%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE056+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 05:12:57 AM UTC 2025
% Result : Theorem 0.16s 0.34s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE056+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.10/0.30 % Computer : n006.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Thu Jun 19 18:56:20 EDT 2025
% 0.10/0.30 % CPUTime :
% 0.16/0.34 % SZS status Theorem
% 0.16/0.34 % SZS output start Proof
% 0.16/0.34 tff(zero_type, type, (
% 0.16/0.34 zero: $i)).
% 0.16/0.34 tff(tptp_fun_X0_0_type, type, (
% 0.16/0.34 tptp_fun_X0_0: $i)).
% 0.16/0.34 tff(addition_type, type, (
% 0.16/0.34 addition: ( $i * $i ) > $i)).
% 0.16/0.34 tff(multiplication_type, type, (
% 0.16/0.34 multiplication: ( $i * $i ) > $i)).
% 0.16/0.34 tff(domain_type, type, (
% 0.16/0.34 domain: $i > $i)).
% 0.16/0.34 tff(1,plain,
% 0.16/0.34 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.16/0.34 inference(bind,[status(th)],[])).
% 0.16/0.34 tff(2,plain,
% 0.16/0.34 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.16/0.34 inference(quant_intro,[status(thm)],[1])).
% 0.16/0.34 tff(3,plain,
% 0.16/0.34 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.16/0.34 inference(rewrite,[status(thm)],[])).
% 0.16/0.34 tff(4,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.16/0.34 tff(5,plain,
% 0.16/0.34 (![A: $i] : (addition(A, zero) = A)),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.16/0.34 tff(6,plain,(
% 0.16/0.34 ![A: $i] : (addition(A, zero) = A)),
% 0.16/0.34 inference(skolemize,[status(sab)],[5])).
% 0.16/0.34 tff(7,plain,
% 0.16/0.34 (![A: $i] : (addition(A, zero) = A)),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.16/0.34 tff(8,plain,
% 0.16/0.34 ((~![A: $i] : (addition(A, zero) = A)) | (addition(addition(X0!0, X0!0), zero) = addition(X0!0, X0!0))),
% 0.16/0.34 inference(quant_inst,[status(thm)],[])).
% 0.16/0.34 tff(9,plain,
% 0.16/0.34 (addition(addition(X0!0, X0!0), zero) = addition(X0!0, X0!0)),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.16/0.34 tff(10,plain,
% 0.16/0.34 (addition(X0!0, X0!0) = addition(addition(X0!0, X0!0), zero)),
% 0.16/0.34 inference(symmetry,[status(thm)],[9])).
% 0.16/0.34 tff(11,plain,
% 0.16/0.34 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.16/0.34 inference(bind,[status(th)],[])).
% 0.16/0.34 tff(12,plain,
% 0.16/0.34 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.16/0.34 inference(quant_intro,[status(thm)],[11])).
% 0.16/0.34 tff(13,plain,
% 0.16/0.34 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.16/0.34 inference(rewrite,[status(thm)],[])).
% 0.16/0.34 tff(14,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.16/0.34 tff(15,plain,
% 0.16/0.34 (![A: $i] : (addition(A, A) = A)),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.16/0.34 tff(16,plain,(
% 0.16/0.34 ![A: $i] : (addition(A, A) = A)),
% 0.16/0.34 inference(skolemize,[status(sab)],[15])).
% 0.16/0.34 tff(17,plain,
% 0.16/0.34 (![A: $i] : (addition(A, A) = A)),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.16/0.34 tff(18,plain,
% 0.16/0.34 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!0, X0!0) = X0!0)),
% 0.16/0.34 inference(quant_inst,[status(thm)],[])).
% 0.16/0.34 tff(19,plain,
% 0.16/0.34 (addition(X0!0, X0!0) = X0!0),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.16/0.34 tff(20,plain,
% 0.16/0.34 (X0!0 = addition(X0!0, X0!0)),
% 0.16/0.34 inference(symmetry,[status(thm)],[19])).
