TSTP Solution File: KLE141+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE141+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 Sep 17 17:24:17 EDT 2022
% Result : Theorem 0.82s 0.75s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE141+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 08:46:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.82/0.75 % SZS status Theorem
% 0.82/0.75 % SZS output start Proof
% 0.82/0.75 tff(strong_iteration_type, type, (
% 0.82/0.75 strong_iteration: $i > $i)).
% 0.82/0.75 tff(one_type, type, (
% 0.82/0.75 one: $i)).
% 0.82/0.75 tff(multiplication_type, type, (
% 0.82/0.75 multiplication: ( $i * $i ) > $i)).
% 0.82/0.75 tff(tptp_fun_X0_0_type, type, (
% 0.82/0.75 tptp_fun_X0_0: $i)).
% 0.82/0.75 tff(addition_type, type, (
% 0.82/0.75 addition: ( $i * $i ) > $i)).
% 0.82/0.75 tff(zero_type, type, (
% 0.82/0.75 zero: $i)).
% 0.82/0.75 tff(star_type, type, (
% 0.82/0.75 star: $i > $i)).
% 0.82/0.75 tff(leq_type, type, (
% 0.82/0.75 leq: ( $i * $i ) > $o)).
% 0.82/0.75 tff(1,plain,
% 0.82/0.75 (^[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))))),
% 0.82/0.75 inference(bind,[status(th)],[])).
% 0.82/0.75 tff(2,plain,
% 0.82/0.75 (![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)))),
% 0.82/0.75 inference(quant_intro,[status(thm)],[1])).
% 0.82/0.75 tff(3,plain,
% 0.82/0.75 (![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)))),
% 0.82/0.75 inference(rewrite,[status(thm)],[])).
% 0.82/0.75 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')).
% 0.82/0.75 tff(5,plain,
% 0.82/0.75 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.82/0.75 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.82/0.75 tff(6,plain,(
% 0.82/0.75 ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.82/0.75 inference(skolemize,[status(sab)],[5])).
% 0.82/0.75 tff(7,plain,
% 0.82/0.75 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.82/0.75 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.82/0.75 tff(8,plain,
% 0.82/0.75 ((~![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))) | (strong_iteration(one) = addition(star(one), multiplication(strong_iteration(one), zero)))),
% 0.82/0.75 inference(quant_inst,[status(thm)],[])).
% 0.82/0.75 tff(9,plain,
% 0.82/0.75 (strong_iteration(one) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 0.82/0.75 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.82/0.75 tff(10,plain,
% 0.82/0.75 (addition(star(one), multiplication(strong_iteration(one), zero)) = strong_iteration(one)),
% 0.82/0.75 inference(symmetry,[status(thm)],[9])).
% 0.82/0.75 tff(11,plain,
% 0.82/0.75 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.82/0.75 inference(bind,[status(th)],[])).
% 0.82/0.75 tff(12,plain,
% 0.82/0.75 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.82/0.75 inference(quant_intro,[status(thm)],[11])).
% 0.82/0.75 tff(13,plain,
% 0.82/0.75 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.82/0.75 inference(rewrite,[status(thm)],[])).
% 0.82/0.75 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')).
% 0.82/0.75 tff(15,plain,
% 0.82/0.75 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.82/0.75 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.82/0.75 tff(16,plain,(
% 0.82/0.75 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.82/0.75 inference(skolemize,[status(sab)],[15])).
% 0.82/0.75 tff(17,plain,
% 0.82/0.75 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.82/0.75 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.82/0.75 tff(18,plain,
% 0.82/0.75 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(one) = addition(multiplication(one, strong_iteration(one)), one))),
% 0.82/0.75 inference(quant_inst,[status(thm)],[])).
% 0.82/0.75 tff(19,plain,
% 0.82/0.75 (strong_iteration(one) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.82/0.75 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.82/0.75 tff(20,plain,
% 0.82/0.75 (multiplication(strong_iteration(one), zero) = multiplication(addition(multiplication(one, strong_iteration(one)), one), zero)),
% 0.82/0.75 inference(monotonicity,[status(thm)],[19])).
% 0.82/0.75 tff(21,plain,
% 0.82/0.75 (multiplication(addition(multiplication(one, strong_iteration(one)), one), zero) = multiplication(strong_iteration(one), zero)),
% 0.82/0.75 inference(symmetry,[status(thm)],[20])).
% 0.82/0.75 tff(22,plain,
% 0.82/0.75 (^[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))))),
% 0.82/0.75 inference(bind,[status(th)],[])).
% 0.82/0.75 tff(23,plain,
% 0.82/0.75 (![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)))),
% 0.82/0.75 inference(quant_intro,[status(thm)],[22])).
% 0.82/0.75 tff(24,plain,
% 0.82/0.75 (![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)))),
% 0.82/0.75 inference(rewrite,[status(thm)],[])).
% 0.82/0.75 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')).
% 0.82/0.75 tff(26,plain,
% 0.82/0.75 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.82/0.75 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.82/0.75 tff(27,plain,(
% 0.82/0.75 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.82/0.75 inference(skolemize,[status(sab)],[26])).
% 0.82/0.75 tff(28,plain,
% 0.82/0.75 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.82/0.75 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.82/0.75 tff(29,plain,
% 0.82/0.75 ((~![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)))),
% 0.82/0.75 inference(quant_inst,[status(thm)],[])).
% 0.82/0.75 tff(30,plain,
% 0.82/0.75 (multiplication(addition(multiplication(one, strong_iteration(one)), one), zero) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.82/0.75 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.82/0.75 tff(31,plain,
% 0.82/0.75 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(addition(multiplication(one, strong_iteration(one)), one), zero)),
% 0.82/0.75 inference(symmetry,[status(thm)],[30])).
% 0.82/0.75 tff(32,plain,
% 0.82/0.75 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(strong_iteration(one), zero)),
% 0.82/0.75 inference(transitivity,[status(thm)],[31, 21])).
% 0.82/0.75 tff(33,plain,
% 0.82/0.75 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 0.82/0.75 inference(bind,[status(th)],[])).
% 0.82/0.75 tff(34,plain,
% 0.82/0.75 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.82/0.75 inference(quant_intro,[status(thm)],[33])).
% 0.82/0.75 tff(35,plain,
% 0.82/0.75 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.82/0.75 inference(rewrite,[status(thm)],[])).
% 0.82/0.75 tff(36,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 0.82/0.76 tff(37,plain,
% 0.82/0.76 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.82/0.76 tff(38,plain,(
% 0.82/0.76 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.82/0.76 inference(skolemize,[status(sab)],[37])).
% 0.82/0.76 tff(39,plain,
% 0.82/0.76 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.82/0.76 tff(40,plain,
% 0.82/0.76 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(one, star(one))) = star(one))),
% 0.82/0.76 inference(quant_inst,[status(thm)],[])).
% 0.82/0.76 tff(41,plain,
% 0.82/0.76 (addition(one, multiplication(one, star(one))) = star(one)),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.82/0.76 tff(42,plain,
% 0.82/0.76 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.82/0.76 inference(bind,[status(th)],[])).
% 0.82/0.76 tff(43,plain,
% 0.82/0.76 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.82/0.76 inference(quant_intro,[status(thm)],[42])).
% 0.82/0.76 tff(44,plain,
% 0.82/0.76 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.82/0.76 inference(rewrite,[status(thm)],[])).
% 0.82/0.76 tff(45,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.82/0.76 tff(46,plain,
% 0.82/0.76 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.82/0.76 tff(47,plain,(
% 0.82/0.76 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.82/0.76 inference(skolemize,[status(sab)],[46])).
% 0.82/0.76 tff(48,plain,
% 0.82/0.76 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.82/0.76 tff(49,plain,
% 0.82/0.76 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(one, star(one))) = addition(multiplication(one, star(one)), one))),
% 0.82/0.76 inference(quant_inst,[status(thm)],[])).
% 0.82/0.76 tff(50,plain,
% 0.82/0.76 (addition(one, multiplication(one, star(one))) = addition(multiplication(one, star(one)), one)),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.82/0.76 tff(51,plain,
% 0.82/0.76 (addition(multiplication(one, star(one)), one) = addition(one, multiplication(one, star(one)))),
% 0.82/0.76 inference(symmetry,[status(thm)],[50])).
