TSTP Solution File: KLE141+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE141+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:24:18 EDT 2022
% Result : Theorem 2.77s 2.02s
% Output : Proof 2.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KLE141+2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 08:46:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 2.77/2.02 % SZS status Theorem
% 2.77/2.02 % SZS output start Proof
% 2.77/2.02 tff(addition_type, type, (
% 2.77/2.02 addition: ( $i * $i ) > $i)).
% 2.77/2.02 tff(one_type, type, (
% 2.77/2.02 one: $i)).
% 2.77/2.02 tff(multiplication_type, type, (
% 2.77/2.02 multiplication: ( $i * $i ) > $i)).
% 2.77/2.02 tff(strong_iteration_type, type, (
% 2.77/2.02 strong_iteration: $i > $i)).
% 2.77/2.02 tff(tptp_fun_X0_0_type, type, (
% 2.77/2.02 tptp_fun_X0_0: $i)).
% 2.77/2.02 tff(zero_type, type, (
% 2.77/2.02 zero: $i)).
% 2.77/2.02 tff(star_type, type, (
% 2.77/2.02 star: $i > $i)).
% 2.77/2.02 tff(leq_type, type, (
% 2.77/2.02 leq: ( $i * $i ) > $o)).
% 2.77/2.02 tff(1,plain,
% 2.77/2.02 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 2.77/2.02 inference(bind,[status(th)],[])).
% 2.77/2.02 tff(2,plain,
% 2.77/2.02 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 2.77/2.02 inference(quant_intro,[status(thm)],[1])).
% 2.77/2.02 tff(3,plain,
% 2.77/2.02 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 2.77/2.02 inference(rewrite,[status(thm)],[])).
% 2.77/2.02 tff(4,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 2.77/2.02 tff(5,plain,
% 2.77/2.02 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.77/2.02 tff(6,plain,(
% 2.77/2.02 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 2.77/2.02 inference(skolemize,[status(sab)],[5])).
% 2.77/2.02 tff(7,plain,
% 2.77/2.02 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.77/2.02 tff(8,plain,
% 2.77/2.02 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(one) = addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(9,plain,
% 2.77/2.02 (strong_iteration(one) = addition(multiplication(one, strong_iteration(one)), one)),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[8, 7])).
% 2.77/2.02 tff(10,plain,
% 2.77/2.02 (^[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))))),
% 2.77/2.02 inference(bind,[status(th)],[])).
% 2.77/2.02 tff(11,plain,
% 2.77/2.02 (![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)))),
% 2.77/2.02 inference(quant_intro,[status(thm)],[10])).
% 2.77/2.02 tff(12,plain,
% 2.77/2.02 (![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)))),
% 2.77/2.02 inference(rewrite,[status(thm)],[])).
% 2.77/2.02 tff(13,axiom,(![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','isolation')).
% 2.77/2.02 tff(14,plain,
% 2.77/2.02 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[13, 12])).
% 2.77/2.02 tff(15,plain,(
% 2.77/2.02 ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 2.77/2.02 inference(skolemize,[status(sab)],[14])).
% 2.77/2.02 tff(16,plain,
% 2.77/2.02 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[15, 11])).
% 2.77/2.02 tff(17,plain,
% 2.77/2.02 ((~![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))) | (strong_iteration(one) = addition(star(one), multiplication(strong_iteration(one), zero)))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(18,plain,
% 2.77/2.02 (strong_iteration(one) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[17, 16])).
% 2.77/2.02 tff(19,plain,
% 2.77/2.02 (addition(star(one), multiplication(strong_iteration(one), zero)) = strong_iteration(one)),
% 2.77/2.02 inference(symmetry,[status(thm)],[18])).
% 2.77/2.02 tff(20,plain,
% 2.77/2.02 (addition(multiplication(one, strong_iteration(one)), one) = strong_iteration(one)),
% 2.77/2.02 inference(symmetry,[status(thm)],[9])).
% 2.77/2.02 tff(21,plain,
% 2.77/2.02 (multiplication(addition(multiplication(one, strong_iteration(one)), one), zero) = multiplication(strong_iteration(one), zero)),
% 2.77/2.02 inference(monotonicity,[status(thm)],[20])).
% 2.77/2.02 tff(22,plain,
% 2.77/2.02 (multiplication(strong_iteration(one), zero) = multiplication(addition(multiplication(one, strong_iteration(one)), one), zero)),
% 2.77/2.02 inference(symmetry,[status(thm)],[21])).
% 2.77/2.02 tff(23,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), multiplication(one, zero)) = addition(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), multiplication(one, zero))),
% 2.77/2.02 inference(monotonicity,[status(thm)],[22])).
% 2.77/2.02 tff(24,plain,
% 2.77/2.02 (addition(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), multiplication(one, zero)) = addition(multiplication(strong_iteration(one), zero), multiplication(one, zero))),
% 2.77/2.02 inference(symmetry,[status(thm)],[23])).
% 2.77/2.02 tff(25,plain,
% 2.77/2.02 (^[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))))),
% 2.77/2.02 inference(bind,[status(th)],[])).
% 2.77/2.02 tff(26,plain,
% 2.77/2.02 (![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)))),
% 2.77/2.02 inference(quant_intro,[status(thm)],[25])).
% 2.77/2.02 tff(27,plain,
% 2.77/2.02 (![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)))),
% 2.77/2.02 inference(rewrite,[status(thm)],[])).
% 2.77/2.02 tff(28,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity2')).
% 2.77/2.02 tff(29,plain,
% 2.77/2.02 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[28, 27])).
% 2.77/2.02 tff(30,plain,(
% 2.77/2.02 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 2.77/2.02 inference(skolemize,[status(sab)],[29])).
% 2.77/2.02 tff(31,plain,
% 2.77/2.02 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[30, 26])).
% 2.77/2.02 tff(32,plain,
% 2.77/2.02 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(one, strong_iteration(one)), one), one), zero) = addition(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), multiplication(one, zero)))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(33,plain,
% 2.77/2.02 (multiplication(addition(addition(multiplication(one, strong_iteration(one)), one), one), zero) = addition(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), multiplication(one, zero))),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[32, 31])).
