%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE148+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:13:06 AM UTC 2025
% Result : Theorem 0.91s 1.15s
% Output : Proof 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : KLE148+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 19:05:26 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.91/1.15 % SZS status Theorem
% 0.91/1.15 % SZS output start Proof
% 0.91/1.15 tff(tptp_fun_X0_1_type, type, (
% 0.91/1.15 tptp_fun_X0_1: $i)).
% 0.91/1.15 tff(addition_type, type, (
% 0.91/1.15 addition: ( $i * $i ) > $i)).
% 0.91/1.15 tff(multiplication_type, type, (
% 0.91/1.15 multiplication: ( $i * $i ) > $i)).
% 0.91/1.15 tff(strong_iteration_type, type, (
% 0.91/1.15 strong_iteration: $i > $i)).
% 0.91/1.15 tff(tptp_fun_X1_0_type, type, (
% 0.91/1.15 tptp_fun_X1_0: $i)).
% 0.91/1.15 tff(zero_type, type, (
% 0.91/1.15 zero: $i)).
% 0.91/1.15 tff(one_type, type, (
% 0.91/1.15 one: $i)).
% 0.91/1.15 tff(leq_type, type, (
% 0.91/1.15 leq: ( $i * $i ) > $o)).
% 0.91/1.15 tff(1,plain,
% 0.91/1.15 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(2,plain,
% 0.91/1.15 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.91/1.15 inference(quant_intro,[status(thm)],[1])).
% 0.91/1.15 tff(3,plain,
% 0.91/1.15 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(4,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_identity')).
% 0.91/1.15 tff(5,plain,
% 0.91/1.15 (![A: $i] : (addition(A, zero) = A)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.91/1.15 tff(6,plain,(
% 0.91/1.15 ![A: $i] : (addition(A, zero) = A)),
% 0.91/1.15 inference(skolemize,[status(sab)],[5])).
% 0.91/1.15 tff(7,plain,
% 0.91/1.15 (![A: $i] : (addition(A, zero) = A)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.91/1.15 tff(8,plain,
% 0.91/1.15 ((~![A: $i] : (addition(A, zero) = A)) | (addition(X0!1, zero) = X0!1)),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(9,plain,
% 0.91/1.15 (addition(X0!1, zero) = X0!1),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.91/1.15 tff(10,plain,
% 0.91/1.15 (^[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))))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(11,plain,
% 0.91/1.15 (![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)))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[10])).
% 0.91/1.15 tff(12,plain,
% 0.91/1.15 (![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)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(13,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','distributivity1')).
% 0.91/1.15 tff(14,plain,
% 0.91/1.15 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.91/1.15 tff(15,plain,(
% 0.91/1.15 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.91/1.15 inference(skolemize,[status(sab)],[14])).
% 0.91/1.15 tff(16,plain,
% 0.91/1.15 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.91/1.15 tff(17,plain,
% 0.91/1.15 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(18,plain,
% 0.91/1.15 (multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.91/1.15 tff(19,plain,
% 0.91/1.15 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(20,plain,
% 0.91/1.15 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[19])).
% 0.91/1.15 tff(21,plain,
% 0.91/1.15 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(22,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 0.91/1.15 tff(23,plain,
% 0.91/1.15 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.91/1.15 tff(24,plain,(
% 0.91/1.15 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.91/1.15 inference(skolemize,[status(sab)],[23])).
% 0.91/1.15 tff(25,plain,
% 0.91/1.15 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.91/1.15 tff(26,plain,
% 0.91/1.15 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(X1!0) = addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(27,plain,
% 0.91/1.15 (strong_iteration(X1!0) = addition(multiplication(X1!0, strong_iteration(X1!0)), one)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.91/1.15 tff(28,plain,
% 0.91/1.15 (multiplication(X1!0, strong_iteration(X1!0)) = multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[27])).
% 0.91/1.15 tff(29,plain,
% 0.91/1.15 (multiplication(X1!0, strong_iteration(X1!0)) = addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))),
% 0.91/1.15 inference(transitivity,[status(thm)],[28, 18])).
% 0.91/1.15 tff(30,plain,
% 0.91/1.15 (multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))) = multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[29])).
% 0.91/1.15 tff(31,plain,
% 0.91/1.15 (multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = multiplication(X1!0, strong_iteration(X1!0))),
% 0.91/1.15 inference(symmetry,[status(thm)],[28])).
