TSTP Solution File: KLE158+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE158+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 17:24:24 EDT 2022
% Result : Theorem 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE158+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 08:59:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(addition_type, type, (
% 0.21/0.49 addition: ( $i * $i ) > $i)).
% 0.21/0.49 tff(tptp_fun_X0_2_type, type, (
% 0.21/0.49 tptp_fun_X0_2: $i)).
% 0.21/0.49 tff(multiplication_type, type, (
% 0.21/0.49 multiplication: ( $i * $i ) > $i)).
% 0.21/0.49 tff(strong_iteration_type, type, (
% 0.21/0.49 strong_iteration: $i > $i)).
% 0.21/0.49 tff(tptp_fun_X1_1_type, type, (
% 0.21/0.49 tptp_fun_X1_1: $i)).
% 0.21/0.49 tff(tptp_fun_X2_0_type, type, (
% 0.21/0.49 tptp_fun_X2_0: $i)).
% 0.21/0.49 tff(one_type, type, (
% 0.21/0.49 one: $i)).
% 0.21/0.49 tff(leq_type, type, (
% 0.21/0.49 leq: ( $i * $i ) > $o)).
% 0.21/0.49 tff(1,plain,
% 0.21/0.49 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(2,plain,
% 0.21/0.49 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.49 tff(6,plain,(
% 0.21/0.49 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.49 inference(skolemize,[status(sab)],[5])).
% 0.21/0.49 tff(7,plain,
% 0.21/0.49 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2) = addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 (addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2) = addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 (addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)),
% 0.21/0.49 inference(symmetry,[status(thm)],[9])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.49 tff(13,plain,
% 0.21/0.49 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(14,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 0.21/0.49 tff(15,plain,
% 0.21/0.49 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.49 tff(16,plain,(
% 0.21/0.49 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.21/0.49 inference(skolemize,[status(sab)],[15])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(X1!1) = addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(19,plain,
% 0.21/0.49 (strong_iteration(X1!1) = addition(multiplication(X1!1, strong_iteration(X1!1)), one)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 (multiplication(X0!2, strong_iteration(X1!1)) = multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[19])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 (multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))) = multiplication(X2!0, multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[20])).
% 0.21/0.49 tff(22,plain,
% 0.21/0.49 (multiplication(X2!0, multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))),
% 0.21/0.49 inference(symmetry,[status(thm)],[21])).
% 0.21/0.49 tff(23,plain,
% 0.21/0.49 (^[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)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(24,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.49 tff(25,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(26,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')).
% 0.21/0.49 tff(27,plain,
% 0.21/0.49 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.49 tff(28,plain,(
% 0.21/0.49 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.21/0.49 inference(skolemize,[status(sab)],[27])).
% 0.21/0.49 tff(29,plain,
% 0.21/0.49 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.49 tff(30,plain,
% 0.21/0.49 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X2!0, multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(31,plain,
% 0.21/0.49 (multiplication(X2!0, multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.21/0.49 tff(32,plain,
% 0.21/0.49 (multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = multiplication(X2!0, multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.21/0.49 inference(symmetry,[status(thm)],[31])).
% 0.21/0.49 tff(33,plain,
% 0.21/0.49 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(34,plain,
% 0.21/0.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.49 tff(35,plain,
% 0.21/0.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(36,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','order')).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.49 tff(38,plain,(
% 0.21/0.49 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.49 inference(skolemize,[status(sab)],[37])).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.49 tff(40,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(41,plain,
% 0.21/0.49 (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.21/0.49 tff(42,plain,
% 0.21/0.49 ((~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(43,plain,
% 0.21/0.49 ((~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X2, X0)) => leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(44,axiom,(~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X2, X0)) => leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.21/0.49 tff(45,plain,
% 0.21/0.49 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.49 tff(46,plain,
% 0.21/0.49 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[45, 42])).
% 0.21/0.49 tff(47,plain,
% 0.21/0.49 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.21/0.49 tff(48,plain,
% 0.21/0.49 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[47, 42])).
% 0.21/0.49 tff(49,plain,
% 0.21/0.49 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[48, 42])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[50, 42])).
% 0.21/0.49 tff(52,plain,(
% 0.21/0.49 ~((~leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) | leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[51])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))),
% 0.21/0.49 inference(or_elim,[status(thm)],[52])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 ((~(leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))) | (~leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) | (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(55,plain,
% 0.21/0.49 ((~(leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))) | (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[55, 41])).
% 0.21/0.49 tff(57,plain,
% 0.21/0.49 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = addition(multiplication(X2!0, X0!2), multiplication(X0!2, X1!1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(58,plain,
% 0.21/0.49 (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = addition(multiplication(X2!0, X0!2), multiplication(X0!2, X1!1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[57, 7])).
