%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE147+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 Jun 21 05:13:05 AM UTC 2025
% Result : Theorem 7.04s 7.28s
% Output : Proof 7.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE147+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:05:16 EDT 2025
% 0.12/0.33 % CPUTime :
% 7.04/7.28 % SZS status Theorem
% 7.04/7.28 % SZS output start Proof
% 7.04/7.28 tff(addition_type, type, (
% 7.04/7.28 addition: ( $i * $i ) > $i)).
% 7.04/7.28 tff(multiplication_type, type, (
% 7.04/7.28 multiplication: ( $i * $i ) > $i)).
% 7.04/7.28 tff(one_type, type, (
% 7.04/7.28 one: $i)).
% 7.04/7.28 tff(star_type, type, (
% 7.04/7.28 star: $i > $i)).
% 7.04/7.28 tff(tptp_fun_X1_0_type, type, (
% 7.04/7.28 tptp_fun_X1_0: $i)).
% 7.04/7.28 tff(strong_iteration_type, type, (
% 7.04/7.28 strong_iteration: $i > $i)).
% 7.04/7.28 tff(tptp_fun_X0_1_type, type, (
% 7.04/7.28 tptp_fun_X0_1: $i)).
% 7.04/7.28 tff(leq_type, type, (
% 7.04/7.28 leq: ( $i * $i ) > $o)).
% 7.04/7.28 tff(1,plain,
% 7.04/7.28 (^[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))))),
% 7.04/7.28 inference(bind,[status(th)],[])).
% 7.04/7.28 tff(2,plain,
% 7.04/7.28 (![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)))),
% 7.04/7.28 inference(quant_intro,[status(thm)],[1])).
% 7.04/7.28 tff(3,plain,
% 7.04/7.28 (![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)))),
% 7.04/7.28 inference(rewrite,[status(thm)],[])).
% 7.04/7.28 tff(4,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','distributivity1')).
% 7.04/7.28 tff(5,plain,
% 7.04/7.28 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 7.04/7.28 inference(modus_ponens,[status(thm)],[4, 3])).
% 7.04/7.28 tff(6,plain,(
% 7.04/7.28 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 7.04/7.28 inference(skolemize,[status(sab)],[5])).
% 7.04/7.28 tff(7,plain,
% 7.04/7.28 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 7.04/7.28 inference(modus_ponens,[status(thm)],[6, 2])).
% 7.04/7.28 tff(8,plain,
% 7.04/7.28 ((~![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)))),
% 7.04/7.28 inference(quant_inst,[status(thm)],[])).
% 7.04/7.28 tff(9,plain,
% 7.04/7.28 (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))),
% 7.04/7.28 inference(unit_resolution,[status(thm)],[8, 7])).
% 7.04/7.28 tff(10,plain,
% 7.04/7.28 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 7.04/7.28 inference(bind,[status(th)],[])).
% 7.04/7.28 tff(11,plain,
% 7.04/7.28 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 7.04/7.28 inference(quant_intro,[status(thm)],[10])).
% 7.04/7.28 tff(12,plain,
% 7.04/7.28 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 7.04/7.28 inference(rewrite,[status(thm)],[])).
% 7.04/7.28 tff(13,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 7.04/7.28 tff(14,plain,
% 7.04/7.28 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 7.04/7.28 inference(modus_ponens,[status(thm)],[13, 12])).
% 7.04/7.28 tff(15,plain,(
% 7.04/7.28 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 7.04/7.28 inference(skolemize,[status(sab)],[14])).
% 7.04/7.28 tff(16,plain,
% 7.04/7.28 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 7.04/7.28 inference(modus_ponens,[status(thm)],[15, 11])).
% 7.04/7.28 tff(17,plain,
% 7.04/7.28 ((~![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))),
% 7.04/7.28 inference(quant_inst,[status(thm)],[])).
% 7.04/7.28 tff(18,plain,
% 7.04/7.28 (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)),
% 7.04/7.28 inference(unit_resolution,[status(thm)],[17, 16])).
% 7.04/7.28 tff(19,plain,
% 7.04/7.28 (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))),
% 7.04/7.28 inference(symmetry,[status(thm)],[18])).
% 7.04/7.28 tff(20,plain,
% 7.04/7.28 (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)))),
% 7.04/7.28 inference(monotonicity,[status(thm)],[19])).
% 7.04/7.28 tff(21,plain,
% 7.04/7.28 (multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))) = multiplication(star(X1!0), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 7.04/7.28 inference(symmetry,[status(thm)],[20])).
% 7.04/7.28 tff(22,plain,
% 7.04/7.28 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 7.04/7.28 inference(bind,[status(th)],[])).
% 7.04/7.28 tff(23,plain,
% 7.04/7.28 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 7.04/7.28 inference(quant_intro,[status(thm)],[22])).
% 7.04/7.28 tff(24,plain,
% 7.04/7.28 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 7.04/7.28 inference(rewrite,[status(thm)],[])).
% 7.04/7.28 tff(25,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 7.04/7.28 tff(26,plain,
% 7.04/7.28 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 7.04/7.28 inference(modus_ponens,[status(thm)],[25, 24])).
% 7.04/7.28 tff(27,plain,(
% 7.04/7.28 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 7.04/7.28 inference(skolemize,[status(sab)],[26])).
% 7.04/7.28 tff(28,plain,
% 7.04/7.28 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 7.04/7.28 inference(modus_ponens,[status(thm)],[27, 23])).
% 7.04/7.28 tff(29,plain,
% 7.04/7.28 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(X1!0), X1!0)) = star(X1!0))),
% 7.04/7.28 inference(quant_inst,[status(thm)],[])).
% 7.04/7.28 tff(30,plain,
% 7.04/7.28 (addition(one, multiplication(star(X1!0), X1!0)) = star(X1!0)),
% 7.04/7.28 inference(unit_resolution,[status(thm)],[29, 28])).
% 7.04/7.28 tff(31,plain,
% 7.04/7.28 (star(X1!0) = addition(one, multiplication(star(X1!0), X1!0))),
% 7.04/7.28 inference(symmetry,[status(thm)],[30])).
% 7.04/7.28 tff(32,plain,
% 7.04/7.28 (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))),
% 7.04/7.28 inference(monotonicity,[status(thm)],[31, 18])).
% 7.04/7.28 tff(33,plain,
% 7.04/7.28 (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)))),
% 7.04/7.28 inference(symmetry,[status(thm)],[32])).
% 7.04/7.28 tff(34,plain,
% 7.04/7.28 (^[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))))),
% 7.04/7.28 inference(bind,[status(th)],[])).
% 7.04/7.28 tff(35,plain,
% 7.04/7.28 (![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)))),
% 7.04/7.28 inference(quant_intro,[status(thm)],[34])).
% 7.04/7.28 tff(36,plain,
% 7.04/7.28 (![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)))),
% 7.04/7.28 inference(rewrite,[status(thm)],[])).