% 0.82/0.76 tff(52,plain,
% 0.82/0.76 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.82/0.76 inference(bind,[status(th)],[])).
% 0.82/0.76 tff(53,plain,
% 0.82/0.76 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.82/0.76 inference(quant_intro,[status(thm)],[52])).
% 0.82/0.76 tff(54,plain,
% 0.82/0.76 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.82/0.76 inference(rewrite,[status(thm)],[])).
% 0.82/0.76 tff(55,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 0.82/0.76 tff(56,plain,
% 0.82/0.76 (![A: $i] : (multiplication(one, A) = A)),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.82/0.76 tff(57,plain,(
% 0.82/0.76 ![A: $i] : (multiplication(one, A) = A)),
% 0.82/0.76 inference(skolemize,[status(sab)],[56])).
% 0.82/0.76 tff(58,plain,
% 0.82/0.76 (![A: $i] : (multiplication(one, A) = A)),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.82/0.76 tff(59,plain,
% 0.82/0.76 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(one)) = star(one))),
% 0.82/0.76 inference(quant_inst,[status(thm)],[])).
% 0.82/0.76 tff(60,plain,
% 0.82/0.76 (multiplication(one, star(one)) = star(one)),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.82/0.76 tff(61,plain,
% 0.82/0.76 (star(one) = multiplication(one, star(one))),
% 0.82/0.76 inference(symmetry,[status(thm)],[60])).
% 0.82/0.76 tff(62,plain,
% 0.82/0.76 (addition(star(one), one) = addition(multiplication(one, star(one)), one)),
% 0.82/0.76 inference(monotonicity,[status(thm)],[61])).
% 0.82/0.76 tff(63,plain,
% 0.82/0.76 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.82/0.76 inference(bind,[status(th)],[])).
% 0.82/0.76 tff(64,plain,
% 0.82/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.82/0.76 inference(quant_intro,[status(thm)],[63])).
% 0.82/0.76 tff(65,plain,
% 0.82/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.82/0.76 inference(rewrite,[status(thm)],[])).
% 0.82/0.76 tff(66,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','order')).
% 0.82/0.76 tff(67,plain,
% 0.82/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.82/0.76 tff(68,plain,(
% 0.82/0.76 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.82/0.76 inference(skolemize,[status(sab)],[67])).
% 0.82/0.76 tff(69,plain,
% 0.82/0.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.82/0.76 tff(70,plain,
% 0.82/0.76 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(star(one), one) <=> (addition(star(one), one) = one))),
% 0.82/0.76 inference(quant_inst,[status(thm)],[])).
% 0.82/0.76 tff(71,plain,
% 0.82/0.76 (leq(star(one), one) <=> (addition(star(one), one) = one)),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.82/0.76 tff(72,plain,
% 0.82/0.76 (leq(star(one), one) <=> leq(multiplication(one, star(one)), one)),
% 0.82/0.76 inference(monotonicity,[status(thm)],[61])).
% 0.82/0.76 tff(73,plain,
% 0.82/0.76 (leq(multiplication(one, star(one)), one) <=> leq(star(one), one)),
% 0.82/0.76 inference(symmetry,[status(thm)],[72])).
% 0.82/0.76 tff(74,plain,
% 0.82/0.76 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.82/0.76 inference(bind,[status(th)],[])).
% 0.82/0.76 tff(75,plain,
% 0.82/0.76 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.82/0.76 inference(quant_intro,[status(thm)],[74])).
% 0.82/0.76 tff(76,plain,
% 0.82/0.76 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.82/0.76 inference(rewrite,[status(thm)],[])).
% 0.82/0.76 tff(77,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.82/0.76 tff(78,plain,
% 0.82/0.76 (![A: $i] : (addition(A, A) = A)),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.82/0.76 tff(79,plain,(
% 0.82/0.76 ![A: $i] : (addition(A, A) = A)),
% 0.82/0.76 inference(skolemize,[status(sab)],[78])).
% 0.82/0.76 tff(80,plain,
% 0.82/0.76 (![A: $i] : (addition(A, A) = A)),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.82/0.76 tff(81,plain,
% 0.82/0.76 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 0.82/0.76 inference(quant_inst,[status(thm)],[])).
% 0.82/0.76 tff(82,plain,
% 0.82/0.76 (addition(one, one) = one),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.82/0.76 tff(83,plain,
% 0.82/0.76 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, one) = one)),
% 0.82/0.76 inference(quant_inst,[status(thm)],[])).
% 0.82/0.76 tff(84,plain,
% 0.82/0.76 (multiplication(one, one) = one),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[83, 58])).
% 0.82/0.76 tff(85,plain,
% 0.82/0.76 (addition(multiplication(one, one), one) = addition(one, one)),
% 0.82/0.76 inference(monotonicity,[status(thm)],[84])).
% 0.82/0.76 tff(86,plain,
% 0.82/0.76 (addition(multiplication(one, one), one) = one),
% 0.82/0.76 inference(transitivity,[status(thm)],[85, 82])).
% 0.82/0.76 tff(87,plain,
% 0.82/0.76 (leq(addition(multiplication(one, one), one), one) <=> leq(one, one)),
% 0.82/0.76 inference(monotonicity,[status(thm)],[86])).
% 0.82/0.76 tff(88,plain,
% 0.82/0.76 (leq(one, one) <=> leq(addition(multiplication(one, one), one), one)),
% 0.82/0.76 inference(symmetry,[status(thm)],[87])).
% 0.82/0.76 tff(89,plain,
% 0.82/0.76 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(one, one) <=> (addition(one, one) = one))),
% 0.82/0.76 inference(quant_inst,[status(thm)],[])).
% 0.82/0.76 tff(90,plain,
% 0.82/0.76 (leq(one, one) <=> (addition(one, one) = one)),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[89, 69])).
% 0.82/0.76 tff(91,plain,
% 0.82/0.76 ((~(leq(one, one) <=> (addition(one, one) = one))) | leq(one, one) | (~(addition(one, one) = one))),
% 0.82/0.76 inference(tautology,[status(thm)],[])).
% 0.82/0.76 tff(92,plain,
% 0.82/0.76 (leq(one, one)),
% 0.82/0.76 inference(unit_resolution,[status(thm)],[91, 82, 90])).
% 0.82/0.76 tff(93,plain,
% 0.82/0.76 (leq(addition(multiplication(one, one), one), one)),
% 0.82/0.76 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.82/0.76 tff(94,plain,
% 0.82/0.76 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)))),
% 0.82/0.76 inference(bind,[status(th)],[])).
% 0.82/0.76 tff(95,plain,
% 0.84/0.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.84/0.76 inference(quant_intro,[status(thm)],[94])).
% 0.84/0.76 tff(96,plain,
% 0.84/0.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.84/0.76 inference(rewrite,[status(thm)],[])).
% 0.84/0.76 tff(97,plain,
% 0.84/0.76 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C)) <=> ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C)))),
% 0.84/0.76 inference(bind,[status(th)],[])).
% 0.84/0.76 tff(98,plain,
% 0.84/0.76 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.84/0.76 inference(quant_intro,[status(thm)],[97])).
% 0.84/0.76 tff(99,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_induction2')).
% 0.84/0.76 tff(100,plain,
% 0.84/0.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.84/0.76 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.84/0.76 tff(101,plain,
% 0.84/0.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.84/0.76 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.84/0.76 tff(102,plain,(
% 0.84/0.76 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.84/0.76 inference(skolemize,[status(sab)],[101])).
% 0.84/0.76 tff(103,plain,
% 0.84/0.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.84/0.76 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.84/0.76 tff(104,plain,
% 0.84/0.76 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | ((~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(one, star(one)), one))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | (~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(one, star(one)), one))),
% 0.84/0.76 inference(rewrite,[status(thm)],[])).
% 0.84/0.76 tff(105,plain,
% 0.84/0.76 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | ((~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(one, star(one)), one))),
% 0.84/0.76 inference(quant_inst,[status(thm)],[])).
