%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE139+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:04 AM UTC 2025
% Result : Theorem 1.16s 1.36s
% Output : Proof 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : KLE139+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 19:03:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 1.16/1.36 % SZS status Theorem
% 1.16/1.36 % SZS output start Proof
% 1.16/1.36 tff(addition_type, type, (
% 1.16/1.36 addition: ( $i * $i ) > $i)).
% 1.16/1.36 tff(one_type, type, (
% 1.16/1.36 one: $i)).
% 1.16/1.36 tff(multiplication_type, type, (
% 1.16/1.36 multiplication: ( $i * $i ) > $i)).
% 1.16/1.36 tff(tptp_fun_X0_0_type, type, (
% 1.16/1.36 tptp_fun_X0_0: $i)).
% 1.16/1.36 tff(strong_iteration_type, type, (
% 1.16/1.36 strong_iteration: $i > $i)).
% 1.16/1.36 tff(zero_type, type, (
% 1.16/1.36 zero: $i)).
% 1.16/1.36 tff(star_type, type, (
% 1.16/1.36 star: $i > $i)).
% 1.16/1.36 tff(leq_type, type, (
% 1.16/1.36 leq: ( $i * $i ) > $o)).
% 1.16/1.36 tff(1,plain,
% 1.16/1.36 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(2,plain,
% 1.16/1.36 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.16/1.36 inference(quant_intro,[status(thm)],[1])).
% 1.16/1.36 tff(3,plain,
% 1.16/1.36 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 1.16/1.36 tff(5,plain,
% 1.16/1.36 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.16/1.36 tff(6,plain,(
% 1.16/1.36 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.16/1.36 inference(skolemize,[status(sab)],[5])).
% 1.16/1.36 tff(7,plain,
% 1.16/1.36 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.16/1.36 tff(8,plain,
% 1.16/1.36 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(strong_iteration(X0!0), X0!0), one) = addition(one, multiplication(strong_iteration(X0!0), X0!0)))),
% 1.16/1.36 inference(quant_inst,[status(thm)],[])).
% 1.16/1.36 tff(9,plain,
% 1.16/1.36 (addition(multiplication(strong_iteration(X0!0), X0!0), one) = addition(one, multiplication(strong_iteration(X0!0), X0!0))),
% 1.16/1.36 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.16/1.36 tff(10,plain,
% 1.16/1.36 (addition(one, multiplication(strong_iteration(X0!0), X0!0)) = addition(multiplication(strong_iteration(X0!0), X0!0), one)),
% 1.16/1.36 inference(symmetry,[status(thm)],[9])).
% 1.16/1.36 tff(11,plain,
% 1.16/1.36 (^[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))))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(12,plain,
% 1.16/1.36 (![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)))),
% 1.16/1.36 inference(quant_intro,[status(thm)],[11])).
% 1.16/1.36 tff(13,plain,
% 1.16/1.36 (![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)))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(14,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')).
% 1.16/1.36 tff(15,plain,
% 1.16/1.36 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.16/1.36 tff(16,plain,(
% 1.16/1.36 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.16/1.36 inference(skolemize,[status(sab)],[15])).
% 1.16/1.36 tff(17,plain,
% 1.16/1.36 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.16/1.36 tff(18,plain,
% 1.16/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)), X0!0) = addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)))),
% 1.16/1.36 inference(quant_inst,[status(thm)],[])).
% 1.16/1.36 tff(19,plain,
% 1.16/1.36 (multiplication(addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)), X0!0) = addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))),
% 1.16/1.36 inference(unit_resolution,[status(thm)],[18, 17])).
% 1.16/1.36 tff(20,plain,
% 1.16/1.36 (^[A: $i] : refl((strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))) <=> (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(21,plain,
% 1.16/1.36 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))) <=> ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 1.16/1.36 inference(quant_intro,[status(thm)],[20])).
% 1.16/1.36 tff(22,plain,
% 1.16/1.36 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero))) <=> ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(23,axiom,(![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','isolation')).
% 1.16/1.36 tff(24,plain,
% 1.16/1.36 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.16/1.36 tff(25,plain,(
% 1.16/1.36 ![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 1.16/1.36 inference(skolemize,[status(sab)],[24])).
% 1.16/1.36 tff(26,plain,
% 1.16/1.36 (![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.16/1.36 tff(27,plain,
% 1.16/1.36 ((~![A: $i] : (strong_iteration(A) = addition(star(A), multiplication(strong_iteration(A), zero)))) | (strong_iteration(X0!0) = addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)))),
% 1.16/1.36 inference(quant_inst,[status(thm)],[])).
% 1.16/1.36 tff(28,plain,
% 1.16/1.36 (strong_iteration(X0!0) = addition(star(X0!0), multiplication(strong_iteration(X0!0), zero))),
% 1.16/1.36 inference(unit_resolution,[status(thm)],[27, 26])).