% 2.77/2.02 tff(34,plain,
% 2.77/2.02 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 2.77/2.02 inference(bind,[status(th)],[])).
% 2.77/2.02 tff(35,plain,
% 2.77/2.02 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 2.77/2.02 inference(quant_intro,[status(thm)],[34])).
% 2.77/2.02 tff(36,plain,
% 2.77/2.02 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 2.77/2.02 inference(rewrite,[status(thm)],[])).
% 2.77/2.02 tff(37,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 2.77/2.02 tff(38,plain,
% 2.77/2.02 (![A: $i] : (multiplication(one, A) = A)),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[37, 36])).
% 2.77/2.02 tff(39,plain,(
% 2.77/2.02 ![A: $i] : (multiplication(one, A) = A)),
% 2.77/2.02 inference(skolemize,[status(sab)],[38])).
% 2.77/2.02 tff(40,plain,
% 2.77/2.02 (![A: $i] : (multiplication(one, A) = A)),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[39, 35])).
% 2.77/2.02 tff(41,plain,
% 2.77/2.02 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, strong_iteration(one)) = strong_iteration(one))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(42,plain,
% 2.77/2.02 (multiplication(one, strong_iteration(one)) = strong_iteration(one)),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[41, 40])).
% 2.77/2.02 tff(43,plain,
% 2.77/2.02 (strong_iteration(one) = multiplication(one, strong_iteration(one))),
% 2.77/2.02 inference(symmetry,[status(thm)],[42])).
% 2.77/2.02 tff(44,plain,
% 2.77/2.02 (addition(multiplication(one, strong_iteration(one)), one) = multiplication(one, strong_iteration(one))),
% 2.77/2.02 inference(transitivity,[status(thm)],[20, 43])).
% 2.77/2.02 tff(45,plain,
% 2.77/2.02 (addition(addition(multiplication(one, strong_iteration(one)), one), one) = addition(multiplication(one, strong_iteration(one)), one)),
% 2.77/2.02 inference(monotonicity,[status(thm)],[44])).
% 2.77/2.02 tff(46,plain,
% 2.77/2.02 (addition(addition(multiplication(one, strong_iteration(one)), one), one) = strong_iteration(one)),
% 2.77/2.02 inference(transitivity,[status(thm)],[45, 20])).
% 2.77/2.02 tff(47,plain,
% 2.77/2.02 (multiplication(addition(addition(multiplication(one, strong_iteration(one)), one), one), zero) = multiplication(strong_iteration(one), zero)),
% 2.77/2.02 inference(monotonicity,[status(thm)],[46])).
% 2.77/2.02 tff(48,plain,
% 2.77/2.02 (multiplication(strong_iteration(one), zero) = multiplication(addition(addition(multiplication(one, strong_iteration(one)), one), one), zero)),
% 2.77/2.02 inference(symmetry,[status(thm)],[47])).
% 2.77/2.02 tff(49,plain,
% 2.77/2.02 (multiplication(strong_iteration(one), zero) = addition(multiplication(strong_iteration(one), zero), multiplication(one, zero))),
% 2.77/2.02 inference(transitivity,[status(thm)],[48, 33, 24])).
% 2.77/2.02 tff(50,plain,
% 2.77/2.02 (addition(star(one), multiplication(strong_iteration(one), zero)) = addition(star(one), addition(multiplication(strong_iteration(one), zero), multiplication(one, zero)))),
% 2.77/2.02 inference(monotonicity,[status(thm)],[49])).
% 2.77/2.02 tff(51,plain,
% 2.77/2.02 (addition(star(one), addition(multiplication(strong_iteration(one), zero), multiplication(one, zero))) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 2.77/2.02 inference(symmetry,[status(thm)],[50])).
% 2.77/2.02 tff(52,plain,
% 2.77/2.02 (^[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)))),
% 2.77/2.02 inference(bind,[status(th)],[])).
% 2.77/2.02 tff(53,plain,
% 2.77/2.02 (![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))),
% 2.77/2.02 inference(quant_intro,[status(thm)],[52])).
% 2.77/2.02 tff(54,plain,
% 2.77/2.02 (![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))),
% 2.77/2.02 inference(rewrite,[status(thm)],[])).
% 2.77/2.02 tff(55,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_associativity')).
% 2.77/2.02 tff(56,plain,
% 2.77/2.02 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[55, 54])).
% 2.77/2.02 tff(57,plain,(
% 2.77/2.02 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 2.77/2.02 inference(skolemize,[status(sab)],[56])).
% 2.77/2.02 tff(58,plain,
% 2.77/2.02 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[57, 53])).
% 2.77/2.02 tff(59,plain,
% 2.77/2.02 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(star(one), addition(multiplication(strong_iteration(one), zero), multiplication(one, zero))) = addition(addition(star(one), multiplication(strong_iteration(one), zero)), multiplication(one, zero)))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(60,plain,
% 2.77/2.02 (addition(star(one), addition(multiplication(strong_iteration(one), zero), multiplication(one, zero))) = addition(addition(star(one), multiplication(strong_iteration(one), zero)), multiplication(one, zero))),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[59, 58])).
% 2.77/2.02 tff(61,plain,
% 2.77/2.02 (addition(addition(star(one), multiplication(strong_iteration(one), zero)), multiplication(one, zero)) = addition(star(one), addition(multiplication(strong_iteration(one), zero), multiplication(one, zero)))),
% 2.77/2.02 inference(symmetry,[status(thm)],[60])).
% 2.77/2.02 tff(62,plain,
% 2.77/2.02 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, zero) = zero)),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(63,plain,
% 2.77/2.02 (multiplication(one, zero) = zero),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[62, 40])).
% 2.77/2.02 tff(64,plain,
% 2.77/2.02 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 2.77/2.02 inference(bind,[status(th)],[])).