% 0.84/0.76 tff(106,plain,
% 0.84/0.76 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))) | (~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(one, star(one)), one)),
% 0.84/0.76 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.84/0.76 tff(107,plain,
% 0.84/0.76 ((~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(one, star(one)), one)),
% 0.84/0.76 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.84/0.76 tff(108,plain,
% 0.84/0.76 (leq(multiplication(one, star(one)), one)),
% 0.84/0.76 inference(unit_resolution,[status(thm)],[107, 93])).
% 0.84/0.76 tff(109,plain,
% 0.84/0.76 (leq(star(one), one)),
% 0.84/0.76 inference(modus_ponens,[status(thm)],[108, 73])).
% 0.84/0.76 tff(110,plain,
% 0.84/0.76 ((~(leq(star(one), one) <=> (addition(star(one), one) = one))) | (~leq(star(one), one)) | (addition(star(one), one) = one)),
% 0.84/0.76 inference(tautology,[status(thm)],[])).
% 0.84/0.76 tff(111,plain,
% 0.84/0.76 (addition(star(one), one) = one),
% 0.84/0.76 inference(unit_resolution,[status(thm)],[110, 109, 71])).
% 0.84/0.76 tff(112,plain,
% 0.84/0.76 (one = addition(star(one), one)),
% 0.84/0.76 inference(symmetry,[status(thm)],[111])).
% 0.84/0.76 tff(113,plain,
% 0.84/0.76 (addition(one, one) = star(one)),
% 0.84/0.76 inference(transitivity,[status(thm)],[82, 112, 62, 51, 41])).
% 0.84/0.76 tff(114,plain,
% 0.84/0.76 (addition(addition(one, one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 0.84/0.76 inference(monotonicity,[status(thm)],[113, 32])).
% 0.84/0.76 tff(115,plain,
% 0.84/0.76 (addition(multiplication(one, strong_iteration(one)), one) = strong_iteration(one)),
% 0.84/0.76 inference(symmetry,[status(thm)],[19])).
% 0.84/0.76 tff(116,plain,
% 0.84/0.76 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one))),
% 0.84/0.76 inference(quant_inst,[status(thm)],[])).
% 0.84/0.76 tff(117,plain,
% 0.84/0.76 (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.84/0.76 inference(unit_resolution,[status(thm)],[116, 58])).
% 0.84/0.76 tff(118,plain,
% 0.84/0.76 (multiplication(one, strong_iteration(one)) = multiplication(one, addition(multiplication(one, strong_iteration(one)), one))),
% 0.84/0.76 inference(monotonicity,[status(thm)],[19])).
% 0.84/0.76 tff(119,plain,
% 0.84/0.76 (multiplication(one, strong_iteration(one)) = strong_iteration(one)),
% 0.84/0.76 inference(transitivity,[status(thm)],[118, 117, 115])).
% 0.84/0.76 tff(120,plain,
% 0.84/0.76 (multiplication(multiplication(one, strong_iteration(one)), zero) = multiplication(strong_iteration(one), zero)),
% 0.84/0.76 inference(monotonicity,[status(thm)],[119])).
% 0.84/0.76 tff(121,plain,
% 0.84/0.76 (multiplication(strong_iteration(one), zero) = multiplication(multiplication(one, strong_iteration(one)), zero)),
% 0.84/0.76 inference(symmetry,[status(thm)],[120])).
% 0.84/0.76 tff(122,plain,
% 0.84/0.76 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(multiplication(one, strong_iteration(one)), zero)),
% 0.84/0.76 inference(transitivity,[status(thm)],[31, 21, 121])).
% 0.84/0.76 tff(123,plain,
% 0.84/0.76 (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))),
% 0.84/0.76 inference(monotonicity,[status(thm)],[122])).
% 0.84/0.76 tff(124,plain,
% 0.84/0.76 ((~![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))))),
% 0.84/0.76 inference(quant_inst,[status(thm)],[])).
% 0.84/0.76 tff(125,plain,
% 0.84/0.76 (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)))),
% 0.84/0.76 inference(unit_resolution,[status(thm)],[124, 48])).
% 0.84/0.76 tff(126,plain,
% 0.84/0.76 (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))),
% 0.84/0.76 inference(symmetry,[status(thm)],[125])).
% 0.84/0.76 tff(127,plain,
% 0.84/0.76 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, zero) = zero)),
% 0.84/0.76 inference(quant_inst,[status(thm)],[])).
% 0.84/0.76 tff(128,plain,
% 0.84/0.76 (multiplication(one, zero) = zero),
% 0.84/0.76 inference(unit_resolution,[status(thm)],[127, 58])).
% 0.84/0.76 tff(129,plain,
% 0.84/0.76 (zero = multiplication(one, zero)),
% 0.84/0.76 inference(symmetry,[status(thm)],[128])).
% 0.84/0.76 tff(130,plain,
% 0.84/0.76 (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)))),
% 0.84/0.76 inference(monotonicity,[status(thm)],[129])).
% 0.84/0.76 tff(131,plain,
% 0.84/0.76 (addition(zero, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.84/0.76 inference(transitivity,[status(thm)],[130, 126, 123])).
% 0.84/0.76 tff(132,plain,
% 0.84/0.76 (one = addition(one, one)),
% 0.84/0.76 inference(symmetry,[status(thm)],[82])).
% 0.84/0.76 tff(133,plain,
% 0.84/0.76 (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)))),
% 0.84/0.76 inference(monotonicity,[status(thm)],[132, 131])).
% 0.84/0.76 tff(134,plain,
% 0.84/0.76 (^[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)))),
% 0.84/0.76 inference(bind,[status(th)],[])).
% 0.84/0.76 tff(135,plain,
% 0.84/0.76 (![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))),
% 0.84/0.76 inference(quant_intro,[status(thm)],[134])).
% 0.84/0.76 tff(136,plain,
% 0.84/0.76 (![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))),
% 0.84/0.76 inference(rewrite,[status(thm)],[])).
% 0.84/0.76 tff(137,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')).
% 0.84/0.76 tff(138,plain,
% 0.84/0.76 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.84/0.76 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.84/0.76 tff(139,plain,(
% 0.84/0.76 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.84/0.76 inference(skolemize,[status(sab)],[138])).
% 0.84/0.76 tff(140,plain,
% 0.84/0.76 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.84/0.76 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.84/0.76 tff(141,plain,
% 0.84/0.76 ((~![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))))),
% 0.84/0.76 inference(quant_inst,[status(thm)],[])).
% 0.84/0.76 tff(142,plain,
% 0.84/0.76 (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)))),
% 0.84/0.76 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.84/0.76 tff(143,plain,
% 0.84/0.76 (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))))),
% 0.84/0.76 inference(symmetry,[status(thm)],[142])).
% 0.84/0.76 tff(144,plain,
% 0.84/0.76 (addition(one, zero) = addition(addition(one, one), zero)),
% 0.84/0.76 inference(monotonicity,[status(thm)],[132])).
% 0.84/0.76 tff(145,plain,
% 0.84/0.76 (addition(addition(one, one), zero) = addition(one, zero)),
% 0.84/0.76 inference(symmetry,[status(thm)],[144])).
% 0.84/0.76 tff(146,plain,
% 0.84/0.76 (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)))),
% 0.84/0.76 inference(monotonicity,[status(thm)],[145])).
% 0.84/0.76 tff(147,plain,
% 0.84/0.76 ((~![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))))),
% 0.84/0.76 inference(quant_inst,[status(thm)],[])).
% 0.84/0.76 tff(148,plain,
% 0.84/0.76 (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)))),
% 0.84/0.76 inference(unit_resolution,[status(thm)],[147, 69])).
% 0.84/0.76 tff(149,plain,
% 0.84/0.76 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.84/0.76 inference(bind,[status(th)],[])).
% 0.84/0.76 tff(150,plain,
% 0.84/0.76 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.84/0.76 inference(quant_intro,[status(thm)],[149])).
% 0.84/0.76 tff(151,plain,
% 0.84/0.76 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.84/0.76 inference(rewrite,[status(thm)],[])).
% 0.84/0.76 tff(152,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_identity')).
