TSTP Solution File: KLE147+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE147+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 17:24:20 EDT 2022
% Result : Theorem 14.55s 9.66s
% Output : Proof 14.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE147+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.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 08:44:47 EDT 2022
% 0.13/0.34 % 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.
% 14.55/9.66 % SZS status Theorem
% 14.55/9.66 % SZS output start Proof
% 14.55/9.66 tff(multiplication_type, type, (
% 14.55/9.66 multiplication: ( $i * $i ) > $i)).
% 14.55/9.66 tff(strong_iteration_type, type, (
% 14.55/9.66 strong_iteration: $i > $i)).
% 14.55/9.66 tff(tptp_fun_X1_0_type, type, (
% 14.55/9.66 tptp_fun_X1_0: $i)).
% 14.55/9.66 tff(star_type, type, (
% 14.55/9.66 star: $i > $i)).
% 14.55/9.66 tff(tptp_fun_X0_1_type, type, (
% 14.55/9.66 tptp_fun_X0_1: $i)).
% 14.55/9.66 tff(addition_type, type, (
% 14.55/9.66 addition: ( $i * $i ) > $i)).
% 14.55/9.66 tff(one_type, type, (
% 14.55/9.66 one: $i)).
% 14.55/9.66 tff(leq_type, type, (
% 14.55/9.66 leq: ( $i * $i ) > $o)).
% 14.55/9.66 tff(1,plain,
% 14.55/9.66 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 14.55/9.66 inference(bind,[status(th)],[])).
% 14.55/9.66 tff(2,plain,
% 14.55/9.66 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 14.55/9.66 inference(quant_intro,[status(thm)],[1])).
% 14.55/9.66 tff(3,plain,
% 14.55/9.66 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 14.55/9.66 inference(rewrite,[status(thm)],[])).
% 14.55/9.66 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')).
% 14.55/9.66 tff(5,plain,
% 14.55/9.66 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[4, 3])).
% 14.55/9.66 tff(6,plain,(
% 14.55/9.66 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 14.55/9.66 inference(skolemize,[status(sab)],[5])).
% 14.55/9.66 tff(7,plain,
% 14.55/9.66 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[6, 2])).
% 14.55/9.66 tff(8,plain,
% 14.55/9.66 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(multiplication(star(X0!1), X1!0)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.66 inference(quant_inst,[status(thm)],[])).
% 14.55/9.66 tff(9,plain,
% 14.55/9.66 (strong_iteration(multiplication(star(X0!1), X1!0)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)),
% 14.55/9.66 inference(unit_resolution,[status(thm)],[8, 7])).
% 14.55/9.66 tff(10,plain,
% 14.55/9.66 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 14.55/9.66 inference(bind,[status(th)],[])).
% 14.55/9.66 tff(11,plain,
% 14.55/9.66 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 14.55/9.66 inference(quant_intro,[status(thm)],[10])).
% 14.55/9.66 tff(12,plain,
% 14.55/9.66 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 14.55/9.66 inference(rewrite,[status(thm)],[])).
% 14.55/9.66 tff(13,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 14.55/9.66 tff(14,plain,
% 14.55/9.66 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[13, 12])).
% 14.55/9.66 tff(15,plain,(
% 14.55/9.66 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 14.55/9.66 inference(skolemize,[status(sab)],[14])).
% 14.55/9.66 tff(16,plain,
% 14.55/9.66 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[15, 11])).
% 14.55/9.66 tff(17,plain,
% 14.55/9.66 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(X1!0), X1!0)) = star(X1!0))),
% 14.55/9.66 inference(quant_inst,[status(thm)],[])).
% 14.55/9.66 tff(18,plain,
% 14.55/9.66 (addition(one, multiplication(star(X1!0), X1!0)) = star(X1!0)),
% 14.55/9.66 inference(unit_resolution,[status(thm)],[17, 16])).
% 14.55/9.66 tff(19,plain,
% 14.55/9.66 (star(X1!0) = addition(one, multiplication(star(X1!0), X1!0))),
% 14.55/9.66 inference(symmetry,[status(thm)],[18])).
% 14.55/9.66 tff(20,plain,
% 14.55/9.66 (multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))) = multiplication(addition(one, multiplication(star(X1!0), X1!0)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.66 inference(monotonicity,[status(thm)],[19, 9])).
% 14.55/9.66 tff(21,plain,
% 14.55/9.66 (multiplication(addition(one, multiplication(star(X1!0), X1!0)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.55/9.66 inference(symmetry,[status(thm)],[20])).
% 14.55/9.66 tff(22,plain,
% 14.55/9.66 (^[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))))),
% 14.55/9.66 inference(bind,[status(th)],[])).
% 14.55/9.66 tff(23,plain,
% 14.55/9.66 (![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)))),
% 14.55/9.66 inference(quant_intro,[status(thm)],[22])).
% 14.55/9.66 tff(24,plain,
% 14.55/9.66 (![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)))),
% 14.55/9.66 inference(rewrite,[status(thm)],[])).
% 14.55/9.66 tff(25,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity2')).
% 14.55/9.66 tff(26,plain,
% 14.55/9.66 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[25, 24])).
% 14.55/9.66 tff(27,plain,(
% 14.55/9.66 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 14.55/9.66 inference(skolemize,[status(sab)],[26])).
% 14.55/9.66 tff(28,plain,
% 14.55/9.66 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[27, 23])).
% 14.55/9.66 tff(29,plain,
% 14.55/9.66 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, multiplication(star(X1!0), X1!0)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(one, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(multiplication(star(X1!0), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))))),
% 14.55/9.66 inference(quant_inst,[status(thm)],[])).
% 14.55/9.66 tff(30,plain,
% 14.55/9.66 (multiplication(addition(one, multiplication(star(X1!0), X1!0)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(one, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(multiplication(star(X1!0), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.55/9.66 inference(unit_resolution,[status(thm)],[29, 28])).
% 14.55/9.66 tff(31,plain,
% 14.55/9.66 (addition(multiplication(one, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(multiplication(star(X1!0), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(addition(one, multiplication(star(X1!0), X1!0)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.66 inference(symmetry,[status(thm)],[30])).
% 14.55/9.66 tff(32,plain,
% 14.55/9.66 (^[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))))),
% 14.55/9.66 inference(bind,[status(th)],[])).
% 14.55/9.66 tff(33,plain,
% 14.55/9.66 (![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)))),
% 14.55/9.66 inference(quant_intro,[status(thm)],[32])).
% 14.55/9.66 tff(34,plain,
% 14.55/9.66 (![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)))),
% 14.55/9.66 inference(rewrite,[status(thm)],[])).
% 14.55/9.66 tff(35,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity1')).
% 14.55/9.66 tff(36,plain,
% 14.55/9.66 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[35, 34])).
% 14.55/9.66 tff(37,plain,(
% 14.55/9.66 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 14.55/9.66 inference(skolemize,[status(sab)],[36])).
% 14.55/9.66 tff(38,plain,
% 14.55/9.66 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[37, 33])).
