%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE158+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:13:07 AM UTC 2025
% Result : Theorem 0.84s 1.03s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE158+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:05:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.84/1.03 % SZS status Theorem
% 0.84/1.03 % SZS output start Proof
% 0.84/1.03 tff(addition_type, type, (
% 0.84/1.03 addition: ( $i * $i ) > $i)).
% 0.84/1.03 tff(tptp_fun_X0_2_type, type, (
% 0.84/1.03 tptp_fun_X0_2: $i)).
% 0.84/1.03 tff(multiplication_type, type, (
% 0.84/1.03 multiplication: ( $i * $i ) > $i)).
% 0.84/1.03 tff(strong_iteration_type, type, (
% 0.84/1.03 strong_iteration: $i > $i)).
% 0.84/1.03 tff(tptp_fun_X1_1_type, type, (
% 0.84/1.03 tptp_fun_X1_1: $i)).
% 0.84/1.03 tff(tptp_fun_X2_0_type, type, (
% 0.84/1.03 tptp_fun_X2_0: $i)).
% 0.84/1.03 tff(one_type, type, (
% 0.84/1.03 one: $i)).
% 0.84/1.03 tff(leq_type, type, (
% 0.84/1.03 leq: ( $i * $i ) > $o)).
% 0.84/1.03 tff(1,plain,
% 0.84/1.03 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(2,plain,
% 0.84/1.03 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[1])).
% 0.84/1.03 tff(3,plain,
% 0.84/1.03 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.84/1.03 tff(5,plain,
% 0.84/1.03 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.84/1.03 tff(6,plain,(
% 0.84/1.03 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.84/1.03 inference(skolemize,[status(sab)],[5])).
% 0.84/1.03 tff(7,plain,
% 0.84/1.03 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.84/1.03 tff(8,plain,
% 0.84/1.03 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2) = addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(9,plain,
% 0.84/1.03 (addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2) = addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.84/1.04 tff(10,plain,
% 0.84/1.04 (addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)),
% 0.84/1.04 inference(symmetry,[status(thm)],[9])).
% 0.84/1.04 tff(11,plain,
% 0.84/1.04 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(12,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[11])).
% 0.84/1.04 tff(13,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(14,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.84/1.04 tff(15,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.84/1.04 tff(16,plain,(
% 0.84/1.04 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.84/1.04 inference(skolemize,[status(sab)],[15])).
% 0.84/1.04 tff(17,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.84/1.04 tff(18,plain,
% 0.84/1.04 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X2!0, multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(19,plain,
% 0.84/1.04 (multiplication(X2!0, multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.84/1.04 tff(20,plain,
% 0.84/1.04 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(21,plain,
% 0.84/1.04 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[20])).
% 0.84/1.04 tff(22,plain,
% 0.84/1.04 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(23,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 0.84/1.04 tff(24,plain,
% 0.84/1.04 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.84/1.04 tff(25,plain,(
% 0.84/1.04 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.84/1.04 inference(skolemize,[status(sab)],[24])).
% 0.84/1.04 tff(26,plain,
% 0.84/1.04 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.84/1.04 tff(27,plain,
% 0.84/1.04 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(X1!1) = addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(28,plain,
% 0.84/1.04 (strong_iteration(X1!1) = addition(multiplication(X1!1, strong_iteration(X1!1)), one)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.84/1.04 tff(29,plain,
% 0.84/1.04 (multiplication(X0!2, strong_iteration(X1!1)) = multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[28])).
% 0.84/1.04 tff(30,plain,
% 0.84/1.04 (multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))) = multiplication(X2!0, multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[29])).
% 0.84/1.04 tff(31,plain,
% 0.84/1.04 (multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))) = multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.84/1.04 inference(transitivity,[status(thm)],[30, 19])).
% 0.84/1.04 tff(32,plain,
% 0.84/1.04 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(33,plain,
% 0.84/1.04 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.84/1.04 inference(quant_intro,[status(thm)],[32])).