% 0.16/0.34 tff(21,plain,
% 0.16/0.34 (X0!0 = addition(addition(X0!0, X0!0), zero)),
% 0.16/0.34 inference(transitivity,[status(thm)],[20, 10])).
% 0.16/0.34 tff(22,plain,
% 0.16/0.34 ((X0!0 = zero) <=> (addition(addition(X0!0, X0!0), zero) = zero)),
% 0.16/0.34 inference(monotonicity,[status(thm)],[21])).
% 0.16/0.34 tff(23,plain,
% 0.16/0.34 ((addition(addition(X0!0, X0!0), zero) = zero) <=> (X0!0 = zero)),
% 0.16/0.34 inference(symmetry,[status(thm)],[22])).
% 0.16/0.34 tff(24,plain,
% 0.16/0.34 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.16/0.34 inference(bind,[status(th)],[])).
% 0.16/0.34 tff(25,plain,
% 0.16/0.34 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.16/0.34 inference(quant_intro,[status(thm)],[24])).
% 0.16/0.34 tff(26,plain,
% 0.16/0.34 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.16/0.34 inference(rewrite,[status(thm)],[])).
% 0.16/0.34 tff(27,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 0.16/0.34 tff(28,plain,
% 0.16/0.34 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.16/0.34 tff(29,plain,(
% 0.16/0.34 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.16/0.34 inference(skolemize,[status(sab)],[28])).
% 0.16/0.34 tff(30,plain,
% 0.16/0.34 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.16/0.34 tff(31,plain,
% 0.16/0.34 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, X0!0) = zero)),
% 0.16/0.34 inference(quant_inst,[status(thm)],[])).
% 0.16/0.34 tff(32,plain,
% 0.16/0.34 (multiplication(zero, X0!0) = zero),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.16/0.34 tff(33,plain,
% 0.16/0.34 ((~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))) <=> (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero)))),
% 0.16/0.34 inference(rewrite,[status(thm)],[])).
% 0.16/0.34 tff(34,plain,
% 0.16/0.34 ((~![X0: $i] : ((domain(X0) = zero) => (X0 = zero))) <=> (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero)))),
% 0.16/0.34 inference(rewrite,[status(thm)],[])).
% 0.16/0.34 tff(35,axiom,(~![X0: $i] : ((domain(X0) = zero) => (X0 = zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.16/0.34 tff(36,plain,
% 0.16/0.34 (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.16/0.34 tff(37,plain,
% 0.16/0.34 (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.16/0.34 tff(38,plain,
% 0.16/0.34 (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.16/0.34 tff(39,plain,
% 0.16/0.34 (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.16/0.34 tff(40,plain,(
% 0.16/0.34 ~((~(domain(X0!0) = zero)) | (X0!0 = zero))),
% 0.16/0.34 inference(skolemize,[status(sab)],[39])).
% 0.16/0.34 tff(41,plain,
% 0.16/0.34 (domain(X0!0) = zero),
% 0.16/0.34 inference(or_elim,[status(thm)],[40])).
% 0.16/0.34 tff(42,plain,
% 0.16/0.34 (multiplication(domain(X0!0), X0!0) = multiplication(zero, X0!0)),
% 0.16/0.34 inference(monotonicity,[status(thm)],[41])).
% 0.16/0.34 tff(43,plain,
% 0.16/0.34 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 0.16/0.34 inference(bind,[status(th)],[])).
% 0.16/0.34 tff(44,plain,
% 0.16/0.34 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.16/0.34 inference(quant_intro,[status(thm)],[43])).
% 0.16/0.34 tff(45,plain,
% 0.16/0.34 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.16/0.34 inference(rewrite,[status(thm)],[])).
% 0.16/0.34 tff(46,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain1')).
% 0.16/0.34 tff(47,plain,
% 0.16/0.34 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.16/0.34 tff(48,plain,(
% 0.16/0.34 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.16/0.34 inference(skolemize,[status(sab)],[47])).