% 0.84/0.76 tff(153,plain,
% 0.84/0.76 (![A: $i] : (addition(A, zero) = A)),
% 0.84/0.76 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.84/0.76 tff(154,plain,(
% 0.84/0.76 ![A: $i] : (addition(A, zero) = A)),
% 0.84/0.76 inference(skolemize,[status(sab)],[153])).
% 0.84/0.76 tff(155,plain,
% 0.84/0.76 (![A: $i] : (addition(A, zero) = A)),
% 0.84/0.76 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.84/0.76 tff(156,plain,
% 0.84/0.76 ((~![A: $i] : (addition(A, zero) = A)) | (addition(addition(one, one), zero) = addition(one, one))),
% 0.84/0.76 inference(quant_inst,[status(thm)],[])).
% 0.84/0.76 tff(157,plain,
% 0.84/0.76 (addition(addition(one, one), zero) = addition(one, one)),
% 0.84/0.76 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.84/0.76 tff(158,plain,
% 0.84/0.76 (addition(addition(one, one), zero) = one),
% 0.84/0.76 inference(transitivity,[status(thm)],[157, 82])).
% 0.84/0.76 tff(159,plain,
% 0.84/0.76 (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)))),
% 0.84/0.76 inference(monotonicity,[status(thm)],[158])).
% 0.84/0.76 tff(160,plain,
% 0.84/0.76 (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)))),
% 0.84/0.76 inference(symmetry,[status(thm)],[159])).
% 0.84/0.76 tff(161,plain,
% 0.84/0.76 (strong_iteration(addition(one, one)) = strong_iteration(one)),
% 0.84/0.76 inference(monotonicity,[status(thm)],[82])).
% 0.84/0.76 tff(162,plain,
% 0.84/0.76 (multiplication(strong_iteration(addition(one, one)), zero) = multiplication(strong_iteration(one), zero)),
% 0.84/0.76 inference(monotonicity,[status(thm)],[161])).
% 0.84/0.76 tff(163,plain,
% 0.84/0.76 (multiplication(strong_iteration(addition(one, one)), zero) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.84/0.76 inference(transitivity,[status(thm)],[162, 20, 30])).
% 0.84/0.76 tff(164,plain,
% 0.84/0.76 (leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero)) <=> leq(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.84/0.76 inference(monotonicity,[status(thm)],[82, 163])).
% 0.84/0.76 tff(165,plain,
% 0.84/0.76 (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)))),
% 0.84/0.76 inference(transitivity,[status(thm)],[164, 160])).
% 0.84/0.76 tff(166,plain,
% 0.84/0.76 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, addition(one, one)) = addition(addition(one, one), zero))),
% 0.84/0.76 inference(quant_inst,[status(thm)],[])).
% 0.84/0.76 tff(167,plain,
% 0.84/0.76 (addition(zero, addition(one, one)) = addition(addition(one, one), zero)),
% 0.84/0.76 inference(unit_resolution,[status(thm)],[166, 48])).
% 0.84/0.76 tff(168,plain,
% 0.84/0.76 (addition(zero, addition(one, one)) = one),
% 0.84/0.76 inference(transitivity,[status(thm)],[167, 157, 82])).
% 0.84/0.77 tff(169,plain,
% 0.84/0.77 (multiplication(addition(one, one), addition(zero, addition(one, one))) = multiplication(one, one)),
% 0.84/0.77 inference(monotonicity,[status(thm)],[82, 168])).
% 0.84/0.77 tff(170,plain,
% 0.84/0.77 (addition(addition(one, one), zero) = addition(zero, addition(one, one))),
% 0.84/0.77 inference(symmetry,[status(thm)],[167])).
% 0.84/0.77 tff(171,plain,
% 0.84/0.77 (multiplication(addition(one, one), addition(addition(one, one), zero)) = multiplication(addition(one, one), addition(zero, addition(one, one)))),
% 0.84/0.77 inference(monotonicity,[status(thm)],[170])).
% 0.84/0.77 tff(172,plain,
% 0.84/0.77 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(173,plain,
% 0.84/0.77 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[172])).
% 0.84/0.77 tff(174,plain,
% 0.84/0.77 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(175,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity1')).
% 0.84/0.77 tff(176,plain,
% 0.84/0.77 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.84/0.77 tff(177,plain,(
% 0.84/0.77 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.84/0.77 inference(skolemize,[status(sab)],[176])).
% 0.84/0.77 tff(178,plain,
% 0.84/0.77 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.84/0.77 tff(179,plain,
% 0.84/0.77 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(one, one), addition(addition(one, one), zero)) = addition(multiplication(addition(one, one), addition(one, one)), multiplication(addition(one, one), zero)))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(180,plain,
% 0.84/0.77 (multiplication(addition(one, one), addition(addition(one, one), zero)) = addition(multiplication(addition(one, one), addition(one, one)), multiplication(addition(one, one), zero))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.84/0.77 tff(181,plain,
% 0.84/0.77 (addition(multiplication(addition(one, one), addition(one, one)), multiplication(addition(one, one), zero)) = multiplication(addition(one, one), addition(addition(one, one), zero))),
% 0.84/0.77 inference(symmetry,[status(thm)],[180])).
% 0.84/0.77 tff(182,plain,
% 0.84/0.77 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, one), zero) = addition(multiplication(one, zero), multiplication(one, zero)))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(183,plain,
% 0.84/0.77 (multiplication(addition(one, one), zero) = addition(multiplication(one, zero), multiplication(one, zero))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[182, 28])).
% 0.84/0.77 tff(184,plain,
% 0.84/0.77 (addition(multiplication(one, zero), multiplication(one, zero)) = multiplication(addition(one, one), zero)),
% 0.84/0.77 inference(symmetry,[status(thm)],[183])).
% 0.84/0.77 tff(185,plain,
% 0.84/0.77 (addition(multiplication(one, zero), multiplication(one, zero)) = addition(zero, zero)),
% 0.84/0.77 inference(monotonicity,[status(thm)],[128, 128])).
% 0.84/0.77 tff(186,plain,
% 0.84/0.77 (addition(zero, zero) = addition(multiplication(one, zero), multiplication(one, zero))),
% 0.84/0.77 inference(symmetry,[status(thm)],[185])).
% 0.84/0.77 tff(187,plain,
% 0.84/0.77 ((~![A: $i] : (addition(A, A) = A)) | (addition(zero, zero) = zero)),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(188,plain,
% 0.84/0.77 (addition(zero, zero) = zero),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[187, 80])).
% 0.84/0.77 tff(189,plain,
% 0.84/0.77 (zero = addition(zero, zero)),
% 0.84/0.77 inference(symmetry,[status(thm)],[188])).
% 0.84/0.77 tff(190,plain,
% 0.84/0.77 (zero = multiplication(addition(one, one), zero)),
% 0.84/0.77 inference(transitivity,[status(thm)],[189, 186, 184])).
% 0.84/0.77 tff(191,plain,
% 0.84/0.77 (addition(multiplication(addition(one, one), addition(one, one)), zero) = addition(multiplication(addition(one, one), addition(one, one)), multiplication(addition(one, one), zero))),
% 0.84/0.77 inference(monotonicity,[status(thm)],[190])).
% 0.84/0.77 tff(192,plain,
% 0.84/0.77 (addition(multiplication(addition(one, one), addition(one, one)), zero) = one),
% 0.84/0.77 inference(transitivity,[status(thm)],[191, 181, 171, 169, 84])).
% 0.84/0.77 tff(193,plain,
% 0.84/0.77 (leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero)) <=> leq(one, one)),
% 0.84/0.77 inference(monotonicity,[status(thm)],[82, 192])).
% 0.84/0.77 tff(194,plain,
% 0.84/0.77 (leq(one, one) <=> leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))),
% 0.84/0.77 inference(symmetry,[status(thm)],[193])).
% 0.84/0.77 tff(195,plain,
% 0.84/0.77 (leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[92, 194])).
% 0.84/0.77 tff(196,plain,
% 0.84/0.77 (^[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))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(197,plain,
% 0.84/0.77 (![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)))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[196])).
% 0.84/0.77 tff(198,plain,
% 0.84/0.77 (![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)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(199,plain,
% 0.84/0.77 (^[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))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(200,plain,
% 0.84/0.77 (![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)))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[199])).