% 14.55/9.66 tff(39,plain,
% 14.55/9.66 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.55/9.66 inference(quant_inst,[status(thm)],[])).
% 14.55/9.66 tff(40,plain,
% 14.55/9.66 (multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))),
% 14.55/9.66 inference(unit_resolution,[status(thm)],[39, 38])).
% 14.55/9.66 tff(41,plain,
% 14.55/9.66 (addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)) = multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.66 inference(symmetry,[status(thm)],[40])).
% 14.55/9.66 tff(42,plain,
% 14.55/9.66 (multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = multiplication(star(X1!0), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.55/9.66 inference(monotonicity,[status(thm)],[41])).
% 14.55/9.66 tff(43,plain,
% 14.55/9.66 (multiplication(star(X1!0), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.55/9.66 inference(symmetry,[status(thm)],[42])).
% 14.55/9.66 tff(44,plain,
% 14.55/9.66 (^[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)))),
% 14.55/9.66 inference(bind,[status(th)],[])).
% 14.55/9.66 tff(45,plain,
% 14.55/9.66 (![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))),
% 14.55/9.66 inference(quant_intro,[status(thm)],[44])).
% 14.55/9.66 tff(46,plain,
% 14.55/9.66 (![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))),
% 14.55/9.66 inference(rewrite,[status(thm)],[])).
% 14.55/9.66 tff(47,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')).
% 14.55/9.66 tff(48,plain,
% 14.55/9.66 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[47, 46])).
% 14.55/9.66 tff(49,plain,(
% 14.55/9.66 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 14.55/9.66 inference(skolemize,[status(sab)],[48])).
% 14.55/9.66 tff(50,plain,
% 14.55/9.66 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[49, 45])).
% 14.55/9.66 tff(51,plain,
% 14.55/9.66 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(star(X1!0), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(multiplication(star(X1!0), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.55/9.66 inference(quant_inst,[status(thm)],[])).
% 14.55/9.66 tff(52,plain,
% 14.55/9.66 (multiplication(star(X1!0), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(multiplication(star(X1!0), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.66 inference(unit_resolution,[status(thm)],[51, 50])).
% 14.55/9.66 tff(53,plain,
% 14.55/9.66 (multiplication(multiplication(star(X1!0), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = multiplication(star(X1!0), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.55/9.66 inference(symmetry,[status(thm)],[52])).
% 14.55/9.66 tff(54,plain,
% 14.55/9.66 (multiplication(multiplication(star(X1!0), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.55/9.66 inference(transitivity,[status(thm)],[53, 43])).
% 14.55/9.66 tff(55,plain,
% 14.55/9.66 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 14.55/9.66 inference(bind,[status(th)],[])).
% 14.55/9.66 tff(56,plain,
% 14.55/9.66 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 14.55/9.66 inference(quant_intro,[status(thm)],[55])).
% 14.55/9.66 tff(57,plain,
% 14.55/9.66 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 14.55/9.66 inference(rewrite,[status(thm)],[])).
% 14.55/9.66 tff(58,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 14.55/9.66 tff(59,plain,
% 14.55/9.66 (![A: $i] : (multiplication(one, A) = A)),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[58, 57])).
% 14.55/9.66 tff(60,plain,(
% 14.55/9.66 ![A: $i] : (multiplication(one, A) = A)),
% 14.55/9.66 inference(skolemize,[status(sab)],[59])).
% 14.55/9.66 tff(61,plain,
% 14.55/9.66 (![A: $i] : (multiplication(one, A) = A)),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[60, 56])).
% 14.55/9.66 tff(62,plain,
% 14.55/9.66 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.66 inference(quant_inst,[status(thm)],[])).
% 14.55/9.66 tff(63,plain,
% 14.55/9.66 (multiplication(one, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)),
% 14.55/9.66 inference(unit_resolution,[status(thm)],[62, 61])).
% 14.55/9.66 tff(64,plain,
% 14.55/9.66 (addition(multiplication(one, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(multiplication(star(X1!0), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.55/9.66 inference(monotonicity,[status(thm)],[63, 54])).
% 14.55/9.66 tff(65,plain,
% 14.55/9.66 (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(multiplication(one, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(multiplication(star(X1!0), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.55/9.66 inference(symmetry,[status(thm)],[64])).
% 14.55/9.66 tff(66,plain,
% 14.55/9.66 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 14.55/9.66 inference(bind,[status(th)],[])).
% 14.55/9.66 tff(67,plain,
% 14.55/9.66 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 14.55/9.66 inference(quant_intro,[status(thm)],[66])).
% 14.55/9.66 tff(68,plain,
% 14.55/9.66 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 14.55/9.66 inference(rewrite,[status(thm)],[])).
% 14.55/9.66 tff(69,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 14.55/9.66 tff(70,plain,
% 14.55/9.66 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[69, 68])).
% 14.55/9.66 tff(71,plain,(
% 14.55/9.66 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 14.55/9.66 inference(skolemize,[status(sab)],[70])).
% 14.55/9.66 tff(72,plain,
% 14.55/9.66 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[71, 67])).
% 14.55/9.66 tff(73,plain,
% 14.55/9.66 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one))))),
% 14.55/9.66 inference(quant_inst,[status(thm)],[])).
% 14.55/9.66 tff(74,plain,
% 14.55/9.66 (addition(addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)))),
% 14.55/9.66 inference(unit_resolution,[status(thm)],[73, 72])).
% 14.55/9.66 tff(75,plain,
% 14.55/9.66 (addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one) = strong_iteration(multiplication(star(X0!1), X1!0))),
% 14.55/9.66 inference(symmetry,[status(thm)],[9])).
% 14.55/9.66 tff(76,plain,
% 14.55/9.66 (multiplication(star(X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.55/9.66 inference(monotonicity,[status(thm)],[75])).
% 14.55/9.66 tff(77,plain,
% 14.55/9.66 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)))),
% 14.55/9.66 inference(quant_inst,[status(thm)],[])).
% 14.55/9.66 tff(78,plain,
% 14.55/9.66 (multiplication(star(X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one))),
% 14.55/9.66 inference(unit_resolution,[status(thm)],[77, 38])).
% 14.55/9.66 tff(79,plain,
% 14.55/9.66 (addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)) = multiplication(star(X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.66 inference(symmetry,[status(thm)],[78])).
% 14.55/9.66 tff(80,plain,
% 14.55/9.66 (addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)) = multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.55/9.66 inference(transitivity,[status(thm)],[79, 76])).
% 14.55/9.66 tff(81,plain,
% 14.55/9.66 (addition(addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.66 inference(monotonicity,[status(thm)],[80])).
% 14.55/9.66 tff(82,plain,
% 14.55/9.66 (addition(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.66 inference(symmetry,[status(thm)],[81])).
% 14.55/9.66 tff(83,plain,
% 14.55/9.66 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 14.55/9.66 inference(bind,[status(th)],[])).
% 14.55/9.66 tff(84,plain,
% 14.55/9.66 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 14.55/9.66 inference(quant_intro,[status(thm)],[83])).
