TSTP Solution File: KLE137+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE137+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 17:24:16 EDT 2022
% Result : Theorem 0.89s 0.80s
% Output : Proof 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : KLE137+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 08:56:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.89/0.80 % SZS status Theorem
% 0.89/0.80 % SZS output start Proof
% 0.89/0.80 tff(strong_iteration_type, type, (
% 0.89/0.80 strong_iteration: $i > $i)).
% 0.89/0.80 tff(one_type, type, (
% 0.89/0.80 one: $i)).
% 0.89/0.80 tff(addition_type, type, (
% 0.89/0.80 addition: ( $i * $i ) > $i)).
% 0.89/0.80 tff(tptp_fun_X0_0_type, type, (
% 0.89/0.80 tptp_fun_X0_0: $i)).
% 0.89/0.80 tff(multiplication_type, type, (
% 0.89/0.80 multiplication: ( $i * $i ) > $i)).
% 0.89/0.80 tff(zero_type, type, (
% 0.89/0.80 zero: $i)).
% 0.89/0.80 tff(star_type, type, (
% 0.89/0.80 star: $i > $i)).
% 0.89/0.80 tff(leq_type, type, (
% 0.89/0.80 leq: ( $i * $i ) > $o)).
% 0.89/0.80 tff(1,plain,
% 0.89/0.80 (^[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))))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(2,plain,
% 0.89/0.80 (![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)))),
% 0.89/0.80 inference(quant_intro,[status(thm)],[1])).
% 0.89/0.80 tff(3,plain,
% 0.89/0.80 (![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)))),
% 0.89/0.80 inference(rewrite,[status(thm)],[])).
% 0.89/0.80 tff(4,axiom,(![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','isolation')).
% 0.89/0.80 tff(5,plain,
% 0.89/0.80 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.89/0.80 tff(6,plain,(
% 0.89/0.80 ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.89/0.80 inference(skolemize,[status(sab)],[5])).
% 0.89/0.80 tff(7,plain,
% 0.89/0.80 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.89/0.80 tff(8,plain,
% 0.89/0.80 ((~![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))) | (strong_iteration(one) = addition(star(one), multiplication(strong_iteration(one), zero)))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(9,plain,
% 0.89/0.80 (strong_iteration(one) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.89/0.80 tff(10,plain,
% 0.89/0.80 (addition(star(one), multiplication(strong_iteration(one), zero)) = strong_iteration(one)),
% 0.89/0.80 inference(symmetry,[status(thm)],[9])).
% 0.89/0.80 tff(11,plain,
% 0.89/0.80 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(12,plain,
% 0.89/0.80 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.89/0.80 inference(quant_intro,[status(thm)],[11])).
% 0.89/0.80 tff(13,plain,
% 0.89/0.80 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.89/0.80 inference(rewrite,[status(thm)],[])).
% 0.89/0.80 tff(14,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.89/0.80 tff(15,plain,
% 0.89/0.80 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.89/0.80 tff(16,plain,(
% 0.89/0.80 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.89/0.80 inference(skolemize,[status(sab)],[15])).
% 0.89/0.80 tff(17,plain,
% 0.89/0.80 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.89/0.80 tff(18,plain,
% 0.89/0.80 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(star(one), multiplication(strong_iteration(one), zero)) = addition(multiplication(strong_iteration(one), zero), star(one)))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(19,plain,
% 0.89/0.80 (addition(star(one), multiplication(strong_iteration(one), zero)) = addition(multiplication(strong_iteration(one), zero), star(one))),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.89/0.80 tff(20,plain,
% 0.89/0.80 (addition(multiplication(strong_iteration(one), zero), star(one)) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 0.89/0.80 inference(symmetry,[status(thm)],[19])).
% 0.89/0.80 tff(21,plain,
% 0.89/0.80 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(22,plain,
% 0.89/0.80 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.89/0.80 inference(quant_intro,[status(thm)],[21])).
% 0.89/0.80 tff(23,plain,
% 0.89/0.80 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.89/0.80 inference(rewrite,[status(thm)],[])).
% 0.89/0.80 tff(24,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 0.89/0.80 tff(25,plain,
% 0.89/0.80 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.89/0.80 tff(26,plain,(
% 0.89/0.80 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.89/0.80 inference(skolemize,[status(sab)],[25])).
% 0.89/0.80 tff(27,plain,
% 0.89/0.80 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.89/0.80 tff(28,plain,
% 0.89/0.80 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(one, star(one))) = star(one))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(29,plain,
% 0.89/0.80 (addition(one, multiplication(one, star(one))) = star(one)),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.89/0.80 tff(30,plain,
% 0.89/0.80 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(31,plain,
% 0.89/0.80 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.89/0.80 inference(quant_intro,[status(thm)],[30])).
% 0.89/0.80 tff(32,plain,
% 0.89/0.80 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.89/0.80 inference(rewrite,[status(thm)],[])).
% 0.89/0.80 tff(33,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 0.89/0.80 tff(34,plain,
% 0.89/0.80 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.89/0.80 tff(35,plain,(
% 0.89/0.80 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.89/0.80 inference(skolemize,[status(sab)],[34])).
% 0.89/0.80 tff(36,plain,
% 0.89/0.80 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.89/0.80 tff(37,plain,
% 0.89/0.80 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(one) = addition(multiplication(one, strong_iteration(one)), one))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(38,plain,
% 0.89/0.80 (strong_iteration(one) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.89/0.80 tff(39,plain,
% 0.89/0.80 (multiplication(strong_iteration(one), zero) = multiplication(addition(multiplication(one, strong_iteration(one)), one), zero)),
% 0.89/0.80 inference(monotonicity,[status(thm)],[38])).
% 0.89/0.80 tff(40,plain,
% 0.89/0.80 (multiplication(addition(multiplication(one, strong_iteration(one)), one), zero) = multiplication(strong_iteration(one), zero)),
% 0.89/0.80 inference(symmetry,[status(thm)],[39])).
% 0.89/0.80 tff(41,plain,
% 0.89/0.80 (^[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))))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(42,plain,
% 0.89/0.80 (![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)))),
% 0.89/0.80 inference(quant_intro,[status(thm)],[41])).
% 0.89/0.80 tff(43,plain,
% 0.89/0.80 (![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)))),
% 0.89/0.80 inference(rewrite,[status(thm)],[])).
% 0.89/0.80 tff(44,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','distributivity2')).
% 0.89/0.80 tff(45,plain,
% 0.89/0.80 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.89/0.80 tff(46,plain,(
% 0.89/0.80 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.89/0.80 inference(skolemize,[status(sab)],[45])).
% 0.89/0.80 tff(47,plain,
% 0.89/0.80 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.89/0.80 tff(48,plain,
% 0.89/0.80 ((~![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)))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(49,plain,
% 0.89/0.80 (multiplication(addition(multiplication(one, strong_iteration(one)), one), zero) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.89/0.80 tff(50,plain,
% 0.89/0.80 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(addition(multiplication(one, strong_iteration(one)), one), zero)),
% 0.89/0.80 inference(symmetry,[status(thm)],[49])).
% 0.89/0.80 tff(51,plain,
% 0.89/0.80 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(strong_iteration(one), zero)),
% 0.89/0.80 inference(transitivity,[status(thm)],[50, 40])).
% 0.89/0.80 tff(52,plain,
% 0.89/0.80 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, multiplication(one, star(one)))) = addition(multiplication(strong_iteration(one), zero), star(one))),
% 0.89/0.80 inference(monotonicity,[status(thm)],[51, 29])).
% 0.89/0.80 tff(53,plain,
% 0.89/0.80 (^[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)))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(54,plain,
% 0.89/0.80 (![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))),
% 0.89/0.80 inference(quant_intro,[status(thm)],[53])).
% 0.89/0.80 tff(55,plain,
% 0.89/0.80 (![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))),
% 0.89/0.80 inference(rewrite,[status(thm)],[])).
% 0.89/0.80 tff(56,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_associativity')).
% 0.89/0.80 tff(57,plain,
% 0.89/0.80 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.89/0.80 tff(58,plain,(
% 0.89/0.80 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.89/0.80 inference(skolemize,[status(sab)],[57])).
% 0.89/0.80 tff(59,plain,
% 0.89/0.80 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.89/0.80 tff(60,plain,
% 0.89/0.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, multiplication(one, star(one)))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), multiplication(one, star(one))))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(61,plain,
% 0.89/0.80 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, multiplication(one, star(one)))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), multiplication(one, star(one)))),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.89/0.80 tff(62,plain,
% 0.89/0.80 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), multiplication(one, star(one))) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, multiplication(one, star(one))))),
% 0.89/0.80 inference(symmetry,[status(thm)],[61])).
% 0.89/0.80 tff(63,plain,
% 0.89/0.80 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(64,plain,
% 0.89/0.80 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.89/0.80 inference(quant_intro,[status(thm)],[63])).
% 0.89/0.80 tff(65,plain,
% 0.89/0.80 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.89/0.80 inference(rewrite,[status(thm)],[])).
% 0.89/0.80 tff(66,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 0.89/0.80 tff(67,plain,
% 0.89/0.80 (![A: $i] : (multiplication(one, A) = A)),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.89/0.80 tff(68,plain,(
% 0.89/0.80 ![A: $i] : (multiplication(one, A) = A)),
% 0.89/0.80 inference(skolemize,[status(sab)],[67])).