% 2.77/2.02 tff(65,plain,
% 2.77/2.02 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 2.77/2.02 inference(quant_intro,[status(thm)],[64])).
% 2.77/2.02 tff(66,plain,
% 2.77/2.02 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 2.77/2.02 inference(rewrite,[status(thm)],[])).
% 2.77/2.02 tff(67,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 2.77/2.02 tff(68,plain,
% 2.77/2.02 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[67, 66])).
% 2.77/2.02 tff(69,plain,(
% 2.77/2.02 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 2.77/2.02 inference(skolemize,[status(sab)],[68])).
% 2.77/2.02 tff(70,plain,
% 2.77/2.02 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[69, 65])).
% 2.77/2.02 tff(71,plain,
% 2.77/2.02 ((~![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)))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(72,plain,
% 2.77/2.02 (addition(star(one), multiplication(strong_iteration(one), zero)) = addition(multiplication(strong_iteration(one), zero), star(one))),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[71, 70])).
% 2.77/2.02 tff(73,plain,
% 2.77/2.02 (addition(addition(star(one), multiplication(strong_iteration(one), zero)), multiplication(one, zero)) = addition(addition(multiplication(strong_iteration(one), zero), star(one)), zero)),
% 2.77/2.02 inference(monotonicity,[status(thm)],[72, 63])).
% 2.77/2.02 tff(74,plain,
% 2.77/2.02 (addition(addition(multiplication(strong_iteration(one), zero), star(one)), zero) = addition(addition(star(one), multiplication(strong_iteration(one), zero)), multiplication(one, zero))),
% 2.77/2.02 inference(symmetry,[status(thm)],[73])).
% 2.77/2.02 tff(75,plain,
% 2.77/2.02 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(strong_iteration(one), zero), addition(star(one), zero)) = addition(addition(multiplication(strong_iteration(one), zero), star(one)), zero))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(76,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), addition(star(one), zero)) = addition(addition(multiplication(strong_iteration(one), zero), star(one)), zero)),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[75, 58])).
% 2.77/2.02 tff(77,plain,
% 2.77/2.02 (addition(multiplication(one, zero), star(one)) = addition(zero, star(one))),
% 2.77/2.02 inference(monotonicity,[status(thm)],[63])).
% 2.77/2.02 tff(78,plain,
% 2.77/2.02 (addition(zero, star(one)) = addition(multiplication(one, zero), star(one))),
% 2.77/2.02 inference(symmetry,[status(thm)],[77])).
% 2.77/2.02 tff(79,plain,
% 2.77/2.02 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, star(one)) = addition(star(one), zero))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(80,plain,
% 2.77/2.02 (addition(zero, star(one)) = addition(star(one), zero)),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[79, 70])).
% 2.77/2.02 tff(81,plain,
% 2.77/2.02 (addition(star(one), zero) = addition(zero, star(one))),
% 2.77/2.02 inference(symmetry,[status(thm)],[80])).
% 2.77/2.02 tff(82,plain,
% 2.77/2.02 (addition(star(one), zero) = addition(multiplication(one, zero), star(one))),
% 2.77/2.02 inference(transitivity,[status(thm)],[81, 78])).
% 2.77/2.02 tff(83,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), multiplication(strong_iteration(one), zero)) = addition(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), multiplication(addition(multiplication(one, strong_iteration(one)), one), zero))),
% 2.77/2.02 inference(monotonicity,[status(thm)],[22, 22])).
% 2.77/2.02 tff(84,plain,
% 2.77/2.02 (addition(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), multiplication(addition(multiplication(one, strong_iteration(one)), one), zero)) = addition(multiplication(strong_iteration(one), zero), multiplication(strong_iteration(one), zero))),
% 2.77/2.02 inference(symmetry,[status(thm)],[83])).
% 2.77/2.02 tff(85,plain,
% 2.77/2.02 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)), zero) = addition(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), multiplication(addition(multiplication(one, strong_iteration(one)), one), zero)))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(86,plain,
% 2.77/2.02 (multiplication(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)), zero) = addition(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), multiplication(addition(multiplication(one, strong_iteration(one)), one), zero))),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[85, 31])).
% 2.77/2.02 tff(87,plain,
% 2.77/2.02 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 2.77/2.02 inference(bind,[status(th)],[])).
% 2.77/2.02 tff(88,plain,
% 2.77/2.02 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 2.77/2.02 inference(quant_intro,[status(thm)],[87])).
% 2.77/2.02 tff(89,plain,
% 2.77/2.02 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 2.77/2.02 inference(rewrite,[status(thm)],[])).
% 2.77/2.02 tff(90,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 2.77/2.02 tff(91,plain,
% 2.77/2.02 (![A: $i] : (addition(A, A) = A)),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[90, 89])).
% 2.77/2.02 tff(92,plain,(
% 2.77/2.02 ![A: $i] : (addition(A, A) = A)),
% 2.77/2.02 inference(skolemize,[status(sab)],[91])).
% 2.77/2.02 tff(93,plain,
% 2.77/2.02 (![A: $i] : (addition(A, A) = A)),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[92, 88])).
% 2.77/2.02 tff(94,plain,
% 2.77/2.02 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(95,plain,
% 2.77/2.02 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[94, 93])).
% 2.77/2.02 tff(96,plain,
% 2.77/2.02 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) = strong_iteration(one)),
% 2.77/2.02 inference(transitivity,[status(thm)],[95, 20])).
% 2.77/2.02 tff(97,plain,
% 2.77/2.02 (multiplication(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)), zero) = multiplication(strong_iteration(one), zero)),
% 2.77/2.02 inference(monotonicity,[status(thm)],[96])).
% 2.77/2.02 tff(98,plain,
% 2.77/2.02 (multiplication(strong_iteration(one), zero) = multiplication(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)), zero)),
% 2.77/2.02 inference(symmetry,[status(thm)],[97])).
% 2.77/2.02 tff(99,plain,
% 2.77/2.02 (multiplication(strong_iteration(one), zero) = addition(multiplication(strong_iteration(one), zero), multiplication(strong_iteration(one), zero))),
% 2.77/2.02 inference(transitivity,[status(thm)],[98, 86, 84])).
