% 0.61/0.76 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.61/0.76 tff(149,plain,(
% 0.61/0.76 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.61/0.76 inference(skolemize,[status(sab)],[148])).
% 0.61/0.76 tff(150,plain,
% 0.61/0.76 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.61/0.76 tff(151,plain,
% 0.61/0.76 ((~![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))))),
% 0.61/0.76 inference(quant_inst,[status(thm)],[])).
% 0.61/0.76 tff(152,plain,
% 0.61/0.76 (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)))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.61/0.76 tff(153,plain,
% 0.61/0.76 (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))))),
% 0.61/0.76 inference(symmetry,[status(thm)],[152])).
% 0.61/0.76 tff(154,plain,
% 0.61/0.76 (addition(one, zero) = addition(addition(one, one), zero)),
% 0.61/0.76 inference(monotonicity,[status(thm)],[142])).
% 0.61/0.76 tff(155,plain,
% 0.61/0.76 (addition(addition(one, one), zero) = addition(one, zero)),
% 0.61/0.76 inference(symmetry,[status(thm)],[154])).
% 0.61/0.76 tff(156,plain,
% 0.61/0.76 (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)))),
% 0.61/0.76 inference(monotonicity,[status(thm)],[155])).
% 0.61/0.76 tff(157,plain,
% 0.61/0.76 ((~![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))))),
% 0.61/0.76 inference(quant_inst,[status(thm)],[])).
% 0.61/0.76 tff(158,plain,
% 0.61/0.76 (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)))),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[157, 69])).
% 0.61/0.76 tff(159,plain,
% 0.61/0.76 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.61/0.76 inference(bind,[status(th)],[])).
% 0.61/0.76 tff(160,plain,
% 0.61/0.76 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.61/0.76 inference(quant_intro,[status(thm)],[159])).
% 0.61/0.76 tff(161,plain,
% 0.61/0.76 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(162,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_identity')).
% 0.61/0.76 tff(163,plain,
% 0.61/0.76 (![A: $i] : (addition(A, zero) = A)),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.61/0.76 tff(164,plain,(
% 0.61/0.76 ![A: $i] : (addition(A, zero) = A)),
% 0.61/0.76 inference(skolemize,[status(sab)],[163])).
% 0.61/0.76 tff(165,plain,
% 0.61/0.76 (![A: $i] : (addition(A, zero) = A)),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.61/0.76 tff(166,plain,
% 0.61/0.76 ((~![A: $i] : (addition(A, zero) = A)) | (addition(addition(one, one), zero) = addition(one, one))),
% 0.61/0.76 inference(quant_inst,[status(thm)],[])).
% 0.61/0.76 tff(167,plain,
% 0.61/0.76 (addition(addition(one, one), zero) = addition(one, one)),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.61/0.76 tff(168,plain,
% 0.61/0.76 (addition(addition(one, one), zero) = one),
% 0.61/0.76 inference(transitivity,[status(thm)],[167, 92])).
% 0.61/0.76 tff(169,plain,
% 0.61/0.76 (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)))),
% 0.61/0.76 inference(monotonicity,[status(thm)],[168])).
% 0.61/0.76 tff(170,plain,
% 0.61/0.76 (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)))),
% 0.61/0.76 inference(symmetry,[status(thm)],[169])).
% 0.61/0.76 tff(171,plain,
% 0.61/0.76 (strong_iteration(addition(one, one)) = strong_iteration(one)),
% 0.61/0.76 inference(monotonicity,[status(thm)],[92])).
% 0.61/0.76 tff(172,plain,
% 0.61/0.76 (multiplication(strong_iteration(addition(one, one)), zero) = multiplication(strong_iteration(one), zero)),
% 0.61/0.76 inference(monotonicity,[status(thm)],[171])).
% 0.61/0.77 tff(173,plain,
% 0.61/0.77 (multiplication(strong_iteration(addition(one, one)), zero) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.61/0.77 inference(transitivity,[status(thm)],[172, 20, 30])).
% 0.61/0.77 tff(174,plain,
% 0.61/0.77 (leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero)) <=> leq(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[92, 173])).
% 0.61/0.77 tff(175,plain,
% 0.61/0.77 (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)))),
% 0.61/0.77 inference(transitivity,[status(thm)],[174, 170])).
% 0.61/0.77 tff(176,plain,
% 0.61/0.77 (multiplication(addition(one, one), addition(one, one)) = multiplication(one, one)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[92, 92])).
% 0.61/0.77 tff(177,plain,
% 0.61/0.77 (multiplication(addition(one, one), addition(one, one)) = addition(one, one)),
% 0.61/0.77 inference(transitivity,[status(thm)],[176, 94, 142])).
