%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE089+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 05:13:00 AM UTC 2025
% Result : Theorem 0.22s 0.38s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE089+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 18:57:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.22/0.38 % SZS status Theorem
% 0.22/0.38 % SZS output start Proof
% 0.22/0.38 tff(zero_type, type, (
% 0.22/0.38 zero: $i)).
% 0.22/0.38 tff(multiplication_type, type, (
% 0.22/0.38 multiplication: ( $i * $i ) > $i)).
% 0.22/0.38 tff(tptp_fun_X1_0_type, type, (
% 0.22/0.38 tptp_fun_X1_0: $i)).
% 0.22/0.38 tff(domain_type, type, (
% 0.22/0.38 domain: $i > $i)).
% 0.22/0.38 tff(tptp_fun_X0_1_type, type, (
% 0.22/0.38 tptp_fun_X0_1: $i)).
% 0.22/0.38 tff(antidomain_type, type, (
% 0.22/0.38 antidomain: $i > $i)).
% 0.22/0.38 tff(addition_type, type, (
% 0.22/0.38 addition: ( $i * $i ) > $i)).
% 0.22/0.38 tff(1,plain,
% 0.22/0.38 (^[X0: $i] : refl((multiplication(antidomain(X0), X0) = zero) <=> (multiplication(antidomain(X0), X0) = zero))),
% 0.22/0.38 inference(bind,[status(th)],[])).
% 0.22/0.38 tff(2,plain,
% 0.22/0.38 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.22/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.38 tff(3,plain,
% 0.22/0.38 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(4,axiom,(![X0: $i] : (multiplication(antidomain(X0), X0) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax','domain1')).
% 0.22/0.38 tff(5,plain,
% 0.22/0.38 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.38 tff(6,plain,(
% 0.22/0.38 ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.22/0.38 inference(skolemize,[status(sab)],[5])).
% 0.22/0.38 tff(7,plain,
% 0.22/0.38 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.38 tff(8,plain,
% 0.22/0.38 ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(X1!0), X1!0) = zero)),
% 0.22/0.38 inference(quant_inst,[status(thm)],[])).
% 0.22/0.38 tff(9,plain,
% 0.22/0.38 (multiplication(antidomain(X1!0), X1!0) = zero),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.22/0.38 tff(10,plain,
% 0.22/0.38 ((~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))) <=> (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero)))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(11,plain,
% 0.22/0.38 ((~![X0: $i, X1: $i] : ((addition(domain(X0), antidomain(X1)) = antidomain(X1)) => (multiplication(domain(X0), X1) = zero))) <=> (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero)))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(12,axiom,(~![X0: $i, X1: $i] : ((addition(domain(X0), antidomain(X1)) = antidomain(X1)) => (multiplication(domain(X0), X1) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.22/0.38 tff(13,plain,
% 0.22/0.38 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.22/0.38 tff(14,plain,
% 0.22/0.38 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.22/0.38 tff(15,plain,
% 0.22/0.38 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.22/0.38 tff(16,plain,
% 0.22/0.38 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.22/0.38 tff(17,plain,(
% 0.22/0.38 ~((~(addition(domain(X0!1), antidomain(X1!0)) = antidomain(X1!0))) | (multiplication(domain(X0!1), X1!0) = zero))),
% 0.22/0.38 inference(skolemize,[status(sab)],[16])).
% 0.22/0.38 tff(18,plain,
% 0.22/0.38 (addition(domain(X0!1), antidomain(X1!0)) = antidomain(X1!0)),
% 0.22/0.38 inference(or_elim,[status(thm)],[17])).
% 0.22/0.38 tff(19,plain,
% 0.22/0.38 (^[X0: $i] : refl((domain(X0) = antidomain(antidomain(X0))) <=> (domain(X0) = antidomain(antidomain(X0))))),
% 0.22/0.38 inference(bind,[status(th)],[])).
% 0.22/0.38 tff(20,plain,
% 0.22/0.38 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.22/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.22/0.38 tff(21,plain,
% 0.22/0.38 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(22,axiom,(![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax','domain4')).
% 0.22/0.38 tff(23,plain,
% 0.22/0.38 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.22/0.38 tff(24,plain,(
% 0.22/0.38 ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.22/0.38 inference(skolemize,[status(sab)],[23])).
% 0.22/0.38 tff(25,plain,
% 0.22/0.38 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.22/0.38 tff(26,plain,
% 0.22/0.38 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(X0!1) = antidomain(antidomain(X0!1)))),
% 0.22/0.38 inference(quant_inst,[status(thm)],[])).
% 0.22/0.38 tff(27,plain,
% 0.22/0.38 (domain(X0!1) = antidomain(antidomain(X0!1))),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.22/0.38 tff(28,plain,
% 0.22/0.38 (antidomain(antidomain(X0!1)) = domain(X0!1)),
% 0.22/0.38 inference(symmetry,[status(thm)],[27])).
% 0.22/0.38 tff(29,plain,
% 0.22/0.38 (addition(antidomain(antidomain(X0!1)), antidomain(X1!0)) = addition(domain(X0!1), antidomain(X1!0))),
% 0.22/0.38 inference(monotonicity,[status(thm)],[28])).