% 2.77/2.02 tff(100,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), addition(star(one), zero)) = addition(addition(multiplication(strong_iteration(one), zero), multiplication(strong_iteration(one), zero)), addition(multiplication(one, zero), star(one)))),
% 2.77/2.02 inference(monotonicity,[status(thm)],[99, 82])).
% 2.77/2.02 tff(101,plain,
% 2.77/2.02 (addition(addition(multiplication(strong_iteration(one), zero), multiplication(strong_iteration(one), zero)), addition(multiplication(one, zero), star(one))) = addition(multiplication(strong_iteration(one), zero), addition(star(one), zero))),
% 2.77/2.02 inference(symmetry,[status(thm)],[100])).
% 2.77/2.02 tff(102,plain,
% 2.77/2.02 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(strong_iteration(one), zero), addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, zero), star(one)))) = addition(addition(multiplication(strong_iteration(one), zero), multiplication(strong_iteration(one), zero)), addition(multiplication(one, zero), star(one))))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(103,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, zero), star(one)))) = addition(addition(multiplication(strong_iteration(one), zero), multiplication(strong_iteration(one), zero)), addition(multiplication(one, zero), star(one)))),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[102, 58])).
% 2.77/2.02 tff(104,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), star(one)) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 2.77/2.02 inference(symmetry,[status(thm)],[72])).
% 2.77/2.02 tff(105,plain,
% 2.77/2.02 (addition(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), multiplication(one, zero)) = multiplication(addition(addition(multiplication(one, strong_iteration(one)), one), one), zero)),
% 2.77/2.02 inference(symmetry,[status(thm)],[33])).
% 2.77/2.02 tff(106,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), multiplication(one, zero)) = multiplication(strong_iteration(one), zero)),
% 2.77/2.02 inference(transitivity,[status(thm)],[23, 105, 47])).
% 2.77/2.02 tff(107,plain,
% 2.77/2.02 (addition(addition(multiplication(strong_iteration(one), zero), multiplication(one, zero)), star(one)) = addition(multiplication(strong_iteration(one), zero), star(one))),
% 2.77/2.02 inference(monotonicity,[status(thm)],[106])).
% 2.77/2.02 tff(108,plain,
% 2.77/2.02 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, zero), star(one))) = addition(addition(multiplication(strong_iteration(one), zero), multiplication(one, zero)), star(one)))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(109,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, zero), star(one))) = addition(addition(multiplication(strong_iteration(one), zero), multiplication(one, zero)), star(one))),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[108, 58])).
% 2.77/2.02 tff(110,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, zero), star(one))) = addition(multiplication(one, strong_iteration(one)), one)),
% 2.77/2.02 inference(transitivity,[status(thm)],[109, 107, 104, 19, 9])).
% 2.77/2.02 tff(111,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, zero), star(one)))) = addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.02 inference(monotonicity,[status(thm)],[110])).
% 2.77/2.02 tff(112,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(strong_iteration(one), zero), addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, zero), star(one))))),
% 2.77/2.02 inference(symmetry,[status(thm)],[111])).
% 2.77/2.02 tff(113,plain,
% 2.77/2.02 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(114,plain,
% 2.77/2.02 (addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero))),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[113, 70])).
% 2.77/2.02 tff(115,plain,
% 2.77/2.02 (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)) = addition(multiplication(strong_iteration(one), zero), addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.02 inference(symmetry,[status(thm)],[114])).
% 2.77/2.02 tff(116,plain,
% 2.77/2.02 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 2.77/2.02 inference(bind,[status(th)],[])).
% 2.77/2.02 tff(117,plain,
% 2.77/2.02 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 2.77/2.02 inference(quant_intro,[status(thm)],[116])).
% 2.77/2.02 tff(118,plain,
% 2.77/2.02 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 2.77/2.02 inference(rewrite,[status(thm)],[])).
% 2.77/2.02 tff(119,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','order')).
% 2.77/2.02 tff(120,plain,
% 2.77/2.02 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[119, 118])).
% 2.77/2.02 tff(121,plain,(
% 2.77/2.02 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 2.77/2.02 inference(skolemize,[status(sab)],[120])).
% 2.77/2.02 tff(122,plain,
% 2.77/2.02 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 2.77/2.02 inference(modus_ponens,[status(thm)],[121, 117])).
% 2.77/2.02 tff(123,plain,
% 2.77/2.02 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)) = multiplication(strong_iteration(one), zero)))),
% 2.77/2.02 inference(quant_inst,[status(thm)],[])).
% 2.77/2.02 tff(124,plain,
% 2.77/2.02 (leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)) = multiplication(strong_iteration(one), zero))),
% 2.77/2.02 inference(unit_resolution,[status(thm)],[123, 122])).
% 2.77/2.02 tff(125,plain,
% 2.77/2.02 (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = multiplication(one, strong_iteration(one))),
% 2.77/2.02 inference(monotonicity,[status(thm)],[20])).
% 2.77/2.02 tff(126,plain,
% 2.77/2.02 (addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), one) = addition(multiplication(one, strong_iteration(one)), one)),
% 2.77/2.02 inference(monotonicity,[status(thm)],[125])).
% 2.77/2.02 tff(127,plain,
% 2.77/2.02 (addition(multiplication(one, strong_iteration(one)), one) = addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), one)),
% 2.77/2.02 inference(symmetry,[status(thm)],[126])).
% 2.77/2.02 tff(128,plain,
% 2.77/2.02 (zero = multiplication(one, zero)),
% 2.77/2.02 inference(symmetry,[status(thm)],[63])).
% 2.77/2.02 tff(129,plain,
% 2.77/2.02 (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(star(one), multiplication(strong_iteration(one), zero))),
% 2.77/2.02 inference(transitivity,[status(thm)],[125, 42, 18])).