% 0.61/0.77 tff(178,plain,
% 0.61/0.77 (addition(multiplication(addition(one, one), addition(one, one)), zero) = addition(addition(one, one), zero)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[177])).
% 0.61/0.77 tff(179,plain,
% 0.61/0.77 (addition(multiplication(addition(one, one), addition(one, one)), zero) = one),
% 0.61/0.77 inference(transitivity,[status(thm)],[178, 167, 92])).
% 0.61/0.77 tff(180,plain,
% 0.61/0.77 (leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero)) <=> leq(one, one)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[92, 179])).
% 0.61/0.77 tff(181,plain,
% 0.61/0.77 (leq(one, one) <=> leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))),
% 0.61/0.77 inference(symmetry,[status(thm)],[180])).
% 0.61/0.77 tff(182,plain,
% 0.61/0.77 (leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[102, 181])).
% 0.61/0.77 tff(183,plain,
% 0.61/0.77 (^[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))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(184,plain,
% 0.61/0.77 (![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)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[183])).
% 0.61/0.77 tff(185,plain,
% 0.61/0.77 (![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)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(186,plain,
% 0.61/0.77 (^[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))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(187,plain,
% 0.61/0.77 (![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)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[186])).
% 0.61/0.77 tff(188,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')).
% 0.61/0.77 tff(189,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.61/0.77 tff(190,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.61/0.77 tff(191,plain,(
% 0.61/0.77 ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.61/0.77 inference(skolemize,[status(sab)],[190])).
% 0.61/0.77 tff(192,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.61/0.77 tff(193,plain,
% 0.61/0.77 (((~![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)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(194,plain,
% 0.61/0.77 ((~![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)))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(195,plain,
% 0.61/0.77 ((~![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))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.61/0.77 tff(196,plain,
% 0.61/0.77 ((~leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))) | leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[195, 192])).
% 0.61/0.77 tff(197,plain,
% 0.61/0.77 (leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[196, 182])).
% 0.61/0.77 tff(198,plain,
% 0.61/0.77 (leq(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[197, 175])).
% 0.61/0.77 tff(199,plain,
% 0.61/0.77 ((~(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)))),
% 0.61/0.77 inference(tautology,[status(thm)],[])).
% 0.61/0.77 tff(200,plain,
% 0.61/0.77 (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))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[199, 198, 158])).
% 0.61/0.77 tff(201,plain,
% 0.61/0.77 (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)))),
% 0.61/0.77 inference(symmetry,[status(thm)],[200])).
% 0.61/0.77 tff(202,plain,
% 0.61/0.77 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(203,plain,
% 0.61/0.77 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.61/0.77 inference(quant_intro,[status(thm)],[202])).
% 0.61/0.77 tff(204,plain,
% 0.61/0.77 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(205,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 0.61/0.77 tff(206,plain,
% 0.61/0.77 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.61/0.77 tff(207,plain,(
% 0.61/0.77 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.61/0.77 inference(skolemize,[status(sab)],[206])).
% 0.61/0.77 tff(208,plain,
% 0.61/0.77 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.61/0.77 tff(209,plain,
% 0.61/0.77 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, X0!0) = zero)),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(210,plain,
% 0.61/0.77 (multiplication(zero, X0!0) = zero),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.61/0.77 tff(211,plain,
% 0.61/0.77 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0)) = multiplication(strong_iteration(one), zero)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[125, 210])).
% 0.61/0.77 tff(212,plain,
% 0.61/0.77 (^[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)))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(213,plain,
% 0.61/0.77 (![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))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[212])).
% 0.61/0.77 tff(214,plain,
% 0.61/0.77 (![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))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(215,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')).
% 0.61/0.77 tff(216,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.61/0.77 tff(217,plain,(
% 0.61/0.77 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.61/0.77 inference(skolemize,[status(sab)],[216])).
% 0.61/0.77 tff(218,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.61/0.77 tff(219,plain,
% 0.61/0.77 ((~![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, X0!0)) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(220,plain,
% 0.61/0.77 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0)) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.61/0.77 tff(221,plain,
% 0.61/0.77 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0))),
% 0.61/0.77 inference(symmetry,[status(thm)],[220])).
% 0.61/0.77 tff(222,plain,
% 0.61/0.77 (multiplication(multiplication(strong_iteration(one), zero), X0!0) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[20])).
% 0.61/0.77 tff(223,plain,
% 0.61/0.77 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) <=> (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) = X0!0))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(224,plain,
% 0.61/0.77 (leq(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) <=> (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) = X0!0)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[223, 69])).
% 0.61/0.77 tff(225,plain,
% 0.61/0.77 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(226,plain,
% 0.61/0.77 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[225])).