% 7.04/7.28 tff(37,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','distributivity2')).
% 7.04/7.28 tff(38,plain,
% 7.04/7.28 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 7.04/7.28 inference(modus_ponens,[status(thm)],[37, 36])).
% 7.04/7.28 tff(39,plain,(
% 7.04/7.28 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 7.04/7.28 inference(skolemize,[status(sab)],[38])).
% 7.04/7.28 tff(40,plain,
% 7.04/7.28 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 7.04/7.28 inference(modus_ponens,[status(thm)],[39, 35])).
% 7.04/7.28 tff(41,plain,
% 7.04/7.28 ((~![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))))),
% 7.04/7.28 inference(quant_inst,[status(thm)],[])).
% 7.04/7.28 tff(42,plain,
% 7.04/7.28 (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)))),
% 7.04/7.28 inference(unit_resolution,[status(thm)],[41, 40])).
% 7.04/7.28 tff(43,plain,
% 7.04/7.28 (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))),
% 7.04/7.28 inference(symmetry,[status(thm)],[42])).
% 7.04/7.28 tff(44,plain,
% 7.04/7.28 ((~![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)))),
% 7.04/7.28 inference(quant_inst,[status(thm)],[])).
% 7.04/7.28 tff(45,plain,
% 7.04/7.28 (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))),
% 7.12/7.28 inference(unit_resolution,[status(thm)],[44, 7])).
% 7.12/7.28 tff(46,plain,
% 7.12/7.28 (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))),
% 7.12/7.28 inference(symmetry,[status(thm)],[45])).
% 7.12/7.28 tff(47,plain,
% 7.12/7.28 (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)))),
% 7.12/7.28 inference(monotonicity,[status(thm)],[46])).
% 7.12/7.28 tff(48,plain,
% 7.12/7.28 (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)))),
% 7.12/7.28 inference(symmetry,[status(thm)],[47])).
% 7.12/7.28 tff(49,plain,
% 7.12/7.28 (^[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)))),
% 7.12/7.28 inference(bind,[status(th)],[])).
% 7.12/7.28 tff(50,plain,
% 7.12/7.28 (![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))),
% 7.12/7.28 inference(quant_intro,[status(thm)],[49])).
% 7.12/7.28 tff(51,plain,
% 7.12/7.28 (![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))),
% 7.12/7.28 inference(rewrite,[status(thm)],[])).
% 7.12/7.28 tff(52,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 7.12/7.28 tff(53,plain,
% 7.12/7.28 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 7.12/7.28 inference(modus_ponens,[status(thm)],[52, 51])).
% 7.12/7.28 tff(54,plain,(
% 7.12/7.28 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 7.12/7.28 inference(skolemize,[status(sab)],[53])).
% 7.12/7.28 tff(55,plain,
% 7.12/7.28 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 7.12/7.28 inference(modus_ponens,[status(thm)],[54, 50])).
% 7.12/7.28 tff(56,plain,
% 7.12/7.28 ((~![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)))),
% 7.12/7.28 inference(quant_inst,[status(thm)],[])).
% 7.12/7.28 tff(57,plain,
% 7.12/7.28 (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))),
% 7.12/7.28 inference(unit_resolution,[status(thm)],[56, 55])).
% 7.12/7.28 tff(58,plain,
% 7.12/7.28 (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)))),
% 7.12/7.28 inference(symmetry,[status(thm)],[57])).
% 7.12/7.28 tff(59,plain,
% 7.12/7.28 (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)))),
% 7.12/7.28 inference(transitivity,[status(thm)],[58, 48])).
% 7.12/7.28 tff(60,plain,
% 7.12/7.28 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 7.12/7.28 inference(bind,[status(th)],[])).
% 7.12/7.28 tff(61,plain,
% 7.12/7.28 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 7.12/7.28 inference(quant_intro,[status(thm)],[60])).
% 7.12/7.28 tff(62,plain,
% 7.12/7.28 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 7.12/7.28 inference(rewrite,[status(thm)],[])).
% 7.12/7.28 tff(63,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 7.12/7.28 tff(64,plain,
% 7.12/7.28 (![A: $i] : (multiplication(one, A) = A)),
% 7.12/7.28 inference(modus_ponens,[status(thm)],[63, 62])).
% 7.12/7.28 tff(65,plain,(
% 7.12/7.28 ![A: $i] : (multiplication(one, A) = A)),
% 7.12/7.28 inference(skolemize,[status(sab)],[64])).
% 7.12/7.28 tff(66,plain,
% 7.12/7.28 (![A: $i] : (multiplication(one, A) = A)),
% 7.12/7.28 inference(modus_ponens,[status(thm)],[65, 61])).
% 7.12/7.28 tff(67,plain,
% 7.12/7.28 ((~![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))),
% 7.12/7.28 inference(quant_inst,[status(thm)],[])).
% 7.12/7.28 tff(68,plain,
% 7.12/7.28 (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)),
% 7.12/7.28 inference(unit_resolution,[status(thm)],[67, 66])).
% 7.12/7.28 tff(69,plain,
% 7.12/7.28 (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))))),
% 7.12/7.28 inference(monotonicity,[status(thm)],[68, 59])).
% 7.12/7.28 tff(70,plain,
% 7.12/7.28 (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)))),
% 7.12/7.28 inference(symmetry,[status(thm)],[69])).
% 7.12/7.28 tff(71,plain,
% 7.12/7.28 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 7.12/7.28 inference(bind,[status(th)],[])).
% 7.12/7.28 tff(72,plain,
% 7.12/7.28 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 7.12/7.28 inference(quant_intro,[status(thm)],[71])).
% 7.12/7.28 tff(73,plain,
% 7.12/7.28 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 7.12/7.28 inference(rewrite,[status(thm)],[])).
% 7.12/7.28 tff(74,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 7.12/7.28 tff(75,plain,
% 7.12/7.28 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 7.12/7.28 inference(modus_ponens,[status(thm)],[74, 73])).
% 7.12/7.28 tff(76,plain,(
% 7.12/7.28 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 7.12/7.28 inference(skolemize,[status(sab)],[75])).
% 7.12/7.28 tff(77,plain,
% 7.12/7.28 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 7.12/7.28 inference(modus_ponens,[status(thm)],[76, 72])).
% 7.12/7.28 tff(78,plain,
% 7.12/7.28 ((~![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))))),
% 7.12/7.28 inference(quant_inst,[status(thm)],[])).
% 7.12/7.28 tff(79,plain,
% 7.12/7.28 (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)))),
% 7.12/7.28 inference(unit_resolution,[status(thm)],[78, 77])).
% 7.12/7.28 tff(80,plain,
% 7.12/7.28 (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))),
% 7.12/7.28 inference(symmetry,[status(thm)],[9])).
% 7.12/7.28 tff(81,plain,
% 7.12/7.28 (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)))),
% 7.12/7.28 inference(transitivity,[status(thm)],[80, 20])).