% 2.77/2.02 tff(130,plain,
% 2.77/2.02 (addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), zero) = addition(addition(star(one), multiplication(strong_iteration(one), zero)), multiplication(one, zero))),
% 2.77/2.02 inference(monotonicity,[status(thm)],[129, 128])).
% 2.77/2.03 tff(131,plain,
% 2.77/2.03 (addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), zero) = addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), one)),
% 2.77/2.03 inference(transitivity,[status(thm)],[130, 61, 51, 19, 9, 127])).
% 2.77/2.03 tff(132,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), zero)) <=> leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), one))),
% 2.77/2.03 inference(monotonicity,[status(thm)],[131])).
% 2.77/2.03 tff(133,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), one)) <=> leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), zero))),
% 2.77/2.03 inference(symmetry,[status(thm)],[132])).
% 2.77/2.03 tff(134,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) <=> leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), one))),
% 2.77/2.03 inference(monotonicity,[status(thm)],[127])).
% 2.77/2.03 tff(135,plain,
% 2.77/2.03 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)))),
% 2.77/2.03 inference(quant_inst,[status(thm)],[])).
% 2.77/2.03 tff(136,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[135, 122])).
% 2.77/2.03 tff(137,plain,
% 2.77/2.03 ((~(leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)))) | leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) | (~(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)))),
% 2.77/2.03 inference(tautology,[status(thm)],[])).
% 2.77/2.03 tff(138,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[137, 95, 136])).
% 2.77/2.03 tff(139,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), one))),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[138, 134])).
% 2.77/2.03 tff(140,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), zero))),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[139, 133])).
% 2.77/2.03 tff(141,plain,
% 2.77/2.03 (^[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))))),
% 2.77/2.03 inference(bind,[status(th)],[])).
% 2.77/2.03 tff(142,plain,
% 2.77/2.03 (![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)))),
% 2.77/2.03 inference(quant_intro,[status(thm)],[141])).
% 2.77/2.03 tff(143,plain,
% 2.77/2.03 (![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)))),
% 2.77/2.03 inference(rewrite,[status(thm)],[])).
% 2.77/2.03 tff(144,plain,
% 2.77/2.03 (^[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))))),
% 2.77/2.03 inference(bind,[status(th)],[])).
% 2.77/2.03 tff(145,plain,
% 2.77/2.03 (![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)))),
% 2.77/2.03 inference(quant_intro,[status(thm)],[144])).
% 2.77/2.03 tff(146,axiom,(![A: $i, B: $i, C: $i] : (leq(C, addition(multiplication(A, C), B)) => leq(C, multiplication(strong_iteration(A), B)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','infty_coinduction')).
% 2.77/2.03 tff(147,plain,
% 2.77/2.03 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[146, 145])).
% 2.77/2.03 tff(148,plain,
% 2.77/2.03 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[147, 143])).
% 2.77/2.03 tff(149,plain,(
% 2.77/2.03 ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 2.77/2.03 inference(skolemize,[status(sab)],[148])).
% 2.77/2.03 tff(150,plain,
% 2.77/2.03 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[149, 142])).
% 2.77/2.03 tff(151,plain,
% 2.77/2.03 (((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), zero))) | leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), zero))) | leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)))),
% 2.77/2.03 inference(rewrite,[status(thm)],[])).
% 2.77/2.03 tff(152,plain,
% 2.77/2.03 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), zero))) | leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)))),
% 2.77/2.03 inference(quant_inst,[status(thm)],[])).
% 2.77/2.03 tff(153,plain,
% 2.77/2.03 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), zero))) | leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero))),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[152, 151])).
% 2.77/2.03 tff(154,plain,
% 2.77/2.03 ((~leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), zero))) | leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero))),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[153, 150])).
% 2.77/2.03 tff(155,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero))),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[154, 140])).
% 2.77/2.03 tff(156,plain,
% 2.77/2.03 ((~(leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)) = multiplication(strong_iteration(one), zero)))) | (~leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero))) | (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)) = multiplication(strong_iteration(one), zero))),
% 2.77/2.03 inference(tautology,[status(thm)],[])).
% 2.77/2.03 tff(157,plain,
% 2.77/2.03 (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero)) = multiplication(strong_iteration(one), zero)),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[156, 155, 124])).
% 2.77/2.03 tff(158,plain,
% 2.77/2.03 (multiplication(strong_iteration(one), zero) = addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), zero))),
% 2.77/2.03 inference(symmetry,[status(thm)],[157])).
% 2.77/2.03 tff(159,plain,
% 2.77/2.03 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 2.77/2.03 inference(bind,[status(th)],[])).
% 2.77/2.03 tff(160,plain,
% 2.77/2.03 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 2.77/2.03 inference(quant_intro,[status(thm)],[159])).
% 2.77/2.03 tff(161,plain,
% 2.77/2.03 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 2.77/2.03 inference(rewrite,[status(thm)],[])).
% 2.77/2.03 tff(162,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 2.77/2.03 tff(163,plain,
% 2.77/2.03 (![A: $i] : (multiplication(zero, A) = zero)),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[162, 161])).
% 2.77/2.03 tff(164,plain,(
% 2.77/2.03 ![A: $i] : (multiplication(zero, A) = zero)),
% 2.77/2.03 inference(skolemize,[status(sab)],[163])).
% 2.77/2.03 tff(165,plain,
% 2.77/2.03 (![A: $i] : (multiplication(zero, A) = zero)),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[164, 160])).
% 2.77/2.03 tff(166,plain,
% 2.77/2.03 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, X0!0) = zero)),
% 2.77/2.03 inference(quant_inst,[status(thm)],[])).
% 2.77/2.03 tff(167,plain,
% 2.77/2.03 (multiplication(zero, X0!0) = zero),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[166, 165])).
% 2.77/2.03 tff(168,plain,
% 2.77/2.03 (zero = multiplication(zero, X0!0)),
% 2.77/2.03 inference(symmetry,[status(thm)],[167])).