% 0.21/0.49 tff(59,plain,
% 0.21/0.49 (addition(multiplication(X2!0, X0!2), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))),
% 0.21/0.49 inference(symmetry,[status(thm)],[58])).
% 0.21/0.49 tff(60,plain,
% 0.21/0.49 (addition(multiplication(X2!0, X0!2), multiplication(X0!2, X1!1)) = multiplication(X2!0, X0!2)),
% 0.21/0.49 inference(transitivity,[status(thm)],[59, 56])).
% 0.21/0.49 tff(61,plain,
% 0.21/0.49 (multiplication(addition(multiplication(X2!0, X0!2), multiplication(X0!2, X1!1)), addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[60])).
% 0.21/0.49 tff(62,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.49 tff(64,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(65,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')).
% 0.21/0.49 tff(66,plain,
% 0.21/0.49 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.49 tff(67,plain,(
% 0.21/0.49 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[66])).
% 0.21/0.49 tff(68,plain,
% 0.21/0.49 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.21/0.49 tff(69,plain,
% 0.21/0.49 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X2!0, X0!2), multiplication(X0!2, X1!1)), addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(70,plain,
% 0.21/0.49 (multiplication(addition(multiplication(X2!0, X0!2), multiplication(X0!2, X1!1)), addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.49 tff(71,plain,
% 0.21/0.49 (addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(addition(multiplication(X2!0, X0!2), multiplication(X0!2, X1!1)), addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.21/0.49 inference(symmetry,[status(thm)],[70])).
% 0.21/0.49 tff(72,plain,
% 0.21/0.49 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!2, multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(73,plain,
% 0.21/0.49 (multiplication(X0!2, multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[72, 29])).
% 0.21/0.49 tff(74,plain,
% 0.21/0.49 (multiplication(X1!1, strong_iteration(X1!1)) = multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[19])).
% 0.21/0.49 tff(75,plain,
% 0.21/0.49 (multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = multiplication(X1!1, strong_iteration(X1!1))),
% 0.21/0.49 inference(symmetry,[status(thm)],[74])).
% 0.21/0.49 tff(76,plain,
% 0.21/0.49 (multiplication(X0!2, multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.49 tff(77,plain,
% 0.21/0.49 (multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))) = multiplication(X0!2, multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.21/0.49 inference(symmetry,[status(thm)],[76])).
% 0.21/0.49 tff(78,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(79,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.49 tff(80,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(81,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')).
% 0.21/0.49 tff(82,plain,
% 0.21/0.49 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.49 tff(83,plain,(
% 0.21/0.49 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[82])).
% 0.21/0.49 tff(84,plain,
% 0.21/0.49 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.21/0.49 tff(85,plain,
% 0.21/0.49 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(86,plain,
% 0.21/0.50 (multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.50 tff(87,plain,
% 0.21/0.50 (multiplication(X1!1, strong_iteration(X1!1)) = addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))),
% 0.21/0.50 inference(transitivity,[status(thm)],[74, 86])).
% 0.21/0.50 tff(88,plain,
% 0.21/0.50 (multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))) = multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[87])).
% 0.21/0.50 tff(89,plain,
% 0.21/0.50 (multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))) = multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[88])).
% 0.21/0.50 tff(90,plain,
% 0.21/0.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))) = addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 (multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))) = addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[90, 84])).
% 0.21/0.50 tff(92,plain,
% 0.21/0.50 (addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))) = multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[91])).
% 0.21/0.50 tff(93,plain,
% 0.21/0.50 (addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))) = multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.21/0.50 inference(transitivity,[status(thm)],[92, 89, 77, 73])).
% 0.21/0.50 tff(94,plain,
% 0.21/0.50 (addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))) = addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.50 tff(95,plain,
% 0.21/0.50 (addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))) = multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[94, 71, 61, 32, 22])).
% 0.21/0.50 tff(96,plain,
% 0.21/0.50 (addition(X0!2, addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))) = addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[95])).
% 0.21/0.50 tff(97,plain,
% 0.21/0.50 (^[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)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(98,plain,
% 0.21/0.50 (![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))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.50 tff(99,plain,
% 0.21/0.50 (![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))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(100,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')).
% 0.21/0.50 tff(101,plain,
% 0.21/0.50 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.50 tff(102,plain,(
% 0.21/0.50 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.21/0.50 inference(skolemize,[status(sab)],[101])).
% 0.21/0.50 tff(103,plain,
% 0.21/0.50 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.21/0.50 tff(104,plain,
% 0.21/0.50 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!2, addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))) = addition(addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(105,plain,
% 0.21/0.50 (addition(X0!2, addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))) = addition(addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.21/0.50 tff(106,plain,
% 0.21/0.50 (addition(addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))) = addition(X0!2, addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))))),
% 0.21/0.50 inference(symmetry,[status(thm)],[105])).