% 0.89/0.80 tff(69,plain,
% 0.89/0.80 (![A: $i] : (multiplication(one, A) = A)),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.89/0.80 tff(70,plain,
% 0.89/0.80 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(one)) = star(one))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(71,plain,
% 0.89/0.80 (multiplication(one, star(one)) = star(one)),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.89/0.80 tff(72,plain,
% 0.89/0.80 (star(one) = multiplication(one, star(one))),
% 0.89/0.80 inference(symmetry,[status(thm)],[71])).
% 0.89/0.80 tff(73,plain,
% 0.89/0.80 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(one, star(one))) = addition(multiplication(one, star(one)), one))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(74,plain,
% 0.89/0.80 (addition(one, multiplication(one, star(one))) = addition(multiplication(one, star(one)), one)),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[73, 17])).
% 0.89/0.80 tff(75,plain,
% 0.89/0.80 (addition(multiplication(one, star(one)), one) = addition(one, multiplication(one, star(one)))),
% 0.89/0.80 inference(symmetry,[status(thm)],[74])).
% 0.89/0.80 tff(76,plain,
% 0.89/0.80 (addition(star(one), one) = addition(multiplication(one, star(one)), one)),
% 0.89/0.80 inference(monotonicity,[status(thm)],[72])).
% 0.89/0.80 tff(77,plain,
% 0.89/0.80 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(78,plain,
% 0.89/0.80 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.89/0.80 inference(quant_intro,[status(thm)],[77])).
% 0.89/0.80 tff(79,plain,
% 0.89/0.80 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.89/0.80 inference(rewrite,[status(thm)],[])).
% 0.89/0.80 tff(80,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','order')).
% 0.89/0.80 tff(81,plain,
% 0.89/0.80 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.89/0.80 tff(82,plain,(
% 0.89/0.80 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.89/0.80 inference(skolemize,[status(sab)],[81])).
% 0.89/0.80 tff(83,plain,
% 0.89/0.80 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.89/0.80 tff(84,plain,
% 0.89/0.80 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(star(one), one) <=> (addition(star(one), one) = one))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(85,plain,
% 0.89/0.80 (leq(star(one), one) <=> (addition(star(one), one) = one)),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.89/0.80 tff(86,plain,
% 0.89/0.80 (leq(star(one), one) <=> leq(multiplication(one, star(one)), one)),
% 0.89/0.80 inference(monotonicity,[status(thm)],[72])).
% 0.89/0.80 tff(87,plain,
% 0.89/0.80 (leq(multiplication(one, star(one)), one) <=> leq(star(one), one)),
% 0.89/0.80 inference(symmetry,[status(thm)],[86])).
% 0.89/0.80 tff(88,plain,
% 0.89/0.80 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(89,plain,
% 0.89/0.80 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.89/0.80 inference(quant_intro,[status(thm)],[88])).
% 0.89/0.80 tff(90,plain,
% 0.89/0.80 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.89/0.80 inference(rewrite,[status(thm)],[])).
% 0.89/0.80 tff(91,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.89/0.80 tff(92,plain,
% 0.89/0.80 (![A: $i] : (addition(A, A) = A)),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.89/0.80 tff(93,plain,(
% 0.89/0.80 ![A: $i] : (addition(A, A) = A)),
% 0.89/0.80 inference(skolemize,[status(sab)],[92])).
% 0.89/0.80 tff(94,plain,
% 0.89/0.80 (![A: $i] : (addition(A, A) = A)),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.89/0.80 tff(95,plain,
% 0.89/0.80 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(96,plain,
% 0.89/0.80 (addition(one, one) = one),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.89/0.80 tff(97,plain,
% 0.89/0.80 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, one) = one)),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(98,plain,
% 0.89/0.80 (multiplication(one, one) = one),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[97, 69])).
% 0.89/0.80 tff(99,plain,
% 0.89/0.80 (addition(multiplication(one, one), one) = addition(one, one)),
% 0.89/0.80 inference(monotonicity,[status(thm)],[98])).
% 0.89/0.80 tff(100,plain,
% 0.89/0.80 (addition(multiplication(one, one), one) = one),
% 0.89/0.80 inference(transitivity,[status(thm)],[99, 96])).
% 0.89/0.80 tff(101,plain,
% 0.89/0.80 (leq(addition(multiplication(one, one), one), one) <=> leq(one, one)),
% 0.89/0.80 inference(monotonicity,[status(thm)],[100])).
% 0.89/0.80 tff(102,plain,
% 0.89/0.80 (leq(one, one) <=> leq(addition(multiplication(one, one), one), one)),
% 0.89/0.80 inference(symmetry,[status(thm)],[101])).
% 0.89/0.80 tff(103,plain,
% 0.89/0.80 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(one, one) <=> (addition(one, one) = one))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(104,plain,
% 0.89/0.80 (leq(one, one) <=> (addition(one, one) = one)),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[103, 83])).
% 0.89/0.80 tff(105,plain,
% 0.89/0.80 ((~(leq(one, one) <=> (addition(one, one) = one))) | leq(one, one) | (~(addition(one, one) = one))),
% 0.89/0.80 inference(tautology,[status(thm)],[])).
% 0.89/0.80 tff(106,plain,
% 0.89/0.80 (leq(one, one)),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[105, 96, 104])).
% 0.89/0.80 tff(107,plain,
% 0.89/0.80 (leq(addition(multiplication(one, one), one), one)),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.89/0.80 tff(108,plain,
% 0.89/0.80 (^[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)))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(109,plain,
% 0.89/0.80 (![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))),
% 0.89/0.80 inference(quant_intro,[status(thm)],[108])).
% 0.89/0.80 tff(110,plain,
% 0.89/0.80 (![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))),
% 0.89/0.80 inference(rewrite,[status(thm)],[])).
% 0.89/0.80 tff(111,plain,
% 0.89/0.80 (^[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)))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(112,plain,
% 0.89/0.80 (![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))),
% 0.89/0.80 inference(quant_intro,[status(thm)],[111])).
% 0.89/0.80 tff(113,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(C, A), B), C) => leq(multiplication(B, star(A)), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_induction2')).
% 0.89/0.80 tff(114,plain,
% 0.89/0.80 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.89/0.80 tff(115,plain,
% 0.89/0.80 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.89/0.80 tff(116,plain,(
% 0.89/0.80 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.89/0.80 inference(skolemize,[status(sab)],[115])).
% 0.89/0.80 tff(117,plain,
% 0.89/0.80 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(C, A), B), C)) | leq(multiplication(B, star(A)), C))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.89/0.80 tff(118,plain,
% 0.89/0.80 (((~![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))),
% 0.89/0.80 inference(rewrite,[status(thm)],[])).
% 0.89/0.80 tff(119,plain,
% 0.89/0.80 ((~![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))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(120,plain,
% 0.89/0.80 ((~![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)),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.89/0.80 tff(121,plain,
% 0.89/0.80 ((~leq(addition(multiplication(one, one), one), one)) | leq(multiplication(one, star(one)), one)),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.89/0.80 tff(122,plain,
% 0.89/0.80 (leq(multiplication(one, star(one)), one)),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[121, 107])).
% 0.89/0.80 tff(123,plain,
% 0.89/0.80 (leq(star(one), one)),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[122, 87])).
% 0.89/0.80 tff(124,plain,
% 0.89/0.80 ((~(leq(star(one), one) <=> (addition(star(one), one) = one))) | (~leq(star(one), one)) | (addition(star(one), one) = one)),
% 0.89/0.80 inference(tautology,[status(thm)],[])).
% 0.89/0.80 tff(125,plain,
% 0.89/0.80 (addition(star(one), one) = one),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[124, 123, 85])).
% 0.89/0.80 tff(126,plain,
% 0.89/0.80 (one = addition(star(one), one)),
% 0.89/0.80 inference(symmetry,[status(thm)],[125])).
% 0.89/0.80 tff(127,plain,
% 0.89/0.80 (addition(one, one) = multiplication(one, star(one))),
% 0.89/0.80 inference(transitivity,[status(thm)],[96, 126, 76, 75, 29, 72])).
% 0.89/0.80 tff(128,plain,
% 0.89/0.80 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), addition(one, one)) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), multiplication(one, star(one)))),
% 0.89/0.80 inference(monotonicity,[status(thm)],[127])).
% 0.89/0.80 tff(129,plain,
% 0.89/0.80 (one = addition(one, one)),
% 0.89/0.80 inference(symmetry,[status(thm)],[96])).
% 0.89/0.80 tff(130,plain,
% 0.89/0.80 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one))),
% 0.89/0.80 inference(monotonicity,[status(thm)],[129])).
% 0.89/0.80 tff(131,plain,
% 0.89/0.80 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one)),
% 0.89/0.80 inference(symmetry,[status(thm)],[130])).
% 0.89/0.80 tff(132,plain,
% 0.89/0.80 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)), addition(one, one)) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), addition(one, one))),
% 0.89/0.80 inference(monotonicity,[status(thm)],[131])).
% 0.89/0.80 tff(133,plain,
% 0.89/0.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(one, one), addition(one, one))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)), addition(one, one)))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(134,plain,
% 0.89/0.80 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(one, one), addition(one, one))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)), addition(one, one))),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[133, 59])).