% 2.77/2.03 tff(169,plain,
% 2.77/2.03 (multiplication(strong_iteration(one), zero) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0))),
% 2.77/2.03 inference(monotonicity,[status(thm)],[9, 168])).
% 2.77/2.03 tff(170,plain,
% 2.77/2.03 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0)) = multiplication(strong_iteration(one), zero)),
% 2.77/2.03 inference(symmetry,[status(thm)],[169])).
% 2.77/2.03 tff(171,plain,
% 2.77/2.03 (^[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)))),
% 2.77/2.03 inference(bind,[status(th)],[])).
% 2.77/2.03 tff(172,plain,
% 2.77/2.03 (![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))),
% 2.77/2.03 inference(quant_intro,[status(thm)],[171])).
% 2.77/2.03 tff(173,plain,
% 2.77/2.03 (![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))),
% 2.77/2.03 inference(rewrite,[status(thm)],[])).
% 2.77/2.03 tff(174,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 2.77/2.03 tff(175,plain,
% 2.77/2.03 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[174, 173])).
% 2.77/2.03 tff(176,plain,(
% 2.77/2.03 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 2.77/2.03 inference(skolemize,[status(sab)],[175])).
% 2.77/2.03 tff(177,plain,
% 2.77/2.03 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[176, 172])).
% 2.77/2.03 tff(178,plain,
% 2.77/2.03 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0)) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0))),
% 2.77/2.03 inference(quant_inst,[status(thm)],[])).
% 2.77/2.03 tff(179,plain,
% 2.77/2.03 (multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0)) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0)),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[178, 177])).
% 2.77/2.03 tff(180,plain,
% 2.77/2.03 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0) = multiplication(addition(multiplication(one, strong_iteration(one)), one), multiplication(zero, X0!0))),
% 2.77/2.03 inference(symmetry,[status(thm)],[179])).
% 2.77/2.03 tff(181,plain,
% 2.77/2.03 (multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0) = multiplication(multiplication(strong_iteration(one), zero), X0!0)),
% 2.77/2.03 inference(monotonicity,[status(thm)],[21])).
% 2.77/2.03 tff(182,plain,
% 2.77/2.03 (multiplication(multiplication(strong_iteration(one), zero), X0!0) = multiplication(multiplication(addition(multiplication(one, strong_iteration(one)), one), zero), X0!0)),
% 2.77/2.03 inference(symmetry,[status(thm)],[181])).
% 2.77/2.03 tff(183,plain,
% 2.77/2.03 (multiplication(strong_iteration(one), zero) = strong_iteration(one)),
% 2.77/2.03 inference(transitivity,[status(thm)],[158, 115, 112, 103, 101, 76, 74, 61, 51, 19])).
% 2.77/2.03 tff(184,plain,
% 2.77/2.03 (multiplication(multiplication(strong_iteration(one), zero), X0!0) = multiplication(strong_iteration(one), X0!0)),
% 2.77/2.03 inference(monotonicity,[status(thm)],[183])).
% 2.77/2.03 tff(185,plain,
% 2.77/2.03 (multiplication(strong_iteration(one), X0!0) = multiplication(multiplication(strong_iteration(one), zero), X0!0)),
% 2.77/2.03 inference(symmetry,[status(thm)],[184])).
% 2.77/2.03 tff(186,plain,
% 2.77/2.03 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0)) = multiplication(strong_iteration(one), X0!0)))),
% 2.77/2.03 inference(quant_inst,[status(thm)],[])).
% 2.77/2.03 tff(187,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0)) = multiplication(strong_iteration(one), X0!0))),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[186, 122])).
% 2.77/2.03 tff(188,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0)) <=> leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0))),
% 2.77/2.03 inference(monotonicity,[status(thm)],[20])).
% 2.77/2.03 tff(189,plain,
% 2.77/2.03 (leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0)) <=> leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0))),
% 2.77/2.03 inference(symmetry,[status(thm)],[188])).
% 2.77/2.03 tff(190,plain,
% 2.77/2.03 (multiplication(one, strong_iteration(one)) = multiplication(one, addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.03 inference(monotonicity,[status(thm)],[9])).
% 2.77/2.03 tff(191,plain,
% 2.77/2.03 (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = multiplication(one, strong_iteration(one))),
% 2.77/2.03 inference(symmetry,[status(thm)],[190])).
% 2.77/2.03 tff(192,plain,
% 2.77/2.03 (addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), X0!0) = addition(multiplication(one, strong_iteration(one)), X0!0)),
% 2.77/2.03 inference(monotonicity,[status(thm)],[191])).
% 2.77/2.03 tff(193,plain,
% 2.77/2.03 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.03 inference(quant_inst,[status(thm)],[])).
% 2.77/2.03 tff(194,plain,
% 2.77/2.03 (multiplication(one, addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[193, 40])).
% 2.77/2.03 tff(195,plain,
% 2.77/2.03 (addition(multiplication(one, strong_iteration(one)), one) = multiplication(one, addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.03 inference(symmetry,[status(thm)],[194])).
% 2.77/2.03 tff(196,plain,
% 2.77/2.03 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)) = multiplication(one, addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.03 inference(transitivity,[status(thm)],[95, 195])).
% 2.77/2.03 tff(197,plain,
% 2.77/2.03 (addition(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)), X0!0) = addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), X0!0)),
% 2.77/2.03 inference(monotonicity,[status(thm)],[196])).
% 2.77/2.03 tff(198,plain,
% 2.77/2.03 ((~![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), X0!0)) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)), X0!0))),
% 2.77/2.03 inference(quant_inst,[status(thm)],[])).
% 2.77/2.03 tff(199,plain,
% 2.77/2.03 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(addition(multiplication(one, strong_iteration(one)), one), X0!0)) = addition(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), one)), X0!0)),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[198, 58])).
% 2.77/2.03 tff(200,plain,
% 2.77/2.03 (addition(addition(multiplication(one, strong_iteration(one)), one), X0!0) = addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), X0!0)),
% 2.77/2.03 inference(monotonicity,[status(thm)],[195])).