% 1.16/1.36 tff(29,plain,
% 1.16/1.36 (addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)) = strong_iteration(X0!0)),
% 1.16/1.36 inference(symmetry,[status(thm)],[28])).
% 1.16/1.36 tff(30,plain,
% 1.16/1.36 (multiplication(addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)), X0!0) = multiplication(strong_iteration(X0!0), X0!0)),
% 1.16/1.36 inference(monotonicity,[status(thm)],[29])).
% 1.16/1.36 tff(31,plain,
% 1.16/1.36 (multiplication(strong_iteration(X0!0), X0!0) = multiplication(addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)), X0!0)),
% 1.16/1.36 inference(symmetry,[status(thm)],[30])).
% 1.16/1.36 tff(32,plain,
% 1.16/1.36 (multiplication(strong_iteration(X0!0), X0!0) = addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))),
% 1.16/1.36 inference(transitivity,[status(thm)],[31, 19])).
% 1.16/1.36 tff(33,plain,
% 1.16/1.36 (addition(one, multiplication(strong_iteration(X0!0), X0!0)) = addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)))),
% 1.16/1.36 inference(monotonicity,[status(thm)],[32])).
% 1.16/1.36 tff(34,plain,
% 1.16/1.36 (addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))) = addition(one, multiplication(strong_iteration(X0!0), X0!0))),
% 1.16/1.36 inference(symmetry,[status(thm)],[33])).
% 1.16/1.36 tff(35,plain,
% 1.16/1.36 (^[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)))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(36,plain,
% 1.16/1.36 (![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))),
% 1.16/1.36 inference(quant_intro,[status(thm)],[35])).
% 1.16/1.36 tff(37,plain,
% 1.16/1.36 (![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))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(38,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')).
% 1.16/1.36 tff(39,plain,
% 1.16/1.36 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.16/1.36 tff(40,plain,(
% 1.16/1.36 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 1.16/1.36 inference(skolemize,[status(sab)],[39])).
% 1.16/1.36 tff(41,plain,
% 1.16/1.36 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.16/1.36 tff(42,plain,
% 1.16/1.36 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)))),
% 1.16/1.36 inference(quant_inst,[status(thm)],[])).
% 1.16/1.36 tff(43,plain,
% 1.16/1.36 (addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))) = addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))),
% 1.16/1.36 inference(unit_resolution,[status(thm)],[42, 41])).
% 1.16/1.36 tff(44,plain,
% 1.16/1.36 (addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)) = addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)))),
% 1.16/1.36 inference(symmetry,[status(thm)],[43])).
% 1.16/1.36 tff(45,plain,
% 1.16/1.36 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(46,plain,
% 1.16/1.36 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 1.16/1.36 inference(quant_intro,[status(thm)],[45])).
% 1.16/1.36 tff(47,plain,
% 1.16/1.36 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(48,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 1.16/1.36 tff(49,plain,
% 1.16/1.36 (![A: $i] : (multiplication(zero, A) = zero)),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.16/1.36 tff(50,plain,(
% 1.16/1.36 ![A: $i] : (multiplication(zero, A) = zero)),
% 1.16/1.36 inference(skolemize,[status(sab)],[49])).
% 1.16/1.36 tff(51,plain,
% 1.16/1.36 (![A: $i] : (multiplication(zero, A) = zero)),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.16/1.36 tff(52,plain,
% 1.16/1.36 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, X0!0) = zero)),
% 1.16/1.36 inference(quant_inst,[status(thm)],[])).
% 1.16/1.36 tff(53,plain,
% 1.16/1.36 (multiplication(zero, X0!0) = zero),
% 1.16/1.36 inference(unit_resolution,[status(thm)],[52, 51])).
% 1.16/1.36 tff(54,plain,
% 1.16/1.36 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(55,plain,
% 1.16/1.36 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 1.16/1.36 inference(quant_intro,[status(thm)],[54])).
% 1.16/1.36 tff(56,plain,
% 1.16/1.36 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(57,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 1.16/1.36 tff(58,plain,
% 1.16/1.36 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.16/1.37 tff(59,plain,(
% 1.16/1.37 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 1.16/1.37 inference(skolemize,[status(sab)],[58])).
% 1.16/1.37 tff(60,plain,
% 1.16/1.37 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[59, 55])).
% 1.16/1.37 tff(61,plain,
% 1.16/1.37 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(X0!0) = addition(multiplication(X0!0, strong_iteration(X0!0)), one))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(62,plain,
% 1.16/1.37 (strong_iteration(X0!0) = addition(multiplication(X0!0, strong_iteration(X0!0)), one)),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[61, 60])).
% 1.16/1.37 tff(63,plain,
% 1.16/1.37 (addition(multiplication(X0!0, strong_iteration(X0!0)), one) = strong_iteration(X0!0)),
% 1.16/1.37 inference(symmetry,[status(thm)],[62])).
