%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE150+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE150+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 19:03:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(addition_type, type, (
% 0.13/0.38 addition: ( $i * $i ) > $i)).
% 0.13/0.38 tff(multiplication_type, type, (
% 0.13/0.38 multiplication: ( $i * $i ) > $i)).
% 0.13/0.38 tff(zero_type, type, (
% 0.13/0.38 zero: $i)).
% 0.13/0.38 tff(tptp_fun_X0_0_type, type, (
% 0.13/0.38 tptp_fun_X0_0: $i)).
% 0.13/0.38 tff(one_type, type, (
% 0.13/0.38 one: $i)).
% 0.13/0.38 tff(strong_iteration_type, type, (
% 0.13/0.38 strong_iteration: $i > $i)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 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')).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.38 tff(6,plain,(
% 0.13/0.38 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.13/0.38 inference(skolemize,[status(sab)],[5])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 ((~![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))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (strong_iteration(multiplication(X0!0, zero)) = addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (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))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[9])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (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)))),
% 0.13/0.38 inference(symmetry,[status(thm)],[10])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (^[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)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (![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))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (![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))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(15,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.38 tff(17,plain,(
% 0.13/0.38 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.13/0.38 inference(skolemize,[status(sab)],[16])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 ((~![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)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (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))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.13/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(24,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.38 tff(26,plain,(
% 0.13/0.38 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.13/0.38 inference(skolemize,[status(sab)],[25])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)) = zero)),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (multiplication(zero, addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)) = zero),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (zero = multiplication(zero, addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one))),
% 0.13/0.38 inference(symmetry,[status(thm)],[29])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (multiplication(X0!0, zero) = multiplication(X0!0, multiplication(zero, addition(multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))), one)))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[30])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (multiplication(X0!0, zero) = multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero)))),
% 0.13/0.38 inference(transitivity,[status(thm)],[31, 20, 11])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (addition(one, multiplication(X0!0, zero)) = addition(one, multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[32])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 (addition(one, multiplication(multiplication(X0!0, zero), strong_iteration(multiplication(X0!0, zero)))) = addition(one, multiplication(X0!0, zero))),
% 0.13/0.38 inference(symmetry,[status(thm)],[33])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.39 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(38,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.13/0.39 tff(40,plain,(
% 0.13/0.39 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.13/0.39 inference(skolemize,[status(sab)],[39])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((~![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)))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (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))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (strong_iteration(multiplication(X0!0, zero)) = addition(one, multiplication(X0!0, zero))),
% 0.13/0.39 inference(transitivity,[status(thm)],[9, 43, 34])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 ((~![X0: $i] : (strong_iteration(multiplication(X0, zero)) = addition(one, multiplication(X0, zero)))) <=> (~![X0: $i] : (strong_iteration(multiplication(X0, zero)) = addition(one, multiplication(X0, zero))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(46,axiom,(~![X0: $i] : (strong_iteration(multiplication(X0, zero)) = addition(one, multiplication(X0, zero)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (~![X0: $i] : (strong_iteration(multiplication(X0, zero)) = addition(one, multiplication(X0, zero)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (~![X0: $i] : (strong_iteration(multiplication(X0, zero)) = addition(one, multiplication(X0, zero)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[47, 45])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (~![X0: $i] : (strong_iteration(multiplication(X0, zero)) = addition(one, multiplication(X0, zero)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (~![X0: $i] : (strong_iteration(multiplication(X0, zero)) = addition(one, multiplication(X0, zero)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.13/0.39 tff(51,plain,(
% 0.13/0.39 ~(strong_iteration(multiplication(X0!0, zero)) = addition(one, multiplication(X0!0, zero)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[50])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[51, 44])).
% 0.13/0.39 % SZS output end Proof
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------