% 0.89/0.80 tff(135,plain,
% 0.89/0.80 (addition(addition(one, one), addition(one, one)) = addition(one, one)),
% 0.89/0.80 inference(monotonicity,[status(thm)],[96, 96])).
% 0.89/0.80 tff(136,plain,
% 0.89/0.80 (addition(one, one) = addition(addition(one, one), addition(one, one))),
% 0.89/0.80 inference(symmetry,[status(thm)],[135])).
% 0.89/0.80 tff(137,plain,
% 0.89/0.80 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(one, one), addition(one, one)))),
% 0.89/0.80 inference(monotonicity,[status(thm)],[136])).
% 0.89/0.80 tff(138,plain,
% 0.89/0.80 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one) = addition(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(139,plain,
% 0.89/0.80 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one) = addition(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[138, 17])).
% 0.89/0.80 tff(140,plain,
% 0.89/0.80 (addition(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one)),
% 0.89/0.80 inference(symmetry,[status(thm)],[139])).
% 0.89/0.80 tff(141,plain,
% 0.89/0.80 (addition(addition(one, one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.89/0.80 inference(monotonicity,[status(thm)],[96])).
% 0.89/0.80 tff(142,plain,
% 0.89/0.80 (addition(multiplication(one, strong_iteration(one)), one) = strong_iteration(one)),
% 0.89/0.80 inference(symmetry,[status(thm)],[38])).
% 0.89/0.80 tff(143,plain,
% 0.89/0.80 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(144,plain,
% 0.89/0.80 (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[143, 69])).
% 0.89/0.80 tff(145,plain,
% 0.89/0.80 (multiplication(one, strong_iteration(one)) = multiplication(one, addition(multiplication(one, strong_iteration(one)), one))),
% 0.89/0.80 inference(monotonicity,[status(thm)],[38])).
% 0.89/0.80 tff(146,plain,
% 0.89/0.80 (multiplication(one, strong_iteration(one)) = strong_iteration(one)),
% 0.89/0.80 inference(transitivity,[status(thm)],[145, 144, 142])).
% 0.89/0.80 tff(147,plain,
% 0.89/0.80 (multiplication(multiplication(one, strong_iteration(one)), zero) = multiplication(strong_iteration(one), zero)),
% 0.89/0.80 inference(monotonicity,[status(thm)],[146])).
% 0.89/0.80 tff(148,plain,
% 0.89/0.80 (multiplication(strong_iteration(one), zero) = multiplication(multiplication(one, strong_iteration(one)), zero)),
% 0.89/0.80 inference(symmetry,[status(thm)],[147])).
% 0.89/0.80 tff(149,plain,
% 0.89/0.80 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(multiplication(one, strong_iteration(one)), zero)),
% 0.89/0.80 inference(transitivity,[status(thm)],[50, 40, 148])).
% 0.89/0.80 tff(150,plain,
% 0.89/0.80 (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))),
% 0.89/0.80 inference(monotonicity,[status(thm)],[149])).
% 0.89/0.80 tff(151,plain,
% 0.89/0.80 ((~![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))))),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(152,plain,
% 0.89/0.80 (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)))),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[151, 17])).
% 0.89/0.80 tff(153,plain,
% 0.89/0.80 (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))),
% 0.89/0.80 inference(symmetry,[status(thm)],[152])).
% 0.89/0.80 tff(154,plain,
% 0.89/0.80 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, zero) = zero)),
% 0.89/0.80 inference(quant_inst,[status(thm)],[])).
% 0.89/0.80 tff(155,plain,
% 0.89/0.80 (multiplication(one, zero) = zero),
% 0.89/0.80 inference(unit_resolution,[status(thm)],[154, 69])).
% 0.89/0.80 tff(156,plain,
% 0.89/0.80 (zero = multiplication(one, zero)),
% 0.89/0.80 inference(symmetry,[status(thm)],[155])).
% 0.89/0.80 tff(157,plain,
% 0.89/0.80 (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)))),
% 0.89/0.80 inference(monotonicity,[status(thm)],[156])).
% 0.89/0.80 tff(158,plain,
% 0.89/0.80 (addition(zero, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.89/0.80 inference(transitivity,[status(thm)],[157, 153, 150])).
% 0.89/0.80 tff(159,plain,
% 0.89/0.80 (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)))),
% 0.89/0.80 inference(monotonicity,[status(thm)],[129, 158])).
% 0.89/0.80 tff(160,plain,
% 0.89/0.80 ((~![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))))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(161,plain,
% 0.89/0.81 (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)))),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[160, 59])).
% 0.89/0.81 tff(162,plain,
% 0.89/0.81 (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))))),
% 0.89/0.81 inference(symmetry,[status(thm)],[161])).
% 0.89/0.81 tff(163,plain,
% 0.89/0.81 (addition(one, zero) = addition(addition(one, one), zero)),
% 0.89/0.81 inference(monotonicity,[status(thm)],[129])).
% 0.89/0.81 tff(164,plain,
% 0.89/0.81 (addition(addition(one, one), zero) = addition(one, zero)),
% 0.89/0.81 inference(symmetry,[status(thm)],[163])).
% 0.89/0.81 tff(165,plain,
% 0.89/0.81 (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)))),
% 0.89/0.81 inference(monotonicity,[status(thm)],[164])).
% 0.89/0.81 tff(166,plain,
% 0.89/0.81 ((~![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))))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(167,plain,
% 0.89/0.81 (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)))),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[166, 83])).
% 0.89/0.81 tff(168,plain,
% 0.89/0.81 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.89/0.81 inference(bind,[status(th)],[])).
% 0.89/0.81 tff(169,plain,
% 0.89/0.81 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.89/0.81 inference(quant_intro,[status(thm)],[168])).
% 0.89/0.81 tff(170,plain,
% 0.89/0.81 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.89/0.81 inference(rewrite,[status(thm)],[])).
% 0.89/0.81 tff(171,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_identity')).
% 0.89/0.81 tff(172,plain,
% 0.89/0.81 (![A: $i] : (addition(A, zero) = A)),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.89/0.81 tff(173,plain,(
% 0.89/0.81 ![A: $i] : (addition(A, zero) = A)),
% 0.89/0.81 inference(skolemize,[status(sab)],[172])).
% 0.89/0.81 tff(174,plain,
% 0.89/0.81 (![A: $i] : (addition(A, zero) = A)),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.89/0.81 tff(175,plain,
% 0.89/0.81 ((~![A: $i] : (addition(A, zero) = A)) | (addition(addition(one, one), zero) = addition(one, one))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(176,plain,
% 0.89/0.81 (addition(addition(one, one), zero) = addition(one, one)),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.89/0.81 tff(177,plain,
% 0.89/0.81 (addition(addition(one, one), zero) = one),
% 0.89/0.81 inference(transitivity,[status(thm)],[176, 96])).
% 0.89/0.81 tff(178,plain,
% 0.89/0.81 (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)))),
% 0.89/0.81 inference(monotonicity,[status(thm)],[177])).
% 0.89/0.81 tff(179,plain,
% 0.89/0.81 (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)))),
% 0.89/0.81 inference(symmetry,[status(thm)],[178])).
% 0.89/0.81 tff(180,plain,
% 0.89/0.81 (strong_iteration(addition(one, one)) = strong_iteration(one)),
% 0.89/0.81 inference(monotonicity,[status(thm)],[96])).
% 0.89/0.81 tff(181,plain,
% 0.89/0.81 (multiplication(strong_iteration(addition(one, one)), zero) = multiplication(strong_iteration(one), zero)),
% 0.89/0.81 inference(monotonicity,[status(thm)],[180])).
% 0.89/0.81 tff(182,plain,
% 0.89/0.81 (multiplication(strong_iteration(addition(one, one)), zero) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.89/0.81 inference(transitivity,[status(thm)],[181, 39, 49])).
% 0.89/0.81 tff(183,plain,
% 0.89/0.81 (leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero)) <=> leq(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.89/0.81 inference(monotonicity,[status(thm)],[96, 182])).
% 0.89/0.81 tff(184,plain,
% 0.89/0.81 (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)))),
% 0.89/0.81 inference(transitivity,[status(thm)],[183, 179])).
% 0.89/0.81 tff(185,plain,
% 0.89/0.81 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, addition(one, one)) = addition(addition(one, one), zero))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(186,plain,
% 0.89/0.81 (addition(zero, addition(one, one)) = addition(addition(one, one), zero)),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[185, 17])).
% 0.89/0.81 tff(187,plain,
% 0.89/0.81 (addition(zero, addition(one, one)) = one),
% 0.89/0.81 inference(transitivity,[status(thm)],[186, 176, 96])).
% 0.89/0.81 tff(188,plain,
% 0.89/0.81 (multiplication(addition(one, one), addition(zero, addition(one, one))) = multiplication(one, one)),
% 0.89/0.81 inference(monotonicity,[status(thm)],[96, 187])).
% 0.89/0.81 tff(189,plain,
% 0.89/0.81 (addition(addition(one, one), zero) = addition(zero, addition(one, one))),
% 0.89/0.81 inference(symmetry,[status(thm)],[186])).
% 0.89/0.81 tff(190,plain,
% 0.89/0.81 (multiplication(addition(one, one), addition(addition(one, one), zero)) = multiplication(addition(one, one), addition(zero, addition(one, one)))),
% 0.89/0.81 inference(monotonicity,[status(thm)],[189])).