% 1.16/1.37 tff(64,plain,
% 1.16/1.37 (multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), multiplication(zero, X0!0)) = multiplication(strong_iteration(X0!0), zero)),
% 1.16/1.37 inference(monotonicity,[status(thm)],[63, 53])).
% 1.16/1.37 tff(65,plain,
% 1.16/1.37 (^[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)))),
% 1.16/1.37 inference(bind,[status(th)],[])).
% 1.16/1.37 tff(66,plain,
% 1.16/1.37 (![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))),
% 1.16/1.37 inference(quant_intro,[status(thm)],[65])).
% 1.16/1.37 tff(67,plain,
% 1.16/1.37 (![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))),
% 1.16/1.37 inference(rewrite,[status(thm)],[])).
% 1.16/1.37 tff(68,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')).
% 1.16/1.37 tff(69,plain,
% 1.16/1.37 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.16/1.37 tff(70,plain,(
% 1.16/1.37 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 1.16/1.37 inference(skolemize,[status(sab)],[69])).
% 1.16/1.37 tff(71,plain,
% 1.16/1.37 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[70, 66])).
% 1.16/1.37 tff(72,plain,
% 1.16/1.37 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), multiplication(zero, X0!0)) = multiplication(multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero), X0!0))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(73,plain,
% 1.16/1.37 (multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), multiplication(zero, X0!0)) = multiplication(multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero), X0!0)),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[72, 71])).
% 1.16/1.37 tff(74,plain,
% 1.16/1.37 (multiplication(multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero), X0!0) = multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), multiplication(zero, X0!0))),
% 1.16/1.37 inference(symmetry,[status(thm)],[73])).
% 1.16/1.37 tff(75,plain,
% 1.16/1.37 (multiplication(strong_iteration(X0!0), zero) = multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero)),
% 1.16/1.37 inference(monotonicity,[status(thm)],[62])).
% 1.16/1.37 tff(76,plain,
% 1.16/1.37 (multiplication(multiplication(strong_iteration(X0!0), zero), X0!0) = multiplication(multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero), X0!0)),
% 1.16/1.37 inference(monotonicity,[status(thm)],[75])).
% 1.16/1.37 tff(77,plain,
% 1.16/1.37 (multiplication(multiplication(strong_iteration(X0!0), zero), X0!0) = multiplication(strong_iteration(X0!0), zero)),
% 1.16/1.37 inference(transitivity,[status(thm)],[76, 74, 64])).
% 1.16/1.37 tff(78,plain,
% 1.16/1.37 (^[A: $i] : refl((addition(one, multiplication(star(A), A)) = star(A)) <=> (addition(one, multiplication(star(A), A)) = star(A)))),
% 1.16/1.37 inference(bind,[status(th)],[])).
% 1.16/1.37 tff(79,plain,
% 1.16/1.37 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 1.16/1.37 inference(quant_intro,[status(thm)],[78])).
% 1.16/1.37 tff(80,plain,
% 1.16/1.37 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A)) <=> ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 1.16/1.37 inference(rewrite,[status(thm)],[])).
% 1.16/1.37 tff(81,axiom,(![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold2')).
% 1.16/1.37 tff(82,plain,
% 1.16/1.37 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.16/1.37 tff(83,plain,(
% 1.16/1.37 ![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 1.16/1.37 inference(skolemize,[status(sab)],[82])).
% 1.16/1.37 tff(84,plain,
% 1.16/1.37 (![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[83, 79])).
% 1.16/1.37 tff(85,plain,
% 1.16/1.37 ((~![A: $i] : (addition(one, multiplication(star(A), A)) = star(A))) | (addition(one, multiplication(star(X0!0), X0!0)) = star(X0!0))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(86,plain,
% 1.16/1.37 (addition(one, multiplication(star(X0!0), X0!0)) = star(X0!0)),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[85, 84])).
% 1.16/1.37 tff(87,plain,
% 1.16/1.37 (addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)) = addition(star(X0!0), multiplication(strong_iteration(X0!0), zero))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[86, 77])).
% 1.16/1.37 tff(88,plain,
% 1.16/1.37 (addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)) = addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))),
% 1.16/1.37 inference(symmetry,[status(thm)],[87])).
% 1.16/1.37 tff(89,plain,
% 1.16/1.37 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 1.16/1.37 inference(bind,[status(th)],[])).
% 1.16/1.37 tff(90,plain,
% 1.16/1.37 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 1.16/1.37 inference(quant_intro,[status(thm)],[89])).
% 1.16/1.37 tff(91,plain,
% 1.16/1.37 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 1.16/1.37 inference(rewrite,[status(thm)],[])).
% 1.16/1.37 tff(92,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','order')).