% 7.12/7.28 tff(82,plain,
% 7.12/7.28 (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))),
% 7.12/7.28 inference(monotonicity,[status(thm)],[81])).
% 7.12/7.28 tff(83,plain,
% 7.12/7.28 (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))),
% 7.12/7.28 inference(symmetry,[status(thm)],[82])).
% 7.12/7.28 tff(84,plain,
% 7.12/7.28 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 7.12/7.28 inference(bind,[status(th)],[])).
% 7.12/7.28 tff(85,plain,
% 7.12/7.28 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 7.12/7.28 inference(quant_intro,[status(thm)],[84])).
% 7.12/7.28 tff(86,plain,
% 7.12/7.28 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 7.12/7.28 inference(rewrite,[status(thm)],[])).
% 7.12/7.28 tff(87,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','order')).
% 7.12/7.28 tff(88,plain,
% 7.12/7.28 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 7.12/7.28 inference(modus_ponens,[status(thm)],[87, 86])).
% 7.12/7.28 tff(89,plain,(
% 7.12/7.28 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 7.12/7.28 inference(skolemize,[status(sab)],[88])).
% 7.12/7.28 tff(90,plain,
% 7.12/7.28 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 7.12/7.28 inference(modus_ponens,[status(thm)],[89, 85])).
% 7.12/7.28 tff(91,plain,
% 7.12/7.28 ((~![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)))),
% 7.12/7.28 inference(quant_inst,[status(thm)],[])).
% 7.12/7.28 tff(92,plain,
% 7.12/7.28 (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))),
% 7.12/7.28 inference(unit_resolution,[status(thm)],[91, 90])).
% 7.12/7.28 tff(93,plain,
% 7.12/7.28 (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)))),
% 7.12/7.28 inference(monotonicity,[status(thm)],[19])).
% 7.12/7.28 tff(94,plain,
% 7.12/7.28 (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))),
% 7.12/7.28 inference(symmetry,[status(thm)],[93])).
% 7.12/7.28 tff(95,plain,
% 7.12/7.28 ((~![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)))))),
% 7.12/7.29 inference(quant_inst,[status(thm)],[])).
% 7.12/7.29 tff(96,plain,
% 7.12/7.29 (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))))),
% 7.12/7.29 inference(unit_resolution,[status(thm)],[95, 77])).
% 7.12/7.29 tff(97,plain,
% 7.12/7.29 (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)),
% 7.12/7.29 inference(symmetry,[status(thm)],[96])).
% 7.12/7.29 tff(98,plain,
% 7.12/7.29 ((~![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)))))),
% 7.12/7.29 inference(quant_inst,[status(thm)],[])).
% 7.12/7.29 tff(99,plain,
% 7.12/7.29 (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))))),
% 7.12/7.29 inference(unit_resolution,[status(thm)],[98, 40])).
% 7.12/7.29 tff(100,plain,
% 7.12/7.29 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 7.12/7.29 inference(bind,[status(th)],[])).
% 7.12/7.29 tff(101,plain,
% 7.12/7.29 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 7.12/7.29 inference(quant_intro,[status(thm)],[100])).
% 7.12/7.29 tff(102,plain,
% 7.12/7.29 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 7.12/7.29 inference(rewrite,[status(thm)],[])).
% 7.12/7.29 tff(103,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 7.12/7.29 tff(104,plain,
% 7.12/7.29 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 7.12/7.29 inference(modus_ponens,[status(thm)],[103, 102])).
% 7.12/7.29 tff(105,plain,(
% 7.12/7.29 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 7.12/7.29 inference(skolemize,[status(sab)],[104])).
% 7.12/7.29 tff(106,plain,
% 7.12/7.29 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 7.12/7.29 inference(modus_ponens,[status(thm)],[105, 101])).
% 7.12/7.29 tff(107,plain,
% 7.12/7.29 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(X0!1, star(X0!1))) = star(X0!1))),
% 7.12/7.29 inference(quant_inst,[status(thm)],[])).
% 7.12/7.29 tff(108,plain,
% 7.12/7.29 (addition(one, multiplication(X0!1, star(X0!1))) = star(X0!1)),
% 7.12/7.29 inference(unit_resolution,[status(thm)],[107, 106])).
% 7.12/7.29 tff(109,plain,
% 7.12/7.29 ((~![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))),
% 7.12/7.29 inference(quant_inst,[status(thm)],[])).
% 7.12/7.29 tff(110,plain,
% 7.12/7.29 (addition(one, multiplication(X0!1, star(X0!1))) = addition(multiplication(X0!1, star(X0!1)), one)),
% 7.12/7.29 inference(unit_resolution,[status(thm)],[109, 77])).
% 7.12/7.29 tff(111,plain,
% 7.12/7.29 (addition(multiplication(X0!1, star(X0!1)), one) = addition(one, multiplication(X0!1, star(X0!1)))),
% 7.12/7.29 inference(symmetry,[status(thm)],[110])).
% 7.12/7.29 tff(112,plain,
% 7.12/7.29 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(X0!1), X0!1)) = star(X0!1))),
% 7.12/7.29 inference(quant_inst,[status(thm)],[])).
% 7.12/7.29 tff(113,plain,
% 7.12/7.29 (addition(one, multiplication(star(X0!1), X0!1)) = star(X0!1)),
% 7.12/7.29 inference(unit_resolution,[status(thm)],[112, 28])).
% 7.12/7.29 tff(114,plain,
% 7.12/7.29 (star(X0!1) = addition(one, multiplication(star(X0!1), X0!1))),
% 7.12/7.29 inference(symmetry,[status(thm)],[113])).
% 7.12/7.29 tff(115,plain,
% 7.13/7.29 (multiplication(X0!1, star(X0!1)) = multiplication(X0!1, addition(one, multiplication(star(X0!1), X0!1)))),
% 7.13/7.29 inference(monotonicity,[status(thm)],[114])).
% 7.13/7.29 tff(116,plain,
% 7.13/7.29 (multiplication(X0!1, addition(one, multiplication(star(X0!1), X0!1))) = multiplication(X0!1, star(X0!1))),
% 7.13/7.29 inference(symmetry,[status(thm)],[115])).
% 7.13/7.29 tff(117,plain,
% 7.13/7.29 ((~![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))))),
% 7.13/7.29 inference(quant_inst,[status(thm)],[])).
% 7.13/7.29 tff(118,plain,
% 7.13/7.29 (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)))),
% 7.13/7.29 inference(unit_resolution,[status(thm)],[117, 7])).
% 7.13/7.29 tff(119,plain,
% 7.13/7.29 (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)))),
% 7.13/7.29 inference(symmetry,[status(thm)],[118])).
% 7.13/7.29 tff(120,plain,
% 7.13/7.29 (addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))) = multiplication(X0!1, star(X0!1))),
% 7.13/7.29 inference(transitivity,[status(thm)],[119, 116])).