% 0.91/1.15 tff(32,plain,
% 0.91/1.15 (multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))) = multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0)))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[31])).
% 0.91/1.15 tff(33,plain,
% 0.91/1.15 (^[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)))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(34,plain,
% 0.91/1.15 (![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))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[33])).
% 0.91/1.15 tff(35,plain,
% 0.91/1.15 (![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))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(36,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.91/1.15 tff(37,plain,
% 0.91/1.15 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.91/1.15 tff(38,plain,(
% 0.91/1.15 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.91/1.15 inference(skolemize,[status(sab)],[37])).
% 0.91/1.15 tff(39,plain,
% 0.91/1.15 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.91/1.15 tff(40,plain,
% 0.91/1.15 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))) = multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(41,plain,
% 0.91/1.15 (multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))) = multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.91/1.15 tff(42,plain,
% 0.91/1.15 (multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)))),
% 0.91/1.15 inference(symmetry,[status(thm)],[41])).
% 0.91/1.15 tff(43,plain,
% 0.91/1.15 (multiplication(X0!1, strong_iteration(X1!0)) = multiplication(X0!1, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[27])).
% 0.91/1.15 tff(44,plain,
% 0.91/1.15 (multiplication(X0!1, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = multiplication(X0!1, strong_iteration(X1!0))),
% 0.91/1.15 inference(symmetry,[status(thm)],[43])).
% 0.91/1.15 tff(45,plain,
% 0.91/1.15 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(46,plain,
% 0.91/1.15 (multiplication(X0!1, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one))),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[45, 16])).
% 0.91/1.15 tff(47,plain,
% 0.91/1.15 (addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)) = multiplication(X0!1, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.91/1.15 inference(symmetry,[status(thm)],[46])).
% 0.91/1.15 tff(48,plain,
% 0.91/1.15 (multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))) = multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0)))),
% 0.91/1.15 inference(symmetry,[status(thm)],[30])).
% 0.91/1.15 tff(49,plain,
% 0.91/1.15 (addition(multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))), multiplication(X0!1, one)) = addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[48])).
% 0.91/1.15 tff(50,plain,
% 0.91/1.15 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(51,plain,
% 0.91/1.15 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.91/1.15 inference(quant_intro,[status(thm)],[50])).
% 0.91/1.15 tff(52,plain,
% 0.91/1.15 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(53,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 0.91/1.15 tff(54,plain,
% 0.91/1.15 (![A: $i] : (multiplication(A, one) = A)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.91/1.15 tff(55,plain,(
% 0.91/1.15 ![A: $i] : (multiplication(A, one) = A)),
% 0.91/1.15 inference(skolemize,[status(sab)],[54])).
% 0.91/1.15 tff(56,plain,
% 0.91/1.15 (![A: $i] : (multiplication(A, one) = A)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.91/1.15 tff(57,plain,
% 0.91/1.15 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!1, one) = X0!1)),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(58,plain,
% 0.91/1.15 (multiplication(X0!1, one) = X0!1),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.91/1.15 tff(59,plain,
% 0.91/1.15 (X0!1 = multiplication(X0!1, one)),
% 0.91/1.15 inference(symmetry,[status(thm)],[58])).
% 0.91/1.15 tff(60,plain,
% 0.91/1.15 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(61,plain,
% 0.91/1.15 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.91/1.15 inference(quant_intro,[status(thm)],[60])).
% 0.91/1.15 tff(62,plain,
% 0.91/1.15 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(63,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.91/1.15 tff(64,plain,
% 0.91/1.15 (![A: $i] : (addition(A, A) = A)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.91/1.15 tff(65,plain,(
% 0.91/1.15 ![A: $i] : (addition(A, A) = A)),
% 0.91/1.15 inference(skolemize,[status(sab)],[64])).
% 0.91/1.15 tff(66,plain,
% 0.91/1.15 (![A: $i] : (addition(A, A) = A)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.91/1.15 tff(67,plain,
% 0.91/1.15 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!1, X0!1) = X0!1)),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(68,plain,
% 0.91/1.15 (addition(X0!1, X0!1) = X0!1),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.91/1.15 tff(69,plain,
% 0.91/1.15 (addition(multiplication(X0!1, one), X0!1) = addition(X0!1, X0!1)),
% 0.91/1.15 inference(monotonicity,[status(thm)],[58])).