% 0.84/0.77 tff(201,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')).
% 0.84/0.77 tff(202,plain,
% 0.84/0.77 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.84/0.77 tff(203,plain,
% 0.84/0.77 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.84/0.77 tff(204,plain,(
% 0.84/0.77 ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.84/0.77 inference(skolemize,[status(sab)],[203])).
% 0.84/0.77 tff(205,plain,
% 0.84/0.77 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.84/0.77 tff(206,plain,
% 0.84/0.77 (((~![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)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(207,plain,
% 0.84/0.77 ((~![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)))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(208,plain,
% 0.84/0.77 ((~![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))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.84/0.77 tff(209,plain,
% 0.84/0.77 ((~leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))) | leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[208, 205])).
% 0.84/0.77 tff(210,plain,
% 0.84/0.77 (leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[209, 195])).
% 0.84/0.77 tff(211,plain,
% 0.84/0.77 (leq(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[210, 165])).
% 0.84/0.77 tff(212,plain,
% 0.84/0.77 ((~(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)))),
% 0.84/0.77 inference(tautology,[status(thm)],[])).
% 0.84/0.77 tff(213,plain,
% 0.84/0.77 (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))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[212, 211, 148])).
% 0.84/0.77 tff(214,plain,
% 0.84/0.77 (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)))),
% 0.84/0.77 inference(symmetry,[status(thm)],[213])).
% 0.84/0.77 tff(215,plain,
% 0.84/0.77 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(216,plain,
% 0.84/0.77 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.84/0.77 inference(quant_intro,[status(thm)],[215])).
% 0.84/0.77 tff(217,plain,
% 0.84/0.77 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(218,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 0.84/0.77 tff(219,plain,
% 0.84/0.77 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.84/0.77 tff(220,plain,(
% 0.84/0.77 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.84/0.77 inference(skolemize,[status(sab)],[219])).
% 0.84/0.77 tff(221,plain,
% 0.84/0.77 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.84/0.77 tff(222,plain,
% 0.84/0.77 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, X0!0) = zero)),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(223,plain,
% 0.84/0.77 (multiplication(zero, X0!0) = zero),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.84/0.77 tff(224,plain,
% 0.84/0.77 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0)) = multiplication(strong_iteration(one), zero)),
% 0.84/0.77 inference(monotonicity,[status(thm)],[115, 223])).
% 0.84/0.77 tff(225,plain,
% 0.84/0.77 (^[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)))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(226,plain,
% 0.84/0.77 (![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))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[225])).
% 0.84/0.77 tff(227,plain,
% 0.84/0.77 (![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))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(228,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')).
% 0.84/0.77 tff(229,plain,
% 0.84/0.77 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.84/0.77 tff(230,plain,(
% 0.84/0.77 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.84/0.77 inference(skolemize,[status(sab)],[229])).
% 0.84/0.77 tff(231,plain,
% 0.84/0.77 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.84/0.77 tff(232,plain,
% 0.84/0.77 ((~![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))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(233,plain,
% 0.84/0.77 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0)) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.84/0.77 tff(234,plain,
% 0.84/0.77 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0))),
% 0.84/0.77 inference(symmetry,[status(thm)],[233])).
% 0.84/0.77 tff(235,plain,
% 0.84/0.77 (multiplication(multiplication(strong_iteration(one), zero), X0!0) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0)),
% 0.84/0.77 inference(monotonicity,[status(thm)],[20])).
% 0.84/0.77 tff(236,plain,
% 0.84/0.77 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0)) <=> (addition(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0)) = multiplication(multiplication(strong_iteration(one), zero), X0!0)))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(237,plain,
% 0.84/0.77 (leq(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0)) <=> (addition(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0)) = multiplication(multiplication(strong_iteration(one), zero), X0!0))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[236, 69])).
% 0.84/0.77 tff(238,plain,
% 0.84/0.77 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0) = multiplication(multiplication(strong_iteration(one), zero), X0!0)),
% 0.84/0.77 inference(symmetry,[status(thm)],[235])).
% 0.84/0.77 tff(239,plain,
% 0.84/0.77 (multiplication(strong_iteration(one), zero) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0))),
% 0.84/0.77 inference(symmetry,[status(thm)],[224])).
% 0.84/0.77 tff(240,plain,
% 0.84/0.77 ((~![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))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(241,plain,
% 0.84/0.77 (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)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[240, 69])).
% 0.84/0.77 tff(242,plain,
% 0.84/0.77 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(243,plain,
% 0.84/0.77 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[242])).
% 0.84/0.77 tff(244,plain,
% 0.84/0.77 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(245,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 0.84/0.77 tff(246,plain,
% 0.84/0.77 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.84/0.77 tff(247,plain,(
% 0.84/0.77 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.84/0.77 inference(skolemize,[status(sab)],[246])).
% 0.84/0.77 tff(248,plain,
% 0.84/0.77 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.84/0.77 tff(249,plain,
% 0.84/0.77 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(one), one)) = star(one))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(250,plain,
% 0.84/0.77 (addition(one, multiplication(star(one), one)) = star(one)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.84/0.77 tff(251,plain,
% 0.84/0.77 (star(one) = addition(one, multiplication(star(one), one))),
% 0.84/0.77 inference(symmetry,[status(thm)],[250])).
% 0.84/0.77 tff(252,plain,
% 0.84/0.77 (multiplication(star(one), zero) = multiplication(addition(one, multiplication(star(one), one)), zero)),
% 0.84/0.77 inference(monotonicity,[status(thm)],[251])).
% 0.84/0.77 tff(253,plain,
% 0.84/0.77 (multiplication(addition(one, multiplication(star(one), one)), zero) = multiplication(star(one), zero)),
% 0.84/0.77 inference(symmetry,[status(thm)],[252])).
% 0.84/0.77 tff(254,plain,
% 0.84/0.77 ((~![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)), zero) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(255,plain,
% 0.84/0.77 (multiplication(addition(one, multiplication(star(one), one)), zero) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[254, 28])).
% 0.84/0.77 tff(256,plain,
% 0.84/0.77 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(addition(one, multiplication(star(one), one)), zero)),
% 0.84/0.77 inference(symmetry,[status(thm)],[255])).
% 0.84/0.77 tff(257,plain,
% 0.84/0.77 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(star(one), zero)),
% 0.84/0.77 inference(transitivity,[status(thm)],[256, 253])).
% 0.84/0.77 tff(258,plain,
% 0.84/0.77 (leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) <=> leq(multiplication(star(one), zero), zero)),
% 0.84/0.77 inference(monotonicity,[status(thm)],[257])).
% 0.84/0.77 tff(259,plain,
% 0.84/0.77 (leq(multiplication(star(one), zero), zero) <=> leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.84/0.77 inference(symmetry,[status(thm)],[258])).
% 0.84/0.77 tff(260,plain,
% 0.84/0.77 (addition(multiplication(one, zero), zero) = addition(multiplication(one, zero), multiplication(one, zero))),
% 0.84/0.77 inference(monotonicity,[status(thm)],[129])).
% 0.84/0.77 tff(261,plain,
% 0.84/0.77 (addition(multiplication(one, zero), zero) = zero),
% 0.84/0.77 inference(transitivity,[status(thm)],[260, 185, 188])).
% 0.84/0.77 tff(262,plain,
% 0.84/0.77 (leq(addition(multiplication(one, zero), zero), zero) <=> leq(zero, zero)),
% 0.84/0.77 inference(monotonicity,[status(thm)],[261])).
% 0.84/0.77 tff(263,plain,
% 0.84/0.77 (leq(zero, zero) <=> leq(addition(multiplication(one, zero), zero), zero)),
% 0.84/0.77 inference(symmetry,[status(thm)],[262])).
% 0.84/0.77 tff(264,plain,
% 0.84/0.77 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(zero, zero) <=> (addition(zero, zero) = zero))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(265,plain,
% 0.84/0.77 (leq(zero, zero) <=> (addition(zero, zero) = zero)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[264, 69])).
% 0.84/0.77 tff(266,plain,
% 0.84/0.77 ((~(leq(zero, zero) <=> (addition(zero, zero) = zero))) | leq(zero, zero) | (~(addition(zero, zero) = zero))),
% 0.84/0.77 inference(tautology,[status(thm)],[])).