% 0.84/1.04 tff(34,plain,
% 0.84/1.04 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(35,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.84/1.04 tff(36,plain,
% 0.84/1.04 (![A: $i] : (addition(A, A) = A)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.84/1.04 tff(37,plain,(
% 0.84/1.04 ![A: $i] : (addition(A, A) = A)),
% 0.84/1.04 inference(skolemize,[status(sab)],[36])).
% 0.84/1.04 tff(38,plain,
% 0.84/1.04 (![A: $i] : (addition(A, A) = A)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.84/1.04 tff(39,plain,
% 0.84/1.04 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!2, X0!2) = X0!2)),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(40,plain,
% 0.84/1.04 (addition(X0!2, X0!2) = X0!2),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.84/1.04 tff(41,plain,
% 0.84/1.04 (X0!2 = addition(X0!2, X0!2)),
% 0.84/1.04 inference(symmetry,[status(thm)],[40])).
% 0.84/1.04 tff(42,plain,
% 0.84/1.04 (addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))) = addition(addition(X0!2, X0!2), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[41, 31])).
% 0.84/1.04 tff(43,plain,
% 0.84/1.04 (addition(addition(X0!2, X0!2), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))),
% 0.84/1.04 inference(symmetry,[status(thm)],[42])).
% 0.84/1.04 tff(44,plain,
% 0.84/1.04 (^[C: $i, B: $i, A: $i] : refl((addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> (addition(A, addition(B, C)) = addition(addition(A, B), C)))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(45,plain,
% 0.84/1.04 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[44])).
% 0.84/1.04 tff(46,plain,
% 0.84/1.04 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(47,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_associativity')).
% 0.84/1.04 tff(48,plain,
% 0.84/1.04 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.84/1.04 tff(49,plain,(
% 0.84/1.04 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.84/1.04 inference(skolemize,[status(sab)],[48])).
% 0.84/1.04 tff(50,plain,
% 0.84/1.04 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.84/1.04 tff(51,plain,
% 0.84/1.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!2, addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))) = addition(addition(X0!2, X0!2), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(52,plain,
% 0.84/1.04 (addition(X0!2, addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))) = addition(addition(X0!2, X0!2), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.84/1.04 tff(53,plain,
% 0.84/1.04 (multiplication(X2!0, multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))),
% 0.84/1.04 inference(symmetry,[status(thm)],[30])).
% 0.84/1.04 tff(54,plain,
% 0.84/1.04 (multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = multiplication(X2!0, multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.04 inference(symmetry,[status(thm)],[19])).
% 0.84/1.04 tff(55,plain,
% 0.84/1.04 (multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))),
% 0.84/1.04 inference(transitivity,[status(thm)],[54, 53])).
% 0.84/1.04 tff(56,plain,
% 0.84/1.04 (addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[55])).
% 0.84/1.04 tff(57,plain,
% 0.84/1.04 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(58,plain,
% 0.84/1.04 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.84/1.04 inference(quant_intro,[status(thm)],[57])).
% 0.84/1.04 tff(59,plain,
% 0.84/1.04 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(60,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 0.84/1.04 tff(61,plain,
% 0.84/1.04 (![A: $i] : (multiplication(A, one) = A)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.84/1.04 tff(62,plain,(
% 0.84/1.04 ![A: $i] : (multiplication(A, one) = A)),
% 0.84/1.04 inference(skolemize,[status(sab)],[61])).
% 0.84/1.04 tff(63,plain,
% 0.84/1.04 (![A: $i] : (multiplication(A, one) = A)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.84/1.04 tff(64,plain,
% 0.84/1.04 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!2, one) = X0!2)),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(65,plain,
% 0.84/1.04 (multiplication(X0!2, one) = X0!2),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.84/1.04 tff(66,plain,
% 0.84/1.04 (X0!2 = multiplication(X0!2, one)),
% 0.84/1.04 inference(symmetry,[status(thm)],[65])).
% 0.84/1.04 tff(67,plain,
% 0.84/1.04 (addition(X0!2, addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))) = addition(multiplication(X0!2, one), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[66, 56])).
% 0.84/1.04 tff(68,plain,
% 0.84/1.04 (addition(multiplication(X0!2, one), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))) = addition(X0!2, addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))))),
% 0.84/1.04 inference(symmetry,[status(thm)],[67])).