% 0.22/0.38 tff(30,plain,
% 0.22/0.38 (addition(antidomain(antidomain(X0!1)), antidomain(X1!0)) = antidomain(X1!0)),
% 0.22/0.38 inference(transitivity,[status(thm)],[29, 18])).
% 0.22/0.38 tff(31,plain,
% 0.22/0.38 (multiplication(addition(antidomain(antidomain(X0!1)), antidomain(X1!0)), X1!0) = multiplication(antidomain(X1!0), X1!0)),
% 0.22/0.38 inference(monotonicity,[status(thm)],[30])).
% 0.22/0.38 tff(32,plain,
% 0.22/0.38 (^[A: $i, B: $i, C: $i] : refl((multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))))),
% 0.22/0.38 inference(bind,[status(th)],[])).
% 0.22/0.38 tff(33,plain,
% 0.22/0.38 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.22/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.22/0.38 tff(34,plain,
% 0.22/0.38 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(35,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 0.22/0.38 tff(36,plain,
% 0.22/0.38 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.22/0.38 tff(37,plain,(
% 0.22/0.38 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.22/0.38 inference(skolemize,[status(sab)],[36])).
% 0.22/0.38 tff(38,plain,
% 0.22/0.38 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.22/0.38 tff(39,plain,
% 0.22/0.38 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(antidomain(antidomain(X0!1)), antidomain(X1!0)), X1!0) = addition(multiplication(antidomain(antidomain(X0!1)), X1!0), multiplication(antidomain(X1!0), X1!0)))),
% 0.22/0.38 inference(quant_inst,[status(thm)],[])).
% 0.22/0.38 tff(40,plain,
% 0.22/0.38 (multiplication(addition(antidomain(antidomain(X0!1)), antidomain(X1!0)), X1!0) = addition(multiplication(antidomain(antidomain(X0!1)), X1!0), multiplication(antidomain(X1!0), X1!0))),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.22/0.38 tff(41,plain,
% 0.22/0.38 (addition(multiplication(antidomain(antidomain(X0!1)), X1!0), multiplication(antidomain(X1!0), X1!0)) = multiplication(addition(antidomain(antidomain(X0!1)), antidomain(X1!0)), X1!0)),
% 0.22/0.38 inference(symmetry,[status(thm)],[40])).
% 0.22/0.39 tff(42,plain,
% 0.22/0.39 (zero = multiplication(antidomain(X1!0), X1!0)),
% 0.22/0.39 inference(symmetry,[status(thm)],[9])).
% 0.22/0.39 tff(43,plain,
% 0.22/0.39 (multiplication(antidomain(antidomain(X0!1)), X1!0) = multiplication(domain(X0!1), X1!0)),
% 0.22/0.39 inference(monotonicity,[status(thm)],[28])).
% 0.22/0.39 tff(44,plain,
% 0.22/0.39 (multiplication(domain(X0!1), X1!0) = multiplication(antidomain(antidomain(X0!1)), X1!0)),
% 0.22/0.39 inference(symmetry,[status(thm)],[43])).
% 0.22/0.39 tff(45,plain,
% 0.22/0.39 (addition(multiplication(domain(X0!1), X1!0), zero) = addition(multiplication(antidomain(antidomain(X0!1)), X1!0), multiplication(antidomain(X1!0), X1!0))),
% 0.22/0.39 inference(monotonicity,[status(thm)],[44, 42])).
% 0.22/0.39 tff(46,plain,
% 0.22/0.39 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(47,plain,
% 0.22/0.39 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.22/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.22/0.39 tff(48,plain,
% 0.22/0.39 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(49,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.22/0.39 tff(50,plain,
% 0.22/0.39 (![A: $i] : (addition(A, zero) = A)),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.22/0.39 tff(51,plain,(
% 0.22/0.39 ![A: $i] : (addition(A, zero) = A)),
% 0.22/0.39 inference(skolemize,[status(sab)],[50])).
% 0.22/0.39 tff(52,plain,
% 0.22/0.39 (![A: $i] : (addition(A, zero) = A)),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.22/0.39 tff(53,plain,
% 0.22/0.39 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(domain(X0!1), X1!0), zero) = multiplication(domain(X0!1), X1!0))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(54,plain,
% 0.22/0.39 (addition(multiplication(domain(X0!1), X1!0), zero) = multiplication(domain(X0!1), X1!0)),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.22/0.39 tff(55,plain,
% 0.22/0.39 (multiplication(domain(X0!1), X1!0) = addition(multiplication(domain(X0!1), X1!0), zero)),
% 0.22/0.39 inference(symmetry,[status(thm)],[54])).
% 0.22/0.39 tff(56,plain,
% 0.22/0.39 (multiplication(domain(X0!1), X1!0) = zero),
% 0.22/0.39 inference(transitivity,[status(thm)],[55, 45, 41, 31, 9])).
% 0.22/0.39 tff(57,plain,
% 0.22/0.39 (~(multiplication(domain(X0!1), X1!0) = zero)),
% 0.22/0.39 inference(or_elim,[status(thm)],[17])).
% 0.22/0.39 tff(58,plain,
% 0.22/0.39 ($false),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.22/0.39 % SZS output end Proof
% 0.22/0.39 % E exiting
%------------------------------------------------------------------------------