% 0.84/0.77 tff(267,plain,
% 0.84/0.77 (leq(zero, zero)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[266, 188, 265])).
% 0.84/0.77 tff(268,plain,
% 0.84/0.77 (leq(addition(multiplication(one, zero), zero), zero)),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[267, 263])).
% 0.84/0.77 tff(269,plain,
% 0.84/0.77 (^[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)))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(270,plain,
% 0.84/0.77 (![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))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[269])).
% 0.84/0.77 tff(271,plain,
% 0.84/0.77 (![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))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(272,plain,
% 0.84/0.77 (^[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)))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(273,plain,
% 0.84/0.77 (![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))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[272])).
% 0.84/0.77 tff(274,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')).
% 0.84/0.77 tff(275,plain,
% 0.84/0.77 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.84/0.77 tff(276,plain,
% 0.84/0.77 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[275, 271])).
% 0.84/0.77 tff(277,plain,(
% 0.84/0.77 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.84/0.78 inference(skolemize,[status(sab)],[276])).
% 0.84/0.78 tff(278,plain,
% 0.84/0.78 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[277, 270])).
% 0.84/0.78 tff(279,plain,
% 0.84/0.78 (((~![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))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(280,plain,
% 0.84/0.78 ((~![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))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(281,plain,
% 0.84/0.78 ((~![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)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.84/0.78 tff(282,plain,
% 0.84/0.78 ((~leq(addition(multiplication(one, zero), zero), zero)) | leq(multiplication(star(one), zero), zero)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[281, 278])).
% 0.84/0.78 tff(283,plain,
% 0.84/0.78 (leq(multiplication(star(one), zero), zero)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[282, 268])).
% 0.84/0.78 tff(284,plain,
% 0.84/0.78 (leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[283, 259])).
% 0.84/0.78 tff(285,plain,
% 0.84/0.78 ((~(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)),
% 0.84/0.78 inference(tautology,[status(thm)],[])).
% 0.84/0.78 tff(286,plain,
% 0.84/0.78 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) = zero),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[285, 284, 241])).
% 0.84/0.78 tff(287,plain,
% 0.84/0.78 ((~![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))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(288,plain,
% 0.84/0.78 (addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[287, 48])).
% 0.84/0.78 tff(289,plain,
% 0.84/0.78 (multiplication(multiplication(one, star(one)), zero) = multiplication(star(one), zero)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[60])).
% 0.84/0.78 tff(290,plain,
% 0.84/0.78 (multiplication(star(one), zero) = multiplication(multiplication(one, star(one)), zero)),
% 0.84/0.78 inference(symmetry,[status(thm)],[289])).
% 0.84/0.78 tff(291,plain,
% 0.84/0.78 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(multiplication(one, star(one)), zero)),
% 0.84/0.78 inference(transitivity,[status(thm)],[256, 253, 290])).
% 0.84/0.78 tff(292,plain,
% 0.84/0.78 (addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[129, 291])).
% 0.84/0.78 tff(293,plain,
% 0.84/0.78 (addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero)) = addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.84/0.78 inference(symmetry,[status(thm)],[292])).
% 0.84/0.78 tff(294,plain,
% 0.84/0.78 ((~![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)))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(295,plain,
% 0.84/0.78 (multiplication(addition(one, multiplication(one, star(one))), zero) = addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[294, 28])).
% 0.84/0.78 tff(296,plain,
% 0.84/0.78 (multiplication(addition(one, multiplication(one, star(one))), zero) = multiplication(star(one), zero)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[41])).
% 0.84/0.78 tff(297,plain,
% 0.84/0.78 (multiplication(star(one), zero) = multiplication(addition(one, multiplication(one, star(one))), zero)),
% 0.84/0.78 inference(symmetry,[status(thm)],[296])).
% 0.84/0.78 tff(298,plain,
% 0.84/0.78 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = zero),
% 0.84/0.78 inference(transitivity,[status(thm)],[256, 253, 297, 295, 293, 288, 286])).
% 0.84/0.78 tff(299,plain,
% 0.84/0.78 (multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(strong_iteration(one), zero)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[298])).
% 0.84/0.78 tff(300,plain,
% 0.84/0.78 (addition(multiplication(one, star(one)), one) = addition(star(one), one)),
% 0.84/0.78 inference(symmetry,[status(thm)],[62])).
% 0.84/0.78 tff(301,plain,
% 0.84/0.78 (star(one) = addition(one, multiplication(one, star(one)))),
% 0.84/0.78 inference(symmetry,[status(thm)],[41])).
% 0.84/0.78 tff(302,plain,
% 0.84/0.78 (star(one) = one),
% 0.84/0.78 inference(transitivity,[status(thm)],[301, 50, 300, 111])).
% 0.84/0.78 tff(303,plain,
% 0.84/0.78 (strong_iteration(star(one)) = strong_iteration(one)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[302])).
% 0.84/0.78 tff(304,plain,
% 0.84/0.78 (multiplication(strong_iteration(star(one)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[303])).
% 0.84/0.78 tff(305,plain,
% 0.84/0.78 (multiplication(strong_iteration(star(one)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(multiplication(strong_iteration(one), zero), X0!0)),
% 0.84/0.78 inference(transitivity,[status(thm)],[304, 299, 239, 233, 238])).
% 0.84/0.78 tff(306,plain,
% 0.84/0.78 (multiplication(addition(one, multiplication(one, star(one))), X0!0) = multiplication(star(one), X0!0)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[41])).
% 0.84/0.78 tff(307,plain,
% 0.84/0.78 ((~![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))), X0!0) = addition(multiplication(one, X0!0), multiplication(multiplication(one, star(one)), X0!0)))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(308,plain,
% 0.84/0.78 (multiplication(addition(one, multiplication(one, star(one))), X0!0) = addition(multiplication(one, X0!0), multiplication(multiplication(one, star(one)), X0!0))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[307, 28])).
% 0.84/0.78 tff(309,plain,
% 0.84/0.78 (addition(multiplication(one, X0!0), multiplication(multiplication(one, star(one)), X0!0)) = multiplication(addition(one, multiplication(one, star(one))), X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[308])).
% 0.84/0.78 tff(310,plain,
% 0.84/0.78 (multiplication(multiplication(one, star(one)), X0!0) = multiplication(star(one), X0!0)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[60])).
% 0.84/0.78 tff(311,plain,
% 0.84/0.78 (multiplication(star(one), X0!0) = multiplication(multiplication(one, star(one)), X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[310])).
% 0.84/0.78 tff(312,plain,
% 0.84/0.78 (multiplication(star(one), X0!0) = multiplication(addition(one, multiplication(star(one), one)), X0!0)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[251])).
% 0.84/0.78 tff(313,plain,
% 0.84/0.78 (multiplication(addition(one, multiplication(star(one), one)), X0!0) = multiplication(star(one), X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[312])).
% 0.84/0.78 tff(314,plain,
% 0.84/0.78 ((~![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)), X0!0) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(315,plain,
% 0.84/0.78 (multiplication(addition(one, multiplication(star(one), one)), X0!0) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[314, 28])).
% 0.84/0.78 tff(316,plain,
% 0.84/0.78 (addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)) = multiplication(addition(one, multiplication(star(one), one)), X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[315])).
% 0.84/0.78 tff(317,plain,
% 0.84/0.78 (addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)) = multiplication(multiplication(one, star(one)), X0!0)),
% 0.84/0.78 inference(transitivity,[status(thm)],[316, 313, 311])).
% 0.84/0.78 tff(318,plain,
% 0.84/0.78 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!0) = X0!0)),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(319,plain,
% 0.84/0.78 (multiplication(one, X0!0) = X0!0),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[318, 58])).
% 0.84/0.78 tff(320,plain,
% 0.84/0.78 (X0!0 = multiplication(one, X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[319])).
% 0.84/0.78 tff(321,plain,
% 0.84/0.78 (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))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[320, 317])).
% 0.84/0.78 tff(322,plain,
% 0.84/0.78 ((~![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))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(323,plain,
% 0.84/0.78 (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)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[322, 48])).