% 0.84/1.04 tff(69,plain,
% 0.84/1.04 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(70,plain,
% 0.84/1.04 (addition(addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[69, 7])).
% 0.84/1.04 tff(71,plain,
% 0.84/1.04 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(72,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[71])).
% 0.84/1.04 tff(73,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(74,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity1')).
% 0.84/1.04 tff(75,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.84/1.04 tff(76,plain,(
% 0.84/1.04 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.84/1.04 inference(skolemize,[status(sab)],[75])).
% 0.84/1.04 tff(77,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.84/1.04 tff(78,plain,
% 0.84/1.04 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))) = addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(79,plain,
% 0.84/1.04 (multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))) = addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.84/1.04 tff(80,plain,
% 0.84/1.04 (addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))) = multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))),
% 0.84/1.04 inference(symmetry,[status(thm)],[79])).
% 0.84/1.04 tff(81,plain,
% 0.84/1.04 (addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))) = addition(multiplication(X0!2, one), multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[66, 80])).
% 0.84/1.04 tff(82,plain,
% 0.84/1.04 (addition(multiplication(X0!2, one), multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))) = addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))),
% 0.84/1.04 inference(symmetry,[status(thm)],[81])).
% 0.84/1.04 tff(83,plain,
% 0.84/1.04 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))) = addition(multiplication(X0!2, one), multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(84,plain,
% 0.84/1.04 (multiplication(X0!2, addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))) = addition(multiplication(X0!2, one), multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[83, 77])).
% 0.84/1.04 tff(85,plain,
% 0.84/1.04 (addition(multiplication(X1!1, strong_iteration(X1!1)), one) = strong_iteration(X1!1)),
% 0.84/1.04 inference(symmetry,[status(thm)],[28])).
% 0.84/1.04 tff(86,plain,
% 0.84/1.04 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!1, strong_iteration(X1!1)), one) = addition(one, multiplication(X1!1, strong_iteration(X1!1))))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(87,plain,
% 0.84/1.04 (addition(multiplication(X1!1, strong_iteration(X1!1)), one) = addition(one, multiplication(X1!1, strong_iteration(X1!1)))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[86, 7])).
% 0.84/1.04 tff(88,plain,
% 0.84/1.04 (addition(one, multiplication(X1!1, strong_iteration(X1!1))) = addition(multiplication(X1!1, strong_iteration(X1!1)), one)),
% 0.84/1.04 inference(symmetry,[status(thm)],[87])).
% 0.84/1.04 tff(89,plain,
% 0.84/1.04 (multiplication(X1!1, strong_iteration(X1!1)) = multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[28])).
% 0.84/1.04 tff(90,plain,
% 0.84/1.04 (multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = multiplication(X1!1, strong_iteration(X1!1))),
% 0.84/1.04 inference(symmetry,[status(thm)],[89])).
% 0.84/1.04 tff(91,plain,
% 0.84/1.04 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(92,plain,
% 0.84/1.04 (multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[91, 77])).
% 0.84/1.04 tff(93,plain,
% 0.84/1.04 (addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)) = multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.84/1.04 inference(symmetry,[status(thm)],[92])).
% 0.84/1.04 tff(94,plain,
% 0.84/1.04 (addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)) = multiplication(X1!1, strong_iteration(X1!1))),
% 0.84/1.04 inference(transitivity,[status(thm)],[93, 90])).
% 0.84/1.04 tff(95,plain,
% 0.84/1.04 (addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))) = addition(one, multiplication(X1!1, strong_iteration(X1!1)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[94])).
% 0.84/1.04 tff(96,plain,
% 0.84/1.04 (addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))) = strong_iteration(X1!1)),
% 0.84/1.04 inference(transitivity,[status(thm)],[95, 88, 85])).
% 0.84/1.04 tff(97,plain,
% 0.84/1.04 (multiplication(X0!2, addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))) = multiplication(X0!2, strong_iteration(X1!1))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[96])).