% 0.61/0.77 tff(227,plain,
% 0.61/0.77 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(228,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 0.61/0.77 tff(229,plain,
% 0.61/0.77 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.61/0.77 tff(230,plain,(
% 0.61/0.77 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.61/0.77 inference(skolemize,[status(sab)],[229])).
% 0.61/0.77 tff(231,plain,
% 0.61/0.77 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.61/0.77 tff(232,plain,
% 0.61/0.77 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(one), one)) = star(one))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(233,plain,
% 0.61/0.77 (addition(one, multiplication(star(one), one)) = star(one)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.61/0.77 tff(234,plain,
% 0.61/0.77 (multiplication(addition(one, multiplication(star(one), one)), X0!0) = multiplication(star(one), X0!0)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[233])).
% 0.61/0.77 tff(235,plain,
% 0.61/0.77 ((~![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)), X0!0) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(236,plain,
% 0.61/0.77 (multiplication(addition(one, multiplication(star(one), one)), X0!0) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[235, 28])).
% 0.61/0.77 tff(237,plain,
% 0.61/0.77 (addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)) = multiplication(addition(one, multiplication(star(one), one)), X0!0)),
% 0.61/0.77 inference(symmetry,[status(thm)],[236])).
% 0.61/0.77 tff(238,plain,
% 0.61/0.77 (addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)) = multiplication(star(one), X0!0)),
% 0.61/0.77 inference(transitivity,[status(thm)],[237, 234])).
% 0.61/0.77 tff(239,plain,
% 0.61/0.77 (leq(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) <=> leq(multiplication(star(one), X0!0), X0!0)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[238])).
% 0.61/0.77 tff(240,plain,
% 0.61/0.77 (leq(multiplication(star(one), X0!0), X0!0) <=> leq(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0)),
% 0.61/0.77 inference(symmetry,[status(thm)],[239])).
% 0.61/0.77 tff(241,plain,
% 0.61/0.77 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!0, X0!0) = X0!0)),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(242,plain,
% 0.61/0.77 (addition(X0!0, X0!0) = X0!0),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[241, 90])).
% 0.61/0.77 tff(243,plain,
% 0.61/0.77 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!0) = X0!0)),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(244,plain,
% 0.61/0.77 (multiplication(one, X0!0) = X0!0),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[243, 58])).
% 0.61/0.77 tff(245,plain,
% 0.61/0.77 (addition(multiplication(one, X0!0), multiplication(one, X0!0)) = addition(X0!0, X0!0)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[244, 244])).
% 0.61/0.77 tff(246,plain,
% 0.61/0.77 (X0!0 = multiplication(one, X0!0)),
% 0.61/0.77 inference(symmetry,[status(thm)],[244])).
% 0.61/0.77 tff(247,plain,
% 0.61/0.77 (addition(multiplication(one, X0!0), X0!0) = addition(multiplication(one, X0!0), multiplication(one, X0!0))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[246])).
% 0.61/0.77 tff(248,plain,
% 0.61/0.77 (addition(multiplication(one, X0!0), X0!0) = X0!0),
% 0.61/0.77 inference(transitivity,[status(thm)],[247, 245, 242])).
% 0.61/0.77 tff(249,plain,
% 0.61/0.77 (leq(addition(multiplication(one, X0!0), X0!0), X0!0) <=> leq(X0!0, X0!0)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[248])).
% 0.61/0.77 tff(250,plain,
% 0.61/0.77 (leq(X0!0, X0!0) <=> leq(addition(multiplication(one, X0!0), X0!0), X0!0)),
% 0.61/0.77 inference(symmetry,[status(thm)],[249])).
% 0.61/0.77 tff(251,plain,
% 0.61/0.77 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!0, X0!0) <=> (addition(X0!0, X0!0) = X0!0))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(252,plain,
% 0.61/0.77 (leq(X0!0, X0!0) <=> (addition(X0!0, X0!0) = X0!0)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[251, 69])).
% 0.61/0.77 tff(253,plain,
% 0.61/0.77 ((~(leq(X0!0, X0!0) <=> (addition(X0!0, X0!0) = X0!0))) | leq(X0!0, X0!0) | (~(addition(X0!0, X0!0) = X0!0))),
% 0.61/0.77 inference(tautology,[status(thm)],[])).
% 0.61/0.77 tff(254,plain,
% 0.61/0.77 (leq(X0!0, X0!0)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[253, 242, 252])).
% 0.61/0.77 tff(255,plain,
% 0.61/0.77 (leq(addition(multiplication(one, X0!0), X0!0), X0!0)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[254, 250])).