% 0.91/1.15 tff(70,plain,
% 0.91/1.15 (addition(multiplication(X0!1, one), X0!1) = multiplication(X0!1, one)),
% 0.91/1.15 inference(transitivity,[status(thm)],[69, 68, 59])).
% 0.91/1.15 tff(71,plain,
% 0.91/1.15 (addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), addition(multiplication(X0!1, one), X0!1)) = addition(multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))), multiplication(X0!1, one))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[30, 70])).
% 0.91/1.15 tff(72,plain,
% 0.91/1.15 (^[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)))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(73,plain,
% 0.91/1.15 (![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))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[72])).
% 0.91/1.15 tff(74,plain,
% 0.91/1.15 (![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))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(75,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_associativity')).
% 0.91/1.15 tff(76,plain,
% 0.91/1.15 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.91/1.15 tff(77,plain,(
% 0.91/1.15 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.91/1.15 inference(skolemize,[status(sab)],[76])).
% 0.91/1.15 tff(78,plain,
% 0.91/1.15 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.91/1.15 tff(79,plain,
% 0.91/1.15 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), addition(multiplication(X0!1, one), X0!1)) = addition(addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)), X0!1))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(80,plain,
% 0.91/1.15 (addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), addition(multiplication(X0!1, one), X0!1)) = addition(addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)), X0!1)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.91/1.15 tff(81,plain,
% 0.91/1.15 (addition(addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)), X0!1) = addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), addition(multiplication(X0!1, one), X0!1))),
% 0.91/1.15 inference(symmetry,[status(thm)],[80])).
% 0.91/1.15 tff(82,plain,
% 0.91/1.15 (multiplication(X0!1, strong_iteration(X1!0)) = addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one))),
% 0.91/1.15 inference(transitivity,[status(thm)],[43, 46])).
% 0.91/1.15 tff(83,plain,
% 0.91/1.15 (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = addition(addition(multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X0!1, one)), X0!1)),
% 0.91/1.15 inference(monotonicity,[status(thm)],[82])).
% 0.91/1.15 tff(84,plain,
% 0.91/1.15 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(85,plain,
% 0.91/1.15 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[84])).
% 0.91/1.15 tff(86,plain,
% 0.91/1.15 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(87,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.91/1.15 tff(88,plain,
% 0.91/1.15 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.91/1.15 tff(89,plain,(
% 0.91/1.15 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.91/1.15 inference(skolemize,[status(sab)],[88])).
% 0.91/1.15 tff(90,plain,
% 0.91/1.15 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.91/1.15 tff(91,plain,
% 0.91/1.15 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(92,plain,
% 0.91/1.15 (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.91/1.15 tff(93,plain,
% 0.91/1.15 (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))),
% 0.91/1.15 inference(transitivity,[status(thm)],[92, 83, 81, 71, 49, 47, 44])).
% 0.91/1.15 tff(94,plain,
% 0.91/1.15 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(95,plain,
% 0.91/1.15 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[94])).
% 0.91/1.15 tff(96,plain,
% 0.91/1.15 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(97,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','order')).
% 0.91/1.15 tff(98,plain,
% 0.91/1.15 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.91/1.15 tff(99,plain,(
% 0.91/1.15 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.91/1.15 inference(skolemize,[status(sab)],[98])).
% 0.91/1.15 tff(100,plain,
% 0.91/1.15 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.91/1.15 tff(101,plain,
% 0.91/1.15 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(102,plain,
% 0.91/1.15 (leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0)))),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.91/1.15 tff(103,assumption,(~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))), introduced(assumption)).
% 0.91/1.16 tff(104,plain,
% 0.91/1.16 ((~(leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))) | leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) | (~(addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))),
% 0.91/1.16 inference(tautology,[status(thm)],[])).
% 0.91/1.16 tff(105,plain,
% 0.91/1.16 ((~(leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))) | (~(addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.91/1.16 tff(106,plain,
% 0.91/1.16 (~(addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0)))),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[105, 102])).
% 0.91/1.16 tff(107,plain,
% 0.91/1.16 ($false),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[106, 93])).
% 0.91/1.16 tff(108,plain,(leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.16 tff(109,plain,
% 0.91/1.16 ((~(~((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))))) <=> ((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(110,plain,
% 0.91/1.16 ((((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))) <=> (~((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(111,plain,
% 0.91/1.16 ((~(((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))) <=> (~(~((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))))))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[110])).