% 0.89/0.81 tff(191,plain,
% 0.89/0.81 (^[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))))),
% 0.89/0.81 inference(bind,[status(th)],[])).
% 0.89/0.81 tff(192,plain,
% 0.89/0.81 (![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)))),
% 0.89/0.81 inference(quant_intro,[status(thm)],[191])).
% 0.89/0.81 tff(193,plain,
% 0.89/0.81 (![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)))),
% 0.89/0.81 inference(rewrite,[status(thm)],[])).
% 0.89/0.81 tff(194,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','distributivity1')).
% 0.89/0.81 tff(195,plain,
% 0.89/0.81 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.89/0.81 tff(196,plain,(
% 0.89/0.81 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.89/0.81 inference(skolemize,[status(sab)],[195])).
% 0.89/0.81 tff(197,plain,
% 0.89/0.81 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.89/0.81 tff(198,plain,
% 0.89/0.81 ((~![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)))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(199,plain,
% 0.89/0.81 (multiplication(addition(one, one), addition(addition(one, one), zero)) = addition(multiplication(addition(one, one), addition(one, one)), multiplication(addition(one, one), zero))),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.89/0.81 tff(200,plain,
% 0.89/0.81 (addition(multiplication(addition(one, one), addition(one, one)), multiplication(addition(one, one), zero)) = multiplication(addition(one, one), addition(addition(one, one), zero))),
% 0.89/0.81 inference(symmetry,[status(thm)],[199])).
% 0.89/0.81 tff(201,plain,
% 0.89/0.81 ((~![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)))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(202,plain,
% 0.89/0.81 (multiplication(addition(one, one), zero) = addition(multiplication(one, zero), multiplication(one, zero))),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[201, 47])).
% 0.89/0.81 tff(203,plain,
% 0.89/0.81 (addition(multiplication(one, zero), multiplication(one, zero)) = multiplication(addition(one, one), zero)),
% 0.89/0.81 inference(symmetry,[status(thm)],[202])).
% 0.89/0.81 tff(204,plain,
% 0.89/0.81 (addition(multiplication(one, zero), multiplication(one, zero)) = addition(zero, zero)),
% 0.89/0.81 inference(monotonicity,[status(thm)],[155, 155])).
% 0.89/0.81 tff(205,plain,
% 0.89/0.81 (addition(zero, zero) = addition(multiplication(one, zero), multiplication(one, zero))),
% 0.89/0.81 inference(symmetry,[status(thm)],[204])).
% 0.89/0.81 tff(206,plain,
% 0.89/0.81 ((~![A: $i] : (addition(A, A) = A)) | (addition(zero, zero) = zero)),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(207,plain,
% 0.89/0.81 (addition(zero, zero) = zero),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[206, 94])).
% 0.89/0.81 tff(208,plain,
% 0.89/0.81 (zero = addition(zero, zero)),
% 0.89/0.81 inference(symmetry,[status(thm)],[207])).
% 0.89/0.81 tff(209,plain,
% 0.89/0.81 (zero = multiplication(addition(one, one), zero)),
% 0.89/0.81 inference(transitivity,[status(thm)],[208, 205, 203])).
% 0.89/0.81 tff(210,plain,
% 0.89/0.81 (addition(multiplication(addition(one, one), addition(one, one)), zero) = addition(multiplication(addition(one, one), addition(one, one)), multiplication(addition(one, one), zero))),
% 0.89/0.81 inference(monotonicity,[status(thm)],[209])).
% 0.89/0.81 tff(211,plain,
% 0.89/0.81 (addition(multiplication(addition(one, one), addition(one, one)), zero) = one),
% 0.89/0.81 inference(transitivity,[status(thm)],[210, 200, 190, 188, 98])).
% 0.89/0.81 tff(212,plain,
% 0.89/0.81 (leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero)) <=> leq(one, one)),
% 0.89/0.81 inference(monotonicity,[status(thm)],[96, 211])).
% 0.89/0.81 tff(213,plain,
% 0.89/0.81 (leq(one, one) <=> leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))),
% 0.89/0.81 inference(symmetry,[status(thm)],[212])).
% 0.89/0.81 tff(214,plain,
% 0.89/0.81 (leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[106, 213])).
% 0.89/0.81 tff(215,plain,
% 0.89/0.81 (^[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))))),
% 0.89/0.81 inference(bind,[status(th)],[])).
% 0.89/0.81 tff(216,plain,
% 0.89/0.81 (![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)))),
% 0.89/0.81 inference(quant_intro,[status(thm)],[215])).
% 0.89/0.81 tff(217,plain,
% 0.89/0.81 (![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)))),
% 0.89/0.81 inference(rewrite,[status(thm)],[])).
% 0.89/0.81 tff(218,plain,
% 0.89/0.81 (^[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))))),
% 0.89/0.81 inference(bind,[status(th)],[])).
% 0.89/0.81 tff(219,plain,
% 0.89/0.81 (![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)))),
% 0.89/0.81 inference(quant_intro,[status(thm)],[218])).
% 0.89/0.81 tff(220,axiom,(![A: $i, B: $i, C: $i] : (leq(C, addition(multiplication(A, C), B)) => leq(C, multiplication(strong_iteration(A), B)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','infty_coinduction')).
% 0.89/0.81 tff(221,plain,
% 0.89/0.81 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.89/0.81 tff(222,plain,
% 0.89/0.81 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.89/0.81 tff(223,plain,(
% 0.89/0.81 ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.89/0.81 inference(skolemize,[status(sab)],[222])).
% 0.89/0.81 tff(224,plain,
% 0.89/0.81 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[223, 216])).
% 0.89/0.81 tff(225,plain,
% 0.89/0.81 (((~![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)))),
% 0.89/0.81 inference(rewrite,[status(thm)],[])).
% 0.89/0.81 tff(226,plain,
% 0.89/0.81 ((~![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)))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(227,plain,
% 0.89/0.81 ((~![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))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.89/0.81 tff(228,plain,
% 0.89/0.81 ((~leq(addition(one, one), addition(multiplication(addition(one, one), addition(one, one)), zero))) | leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero))),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[227, 224])).
% 0.89/0.81 tff(229,plain,
% 0.89/0.81 (leq(addition(one, one), multiplication(strong_iteration(addition(one, one)), zero))),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[228, 214])).
% 0.89/0.81 tff(230,plain,
% 0.89/0.81 (leq(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[229, 184])).
% 0.89/0.81 tff(231,plain,
% 0.89/0.81 ((~(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)))),
% 0.89/0.81 inference(tautology,[status(thm)],[])).
% 0.89/0.81 tff(232,plain,
% 0.89/0.81 (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))),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[231, 230, 167])).
% 0.89/0.81 tff(233,plain,
% 0.89/0.81 (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)))),
% 0.89/0.81 inference(symmetry,[status(thm)],[232])).
% 0.89/0.81 tff(234,plain,
% 0.89/0.81 ((~![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))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(235,plain,
% 0.89/0.81 (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)),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[234, 83])).
% 0.89/0.81 tff(236,plain,
% 0.89/0.81 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 0.89/0.81 inference(bind,[status(th)],[])).
% 0.89/0.81 tff(237,plain,
% 0.89/0.81 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.89/0.81 inference(quant_intro,[status(thm)],[236])).
% 0.89/0.81 tff(238,plain,
% 0.89/0.81 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.89/0.81 inference(rewrite,[status(thm)],[])).
% 0.89/0.81 tff(239,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 0.89/0.81 tff(240,plain,
% 0.89/0.81 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.89/0.81 tff(241,plain,(
% 0.89/0.81 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.89/0.81 inference(skolemize,[status(sab)],[240])).
% 0.89/0.81 tff(242,plain,
% 0.89/0.81 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[241, 237])).
% 0.89/0.81 tff(243,plain,
% 0.89/0.81 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(one), one)) = star(one))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(244,plain,
% 0.89/0.81 (addition(one, multiplication(star(one), one)) = star(one)),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.89/0.81 tff(245,plain,
% 0.89/0.81 (star(one) = addition(one, multiplication(star(one), one))),
% 0.89/0.81 inference(symmetry,[status(thm)],[244])).
% 0.89/0.81 tff(246,plain,
% 0.89/0.81 (multiplication(star(one), zero) = multiplication(addition(one, multiplication(star(one), one)), zero)),
% 0.89/0.81 inference(monotonicity,[status(thm)],[245])).
% 0.89/0.81 tff(247,plain,
% 0.89/0.81 (multiplication(addition(one, multiplication(star(one), one)), zero) = multiplication(star(one), zero)),
% 0.89/0.81 inference(symmetry,[status(thm)],[246])).
% 0.89/0.81 tff(248,plain,
% 0.89/0.81 ((~![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)))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(249,plain,
% 0.89/0.81 (multiplication(addition(one, multiplication(star(one), one)), zero) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[248, 47])).
% 0.89/0.81 tff(250,plain,
% 0.89/0.81 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(addition(one, multiplication(star(one), one)), zero)),
% 0.89/0.81 inference(symmetry,[status(thm)],[249])).
% 0.89/0.81 tff(251,plain,
% 0.89/0.81 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(star(one), zero)),
% 0.89/0.81 inference(transitivity,[status(thm)],[250, 247])).
% 0.89/0.81 tff(252,plain,
% 0.89/0.81 (leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) <=> leq(multiplication(star(one), zero), zero)),
% 0.89/0.81 inference(monotonicity,[status(thm)],[251])).