% 0.61/0.77 tff(256,plain,
% 0.61/0.77 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(one, X0!0), X0!0), X0!0)) | leq(multiplication(star(one), X0!0), X0!0))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(one, X0!0), X0!0), X0!0)) | leq(multiplication(star(one), X0!0), X0!0))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(257,plain,
% 0.61/0.77 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(one, X0!0), X0!0), X0!0)) | leq(multiplication(star(one), X0!0), X0!0))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(258,plain,
% 0.61/0.77 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(one, X0!0), X0!0), X0!0)) | leq(multiplication(star(one), X0!0), X0!0)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.61/0.77 tff(259,plain,
% 0.61/0.77 ((~leq(addition(multiplication(one, X0!0), X0!0), X0!0)) | leq(multiplication(star(one), X0!0), X0!0)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[258, 113])).
% 0.61/0.77 tff(260,plain,
% 0.61/0.77 (leq(multiplication(star(one), X0!0), X0!0)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[259, 255])).
% 0.61/0.77 tff(261,plain,
% 0.61/0.77 (leq(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[260, 240])).
% 0.61/0.77 tff(262,plain,
% 0.61/0.77 ((~(leq(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) <=> (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) = X0!0))) | (~leq(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0)) | (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) = X0!0)),
% 0.61/0.77 inference(tautology,[status(thm)],[])).
% 0.61/0.77 tff(263,plain,
% 0.61/0.77 (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) = X0!0),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[262, 261, 224])).
% 0.61/0.77 tff(264,plain,
% 0.61/0.77 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(265,plain,
% 0.61/0.77 (addition(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[264, 48])).
% 0.61/0.77 tff(266,plain,
% 0.61/0.77 (multiplication(multiplication(one, star(one)), X0!0) = multiplication(star(one), X0!0)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[60])).
% 0.61/0.77 tff(267,plain,
% 0.61/0.77 (multiplication(star(one), X0!0) = multiplication(multiplication(one, star(one)), X0!0)),
% 0.61/0.77 inference(symmetry,[status(thm)],[266])).
% 0.61/0.77 tff(268,plain,
% 0.61/0.77 (addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)) = multiplication(multiplication(one, star(one)), X0!0)),
% 0.61/0.77 inference(transitivity,[status(thm)],[237, 234, 267])).
% 0.61/0.77 tff(269,plain,
% 0.61/0.77 (addition(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(multiplication(one, X0!0), multiplication(multiplication(one, star(one)), X0!0))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[246, 268])).
% 0.61/0.77 tff(270,plain,
% 0.61/0.77 (addition(multiplication(one, X0!0), multiplication(multiplication(one, star(one)), X0!0)) = addition(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.77 inference(symmetry,[status(thm)],[269])).
% 0.61/0.77 tff(271,plain,
% 0.61/0.77 ((~![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))), X0!0) = addition(multiplication(one, X0!0), multiplication(multiplication(one, star(one)), X0!0)))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(272,plain,
% 0.61/0.77 (multiplication(addition(one, multiplication(one, star(one))), X0!0) = addition(multiplication(one, X0!0), multiplication(multiplication(one, star(one)), X0!0))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[271, 28])).
% 0.61/0.77 tff(273,plain,
% 0.61/0.77 (multiplication(addition(one, multiplication(one, star(one))), X0!0) = multiplication(star(one), X0!0)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[41])).
% 0.61/0.77 tff(274,plain,
% 0.61/0.77 (multiplication(star(one), X0!0) = multiplication(addition(one, multiplication(one, star(one))), X0!0)),
% 0.61/0.77 inference(symmetry,[status(thm)],[273])).
% 0.61/0.77 tff(275,plain,
% 0.61/0.77 (addition(multiplication(one, zero), star(one)) = addition(zero, star(one))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[138])).
% 0.61/0.77 tff(276,plain,
% 0.61/0.77 (addition(zero, star(one)) = addition(multiplication(one, zero), star(one))),
% 0.61/0.77 inference(symmetry,[status(thm)],[275])).
% 0.61/0.77 tff(277,plain,
% 0.61/0.77 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, star(one)) = addition(star(one), zero))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(278,plain,
% 0.61/0.77 (addition(zero, star(one)) = addition(star(one), zero)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[277, 48])).
% 0.61/0.77 tff(279,plain,
% 0.61/0.77 (addition(star(one), zero) = addition(zero, star(one))),
% 0.61/0.77 inference(symmetry,[status(thm)],[278])).
% 0.61/0.77 tff(280,plain,
% 0.61/0.77 ((~![A: $i] : (addition(A, zero) = A)) | (addition(star(one), zero) = star(one))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(281,plain,
% 0.61/0.77 (addition(star(one), zero) = star(one)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[280, 165])).