% 0.91/1.16 tff(112,plain,
% 0.91/1.16 ((~(((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))) <=> ((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))))),
% 0.91/1.16 inference(transitivity,[status(thm)],[111, 109])).
% 0.91/1.16 tff(113,plain,
% 0.91/1.16 ((~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))) <=> (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1)))))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(114,plain,
% 0.91/1.16 ((~![X0: $i, X1: $i] : (((multiplication(X0, X1) = zero) => leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))) <=> (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1)))))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(115,axiom,(~![X0: $i, X1: $i] : (((multiplication(X0, X1) = zero) => leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.91/1.16 tff(116,plain,
% 0.91/1.16 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.91/1.16 tff(117,plain,
% 0.91/1.16 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[116, 113])).
% 0.91/1.16 tff(118,plain,
% 0.91/1.16 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.91/1.16 tff(119,plain,
% 0.91/1.16 (~![X0: $i, X1: $i] : (((~(multiplication(X0, X1) = zero)) | leq(multiplication(X0, strong_iteration(X1)), X0)) & leq(X0, multiplication(X0, strong_iteration(X1))))),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[118, 113])).
% 0.91/1.16 tff(120,plain,(
% 0.91/1.16 ~(((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) & leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))),
% 0.91/1.16 inference(skolemize,[status(sab)],[119])).
% 0.91/1.16 tff(121,plain,
% 0.91/1.16 ((~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))))),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[120, 112])).
% 0.91/1.16 tff(122,plain,
% 0.91/1.16 (~((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[121, 108])).
% 0.91/1.16 tff(123,plain,
% 0.91/1.16 (((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) | (multiplication(X0!1, X1!0) = zero)),
% 0.91/1.16 inference(tautology,[status(thm)],[])).
% 0.91/1.16 tff(124,plain,
% 0.91/1.16 (multiplication(X0!1, X1!0) = zero),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.91/1.16 tff(125,plain,
% 0.91/1.16 (zero = multiplication(X0!1, X1!0)),
% 0.91/1.16 inference(symmetry,[status(thm)],[124])).
% 0.91/1.16 tff(126,plain,
% 0.91/1.16 (multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[125])).
% 0.91/1.16 tff(127,plain,
% 0.91/1.16 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.91/1.16 inference(bind,[status(th)],[])).
% 0.91/1.16 tff(128,plain,
% 0.91/1.16 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.91/1.16 inference(quant_intro,[status(thm)],[127])).
% 0.91/1.16 tff(129,plain,
% 0.91/1.16 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(130,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 0.91/1.16 tff(131,plain,
% 0.91/1.16 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.91/1.16 tff(132,plain,(
% 0.91/1.16 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.91/1.16 inference(skolemize,[status(sab)],[131])).
% 0.91/1.16 tff(133,plain,
% 0.91/1.16 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.91/1.16 tff(134,plain,
% 0.91/1.16 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = zero)),
% 0.91/1.16 inference(quant_inst,[status(thm)],[])).
% 0.91/1.16 tff(135,plain,
% 0.91/1.16 (multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = zero),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.91/1.16 tff(136,plain,
% 0.91/1.16 (zero = multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.91/1.16 inference(symmetry,[status(thm)],[135])).
% 0.91/1.16 tff(137,plain,
% 0.91/1.16 (zero = multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))),
% 0.91/1.16 inference(transitivity,[status(thm)],[136, 126, 42, 32, 30])).
% 0.91/1.16 tff(138,plain,
% 0.91/1.16 (addition(X0!1, zero) = addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[59, 137])).
% 0.91/1.16 tff(139,plain,
% 0.91/1.16 (addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = addition(X0!1, zero)),
% 0.91/1.16 inference(symmetry,[status(thm)],[138])).
% 0.91/1.16 tff(140,plain,
% 0.91/1.16 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))))),
% 0.91/1.16 inference(quant_inst,[status(thm)],[])).
% 0.91/1.16 tff(141,plain,
% 0.91/1.16 (multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))))),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[140, 16])).
% 0.91/1.16 tff(142,plain,
% 0.91/1.16 (addition(multiplication(X1!0, strong_iteration(X1!0)), one) = strong_iteration(X1!0)),
% 0.91/1.16 inference(symmetry,[status(thm)],[27])).
% 0.91/1.16 tff(143,plain,
% 0.91/1.16 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!0, strong_iteration(X1!0)), one) = addition(one, multiplication(X1!0, strong_iteration(X1!0))))),
% 0.91/1.16 inference(quant_inst,[status(thm)],[])).