% 14.55/9.66 tff(85,plain,
% 14.55/9.66 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 14.55/9.66 inference(rewrite,[status(thm)],[])).
% 14.55/9.66 tff(86,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','order')).
% 14.55/9.66 tff(87,plain,
% 14.55/9.66 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[86, 85])).
% 14.55/9.66 tff(88,plain,(
% 14.55/9.66 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 14.55/9.66 inference(skolemize,[status(sab)],[87])).
% 14.55/9.66 tff(89,plain,
% 14.55/9.66 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 14.55/9.66 inference(modus_ponens,[status(thm)],[88, 84])).
% 14.55/9.66 tff(90,plain,
% 14.55/9.66 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) <=> (addition(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.55/9.66 inference(quant_inst,[status(thm)],[])).
% 14.55/9.66 tff(91,plain,
% 14.55/9.66 (leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) <=> (addition(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.66 inference(unit_resolution,[status(thm)],[90, 89])).
% 14.55/9.66 tff(92,plain,
% 14.55/9.66 (leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) <=> leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.55/9.66 inference(monotonicity,[status(thm)],[75])).
% 14.55/9.66 tff(93,plain,
% 14.55/9.66 (leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) <=> leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.66 inference(symmetry,[status(thm)],[92])).
% 14.55/9.66 tff(94,plain,
% 14.55/9.66 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one) = addition(one, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))))),
% 14.55/9.66 inference(quant_inst,[status(thm)],[])).
% 14.55/9.66 tff(95,plain,
% 14.55/9.66 (addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one) = addition(one, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.55/9.66 inference(unit_resolution,[status(thm)],[94, 72])).
% 14.55/9.66 tff(96,plain,
% 14.55/9.66 (addition(one, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)),
% 14.55/9.66 inference(symmetry,[status(thm)],[95])).
% 14.55/9.66 tff(97,plain,
% 14.55/9.66 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), one), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))))),
% 14.55/9.67 inference(quant_inst,[status(thm)],[])).
% 14.55/9.67 tff(98,plain,
% 14.55/9.67 (multiplication(addition(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), one), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.55/9.67 inference(unit_resolution,[status(thm)],[97, 28])).
% 14.55/9.67 tff(99,plain,
% 14.55/9.67 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 14.55/9.67 inference(bind,[status(th)],[])).
% 14.55/9.67 tff(100,plain,
% 14.55/9.67 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 14.55/9.67 inference(quant_intro,[status(thm)],[99])).
% 14.55/9.67 tff(101,plain,
% 14.55/9.67 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 14.55/9.67 inference(rewrite,[status(thm)],[])).
% 14.55/9.67 tff(102,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 14.55/9.67 tff(103,plain,
% 14.55/9.67 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 14.55/9.67 inference(modus_ponens,[status(thm)],[102, 101])).
% 14.55/9.67 tff(104,plain,(
% 14.55/9.67 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 14.55/9.67 inference(skolemize,[status(sab)],[103])).
% 14.55/9.67 tff(105,plain,
% 14.55/9.67 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 14.55/9.67 inference(modus_ponens,[status(thm)],[104, 100])).
% 14.55/9.67 tff(106,plain,
% 14.55/9.67 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(X0!1, star(X0!1))) = star(X0!1))),
% 14.55/9.67 inference(quant_inst,[status(thm)],[])).
% 14.55/9.67 tff(107,plain,
% 14.55/9.67 (addition(one, multiplication(X0!1, star(X0!1))) = star(X0!1)),
% 14.55/9.67 inference(unit_resolution,[status(thm)],[106, 105])).
% 14.55/9.67 tff(108,plain,
% 14.55/9.67 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(X0!1, star(X0!1))) = addition(multiplication(X0!1, star(X0!1)), one))),
% 14.55/9.67 inference(quant_inst,[status(thm)],[])).
% 14.55/9.67 tff(109,plain,
% 14.55/9.67 (addition(one, multiplication(X0!1, star(X0!1))) = addition(multiplication(X0!1, star(X0!1)), one)),
% 14.55/9.67 inference(unit_resolution,[status(thm)],[108, 72])).
% 14.55/9.67 tff(110,plain,
% 14.55/9.67 (addition(multiplication(X0!1, star(X0!1)), one) = addition(one, multiplication(X0!1, star(X0!1)))),
% 14.55/9.67 inference(symmetry,[status(thm)],[109])).
% 14.55/9.67 tff(111,plain,
% 14.55/9.67 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(X0!1), X0!1)) = star(X0!1))),
% 14.55/9.67 inference(quant_inst,[status(thm)],[])).
% 14.55/9.67 tff(112,plain,
% 14.55/9.67 (addition(one, multiplication(star(X0!1), X0!1)) = star(X0!1)),
% 14.55/9.67 inference(unit_resolution,[status(thm)],[111, 16])).
% 14.55/9.67 tff(113,plain,
% 14.55/9.67 (star(X0!1) = addition(one, multiplication(star(X0!1), X0!1))),
% 14.55/9.67 inference(symmetry,[status(thm)],[112])).
% 14.55/9.67 tff(114,plain,
% 14.55/9.67 (multiplication(X0!1, star(X0!1)) = multiplication(X0!1, addition(one, multiplication(star(X0!1), X0!1)))),
% 14.55/9.67 inference(monotonicity,[status(thm)],[113])).
% 14.55/9.67 tff(115,plain,
% 14.55/9.67 (multiplication(X0!1, addition(one, multiplication(star(X0!1), X0!1))) = multiplication(X0!1, star(X0!1))),
% 14.55/9.67 inference(symmetry,[status(thm)],[114])).
% 14.55/9.67 tff(116,plain,
% 14.55/9.67 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(one, multiplication(star(X0!1), X0!1))) = addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))))),
% 14.55/9.67 inference(quant_inst,[status(thm)],[])).
% 14.55/9.67 tff(117,plain,
% 14.55/9.67 (multiplication(X0!1, addition(one, multiplication(star(X0!1), X0!1))) = addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1)))),
% 14.55/9.67 inference(unit_resolution,[status(thm)],[116, 38])).
% 14.55/9.67 tff(118,plain,
% 14.55/9.67 (addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))) = multiplication(X0!1, addition(one, multiplication(star(X0!1), X0!1)))),
% 14.55/9.67 inference(symmetry,[status(thm)],[117])).
% 14.55/9.67 tff(119,plain,
% 14.55/9.67 (addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))) = multiplication(X0!1, star(X0!1))),
% 14.55/9.67 inference(transitivity,[status(thm)],[118, 115])).
% 14.55/9.67 tff(120,plain,
% 14.55/9.67 (addition(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), one) = addition(multiplication(X0!1, star(X0!1)), one)),
% 14.55/9.67 inference(monotonicity,[status(thm)],[119])).
% 14.55/9.67 tff(121,plain,
% 14.55/9.67 (addition(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), one) = star(X0!1)),
% 14.55/9.67 inference(transitivity,[status(thm)],[120, 110, 107])).
% 14.55/9.67 tff(122,plain,
% 14.55/9.67 (multiplication(addition(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), one), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = multiplication(star(X0!1), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.55/9.67 inference(monotonicity,[status(thm)],[121, 41])).