% 7.13/7.29 tff(121,plain,
% 7.13/7.29 (addition(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), one) = addition(multiplication(X0!1, star(X0!1)), one)),
% 7.13/7.29 inference(monotonicity,[status(thm)],[120])).
% 7.13/7.29 tff(122,plain,
% 7.13/7.29 (addition(addition(multiplication(X0!1, one), multiplication(X0!1, multiplication(star(X0!1), X0!1))), one) = star(X0!1)),
% 7.13/7.29 inference(transitivity,[status(thm)],[121, 111, 108])).
% 7.13/7.29 tff(123,plain,
% 7.13/7.29 (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)))),
% 7.13/7.29 inference(monotonicity,[status(thm)],[122, 46])).
% 7.13/7.29 tff(124,plain,
% 7.13/7.29 (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)))),
% 7.13/7.29 inference(symmetry,[status(thm)],[123])).
% 7.13/7.29 tff(125,plain,
% 7.13/7.29 ((~![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)))),
% 7.13/7.29 inference(quant_inst,[status(thm)],[])).
% 7.13/7.29 tff(126,plain,
% 7.13/7.29 (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))),
% 7.13/7.29 inference(unit_resolution,[status(thm)],[125, 55])).
% 7.13/7.29 tff(127,plain,
% 7.13/7.29 (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)))),
% 7.13/7.29 inference(symmetry,[status(thm)],[126])).
% 7.13/7.29 tff(128,plain,
% 7.13/7.29 (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))),
% 7.13/7.29 inference(monotonicity,[status(thm)],[18])).
% 7.13/7.29 tff(129,plain,
% 7.13/7.29 (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))))),
% 7.13/7.29 inference(transitivity,[status(thm)],[128, 127, 124, 99])).
% 7.13/7.29 tff(130,plain,
% 7.13/7.29 (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)))))),
% 7.13/7.29 inference(monotonicity,[status(thm)],[129])).
% 7.13/7.29 tff(131,plain,
% 7.13/7.29 (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))))),
% 7.13/7.29 inference(symmetry,[status(thm)],[130])).
% 7.13/7.29 tff(132,plain,
% 7.13/7.29 (^[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)))),
% 7.13/7.29 inference(bind,[status(th)],[])).
% 7.13/7.29 tff(133,plain,
% 7.13/7.29 (![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))),
% 7.13/7.29 inference(quant_intro,[status(thm)],[132])).
% 7.13/7.29 tff(134,plain,
% 7.13/7.29 (![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))),
% 7.13/7.29 inference(rewrite,[status(thm)],[])).
% 7.13/7.29 tff(135,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_associativity')).
% 7.13/7.29 tff(136,plain,
% 7.13/7.29 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 7.13/7.29 inference(modus_ponens,[status(thm)],[135, 134])).
% 7.13/7.29 tff(137,plain,(
% 7.13/7.29 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 7.13/7.29 inference(skolemize,[status(sab)],[136])).
% 7.13/7.29 tff(138,plain,
% 7.13/7.29 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 7.13/7.29 inference(modus_ponens,[status(thm)],[137, 133])).
% 7.13/7.29 tff(139,plain,
% 7.13/7.29 ((~![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)))))),
% 7.13/7.29 inference(quant_inst,[status(thm)],[])).
% 7.13/7.29 tff(140,plain,
% 7.13/7.29 (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))))),
% 7.13/7.29 inference(unit_resolution,[status(thm)],[139, 138])).
% 7.13/7.29 tff(141,plain,
% 7.13/7.29 (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)))))),
% 7.13/7.29 inference(symmetry,[status(thm)],[140])).
% 7.13/7.29 tff(142,plain,
% 7.13/7.29 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 7.13/7.29 inference(bind,[status(th)],[])).
% 7.13/7.29 tff(143,plain,
% 7.13/7.29 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 7.13/7.29 inference(quant_intro,[status(thm)],[142])).
% 7.13/7.29 tff(144,plain,
% 7.13/7.29 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 7.13/7.29 inference(rewrite,[status(thm)],[])).
% 7.13/7.29 tff(145,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 7.13/7.29 tff(146,plain,
% 7.13/7.29 (![A: $i] : (addition(A, A) = A)),
% 7.13/7.29 inference(modus_ponens,[status(thm)],[145, 144])).
% 7.13/7.29 tff(147,plain,(
% 7.13/7.29 ![A: $i] : (addition(A, A) = A)),
% 7.13/7.29 inference(skolemize,[status(sab)],[146])).
% 7.13/7.29 tff(148,plain,
% 7.13/7.29 (![A: $i] : (addition(A, A) = A)),
% 7.13/7.29 inference(modus_ponens,[status(thm)],[147, 143])).
% 7.13/7.29 tff(149,plain,
% 7.13/7.29 ((~![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)))),
% 7.13/7.29 inference(quant_inst,[status(thm)],[])).
% 7.13/7.29 tff(150,plain,
% 7.13/7.29 (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))),
% 7.13/7.29 inference(unit_resolution,[status(thm)],[149, 148])).
% 7.13/7.29 tff(151,plain,
% 7.13/7.29 (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)))),
% 7.13/7.29 inference(symmetry,[status(thm)],[150])).
% 7.13/7.29 tff(152,plain,
% 7.13/7.29 ((~![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)))),
% 7.13/7.29 inference(quant_inst,[status(thm)],[])).
% 7.13/7.29 tff(153,plain,
% 7.13/7.29 (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))),
% 7.13/7.29 inference(unit_resolution,[status(thm)],[152, 66])).
% 7.13/7.29 tff(154,plain,
% 7.13/7.29 (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)))),
% 7.13/7.29 inference(transitivity,[status(thm)],[153, 151])).
% 7.13/7.29 tff(155,plain,
% 7.13/7.29 (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))))),
% 7.13/7.29 inference(monotonicity,[status(thm)],[154])).
% 7.13/7.29 tff(156,plain,
% 7.13/7.29 (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))))),
% 7.13/7.29 inference(symmetry,[status(thm)],[155])).
% 7.13/7.29 tff(157,plain,
% 7.13/7.29 ((~![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))))),
% 7.13/7.29 inference(quant_inst,[status(thm)],[])).
% 7.13/7.29 tff(158,plain,
% 7.13/7.29 (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)))),
% 7.13/7.29 inference(unit_resolution,[status(thm)],[157, 138])).
% 7.13/7.29 tff(159,plain,
% 7.13/7.29 (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))))),
% 7.13/7.29 inference(symmetry,[status(thm)],[158])).
% 7.13/7.29 tff(160,plain,
% 7.13/7.29 (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))),
% 7.13/7.29 inference(monotonicity,[status(thm)],[18])).
% 7.13/7.29 tff(161,plain,
% 7.13/7.29 (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)))),
% 7.13/7.29 inference(symmetry,[status(thm)],[160])).
% 7.13/7.29 tff(162,plain,
% 7.13/7.29 (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)))),
% 7.13/7.29 inference(transitivity,[status(thm)],[46, 161])).