% 1.16/1.37 tff(93,plain,
% 1.16/1.37 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.16/1.37 tff(94,plain,(
% 1.16/1.37 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 1.16/1.37 inference(skolemize,[status(sab)],[93])).
% 1.16/1.37 tff(95,plain,
% 1.16/1.37 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[94, 90])).
% 1.16/1.37 tff(96,plain,
% 1.16/1.37 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) <=> (addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0)))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(97,plain,
% 1.16/1.37 (leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) <=> (addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[96, 95])).
% 1.16/1.37 tff(98,plain,
% 1.16/1.37 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 1.16/1.37 inference(bind,[status(th)],[])).
% 1.16/1.37 tff(99,plain,
% 1.16/1.37 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.16/1.37 inference(quant_intro,[status(thm)],[98])).
% 1.16/1.37 tff(100,plain,
% 1.16/1.37 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.16/1.37 inference(rewrite,[status(thm)],[])).
% 1.16/1.37 tff(101,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 1.16/1.37 tff(102,plain,
% 1.16/1.37 (![A: $i] : (addition(A, A) = A)),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.16/1.37 tff(103,plain,(
% 1.16/1.37 ![A: $i] : (addition(A, A) = A)),
% 1.16/1.37 inference(skolemize,[status(sab)],[102])).
% 1.16/1.37 tff(104,plain,
% 1.16/1.37 (![A: $i] : (addition(A, A) = A)),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.16/1.37 tff(105,plain,
% 1.16/1.37 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(X0!0, strong_iteration(X0!0)), one), addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = addition(multiplication(X0!0, strong_iteration(X0!0)), one))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(106,plain,
% 1.16/1.37 (addition(addition(multiplication(X0!0, strong_iteration(X0!0)), one), addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = addition(multiplication(X0!0, strong_iteration(X0!0)), one)),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[105, 104])).
% 1.16/1.37 tff(107,plain,
% 1.16/1.37 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!0, strong_iteration(X0!0)), one) = addition(one, multiplication(X0!0, strong_iteration(X0!0))))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(108,plain,
% 1.16/1.37 (addition(multiplication(X0!0, strong_iteration(X0!0)), one) = addition(one, multiplication(X0!0, strong_iteration(X0!0)))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[107, 7])).
% 1.16/1.37 tff(109,plain,
% 1.16/1.37 (addition(one, multiplication(X0!0, strong_iteration(X0!0))) = addition(multiplication(X0!0, strong_iteration(X0!0)), one)),
% 1.16/1.37 inference(symmetry,[status(thm)],[108])).
% 1.16/1.37 tff(110,plain,
% 1.16/1.37 (multiplication(X0!0, addition(star(X0!0), multiplication(strong_iteration(X0!0), zero))) = multiplication(X0!0, strong_iteration(X0!0))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[29])).
% 1.16/1.37 tff(111,plain,
% 1.16/1.37 (^[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))))),
% 1.16/1.37 inference(bind,[status(th)],[])).
% 1.16/1.37 tff(112,plain,
% 1.16/1.37 (![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)))),
% 1.16/1.37 inference(quant_intro,[status(thm)],[111])).
% 1.16/1.37 tff(113,plain,
% 1.16/1.37 (![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)))),
% 1.16/1.37 inference(rewrite,[status(thm)],[])).
% 1.16/1.37 tff(114,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')).
% 1.16/1.37 tff(115,plain,
% 1.16/1.37 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.16/1.37 tff(116,plain,(
% 1.16/1.37 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 1.16/1.37 inference(skolemize,[status(sab)],[115])).
% 1.16/1.37 tff(117,plain,
% 1.16/1.37 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[116, 112])).
% 1.16/1.37 tff(118,plain,
% 1.16/1.37 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(star(X0!0), multiplication(strong_iteration(X0!0), zero))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(119,plain,
% 1.16/1.37 (multiplication(X0!0, addition(star(X0!0), multiplication(strong_iteration(X0!0), zero))) = addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[118, 117])).
% 1.16/1.37 tff(120,plain,
% 1.16/1.37 (addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))) = multiplication(X0!0, addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)))),
% 1.16/1.37 inference(symmetry,[status(thm)],[119])).
% 1.16/1.37 tff(121,plain,
% 1.16/1.37 (addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))) = multiplication(X0!0, strong_iteration(X0!0))),
% 1.16/1.37 inference(transitivity,[status(thm)],[120, 110])).
% 1.16/1.37 tff(122,plain,
% 1.16/1.37 (addition(one, addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))) = addition(one, multiplication(X0!0, strong_iteration(X0!0)))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[121])).
% 1.16/1.37 tff(123,plain,
% 1.16/1.37 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))) = addition(addition(one, multiplication(X0!0, star(X0!0))), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(124,plain,
% 1.16/1.37 (addition(one, addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))) = addition(addition(one, multiplication(X0!0, star(X0!0))), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[123, 41])).