% 14.55/9.67 tff(123,plain,
% 14.55/9.67 (multiplication(star(X0!1), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(addition(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), one), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.55/9.67 inference(symmetry,[status(thm)],[122])).
% 14.55/9.67 tff(124,plain,
% 14.55/9.67 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(star(X0!1), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(multiplication(star(X0!1), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.55/9.67 inference(quant_inst,[status(thm)],[])).
% 14.55/9.67 tff(125,plain,
% 14.55/9.67 (multiplication(star(X0!1), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(multiplication(star(X0!1), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.67 inference(unit_resolution,[status(thm)],[124, 50])).
% 14.55/9.67 tff(126,plain,
% 14.55/9.67 (multiplication(multiplication(star(X0!1), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = multiplication(star(X0!1), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.55/9.67 inference(symmetry,[status(thm)],[125])).
% 14.55/9.67 tff(127,plain,
% 14.55/9.67 (multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))) = multiplication(multiplication(star(X0!1), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.55/9.67 inference(monotonicity,[status(thm)],[9])).
% 14.55/9.67 tff(128,plain,
% 14.55/9.67 (multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))) = addition(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.55/9.67 inference(transitivity,[status(thm)],[127, 126, 123, 98])).
% 14.55/9.67 tff(129,plain,
% 14.55/9.67 (addition(one, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) = addition(one, addition(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))))),
% 14.55/9.67 inference(monotonicity,[status(thm)],[128])).
% 14.55/9.67 tff(130,plain,
% 14.55/9.67 (addition(one, addition(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))) = addition(one, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.55/9.67 inference(symmetry,[status(thm)],[129])).
% 14.55/9.67 tff(131,plain,
% 14.55/9.67 (^[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)))),
% 14.55/9.67 inference(bind,[status(th)],[])).
% 14.55/9.67 tff(132,plain,
% 14.55/9.67 (![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))),
% 14.55/9.67 inference(quant_intro,[status(thm)],[131])).
% 14.55/9.67 tff(133,plain,
% 14.55/9.67 (![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))),
% 14.55/9.67 inference(rewrite,[status(thm)],[])).
% 14.55/9.67 tff(134,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')).
% 14.55/9.67 tff(135,plain,
% 14.55/9.67 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 14.55/9.67 inference(modus_ponens,[status(thm)],[134, 133])).
% 14.55/9.67 tff(136,plain,(
% 14.55/9.67 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 14.55/9.67 inference(skolemize,[status(sab)],[135])).
% 14.55/9.67 tff(137,plain,
% 14.55/9.67 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 14.55/9.67 inference(modus_ponens,[status(thm)],[136, 132])).
% 14.55/9.67 tff(138,plain,
% 14.55/9.67 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))) = addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))))),
% 14.55/9.67 inference(quant_inst,[status(thm)],[])).
% 14.55/9.67 tff(139,plain,
% 14.55/9.67 (addition(one, addition(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))) = addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.55/9.67 inference(unit_resolution,[status(thm)],[138, 137])).
% 14.55/9.67 tff(140,plain,
% 14.55/9.67 (addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(one, addition(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))))),
% 14.55/9.67 inference(symmetry,[status(thm)],[139])).
% 14.55/9.67 tff(141,plain,
% 14.55/9.67 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 14.55/9.67 inference(bind,[status(th)],[])).
% 14.55/9.67 tff(142,plain,
% 14.55/9.67 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 14.55/9.67 inference(quant_intro,[status(thm)],[141])).
% 14.55/9.67 tff(143,plain,
% 14.55/9.67 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 14.55/9.67 inference(rewrite,[status(thm)],[])).
% 14.55/9.67 tff(144,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 14.55/9.67 tff(145,plain,
% 14.55/9.67 (![A: $i] : (addition(A, A) = A)),
% 14.55/9.67 inference(modus_ponens,[status(thm)],[144, 143])).
% 14.55/9.67 tff(146,plain,(
% 14.55/9.67 ![A: $i] : (addition(A, A) = A)),
% 14.55/9.67 inference(skolemize,[status(sab)],[145])).
% 14.55/9.67 tff(147,plain,
% 14.55/9.67 (![A: $i] : (addition(A, A) = A)),
% 14.55/9.67 inference(modus_ponens,[status(thm)],[146, 142])).
% 14.55/9.67 tff(148,plain,
% 14.55/9.67 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.55/9.67 inference(quant_inst,[status(thm)],[])).
% 14.55/9.67 tff(149,plain,
% 14.55/9.67 (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))),
% 14.70/9.67 inference(unit_resolution,[status(thm)],[148, 147])).
% 14.70/9.67 tff(150,plain,
% 14.70/9.67 (addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)) = addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.70/9.67 inference(symmetry,[status(thm)],[149])).
% 14.70/9.67 tff(151,plain,
% 14.70/9.67 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.70/9.67 inference(quant_inst,[status(thm)],[])).
% 14.70/9.67 tff(152,plain,
% 14.70/9.67 (multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))),
% 14.70/9.67 inference(unit_resolution,[status(thm)],[151, 61])).
% 14.70/9.67 tff(153,plain,
% 14.70/9.67 (multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.70/9.67 inference(transitivity,[status(thm)],[152, 150])).
% 14.70/9.67 tff(154,plain,
% 14.70/9.67 (addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.70/9.67 inference(monotonicity,[status(thm)],[153])).
% 14.70/9.67 tff(155,plain,
% 14.70/9.67 (addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), multiplication(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.70/9.67 inference(symmetry,[status(thm)],[154])).
% 14.70/9.67 tff(156,plain,
% 14.70/9.67 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.70/9.67 inference(quant_inst,[status(thm)],[])).
% 14.70/9.67 tff(157,plain,
% 14.70/9.67 (addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.70/9.67 inference(unit_resolution,[status(thm)],[156, 137])).
% 14.70/9.67 tff(158,plain,
% 14.70/9.67 (addition(addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.70/9.67 inference(symmetry,[status(thm)],[157])).
% 14.70/9.67 tff(159,plain,
% 14.70/9.67 (multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))) = multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.67 inference(monotonicity,[status(thm)],[9])).
% 14.70/9.67 tff(160,plain,
% 14.70/9.67 (multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.67 inference(symmetry,[status(thm)],[159])).
% 14.70/9.67 tff(161,plain,
% 14.70/9.67 (addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)) = multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.67 inference(transitivity,[status(thm)],[41, 160])).
% 14.70/9.67 tff(162,plain,
% 14.70/9.67 (multiplication(addition(one, multiplication(X0!1, star(X0!1))), X1!0) = multiplication(star(X0!1), X1!0)),
% 14.70/9.67 inference(monotonicity,[status(thm)],[107])).
% 14.70/9.67 tff(163,plain,
% 14.70/9.67 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(one, multiplication(X0!1, star(X0!1))), X1!0) = addition(multiplication(one, X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)))),
% 14.70/9.67 inference(quant_inst,[status(thm)],[])).