% 0.84/1.04 tff(98,plain,
% 0.84/1.04 (multiplication(X0!2, strong_iteration(X1!1)) = multiplication(X0!2, addition(one, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))))),
% 0.84/1.04 inference(symmetry,[status(thm)],[97])).
% 0.84/1.04 tff(99,plain,
% 0.84/1.04 (multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = multiplication(X0!2, strong_iteration(X1!1))),
% 0.84/1.04 inference(symmetry,[status(thm)],[29])).
% 0.84/1.04 tff(100,plain,
% 0.84/1.04 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(101,plain,
% 0.84/1.04 (multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[100, 77])).
% 0.84/1.04 tff(102,plain,
% 0.84/1.04 (addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)) = multiplication(X0!2, addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.84/1.04 inference(symmetry,[status(thm)],[101])).
% 0.84/1.04 tff(103,plain,
% 0.84/1.04 (addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)) = addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))))),
% 0.84/1.04 inference(transitivity,[status(thm)],[102, 99, 98, 84, 82])).
% 0.84/1.04 tff(104,plain,
% 0.84/1.04 (addition(addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = addition(addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[103])).
% 0.84/1.04 tff(105,plain,
% 0.84/1.04 (addition(addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = addition(addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.04 inference(symmetry,[status(thm)],[104])).
% 0.84/1.04 tff(106,plain,
% 0.84/1.04 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!2, addition(addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))) = addition(addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(107,plain,
% 0.84/1.04 (addition(X0!2, addition(addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))) = addition(addition(X0!2, addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one)))), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[106, 50])).
% 0.84/1.04 tff(108,plain,
% 0.84/1.04 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(109,plain,
% 0.84/1.04 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[108])).
% 0.84/1.04 tff(110,plain,
% 0.84/1.04 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(111,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','order')).
% 0.84/1.04 tff(112,plain,
% 0.84/1.04 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.84/1.04 tff(113,plain,(
% 0.84/1.04 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.84/1.04 inference(skolemize,[status(sab)],[112])).
% 0.84/1.04 tff(114,plain,
% 0.84/1.04 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.84/1.04 tff(115,plain,
% 0.84/1.04 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(116,plain,
% 0.84/1.04 (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.84/1.04 tff(117,plain,
% 0.84/1.04 ((~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0))))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(118,plain,
% 0.84/1.04 ((~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X2, X0)) => leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0))))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(119,axiom,(~![X0: $i, X1: $i, X2: $i] : (leq(multiplication(X0, X1), multiplication(X2, X0)) => leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.84/1.04 tff(120,plain,
% 0.84/1.04 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.84/1.04 tff(121,plain,
% 0.84/1.04 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[120, 117])).
% 0.84/1.04 tff(122,plain,
% 0.84/1.04 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.84/1.04 tff(123,plain,
% 0.84/1.04 (~![X0: $i, X1: $i, X2: $i] : ((~leq(multiplication(X0, X1), multiplication(X2, X0))) | leq(multiplication(X0, strong_iteration(X1)), multiplication(strong_iteration(X2), X0)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[122, 117])).
% 0.84/1.04 tff(124,plain,(
% 0.84/1.04 ~((~leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) | leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2)))),
% 0.84/1.04 inference(skolemize,[status(sab)],[123])).
% 0.84/1.04 tff(125,plain,
% 0.84/1.04 (leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))),
% 0.84/1.04 inference(or_elim,[status(thm)],[124])).
% 0.84/1.04 tff(126,plain,
% 0.84/1.04 ((~(leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))) | (~leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2))) | (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.84/1.04 inference(tautology,[status(thm)],[])).
% 0.84/1.04 tff(127,plain,
% 0.84/1.04 ((~(leq(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) <=> (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)))) | (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.84/1.04 tff(128,plain,
% 0.84/1.04 (addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)) = multiplication(X2!0, X0!2)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[127, 116])).
% 0.84/1.04 tff(129,plain,
% 0.84/1.04 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)), addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[128])).
% 0.84/1.04 tff(130,plain,
% 0.84/1.04 (^[A: $i, B: $i, C: $i] : refl((multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(131,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[130])).
% 0.84/1.04 tff(132,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(133,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity2')).