% 1.16/1.37 tff(125,plain,
% 1.16/1.37 (addition(addition(one, multiplication(X0!0, star(X0!0))), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))) = addition(one, addition(multiplication(X0!0, star(X0!0)), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))))),
% 1.16/1.37 inference(symmetry,[status(thm)],[124])).
% 1.16/1.37 tff(126,plain,
% 1.16/1.37 (multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)) = multiplication(X0!0, multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[75])).
% 1.16/1.37 tff(127,plain,
% 1.16/1.37 (multiplication(X0!0, multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero)) = multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))),
% 1.16/1.37 inference(symmetry,[status(thm)],[126])).
% 1.16/1.37 tff(128,plain,
% 1.16/1.37 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!0, multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero)) = multiplication(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), zero))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(129,plain,
% 1.16/1.37 (multiplication(X0!0, multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero)) = multiplication(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), zero)),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[128, 71])).
% 1.16/1.37 tff(130,plain,
% 1.16/1.37 (multiplication(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), zero) = multiplication(X0!0, multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero))),
% 1.16/1.37 inference(symmetry,[status(thm)],[129])).
% 1.16/1.37 tff(131,plain,
% 1.16/1.37 (multiplication(X0!0, strong_iteration(X0!0)) = multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[62])).
% 1.16/1.37 tff(132,plain,
% 1.16/1.37 (multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = multiplication(X0!0, strong_iteration(X0!0))),
% 1.16/1.37 inference(symmetry,[status(thm)],[131])).
% 1.16/1.37 tff(133,plain,
% 1.16/1.37 (multiplication(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), zero) = multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero)),
% 1.16/1.37 inference(monotonicity,[status(thm)],[132])).
% 1.16/1.37 tff(134,plain,
% 1.16/1.37 (multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero) = multiplication(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), zero)),
% 1.16/1.37 inference(symmetry,[status(thm)],[133])).
% 1.16/1.37 tff(135,plain,
% 1.16/1.37 (multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero) = multiplication(X0!0, multiplication(strong_iteration(X0!0), zero))),
% 1.16/1.37 inference(transitivity,[status(thm)],[134, 130, 127])).
% 1.16/1.37 tff(136,plain,
% 1.16/1.37 (^[A: $i] : refl((addition(one, multiplication(A, star(A))) = star(A)) <=> (addition(one, multiplication(A, star(A))) = star(A)))),
% 1.16/1.37 inference(bind,[status(th)],[])).
% 1.16/1.37 tff(137,plain,
% 1.16/1.37 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 1.16/1.37 inference(quant_intro,[status(thm)],[136])).
% 1.16/1.37 tff(138,plain,
% 1.16/1.37 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A)) <=> ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 1.16/1.37 inference(rewrite,[status(thm)],[])).
% 1.16/1.37 tff(139,axiom,(![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','star_unfold1')).
% 1.16/1.37 tff(140,plain,
% 1.16/1.37 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.16/1.37 tff(141,plain,(
% 1.16/1.37 ![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 1.16/1.37 inference(skolemize,[status(sab)],[140])).
% 1.16/1.37 tff(142,plain,
% 1.16/1.37 (![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[141, 137])).
% 1.16/1.37 tff(143,plain,
% 1.16/1.37 ((~![A: $i] : (addition(one, multiplication(A, star(A))) = star(A))) | (addition(one, multiplication(X0!0, star(X0!0))) = star(X0!0))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(144,plain,
% 1.16/1.37 (addition(one, multiplication(X0!0, star(X0!0))) = star(X0!0)),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[143, 142])).
% 1.16/1.37 tff(145,plain,
% 1.16/1.37 (star(X0!0) = addition(one, multiplication(X0!0, star(X0!0)))),
% 1.16/1.37 inference(symmetry,[status(thm)],[144])).
% 1.16/1.37 tff(146,plain,
% 1.16/1.37 (addition(star(X0!0), multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero)) = addition(addition(one, multiplication(X0!0, star(X0!0))), multiplication(X0!0, multiplication(strong_iteration(X0!0), zero)))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[145, 135])).
% 1.16/1.37 tff(147,plain,
% 1.16/1.37 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(148,plain,
% 1.16/1.37 (multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[147, 117])).
% 1.16/1.37 tff(149,plain,
% 1.16/1.37 (multiplication(X0!0, strong_iteration(X0!0)) = addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one))),
% 1.16/1.37 inference(transitivity,[status(thm)],[131, 148])).
% 1.16/1.37 tff(150,plain,
% 1.16/1.37 (multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero) = multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero)),
% 1.16/1.37 inference(monotonicity,[status(thm)],[149])).