% 0.61/0.77 tff(282,plain,
% 0.61/0.77 (star(one) = addition(star(one), zero)),
% 0.61/0.77 inference(symmetry,[status(thm)],[281])).
% 0.61/0.77 tff(283,plain,
% 0.61/0.77 (star(one) = addition(multiplication(one, zero), star(one))),
% 0.61/0.77 inference(transitivity,[status(thm)],[282, 279, 276])).
% 0.61/0.77 tff(284,plain,
% 0.61/0.77 (multiplication(star(one), X0!0) = multiplication(addition(multiplication(one, zero), star(one)), X0!0)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[283])).
% 0.61/0.78 tff(285,plain,
% 0.61/0.78 (multiplication(addition(multiplication(one, zero), star(one)), X0!0) = multiplication(star(one), X0!0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[284])).
% 0.61/0.78 tff(286,plain,
% 0.61/0.78 (multiplication(addition(multiplication(one, zero), star(one)), X0!0) = multiplication(addition(zero, star(one)), X0!0)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[275])).
% 0.61/0.78 tff(287,plain,
% 0.61/0.78 (multiplication(addition(zero, star(one)), X0!0) = multiplication(addition(multiplication(one, zero), star(one)), X0!0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[286])).
% 0.61/0.78 tff(288,plain,
% 0.61/0.78 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(zero, star(one)), X0!0) = addition(multiplication(zero, X0!0), multiplication(star(one), X0!0)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(289,plain,
% 0.61/0.78 (multiplication(addition(zero, star(one)), X0!0) = addition(multiplication(zero, X0!0), multiplication(star(one), X0!0))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[288, 28])).
% 0.61/0.78 tff(290,plain,
% 0.61/0.78 (addition(multiplication(zero, X0!0), multiplication(star(one), X0!0)) = multiplication(addition(zero, star(one)), X0!0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[289])).
% 0.61/0.78 tff(291,plain,
% 0.61/0.78 (multiplication(star(one), X0!0) = multiplication(addition(one, multiplication(star(one), one)), X0!0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[234])).
% 0.61/0.78 tff(292,plain,
% 0.61/0.78 (multiplication(star(one), X0!0) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))),
% 0.61/0.78 inference(transitivity,[status(thm)],[291, 236])).
% 0.61/0.78 tff(293,plain,
% 0.61/0.78 (addition(multiplication(zero, X0!0), multiplication(star(one), X0!0)) = addition(multiplication(zero, X0!0), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[292])).
% 0.61/0.78 tff(294,plain,
% 0.61/0.78 (addition(multiplication(zero, X0!0), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(multiplication(zero, X0!0), multiplication(star(one), X0!0))),
% 0.61/0.78 inference(symmetry,[status(thm)],[293])).
% 0.61/0.78 tff(295,plain,
% 0.61/0.78 (addition(multiplication(zero, X0!0), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(zero, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[210])).
% 0.61/0.78 tff(296,plain,
% 0.61/0.78 (addition(zero, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(multiplication(zero, X0!0), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.78 inference(symmetry,[status(thm)],[295])).
% 0.61/0.78 tff(297,plain,
% 0.61/0.78 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), zero))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(298,plain,
% 0.61/0.78 (addition(zero, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), zero)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[297, 48])).
% 0.61/0.78 tff(299,plain,
% 0.61/0.78 (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), zero) = addition(zero, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.78 inference(symmetry,[status(thm)],[298])).
% 0.61/0.78 tff(300,plain,
% 0.61/0.78 (zero = multiplication(zero, X0!0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[210])).
% 0.61/0.78 tff(301,plain,
% 0.61/0.78 (multiplication(one, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = multiplication(one, multiplication(star(one), X0!0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[238])).
% 0.61/0.78 tff(302,plain,
% 0.61/0.78 (multiplication(one, multiplication(star(one), X0!0)) = multiplication(one, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.78 inference(symmetry,[status(thm)],[301])).
% 0.61/0.78 tff(303,plain,
% 0.61/0.78 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(one, multiplication(star(one), X0!0)) = multiplication(multiplication(one, star(one)), X0!0))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(304,plain,
% 0.61/0.78 (multiplication(one, multiplication(star(one), X0!0)) = multiplication(multiplication(one, star(one)), X0!0)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[303, 218])).
% 0.61/0.78 tff(305,plain,
% 0.61/0.78 (multiplication(multiplication(one, star(one)), X0!0) = multiplication(one, multiplication(star(one), X0!0))),
% 0.61/0.78 inference(symmetry,[status(thm)],[304])).
% 0.61/0.78 tff(306,plain,
% 0.61/0.78 (addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)) = multiplication(one, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.78 inference(transitivity,[status(thm)],[237, 234, 267, 305, 302])).
