%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE065+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:12:58 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE065+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.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 18:57:32 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(zero_type, type, (
% 0.12/0.38 zero: $i)).
% 0.12/0.38 tff(multiplication_type, type, (
% 0.12/0.38 multiplication: ( $i * $i ) > $i)).
% 0.12/0.38 tff(domain_type, type, (
% 0.12/0.38 domain: $i > $i)).
% 0.12/0.38 tff(tptp_fun_X1_0_type, type, (
% 0.12/0.38 tptp_fun_X1_0: $i)).
% 0.12/0.38 tff(tptp_fun_X0_1_type, type, (
% 0.12/0.38 tptp_fun_X0_1: $i)).
% 0.12/0.38 tff(addition_type, type, (
% 0.12/0.38 addition: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![A: $i] : (addition(A, zero) = A)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,(
% 0.12/0.38 ![A: $i] : (addition(A, zero) = A)),
% 0.12/0.38 inference(skolemize,[status(sab)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![A: $i] : (addition(A, zero) = A)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![A: $i] : (addition(A, zero) = A)) | (addition(addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0))), zero) = addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (addition(addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0))), zero) = addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0))) = addition(addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0))), zero)),
% 0.12/0.38 inference(symmetry,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.12/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![A: $i] : (addition(A, A) = A)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.38 tff(16,plain,(
% 0.12/0.38 ![A: $i] : (addition(A, A) = A)),
% 0.12/0.38 inference(skolemize,[status(sab)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![A: $i] : (addition(A, A) = A)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((~![A: $i] : (addition(A, A) = A)) | (addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0))) = multiplication(X0!1, domain(X1!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0))) = multiplication(X0!1, domain(X1!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (multiplication(X0!1, domain(X1!0)) = addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0)))),
% 0.12/0.38 inference(symmetry,[status(thm)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (multiplication(X0!1, domain(X1!0)) = addition(addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0))), zero)),
% 0.12/0.38 inference(transitivity,[status(thm)],[20, 10])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((multiplication(X0!1, domain(X1!0)) = zero) <=> (addition(addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0))), zero) = zero)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((addition(addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0))), zero) = zero) <=> (multiplication(X0!1, domain(X1!0)) = zero)),
% 0.12/0.38 inference(symmetry,[status(thm)],[22])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.12/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(27,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.38 tff(29,plain,(
% 0.12/0.38 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.12/0.38 inference(skolemize,[status(sab)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, multiplication(X0!1, domain(X1!0))) = zero)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (multiplication(zero, multiplication(X0!1, domain(X1!0))) = zero),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((domain(zero) = zero) <=> (domain(zero) = zero)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(34,axiom,(domain(zero) = zero), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain4')).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (domain(zero) = zero),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, domain(X1)) = zero))) <=> (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, domain(X1)) = zero)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : ((multiplication(X0, X1) = zero) => (multiplication(X0, domain(X1)) = zero))) <=> (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, domain(X1)) = zero)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(38,axiom,(~![X0: $i, X1: $i] : ((multiplication(X0, X1) = zero) => (multiplication(X0, domain(X1)) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, domain(X1)) = zero))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, domain(X1)) = zero))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, domain(X1)) = zero))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, domain(X1)) = zero))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[41, 36])).
% 0.12/0.38 tff(43,plain,(
% 0.12/0.38 ~((~(multiplication(X0!1, X1!0) = zero)) | (multiplication(X0!1, domain(X1!0)) = zero))),
% 0.12/0.38 inference(skolemize,[status(sab)],[42])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (multiplication(X0!1, X1!0) = zero),
% 0.12/0.38 inference(or_elim,[status(thm)],[43])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (domain(multiplication(X0!1, X1!0)) = domain(zero)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[44])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (^[X0: $i, X1: $i] : refl((domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(49,axiom,(![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain2')).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.39 tff(51,plain,(
% 0.12/0.39 ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[50])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(X0!1, X1!0)) = domain(multiplication(X0!1, domain(X1!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (domain(multiplication(X0!1, X1!0)) = domain(multiplication(X0!1, domain(X1!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (domain(multiplication(X0!1, domain(X1!0))) = domain(multiplication(X0!1, X1!0))),
% 0.12/0.39 inference(symmetry,[status(thm)],[54])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (domain(multiplication(X0!1, domain(X1!0))) = zero),
% 0.12/0.39 inference(transitivity,[status(thm)],[55, 45, 35])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (multiplication(domain(multiplication(X0!1, domain(X1!0))), multiplication(X0!1, domain(X1!0))) = multiplication(zero, multiplication(X0!1, domain(X1!0)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[56])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(61,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain1')).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.12/0.39 tff(63,plain,(
% 0.12/0.39 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.12/0.39 inference(skolemize,[status(sab)],[62])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(multiplication(X0!1, domain(X1!0)), multiplication(domain(multiplication(X0!1, domain(X1!0))), multiplication(X0!1, domain(X1!0)))) = multiplication(domain(multiplication(X0!1, domain(X1!0))), multiplication(X0!1, domain(X1!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (addition(multiplication(X0!1, domain(X1!0)), multiplication(domain(multiplication(X0!1, domain(X1!0))), multiplication(X0!1, domain(X1!0)))) = multiplication(domain(multiplication(X0!1, domain(X1!0))), multiplication(X0!1, domain(X1!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (multiplication(zero, multiplication(X0!1, domain(X1!0))) = multiplication(domain(multiplication(X0!1, domain(X1!0))), multiplication(X0!1, domain(X1!0)))),
% 0.12/0.39 inference(symmetry,[status(thm)],[57])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (zero = multiplication(zero, multiplication(X0!1, domain(X1!0)))),
% 0.12/0.39 inference(symmetry,[status(thm)],[32])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (zero = multiplication(domain(multiplication(X0!1, domain(X1!0))), multiplication(X0!1, domain(X1!0)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[68, 67])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (addition(multiplication(X0!1, domain(X1!0)), zero) = addition(multiplication(X0!1, domain(X1!0)), multiplication(domain(multiplication(X0!1, domain(X1!0))), multiplication(X0!1, domain(X1!0))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[69])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(X0!1, domain(X1!0)), zero) = multiplication(X0!1, domain(X1!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (addition(multiplication(X0!1, domain(X1!0)), zero) = multiplication(X0!1, domain(X1!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[71, 7])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (multiplication(X0!1, domain(X1!0)) = addition(multiplication(X0!1, domain(X1!0)), zero)),
% 0.12/0.39 inference(symmetry,[status(thm)],[72])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (addition(addition(multiplication(X0!1, domain(X1!0)), multiplication(X0!1, domain(X1!0))), zero) = zero),
% 0.12/0.39 inference(transitivity,[status(thm)],[9, 19, 73, 70, 66, 57, 32])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (multiplication(X0!1, domain(X1!0)) = zero),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[74, 23])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (~(multiplication(X0!1, domain(X1!0)) = zero)),
% 0.12/0.39 inference(or_elim,[status(thm)],[43])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------