% 7.13/7.29 tff(163,plain,
% 7.13/7.29 (multiplication(addition(one, multiplication(X0!1, star(X0!1))), X1!0) = multiplication(star(X0!1), X1!0)),
% 7.13/7.29 inference(monotonicity,[status(thm)],[108])).
% 7.13/7.29 tff(164,plain,
% 7.13/7.29 ((~![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)))),
% 7.13/7.29 inference(quant_inst,[status(thm)],[])).
% 7.13/7.29 tff(165,plain,
% 7.13/7.29 (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))),
% 7.13/7.29 inference(unit_resolution,[status(thm)],[164, 40])).
% 7.13/7.29 tff(166,plain,
% 7.13/7.29 (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)),
% 7.13/7.29 inference(symmetry,[status(thm)],[165])).
% 7.13/7.29 tff(167,plain,
% 7.13/7.29 (addition(multiplication(one, X1!0), multiplication(multiplication(X0!1, star(X0!1)), X1!0)) = multiplication(star(X0!1), X1!0)),
% 7.13/7.29 inference(transitivity,[status(thm)],[166, 163])).
% 7.13/7.29 tff(168,plain,
% 7.13/7.29 (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)))),
% 7.13/7.29 inference(monotonicity,[status(thm)],[167, 19])).
% 7.13/7.29 tff(169,plain,
% 7.13/7.29 ((~![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))))),
% 7.13/7.30 inference(quant_inst,[status(thm)],[])).
% 7.13/7.30 tff(170,plain,
% 7.13/7.30 (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)))),
% 7.13/7.30 inference(unit_resolution,[status(thm)],[169, 40])).
% 7.13/7.30 tff(171,plain,
% 7.13/7.30 (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))),
% 7.13/7.30 inference(symmetry,[status(thm)],[170])).
% 7.13/7.30 tff(172,plain,
% 7.13/7.30 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!0) = X1!0)),
% 7.13/7.30 inference(quant_inst,[status(thm)],[])).
% 7.13/7.30 tff(173,plain,
% 7.13/7.30 (multiplication(one, X1!0) = X1!0),
% 7.13/7.30 inference(unit_resolution,[status(thm)],[172, 66])).
% 7.13/7.30 tff(174,plain,
% 7.13/7.30 (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)))),
% 7.13/7.30 inference(monotonicity,[status(thm)],[173, 19])).
% 7.13/7.30 tff(175,plain,
% 7.13/7.30 (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))),
% 7.13/7.30 inference(symmetry,[status(thm)],[174])).
% 7.13/7.30 tff(176,plain,
% 7.13/7.30 (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))),
% 7.13/7.30 inference(transitivity,[status(thm)],[46, 161, 175])).
% 7.13/7.30 tff(177,plain,
% 7.13/7.30 (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)))),
% 7.13/7.30 inference(monotonicity,[status(thm)],[176])).
% 7.13/7.30 tff(178,plain,
% 7.13/7.30 (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)))),
% 7.13/7.30 inference(transitivity,[status(thm)],[177, 171, 168])).
% 7.13/7.30 tff(179,plain,
% 7.13/7.30 (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))))),
% 7.13/7.30 inference(monotonicity,[status(thm)],[178])).
% 7.13/7.30 tff(180,plain,
% 7.13/7.30 ((~![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))))),
% 7.13/7.30 inference(quant_inst,[status(thm)],[])).
% 7.13/7.30 tff(181,plain,
% 7.13/7.30 (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)))),
% 7.13/7.30 inference(unit_resolution,[status(thm)],[180, 138])).
% 7.13/7.30 tff(182,plain,
% 7.13/7.30 (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))))),
% 7.13/7.30 inference(symmetry,[status(thm)],[181])).
% 7.13/7.30 tff(183,plain,
% 7.13/7.30 (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)),
% 7.13/7.30 inference(monotonicity,[status(thm)],[120])).
% 7.13/7.30 tff(184,plain,
% 7.13/7.30 (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)),
% 7.13/7.30 inference(symmetry,[status(thm)],[183])).
% 7.13/7.30 tff(185,plain,
% 7.13/7.30 (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))),
% 7.13/7.30 inference(monotonicity,[status(thm)],[184])).
% 7.13/7.30 tff(186,plain,
% 7.13/7.30 (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))),
% 7.13/7.30 inference(symmetry,[status(thm)],[185])).
% 7.13/7.30 tff(187,plain,
% 7.13/7.30 ((~![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)))),
% 7.13/7.30 inference(quant_inst,[status(thm)],[])).
% 7.13/7.30 tff(188,plain,
% 7.13/7.30 (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))),
% 7.13/7.30 inference(unit_resolution,[status(thm)],[187, 55])).
% 7.13/7.30 tff(189,plain,
% 7.13/7.30 (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)))),
% 7.13/7.30 inference(monotonicity,[status(thm)],[45])).
% 7.13/7.30 tff(190,plain,
% 7.13/7.30 (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)))),
% 7.13/7.30 inference(symmetry,[status(thm)],[189])).
% 7.13/7.30 tff(191,plain,
% 7.13/7.30 (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))),
% 7.13/7.30 inference(transitivity,[status(thm)],[190, 188, 186])).
% 7.13/7.30 tff(192,plain,
% 7.13/7.30 ((~![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))))),
% 7.13/7.30 inference(quant_inst,[status(thm)],[])).
% 7.13/7.30 tff(193,plain,
% 7.13/7.30 (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)))),
% 7.13/7.30 inference(unit_resolution,[status(thm)],[192, 77])).
% 7.13/7.30 tff(194,plain,
% 7.13/7.30 (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)))),
% 7.13/7.30 inference(monotonicity,[status(thm)],[193, 191])).
% 7.13/7.30 tff(195,plain,
% 7.13/7.30 ((~![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)))))),
% 7.13/7.30 inference(quant_inst,[status(thm)],[])).
% 7.13/7.30 tff(196,plain,
% 7.13/7.30 (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))))),
% 7.13/7.30 inference(unit_resolution,[status(thm)],[195, 138])).
% 7.13/7.30 tff(197,plain,
% 7.13/7.30 ((~![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))))))),
% 7.13/7.30 inference(quant_inst,[status(thm)],[])).
% 7.13/7.30 tff(198,plain,
% 7.13/7.30 (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)))))),
% 7.13/7.30 inference(unit_resolution,[status(thm)],[197, 77])).
% 7.13/7.30 tff(199,plain,
% 7.13/7.30 (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)),
% 7.13/7.30 inference(transitivity,[status(thm)],[198, 196, 194, 182, 179, 97])).
% 7.13/7.30 tff(200,plain,
% 7.13/7.30 (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))))),
% 7.13/7.30 inference(monotonicity,[status(thm)],[199, 162])).
