%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE150+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE150+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 19:04:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(addition_type, type, (
% 0.20/0.43 addition: ( $i * $i ) > $i)).
% 0.20/0.43 tff(multiplication_type, type, (
% 0.20/0.43 multiplication: ( $i * $i ) > $i)).
% 0.20/0.43 tff(zero_type, type, (
% 0.20/0.43 zero: $i)).
% 0.20/0.43 tff(tptp_fun_X0_0_type, type, (
% 0.20/0.43 tptp_fun_X0_0: $i)).
% 0.20/0.43 tff(one_type, type, (
% 0.20/0.43 one: $i)).
% 0.20/0.43 tff(strong_iteration_type, type, (
% 0.20/0.43 strong_iteration: $i > $i)).
% 0.20/0.43 tff(leq_type, type, (
% 0.20/0.43 leq: ( $i * $i ) > $o)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(4,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.43 tff(6,plain,(
% 0.20/0.43 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.20/0.43 inference(skolemize,[status(sab)],[5])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(multiplication(X0!0, zero)) = addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (strong_iteration(multiplication(X0!0, zero)) = addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))) = multiplication(multiplication(X0!0, zero), addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 (multiplication(multiplication(X0!0, zero), addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)) = multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero)))),
% 0.20/0.43 inference(symmetry,[status(thm)],[10])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (^[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)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(15,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.43 tff(17,plain,(
% 0.20/0.43 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.20/0.43 inference(skolemize,[status(sab)],[16])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!0, multiplication(zero, addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one))) = multiplication(multiplication(X0!0, zero), addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (multiplication(X0!0, multiplication(zero, addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one))) = multiplication(multiplication(X0!0, zero), addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.20/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(24,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.43 tff(26,plain,(
% 0.20/0.43 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.20/0.43 inference(skolemize,[status(sab)],[25])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)) = zero)),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (multiplication(zero, addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)) = zero),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (zero = multiplication(zero, addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one))),
% 0.20/0.43 inference(symmetry,[status(thm)],[29])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (multiplication(X0!0, zero) = multiplication(X0!0, multiplication(zero, addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[30])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (multiplication(X0!0, zero) = multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[31, 20, 11])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (addition(one, multiplication(X0!0, zero)) = addition(one, multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (addition(one, multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero)))) = addition(one, multiplication(X0!0, zero))),
% 0.20/0.43 inference(symmetry,[status(thm)],[33])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(38,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.44 tff(40,plain,(
% 0.20/0.44 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.44 inference(skolemize,[status(sab)],[39])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one) = addition(one, multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one) = addition(one, multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(47,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','order')).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.44 tff(49,plain,(
% 0.20/0.44 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.44 inference(skolemize,[status(sab)],[48])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) <=> (addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) <=> (addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one) = strong_iteration(multiplication(X0!0, zero))),
% 0.20/0.44 inference(symmetry,[status(thm)],[9])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.20/0.44 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(57,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','idempotence')).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (![A: $i] : (addition(A, A) = A)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.44 tff(59,plain,(
% 0.20/0.44 ![A: $i] : (addition(A, A) = A)),
% 0.20/0.44 inference(skolemize,[status(sab)],[58])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (![A: $i] : (addition(A, A) = A)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one), addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)) = addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (addition(addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one), addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)) = addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (addition(one, multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero)))) = addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)),
% 0.20/0.44 inference(symmetry,[status(thm)],[43])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (addition(one, multiplication(X0!0, zero)) = addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)),
% 0.20/0.44 inference(transitivity,[status(thm)],[33, 63])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = addition(addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one), addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[64, 9])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero))),
% 0.20/0.44 inference(transitivity,[status(thm)],[65, 62, 53])).
% 0.20/0.44 tff(67,assumption,(~leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero)))), introduced(assumption)).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 ((~(leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) <=> (addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero))))) | leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) | (~(addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 ((~(leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) <=> (addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero))))) | (~(addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (~(addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[69, 52])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[70, 66])).