% 0.89/0.81 tff(253,plain,
% 0.89/0.81 (leq(multiplication(star(one), zero), zero) <=> leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.89/0.81 inference(symmetry,[status(thm)],[252])).
% 0.89/0.81 tff(254,plain,
% 0.89/0.81 (addition(multiplication(one, zero), zero) = addition(multiplication(one, zero), multiplication(one, zero))),
% 0.89/0.81 inference(monotonicity,[status(thm)],[156])).
% 0.89/0.81 tff(255,plain,
% 0.89/0.81 (addition(multiplication(one, zero), zero) = zero),
% 0.89/0.81 inference(transitivity,[status(thm)],[254, 204, 207])).
% 0.89/0.81 tff(256,plain,
% 0.89/0.81 (leq(addition(multiplication(one, zero), zero), zero) <=> leq(zero, zero)),
% 0.89/0.81 inference(monotonicity,[status(thm)],[255])).
% 0.89/0.81 tff(257,plain,
% 0.89/0.81 (leq(zero, zero) <=> leq(addition(multiplication(one, zero), zero), zero)),
% 0.89/0.81 inference(symmetry,[status(thm)],[256])).
% 0.89/0.81 tff(258,plain,
% 0.89/0.81 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(zero, zero) <=> (addition(zero, zero) = zero))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(259,plain,
% 0.89/0.81 (leq(zero, zero) <=> (addition(zero, zero) = zero)),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[258, 83])).
% 0.89/0.81 tff(260,plain,
% 0.89/0.81 ((~(leq(zero, zero) <=> (addition(zero, zero) = zero))) | leq(zero, zero) | (~(addition(zero, zero) = zero))),
% 0.89/0.81 inference(tautology,[status(thm)],[])).
% 0.89/0.81 tff(261,plain,
% 0.89/0.81 (leq(zero, zero)),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[260, 207, 259])).
% 0.89/0.81 tff(262,plain,
% 0.89/0.81 (leq(addition(multiplication(one, zero), zero), zero)),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[261, 257])).
% 0.89/0.81 tff(263,plain,
% 0.89/0.81 (^[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)))),
% 0.89/0.81 inference(bind,[status(th)],[])).
% 0.89/0.81 tff(264,plain,
% 0.89/0.81 (![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))),
% 0.89/0.81 inference(quant_intro,[status(thm)],[263])).
% 0.89/0.81 tff(265,plain,
% 0.89/0.81 (![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))),
% 0.89/0.81 inference(rewrite,[status(thm)],[])).
% 0.89/0.81 tff(266,plain,
% 0.89/0.81 (^[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)))),
% 0.89/0.81 inference(bind,[status(th)],[])).
% 0.89/0.81 tff(267,plain,
% 0.89/0.81 (![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))),
% 0.89/0.81 inference(quant_intro,[status(thm)],[266])).
% 0.89/0.81 tff(268,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_induction1')).
% 0.89/0.81 tff(269,plain,
% 0.89/0.81 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.89/0.81 tff(270,plain,
% 0.89/0.81 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[269, 265])).
% 0.89/0.81 tff(271,plain,(
% 0.89/0.81 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.89/0.81 inference(skolemize,[status(sab)],[270])).
% 0.89/0.81 tff(272,plain,
% 0.89/0.81 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[271, 264])).
% 0.89/0.81 tff(273,plain,
% 0.89/0.81 (((~![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))),
% 0.89/0.81 inference(rewrite,[status(thm)],[])).
% 0.89/0.81 tff(274,plain,
% 0.89/0.81 ((~![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))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(275,plain,
% 0.89/0.81 ((~![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)),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.89/0.81 tff(276,plain,
% 0.89/0.81 ((~leq(addition(multiplication(one, zero), zero), zero)) | leq(multiplication(star(one), zero), zero)),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[275, 272])).
% 0.89/0.81 tff(277,plain,
% 0.89/0.81 (leq(multiplication(star(one), zero), zero)),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[276, 262])).
% 0.89/0.81 tff(278,plain,
% 0.89/0.81 (leq(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[277, 253])).
% 0.89/0.81 tff(279,plain,
% 0.89/0.81 ((~(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)),
% 0.89/0.81 inference(tautology,[status(thm)],[])).
% 0.89/0.81 tff(280,plain,
% 0.89/0.81 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) = zero),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[279, 278, 235])).
% 0.89/0.81 tff(281,plain,
% 0.89/0.81 ((~![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))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(282,plain,
% 0.89/0.81 (addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[281, 17])).
% 0.89/0.81 tff(283,plain,
% 0.89/0.81 (multiplication(multiplication(one, star(one)), zero) = multiplication(star(one), zero)),
% 0.89/0.81 inference(monotonicity,[status(thm)],[71])).
% 0.89/0.82 tff(284,plain,
% 0.89/0.82 (multiplication(star(one), zero) = multiplication(multiplication(one, star(one)), zero)),
% 0.89/0.82 inference(symmetry,[status(thm)],[283])).
% 0.89/0.82 tff(285,plain,
% 0.89/0.82 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = multiplication(multiplication(one, star(one)), zero)),
% 0.89/0.82 inference(transitivity,[status(thm)],[250, 247, 284])).
% 0.89/0.82 tff(286,plain,
% 0.89/0.82 (addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[156, 285])).
% 0.89/0.82 tff(287,plain,
% 0.89/0.82 (addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero)) = addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.89/0.82 inference(symmetry,[status(thm)],[286])).
% 0.89/0.82 tff(288,plain,
% 0.89/0.82 ((~![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)))),
% 0.89/0.82 inference(quant_inst,[status(thm)],[])).
% 0.89/0.82 tff(289,plain,
% 0.89/0.82 (multiplication(addition(one, multiplication(one, star(one))), zero) = addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero))),
% 0.89/0.82 inference(unit_resolution,[status(thm)],[288, 47])).
% 0.89/0.82 tff(290,plain,
% 0.89/0.82 (multiplication(addition(one, multiplication(one, star(one))), zero) = multiplication(star(one), zero)),
% 0.89/0.82 inference(monotonicity,[status(thm)],[29])).
% 0.89/0.82 tff(291,plain,
% 0.89/0.82 (multiplication(star(one), zero) = multiplication(addition(one, multiplication(one, star(one))), zero)),
% 0.89/0.82 inference(symmetry,[status(thm)],[290])).
% 0.89/0.82 tff(292,plain,
% 0.89/0.82 (addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)) = zero),
% 0.89/0.82 inference(transitivity,[status(thm)],[250, 247, 291, 289, 287, 282, 280])).
% 0.89/0.82 tff(293,plain,
% 0.89/0.82 (multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(strong_iteration(one), zero)),
% 0.89/0.82 inference(monotonicity,[status(thm)],[292])).
% 0.89/0.82 tff(294,plain,
% 0.89/0.82 (addition(multiplication(one, zero), multiplication(multiplication(one, star(one)), zero)) = multiplication(addition(one, multiplication(one, star(one))), zero)),
% 0.89/0.82 inference(symmetry,[status(thm)],[289])).
% 0.89/0.82 tff(295,plain,
% 0.89/0.82 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero) = addition(zero, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.89/0.82 inference(symmetry,[status(thm)],[282])).
% 0.89/0.82 tff(296,plain,
% 0.89/0.82 (zero = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), zero)),
% 0.89/0.82 inference(symmetry,[status(thm)],[280])).
% 0.89/0.82 tff(297,plain,
% 0.89/0.82 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.89/0.82 inference(bind,[status(th)],[])).
% 0.89/0.82 tff(298,plain,
% 0.89/0.82 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.89/0.82 inference(quant_intro,[status(thm)],[297])).
% 0.89/0.82 tff(299,plain,
% 0.89/0.82 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.89/0.82 inference(rewrite,[status(thm)],[])).
% 0.89/0.82 tff(300,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 0.89/0.82 tff(301,plain,
% 0.89/0.82 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.89/0.82 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.89/0.82 tff(302,plain,(
% 0.89/0.82 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.89/0.82 inference(skolemize,[status(sab)],[301])).
% 0.89/0.82 tff(303,plain,
% 0.89/0.82 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.89/0.82 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.89/0.82 tff(304,plain,
% 0.89/0.82 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = zero)),
% 0.89/0.82 inference(quant_inst,[status(thm)],[])).
% 0.89/0.82 tff(305,plain,
% 0.89/0.82 (multiplication(zero, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = zero),
% 0.89/0.82 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.89/0.82 tff(306,plain,
% 0.89/0.82 (multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(zero, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[292])).
% 0.89/0.82 tff(307,plain,
% 0.89/0.82 (multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))),
% 0.89/0.82 inference(transitivity,[status(thm)],[306, 305, 296, 295, 286, 294, 290, 246, 249])).
% 0.89/0.82 tff(308,plain,
% 0.89/0.82 (addition(multiplication(one, star(one)), one) = addition(star(one), one)),
% 0.89/0.82 inference(symmetry,[status(thm)],[76])).
% 0.89/0.82 tff(309,plain,
% 0.89/0.82 (star(one) = addition(one, multiplication(one, star(one)))),
% 0.89/0.82 inference(symmetry,[status(thm)],[29])).
% 0.89/0.82 tff(310,plain,
% 0.89/0.82 (star(one) = one),
% 0.89/0.82 inference(transitivity,[status(thm)],[309, 74, 308, 125])).