% 7.13/7.30 tff(201,plain,
% 7.13/7.30 (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)))),
% 7.13/7.30 inference(symmetry,[status(thm)],[200])).
% 7.13/7.30 tff(202,plain,
% 7.13/7.30 ((~![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)))))),
% 7.15/7.30 inference(quant_inst,[status(thm)],[])).
% 7.15/7.30 tff(203,plain,
% 7.15/7.30 (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))))),
% 7.15/7.30 inference(unit_resolution,[status(thm)],[202, 77])).
% 7.15/7.30 tff(204,plain,
% 7.15/7.30 (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)),
% 7.15/7.30 inference(transitivity,[status(thm)],[203, 201, 159, 156, 141, 131, 97])).
% 7.15/7.30 tff(205,plain,
% 7.15/7.30 (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))),
% 7.15/7.30 inference(monotonicity,[status(thm)],[18])).
% 7.15/7.30 tff(206,plain,
% 7.15/7.30 (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)))),
% 7.15/7.30 inference(symmetry,[status(thm)],[205])).
% 7.15/7.30 tff(207,plain,
% 7.15/7.30 ((~![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(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))), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), one))),
% 7.15/7.30 inference(quant_inst,[status(thm)],[])).
% 7.15/7.30 tff(208,plain,
% 7.15/7.30 (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(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), one)),
% 7.15/7.30 inference(unit_resolution,[status(thm)],[207, 138])).
% 7.15/7.30 tff(209,plain,
% 7.15/7.30 (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), 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))),
% 7.15/7.30 inference(symmetry,[status(thm)],[208])).
% 7.15/7.30 tff(210,plain,
% 7.15/7.30 (addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), 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)))),
% 7.15/7.30 inference(transitivity,[status(thm)],[209, 206])).
% 7.15/7.30 tff(211,plain,
% 7.15/7.30 (addition(addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), 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))), addition(multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), one))),
% 7.15/7.30 inference(monotonicity,[status(thm)],[210])).
% 7.15/7.30 tff(212,plain,
% 7.15/7.30 (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, strong_iteration(multiplication(star(X0!1), X1!0))), 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))),
% 7.15/7.30 inference(symmetry,[status(thm)],[211])).
% 7.15/7.30 tff(213,plain,
% 7.15/7.30 (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))),
% 7.15/7.30 inference(monotonicity,[status(thm)],[46])).
% 7.15/7.30 tff(214,plain,
% 7.15/7.30 (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))),
% 7.15/7.30 inference(symmetry,[status(thm)],[213])).
% 7.15/7.30 tff(215,plain,
% 7.15/7.30 (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)))),
% 7.15/7.30 inference(monotonicity,[status(thm)],[161, 19])).
% 7.15/7.30 tff(216,plain,
% 7.15/7.30 (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))),
% 7.15/7.30 inference(symmetry,[status(thm)],[215])).
% 7.15/7.30 tff(217,plain,
% 7.15/7.30 (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))),
% 7.15/7.30 inference(transitivity,[status(thm)],[216, 214])).
% 7.15/7.30 tff(218,plain,
% 7.15/7.30 (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))),
% 7.15/7.31 inference(monotonicity,[status(thm)],[217])).
% 7.15/7.31 tff(219,plain,
% 7.15/7.31 (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, 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))),
% 7.15/7.31 inference(symmetry,[status(thm)],[218])).
% 7.15/7.31 tff(220,plain,
% 7.15/7.31 ((~![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)))),
% 7.15/7.31 inference(quant_inst,[status(thm)],[])).
% 7.15/7.31 tff(221,plain,
% 7.15/7.31 (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))),
% 7.15/7.31 inference(unit_resolution,[status(thm)],[220, 138])).
% 7.15/7.31 tff(222,plain,
% 7.15/7.31 ((~![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))),
% 7.15/7.31 inference(quant_inst,[status(thm)],[])).
% 7.15/7.31 tff(223,plain,
% 7.15/7.31 (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)),
% 7.15/7.31 inference(unit_resolution,[status(thm)],[222, 148])).
% 7.15/7.31 tff(224,plain,
% 7.15/7.31 (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))),
% 7.15/7.31 inference(monotonicity,[status(thm)],[46, 223])).
% 7.15/7.31 tff(225,plain,
% 7.15/7.31 (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(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)))),
% 7.15/7.31 inference(symmetry,[status(thm)],[224])).
% 7.15/7.31 tff(226,plain,
% 7.15/7.31 (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(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), 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))),
% 7.15/7.31 inference(transitivity,[status(thm)],[206, 216, 225, 221, 219, 212])).
% 7.15/7.31 tff(227,plain,
% 7.15/7.31 ((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(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), 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))),
% 7.15/7.31 inference(monotonicity,[status(thm)],[226])).
% 7.15/7.31 tff(228,plain,
% 7.15/7.31 ((addition(addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), 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)) <=> (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))),
% 7.15/7.31 inference(symmetry,[status(thm)],[227])).
% 7.15/7.31 tff(229,plain,
% 7.15/7.31 ((~(addition(addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), 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))) <=> (~(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)))),
% 7.15/7.31 inference(monotonicity,[status(thm)],[228])).
% 7.15/7.31 tff(230,plain,
% 7.15/7.31 ((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(addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), 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))),
% 7.15/7.31 inference(monotonicity,[status(thm)],[212])).
% 7.15/7.31 tff(231,plain,
% 7.15/7.31 ((~(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(addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), 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)))),
% 7.15/7.31 inference(monotonicity,[status(thm)],[230])).
% 7.15/7.31 tff(232,plain,
% 7.15/7.31 ((~![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)))),
% 7.15/7.31 inference(quant_inst,[status(thm)],[])).
% 7.15/7.31 tff(233,plain,
% 7.15/7.31 (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))),
% 7.15/7.31 inference(unit_resolution,[status(thm)],[232, 90])).
% 7.15/7.31 tff(234,plain,
% 7.15/7.31 (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)))),
% 7.15/7.31 inference(monotonicity,[status(thm)],[19])).
% 7.15/7.31 tff(235,plain,
% 7.15/7.31 (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))),
% 7.15/7.31 inference(symmetry,[status(thm)],[234])).
% 7.15/7.31 tff(236,plain,
% 7.15/7.31 ((~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)))),
% 7.15/7.31 inference(monotonicity,[status(thm)],[235])).
% 7.15/7.31 tff(237,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)).
% 7.15/7.31 tff(238,plain,
% 7.15/7.31 (~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))),
% 7.15/7.31 inference(modus_ponens,[status(thm)],[237, 236])).
% 7.15/7.31 tff(239,plain,
% 7.15/7.31 ((~(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)))),
% 7.15/7.31 inference(tautology,[status(thm)],[])).
% 7.15/7.31 tff(240,plain,
% 7.15/7.31 (~(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))),
% 7.15/7.31 inference(unit_resolution,[status(thm)],[239, 238, 233])).