% 0.16/0.34 tff(49,plain,
% 0.16/0.34 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.16/0.34 tff(50,plain,
% 0.16/0.34 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(X0!0, multiplication(domain(X0!0), X0!0)) = multiplication(domain(X0!0), X0!0))),
% 0.16/0.34 inference(quant_inst,[status(thm)],[])).
% 0.16/0.34 tff(51,plain,
% 0.16/0.34 (addition(X0!0, multiplication(domain(X0!0), X0!0)) = multiplication(domain(X0!0), X0!0)),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.16/0.34 tff(52,plain,
% 0.16/0.34 (addition(X0!0, addition(X0!0, multiplication(domain(X0!0), X0!0))) = addition(X0!0, multiplication(domain(X0!0), X0!0))),
% 0.16/0.34 inference(monotonicity,[status(thm)],[51])).
% 0.16/0.34 tff(53,plain,
% 0.16/0.34 (^[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)))),
% 0.16/0.34 inference(bind,[status(th)],[])).
% 0.16/0.34 tff(54,plain,
% 0.16/0.34 (![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))),
% 0.16/0.34 inference(quant_intro,[status(thm)],[53])).
% 0.16/0.34 tff(55,plain,
% 0.16/0.34 (![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))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(56,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 0.16/0.35 tff(57,plain,
% 0.16/0.35 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.16/0.35 tff(58,plain,(
% 0.16/0.35 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.16/0.35 inference(skolemize,[status(sab)],[57])).
% 0.16/0.35 tff(59,plain,
% 0.16/0.35 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.16/0.35 tff(60,plain,
% 0.16/0.35 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!0, addition(X0!0, multiplication(domain(X0!0), X0!0))) = addition(addition(X0!0, X0!0), multiplication(domain(X0!0), X0!0)))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(61,plain,
% 0.16/0.35 (addition(X0!0, addition(X0!0, multiplication(domain(X0!0), X0!0))) = addition(addition(X0!0, X0!0), multiplication(domain(X0!0), X0!0))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.16/0.35 tff(62,plain,
% 0.16/0.35 (addition(addition(X0!0, X0!0), multiplication(domain(X0!0), X0!0)) = addition(X0!0, addition(X0!0, multiplication(domain(X0!0), X0!0)))),
% 0.16/0.35 inference(symmetry,[status(thm)],[61])).
% 0.16/0.35 tff(63,plain,
% 0.16/0.35 (multiplication(zero, X0!0) = multiplication(domain(X0!0), X0!0)),
% 0.16/0.35 inference(symmetry,[status(thm)],[42])).
% 0.16/0.35 tff(64,plain,
% 0.16/0.35 (zero = multiplication(zero, X0!0)),
% 0.16/0.35 inference(symmetry,[status(thm)],[32])).
% 0.16/0.35 tff(65,plain,
% 0.16/0.35 (zero = multiplication(domain(X0!0), X0!0)),
% 0.16/0.35 inference(transitivity,[status(thm)],[64, 63])).
% 0.16/0.35 tff(66,plain,
% 0.16/0.35 (addition(addition(X0!0, X0!0), zero) = addition(addition(X0!0, X0!0), multiplication(domain(X0!0), X0!0))),
% 0.16/0.35 inference(monotonicity,[status(thm)],[65])).
% 0.16/0.35 tff(67,plain,
% 0.16/0.35 (addition(addition(X0!0, X0!0), zero) = zero),
% 0.16/0.35 inference(transitivity,[status(thm)],[66, 62, 52, 51, 42, 32])).
% 0.16/0.35 tff(68,plain,
% 0.16/0.35 (X0!0 = zero),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[67, 23])).
% 0.16/0.35 tff(69,plain,
% 0.16/0.35 (~(X0!0 = zero)),
% 0.16/0.35 inference(or_elim,[status(thm)],[40])).
% 0.16/0.35 tff(70,plain,
% 0.16/0.35 ($false),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.16/0.35 % SZS output end Proof
% 0.16/0.35 % E exiting
%------------------------------------------------------------------------------