% 0.89/0.82 tff(311,plain,
% 0.89/0.82 (strong_iteration(star(one)) = strong_iteration(one)),
% 0.89/0.82 inference(monotonicity,[status(thm)],[310])).
% 0.89/0.82 tff(312,plain,
% 0.89/0.82 (multiplication(strong_iteration(star(one)), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[311, 307])).
% 0.89/0.82 tff(313,plain,
% 0.89/0.82 (strong_iteration(one) = strong_iteration(star(one))),
% 0.89/0.82 inference(symmetry,[status(thm)],[311])).
% 0.89/0.82 tff(314,plain,
% 0.89/0.82 (addition(multiplication(one, strong_iteration(one)), one) = strong_iteration(star(one))),
% 0.89/0.82 inference(transitivity,[status(thm)],[142, 313])).
% 0.89/0.82 tff(315,plain,
% 0.89/0.82 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(strong_iteration(star(one)), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[314])).
% 0.89/0.82 tff(316,plain,
% 0.89/0.82 (^[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)))),
% 0.89/0.82 inference(bind,[status(th)],[])).
% 0.89/0.82 tff(317,plain,
% 0.89/0.82 (![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))),
% 0.89/0.82 inference(quant_intro,[status(thm)],[316])).
% 0.89/0.82 tff(318,plain,
% 0.89/0.82 (![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))),
% 0.89/0.82 inference(rewrite,[status(thm)],[])).
% 0.89/0.82 tff(319,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.89/0.82 tff(320,plain,
% 0.89/0.82 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.89/0.82 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.89/0.82 tff(321,plain,(
% 0.89/0.82 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.89/0.82 inference(skolemize,[status(sab)],[320])).
% 0.89/0.82 tff(322,plain,
% 0.89/0.82 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.89/0.82 inference(modus_ponens,[status(thm)],[321, 317])).
% 0.89/0.82 tff(323,plain,
% 0.89/0.82 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.89/0.82 inference(quant_inst,[status(thm)],[])).
% 0.89/0.82 tff(324,plain,
% 0.89/0.82 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.82 inference(unit_resolution,[status(thm)],[323, 322])).
% 0.89/0.82 tff(325,plain,
% 0.89/0.82 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.89/0.82 inference(symmetry,[status(thm)],[324])).
% 0.89/0.82 tff(326,plain,
% 0.89/0.82 (multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[142])).
% 0.89/0.82 tff(327,plain,
% 0.89/0.82 (multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.89/0.82 inference(symmetry,[status(thm)],[326])).
% 0.89/0.82 tff(328,plain,
% 0.89/0.82 (multiplication(strong_iteration(one), zero) = multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.89/0.82 inference(symmetry,[status(thm)],[293])).
% 0.89/0.82 tff(329,plain,
% 0.89/0.82 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.89/0.82 inference(transitivity,[status(thm)],[50, 40, 328, 327])).
% 0.89/0.82 tff(330,plain,
% 0.89/0.82 (multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[329])).
% 0.89/0.82 tff(331,plain,
% 0.89/0.82 (addition(addition(one, zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(addition(one, one), zero), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.89/0.82 inference(symmetry,[status(thm)],[165])).
% 0.89/0.82 tff(332,plain,
% 0.89/0.82 (addition(addition(one, one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(one, addition(zero, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))))),
% 0.89/0.82 inference(symmetry,[status(thm)],[159])).
% 0.89/0.82 tff(333,plain,
% 0.89/0.82 (addition(one, addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(one, one), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.89/0.82 inference(symmetry,[status(thm)],[141])).
% 0.89/0.82 tff(334,plain,
% 0.89/0.82 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(one, one), addition(one, one))) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one))),
% 0.89/0.82 inference(symmetry,[status(thm)],[137])).
% 0.89/0.82 tff(335,plain,
% 0.89/0.82 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)), addition(one, one)) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(one, one), addition(one, one)))),
% 0.89/0.82 inference(symmetry,[status(thm)],[134])).
% 0.89/0.82 tff(336,plain,
% 0.89/0.82 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), addition(one, one)) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, one)), addition(one, one))),
% 0.89/0.82 inference(symmetry,[status(thm)],[132])).
% 0.89/0.82 tff(337,plain,
% 0.89/0.82 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), multiplication(one, star(one))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), one), addition(one, one))),
% 0.89/0.82 inference(symmetry,[status(thm)],[128])).
% 0.89/0.82 tff(338,plain,
% 0.89/0.82 (addition(multiplication(strong_iteration(one), zero), star(one)) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(one, multiplication(one, star(one))))),
% 0.89/0.82 inference(symmetry,[status(thm)],[52])).
% 0.89/0.82 tff(339,plain,
% 0.89/0.82 (strong_iteration(one) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.89/0.82 inference(transitivity,[status(thm)],[9, 19, 338, 61, 337, 336, 335, 334, 131, 139, 333, 332, 161, 331, 232])).
% 0.89/0.82 tff(340,plain,
% 0.89/0.82 (multiplication(strong_iteration(one), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[339])).
% 0.89/0.82 tff(341,plain,
% 0.89/0.82 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), star(one)) = addition(multiplication(strong_iteration(one), zero), star(one))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[51])).
% 0.89/0.82 tff(342,plain,
% 0.89/0.82 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), star(one)) = strong_iteration(one)),
% 0.89/0.82 inference(transitivity,[status(thm)],[341, 20, 10])).
% 0.89/0.82 tff(343,plain,
% 0.89/0.82 (multiplication(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), star(one)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(strong_iteration(one), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[342])).
% 0.89/0.82 tff(344,plain,
% 0.89/0.82 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), star(one)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = addition(multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)), multiplication(star(one), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))))),
% 0.89/0.82 inference(quant_inst,[status(thm)],[])).
% 0.89/0.82 tff(345,plain,
% 0.89/0.82 (multiplication(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), star(one)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = addition(multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)), multiplication(star(one), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.89/0.82 inference(unit_resolution,[status(thm)],[344, 47])).
% 0.89/0.82 tff(346,plain,
% 0.89/0.82 (addition(multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)), multiplication(star(one), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), star(one)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.82 inference(symmetry,[status(thm)],[345])).
% 0.89/0.82 tff(347,plain,
% 0.89/0.82 (multiplication(star(one), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(one, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[310])).
% 0.89/0.82 tff(348,plain,
% 0.89/0.82 (multiplication(one, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(star(one), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.82 inference(symmetry,[status(thm)],[347])).
% 0.89/0.82 tff(349,plain,
% 0.89/0.82 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.82 inference(quant_inst,[status(thm)],[])).
% 0.89/0.82 tff(350,plain,
% 0.89/0.82 (multiplication(one, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)),
% 0.89/0.82 inference(unit_resolution,[status(thm)],[349, 69])).
% 0.89/0.82 tff(351,plain,
% 0.89/0.82 (addition(addition(X0!0, multiplication(one, strong_iteration(one))), one) = multiplication(one, addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.82 inference(symmetry,[status(thm)],[350])).
% 0.89/0.82 tff(352,plain,
% 0.89/0.82 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!0, addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.82 inference(quant_inst,[status(thm)],[])).
% 0.89/0.82 tff(353,plain,
% 0.89/0.82 (addition(X0!0, addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)),
% 0.89/0.82 inference(unit_resolution,[status(thm)],[352, 59])).
% 0.89/0.82 tff(354,plain,
% 0.89/0.82 (addition(X0!0, addition(multiplication(one, strong_iteration(one)), one)) = addition(X0!0, strong_iteration(one))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[142])).
% 0.89/0.82 tff(355,plain,
% 0.89/0.82 (addition(X0!0, strong_iteration(one)) = addition(X0!0, addition(multiplication(one, strong_iteration(one)), one))),
% 0.89/0.82 inference(symmetry,[status(thm)],[354])).
% 0.89/0.82 tff(356,plain,
% 0.89/0.82 (multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), zero) = multiplication(strong_iteration(one), zero)),
% 0.89/0.82 inference(monotonicity,[status(thm)],[10])).
% 0.89/0.82 tff(357,plain,
% 0.89/0.82 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), zero) = addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)))),
% 0.89/0.82 inference(quant_inst,[status(thm)],[])).
% 0.89/0.82 tff(358,plain,
% 0.89/0.82 (multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), zero) = addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero))),
% 0.89/0.82 inference(unit_resolution,[status(thm)],[357, 47])).
% 0.89/0.82 tff(359,plain,
% 0.89/0.82 (addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)) = multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), zero)),
% 0.89/0.82 inference(symmetry,[status(thm)],[358])).
% 0.89/0.82 tff(360,plain,
% 0.89/0.82 (addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)) = multiplication(strong_iteration(one), zero)),
% 0.89/0.82 inference(transitivity,[status(thm)],[359, 356])).
% 0.89/0.82 tff(361,plain,
% 0.89/0.82 (addition(addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)), star(one)) = addition(multiplication(strong_iteration(one), zero), star(one))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[360])).
% 0.89/0.82 tff(362,plain,
% 0.89/0.82 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(one), zero), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))) = addition(addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)), star(one)))),
% 0.89/0.82 inference(quant_inst,[status(thm)],[])).