% 0.84/1.04 tff(134,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.84/1.04 tff(135,plain,(
% 0.84/1.04 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.84/1.04 inference(skolemize,[status(sab)],[134])).
% 0.84/1.04 tff(136,plain,
% 0.84/1.04 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.84/1.04 tff(137,plain,
% 0.84/1.04 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)), addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(138,plain,
% 0.84/1.04 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)), addition(multiplication(X1!1, strong_iteration(X1!1)), one)) = addition(multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.84/1.04 tff(139,plain,
% 0.84/1.04 (addition(multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(X2!0, X0!2)), addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.84/1.04 inference(symmetry,[status(thm)],[138])).
% 0.84/1.04 tff(140,plain,
% 0.84/1.04 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!2, multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(141,plain,
% 0.84/1.04 (multiplication(X0!2, multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[140, 17])).
% 0.84/1.04 tff(142,plain,
% 0.84/1.04 (multiplication(X0!2, multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[90])).
% 0.84/1.04 tff(143,plain,
% 0.84/1.04 (multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))) = multiplication(X0!2, multiplication(X1!1, addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.04 inference(symmetry,[status(thm)],[142])).
% 0.84/1.04 tff(144,plain,
% 0.84/1.04 (multiplication(X1!1, strong_iteration(X1!1)) = addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))),
% 0.84/1.04 inference(transitivity,[status(thm)],[89, 92])).
% 0.84/1.04 tff(145,plain,
% 0.84/1.04 (multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))) = multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[144])).
% 0.84/1.04 tff(146,plain,
% 0.84/1.04 (multiplication(X0!2, addition(multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X1!1, one))) = multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1)))),
% 0.84/1.05 inference(symmetry,[status(thm)],[145])).
% 0.84/1.05 tff(147,plain,
% 0.84/1.05 (addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))) = multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one))),
% 0.84/1.05 inference(transitivity,[status(thm)],[80, 146, 143, 141])).
% 0.84/1.05 tff(148,plain,
% 0.84/1.05 (addition(addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = addition(multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[147])).
% 0.84/1.05 tff(149,plain,
% 0.84/1.05 (addition(addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))) = multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[148, 139, 129, 54, 53])).
% 0.84/1.05 tff(150,plain,
% 0.84/1.05 (addition(X0!2, addition(addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)))) = addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[149])).
% 0.84/1.05 tff(151,plain,
% 0.84/1.05 (addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))) = addition(X0!2, addition(addition(multiplication(X0!2, multiplication(X1!1, multiplication(X1!1, strong_iteration(X1!1)))), multiplication(X0!2, multiplication(X1!1, one))), multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))))),
% 0.84/1.05 inference(symmetry,[status(thm)],[150])).
% 0.84/1.05 tff(152,plain,
% 0.84/1.05 (addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))) = addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[151, 107, 105, 70])).
% 0.84/1.05 tff(153,plain,
% 0.84/1.05 (addition(multiplication(X0!2, one), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))) = addition(X0!2, addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[65, 152])).
% 0.84/1.05 tff(154,plain,
% 0.84/1.05 (addition(X0!2, addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))) = addition(multiplication(X0!2, one), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))))),
% 0.84/1.05 inference(symmetry,[status(thm)],[153])).
% 0.84/1.05 tff(155,plain,
% 0.84/1.05 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!2, addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))) = addition(addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(156,plain,
% 0.84/1.05 (addition(X0!2, addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))) = addition(addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[155, 50])).
% 0.84/1.05 tff(157,plain,
% 0.84/1.05 (addition(addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))) = addition(X0!2, addition(multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one)), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))))),
% 0.84/1.05 inference(symmetry,[status(thm)],[156])).
% 0.84/1.05 tff(158,plain,
% 0.84/1.05 (addition(addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))) = addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[56])).
% 0.84/1.05 tff(159,plain,
% 0.84/1.05 (addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))) = addition(addition(X0!2, multiplication(multiplication(X2!0, X0!2), addition(multiplication(X1!1, strong_iteration(X1!1)), one))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))),
% 0.84/1.05 inference(symmetry,[status(thm)],[158])).