% 2.77/2.03 tff(201,plain,
% 2.77/2.03 (addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), X0!0) = addition(addition(multiplication(one, strong_iteration(one)), one), X0!0)),
% 2.77/2.03 inference(symmetry,[status(thm)],[200])).
% 2.77/2.03 tff(202,plain,
% 2.77/2.03 (addition(multiplication(one, strong_iteration(one)), X0!0) = addition(multiplication(one, addition(multiplication(one, strong_iteration(one)), one)), X0!0)),
% 2.77/2.03 inference(symmetry,[status(thm)],[192])).
% 2.77/2.03 tff(203,plain,
% 2.77/2.03 (addition(multiplication(one, strong_iteration(one)), X0!0) = addition(addition(multiplication(one, strong_iteration(one)), one), X0!0)),
% 2.77/2.03 inference(transitivity,[status(thm)],[202, 201])).
% 2.77/2.03 tff(204,plain,
% 2.77/2.03 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) = addition(addition(multiplication(one, strong_iteration(one)), one), addition(addition(multiplication(one, strong_iteration(one)), one), X0!0))),
% 2.77/2.03 inference(monotonicity,[status(thm)],[203])).
% 2.77/2.03 tff(205,plain,
% 2.77/2.03 (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) = addition(multiplication(one, strong_iteration(one)), X0!0)),
% 2.77/2.03 inference(transitivity,[status(thm)],[204, 199, 197, 192])).
% 2.77/2.03 tff(206,plain,
% 2.77/2.03 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) = addition(multiplication(one, strong_iteration(one)), X0!0)))),
% 2.77/2.03 inference(quant_inst,[status(thm)],[])).
% 2.77/2.03 tff(207,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) = addition(multiplication(one, strong_iteration(one)), X0!0))),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[206, 122])).
% 2.77/2.03 tff(208,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) <=> leq(strong_iteration(one), addition(multiplication(one, strong_iteration(one)), X0!0))),
% 2.77/2.03 inference(monotonicity,[status(thm)],[20])).
% 2.77/2.03 tff(209,plain,
% 2.77/2.03 (leq(strong_iteration(one), addition(multiplication(one, strong_iteration(one)), X0!0)) <=> leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0))),
% 2.77/2.03 inference(symmetry,[status(thm)],[208])).
% 2.77/2.03 tff(210,plain,
% 2.77/2.03 ((~leq(strong_iteration(one), addition(multiplication(one, strong_iteration(one)), X0!0))) <=> (~leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)))),
% 2.77/2.03 inference(monotonicity,[status(thm)],[209])).
% 2.77/2.03 tff(211,assumption,(~leq(strong_iteration(one), addition(multiplication(one, strong_iteration(one)), X0!0))), introduced(assumption)).
% 2.77/2.03 tff(212,plain,
% 2.77/2.03 (~leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0))),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[211, 210])).
% 2.77/2.03 tff(213,plain,
% 2.77/2.03 ((~(leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) = addition(multiplication(one, strong_iteration(one)), X0!0)))) | leq(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) | (~(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) = addition(multiplication(one, strong_iteration(one)), X0!0)))),
% 2.77/2.03 inference(tautology,[status(thm)],[])).
% 2.77/2.03 tff(214,plain,
% 2.77/2.03 (~(addition(addition(multiplication(one, strong_iteration(one)), one), addition(multiplication(one, strong_iteration(one)), X0!0)) = addition(multiplication(one, strong_iteration(one)), X0!0))),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[213, 212, 207])).
% 2.77/2.03 tff(215,plain,
% 2.77/2.03 ($false),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[214, 205])).
% 2.77/2.03 tff(216,plain,(leq(strong_iteration(one), addition(multiplication(one, strong_iteration(one)), X0!0))), inference(lemma,lemma(discharge,[]))).
% 2.77/2.03 tff(217,plain,
% 2.77/2.03 (((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(strong_iteration(one), addition(multiplication(one, strong_iteration(one)), X0!0))) | leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(strong_iteration(one), addition(multiplication(one, strong_iteration(one)), X0!0))) | leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0)))),
% 2.77/2.03 inference(rewrite,[status(thm)],[])).
% 2.77/2.03 tff(218,plain,
% 2.77/2.03 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(strong_iteration(one), addition(multiplication(one, strong_iteration(one)), X0!0))) | leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0)))),
% 2.77/2.03 inference(quant_inst,[status(thm)],[])).
% 2.77/2.03 tff(219,plain,
% 2.77/2.03 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(strong_iteration(one), addition(multiplication(one, strong_iteration(one)), X0!0))) | leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0))),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[218, 217])).
% 2.77/2.03 tff(220,plain,
% 2.77/2.03 (leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0))),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[219, 150, 216])).
% 2.77/2.03 tff(221,plain,
% 2.77/2.03 (leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0))),
% 2.77/2.03 inference(modus_ponens,[status(thm)],[220, 189])).
% 2.77/2.03 tff(222,plain,
% 2.77/2.03 ((~(leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0)) <=> (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0)) = multiplication(strong_iteration(one), X0!0)))) | (~leq(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0))) | (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0)) = multiplication(strong_iteration(one), X0!0))),
% 2.77/2.03 inference(tautology,[status(thm)],[])).
% 2.77/2.03 tff(223,plain,
% 2.77/2.03 (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0)) = multiplication(strong_iteration(one), X0!0)),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[222, 221, 187])).
% 2.77/2.03 tff(224,plain,
% 2.77/2.03 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0)) = addition(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)))),
% 2.77/2.03 inference(quant_inst,[status(thm)],[])).
% 2.77/2.03 tff(225,plain,
% 2.77/2.03 (addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0)) = addition(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[224, 70])).
% 2.77/2.03 tff(226,plain,
% 2.77/2.03 (addition(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) = addition(addition(multiplication(one, strong_iteration(one)), one), multiplication(strong_iteration(one), X0!0))),
% 2.77/2.03 inference(symmetry,[status(thm)],[225])).