% 14.70/9.67 tff(164,plain,
% 14.70/9.67 (multiplication(addition(one, multiplication(X0!1, star(X0!1))), X1!0) = addition(multiplication(one, X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0))),
% 14.70/9.67 inference(unit_resolution,[status(thm)],[163, 28])).
% 14.70/9.67 tff(165,plain,
% 14.70/9.67 (addition(multiplication(one, X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = multiplication(addition(one, multiplication(X0!1, star(X0!1))), X1!0)),
% 14.70/9.67 inference(symmetry,[status(thm)],[164])).
% 14.70/9.67 tff(166,plain,
% 14.70/9.67 (addition(multiplication(one, X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = multiplication(star(X0!1), X1!0)),
% 14.70/9.67 inference(transitivity,[status(thm)],[165, 162])).
% 14.70/9.67 tff(167,plain,
% 14.70/9.67 (multiplication(addition(multiplication(one, X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.67 inference(monotonicity,[status(thm)],[166, 75])).
% 14.70/9.67 tff(168,plain,
% 14.70/9.67 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(one, X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(one, X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))))),
% 14.70/9.67 inference(quant_inst,[status(thm)],[])).
% 14.70/9.67 tff(169,plain,
% 14.70/9.67 (multiplication(addition(multiplication(one, X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(one, X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.68 inference(unit_resolution,[status(thm)],[168, 28])).
% 14.70/9.68 tff(170,plain,
% 14.70/9.68 (addition(multiplication(multiplication(one, X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(addition(multiplication(one, X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(symmetry,[status(thm)],[169])).
% 14.70/9.68 tff(171,plain,
% 14.70/9.68 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!0) = X1!0)),
% 14.70/9.68 inference(quant_inst,[status(thm)],[])).
% 14.70/9.68 tff(172,plain,
% 14.70/9.68 (multiplication(one, X1!0) = X1!0),
% 14.70/9.68 inference(unit_resolution,[status(thm)],[171, 61])).
% 14.70/9.68 tff(173,plain,
% 14.70/9.68 (multiplication(multiplication(one, X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.68 inference(monotonicity,[status(thm)],[172, 75])).
% 14.70/9.68 tff(174,plain,
% 14.70/9.68 (multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))) = multiplication(multiplication(one, X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(symmetry,[status(thm)],[173])).
% 14.70/9.68 tff(175,plain,
% 14.70/9.68 (addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)) = multiplication(multiplication(one, X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(transitivity,[status(thm)],[41, 160, 174])).
% 14.70/9.68 tff(176,plain,
% 14.70/9.68 (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = addition(multiplication(multiplication(one, X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.68 inference(monotonicity,[status(thm)],[175])).
% 14.70/9.68 tff(177,plain,
% 14.70/9.68 (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.68 inference(transitivity,[status(thm)],[176, 170, 167])).
% 14.70/9.68 tff(178,plain,
% 14.70/9.68 (addition(one, addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))) = addition(one, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.70/9.68 inference(monotonicity,[status(thm)],[177])).
% 14.70/9.68 tff(179,plain,
% 14.70/9.68 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))) = addition(addition(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))))),
% 14.70/9.68 inference(quant_inst,[status(thm)],[])).
% 14.70/9.68 tff(180,plain,
% 14.70/9.68 (addition(one, addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))) = addition(addition(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.68 inference(unit_resolution,[status(thm)],[179, 137])).
% 14.70/9.68 tff(181,plain,
% 14.70/9.68 (addition(addition(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = addition(one, addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))))),
% 14.70/9.68 inference(symmetry,[status(thm)],[180])).
% 14.70/9.68 tff(182,plain,
% 14.70/9.68 (multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), X1!0) = multiplication(multiplication(X0!1, star(X0!1)), X1!0)),
% 14.70/9.68 inference(monotonicity,[status(thm)],[119])).
% 14.70/9.68 tff(183,plain,
% 14.70/9.68 (multiplication(multiplication(X0!1, star(X0!1)), X1!0) = multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), X1!0)),
% 14.70/9.68 inference(symmetry,[status(thm)],[182])).
% 14.70/9.68 tff(184,plain,
% 14.70/9.68 (multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = multiplication(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(monotonicity,[status(thm)],[183])).
% 14.70/9.68 tff(185,plain,
% 14.70/9.68 (multiplication(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(symmetry,[status(thm)],[184])).
% 14.70/9.68 tff(186,plain,
% 14.70/9.68 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.68 inference(quant_inst,[status(thm)],[])).
% 14.70/9.68 tff(187,plain,
% 14.70/9.68 (multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(unit_resolution,[status(thm)],[186, 50])).
% 14.70/9.68 tff(188,plain,
% 14.70/9.68 (multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.70/9.68 inference(monotonicity,[status(thm)],[40])).
% 14.70/9.68 tff(189,plain,
% 14.70/9.68 (multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.68 inference(symmetry,[status(thm)],[188])).
% 14.70/9.68 tff(190,plain,
% 14.70/9.68 (multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(transitivity,[status(thm)],[189, 187, 185])).
% 14.70/9.68 tff(191,plain,
% 14.70/9.68 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), one) = addition(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.70/9.68 inference(quant_inst,[status(thm)],[])).
% 14.70/9.68 tff(192,plain,
% 14.70/9.68 (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), one) = addition(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.70/9.68 inference(unit_resolution,[status(thm)],[191, 72])).
% 14.70/9.68 tff(193,plain,
% 14.70/9.68 (addition(addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), one), multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(addition(one, addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), multiplication(multiplication(multiplication(X0!1, star(X0!1)), X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.68 inference(monotonicity,[status(thm)],[192, 190])).
% 14.70/9.68 tff(194,plain,
% 14.70/9.68 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))) = addition(addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), one), multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))))),
% 14.70/9.68 inference(quant_inst,[status(thm)],[])).
% 14.70/9.68 tff(195,plain,
% 14.70/9.68 (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))) = addition(addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), one), multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.70/9.68 inference(unit_resolution,[status(thm)],[194, 137])).
% 14.70/9.68 tff(196,plain,
% 14.70/9.68 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))))),
% 14.70/9.68 inference(quant_inst,[status(thm)],[])).
% 14.70/9.68 tff(197,plain,
% 14.70/9.68 (addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))))),
% 14.70/9.68 inference(unit_resolution,[status(thm)],[196, 72])).
% 14.70/9.68 tff(198,plain,
% 14.70/9.68 (addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)),
% 14.70/9.68 inference(transitivity,[status(thm)],[197, 195, 193, 181, 178, 96])).
% 14.70/9.68 tff(199,plain,
% 14.70/9.68 (addition(addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.70/9.68 inference(monotonicity,[status(thm)],[198, 161])).
% 14.70/9.68 tff(200,plain,
% 14.70/9.68 (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0)))) = addition(addition(addition(one, multiplication(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))),
% 14.70/9.68 inference(symmetry,[status(thm)],[199])).
% 14.70/9.68 tff(201,plain,
% 14.70/9.68 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0)))))),
% 14.70/9.68 inference(quant_inst,[status(thm)],[])).