% 1.16/1.37 tff(151,plain,
% 1.16/1.37 (multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero) = multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero)),
% 1.16/1.37 inference(symmetry,[status(thm)],[150])).
% 1.16/1.37 tff(152,plain,
% 1.16/1.37 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero) = addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(153,plain,
% 1.16/1.37 (multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero) = addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[152, 17])).
% 1.16/1.37 tff(154,plain,
% 1.16/1.37 (addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)) = multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero)),
% 1.16/1.37 inference(symmetry,[status(thm)],[153])).
% 1.16/1.37 tff(155,plain,
% 1.16/1.37 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 1.16/1.37 inference(bind,[status(th)],[])).
% 1.16/1.37 tff(156,plain,
% 1.16/1.37 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 1.16/1.37 inference(quant_intro,[status(thm)],[155])).
% 1.16/1.37 tff(157,plain,
% 1.16/1.37 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 1.16/1.37 inference(rewrite,[status(thm)],[])).
% 1.16/1.37 tff(158,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_identity')).
% 1.16/1.37 tff(159,plain,
% 1.16/1.37 (![A: $i] : (addition(A, zero) = A)),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.16/1.37 tff(160,plain,(
% 1.16/1.37 ![A: $i] : (addition(A, zero) = A)),
% 1.16/1.37 inference(skolemize,[status(sab)],[159])).
% 1.16/1.37 tff(161,plain,
% 1.16/1.37 (![A: $i] : (addition(A, zero) = A)),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[160, 156])).
% 1.16/1.37 tff(162,plain,
% 1.16/1.37 ((~![A: $i] : (addition(A, zero) = A)) | (addition(addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)), zero) = addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(163,plain,
% 1.16/1.37 (addition(addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)), zero) = addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[162, 161])).
% 1.16/1.37 tff(164,plain,
% 1.16/1.37 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 1.16/1.37 inference(bind,[status(th)],[])).
% 1.16/1.37 tff(165,plain,
% 1.16/1.37 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.16/1.37 inference(quant_intro,[status(thm)],[164])).
% 1.16/1.37 tff(166,plain,
% 1.16/1.37 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.16/1.37 inference(rewrite,[status(thm)],[])).
% 1.16/1.37 tff(167,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_left_identity')).
% 1.16/1.37 tff(168,plain,
% 1.16/1.37 (![A: $i] : (multiplication(one, A) = A)),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.16/1.37 tff(169,plain,(
% 1.16/1.37 ![A: $i] : (multiplication(one, A) = A)),
% 1.16/1.37 inference(skolemize,[status(sab)],[168])).
% 1.16/1.37 tff(170,plain,
% 1.16/1.37 (![A: $i] : (multiplication(one, A) = A)),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[169, 165])).
% 1.16/1.37 tff(171,plain,
% 1.16/1.37 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, zero) = zero)),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(172,plain,
% 1.16/1.37 (multiplication(one, zero) = zero),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[171, 170])).
% 1.16/1.37 tff(173,plain,
% 1.16/1.37 (addition(multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero), multiplication(one, zero)) = addition(addition(multiplication(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), zero), multiplication(multiplication(X0!0, one), zero)), zero)),
% 1.16/1.37 inference(monotonicity,[status(thm)],[153, 172])).
% 1.16/1.37 tff(174,plain,
% 1.16/1.37 (addition(multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero), multiplication(one, zero)) = addition(multiplication(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), zero), multiplication(one, zero))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[150])).
% 1.16/1.37 tff(175,plain,
% 1.16/1.37 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero) = addition(multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero), multiplication(one, zero)))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(176,plain,
% 1.16/1.37 (multiplication(addition(multiplication(X0!0, strong_iteration(X0!0)), one), zero) = addition(multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero), multiplication(one, zero))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[175, 17])).
% 1.16/1.37 tff(177,plain,
% 1.16/1.37 (multiplication(multiplication(strong_iteration(X0!0), zero), X0!0) = multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero)),
% 1.16/1.37 inference(transitivity,[status(thm)],[76, 74, 64, 75, 176, 174, 173, 163, 154, 151])).
% 1.16/1.37 tff(178,plain,
% 1.16/1.37 (addition(addition(one, multiplication(star(X0!0), X0!0)), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)) = addition(star(X0!0), multiplication(multiplication(X0!0, strong_iteration(X0!0)), zero))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[86, 177])).
% 1.16/1.37 tff(179,plain,
% 1.16/1.37 (multiplication(strong_iteration(X0!0), X0!0) = multiplication(addition(star(X0!0), multiplication(strong_iteration(X0!0), zero)), X0!0)),
% 1.16/1.37 inference(monotonicity,[status(thm)],[28])).
% 1.16/1.37 tff(180,plain,
% 1.16/1.37 (multiplication(strong_iteration(X0!0), X0!0) = addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0))),
% 1.16/1.37 inference(transitivity,[status(thm)],[179, 19])).