% 0.61/0.78 tff(307,plain,
% 0.61/0.78 (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), zero) = addition(multiplication(one, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))), multiplication(zero, X0!0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[306, 300])).
% 0.61/0.78 tff(308,plain,
% 0.61/0.78 (addition(multiplication(one, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))), multiplication(zero, X0!0)) = addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), zero)),
% 0.61/0.78 inference(symmetry,[status(thm)],[307])).
% 0.61/0.78 tff(309,plain,
% 0.61/0.78 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(star(one), multiplication(zero, X0!0)) = multiplication(multiplication(star(one), zero), X0!0))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(310,plain,
% 0.61/0.78 (multiplication(star(one), multiplication(zero, X0!0)) = multiplication(multiplication(star(one), zero), X0!0)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[309, 218])).
% 0.61/0.78 tff(311,plain,
% 0.61/0.78 (multiplication(star(one), multiplication(zero, X0!0)) = multiplication(star(one), zero)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[210])).
% 0.61/0.78 tff(312,plain,
% 0.61/0.78 (multiplication(star(one), zero) = multiplication(star(one), multiplication(zero, X0!0))),
% 0.61/0.78 inference(symmetry,[status(thm)],[311])).
% 0.61/0.78 tff(313,plain,
% 0.61/0.78 (multiplication(addition(one, multiplication(one, star(one))), zero) = multiplication(star(one), zero)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[41])).
% 0.61/0.78 tff(314,plain,
% 0.61/0.78 ((~![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)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(315,plain,
% 0.61/0.78 (multiplication(addition(one, multiplication(one, star(one))), zero) = addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[314, 28])).
% 0.61/0.78 tff(316,plain,
% 0.61/0.78 (addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero)) = multiplication(addition(one, multiplication(one, star(one))), zero)),
% 0.61/0.78 inference(symmetry,[status(thm)],[315])).
% 0.61/0.78 tff(317,plain,
% 0.61/0.78 (multiplication(multiplication(one, star(one)), zero) = multiplication(star(one), zero)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[60])).
% 0.61/0.78 tff(318,plain,
% 0.61/0.78 (multiplication(star(one), zero) = multiplication(multiplication(one, star(one)), zero)),
% 0.61/0.78 inference(symmetry,[status(thm)],[317])).
% 0.61/0.78 tff(319,plain,
% 0.61/0.78 (star(one) = addition(one, multiplication(star(one), one))),
% 0.61/0.78 inference(symmetry,[status(thm)],[233])).
% 0.61/0.78 tff(320,plain,
% 0.61/0.78 (multiplication(star(one), zero) = multiplication(addition(one, multiplication(star(one), one)), zero)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[319])).
% 0.61/0.78 tff(321,plain,
% 0.61/0.78 (multiplication(addition(one, multiplication(star(one), one)), zero) = multiplication(star(one), zero)),
% 0.61/0.78 inference(symmetry,[status(thm)],[320])).
% 0.61/0.78 tff(322,plain,
% 0.61/0.78 ((~![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)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(323,plain,
% 0.61/0.78 (multiplication(addition(one, multiplication(star(one), one)), zero) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[322, 28])).
% 0.61/0.78 tff(324,plain,
% 0.61/0.78 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(addition(one, multiplication(star(one), one)), zero)),
% 0.61/0.78 inference(symmetry,[status(thm)],[323])).
% 0.61/0.78 tff(325,plain,
% 0.61/0.78 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(multiplication(one, star(one)), zero)),
% 0.61/0.78 inference(transitivity,[status(thm)],[324, 321, 318])).
% 0.61/0.78 tff(326,plain,
% 0.61/0.78 (addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[139, 325])).
% 0.61/0.78 tff(327,plain,
% 0.61/0.78 ((~![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))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(328,plain,
% 0.61/0.78 (addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[327, 48])).
% 0.61/0.78 tff(329,plain,
% 0.61/0.78 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) = addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.61/0.78 inference(symmetry,[status(thm)],[328])).
% 0.61/0.78 tff(330,plain,
% 0.61/0.78 ((~![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))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(331,plain,
% 0.61/0.78 (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)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[330, 69])).
% 0.61/0.78 tff(332,plain,
% 0.61/0.78 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(star(one), zero)),
% 0.61/0.78 inference(transitivity,[status(thm)],[324, 321])).
% 0.61/0.78 tff(333,plain,
% 0.61/0.78 (leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) <=> leq(multiplication(star(one), zero), zero)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[332])).
% 0.61/0.78 tff(334,plain,
% 0.61/0.78 (leq(multiplication(star(one), zero), zero) <=> leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.61/0.78 inference(symmetry,[status(thm)],[333])).