% 2.77/2.03 tff(227,plain,
% 2.77/2.03 (addition(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)),
% 2.77/2.03 inference(transitivity,[status(thm)],[226, 223, 185, 182, 180, 170, 158, 115, 112, 103, 101, 76, 74, 61, 51, 19, 9])).
% 2.77/2.03 tff(228,plain,
% 2.77/2.03 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) <=> (addition(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)))),
% 2.77/2.03 inference(quant_inst,[status(thm)],[])).
% 2.77/2.03 tff(229,plain,
% 2.77/2.03 (leq(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) <=> (addition(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.03 inference(unit_resolution,[status(thm)],[228, 122])).
% 2.77/2.03 tff(230,plain,
% 2.77/2.03 (leq(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) <=> leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one))),
% 2.77/2.03 inference(monotonicity,[status(thm)],[20])).
% 2.77/2.03 tff(231,plain,
% 2.77/2.03 (leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one)) <=> leq(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.03 inference(symmetry,[status(thm)],[230])).
% 2.77/2.03 tff(232,plain,
% 2.77/2.03 ((~leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one))) <=> (~leq(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)))),
% 2.77/2.03 inference(monotonicity,[status(thm)],[231])).
% 2.77/2.03 tff(233,plain,
% 2.77/2.03 ((~(~((~leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one))) | (~leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0)))))) <=> ((~leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one))) | (~leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0))))),
% 2.77/2.03 inference(rewrite,[status(thm)],[])).
% 2.77/2.03 tff(234,plain,
% 2.77/2.03 ((leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0))) <=> (~((~leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one))) | (~leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0)))))),
% 2.77/2.04 inference(rewrite,[status(thm)],[])).
% 2.77/2.04 tff(235,plain,
% 2.77/2.04 ((~(leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0)))) <=> (~(~((~leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one))) | (~leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0))))))),
% 2.77/2.04 inference(monotonicity,[status(thm)],[234])).
% 2.77/2.04 tff(236,plain,
% 2.77/2.04 ((~(leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0)))) <=> ((~leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one))) | (~leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0))))),
% 2.77/2.04 inference(transitivity,[status(thm)],[235, 233])).
% 2.77/2.04 tff(237,plain,
% 2.77/2.04 ((~![X0: $i] : (leq(multiplication(strong_iteration(one), X0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0)))) <=> (~![X0: $i] : (leq(multiplication(strong_iteration(one), X0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0))))),
% 2.77/2.04 inference(rewrite,[status(thm)],[])).
% 2.77/2.04 tff(238,axiom,(~![X0: $i] : (leq(multiplication(strong_iteration(one), X0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 2.77/2.04 tff(239,plain,
% 2.77/2.04 (~![X0: $i] : (leq(multiplication(strong_iteration(one), X0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0)))),
% 2.77/2.04 inference(modus_ponens,[status(thm)],[238, 237])).
% 2.77/2.04 tff(240,plain,
% 2.77/2.04 (~![X0: $i] : (leq(multiplication(strong_iteration(one), X0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0)))),
% 2.77/2.04 inference(modus_ponens,[status(thm)],[239, 237])).
% 2.77/2.04 tff(241,plain,
% 2.77/2.04 (~![X0: $i] : (leq(multiplication(strong_iteration(one), X0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0)))),
% 2.77/2.04 inference(modus_ponens,[status(thm)],[240, 237])).
% 2.77/2.04 tff(242,plain,
% 2.77/2.04 (~![X0: $i] : (leq(multiplication(strong_iteration(one), X0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0)))),
% 2.77/2.04 inference(modus_ponens,[status(thm)],[241, 237])).
% 2.77/2.04 tff(243,plain,
% 2.77/2.04 (~![X0: $i] : (leq(multiplication(strong_iteration(one), X0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0)))),
% 2.77/2.04 inference(modus_ponens,[status(thm)],[242, 237])).
% 2.77/2.04 tff(244,plain,
% 2.77/2.04 (~![X0: $i] : (leq(multiplication(strong_iteration(one), X0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0)))),
% 2.77/2.04 inference(modus_ponens,[status(thm)],[243, 237])).
% 2.77/2.04 tff(245,plain,
% 2.77/2.04 (~![X0: $i] : (leq(multiplication(strong_iteration(one), X0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0)))),
% 2.77/2.04 inference(modus_ponens,[status(thm)],[244, 237])).
% 2.77/2.04 tff(246,plain,(
% 2.77/2.04 ~(leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one)) & leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0)))),
% 2.77/2.04 inference(skolemize,[status(sab)],[245])).
% 2.77/2.04 tff(247,plain,
% 2.77/2.04 ((~leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one))) | (~leq(strong_iteration(one), multiplication(strong_iteration(one), X0!0)))),
% 2.77/2.04 inference(modus_ponens,[status(thm)],[246, 236])).
% 2.77/2.04 tff(248,plain,
% 2.77/2.04 (~leq(multiplication(strong_iteration(one), X0!0), strong_iteration(one))),
% 2.77/2.04 inference(unit_resolution,[status(thm)],[247, 220])).
% 2.77/2.04 tff(249,plain,
% 2.77/2.04 (~leq(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.04 inference(modus_ponens,[status(thm)],[248, 232])).
% 2.77/2.04 tff(250,plain,
% 2.77/2.04 ((~(leq(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) <=> (addition(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)))) | leq(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) | (~(addition(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one)))),
% 2.77/2.04 inference(tautology,[status(thm)],[])).
% 2.77/2.04 tff(251,plain,
% 2.77/2.04 (~(addition(multiplication(strong_iteration(one), X0!0), addition(multiplication(one, strong_iteration(one)), one)) = addition(multiplication(one, strong_iteration(one)), one))),
% 2.77/2.04 inference(unit_resolution,[status(thm)],[250, 249, 229])).
% 2.77/2.04 tff(252,plain,
% 2.77/2.04 ($false),
% 2.77/2.04 inference(unit_resolution,[status(thm)],[251, 227])).
% 2.77/2.04 % SZS output end Proof
%------------------------------------------------------------------------------