% 0.89/0.82 tff(363,plain,
% 0.89/0.82 (addition(multiplication(star(one), zero), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))) = addition(addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)), star(one))),
% 0.89/0.82 inference(unit_resolution,[status(thm)],[362, 59])).
% 0.89/0.82 tff(364,plain,
% 0.89/0.82 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))) = addition(multiplication(star(one), zero), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[251])).
% 0.89/0.82 tff(365,plain,
% 0.89/0.82 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))) = strong_iteration(one)),
% 0.89/0.82 inference(transitivity,[status(thm)],[364, 363, 361, 20, 10])).
% 0.89/0.82 tff(366,plain,
% 0.89/0.82 (addition(X0!0, addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))) = addition(X0!0, strong_iteration(one))),
% 0.89/0.82 inference(monotonicity,[status(thm)],[365])).
% 0.89/0.82 tff(367,plain,
% 0.89/0.82 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!0, addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))) = addition(addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))))),
% 0.89/0.82 inference(quant_inst,[status(thm)],[])).
% 0.89/0.82 tff(368,plain,
% 0.89/0.82 (addition(X0!0, addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))) = addition(addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))),
% 0.89/0.82 inference(unit_resolution,[status(thm)],[367, 59])).
% 0.89/0.82 tff(369,plain,
% 0.89/0.82 (addition(addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))) = addition(X0!0, addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))))),
% 0.89/0.82 inference(symmetry,[status(thm)],[368])).
% 0.89/0.82 tff(370,plain,
% 0.89/0.82 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, zero) = zero)),
% 0.89/0.82 inference(quant_inst,[status(thm)],[])).
% 0.89/0.82 tff(371,plain,
% 0.89/0.82 (multiplication(zero, zero) = zero),
% 0.89/0.82 inference(unit_resolution,[status(thm)],[370, 303])).
% 0.89/0.82 tff(372,plain,
% 0.89/0.82 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, zero)) = multiplication(strong_iteration(one), zero)),
% 0.89/0.82 inference(monotonicity,[status(thm)],[142, 371])).
% 0.89/0.82 tff(373,plain,
% 0.89/0.82 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, zero)) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero))),
% 0.89/0.82 inference(quant_inst,[status(thm)],[])).
% 0.89/0.82 tff(374,plain,
% 0.89/0.82 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, zero)) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero)),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[373, 322])).
% 0.89/0.83 tff(375,plain,
% 0.89/0.83 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, zero))),
% 0.89/0.83 inference(symmetry,[status(thm)],[374])).
% 0.89/0.83 tff(376,plain,
% 0.89/0.83 (multiplication(multiplication(strong_iteration(one), zero), zero) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero)),
% 0.89/0.83 inference(monotonicity,[status(thm)],[39])).
% 0.89/0.83 tff(377,plain,
% 0.89/0.83 (multiplication(multiplication(strong_iteration(one), zero), zero) = multiplication(strong_iteration(one), zero)),
% 0.89/0.83 inference(transitivity,[status(thm)],[376, 375, 372])).
% 0.89/0.83 tff(378,plain,
% 0.89/0.83 (addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)) = addition(multiplication(strong_iteration(one), zero), star(one))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[377])).
% 0.89/0.83 tff(379,plain,
% 0.89/0.83 (addition(multiplication(strong_iteration(one), zero), star(one)) = addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))),
% 0.89/0.83 inference(symmetry,[status(thm)],[378])).
% 0.89/0.83 tff(380,plain,
% 0.89/0.83 (addition(multiplication(one, strong_iteration(one)), one) = addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one))),
% 0.89/0.83 inference(transitivity,[status(thm)],[142, 9, 19, 379])).
% 0.89/0.83 tff(381,plain,
% 0.89/0.83 (addition(addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(multiplication(strong_iteration(one), zero), zero), star(one)))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[380])).
% 0.89/0.83 tff(382,plain,
% 0.89/0.83 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(383,plain,
% 0.89/0.83 (addition(addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[382, 17])).
% 0.89/0.83 tff(384,plain,
% 0.89/0.83 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(multiplication(one, strong_iteration(one)), one))),
% 0.89/0.83 inference(symmetry,[status(thm)],[383])).
% 0.89/0.83 tff(385,plain,
% 0.89/0.83 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = multiplication(star(one), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.83 inference(transitivity,[status(thm)],[384, 381, 369, 366, 355, 353, 351, 348])).
% 0.89/0.83 tff(386,plain,
% 0.89/0.83 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)) = multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.83 inference(symmetry,[status(thm)],[330])).
% 0.89/0.83 tff(387,plain,
% 0.89/0.83 (multiplication(strong_iteration(star(one)), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.89/0.83 inference(symmetry,[status(thm)],[315])).
% 0.89/0.83 tff(388,plain,
% 0.89/0.83 (multiplication(strong_iteration(one), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = multiplication(strong_iteration(star(one)), multiplication(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.89/0.83 inference(symmetry,[status(thm)],[312])).
% 0.89/0.83 tff(389,plain,
% 0.89/0.83 (addition(multiplication(one, strong_iteration(one)), one) = multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one))),
% 0.89/0.83 inference(transitivity,[status(thm)],[142, 9, 19, 338, 61, 337, 336, 335, 334, 131, 139, 333, 332, 161, 331, 232, 50, 40, 328, 388, 387, 324, 386])).
% 0.89/0.83 tff(390,plain,
% 0.89/0.83 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))) = addition(multiplication(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)), multiplication(star(one), addition(addition(X0!0, multiplication(one, strong_iteration(one))), one)))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[389, 385])).
% 0.89/0.83 tff(391,plain,
% 0.89/0.83 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(one, strong_iteration(one)), one), addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(392,plain,
% 0.89/0.83 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[391, 59])).
% 0.89/0.83 tff(393,plain,
% 0.89/0.83 (addition(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(addition(multiplication(one, strong_iteration(one)), one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))))),
% 0.89/0.83 inference(symmetry,[status(thm)],[392])).
% 0.89/0.83 tff(394,plain,
% 0.89/0.83 (multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)) = multiplication(one, strong_iteration(one))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[96, 142])).
% 0.89/0.83 tff(395,plain,
% 0.89/0.83 (multiplication(one, strong_iteration(one)) = multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one))),
% 0.89/0.83 inference(symmetry,[status(thm)],[394])).
% 0.89/0.83 tff(396,plain,
% 0.89/0.83 (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = multiplication(one, strong_iteration(one))),
% 0.89/0.83 inference(symmetry,[status(thm)],[145])).
% 0.89/0.83 tff(397,plain,
% 0.89/0.83 (addition(multiplication(one, strong_iteration(one)), one) = multiplication(one, addition(multiplication(one, strong_iteration(one)), one))),
% 0.89/0.83 inference(symmetry,[status(thm)],[144])).
% 0.89/0.83 tff(398,plain,
% 0.89/0.83 (addition(multiplication(one, strong_iteration(one)), one) = multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one))),
% 0.89/0.83 inference(transitivity,[status(thm)],[397, 396, 395])).
% 0.89/0.83 tff(399,plain,
% 0.89/0.83 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[398, 398])).
% 0.89/0.83 tff(400,plain,
% 0.89/0.83 (addition(multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one))) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one))),
% 0.89/0.83 inference(symmetry,[status(thm)],[399])).
% 0.89/0.83 tff(401,plain,
% 0.89/0.83 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(one, one), addition(one, one)), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one))))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(402,plain,
% 0.89/0.83 (multiplication(addition(addition(one, one), addition(one, one)), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)), multiplication(addition(one, one), addition(multiplication(one, strong_iteration(one)), one)))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[401, 47])).
% 0.89/0.83 tff(403,plain,
% 0.89/0.83 (addition(addition(one, one), addition(one, one)) = one),
% 0.89/0.83 inference(transitivity,[status(thm)],[135, 96])).
% 0.89/0.83 tff(404,plain,
% 0.89/0.83 (multiplication(addition(addition(one, one), addition(one, one)), addition(multiplication(one, strong_iteration(one)), one)) = multiplication(one, strong_iteration(one))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[403, 142])).
% 0.89/0.83 tff(405,plain,
% 0.89/0.83 (multiplication(one, strong_iteration(one)) = multiplication(addition(addition(one, one), addition(one, one)), addition(multiplication(one, strong_iteration(one)), one))),
% 0.89/0.83 inference(symmetry,[status(thm)],[404])).
% 0.89/0.83 tff(406,plain,
% 0.89/0.83 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), star(one)) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one))),
% 0.89/0.83 inference(transitivity,[status(thm)],[341, 20, 10, 38, 397, 396, 405, 402, 400])).
% 0.89/0.83 tff(407,plain,
% 0.89/0.83 (addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), star(one)), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[406])).
% 0.89/0.83 tff(408,plain,
% 0.89/0.83 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(star(one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), star(one)), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(409,plain,
% 0.89/0.83 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(star(one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))) = addition(addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), star(one)), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[408, 59])).
% 0.89/0.83 tff(410,plain,
% 0.89/0.83 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(411,plain,
% 0.89/0.83 (addition(star(one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))) = addition(addition(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[410, 59])).
% 0.89/0.83 tff(412,plain,
% 0.89/0.83 (addition(addition(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(star(one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.89/0.83 inference(symmetry,[status(thm)],[411])).
% 0.89/0.83 tff(413,plain,
% 0.89/0.83 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(star(one), X0!0)))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(414,plain,
% 0.89/0.83 (addition(addition(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(star(one), X0!0))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[413, 17])).