% 14.70/9.68 tff(202,plain,
% 14.70/9.68 (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.70/9.68 inference(unit_resolution,[status(thm)],[201, 72])).
% 14.70/9.68 tff(203,plain,
% 14.70/9.68 (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)),
% 14.70/9.68 inference(transitivity,[status(thm)],[202, 200, 158, 155, 140, 130, 96])).
% 14.70/9.68 tff(204,plain,
% 14.70/9.68 (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(monotonicity,[status(thm)],[9])).
% 14.70/9.68 tff(205,plain,
% 14.70/9.68 (addition(multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.68 inference(monotonicity,[status(thm)],[160, 75])).
% 14.70/9.68 tff(206,plain,
% 14.70/9.68 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(quant_inst,[status(thm)],[])).
% 14.70/9.68 tff(207,plain,
% 14.70/9.68 (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)),
% 14.70/9.68 inference(unit_resolution,[status(thm)],[206, 147])).
% 14.70/9.68 tff(208,plain,
% 14.70/9.68 (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = addition(multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(monotonicity,[status(thm)],[41, 207])).
% 14.70/9.68 tff(209,plain,
% 14.70/9.68 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = addition(addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.68 inference(quant_inst,[status(thm)],[])).
% 14.70/9.68 tff(210,plain,
% 14.70/9.68 (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = addition(addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(unit_resolution,[status(thm)],[209, 137])).
% 14.70/9.68 tff(211,plain,
% 14.70/9.68 (addition(addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.68 inference(symmetry,[status(thm)],[210])).
% 14.70/9.68 tff(212,plain,
% 14.70/9.68 (addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(monotonicity,[status(thm)],[41])).
% 14.70/9.68 tff(213,plain,
% 14.70/9.68 (addition(multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(symmetry,[status(thm)],[212])).
% 14.70/9.68 tff(214,plain,
% 14.70/9.68 (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = addition(multiplication(X1!0, addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.68 inference(symmetry,[status(thm)],[205])).
% 14.70/9.68 tff(215,plain,
% 14.70/9.68 (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(transitivity,[status(thm)],[214, 213])).
% 14.70/9.69 tff(216,plain,
% 14.70/9.69 (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(addition(addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(monotonicity,[status(thm)],[215])).
% 14.70/9.69 tff(217,plain,
% 14.70/9.69 (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(transitivity,[status(thm)],[216, 211, 208, 205, 204])).
% 14.70/9.69 tff(218,plain,
% 14.70/9.69 ((addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) <=> (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(monotonicity,[status(thm)],[217])).
% 14.70/9.69 tff(219,plain,
% 14.70/9.69 ((~(addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) <=> (~(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.69 inference(monotonicity,[status(thm)],[218])).
% 14.70/9.69 tff(220,plain,
% 14.70/9.69 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) <=> (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.69 inference(quant_inst,[status(thm)],[])).
% 14.70/9.69 tff(221,plain,
% 14.70/9.69 (leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) <=> (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(unit_resolution,[status(thm)],[220, 89])).
% 14.70/9.69 tff(222,plain,
% 14.70/9.69 (leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) <=> leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.69 inference(monotonicity,[status(thm)],[75])).
% 14.70/9.69 tff(223,plain,
% 14.70/9.69 (leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) <=> leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(symmetry,[status(thm)],[222])).
% 14.70/9.69 tff(224,plain,
% 14.70/9.69 ((~leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))) <=> (~leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.69 inference(monotonicity,[status(thm)],[223])).
% 14.70/9.69 tff(225,assumption,(~leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))), introduced(assumption)).
% 14.70/9.69 tff(226,plain,
% 14.70/9.69 (~leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(modus_ponens,[status(thm)],[225, 224])).
% 14.70/9.69 tff(227,plain,
% 14.70/9.69 ((~(leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) <=> (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))) | leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) | (~(addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.69 inference(tautology,[status(thm)],[])).
% 14.70/9.69 tff(228,plain,
% 14.70/9.69 (~(addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(unit_resolution,[status(thm)],[227, 226, 221])).
% 14.70/9.69 tff(229,plain,
% 14.70/9.69 (~(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(modus_ponens,[status(thm)],[228, 219])).
% 14.70/9.69 tff(230,plain,
% 14.70/9.69 ($false),
% 14.70/9.69 inference(unit_resolution,[status(thm)],[229, 203])).
% 14.70/9.69 tff(231,plain,(leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))), inference(lemma,lemma(discharge,[]))).
% 14.70/9.69 tff(232,plain,
% 14.70/9.69 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)))),
% 14.70/9.69 inference(bind,[status(th)],[])).
% 14.70/9.69 tff(233,plain,
% 14.70/9.69 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 14.70/9.69 inference(quant_intro,[status(thm)],[232])).
% 14.70/9.69 tff(234,plain,
% 14.70/9.69 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 14.70/9.69 inference(rewrite,[status(thm)],[])).
% 14.70/9.69 tff(235,plain,
% 14.70/9.69 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C)) <=> ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C)))),
% 14.70/9.69 inference(bind,[status(th)],[])).
% 14.70/9.69 tff(236,plain,
% 14.70/9.69 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 14.70/9.69 inference(quant_intro,[status(thm)],[235])).
% 14.70/9.69 tff(237,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_induction1')).
% 14.70/9.69 tff(238,plain,
% 14.70/9.69 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 14.70/9.69 inference(modus_ponens,[status(thm)],[237, 236])).
% 14.70/9.69 tff(239,plain,
% 14.70/9.69 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 14.70/9.69 inference(modus_ponens,[status(thm)],[238, 234])).
% 14.70/9.69 tff(240,plain,(
% 14.70/9.69 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 14.70/9.69 inference(skolemize,[status(sab)],[239])).
% 14.70/9.69 tff(241,plain,
% 14.70/9.69 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 14.70/9.69 inference(modus_ponens,[status(thm)],[240, 233])).
% 14.70/9.69 tff(242,plain,
% 14.70/9.69 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))) | leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))) | leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.70/9.69 inference(rewrite,[status(thm)],[])).
% 14.70/9.69 tff(243,plain,
% 14.70/9.69 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | ((~leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))) | leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.70/9.69 inference(quant_inst,[status(thm)],[])).
% 14.70/9.69 tff(244,plain,
% 14.70/9.69 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))) | (~leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))) | leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.69 inference(modus_ponens,[status(thm)],[243, 242])).
% 14.70/9.69 tff(245,plain,
% 14.70/9.69 (leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.69 inference(unit_resolution,[status(thm)],[244, 241, 231])).
% 14.70/9.69 tff(246,plain,
% 14.70/9.69 (leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(modus_ponens,[status(thm)],[245, 93])).
% 14.70/9.69 tff(247,plain,
% 14.70/9.69 ((~(leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) <=> (addition(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))) | (~leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) | (addition(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(tautology,[status(thm)],[])).
% 14.70/9.69 tff(248,plain,
% 14.70/9.69 (addition(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)),
% 14.70/9.69 inference(unit_resolution,[status(thm)],[247, 246, 91])).