% 1.16/1.37 tff(181,plain,
% 1.16/1.37 (addition(one, multiplication(strong_iteration(X0!0), X0!0)) = addition(one, addition(multiplication(star(X0!0), X0!0), multiplication(multiplication(strong_iteration(X0!0), zero), X0!0)))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[180])).
% 1.16/1.37 tff(182,plain,
% 1.16/1.37 (addition(multiplication(strong_iteration(X0!0), X0!0), one) = addition(multiplication(X0!0, strong_iteration(X0!0)), one)),
% 1.16/1.37 inference(transitivity,[status(thm)],[9, 181, 43, 178, 146, 125, 122, 109])).
% 1.16/1.37 tff(183,plain,
% 1.16/1.37 (addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = addition(addition(multiplication(X0!0, strong_iteration(X0!0)), one), addition(multiplication(X0!0, strong_iteration(X0!0)), one))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[182, 62])).
% 1.16/1.37 tff(184,plain,
% 1.16/1.37 (addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0)),
% 1.16/1.37 inference(transitivity,[status(thm)],[183, 106, 63])).
% 1.16/1.37 tff(185,assumption,(~leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0))), introduced(assumption)).
% 1.16/1.37 tff(186,plain,
% 1.16/1.37 ((~(leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) <=> (addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0)))) | leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) | (~(addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0)))),
% 1.16/1.37 inference(tautology,[status(thm)],[])).
% 1.16/1.37 tff(187,plain,
% 1.16/1.37 ((~(leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) <=> (addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0)))) | (~(addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0)))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[186, 185])).
% 1.16/1.37 tff(188,plain,
% 1.16/1.37 (~(addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[187, 97])).
% 1.16/1.37 tff(189,plain,
% 1.16/1.37 ($false),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[188, 184])).
% 1.16/1.37 tff(190,plain,(leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0))), inference(lemma,lemma(discharge,[]))).
% 1.16/1.37 tff(191,plain,
% 1.16/1.37 ((~(leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) <=> (addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0)))) | (~leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0))) | (addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0))),
% 1.16/1.37 inference(tautology,[status(thm)],[])).
% 1.16/1.37 tff(192,plain,
% 1.16/1.37 ((~(leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) <=> (addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0)))) | (addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[191, 190])).
% 1.16/1.37 tff(193,plain,
% 1.16/1.37 (addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)) = strong_iteration(X0!0)),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[192, 97])).
% 1.16/1.37 tff(194,plain,
% 1.16/1.37 (addition(addition(one, multiplication(strong_iteration(X0!0), X0!0)), addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = addition(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[10, 63])).
% 1.16/1.37 tff(195,plain,
% 1.16/1.37 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(one, multiplication(strong_iteration(X0!0), X0!0)), addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = addition(addition(multiplication(X0!0, strong_iteration(X0!0)), one), addition(one, multiplication(strong_iteration(X0!0), X0!0))))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(196,plain,
% 1.16/1.37 (addition(addition(one, multiplication(strong_iteration(X0!0), X0!0)), addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = addition(addition(multiplication(X0!0, strong_iteration(X0!0)), one), addition(one, multiplication(strong_iteration(X0!0), X0!0)))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[195, 7])).
% 1.16/1.37 tff(197,plain,
% 1.16/1.37 (addition(addition(multiplication(X0!0, strong_iteration(X0!0)), one), addition(one, multiplication(strong_iteration(X0!0), X0!0))) = addition(addition(one, multiplication(strong_iteration(X0!0), X0!0)), addition(multiplication(X0!0, strong_iteration(X0!0)), one))),
% 1.16/1.37 inference(symmetry,[status(thm)],[196])).
% 1.16/1.37 tff(198,plain,
% 1.16/1.37 (addition(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) = addition(addition(multiplication(X0!0, strong_iteration(X0!0)), one), addition(one, multiplication(strong_iteration(X0!0), X0!0)))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[62, 9])).
% 1.16/1.37 tff(199,plain,
% 1.16/1.37 (addition(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) = addition(multiplication(strong_iteration(X0!0), X0!0), one)),
% 1.16/1.37 inference(transitivity,[status(thm)],[198, 197, 194, 193, 28, 88, 44, 34, 10])).
% 1.16/1.37 tff(200,plain,
% 1.16/1.37 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) <=> (addition(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) = addition(multiplication(strong_iteration(X0!0), X0!0), one)))),
% 1.16/1.37 inference(quant_inst,[status(thm)],[])).
% 1.16/1.37 tff(201,plain,
% 1.16/1.37 (leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) <=> (addition(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) = addition(multiplication(strong_iteration(X0!0), X0!0), one))),
% 1.16/1.37 inference(unit_resolution,[status(thm)],[200, 95])).