% 7.15/7.31 tff(241,plain,
% 7.15/7.31 (~(addition(addition(addition(multiplication(X1!0, strong_iteration(multiplication(star(X0!1), X1!0))), 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))),
% 7.15/7.31 inference(modus_ponens,[status(thm)],[240, 231])).
% 7.15/7.31 tff(242,plain,
% 7.15/7.31 (~(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))),
% 7.15/7.31 inference(modus_ponens,[status(thm)],[241, 229])).
% 7.15/7.31 tff(243,plain,
% 7.15/7.31 ($false),
% 7.15/7.31 inference(unit_resolution,[status(thm)],[242, 204])).
% 7.15/7.31 tff(244,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,[]))).
% 7.15/7.31 tff(245,plain,
% 7.15/7.31 (^[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)))),
% 7.15/7.31 inference(bind,[status(th)],[])).
% 7.15/7.31 tff(246,plain,
% 7.15/7.31 (![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))),
% 7.15/7.31 inference(quant_intro,[status(thm)],[245])).
% 7.15/7.31 tff(247,plain,
% 7.15/7.31 (![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))),
% 7.15/7.31 inference(rewrite,[status(thm)],[])).
% 7.15/7.31 tff(248,plain,
% 7.15/7.31 (^[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)))),
% 7.15/7.31 inference(bind,[status(th)],[])).
% 7.15/7.31 tff(249,plain,
% 7.15/7.31 (![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))),
% 7.15/7.31 inference(quant_intro,[status(thm)],[248])).
% 7.15/7.31 tff(250,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, C), B), C) => leq(multiplication(star(A), B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','star_induction1')).
% 7.15/7.31 tff(251,plain,
% 7.15/7.31 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 7.15/7.31 inference(modus_ponens,[status(thm)],[250, 249])).
% 7.15/7.31 tff(252,plain,
% 7.15/7.31 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 7.15/7.31 inference(modus_ponens,[status(thm)],[251, 247])).
% 7.15/7.31 tff(253,plain,(
% 7.15/7.31 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 7.15/7.31 inference(skolemize,[status(sab)],[252])).
% 7.15/7.31 tff(254,plain,
% 7.15/7.31 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, C), B), C)) | leq(multiplication(star(A), B), C))),
% 7.15/7.31 inference(modus_ponens,[status(thm)],[253, 246])).
% 7.15/7.31 tff(255,plain,
% 7.15/7.31 (((~![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))))),
% 7.15/7.31 inference(rewrite,[status(thm)],[])).
% 7.15/7.31 tff(256,plain,
% 7.15/7.31 ((~![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))))),
% 7.15/7.31 inference(quant_inst,[status(thm)],[])).
% 7.15/7.31 tff(257,plain,
% 7.15/7.31 ((~![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)))),
% 7.15/7.31 inference(modus_ponens,[status(thm)],[256, 255])).
% 7.15/7.31 tff(258,plain,
% 7.15/7.31 (leq(multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))), strong_iteration(multiplication(star(X0!1), X1!0)))),
% 7.15/7.31 inference(unit_resolution,[status(thm)],[257, 254, 244])).
% 7.15/7.31 tff(259,plain,
% 7.15/7.31 (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))),
% 7.15/7.31 inference(modus_ponens,[status(thm)],[258, 94])).
% 7.15/7.31 tff(260,plain,
% 7.15/7.31 ((~(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))),
% 7.15/7.31 inference(tautology,[status(thm)],[])).
% 7.15/7.31 tff(261,plain,
% 7.15/7.31 (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)),
% 7.15/7.31 inference(unit_resolution,[status(thm)],[260, 259, 92])).
% 7.15/7.31 tff(262,plain,
% 7.15/7.31 (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))),
% 7.15/7.31 inference(symmetry,[status(thm)],[261])).
% 7.15/7.31 tff(263,plain,
% 7.15/7.31 (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)))),
% 7.15/7.31 inference(transitivity,[status(thm)],[262, 83, 79])).
% 7.15/7.31 tff(264,plain,
% 7.15/7.31 (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))))),
% 7.15/7.31 inference(monotonicity,[status(thm)],[263])).
% 7.15/7.31 tff(265,plain,
% 7.15/7.31 (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))))),
% 7.15/7.31 inference(symmetry,[status(thm)],[264])).
% 7.15/7.31 tff(266,plain,
% 7.15/7.31 ((~![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)))))),
% 7.15/7.31 inference(quant_inst,[status(thm)],[])).
% 7.15/7.31 tff(267,plain,
% 7.15/7.31 (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))))),
% 7.15/7.31 inference(unit_resolution,[status(thm)],[266, 138])).
% 7.15/7.31 tff(268,plain,
% 7.15/7.31 ((~![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))))),
% 7.15/7.31 inference(quant_inst,[status(thm)],[])).
% 7.15/7.31 tff(269,plain,
% 7.15/7.31 (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)))),
% 7.15/7.31 inference(unit_resolution,[status(thm)],[268, 90])).
% 7.15/7.31 tff(270,plain,
% 7.15/7.31 ((~(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)))),
% 7.15/7.31 inference(tautology,[status(thm)],[])).
% 7.15/7.31 tff(271,plain,
% 7.15/7.31 ((~(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)))),
% 7.15/7.31 inference(unit_resolution,[status(thm)],[270, 244])).
% 7.15/7.31 tff(272,plain,
% 7.15/7.31 (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))),
% 7.15/7.31 inference(unit_resolution,[status(thm)],[271, 269])).
% 7.15/7.31 tff(273,plain,
% 7.15/7.31 (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)))),
% 7.15/7.31 inference(monotonicity,[status(thm)],[19])).
% 7.15/7.31 tff(274,plain,
% 7.15/7.31 (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)))),
% 7.15/7.31 inference(monotonicity,[status(thm)],[273, 19])).
% 7.15/7.31 tff(275,plain,
% 7.15/7.31 ((~![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)))),
% 7.15/7.32 inference(quant_inst,[status(thm)],[])).
% 7.15/7.32 tff(276,plain,
% 7.15/7.32 (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))),
% 7.15/7.32 inference(unit_resolution,[status(thm)],[275, 138])).
% 7.15/7.32 tff(277,plain,
% 7.15/7.32 (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))),
% 7.15/7.32 inference(symmetry,[status(thm)],[223])).
% 7.15/7.32 tff(278,plain,
% 7.15/7.32 (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))),
% 7.15/7.32 inference(transitivity,[status(thm)],[18, 277])).
% 7.15/7.32 tff(279,plain,
% 7.15/7.32 (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)))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[278])).
% 7.15/7.32 tff(280,plain,
% 7.15/7.32 ((~![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)))))),
% 7.15/7.32 inference(quant_inst,[status(thm)],[])).
% 7.15/7.32 tff(281,plain,
% 7.15/7.32 (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))))),
% 7.15/7.32 inference(unit_resolution,[status(thm)],[280, 77])).