% 0.91/1.16 tff(144,plain,
% 0.91/1.16 (addition(multiplication(X1!0, strong_iteration(X1!0)), one) = addition(one, multiplication(X1!0, strong_iteration(X1!0)))),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[143, 90])).
% 0.91/1.16 tff(145,plain,
% 0.91/1.16 (addition(one, multiplication(X1!0, strong_iteration(X1!0))) = addition(multiplication(X1!0, strong_iteration(X1!0)), one)),
% 0.91/1.16 inference(symmetry,[status(thm)],[144])).
% 0.91/1.16 tff(146,plain,
% 0.91/1.16 (addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)) = multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.91/1.16 inference(symmetry,[status(thm)],[18])).
% 0.91/1.16 tff(147,plain,
% 0.91/1.16 (addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)) = multiplication(X1!0, strong_iteration(X1!0))),
% 0.91/1.16 inference(transitivity,[status(thm)],[146, 31])).
% 0.91/1.16 tff(148,plain,
% 0.91/1.16 (addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))) = addition(one, multiplication(X1!0, strong_iteration(X1!0)))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[147])).
% 0.91/1.16 tff(149,plain,
% 0.91/1.16 (addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))) = strong_iteration(X1!0)),
% 0.91/1.16 inference(transitivity,[status(thm)],[148, 145, 142])).
% 0.91/1.16 tff(150,plain,
% 0.91/1.16 (multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = multiplication(X0!1, strong_iteration(X1!0))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[149])).
% 0.91/1.16 tff(151,plain,
% 0.91/1.16 (multiplication(X0!1, strong_iteration(X1!0)) = multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))))),
% 0.91/1.16 inference(symmetry,[status(thm)],[150])).
% 0.91/1.16 tff(152,plain,
% 0.91/1.16 ((~(leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))) | (~leq(X0!1, multiplication(X0!1, strong_iteration(X1!0)))) | (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0)))),
% 0.91/1.16 inference(tautology,[status(thm)],[])).
% 0.91/1.16 tff(153,plain,
% 0.91/1.16 ((~(leq(X0!1, multiplication(X0!1, strong_iteration(X1!0))) <=> (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))))) | (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0)))),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[152, 108])).
% 0.91/1.16 tff(154,plain,
% 0.91/1.16 (addition(X0!1, multiplication(X0!1, strong_iteration(X1!0))) = multiplication(X0!1, strong_iteration(X1!0))),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[153, 102])).
% 0.91/1.16 tff(155,plain,
% 0.91/1.16 (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = addition(X0!1, multiplication(X0!1, strong_iteration(X1!0)))),
% 0.91/1.16 inference(symmetry,[status(thm)],[92])).
% 0.91/1.16 tff(156,plain,
% 0.91/1.16 (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1),
% 0.91/1.16 inference(transitivity,[status(thm)],[155, 154, 151, 141, 139, 9])).
% 0.91/1.16 tff(157,plain,
% 0.91/1.16 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1) <=> (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1))),
% 0.91/1.16 inference(quant_inst,[status(thm)],[])).
% 0.91/1.16 tff(158,plain,
% 0.91/1.16 (leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1) <=> (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[157, 100])).
% 0.91/1.16 tff(159,plain,
% 0.91/1.16 (((~(multiplication(X0!1, X1!0) = zero)) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)) | (~leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1))),
% 0.91/1.16 inference(tautology,[status(thm)],[])).
% 0.91/1.16 tff(160,plain,
% 0.91/1.16 (~leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[159, 122])).
% 0.91/1.16 tff(161,plain,
% 0.91/1.16 ((~(leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1) <=> (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1))) | leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1) | (~(addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1))),
% 0.91/1.16 inference(tautology,[status(thm)],[])).
% 0.91/1.16 tff(162,plain,
% 0.91/1.16 ((~(leq(multiplication(X0!1, strong_iteration(X1!0)), X0!1) <=> (addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1))) | (~(addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1))),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.91/1.16 tff(163,plain,
% 0.91/1.16 (~(addition(multiplication(X0!1, strong_iteration(X1!0)), X0!1) = X0!1)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[162, 158])).
% 0.91/1.16 tff(164,plain,
% 0.91/1.16 ($false),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[163, 156])).
% 0.91/1.16 % SZS output end Proof
% 0.91/1.16 % E exiting
%------------------------------------------------------------------------------