% 0.84/0.78 tff(324,plain,
% 0.84/0.78 (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)))),
% 0.84/0.78 inference(symmetry,[status(thm)],[323])).
% 0.84/0.78 tff(325,plain,
% 0.84/0.78 ((~![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))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(326,plain,
% 0.84/0.78 (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)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[325, 69])).
% 0.84/0.78 tff(327,plain,
% 0.84/0.78 (addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)) = multiplication(star(one), X0!0)),
% 0.84/0.78 inference(transitivity,[status(thm)],[316, 313])).
% 0.84/0.78 tff(328,plain,
% 0.84/0.78 (leq(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) <=> leq(multiplication(star(one), X0!0), X0!0)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[327])).
% 0.84/0.78 tff(329,plain,
% 0.84/0.78 (leq(multiplication(star(one), X0!0), X0!0) <=> leq(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[328])).
% 0.84/0.78 tff(330,plain,
% 0.84/0.78 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!0, X0!0) = X0!0)),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(331,plain,
% 0.84/0.78 (addition(X0!0, X0!0) = X0!0),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[330, 80])).
% 0.84/0.78 tff(332,plain,
% 0.84/0.78 (addition(multiplication(one, X0!0), multiplication(one, X0!0)) = addition(X0!0, X0!0)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[319, 319])).
% 0.84/0.78 tff(333,plain,
% 0.84/0.78 (addition(multiplication(one, X0!0), X0!0) = addition(multiplication(one, X0!0), multiplication(one, X0!0))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[320])).
% 0.84/0.78 tff(334,plain,
% 0.84/0.78 (addition(multiplication(one, X0!0), X0!0) = X0!0),
% 0.84/0.78 inference(transitivity,[status(thm)],[333, 332, 331])).
% 0.84/0.78 tff(335,plain,
% 0.84/0.78 (leq(addition(multiplication(one, X0!0), X0!0), X0!0) <=> leq(X0!0, X0!0)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[334])).
% 0.84/0.78 tff(336,plain,
% 0.84/0.78 (leq(X0!0, X0!0) <=> leq(addition(multiplication(one, X0!0), X0!0), X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[335])).
% 0.84/0.78 tff(337,plain,
% 0.84/0.78 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!0, X0!0) <=> (addition(X0!0, X0!0) = X0!0))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(338,plain,
% 0.84/0.78 (leq(X0!0, X0!0) <=> (addition(X0!0, X0!0) = X0!0)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[337, 69])).
% 0.84/0.78 tff(339,plain,
% 0.84/0.78 ((~(leq(X0!0, X0!0) <=> (addition(X0!0, X0!0) = X0!0))) | leq(X0!0, X0!0) | (~(addition(X0!0, X0!0) = X0!0))),
% 0.84/0.78 inference(tautology,[status(thm)],[])).
% 0.84/0.78 tff(340,plain,
% 0.84/0.78 (leq(X0!0, X0!0)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[339, 331, 338])).
% 0.84/0.78 tff(341,plain,
% 0.84/0.78 (leq(addition(multiplication(one, X0!0), X0!0), X0!0)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[340, 336])).
% 0.84/0.78 tff(342,plain,
% 0.84/0.78 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(one, 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))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(343,plain,
% 0.84/0.78 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(one, X0!0), X0!0), X0!0)) | leq(multiplication(star(one), X0!0), X0!0))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(344,plain,
% 0.84/0.78 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(one, X0!0), X0!0), X0!0)) | leq(multiplication(star(one), X0!0), X0!0)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.84/0.78 tff(345,plain,
% 0.84/0.78 ((~leq(addition(multiplication(one, X0!0), X0!0), X0!0)) | leq(multiplication(star(one), X0!0), X0!0)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[344, 278])).
% 0.84/0.78 tff(346,plain,
% 0.84/0.78 (leq(multiplication(star(one), X0!0), X0!0)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[345, 341])).
% 0.84/0.78 tff(347,plain,
% 0.84/0.78 (leq(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[346, 329])).
% 0.84/0.78 tff(348,plain,
% 0.84/0.78 ((~(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)),
% 0.84/0.78 inference(tautology,[status(thm)],[])).
% 0.84/0.78 tff(349,plain,
% 0.84/0.78 (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0) = X0!0),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[348, 347, 326])).
% 0.84/0.78 tff(350,plain,
% 0.84/0.78 (X0!0 = addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[349])).
% 0.84/0.78 tff(351,plain,
% 0.84/0.78 (X0!0 = multiplication(star(one), X0!0)),
% 0.84/0.78 inference(transitivity,[status(thm)],[350, 324, 321, 309, 306])).
% 0.84/0.78 tff(352,plain,
% 0.84/0.78 (leq(X0!0, multiplication(strong_iteration(star(one)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) <=> leq(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[351, 305])).
% 0.84/0.78 tff(353,plain,
% 0.84/0.78 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, one), X0!0) = addition(multiplication(one, X0!0), multiplication(one, X0!0)))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(354,plain,
% 0.84/0.78 (multiplication(addition(one, one), X0!0) = addition(multiplication(one, X0!0), multiplication(one, X0!0))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[353, 28])).
% 0.84/0.78 tff(355,plain,
% 0.84/0.78 (addition(zero, addition(one, one)) = addition(one, one)),
% 0.84/0.78 inference(transitivity,[status(thm)],[167, 157])).
% 0.84/0.78 tff(356,plain,
% 0.84/0.78 (multiplication(addition(zero, addition(one, one)), X0!0) = multiplication(addition(one, one), X0!0)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[355])).
% 0.84/0.78 tff(357,plain,
% 0.84/0.78 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(zero, addition(one, one)), X0!0) = addition(multiplication(zero, X0!0), multiplication(addition(one, one), X0!0)))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(358,plain,
% 0.84/0.78 (multiplication(addition(zero, addition(one, one)), X0!0) = addition(multiplication(zero, X0!0), multiplication(addition(one, one), X0!0))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[357, 28])).
% 0.84/0.78 tff(359,plain,
% 0.84/0.78 (addition(multiplication(zero, X0!0), multiplication(addition(one, one), X0!0)) = multiplication(addition(zero, addition(one, one)), X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[358])).
% 0.84/0.78 tff(360,plain,
% 0.84/0.78 (addition(multiplication(one, X0!0), multiplication(one, X0!0)) = multiplication(addition(one, one), X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[354])).
% 0.84/0.78 tff(361,plain,
% 0.84/0.78 (addition(X0!0, X0!0) = addition(multiplication(one, X0!0), multiplication(one, X0!0))),
% 0.84/0.78 inference(symmetry,[status(thm)],[332])).
% 0.84/0.78 tff(362,plain,
% 0.84/0.78 (X0!0 = addition(X0!0, X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[331])).
% 0.84/0.78 tff(363,plain,
% 0.84/0.78 (X0!0 = multiplication(addition(one, one), X0!0)),
% 0.84/0.78 inference(transitivity,[status(thm)],[362, 361, 360])).
% 0.84/0.78 tff(364,plain,
% 0.84/0.78 (addition(multiplication(zero, X0!0), X0!0) = addition(multiplication(zero, X0!0), multiplication(addition(one, one), X0!0))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[363])).
% 0.84/0.78 tff(365,plain,
% 0.84/0.78 (zero = multiplication(zero, X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[223])).
% 0.84/0.78 tff(366,plain,
% 0.84/0.78 (addition(zero, X0!0) = addition(multiplication(zero, X0!0), X0!0)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[365])).
% 0.84/0.78 tff(367,plain,
% 0.84/0.78 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, X0!0) = addition(X0!0, zero))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(368,plain,
% 0.84/0.78 (addition(zero, X0!0) = addition(X0!0, zero)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[367, 48])).
% 0.84/0.78 tff(369,plain,
% 0.84/0.78 (addition(X0!0, zero) = addition(zero, X0!0)),
% 0.84/0.78 inference(symmetry,[status(thm)],[368])).
% 0.84/0.78 tff(370,plain,
% 0.84/0.78 (addition(X0!0, zero) = X0!0),
% 0.84/0.78 inference(transitivity,[status(thm)],[369, 366, 364, 359, 356, 354, 332, 331])).