% 0.84/1.05 tff(160,plain,
% 0.84/1.05 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))) = addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(161,plain,
% 0.84/1.05 (addition(addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))))) = addition(addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))), addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[160, 7])).
% 0.84/1.05 tff(162,plain,
% 0.84/1.05 (multiplication(X0!2, strong_iteration(X1!1)) = addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one))),
% 0.84/1.05 inference(transitivity,[status(thm)],[29, 101])).
% 0.84/1.05 tff(163,plain,
% 0.84/1.05 (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(addition(multiplication(X0!2, multiplication(X1!1, strong_iteration(X1!1))), multiplication(X0!2, one)), addition(X0!2, multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1)))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[162, 9])).
% 0.84/1.05 tff(164,plain,
% 0.84/1.05 (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)),
% 0.84/1.05 inference(transitivity,[status(thm)],[163, 161, 159, 157, 154, 68, 52, 43, 10])).
% 0.84/1.05 tff(165,plain,
% 0.84/1.05 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) <=> (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(166,plain,
% 0.84/1.05 (leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) <=> (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[165, 114])).
% 0.84/1.05 tff(167,plain,
% 0.84/1.05 (~leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2))),
% 0.84/1.05 inference(or_elim,[status(thm)],[124])).
% 0.84/1.05 tff(168,plain,
% 0.84/1.05 (^[A: $i, B: $i, C: $i] : refl(((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B))) <=> ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(169,plain,
% 0.84/1.05 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B))) <=> ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[168])).
% 0.84/1.05 tff(170,plain,
% 0.84/1.05 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B))) <=> ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(171,plain,
% 0.84/1.05 (^[A: $i, B: $i, C: $i] : rewrite((leq(C, addition(multiplication(A, C), B)) => leq(C, multiplication(strong_iteration(A), B))) <=> ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(172,plain,
% 0.84/1.05 (![A: $i, B: $i, C: $i] : (leq(C, addition(multiplication(A, C), B)) => leq(C, multiplication(strong_iteration(A), B))) <=> ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[171])).
% 0.84/1.05 tff(173,axiom,(![A: $i, B: $i, C: $i] : (leq(C, addition(multiplication(A, C), B)) => leq(C, multiplication(strong_iteration(A), B)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','infty_coinduction')).
% 0.84/1.05 tff(174,plain,
% 0.84/1.05 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.84/1.05 tff(175,plain,
% 0.84/1.05 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.84/1.05 tff(176,plain,(
% 0.84/1.05 ![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.84/1.05 inference(skolemize,[status(sab)],[175])).
% 0.84/1.05 tff(177,plain,
% 0.84/1.05 (![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.84/1.05 tff(178,plain,
% 0.84/1.05 (((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))) | leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))) | leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(179,plain,
% 0.84/1.05 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | ((~leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))) | leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2)))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(180,plain,
% 0.84/1.05 ((~![A: $i, B: $i, C: $i] : ((~leq(C, addition(multiplication(A, C), B))) | leq(C, multiplication(strong_iteration(A), B)))) | (~leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))) | leq(multiplication(X0!2, strong_iteration(X1!1)), multiplication(strong_iteration(X2!0), X0!2))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.84/1.05 tff(181,plain,
% 0.84/1.05 (~leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[180, 177, 167])).
% 0.84/1.05 tff(182,plain,
% 0.84/1.05 ((~(leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) <=> (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)))) | leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) | (~(addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)))),
% 0.84/1.05 inference(tautology,[status(thm)],[])).
% 0.84/1.05 tff(183,plain,
% 0.84/1.05 ((~(leq(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) <=> (addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)))) | (~(addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.84/1.05 tff(184,plain,
% 0.84/1.05 (~(addition(multiplication(X0!2, strong_iteration(X1!1)), addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2)) = addition(multiplication(X2!0, multiplication(X0!2, strong_iteration(X1!1))), X0!2))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[183, 166])).
% 0.84/1.05 tff(185,plain,
% 0.84/1.05 ($false),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[184, 164])).
% 0.84/1.05 % SZS output end Proof
% 0.84/1.05 % E exiting
%------------------------------------------------------------------------------