% 0.20/0.44 tff(72,plain,(leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 ((~(leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) <=> (addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero))))) | (~leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero)))) | (addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 ((~(leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) <=> (addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero))))) | (addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))) = strong_iteration(multiplication(X0!0, zero))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[74, 52])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(X0!0, zero)) = addition(multiplication(X0!0, zero), one))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (addition(one, multiplication(X0!0, zero)) = addition(multiplication(X0!0, zero), one)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[76, 41])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (addition(multiplication(X0!0, zero), one) = addition(one, multiplication(X0!0, zero))),
% 0.20/0.44 inference(symmetry,[status(thm)],[77])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (addition(addition(multiplication(X0!0, zero), one), addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)) = addition(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[78, 53])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!0, zero), one), addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)) = addition(addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one), addition(multiplication(X0!0, zero), one)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (addition(addition(multiplication(X0!0, zero), one), addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)) = addition(addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one), addition(multiplication(X0!0, zero), one))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[80, 41])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (addition(addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one), addition(multiplication(X0!0, zero), one)) = addition(addition(multiplication(X0!0, zero), one), addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one))),
% 0.20/0.44 inference(symmetry,[status(thm)],[81])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (addition(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) = addition(addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one), addition(multiplication(X0!0, zero), one))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[9, 77])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (addition(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) = addition(one, multiplication(X0!0, zero))),
% 0.20/0.44 inference(transitivity,[status(thm)],[83, 82, 79, 75, 9, 43, 34])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) <=> (addition(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) = addition(one, multiplication(X0!0, zero))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) <=> (addition(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) = addition(one, multiplication(X0!0, zero)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[85, 50])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 ((~(~((~leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero)))) | (~leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))))))) <=> ((~leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero)))) | (~leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 ((leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) & leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero)))) <=> (~((~leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero)))) | (~leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 ((~(leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) & leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))))) <=> (~(~((~leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero)))) | (~leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero)))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 ((~(leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) & leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))))) <=> ((~leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero)))) | (~leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero)))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 ((~![X0: $i] : (leq(strong_iteration(multiplication(X0, zero)), addition(one, multiplication(X0, zero))) & leq(addition(one, multiplication(X0, zero)), strong_iteration(multiplication(X0, zero))))) <=> (~![X0: $i] : (leq(strong_iteration(multiplication(X0, zero)), addition(one, multiplication(X0, zero))) & leq(addition(one, multiplication(X0, zero)), strong_iteration(multiplication(X0, zero)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(92,axiom,(~![X0: $i] : (leq(strong_iteration(multiplication(X0, zero)), addition(one, multiplication(X0, zero))) & leq(addition(one, multiplication(X0, zero)), strong_iteration(multiplication(X0, zero))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (~![X0: $i] : (leq(strong_iteration(multiplication(X0, zero)), addition(one, multiplication(X0, zero))) & leq(addition(one, multiplication(X0, zero)), strong_iteration(multiplication(X0, zero))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (~![X0: $i] : (leq(strong_iteration(multiplication(X0, zero)), addition(one, multiplication(X0, zero))) & leq(addition(one, multiplication(X0, zero)), strong_iteration(multiplication(X0, zero))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[93, 91])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (~![X0: $i] : (leq(strong_iteration(multiplication(X0, zero)), addition(one, multiplication(X0, zero))) & leq(addition(one, multiplication(X0, zero)), strong_iteration(multiplication(X0, zero))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (~![X0: $i] : (leq(strong_iteration(multiplication(X0, zero)), addition(one, multiplication(X0, zero))) & leq(addition(one, multiplication(X0, zero)), strong_iteration(multiplication(X0, zero))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.44 tff(97,plain,(
% 0.20/0.44 ~(leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) & leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[96])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 ((~leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero)))) | (~leq(addition(one, multiplication(X0!0, zero)), strong_iteration(multiplication(X0!0, zero))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (~leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[98, 72])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 ((~(leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) <=> (addition(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) = addition(one, multiplication(X0!0, zero))))) | leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) | (~(addition(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) = addition(one, multiplication(X0!0, zero))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 ((~(leq(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) <=> (addition(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) = addition(one, multiplication(X0!0, zero))))) | (~(addition(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) = addition(one, multiplication(X0!0, zero))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (~(addition(strong_iteration(multiplication(X0!0, zero)), addition(one, multiplication(X0!0, zero))) = addition(one, multiplication(X0!0, zero)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[101, 86])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[102, 84])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------