%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE146+1 : 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 05:13:05 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE146+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % 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 19:05:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(strong_iteration_type, type, (
% 0.20/0.39 strong_iteration: $i > $i)).
% 0.20/0.39 tff(tptp_fun_X0_0_type, type, (
% 0.20/0.39 tptp_fun_X0_0: $i)).
% 0.20/0.39 tff(addition_type, type, (
% 0.20/0.39 addition: ( $i * $i ) > $i)).
% 0.20/0.39 tff(one_type, type, (
% 0.20/0.39 one: $i)).
% 0.20/0.39 tff(multiplication_type, type, (
% 0.20/0.39 multiplication: ( $i * $i ) > $i)).
% 0.20/0.39 tff(leq_type, type, (
% 0.20/0.39 leq: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(4,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.39 tff(6,plain,(
% 0.20/0.39 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.20/0.39 inference(skolemize,[status(sab)],[5])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 ((~![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))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (strong_iteration(X0!0) = addition(multiplication(X0!0, strong_iteration(X0!0)), one)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (addition(multiplication(X0!0, strong_iteration(X0!0)), one) = strong_iteration(X0!0)),
% 0.20/0.39 inference(symmetry,[status(thm)],[9])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (multiplication(X0!0, strong_iteration(X0!0)) = multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = multiplication(X0!0, strong_iteration(X0!0))),
% 0.20/0.39 inference(symmetry,[status(thm)],[11])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (addition(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), one) = addition(multiplication(X0!0, strong_iteration(X0!0)), one)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.20/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(17,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (![A: $i] : (addition(A, A) = A)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.39 tff(19,plain,(
% 0.20/0.39 ![A: $i] : (addition(A, A) = A)),
% 0.20/0.39 inference(skolemize,[status(sab)],[18])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![A: $i] : (addition(A, A) = A)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (addition(one, one) = one),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (^[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))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(26,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')).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.39 tff(28,plain,(
% 0.20/0.39 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[27])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~![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)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (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))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)) = multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one))),
% 0.20/0.39 inference(symmetry,[status(thm)],[31])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (addition(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), addition(one, one)) = addition(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), one)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[32, 22])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (^[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)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (![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))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (![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))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(37,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')).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.39 tff(39,plain,(
% 0.20/0.39 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.20/0.39 inference(skolemize,[status(sab)],[38])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), addition(one, one)) = addition(addition(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), one), one))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (addition(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), addition(one, one)) = addition(addition(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), one), one)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (addition(addition(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), one), one) = addition(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), addition(one, one))),
% 0.20/0.40 inference(symmetry,[status(thm)],[42])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (addition(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), one) = addition(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), one)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (addition(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), one) = addition(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), one)),
% 0.20/0.40 inference(symmetry,[status(thm)],[44])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (addition(multiplication(X0!0, strong_iteration(X0!0)), one) = addition(multiplication(X0!0, addition(multiplication(X0!0, strong_iteration(X0!0)), one)), one)),
% 0.20/0.40 inference(symmetry,[status(thm)],[13])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (addition(multiplication(X0!0, strong_iteration(X0!0)), one) = addition(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), one)),
% 0.20/0.40 inference(transitivity,[status(thm)],[46, 45])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (addition(addition(multiplication(X0!0, strong_iteration(X0!0)), one), one) = addition(addition(addition(multiplication(X0!0, multiplication(X0!0, strong_iteration(X0!0))), multiplication(X0!0, one)), one), one)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(52,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.40 tff(54,plain,(
% 0.20/0.40 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.40 inference(skolemize,[status(sab)],[53])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = addition(addition(multiplication(X0!0, strong_iteration(X0!0)), one), one))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (addition(one, addition(multiplication(X0!0, strong_iteration(X0!0)), one)) = addition(addition(multiplication(X0!0, strong_iteration(X0!0)), one), one)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (addition(one, strong_iteration(X0!0)) = addition(one, addition(multiplication(X0!0, strong_iteration(X0!0)), one))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (addition(one, strong_iteration(X0!0)) = strong_iteration(X0!0)),
% 0.20/0.40 inference(transitivity,[status(thm)],[58, 57, 48, 43, 33, 13, 10])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(63,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','order')).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.40 tff(65,plain,(
% 0.20/0.40 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.40 inference(skolemize,[status(sab)],[64])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(one, strong_iteration(X0!0)) <=> (addition(one, strong_iteration(X0!0)) = strong_iteration(X0!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (leq(one, strong_iteration(X0!0)) <=> (addition(one, strong_iteration(X0!0)) = strong_iteration(X0!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ((~![X0: $i] : leq(one, strong_iteration(X0))) <=> (~![X0: $i] : leq(one, strong_iteration(X0)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(70,axiom,(~![X0: $i] : leq(one, strong_iteration(X0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (~![X0: $i] : leq(one, strong_iteration(X0))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (~![X0: $i] : leq(one, strong_iteration(X0))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[71, 69])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (~![X0: $i] : leq(one, strong_iteration(X0))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[72, 69])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (~![X0: $i] : leq(one, strong_iteration(X0))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.40 tff(75,plain,(
% 0.20/0.40 ~leq(one, strong_iteration(X0!0))),
% 0.20/0.40 inference(skolemize,[status(sab)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 ((~(leq(one, strong_iteration(X0!0)) <=> (addition(one, strong_iteration(X0!0)) = strong_iteration(X0!0)))) | leq(one, strong_iteration(X0!0)) | (~(addition(one, strong_iteration(X0!0)) = strong_iteration(X0!0)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 ((~(leq(one, strong_iteration(X0!0)) <=> (addition(one, strong_iteration(X0!0)) = strong_iteration(X0!0)))) | (~(addition(one, strong_iteration(X0!0)) = strong_iteration(X0!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (~(addition(one, strong_iteration(X0!0)) = strong_iteration(X0!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[77, 68])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[78, 59])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------