% 14.70/9.69 tff(249,plain,
% 14.70/9.69 (addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one) = addition(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(symmetry,[status(thm)],[248])).
% 14.70/9.69 tff(250,plain,
% 14.70/9.69 (addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)))),
% 14.70/9.69 inference(transitivity,[status(thm)],[249, 82, 74])).
% 14.70/9.69 tff(251,plain,
% 14.70/9.69 (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one))), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.70/9.69 inference(monotonicity,[status(thm)],[250])).
% 14.70/9.69 tff(252,plain,
% 14.70/9.69 (addition(addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one))), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.70/9.69 inference(symmetry,[status(thm)],[251])).
% 14.70/9.69 tff(253,plain,
% 14.70/9.69 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))) = addition(addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one))), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))))),
% 14.70/9.69 inference(quant_inst,[status(thm)],[])).
% 14.70/9.69 tff(254,plain,
% 14.70/9.69 (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))) = addition(addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one))), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.70/9.69 inference(unit_resolution,[status(thm)],[253, 137])).
% 14.70/9.69 tff(255,plain,
% 14.70/9.69 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) <=> (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.70/9.69 inference(quant_inst,[status(thm)],[])).
% 14.70/9.69 tff(256,plain,
% 14.70/9.69 (leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) <=> (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.69 inference(unit_resolution,[status(thm)],[255, 89])).
% 14.70/9.69 tff(257,plain,
% 14.70/9.69 ((~(leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) <=> (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = strong_iteration(multiplication(star(X0!1), X1!0))))) | (~leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))) | (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.69 inference(tautology,[status(thm)],[])).
% 14.70/9.69 tff(258,plain,
% 14.70/9.69 ((~(leq(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) <=> (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = strong_iteration(multiplication(star(X0!1), X1!0))))) | (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.69 inference(unit_resolution,[status(thm)],[257, 231])).
% 14.70/9.69 tff(259,plain,
% 14.70/9.69 (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = strong_iteration(multiplication(star(X0!1), X1!0))),
% 14.70/9.69 inference(unit_resolution,[status(thm)],[258, 256])).
% 14.70/9.69 tff(260,plain,
% 14.70/9.69 (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.69 inference(monotonicity,[status(thm)],[75])).
% 14.70/9.69 tff(261,plain,
% 14.70/9.69 (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)) = addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.69 inference(monotonicity,[status(thm)],[260, 75])).
% 14.70/9.69 tff(262,plain,
% 14.70/9.69 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.69 inference(quant_inst,[status(thm)],[])).
% 14.70/9.69 tff(263,plain,
% 14.70/9.69 (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))) = addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(unit_resolution,[status(thm)],[262, 137])).
% 14.70/9.69 tff(264,plain,
% 14.70/9.69 (addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(symmetry,[status(thm)],[207])).
% 14.70/9.69 tff(265,plain,
% 14.70/9.69 (strong_iteration(multiplication(star(X0!1), X1!0)) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 14.70/9.69 inference(transitivity,[status(thm)],[9, 264])).
% 14.70/9.69 tff(266,plain,
% 14.70/9.69 (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)))),
% 14.70/9.69 inference(monotonicity,[status(thm)],[265])).
% 14.70/9.69 tff(267,plain,
% 14.70/9.69 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = addition(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0)))))),
% 14.70/9.69 inference(quant_inst,[status(thm)],[])).
% 14.70/9.69 tff(268,plain,
% 14.70/9.69 (addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))) = addition(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.70/9.69 inference(unit_resolution,[status(thm)],[267, 72])).
% 14.70/9.69 tff(269,plain,
% 14.70/9.69 (addition(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0)))) = addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.70/9.69 inference(symmetry,[status(thm)],[268])).
% 14.70/9.69 tff(270,plain,
% 14.70/9.69 (addition(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0)))) = strong_iteration(multiplication(star(X0!1), X1!0))),
% 14.72/9.70 inference(transitivity,[status(thm)],[269, 266, 263, 261, 259])).
% 14.72/9.70 tff(271,plain,
% 14.72/9.70 (multiplication(star(X1!0), addition(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))))) = multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.72/9.70 inference(monotonicity,[status(thm)],[270])).
% 14.72/9.70 tff(272,plain,
% 14.72/9.70 (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))) = addition(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.72/9.70 inference(monotonicity,[status(thm)],[75, 161])).
% 14.72/9.70 tff(273,plain,
% 14.72/9.70 (multiplication(star(X1!0), addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = multiplication(star(X1!0), addition(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0)))))),
% 14.72/9.70 inference(monotonicity,[status(thm)],[272])).
% 14.72/9.70 tff(274,plain,
% 14.72/9.70 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X1!0), addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(multiplication(star(X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))))),
% 14.72/9.70 inference(quant_inst,[status(thm)],[])).
% 14.72/9.70 tff(275,plain,
% 14.72/9.70 (multiplication(star(X1!0), addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(multiplication(star(X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.72/9.70 inference(unit_resolution,[status(thm)],[274, 38])).
% 14.72/9.70 tff(276,plain,
% 14.72/9.70 (addition(multiplication(star(X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = multiplication(star(X1!0), addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.72/9.70 inference(symmetry,[status(thm)],[275])).
% 14.72/9.70 tff(277,plain,
% 14.72/9.70 (addition(addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = addition(multiplication(star(X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one)), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))),
% 14.72/9.70 inference(monotonicity,[status(thm)],[79])).
% 14.72/9.70 tff(278,plain,
% 14.72/9.70 (addition(addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))) = multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.72/9.70 inference(transitivity,[status(thm)],[277, 276, 273, 271])).
% 14.72/9.70 tff(279,plain,
% 14.72/9.70 (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one))))) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.72/9.70 inference(monotonicity,[status(thm)],[278])).
% 14.72/9.70 tff(280,plain,
% 14.72/9.70 (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) = addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), addition(addition(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)), multiplication(star(X1!0), addition(multiplication(X1!0, multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(X1!0, one)))))),
% 14.72/9.70 inference(symmetry,[status(thm)],[279])).
% 14.72/9.70 tff(281,plain,
% 14.72/9.70 (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) = multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 14.72/9.70 inference(transitivity,[status(thm)],[280, 254, 252, 65, 31, 21])).
% 14.72/9.70 tff(282,plain,
% 14.72/9.70 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) <=> (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) = multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))))),
% 14.72/9.70 inference(quant_inst,[status(thm)],[])).
% 14.72/9.70 tff(283,plain,
% 14.72/9.70 (leq(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) <=> (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) = multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.72/9.70 inference(unit_resolution,[status(thm)],[282, 89])).
% 14.72/9.70 tff(284,plain,
% 14.72/9.70 (leq(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) <=> leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.72/9.70 inference(monotonicity,[status(thm)],[75])).
% 14.72/9.70 tff(285,plain,
% 14.72/9.70 (leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) <=> leq(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.72/9.70 inference(symmetry,[status(thm)],[284])).