% 0.61/0.78 tff(335,plain,
% 0.61/0.78 ((~![A: $i] : (addition(A, A) = A)) | (addition(zero, zero) = zero)),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(336,plain,
% 0.61/0.78 (addition(zero, zero) = zero),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[335, 90])).
% 0.61/0.78 tff(337,plain,
% 0.61/0.78 (addition(multiplication(one, zero), multiplication(one, zero)) = addition(zero, zero)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[138, 138])).
% 0.61/0.78 tff(338,plain,
% 0.61/0.78 (addition(multiplication(one, zero), zero) = addition(multiplication(one, zero), multiplication(one, zero))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[139])).
% 0.61/0.78 tff(339,plain,
% 0.61/0.78 (addition(multiplication(one, zero), zero) = zero),
% 0.61/0.78 inference(transitivity,[status(thm)],[338, 337, 336])).
% 0.61/0.78 tff(340,plain,
% 0.61/0.78 (leq(addition(multiplication(one, zero), zero), zero) <=> leq(zero, zero)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[339])).
% 0.61/0.78 tff(341,plain,
% 0.61/0.78 (leq(zero, zero) <=> leq(addition(multiplication(one, zero), zero), zero)),
% 0.61/0.78 inference(symmetry,[status(thm)],[340])).
% 0.61/0.78 tff(342,plain,
% 0.61/0.78 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(zero, zero) <=> (addition(zero, zero) = zero))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(343,plain,
% 0.61/0.78 (leq(zero, zero) <=> (addition(zero, zero) = zero)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[342, 69])).
% 0.61/0.78 tff(344,plain,
% 0.61/0.78 ((~(leq(zero, zero) <=> (addition(zero, zero) = zero))) | leq(zero, zero) | (~(addition(zero, zero) = zero))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(345,plain,
% 0.61/0.78 (leq(zero, zero)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[344, 336, 343])).
% 0.61/0.78 tff(346,plain,
% 0.61/0.78 (leq(addition(multiplication(one, zero), zero), zero)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[345, 341])).
% 0.61/0.78 tff(347,plain,
% 0.61/0.78 (((~![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))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(348,plain,
% 0.61/0.78 ((~![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))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(349,plain,
% 0.61/0.78 ((~![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)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.61/0.78 tff(350,plain,
% 0.61/0.78 ((~leq(addition(multiplication(one, zero), zero), zero)) | leq(multiplication(star(one), zero), zero)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[349, 113])).
% 0.61/0.78 tff(351,plain,
% 0.61/0.78 (leq(multiplication(star(one), zero), zero)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[350, 346])).
% 0.61/0.78 tff(352,plain,
% 0.61/0.78 (leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[351, 334])).
% 0.61/0.78 tff(353,plain,
% 0.61/0.78 ((~(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)),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(354,plain,
% 0.61/0.78 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) = zero),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[353, 352, 331])).
% 0.61/0.78 tff(355,plain,
% 0.61/0.78 (zero = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.61/0.78 inference(symmetry,[status(thm)],[354])).
% 0.61/0.78 tff(356,plain,
% 0.61/0.78 (multiplication(zero, X0!0) = multiplication(multiplication(star(one), zero), X0!0)),
% 0.61/0.78 inference(transitivity,[status(thm)],[210, 355, 329, 326, 316, 313, 312, 310])).
% 0.61/0.78 tff(357,plain,
% 0.61/0.78 (multiplication(one, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))),
% 0.61/0.78 inference(transitivity,[status(thm)],[301, 304, 266, 291, 236])).
% 0.61/0.78 tff(358,plain,
% 0.61/0.78 (addition(multiplication(one, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))), multiplication(zero, X0!0)) = addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), multiplication(multiplication(star(one), zero), X0!0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[357, 356])).
% 0.61/0.78 tff(359,plain,
% 0.61/0.78 (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), multiplication(multiplication(star(one), zero), X0!0)) = addition(multiplication(one, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))), multiplication(zero, X0!0))),
% 0.61/0.78 inference(symmetry,[status(thm)],[358])).
% 0.61/0.78 tff(360,plain,
% 0.61/0.78 (multiplication(multiplication(star(one), zero), X0!0) = multiplication(star(one), multiplication(zero, X0!0))),
% 0.61/0.78 inference(symmetry,[status(thm)],[310])).
% 0.61/0.78 tff(361,plain,
% 0.61/0.78 (multiplication(multiplication(star(one), zero), X0!0) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))),
% 0.61/0.78 inference(transitivity,[status(thm)],[360, 311, 320, 323])).
% 0.61/0.78 tff(362,plain,
% 0.61/0.78 (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), multiplication(multiplication(star(one), zero), X0!0)) = addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[361])).