% 0.84/0.78 tff(371,plain,
% 0.84/0.78 (multiplication(star(one), addition(X0!0, zero)) = multiplication(star(one), X0!0)),
% 0.84/0.78 inference(monotonicity,[status(thm)],[370])).
% 0.84/0.78 tff(372,plain,
% 0.84/0.78 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(one), addition(X0!0, zero)) = addition(multiplication(star(one), X0!0), multiplication(star(one), zero)))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(373,plain,
% 0.84/0.79 (multiplication(star(one), addition(X0!0, zero)) = addition(multiplication(star(one), X0!0), multiplication(star(one), zero))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[372, 178])).
% 0.84/0.79 tff(374,plain,
% 0.84/0.79 (addition(multiplication(star(one), X0!0), multiplication(star(one), zero)) = multiplication(star(one), addition(X0!0, zero))),
% 0.84/0.79 inference(symmetry,[status(thm)],[373])).
% 0.84/0.79 tff(375,plain,
% 0.84/0.79 (multiplication(star(one), multiplication(zero, X0!0)) = multiplication(star(one), zero)),
% 0.84/0.79 inference(monotonicity,[status(thm)],[223])).
% 0.84/0.79 tff(376,plain,
% 0.84/0.79 ((~![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))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(377,plain,
% 0.84/0.79 (multiplication(star(one), multiplication(zero, X0!0)) = multiplication(multiplication(star(one), zero), X0!0)),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[376, 231])).
% 0.84/0.79 tff(378,plain,
% 0.84/0.79 (multiplication(multiplication(star(one), zero), X0!0) = multiplication(star(one), multiplication(zero, X0!0))),
% 0.84/0.79 inference(symmetry,[status(thm)],[377])).
% 0.84/0.79 tff(379,plain,
% 0.84/0.79 (multiplication(multiplication(star(one), zero), X0!0) = multiplication(star(one), zero)),
% 0.84/0.79 inference(transitivity,[status(thm)],[378, 375])).
% 0.84/0.79 tff(380,plain,
% 0.84/0.79 (addition(addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)), multiplication(multiplication(star(one), zero), X0!0)) = addition(multiplication(star(one), X0!0), multiplication(star(one), zero))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[327, 379])).
% 0.84/0.79 tff(381,plain,
% 0.84/0.79 (multiplication(star(one), zero) = multiplication(star(one), multiplication(zero, X0!0))),
% 0.84/0.79 inference(symmetry,[status(thm)],[375])).
% 0.84/0.79 tff(382,plain,
% 0.84/0.79 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(multiplication(star(one), zero), X0!0)),
% 0.84/0.79 inference(transitivity,[status(thm)],[256, 253, 381, 377])).
% 0.84/0.79 tff(383,plain,
% 0.84/0.79 (multiplication(star(one), X0!0) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))),
% 0.84/0.79 inference(transitivity,[status(thm)],[312, 315])).
% 0.84/0.79 tff(384,plain,
% 0.84/0.79 (addition(multiplication(star(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))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[383, 382])).
% 0.84/0.79 tff(385,plain,
% 0.84/0.79 (addition(multiplication(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))),
% 0.84/0.79 inference(transitivity,[status(thm)],[384, 380, 374, 371, 312, 315])).
% 0.84/0.79 tff(386,plain,
% 0.84/0.79 (leq(X0!0, addition(multiplication(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) <=> leq(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[385])).
% 0.84/0.79 tff(387,plain,
% 0.84/0.79 (leq(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) <=> leq(X0!0, addition(multiplication(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.84/0.79 inference(symmetry,[status(thm)],[386])).
% 0.84/0.79 tff(388,plain,
% 0.84/0.79 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) <=> (addition(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(389,plain,
% 0.84/0.79 (leq(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) <=> (addition(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[388, 69])).
% 0.84/0.79 tff(390,plain,
% 0.84/0.79 (addition(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))),
% 0.84/0.79 inference(transitivity,[status(thm)],[321, 309, 306, 312, 315])).
% 0.84/0.79 tff(391,plain,
% 0.84/0.79 ((~(leq(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) <=> (addition(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))))) | leq(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) | (~(addition(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))) = addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0))))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(392,plain,
% 0.84/0.79 (leq(X0!0, addition(multiplication(one, X0!0), multiplication(multiplication(star(one), one), X0!0)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[391, 390, 389])).
% 0.84/0.79 tff(393,plain,
% 0.84/0.79 (leq(X0!0, addition(multiplication(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[392, 387])).
% 0.84/0.79 tff(394,plain,
% 0.84/0.79 (((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(X0!0, addition(multiplication(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))) | leq(X0!0, multiplication(strong_iteration(star(one)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(X0!0, addition(multiplication(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))) | leq(X0!0, multiplication(strong_iteration(star(one)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(395,plain,
% 0.84/0.79 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(X0!0, addition(multiplication(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))) | leq(X0!0, multiplication(strong_iteration(star(one)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(396,plain,
% 0.84/0.79 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(X0!0, addition(multiplication(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))) | leq(X0!0, multiplication(strong_iteration(star(one)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.84/0.79 tff(397,plain,
% 0.84/0.79 ((~leq(X0!0, addition(multiplication(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))) | leq(X0!0, multiplication(strong_iteration(star(one)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[396, 205])).
% 0.84/0.79 tff(398,plain,
% 0.84/0.79 (leq(X0!0, multiplication(strong_iteration(star(one)), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[397, 393])).
% 0.84/0.79 tff(399,plain,
% 0.84/0.79 (leq(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[398, 352])).
% 0.84/0.79 tff(400,plain,
% 0.84/0.79 ((~(leq(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0)) <=> (addition(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0)) = multiplication(multiplication(strong_iteration(one), zero), X0!0)))) | (~leq(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0))) | (addition(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0)) = multiplication(multiplication(strong_iteration(one), zero), X0!0))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(401,plain,
% 0.84/0.79 (addition(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0)) = multiplication(multiplication(strong_iteration(one), zero), X0!0)),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[400, 399, 237])).
% 0.84/0.79 tff(402,plain,
% 0.84/0.79 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), X0!0) = addition(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0)))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(403,plain,
% 0.84/0.79 (multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), X0!0) = addition(multiplication(star(one), X0!0), multiplication(multiplication(strong_iteration(one), zero), X0!0))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[402, 28])).
% 0.84/0.79 tff(404,plain,
% 0.84/0.79 (multiplication(strong_iteration(one), X0!0) = multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), X0!0)),
% 0.84/0.79 inference(monotonicity,[status(thm)],[9])).
% 0.84/0.79 tff(405,plain,
% 0.84/0.79 (multiplication(strong_iteration(one), X0!0) = strong_iteration(one)),
% 0.84/0.79 inference(transitivity,[status(thm)],[404, 403, 401, 235, 234, 224, 20, 30, 214, 146, 143, 133, 114, 10])).
% 0.84/0.79 tff(406,plain,
% 0.84/0.79 ((~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))) <=> (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(407,axiom,(~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.84/0.79 tff(408,plain,
% 0.84/0.79 (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.84/0.79 tff(409,plain,
% 0.84/0.79 (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[408, 406])).
% 0.84/0.79 tff(410,plain,
% 0.84/0.79 (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[409, 406])).
% 0.84/0.79 tff(411,plain,
% 0.84/0.79 (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[410, 406])).
% 0.84/0.79 tff(412,plain,
% 0.84/0.79 (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[411, 406])).
% 0.84/0.79 tff(413,plain,
% 0.84/0.79 (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[412, 406])).
% 0.84/0.79 tff(414,plain,
% 0.84/0.79 (~![X0: $i] : (multiplication(strong_iteration(one), X0) = strong_iteration(one))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[413, 406])).
% 0.84/0.79 tff(415,plain,(
% 0.84/0.79 ~(multiplication(strong_iteration(one), X0!0) = strong_iteration(one))),
% 0.84/0.79 inference(skolemize,[status(sab)],[414])).
% 0.84/0.79 tff(416,plain,
% 0.84/0.79 ($false),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[415, 405])).
% 0.84/0.79 % SZS output end Proof
%------------------------------------------------------------------------------