% 0.21/0.50 tff(107,plain,
% 0.21/0.50 (multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[32, 22])).
% 0.21/0.50 tff(108,plain,
% 0.21/0.50 (addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[107])).
% 0.21/0.50 tff(109,plain,
% 0.21/0.50 (addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))) = addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[108])).
% 0.21/0.50 tff(110,plain,
% 0.21/0.50 (addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))) = addition(addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.50 tff(111,plain,
% 0.21/0.50 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(112,plain,
% 0.21/0.50 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.21/0.50 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.50 tff(113,plain,
% 0.21/0.50 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(114,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.21/0.50 tff(115,plain,
% 0.21/0.50 (![A: $i] : (addition(A, A) = A)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.50 tff(116,plain,(
% 0.21/0.50 ![A: $i] : (addition(A, A) = A)),
% 0.21/0.50 inference(skolemize,[status(sab)],[115])).
% 0.21/0.50 tff(117,plain,
% 0.21/0.50 (![A: $i] : (addition(A, A) = A)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.21/0.50 tff(118,plain,
% 0.21/0.50 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!2, X0!2) = X0!2)),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(119,plain,
% 0.21/0.50 (addition(X0!2, X0!2) = X0!2),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.21/0.50 tff(120,plain,
% 0.21/0.50 (addition(addition(X0!2, X0!2), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[119, 107])).
% 0.21/0.50 tff(121,plain,
% 0.21/0.50 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!2, addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))) = addition(addition(X0!2, X0!2), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(122,plain,
% 0.21/0.50 (addition(X0!2, addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))) = addition(addition(X0!2, X0!2), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[121, 103])).
% 0.21/0.50 tff(123,plain,
% 0.21/0.50 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(124,plain,
% 0.21/0.50 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.21/0.50 inference(quant_intro,[status(thm)],[123])).
% 0.21/0.50 tff(125,plain,
% 0.21/0.50 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(126,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 0.21/0.50 tff(127,plain,
% 0.21/0.50 (![A: $i] : (multiplication(A, one) = A)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.50 tff(128,plain,(
% 0.21/0.50 ![A: $i] : (multiplication(A, one) = A)),
% 0.21/0.50 inference(skolemize,[status(sab)],[127])).
% 0.21/0.50 tff(129,plain,
% 0.21/0.50 (![A: $i] : (multiplication(A, one) = A)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.21/0.50 tff(130,plain,
% 0.21/0.50 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!2, one) = X0!2)),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(131,plain,
% 0.21/0.50 (multiplication(X0!2, one) = X0!2),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.21/0.50 tff(132,plain,
% 0.21/0.50 (addition(multiplication(X0!2, one), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))) = addition(X0!2, addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[131, 109])).
% 0.21/0.50 tff(133,plain,
% 0.21/0.50 (X0!2 = multiplication(X0!2, one)),
% 0.21/0.50 inference(symmetry,[status(thm)],[131])).
% 0.21/0.50 tff(134,plain,
% 0.21/0.50 (addition(X0!2, addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))) = addition(multiplication(X0!2, one), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[133])).
% 0.21/0.50 tff(135,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))) = addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), X0!2))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(136,plain,
% 0.21/0.50 (addition(X0!2, addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))) = addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), X0!2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[135, 7])).
% 0.21/0.50 tff(137,plain,
% 0.21/0.50 (addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), X0!2) = addition(X0!2, addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))))),
% 0.21/0.50 inference(symmetry,[status(thm)],[136])).
% 0.21/0.50 tff(138,plain,
% 0.21/0.50 (addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), X0!2) = addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[137, 134, 132, 122, 120])).
% 0.21/0.50 tff(139,plain,
% 0.21/0.50 (addition(addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), X0!2), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))) = addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.50 tff(140,plain,
% 0.21/0.50 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))) = addition(addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), X0!2), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(141,plain,
% 0.21/0.50 (addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))) = addition(addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), X0!2), addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[140, 103])).
% 0.21/0.50 tff(142,plain,
% 0.21/0.50 (addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))) = addition(multiplication(X0!2, one), multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[133, 92])).
% 0.21/0.50 tff(143,plain,
% 0.21/0.50 (addition(multiplication(X0!2, one), multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))) = addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))),
% 0.21/0.50 inference(symmetry,[status(thm)],[142])).
% 0.21/0.50 tff(144,plain,
% 0.21/0.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))) = addition(multiplication(X0!2, one), multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(145,plain,
% 0.21/0.50 (multiplication(X0!2, addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))) = addition(multiplication(X0!2, one), multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[144, 84])).
% 0.21/0.50 tff(146,plain,
% 0.21/0.50 (addition(multiplication(X1!1, strong_iteration(X1!1)), one) = strong_iteration(X1!1)),
% 0.21/0.50 inference(symmetry,[status(thm)],[19])).