% 0.89/0.83 tff(415,plain,
% 0.89/0.83 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(star(one), X0!0)) = addition(addition(star(one), X0!0), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.89/0.83 inference(symmetry,[status(thm)],[414])).
% 0.89/0.83 tff(416,plain,
% 0.89/0.83 (addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(star(one), X0!0)) = addition(star(one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))))),
% 0.89/0.83 inference(transitivity,[status(thm)],[415, 412])).
% 0.89/0.83 tff(417,plain,
% 0.89/0.83 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.89/0.83 inference(transitivity,[status(thm)],[375, 372, 39, 49])).
% 0.89/0.83 tff(418,plain,
% 0.89/0.83 (addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(star(one), X0!0))) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(star(one), addition(X0!0, addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[417, 416])).
% 0.89/0.83 tff(419,plain,
% 0.89/0.83 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(star(one), X0!0))) = addition(addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(star(one), X0!0)))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(420,plain,
% 0.89/0.83 (addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(star(one), X0!0))) = addition(addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(star(one), X0!0))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[419, 59])).
% 0.89/0.83 tff(421,plain,
% 0.89/0.83 (addition(addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(star(one), X0!0)) = addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), addition(addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)), addition(star(one), X0!0)))),
% 0.89/0.83 inference(symmetry,[status(thm)],[420])).
% 0.89/0.83 tff(422,plain,
% 0.89/0.83 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero) = multiplication(multiplication(strong_iteration(one), zero), zero)),
% 0.89/0.83 inference(symmetry,[status(thm)],[376])).
% 0.89/0.83 tff(423,plain,
% 0.89/0.83 (addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))) = addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(star(one), zero))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[422, 251])).
% 0.89/0.83 tff(424,plain,
% 0.89/0.83 (addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(star(one), zero)) = addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.89/0.83 inference(symmetry,[status(thm)],[423])).
% 0.89/0.83 tff(425,plain,
% 0.89/0.83 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)) = addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(star(one), zero)))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(426,plain,
% 0.89/0.83 (addition(multiplication(star(one), zero), multiplication(multiplication(strong_iteration(one), zero), zero)) = addition(multiplication(multiplication(strong_iteration(one), zero), zero), multiplication(star(one), zero))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[425, 17])).
% 0.89/0.83 tff(427,plain,
% 0.89/0.83 (multiplication(strong_iteration(one), zero) = multiplication(addition(star(one), multiplication(strong_iteration(one), zero)), zero)),
% 0.89/0.83 inference(symmetry,[status(thm)],[356])).
% 0.89/0.83 tff(428,plain,
% 0.89/0.83 (addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)) = addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero)))),
% 0.89/0.83 inference(transitivity,[status(thm)],[50, 40, 427, 358, 426, 424])).
% 0.89/0.83 tff(429,plain,
% 0.89/0.83 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(star(one), X0!0)) = addition(addition(multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), zero), addition(multiplication(one, zero), multiplication(multiplication(star(one), one), zero))), addition(star(one), X0!0))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[428])).
% 0.89/0.83 tff(430,plain,
% 0.89/0.83 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!0, star(one)) = addition(star(one), X0!0))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(431,plain,
% 0.89/0.83 (addition(X0!0, star(one)) = addition(star(one), X0!0)),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[430, 17])).
% 0.89/0.83 tff(432,plain,
% 0.89/0.83 (addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(X0!0, star(one))) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(star(one), X0!0))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[431])).
% 0.89/0.83 tff(433,plain,
% 0.89/0.83 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(X0!0, star(one)), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(X0!0, star(one))))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(434,plain,
% 0.89/0.83 (addition(addition(X0!0, star(one)), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))) = addition(addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)), addition(X0!0, star(one)))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[433, 17])).
% 0.89/0.83 tff(435,plain,
% 0.89/0.83 (multiplication(strong_iteration(one), zero) = addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero))),
% 0.89/0.83 inference(transitivity,[status(thm)],[39, 49])).
% 0.89/0.83 tff(436,plain,
% 0.89/0.83 (addition(addition(X0!0, star(one)), multiplication(strong_iteration(one), zero)) = addition(addition(X0!0, star(one)), addition(multiplication(multiplication(one, strong_iteration(one)), zero), multiplication(one, zero)))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[435])).
% 0.89/0.83 tff(437,plain,
% 0.89/0.83 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!0, addition(star(one), multiplication(strong_iteration(one), zero))) = addition(addition(X0!0, star(one)), multiplication(strong_iteration(one), zero)))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(438,plain,
% 0.89/0.83 (addition(X0!0, addition(star(one), multiplication(strong_iteration(one), zero))) = addition(addition(X0!0, star(one)), multiplication(strong_iteration(one), zero))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[437, 59])).
% 0.89/0.83 tff(439,plain,
% 0.89/0.83 (addition(X0!0, strong_iteration(one)) = addition(X0!0, addition(star(one), multiplication(strong_iteration(one), zero)))),
% 0.89/0.83 inference(monotonicity,[status(thm)],[9])).
% 0.89/0.83 tff(440,plain,
% 0.89/0.83 (addition(X0!0, strong_iteration(one)) = strong_iteration(one)),
% 0.89/0.83 inference(transitivity,[status(thm)],[439, 438, 436, 434, 432, 429, 421, 418, 409, 407, 393, 390, 346, 343, 340, 330, 325, 315, 312, 293, 39, 49, 233, 165, 162, 159, 141, 140, 130, 137, 134, 132, 128, 62, 52, 20, 10])).
% 0.89/0.83 tff(441,plain,
% 0.89/0.83 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!0, strong_iteration(one)) <=> (addition(X0!0, strong_iteration(one)) = strong_iteration(one)))),
% 0.89/0.83 inference(quant_inst,[status(thm)],[])).
% 0.89/0.83 tff(442,plain,
% 0.89/0.83 (leq(X0!0, strong_iteration(one)) <=> (addition(X0!0, strong_iteration(one)) = strong_iteration(one))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[441, 83])).
% 0.89/0.83 tff(443,plain,
% 0.89/0.83 ((~![X0: $i] : leq(X0, strong_iteration(one))) <=> (~![X0: $i] : leq(X0, strong_iteration(one)))),
% 0.89/0.83 inference(rewrite,[status(thm)],[])).
% 0.89/0.83 tff(444,axiom,(~![X0: $i] : leq(X0, strong_iteration(one))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.89/0.83 tff(445,plain,
% 0.89/0.83 (~![X0: $i] : leq(X0, strong_iteration(one))),
% 0.89/0.83 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.89/0.83 tff(446,plain,
% 0.89/0.83 (~![X0: $i] : leq(X0, strong_iteration(one))),
% 0.89/0.83 inference(modus_ponens,[status(thm)],[445, 443])).
% 0.89/0.83 tff(447,plain,
% 0.89/0.83 (~![X0: $i] : leq(X0, strong_iteration(one))),
% 0.89/0.83 inference(modus_ponens,[status(thm)],[446, 443])).
% 0.89/0.83 tff(448,plain,
% 0.89/0.83 (~![X0: $i] : leq(X0, strong_iteration(one))),
% 0.89/0.83 inference(modus_ponens,[status(thm)],[447, 443])).
% 0.89/0.83 tff(449,plain,
% 0.89/0.83 (~![X0: $i] : leq(X0, strong_iteration(one))),
% 0.89/0.83 inference(modus_ponens,[status(thm)],[448, 443])).
% 0.89/0.83 tff(450,plain,
% 0.89/0.83 (~![X0: $i] : leq(X0, strong_iteration(one))),
% 0.89/0.83 inference(modus_ponens,[status(thm)],[449, 443])).
% 0.89/0.83 tff(451,plain,
% 0.89/0.83 (~![X0: $i] : leq(X0, strong_iteration(one))),
% 0.89/0.83 inference(modus_ponens,[status(thm)],[450, 443])).
% 0.89/0.83 tff(452,plain,(
% 0.89/0.83 ~leq(X0!0, strong_iteration(one))),
% 0.89/0.83 inference(skolemize,[status(sab)],[451])).
% 0.89/0.83 tff(453,plain,
% 0.89/0.83 ((~(leq(X0!0, strong_iteration(one)) <=> (addition(X0!0, strong_iteration(one)) = strong_iteration(one)))) | leq(X0!0, strong_iteration(one)) | (~(addition(X0!0, strong_iteration(one)) = strong_iteration(one)))),
% 0.89/0.83 inference(tautology,[status(thm)],[])).
% 0.89/0.83 tff(454,plain,
% 0.89/0.83 ((~(leq(X0!0, strong_iteration(one)) <=> (addition(X0!0, strong_iteration(one)) = strong_iteration(one)))) | (~(addition(X0!0, strong_iteration(one)) = strong_iteration(one)))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[453, 452])).
% 0.89/0.83 tff(455,plain,
% 0.89/0.83 (~(addition(X0!0, strong_iteration(one)) = strong_iteration(one))),
% 0.89/0.83 inference(unit_resolution,[status(thm)],[454, 442])).
% 0.89/0.84 tff(456,plain,
% 0.89/0.84 ($false),
% 0.89/0.84 inference(unit_resolution,[status(thm)],[455, 440])).
% 0.89/0.84 % SZS output end Proof
%------------------------------------------------------------------------------