% 0.61/0.78 tff(363,plain,
% 0.61/0.78 (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), multiplication(multiplication(star(one), zero), X0!0))),
% 0.61/0.78 inference(symmetry,[status(thm)],[362])).
% 0.61/0.78 tff(364,plain,
% 0.61/0.78 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(365,plain,
% 0.61/0.78 (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[364, 48])).
% 0.61/0.78 tff(366,plain,
% 0.61/0.78 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.61/0.78 inference(symmetry,[status(thm)],[365])).
% 0.61/0.78 tff(367,plain,
% 0.61/0.78 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = X0!0),
% 0.61/0.78 inference(transitivity,[status(thm)],[366, 363, 359, 308, 299, 296, 294, 290, 287, 285, 274, 272, 270, 265, 263])).
% 0.61/0.78 tff(368,plain,
% 0.61/0.78 (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)))),
% 0.61/0.78 inference(symmetry,[status(thm)],[156])).
% 0.61/0.78 tff(369,plain,
% 0.61/0.78 (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))))),
% 0.61/0.78 inference(symmetry,[status(thm)],[143])).
% 0.61/0.78 tff(370,plain,
% 0.61/0.78 (addition(star(one), multiplication(strong_iteration(one), zero)) = addition(addition(one, one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.61/0.78 inference(symmetry,[status(thm)],[124])).
% 0.61/0.78 tff(371,plain,
% 0.61/0.78 (strong_iteration(addition(one, one)) = multiplication(strong_iteration(one), zero)),
% 0.61/0.78 inference(transitivity,[status(thm)],[171, 9, 370, 369, 152, 368, 200, 31, 21])).
% 0.61/0.78 tff(372,plain,
% 0.61/0.78 (multiplication(strong_iteration(addition(one, one)), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))) = multiplication(multiplication(strong_iteration(one), zero), X0!0)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[371, 367])).
% 0.61/0.78 tff(373,plain,
% 0.61/0.78 (addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.78 inference(transitivity,[status(thm)],[237, 234, 284, 286, 289, 293, 295, 298, 307, 358, 362, 365])).
% 0.61/0.78 tff(374,plain,
% 0.61/0.78 (strong_iteration(one) = strong_iteration(addition(one, one))),
% 0.61/0.78 inference(symmetry,[status(thm)],[171])).
% 0.61/0.78 tff(375,plain,
% 0.61/0.78 (multiplication(strong_iteration(one), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = multiplication(strong_iteration(addition(one, one)), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[374, 373])).
% 0.61/0.78 tff(376,plain,
% 0.61/0.78 (addition(multiplication(one, X0!0), multiplication(multiplication(one, star(one)), X0!0)) = multiplication(addition(one, multiplication(one, star(one))), X0!0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[272])).
% 0.61/0.78 tff(377,plain,
% 0.61/0.78 (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) = addition(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.78 inference(symmetry,[status(thm)],[265])).
% 0.61/0.78 tff(378,plain,
% 0.61/0.78 (X0!0 = addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[263])).
% 0.61/0.78 tff(379,plain,
% 0.61/0.78 (X0!0 = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))),
% 0.61/0.78 inference(transitivity,[status(thm)],[378, 377, 269, 376, 273, 291, 236])).
% 0.61/0.78 tff(380,plain,
% 0.61/0.78 (multiplication(strong_iteration(one), X0!0) = multiplication(strong_iteration(one), addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[379])).
% 0.61/0.78 tff(381,plain,
% 0.61/0.78 (multiplication(strong_iteration(one), X0!0) = strong_iteration(one)),
% 0.61/0.78 inference(transitivity,[status(thm)],[380, 375, 372, 222, 221, 211, 20, 30, 201, 156, 153, 143, 124, 10])).
% 0.61/0.78 tff(382,plain,
% 0.61/0.78 ((~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))) <=> (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(383,axiom,(~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.61/0.79 tff(384,plain,
% 0.61/0.79 (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.61/0.79 tff(385,plain,
% 0.61/0.79 (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[384, 382])).
% 0.61/0.79 tff(386,plain,
% 0.61/0.79 (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[385, 382])).
% 0.61/0.79 tff(387,plain,
% 0.61/0.79 (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[386, 382])).
% 0.61/0.79 tff(388,plain,(
% 0.61/0.79 ~(multiplication(strong_iteration(one), X0!0) = strong_iteration(one))),
% 0.61/0.79 inference(skolemize,[status(sab)],[387])).
% 0.61/0.79 tff(389,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[388, 381])).
% 0.61/0.79 % SZS output end Proof
% 0.61/0.79 % E exiting
%------------------------------------------------------------------------------