% 14.72/9.70 tff(286,plain,
% 14.72/9.70 ((~leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))) <=> (~leq(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))))),
% 14.72/9.70 inference(monotonicity,[status(thm)],[285])).
% 14.72/9.70 tff(287,plain,
% 14.72/9.70 ((~(~((~leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))) | (~leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))))))) <=> ((~leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))) | (~leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))))),
% 14.72/9.70 inference(rewrite,[status(thm)],[])).
% 14.72/9.70 tff(288,plain,
% 14.72/9.70 ((leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) & leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))) <=> (~((~leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))) | (~leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))))))),
% 14.72/9.70 inference(rewrite,[status(thm)],[])).
% 14.72/9.70 tff(289,plain,
% 14.72/9.70 ((~(leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) & leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))))) <=> (~(~((~leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))) | (~leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))))))),
% 14.72/9.70 inference(monotonicity,[status(thm)],[288])).
% 14.72/9.70 tff(290,plain,
% 14.72/9.70 ((~(leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) & leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))))) <=> ((~leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))) | (~leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))))),
% 14.72/9.70 inference(transitivity,[status(thm)],[289, 287])).
% 14.72/9.70 tff(291,plain,
% 14.72/9.70 ((~![X0: $i, X1: $i] : (leq(strong_iteration(multiplication(star(X0), X1)), multiplication(star(X1), strong_iteration(multiplication(star(X0), X1)))) & leq(multiplication(star(X1), strong_iteration(multiplication(star(X0), X1))), strong_iteration(multiplication(star(X0), X1))))) <=> (~![X0: $i, X1: $i] : (leq(strong_iteration(multiplication(star(X0), X1)), multiplication(star(X1), strong_iteration(multiplication(star(X0), X1)))) & leq(multiplication(star(X1), strong_iteration(multiplication(star(X0), X1))), strong_iteration(multiplication(star(X0), X1)))))),
% 14.72/9.70 inference(rewrite,[status(thm)],[])).
% 14.72/9.70 tff(292,axiom,(~![X0: $i, X1: $i] : (leq(strong_iteration(multiplication(star(X0), X1)), multiplication(star(X1), strong_iteration(multiplication(star(X0), X1)))) & leq(multiplication(star(X1), strong_iteration(multiplication(star(X0), X1))), strong_iteration(multiplication(star(X0), X1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 14.72/9.70 tff(293,plain,
% 14.72/9.70 (~![X0: $i, X1: $i] : (leq(strong_iteration(multiplication(star(X0), X1)), multiplication(star(X1), strong_iteration(multiplication(star(X0), X1)))) & leq(multiplication(star(X1), strong_iteration(multiplication(star(X0), X1))), strong_iteration(multiplication(star(X0), X1))))),
% 14.72/9.70 inference(modus_ponens,[status(thm)],[292, 291])).
% 14.72/9.70 tff(294,plain,
% 14.72/9.70 (~![X0: $i, X1: $i] : (leq(strong_iteration(multiplication(star(X0), X1)), multiplication(star(X1), strong_iteration(multiplication(star(X0), X1)))) & leq(multiplication(star(X1), strong_iteration(multiplication(star(X0), X1))), strong_iteration(multiplication(star(X0), X1))))),
% 14.72/9.70 inference(modus_ponens,[status(thm)],[293, 291])).
% 14.72/9.70 tff(295,plain,
% 14.72/9.70 (~![X0: $i, X1: $i] : (leq(strong_iteration(multiplication(star(X0), X1)), multiplication(star(X1), strong_iteration(multiplication(star(X0), X1)))) & leq(multiplication(star(X1), strong_iteration(multiplication(star(X0), X1))), strong_iteration(multiplication(star(X0), X1))))),
% 14.72/9.70 inference(modus_ponens,[status(thm)],[294, 291])).
% 14.72/9.70 tff(296,plain,
% 14.72/9.70 (~![X0: $i, X1: $i] : (leq(strong_iteration(multiplication(star(X0), X1)), multiplication(star(X1), strong_iteration(multiplication(star(X0), X1)))) & leq(multiplication(star(X1), strong_iteration(multiplication(star(X0), X1))), strong_iteration(multiplication(star(X0), X1))))),
% 14.72/9.70 inference(modus_ponens,[status(thm)],[295, 291])).
% 14.72/9.70 tff(297,plain,
% 14.72/9.70 (~![X0: $i, X1: $i] : (leq(strong_iteration(multiplication(star(X0), X1)), multiplication(star(X1), strong_iteration(multiplication(star(X0), X1)))) & leq(multiplication(star(X1), strong_iteration(multiplication(star(X0), X1))), strong_iteration(multiplication(star(X0), X1))))),
% 14.72/9.70 inference(modus_ponens,[status(thm)],[296, 291])).
% 14.72/9.70 tff(298,plain,
% 14.72/9.70 (~![X0: $i, X1: $i] : (leq(strong_iteration(multiplication(star(X0), X1)), multiplication(star(X1), strong_iteration(multiplication(star(X0), X1)))) & leq(multiplication(star(X1), strong_iteration(multiplication(star(X0), X1))), strong_iteration(multiplication(star(X0), X1))))),
% 14.72/9.70 inference(modus_ponens,[status(thm)],[297, 291])).
% 14.72/9.70 tff(299,plain,
% 14.72/9.70 (~![X0: $i, X1: $i] : (leq(strong_iteration(multiplication(star(X0), X1)), multiplication(star(X1), strong_iteration(multiplication(star(X0), X1)))) & leq(multiplication(star(X1), strong_iteration(multiplication(star(X0), X1))), strong_iteration(multiplication(star(X0), X1))))),
% 14.72/9.70 inference(modus_ponens,[status(thm)],[298, 291])).
% 14.72/9.70 tff(300,plain,(
% 14.72/9.70 ~(leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) & leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.72/9.70 inference(skolemize,[status(sab)],[299])).
% 14.72/9.70 tff(301,plain,
% 14.72/9.70 ((~leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))) | (~leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.72/9.70 inference(modus_ponens,[status(thm)],[300, 290])).
% 14.72/9.70 tff(302,plain,
% 14.72/9.70 (~leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.72/9.70 inference(unit_resolution,[status(thm)],[301, 245])).
% 14.72/9.70 tff(303,plain,
% 14.72/9.70 (~leq(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.72/9.70 inference(modus_ponens,[status(thm)],[302, 286])).
% 14.72/9.70 tff(304,plain,
% 14.72/9.70 ((~(leq(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) <=> (addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) = multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))))) | leq(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) | (~(addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) = multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))))),
% 14.72/9.70 inference(tautology,[status(thm)],[])).
% 14.72/9.70 tff(305,plain,
% 14.72/9.70 (~(addition(addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))) = multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 14.72/9.70 inference(unit_resolution,[status(thm)],[304, 303, 283])).
% 14.72/9.70 tff(306,plain,
% 14.72/9.70 ($false),
% 14.72/9.70 inference(unit_resolution,[status(thm)],[305, 281])).
% 14.72/9.70 % SZS output end Proof
%------------------------------------------------------------------------------