% 0.21/0.50 tff(147,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!1, strong_iteration(X1!1)), one) = addition(one, multiplication(X1!1, strong_iteration(X1!1))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(148,plain,
% 0.21/0.50 (addition(multiplication(X1!1, strong_iteration(X1!1)), one) = addition(one, multiplication(X1!1, strong_iteration(X1!1)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[147, 7])).
% 0.21/0.50 tff(149,plain,
% 0.21/0.50 (addition(one, multiplication(X1!1, strong_iteration(X1!1))) = addition(multiplication(X1!1, strong_iteration(X1!1)), one)),
% 0.21/0.50 inference(symmetry,[status(thm)],[148])).
% 0.21/0.50 tff(150,plain,
% 0.21/0.50 (addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)) = multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.21/0.50 inference(symmetry,[status(thm)],[86])).
% 0.21/0.50 tff(151,plain,
% 0.21/0.50 (addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)) = multiplication(X1!1, strong_iteration(X1!1))),
% 0.21/0.50 inference(transitivity,[status(thm)],[150, 75])).
% 0.21/0.50 tff(152,plain,
% 0.21/0.50 (addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))) = addition(one, multiplication(X1!1, strong_iteration(X1!1)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[151])).
% 0.21/0.50 tff(153,plain,
% 0.21/0.50 (addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))) = strong_iteration(X1!1)),
% 0.21/0.50 inference(transitivity,[status(thm)],[152, 149, 146])).
% 0.21/0.50 tff(154,plain,
% 0.21/0.50 (multiplication(X0!2, addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))) = multiplication(X0!2, strong_iteration(X1!1))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[153])).
% 0.21/0.50 tff(155,plain,
% 0.21/0.50 (multiplication(X0!2, strong_iteration(X1!1)) = multiplication(X0!2, addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))))),
% 0.21/0.50 inference(symmetry,[status(thm)],[154])).
% 0.21/0.50 tff(156,plain,
% 0.21/0.50 (multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = multiplication(X0!2, strong_iteration(X1!1))),
% 0.21/0.50 inference(symmetry,[status(thm)],[20])).
% 0.21/0.50 tff(157,plain,
% 0.21/0.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(158,plain,
% 0.21/0.50 (multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[157, 84])).
% 0.21/0.50 tff(159,plain,
% 0.21/0.50 (addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)) = multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.21/0.50 inference(symmetry,[status(thm)],[158])).
% 0.21/0.50 tff(160,plain,
% 0.21/0.50 (addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)) = addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[159, 156, 155, 145, 143])).
% 0.21/0.50 tff(161,plain,
% 0.21/0.50 (addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))) = addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[160])).
% 0.21/0.50 tff(162,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))) = addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(163,plain,
% 0.21/0.50 (addition(addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))) = addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[162, 7])).
% 0.21/0.50 tff(164,plain,
% 0.21/0.50 (multiplication(X0!2, strong_iteration(X1!1)) = addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))),
% 0.21/0.50 inference(transitivity,[status(thm)],[20, 158])).
% 0.21/0.50 tff(165,plain,
% 0.21/0.50 (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[164, 9])).
% 0.21/0.50 tff(166,plain,
% 0.21/0.50 (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)),
% 0.21/0.50 inference(transitivity,[status(thm)],[165, 163, 161, 141, 139, 110, 106, 96, 10])).
% 0.21/0.50 tff(167,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) <=> (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(168,plain,
% 0.21/0.50 (leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) <=> (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[167, 39])).
% 0.21/0.51 tff(169,plain,
% 0.21/0.51 (~leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2))),
% 0.21/0.51 inference(or_elim,[status(thm)],[52])).
% 0.21/0.51 tff(170,plain,
% 0.21/0.51 (^[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))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(171,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[170])).
% 0.21/0.51 tff(172,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(173,plain,
% 0.21/0.51 (^[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))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(174,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.51 tff(175,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')).
% 0.21/0.51 tff(176,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.21/0.51 tff(177,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.21/0.51 tff(178,plain,(
% 0.21/0.51 ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[177])).
% 0.21/0.51 tff(179,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.21/0.51 tff(180,plain,
% 0.21/0.51 (((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))) | leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))) | leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(181,plain,
% 0.21/0.51 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))) | leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(182,plain,
% 0.21/0.51 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))) | leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.21/0.51 tff(183,plain,
% 0.21/0.51 (~leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[182, 179, 169])).
% 0.21/0.51 tff(184,plain,
% 0.21/0.51 ((~(leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) <=> (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)))) | leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) | (~(addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(185,plain,
% 0.21/0.51 ((~(leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) <=> (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)))) | (~(addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.21/0.51 tff(186,plain,
% 0.21/0.51 (~(addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[185, 168])).
% 0.21/0.51 tff(187,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[186, 166])).
% 0.21/0.51 % SZS output end Proof
%------------------------------------------------------------------------------