% 1.16/1.37 tff(202,plain,
% 1.16/1.37 ((~(~((~leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one))) | (~leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)))))) <=> ((~leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one))) | (~leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0))))),
% 1.16/1.37 inference(rewrite,[status(thm)],[])).
% 1.16/1.37 tff(203,plain,
% 1.16/1.37 ((leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) & leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0))) <=> (~((~leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one))) | (~leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)))))),
% 1.16/1.37 inference(rewrite,[status(thm)],[])).
% 1.16/1.37 tff(204,plain,
% 1.16/1.37 ((~(leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) & leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)))) <=> (~(~((~leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one))) | (~leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0))))))),
% 1.16/1.37 inference(monotonicity,[status(thm)],[203])).
% 1.16/1.37 tff(205,plain,
% 1.16/1.37 ((~(leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) & leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)))) <=> ((~leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one))) | (~leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0))))),
% 1.16/1.37 inference(transitivity,[status(thm)],[204, 202])).
% 1.16/1.37 tff(206,plain,
% 1.16/1.37 ((~![X0: $i] : (leq(strong_iteration(X0), addition(multiplication(strong_iteration(X0), X0), one)) & leq(addition(multiplication(strong_iteration(X0), X0), one), strong_iteration(X0)))) <=> (~![X0: $i] : (leq(strong_iteration(X0), addition(multiplication(strong_iteration(X0), X0), one)) & leq(addition(multiplication(strong_iteration(X0), X0), one), strong_iteration(X0))))),
% 1.16/1.37 inference(rewrite,[status(thm)],[])).
% 1.16/1.37 tff(207,axiom,(~![X0: $i] : (leq(strong_iteration(X0), addition(multiplication(strong_iteration(X0), X0), one)) & leq(addition(multiplication(strong_iteration(X0), X0), one), strong_iteration(X0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 1.16/1.37 tff(208,plain,
% 1.16/1.37 (~![X0: $i] : (leq(strong_iteration(X0), addition(multiplication(strong_iteration(X0), X0), one)) & leq(addition(multiplication(strong_iteration(X0), X0), one), strong_iteration(X0)))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.16/1.37 tff(209,plain,
% 1.16/1.37 (~![X0: $i] : (leq(strong_iteration(X0), addition(multiplication(strong_iteration(X0), X0), one)) & leq(addition(multiplication(strong_iteration(X0), X0), one), strong_iteration(X0)))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[208, 206])).
% 1.16/1.37 tff(210,plain,
% 1.16/1.37 (~![X0: $i] : (leq(strong_iteration(X0), addition(multiplication(strong_iteration(X0), X0), one)) & leq(addition(multiplication(strong_iteration(X0), X0), one), strong_iteration(X0)))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[209, 206])).
% 1.16/1.37 tff(211,plain,
% 1.16/1.37 (~![X0: $i] : (leq(strong_iteration(X0), addition(multiplication(strong_iteration(X0), X0), one)) & leq(addition(multiplication(strong_iteration(X0), X0), one), strong_iteration(X0)))),
% 1.16/1.37 inference(modus_ponens,[status(thm)],[210, 206])).
% 1.16/1.37 tff(212,plain,(
% 1.16/1.37 ~(leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) & leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)))),
% 1.16/1.37 inference(skolemize,[status(sab)],[211])).
% 1.16/1.37 tff(213,plain,
% 1.22/1.38 ((~leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one))) | (~leq(addition(multiplication(strong_iteration(X0!0), X0!0), one), strong_iteration(X0!0)))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[212, 205])).
% 1.22/1.38 tff(214,plain,
% 1.22/1.38 (~leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[213, 190])).
% 1.22/1.38 tff(215,plain,
% 1.22/1.38 ((~(leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) <=> (addition(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) = addition(multiplication(strong_iteration(X0!0), X0!0), one)))) | leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) | (~(addition(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) = addition(multiplication(strong_iteration(X0!0), X0!0), one)))),
% 1.22/1.38 inference(tautology,[status(thm)],[])).
% 1.22/1.38 tff(216,plain,
% 1.22/1.38 ((~(leq(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) <=> (addition(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) = addition(multiplication(strong_iteration(X0!0), X0!0), one)))) | (~(addition(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) = addition(multiplication(strong_iteration(X0!0), X0!0), one)))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[215, 214])).
% 1.22/1.38 tff(217,plain,
% 1.22/1.38 (~(addition(strong_iteration(X0!0), addition(multiplication(strong_iteration(X0!0), X0!0), one)) = addition(multiplication(strong_iteration(X0!0), X0!0), one))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[216, 201])).
% 1.22/1.38 tff(218,plain,
% 1.22/1.38 ($false),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[217, 199])).
% 1.22/1.38 % SZS output end Proof
% 1.22/1.38 % E exiting
%------------------------------------------------------------------------------