% 7.15/7.32 tff(282,plain,
% 7.15/7.32 (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)))),
% 7.15/7.32 inference(symmetry,[status(thm)],[281])).
% 7.15/7.32 tff(283,plain,
% 7.15/7.32 (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))),
% 7.15/7.32 inference(transitivity,[status(thm)],[282, 279, 276, 274, 272])).
% 7.15/7.32 tff(284,plain,
% 7.15/7.32 (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)))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[283])).
% 7.15/7.32 tff(285,plain,
% 7.15/7.32 (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))))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[19, 162])).
% 7.15/7.32 tff(286,plain,
% 7.15/7.32 (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)))))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[285])).
% 7.15/7.32 tff(287,plain,
% 7.15/7.32 ((~![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)))))),
% 7.15/7.32 inference(quant_inst,[status(thm)],[])).
% 7.15/7.32 tff(288,plain,
% 7.15/7.32 (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))))),
% 7.15/7.32 inference(unit_resolution,[status(thm)],[287, 7])).
% 7.15/7.32 tff(289,plain,
% 7.15/7.32 (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))))),
% 7.15/7.32 inference(symmetry,[status(thm)],[288])).
% 7.15/7.32 tff(290,plain,
% 7.15/7.32 (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))))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[80])).
% 7.15/7.32 tff(291,plain,
% 7.15/7.32 (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)))),
% 7.15/7.32 inference(transitivity,[status(thm)],[290, 289, 286, 284])).
% 7.15/7.32 tff(292,plain,
% 7.15/7.32 (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))))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[291])).
% 7.15/7.32 tff(293,plain,
% 7.15/7.32 (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)))))),
% 7.15/7.32 inference(symmetry,[status(thm)],[292])).
% 7.15/7.32 tff(294,plain,
% 7.15/7.32 (multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))) = 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))),
% 7.15/7.32 inference(transitivity,[status(thm)],[21, 9])).
% 7.15/7.32 tff(295,plain,
% 7.15/7.32 (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(multiplication(star(X1!0), multiplication(multiplication(star(X0!1), X1!0), strong_iteration(multiplication(star(X0!1), X1!0)))), multiplication(star(X1!0), one)))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[294])).
% 7.15/7.32 tff(296,plain,
% 7.15/7.32 (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))) = 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))))),
% 7.15/7.32 inference(symmetry,[status(thm)],[295])).
% 7.15/7.32 tff(297,plain,
% 7.15/7.32 (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))) = 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))),
% 7.15/7.32 inference(transitivity,[status(thm)],[296, 293, 267, 265, 70, 43, 33, 21, 9])).
% 7.15/7.32 tff(298,plain,
% 7.15/7.32 ((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)))) <=> (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))) = 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)))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[295, 294])).
% 7.15/7.32 tff(299,plain,
% 7.15/7.32 ((~(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))))) <=> (~(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))) = 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))))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[298])).
% 7.15/7.32 tff(300,plain,
% 7.15/7.32 ((~![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)))))),
% 7.15/7.32 inference(quant_inst,[status(thm)],[])).
% 7.15/7.32 tff(301,plain,
% 7.15/7.32 (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))))),
% 7.15/7.32 inference(unit_resolution,[status(thm)],[300, 90])).
% 7.15/7.32 tff(302,plain,
% 7.15/7.32 (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))))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[19])).
% 7.15/7.32 tff(303,plain,
% 7.15/7.32 (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))))),
% 7.15/7.32 inference(symmetry,[status(thm)],[302])).
% 7.15/7.32 tff(304,plain,
% 7.15/7.32 ((~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)))))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[303])).
% 7.15/7.32 tff(305,plain,
% 7.15/7.32 ((~(~((~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)))))),
% 7.15/7.32 inference(rewrite,[status(thm)],[])).
% 7.15/7.32 tff(306,plain,
% 7.15/7.32 ((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))))))),
% 7.15/7.32 inference(rewrite,[status(thm)],[])).
% 7.15/7.32 tff(307,plain,
% 7.15/7.32 ((~(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)))))))),
% 7.15/7.32 inference(monotonicity,[status(thm)],[306])).
% 7.15/7.32 tff(308,plain,
% 7.15/7.32 ((~(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)))))),
% 7.15/7.32 inference(transitivity,[status(thm)],[307, 305])).
% 7.15/7.32 tff(309,plain,
% 7.15/7.32 ((~![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)))))),
% 7.15/7.32 inference(rewrite,[status(thm)],[])).
% 7.15/7.32 tff(310,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/sandbox2/benchmark/theBenchmark.p','goals')).
% 7.15/7.32 tff(311,plain,
% 7.15/7.32 (~![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))))),
% 7.15/7.32 inference(modus_ponens,[status(thm)],[310, 309])).
% 7.15/7.32 tff(312,plain,
% 7.15/7.32 (~![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))))),
% 7.15/7.32 inference(modus_ponens,[status(thm)],[311, 309])).
% 7.15/7.32 tff(313,plain,
% 7.15/7.32 (~![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))))),
% 7.15/7.32 inference(modus_ponens,[status(thm)],[312, 309])).
% 7.15/7.32 tff(314,plain,
% 7.15/7.32 (~![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))))),
% 7.15/7.32 inference(modus_ponens,[status(thm)],[313, 309])).
% 7.15/7.32 tff(315,plain,(
% 7.15/7.32 ~(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))))),
% 7.15/7.32 inference(skolemize,[status(sab)],[314])).
% 7.15/7.32 tff(316,plain,
% 7.15/7.32 ((~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))))),
% 7.15/7.32 inference(modus_ponens,[status(thm)],[315, 308])).
% 7.15/7.32 tff(317,plain,
% 7.15/7.32 (~leq(strong_iteration(multiplication(star(X0!1), X1!0)), multiplication(star(X1!0), strong_iteration(multiplication(star(X0!1), X1!0))))),
% 7.15/7.32 inference(unit_resolution,[status(thm)],[316, 258])).
% 7.15/7.32 tff(318,plain,
% 7.15/7.32 (~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))))),
% 7.15/7.32 inference(modus_ponens,[status(thm)],[317, 304])).
% 7.15/7.32 tff(319,plain,
% 7.15/7.32 ((~(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)))))),
% 7.15/7.32 inference(tautology,[status(thm)],[])).
% 7.15/7.32 tff(320,plain,
% 7.15/7.32 (~(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))))),
% 7.15/7.32 inference(unit_resolution,[status(thm)],[319, 318, 301])).
% 7.15/7.32 tff(321,plain,
% 7.15/7.32 (~(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))) = 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)))),
% 7.15/7.33 inference(modus_ponens,[status(thm)],[320, 299])).
% 7.15/7.33 tff(322,plain,
% 7.15/7.33 ($false),
% 7.15/7.33 inference(unit_resolution,[status(thm)],[321, 297])).
% 7.15/7.33 % SZS output end Proof
% 7.15/7.34 % E exiting
%------------------------------------------------------------------------------